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Fourier Analysis of SDP (ProShares UltraShort Utilities)


SDP (ProShares UltraShort Utilities) appears to have interesting cyclic behaviour every 37 weeks (9.2712*sine), 47 weeks (8.3046*sine), and 27 weeks (7.3994*cosine).

SDP (ProShares UltraShort Utilities) has an average price of 171.12 (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 3/14/2007 to 1/9/2017 for SDP (ProShares UltraShort Utilities), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0171.1177   0 
122.50856 142.3521 (1*2π)/514514 weeks
2-27.27793 57.02607 (2*2π)/514257 weeks
3-15.02625 13.40206 (3*2π)/514171 weeks
42.11556 4.64226 (4*2π)/514129 weeks
514.1664 14.05904 (5*2π)/514103 weeks
68.98002 24.96201 (6*2π)/51486 weeks
7-2.42956 21.74696 (7*2π)/51473 weeks
8-7.72458 8.62306 (8*2π)/51464 weeks
9.88631 4.78296 (9*2π)/51457 weeks
102.47991 6.4687 (10*2π)/51451 weeks
11-.488 8.30461 (11*2π)/51447 weeks
122.36 6.99909 (12*2π)/51443 weeks
131.12573 6.48879 (13*2π)/51440 weeks
14-.75589 9.2712 (14*2π)/51437 weeks
15-3.06322 6.72198 (15*2π)/51434 weeks
16-6.15329 6.21054 (16*2π)/51432 weeks
17-3.30229 -3.87119 (17*2π)/51430 weeks
184.01063 -3.39442 (18*2π)/51429 weeks
197.39938 2.95429 (19*2π)/51427 weeks
204.81462 7.55555 (20*2π)/51426 weeks
21-1.06831 7.37568 (21*2π)/51424 weeks
22-2.11406 2.85164 (22*2π)/51423 weeks
23.356 .16176 (23*2π)/51422 weeks
244.03016 2.36369 (24*2π)/51421 weeks
252.81693 6.11383 (25*2π)/51421 weeks
26.16854 5.43432 (26*2π)/51420 weeks
27-.99564 4.42904 (27*2π)/51419 weeks
28-2.83175 .85101 (28*2π)/51418 weeks
291.79323 -1.57862 (29*2π)/51418 weeks
305.55935 1.41927 (30*2π)/51417 weeks
313.41465 5.9564 (31*2π)/51417 weeks
32-.79285 5.5814 (32*2π)/51416 weeks
33-.95114 1.62607 (33*2π)/51416 weeks
34.22182 1.71823 (34*2π)/51415 weeks
35.35792 2.78777 (35*2π)/51415 weeks
361.4422 1.02545 (36*2π)/51414 weeks
371.59195 2.57286 (37*2π)/51414 weeks
381.227 3.45026 (38*2π)/51414 weeks
39-.06767 1.38377 (39*2π)/51413 weeks
40.75075 3.17185 (40*2π)/51413 weeks
41-.23836 2.49333 (41*2π)/51413 weeks
42-.31846 .72875 (42*2π)/51412 weeks
431.77428 .00144 (43*2π)/51412 weeks
444.08654 1.1653 (44*2π)/51412 weeks
452.8126 4.42408 (45*2π)/51411 weeks
46-.64823 4.5854 (46*2π)/51411 weeks
47-1.71218 2.05072 (47*2π)/51411 weeks
48-.22068 -.91739 (48*2π)/51411 weeks
492.85144 .42928 (49*2π)/51410 weeks
503.70875 2.40853 (50*2π)/51410 weeks
512.12361 5.587 (51*2π)/51410 weeks
52-1.41962 4.8473 (52*2π)/51410 weeks
53-3.61251 .62429 (53*2π)/51410 weeks
54-.42602 -1.57724 (54*2π)/51410 weeks
552.84448 -.22094 (55*2π)/5149 weeks
563.14504 3.0835 (56*2π)/5149 weeks
57-.06831 3.38372 (57*2π)/5149 weeks
58-.20769 1.46714 (58*2π)/5149 weeks
59.48992 1.68414 (59*2π)/5149 weeks
60.3476 1.20962 (60*2π)/5149 weeks
61.24556 1.91476 (61*2π)/5148 weeks
62-.3029 .93348 (62*2π)/5148 weeks
63.72233 1.77159 (63*2π)/5148 weeks
64.49296 1.07633 (64*2π)/5148 weeks
65.47206 2.17089 (65*2π)/5148 weeks
66-1.1573 1.25398 (66*2π)/5148 weeks
67-.10724 -.69886 (67*2π)/5148 weeks
681.27553 -.45505 (68*2π)/5148 weeks
692.77242 .67432 (69*2π)/5147 weeks
701.35435 2.59251 (70*2π)/5147 weeks
71.13107 2.36867 (71*2π)/5147 weeks
72-1.13611 1.88957 (72*2π)/5147 weeks
73-.64508 -.95699 (73*2π)/5147 weeks
741.84358 -.92697 (74*2π)/5147 weeks
752.45143 1.25928 (75*2π)/5147 weeks
761.28781 2.36282 (76*2π)/5147 weeks
77-.35386 2.03888 (77*2π)/5147 weeks
78-.39915 .71551 (78*2π)/5147 weeks
79.38785 -1.05018 (79*2π)/5147 weeks
802.78713 -.01616 (80*2π)/5146 weeks
812.72813 2.06896 (81*2π)/5146 weeks
82.06587 3.1925 (82*2π)/5146 weeks
83-.81162 1.06073 (83*2π)/5146 weeks
84.0029 .43116 (84*2π)/5146 weeks
851.12581 .44549 (85*2π)/5146 weeks
861.16016 1.56443 (86*2π)/5146 weeks
87.35031 1.44836 (87*2π)/5146 weeks
88.25022 .62607 (88*2π)/5146 weeks
891.26593 1.03513 (89*2π)/5146 weeks
90.42767 2.02293 (90*2π)/5146 weeks
91-.97166 1.57196 (91*2π)/5146 weeks
92-.68659 -.18566 (92*2π)/5146 weeks
93.81097 -.83124 (93*2π)/5146 weeks
942.06901 .37473 (94*2π)/5145 weeks
951.59253 2.32389 (95*2π)/5145 weeks
96-.68117 2.84037 (96*2π)/5145 weeks
97-2.08789 .27219 (97*2π)/5145 weeks
98-.15326 -1.90561 (98*2π)/5145 weeks
992.09714 -.76887 (99*2π)/5145 weeks
1002.31326 .32554 (100*2π)/5145 weeks
1011.89856 1.77847 (101*2π)/5145 weeks
102.15058 1.75114 (102*2π)/5145 weeks
103-.23541 .77498 (103*2π)/5145 weeks
104.47446 -.0521 (104*2π)/5145 weeks
1051.49043 .28 (105*2π)/5145 weeks
1062.05601 .90354 (106*2π)/5145 weeks
1071.47309 1.66322 (107*2π)/5145 weeks
108.44278 2.254 (108*2π)/5145 weeks
109-.87758 1.07271 (109*2π)/5145 weeks
110-.53801 .05517 (110*2π)/5145 weeks
111.36534 -.67152 (111*2π)/5145 weeks
1121.71396 -.00767 (112*2π)/5145 weeks
1131.66972 1.56919 (113*2π)/5145 weeks
114.65843 1.66655 (114*2π)/5145 weeks
115-.32139 1.21801 (115*2π)/5144 weeks
116.28602 .45805 (116*2π)/5144 weeks
117.25416 .25078 (117*2π)/5144 weeks
118.64511 .09356 (118*2π)/5144 weeks
119.90517 .76287 (119*2π)/5144 weeks
120.728 1.681 (120*2π)/5144 weeks
121-.6076 1.21916 (121*2π)/5144 weeks
122-.59194 -.43789 (122*2π)/5144 weeks
123.73628 -.56413 (123*2π)/5144 weeks
124.50723 .10214 (124*2π)/5144 weeks
125.92458 .0385 (125*2π)/5144 weeks
1261.17146 .70433 (126*2π)/5144 weeks
127.69173 .82917 (127*2π)/5144 weeks
128.32331 .67916 (128*2π)/5144 weeks
129-.04074 .09945 (129*2π)/5144 weeks
130.84879 -.47886 (130*2π)/5144 weeks
1311.82167 .01114 (131*2π)/5144 weeks
1321.87876 1.59734 (132*2π)/5144 weeks
133-.16599 1.4749 (133*2π)/5144 weeks
134.03791 -.13452 (134*2π)/5144 weeks
1351.09182 .5222 (135*2π)/5144 weeks
136.57576 .5437 (136*2π)/5144 weeks
137.72166 .24404 (137*2π)/5144 weeks
1381.08953 .27567 (138*2π)/5144 weeks
1391.17422 .88824 (139*2π)/5144 weeks
140.75588 1.35742 (140*2π)/5144 weeks
141-.20673 1.29498 (141*2π)/5144 weeks
142-.81285 -.31745 (142*2π)/5144 weeks
1431.05021 -.54486 (143*2π)/5144 weeks
1441.57942 .39254 (144*2π)/5144 weeks
145.93337 1.20886 (145*2π)/5144 weeks
146.11651 .90333 (146*2π)/5144 weeks
147.40989 .37965 (147*2π)/5143 weeks
148-.03145 .17936 (148*2π)/5143 weeks
149.97562 -.51184 (149*2π)/5143 weeks
1501.55582 .93336 (150*2π)/5143 weeks
151.25639 1.11978 (151*2π)/5143 weeks
152.21644 .2329 (152*2π)/5143 weeks
153.79491 .23949 (153*2π)/5143 weeks
154.36066 .59701 (154*2π)/5143 weeks
155.42933 .52413 (155*2π)/5143 weeks
156-.02961 .39635 (156*2π)/5143 weeks
157.54249 -.04695 (157*2π)/5143 weeks
158.725 .01337 (158*2π)/5143 weeks
1591.00374 .20902 (159*2π)/5143 weeks
160.29547 .47408 (160*2π)/5143 weeks
161.29074 -.18556 (161*2π)/5143 weeks
1621.12217 -.32605 (162*2π)/5143 weeks
1631.68124 .17237 (163*2π)/5143 weeks
1641.57107 1.17385 (164*2π)/5143 weeks
165.36179 1.33623 (165*2π)/5143 weeks
166-.10937 .75874 (166*2π)/5143 weeks
167-.0047 -.01487 (167*2π)/5143 weeks
1681.00703 -.465 (168*2π)/5143 weeks
1691.20939 .5377 (169*2π)/5143 weeks
1701.04176 1.11154 (170*2π)/5143 weeks
171-.10107 .81592 (171*2π)/5143 weeks
172-.00048 .12135 (172*2π)/5143 weeks
173.46863 -.26408 (173*2π)/5143 weeks
174.91859 .22159 (174*2π)/5143 weeks
175.66283 .50173 (175*2π)/5143 weeks
176.50183 .37419 (176*2π)/5143 weeks
177.40586 .7328 (177*2π)/5143 weeks
178.12184 .4852 (178*2π)/5143 weeks
179-.20308 -.10348 (179*2π)/5143 weeks
180.02533 -.52374 (180*2π)/5143 weeks
181.56272 -.85542 (181*2π)/5143 weeks
1821.8111 -.80785 (182*2π)/5143 weeks
1831.65418 1.17727 (183*2π)/5143 weeks
184.55081 1.10594 (184*2π)/5143 weeks
185.09424 .3488 (185*2π)/5143 weeks
186.41403 -.12402 (186*2π)/5143 weeks
1871.03328 .21669 (187*2π)/5143 weeks
188.96053 .30794 (188*2π)/5143 weeks
1891.30347 1.12936 (189*2π)/5143 weeks
190-.123 1.19898 (190*2π)/5143 weeks
191-.55882 .41698 (191*2π)/5143 weeks
192-.34653 -.45706 (192*2π)/5143 weeks
193.41889 -1.0393 (193*2π)/5143 weeks
1941.75154 -.4405 (194*2π)/5143 weeks
1951.74411 .9762 (195*2π)/5143 weeks
196.16551 1.55544 (196*2π)/5143 weeks
197-.59419 .18953 (197*2π)/5143 weeks
198-.00019 -.71645 (198*2π)/5143 weeks
199.79959 -.59657 (199*2π)/5143 weeks
2001.62814 .12022 (200*2π)/5143 weeks
201.96715 .8827 (201*2π)/5143 weeks
202-.237 .81248 (202*2π)/5143 weeks
203-.24093 -.22099 (203*2π)/5143 weeks
204.55182 -.54362 (204*2π)/5143 weeks
205.45328 -.17647 (205*2π)/5143 weeks
206.76909 -.5913 (206*2π)/5142 weeks
2071.42311 -.21298 (207*2π)/5142 weeks
208.87766 .51634 (208*2π)/5142 weeks
209.79541 .20817 (209*2π)/5142 weeks
210.56063 .36281 (210*2π)/5142 weeks
211.26439 .17867 (211*2π)/5142 weeks
212.36679 -.60066 (212*2π)/5142 weeks
2131.65514 -.76981 (213*2π)/5142 weeks
2141.60381 .63708 (214*2π)/5142 weeks
215.49516 .95964 (215*2π)/5142 weeks
216.41666 .39218 (216*2π)/5142 weeks
217.2506 .0079 (217*2π)/5142 weeks
218.65721 -.45719 (218*2π)/5142 weeks
2191.2949 -.31966 (219*2π)/5142 weeks
2201.5907 .49595 (220*2π)/5142 weeks
2211.12272 1.15059 (221*2π)/5142 weeks
222.17953 1.06945 (222*2π)/5142 weeks
223-.10741 .44848 (223*2π)/5142 weeks
224.11468 -.21706 (224*2π)/5142 weeks
225.45743 -.10225 (225*2π)/5142 weeks
226.99055 -.23324 (226*2π)/5142 weeks
227.66299 .53719 (227*2π)/5142 weeks
228.48464 .40296 (228*2π)/5142 weeks
229-.00703 .48834 (229*2π)/5142 weeks
230.00048 -.29754 (230*2π)/5142 weeks
231.65873 -.68779 (231*2π)/5142 weeks
2321.05148 -.31887 (232*2π)/5142 weeks
2331.3754 .40233 (233*2π)/5142 weeks
234.45309 1.00524 (234*2π)/5142 weeks
235-.1971 .42414 (235*2π)/5142 weeks
236-.23764 -.31547 (236*2π)/5142 weeks
237.41 -.8336 (237*2π)/5142 weeks
2381.12824 -.54814 (238*2π)/5142 weeks
2391.5174 .22748 (239*2π)/5142 weeks
240.74361 .87041 (240*2π)/5142 weeks
241-.17149 .5029 (241*2π)/5142 weeks
242-.13238 -.01404 (242*2π)/5142 weeks
243-.06612 -.94607 (243*2π)/5142 weeks
2441.22301 -.70631 (244*2π)/5142 weeks
2451.13661 -.02169 (245*2π)/5142 weeks
246.33482 .38756 (246*2π)/5142 weeks
247.29052 -.24374 (247*2π)/5142 weeks
248.48032 -.44508 (248*2π)/5142 weeks
249.61063 -.56136 (249*2π)/5142 weeks
2501.43635 -.72071 (250*2π)/5142 weeks
2511.68672 .20007 (251*2π)/5142 weeks
252.66942 .65798 (252*2π)/5142 weeks
253.39387 .14325 (253*2π)/5142 weeks
254.26367 -.05441 (254*2π)/5142 weeks
255.33819 -.56002 (255*2π)/5142 weeks
2561.18438 -.96244 (256*2π)/5142 weeks
2571.94279   (257*2π)/5142 weeks
2581.18438 .96244 (258*2π)/5142 weeks
259.33819 .56002 (259*2π)/5142 weeks
260.26367 .05441 (260*2π)/5142 weeks
261.39387 -.14325 (261*2π)/5142 weeks
262.66942 -.65798 (262*2π)/5142 weeks
2631.68672 -.20007 (263*2π)/5142 weeks
2641.43635 .72071 (264*2π)/5142 weeks
265.61063 .56136 (265*2π)/5142 weeks
266.48032 .44508 (266*2π)/5142 weeks
267.29052 .24374 (267*2π)/5142 weeks
268.33482 -.38756 (268*2π)/5142 weeks
2691.13661 .02169 (269*2π)/5142 weeks
2701.22301 .70631 (270*2π)/5142 weeks
271-.06612 .94607 (271*2π)/5142 weeks
272-.13238 .01404 (272*2π)/5142 weeks
273-.17149 -.5029 (273*2π)/5142 weeks
274.74361 -.87041 (274*2π)/5142 weeks
2751.5174 -.22748 (275*2π)/5142 weeks
2761.12824 .54814 (276*2π)/5142 weeks
277.41 .8336 (277*2π)/5142 weeks
278-.23764 .31547 (278*2π)/5142 weeks
279-.1971 -.42414 (279*2π)/5142 weeks
280.45309 -1.00524 (280*2π)/5142 weeks
2811.3754 -.40233 (281*2π)/5142 weeks
2821.05148 .31887 (282*2π)/5142 weeks
283.65873 .68779 (283*2π)/5142 weeks
284.00048 .29754 (284*2π)/5142 weeks
285-.00703 -.48834 (285*2π)/5142 weeks
286.48464 -.40296 (286*2π)/5142 weeks
287.66299 -.53719 (287*2π)/5142 weeks
288.99055 .23324 (288*2π)/5142 weeks
289.45743 .10225 (289*2π)/5142 weeks
290.11468 .21706 (290*2π)/5142 weeks
291-.10741 -.44848 (291*2π)/5142 weeks
292.17953 -1.06945 (292*2π)/5142 weeks
2931.12272 -1.15059 (293*2π)/5142 weeks
2941.5907 -.49595 (294*2π)/5142 weeks
2951.2949 .31966 (295*2π)/5142 weeks
296.65721 .45719 (296*2π)/5142 weeks
297.2506 -.0079 (297*2π)/5142 weeks
298.41666 -.39218 (298*2π)/5142 weeks
299.49516 -.95964 (299*2π)/5142 weeks
3001.60381 -.63708 (300*2π)/5142 weeks
3011.65514 .76981 (301*2π)/5142 weeks
302.36679 .60066 (302*2π)/5142 weeks
303.26439 -.17867 (303*2π)/5142 weeks
304.56063 -.36281 (304*2π)/5142 weeks
305.79541 -.20817 (305*2π)/5142 weeks
306.87766 -.51634 (306*2π)/5142 weeks
3071.42311 .21298 (307*2π)/5142 weeks
308.76909 .5913 (308*2π)/5142 weeks
309.45328 .17647 (309*2π)/5142 weeks
310.55182 .54362 (310*2π)/5142 weeks
311-.24093 .22099 (311*2π)/5142 weeks
312-.237 -.81248 (312*2π)/5142 weeks
313.96715 -.8827 (313*2π)/5142 weeks
3141.62814 -.12022 (314*2π)/5142 weeks
315.79959 .59657 (315*2π)/5142 weeks
316-.00019 .71645 (316*2π)/5142 weeks
317-.59419 -.18953 (317*2π)/5142 weeks
318.16551 -1.55544 (318*2π)/5142 weeks
3191.74411 -.9762 (319*2π)/5142 weeks
3201.75154 .4405 (320*2π)/5142 weeks
321.41889 1.0393 (321*2π)/5142 weeks
322-.34653 .45706 (322*2π)/5142 weeks
323-.55882 -.41698 (323*2π)/5142 weeks
324-.123 -1.19898 (324*2π)/5142 weeks
3251.30347 -1.12936 (325*2π)/5142 weeks
326.96053 -.30794 (326*2π)/5142 weeks
3271.03328 -.21669 (327*2π)/5142 weeks
328.41403 .12402 (328*2π)/5142 weeks
329.09424 -.3488 (329*2π)/5142 weeks
330.55081 -1.10594 (330*2π)/5142 weeks
3311.65418 -1.17727 (331*2π)/5142 weeks
3321.8111 .80785 (332*2π)/5142 weeks
333.56272 .85542 (333*2π)/5142 weeks
334.02533 .52374 (334*2π)/5142 weeks
335-.20308 .10348 (335*2π)/5142 weeks
336.12184 -.4852 (336*2π)/5142 weeks
337.40586 -.7328 (337*2π)/5142 weeks
338.50183 -.37419 (338*2π)/5142 weeks
339.66283 -.50173 (339*2π)/5142 weeks
340.91859 -.22159 (340*2π)/5142 weeks
341.46863 .26408 (341*2π)/5142 weeks
342-.00048 -.12135 (342*2π)/5142 weeks
343-.10107 -.81592 (343*2π)/5141 weeks
3441.04176 -1.11154 (344*2π)/5141 weeks
3451.20939 -.5377 (345*2π)/5141 weeks
3461.00703 .465 (346*2π)/5141 weeks
347-.0047 .01487 (347*2π)/5141 weeks
348-.10937 -.75874 (348*2π)/5141 weeks
349.36179 -1.33623 (349*2π)/5141 weeks
3501.57107 -1.17385 (350*2π)/5141 weeks
3511.68124 -.17237 (351*2π)/5141 weeks
3521.12217 .32605 (352*2π)/5141 weeks
353.29074 .18556 (353*2π)/5141 weeks
354.29547 -.47408 (354*2π)/5141 weeks
3551.00374 -.20902 (355*2π)/5141 weeks
356.725 -.01337 (356*2π)/5141 weeks
357.54249 .04695 (357*2π)/5141 weeks
358-.02961 -.39635 (358*2π)/5141 weeks
359.42933 -.52413 (359*2π)/5141 weeks
360.36066 -.59701 (360*2π)/5141 weeks
361.79491 -.23949 (361*2π)/5141 weeks
362.21644 -.2329 (362*2π)/5141 weeks
363.25639 -1.11978 (363*2π)/5141 weeks
3641.55582 -.93336 (364*2π)/5141 weeks
365.97562 .51184 (365*2π)/5141 weeks
366-.03145 -.17936 (366*2π)/5141 weeks
367.40989 -.37965 (367*2π)/5141 weeks
368.11651 -.90333 (368*2π)/5141 weeks
369.93337 -1.20886 (369*2π)/5141 weeks
3701.57942 -.39254 (370*2π)/5141 weeks
3711.05021 .54486 (371*2π)/5141 weeks
372-.81285 .31745 (372*2π)/5141 weeks
373-.20673 -1.29498 (373*2π)/5141 weeks
374.75588 -1.35742 (374*2π)/5141 weeks
3751.17422 -.88824 (375*2π)/5141 weeks
3761.08953 -.27567 (376*2π)/5141 weeks
377.72166 -.24404 (377*2π)/5141 weeks
378.57576 -.5437 (378*2π)/5141 weeks
3791.09182 -.5222 (379*2π)/5141 weeks
380.03791 .13452 (380*2π)/5141 weeks
381-.16599 -1.4749 (381*2π)/5141 weeks
3821.87876 -1.59734 (382*2π)/5141 weeks
3831.82167 -.01114 (383*2π)/5141 weeks
384.84879 .47886 (384*2π)/5141 weeks
385-.04074 -.09945 (385*2π)/5141 weeks
386.32331 -.67916 (386*2π)/5141 weeks
387.69173 -.82917 (387*2π)/5141 weeks
3881.17146 -.70433 (388*2π)/5141 weeks
389.92458 -.0385 (389*2π)/5141 weeks
390.50723 -.10214 (390*2π)/5141 weeks
391.73628 .56413 (391*2π)/5141 weeks
392-.59194 .43789 (392*2π)/5141 weeks
393-.6076 -1.21916 (393*2π)/5141 weeks
394.728 -1.681 (394*2π)/5141 weeks
395.90517 -.76287 (395*2π)/5141 weeks
396.64511 -.09356 (396*2π)/5141 weeks
397.25416 -.25078 (397*2π)/5141 weeks
398.28602 -.45805 (398*2π)/5141 weeks
399-.32139 -1.21801 (399*2π)/5141 weeks
400.65843 -1.66655 (400*2π)/5141 weeks
4011.66972 -1.56919 (401*2π)/5141 weeks
4021.71396 .00767 (402*2π)/5141 weeks
403.36534 .67152 (403*2π)/5141 weeks
404-.53801 -.05517 (404*2π)/5141 weeks
405-.87758 -1.07271 (405*2π)/5141 weeks
406.44278 -2.254 (406*2π)/5141 weeks
4071.47309 -1.66322 (407*2π)/5141 weeks
4082.05601 -.90354 (408*2π)/5141 weeks
4091.49043 -.28 (409*2π)/5141 weeks
410.47446 .0521 (410*2π)/5141 weeks
411-.23541 -.77498 (411*2π)/5141 weeks
412.15058 -1.75114 (412*2π)/5141 weeks
4131.89856 -1.77847 (413*2π)/5141 weeks
4142.31326 -.32554 (414*2π)/5141 weeks
4152.09714 .76887 (415*2π)/5141 weeks
416-.15326 1.90561 (416*2π)/5141 weeks
417-2.08789 -.27219 (417*2π)/5141 weeks
418-.68117 -2.84037 (418*2π)/5141 weeks
4191.59253 -2.32389 (419*2π)/5141 weeks
4202.06901 -.37473 (420*2π)/5141 weeks
421.81097 .83124 (421*2π)/5141 weeks
422-.68659 .18566 (422*2π)/5141 weeks
423-.97166 -1.57196 (423*2π)/5141 weeks
424.42767 -2.02293 (424*2π)/5141 weeks
4251.26593 -1.03513 (425*2π)/5141 weeks
426.25022 -.62607 (426*2π)/5141 weeks
427.35031 -1.44836 (427*2π)/5141 weeks
4281.16016 -1.56443 (428*2π)/5141 weeks
4291.12581 -.44549 (429*2π)/5141 weeks
430.0029 -.43116 (430*2π)/5141 weeks
431-.81162 -1.06073 (431*2π)/5141 weeks
432.06587 -3.1925 (432*2π)/5141 weeks
4332.72813 -2.06896 (433*2π)/5141 weeks
4342.78713 .01616 (434*2π)/5141 weeks
435.38785 1.05018 (435*2π)/5141 weeks
436-.39915 -.71551 (436*2π)/5141 weeks
437-.35386 -2.03888 (437*2π)/5141 weeks
4381.28781 -2.36282 (438*2π)/5141 weeks
4392.45143 -1.25928 (439*2π)/5141 weeks
4401.84358 .92697 (440*2π)/5141 weeks
441-.64508 .95699 (441*2π)/5141 weeks
442-1.13611 -1.88957 (442*2π)/5141 weeks
443.13107 -2.36867 (443*2π)/5141 weeks
4441.35435 -2.59251 (444*2π)/5141 weeks
4452.77242 -.67432 (445*2π)/5141 weeks
4461.27553 .45505 (446*2π)/5141 weeks
447-.10724 .69886 (447*2π)/5141 weeks
448-1.1573 -1.25398 (448*2π)/5141 weeks
449.47206 -2.17089 (449*2π)/5141 weeks
450.49296 -1.07633 (450*2π)/5141 weeks
451.72233 -1.77159 (451*2π)/5141 weeks
452-.3029 -.93348 (452*2π)/5141 weeks
453.24556 -1.91476 (453*2π)/5141 weeks
454.3476 -1.20962 (454*2π)/5141 weeks
455.48992 -1.68414 (455*2π)/5141 weeks
456-.20769 -1.46714 (456*2π)/5141 weeks
457-.06831 -3.38372 (457*2π)/5141 weeks
4583.14504 -3.0835 (458*2π)/5141 weeks
4592.84448 .22094 (459*2π)/5141 weeks
460-.42602 1.57724 (460*2π)/5141 weeks
461-3.61251 -.62429 (461*2π)/5141 weeks
462-1.41962 -4.8473 (462*2π)/5141 weeks
4632.12361 -5.587 (463*2π)/5141 weeks
4643.70875 -2.40853 (464*2π)/5141 weeks
4652.85144 -.42928 (465*2π)/5141 weeks
466-.22068 .91739 (466*2π)/5141 weeks
467-1.71218 -2.05072 (467*2π)/5141 weeks
468-.64823 -4.5854 (468*2π)/5141 weeks
4692.8126 -4.42408 (469*2π)/5141 weeks
4704.08654 -1.1653 (470*2π)/5141 weeks
4711.77428 -.00144 (471*2π)/5141 weeks
472-.31846 -.72875 (472*2π)/5141 weeks
473-.23836 -2.49333 (473*2π)/5141 weeks
474.75075 -3.17185 (474*2π)/5141 weeks
475-.06767 -1.38377 (475*2π)/5141 weeks
4761.227 -3.45026 (476*2π)/5141 weeks
4771.59195 -2.57286 (477*2π)/5141 weeks
4781.4422 -1.02545 (478*2π)/5141 weeks
479.35792 -2.78777 (479*2π)/5141 weeks
480.22182 -1.71823 (480*2π)/5141 weeks
481-.95114 -1.62607 (481*2π)/5141 weeks
482-.79285 -5.5814 (482*2π)/5141 weeks
4833.41465 -5.9564 (483*2π)/5141 weeks
4845.55935 -1.41927 (484*2π)/5141 weeks
4851.79323 1.57862 (485*2π)/5141 weeks
486-2.83175 -.85101 (486*2π)/5141 weeks
487-.99564 -4.42904 (487*2π)/5141 weeks
488.16854 -5.43432 (488*2π)/5141 weeks
4892.81693 -6.11383 (489*2π)/5141 weeks
4904.03016 -2.36369 (490*2π)/5141 weeks
491.356 -.16176 (491*2π)/5141 weeks
492-2.11406 -2.85164 (492*2π)/5141 weeks
493-1.06831 -7.37568 (493*2π)/5141 weeks
4944.81462 -7.55555 (494*2π)/5141 weeks
4957.39938 -2.95429 (495*2π)/5141 weeks
4964.01063 3.39442 (496*2π)/5141 weeks
497-3.30229 3.87119 (497*2π)/5141 weeks
498-6.15329 -6.21054 (498*2π)/5141 weeks
499-3.06322 -6.72198 (499*2π)/5141 weeks
500-.75589 -9.2712 (500*2π)/5141 weeks
5011.12573 -6.48879 (501*2π)/5141 weeks
5022.36 -6.99909 (502*2π)/5141 weeks
503-.488 -8.30461 (503*2π)/5141 weeks
5042.47991 -6.4687 (504*2π)/5141 weeks
505.88631 -4.78296 (505*2π)/5141 weeks
506-7.72458 -8.62306 (506*2π)/5141 weeks
507-2.42956 -21.74696 (507*2π)/5141 weeks
5088.98002 -24.96201 (508*2π)/5141 weeks
50914.1664 -14.05904 (509*2π)/5141 weeks
5102.11556 -4.64226 (510*2π)/5141 weeks
511-15.02625 -13.40206 (511*2π)/5141 weeks
512-27.27793 -57.02607 (512*2π)/5141 weeks

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