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Fourier Analysis of MZZ (ProShares UltraShort MidCap 400 ETF)


MZZ (ProShares UltraShort MidCap 400 ETF) appears to have interesting cyclic behaviour every 59 weeks (52.8153*sine), 54 weeks (37.1387*sine), and 42 weeks (18.9049*cosine).

MZZ (ProShares UltraShort MidCap 400 ETF) has an average price of 284.64 (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 10/16/2017 for MZZ (ProShares UltraShort MidCap 400 ETF), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0284.6395   0 
1135.0933 323.1053 (1*2π)/589589 weeks
2-66.67892 154.933 (2*2π)/589295 weeks
3-40.86338 7.40177 (3*2π)/589196 weeks
453.29235 9.34238 (4*2π)/589147 weeks
550.91999 69.66846 (5*2π)/589118 weeks
6-4.38623 77.30738 (6*2π)/58998 weeks
7-26.45037 24.73059 (7*2π)/58984 weeks
815.55377 -4.02695 (8*2π)/58974 weeks
937.86427 36.10984 (9*2π)/58965 weeks
103.81572 52.81525 (10*2π)/58959 weeks
11-15.64636 37.13873 (11*2π)/58954 weeks
12-18.36549 5.96307 (12*2π)/58949 weeks
1313.36798 -1.22131 (13*2π)/58945 weeks
1418.90494 20.97785 (14*2π)/58942 weeks
156.42494 29.16331 (15*2π)/58939 weeks
16-5.7261 23.18516 (16*2π)/58937 weeks
17-5.38635 12.84356 (17*2π)/58935 weeks
18-2.67575 7.94696 (18*2π)/58933 weeks
198.58128 4.79808 (19*2π)/58931 weeks
2010.47917 15.77982 (20*2π)/58929 weeks
214.42356 17.37764 (21*2π)/58928 weeks
22.76502 16.08515 (22*2π)/58927 weeks
23-1.56848 13.07086 (23*2π)/58926 weeks
24.27543 8.20388 (24*2π)/58925 weeks
255.66211 12.4812 (25*2π)/58924 weeks
26-.29227 16.24638 (26*2π)/58923 weeks
27-8.67768 10.44233 (27*2π)/58922 weeks
28-2.73098 -3.47076 (28*2π)/58921 weeks
2911.89558 2.58404 (29*2π)/58920 weeks
3011.3719 16.18119 (30*2π)/58920 weeks
31-3.83599 21.74075 (31*2π)/58919 weeks
32-12.86168 5.02483 (32*2π)/58918 weeks
332.46863 -7.36016 (33*2π)/58918 weeks
3416.73479 4.90124 (34*2π)/58917 weeks
357.40913 23.3147 (35*2π)/58917 weeks
36-13.89039 16.76509 (36*2π)/58916 weeks
37-9.72004 -4.00541 (37*2π)/58916 weeks
386.41067 -3.7633 (38*2π)/58916 weeks
3910.4017 7.6541 (39*2π)/58915 weeks
40.87093 13.41802 (40*2π)/58915 weeks
41-4.32678 6.47183 (41*2π)/58914 weeks
42-.83433 1.21328 (42*2π)/58914 weeks
434.57084 1.7361 (43*2π)/58914 weeks
445.68801 8.3123 (44*2π)/58913 weeks
45-.58978 7.76267 (45*2π)/58913 weeks
46.69206 3.83674 (46*2π)/58913 weeks
471.84846 4.759 (47*2π)/58913 weeks
481.1881 5.47477 (48*2π)/58912 weeks
49.03738 3.17328 (49*2π)/58912 weeks
503.60076 1.51464 (50*2π)/58912 weeks
515.22175 5.64302 (51*2π)/58912 weeks
523.66454 7.61052 (52*2π)/58911 weeks
53.49701 6.70091 (53*2π)/58911 weeks
54.58613 4.99621 (54*2π)/58911 weeks
552.44534 4.77654 (55*2π)/58911 weeks
561.20114 7.4187 (56*2π)/58911 weeks
57-2.0371 5.86916 (57*2π)/58910 weeks
58-2.45878 1.82344 (58*2π)/58910 weeks
592.3875 -1.55369 (59*2π)/58910 weeks
607.67053 3.95646 (60*2π)/58910 weeks
611.34798 8.95168 (61*2π)/58910 weeks
62-2.77763 4.39164 (62*2π)/58910 weeks
63.59894 .57345 (63*2π)/5899 weeks
643.54495 2.15158 (64*2π)/5899 weeks
652.32657 5.57497 (65*2π)/5899 weeks
66-.87186 2.25949 (66*2π)/5899 weeks
674.01478 .38737 (67*2π)/5899 weeks
685.66729 4.19807 (68*2π)/5899 weeks
692.73527 7.98116 (69*2π)/5899 weeks
70-1.7443 5.08739 (70*2π)/5898 weeks
71.73835 .81236 (71*2π)/5898 weeks
722.63863 3.07531 (72*2π)/5898 weeks
732.56924 3.96597 (73*2π)/5898 weeks
74.15213 3.54245 (74*2π)/5898 weeks
753.13232 .17298 (75*2π)/5898 weeks
766.68879 5.56376 (76*2π)/5898 weeks
77.84113 9.75577 (77*2π)/5898 weeks
78-4.56857 5.39676 (78*2π)/5898 weeks
79-2.43002 -2.09521 (79*2π)/5897 weeks
805.20184 -.32522 (80*2π)/5897 weeks
813.8743 4.82749 (81*2π)/5897 weeks
821.80094 5.78395 (82*2π)/5897 weeks
83-2.96113 4.07705 (83*2π)/5897 weeks
84.24915 -2.3262 (84*2π)/5897 weeks
856.5653 1.3594 (85*2π)/5897 weeks
864.43358 6.82825 (86*2π)/5897 weeks
87-1.57736 7.30377 (87*2π)/5897 weeks
88-3.28647 .9485 (88*2π)/5897 weeks
891.65524 -1.21089 (89*2π)/5897 weeks
905.61184 1.40972 (90*2π)/5897 weeks
913.73375 7.79522 (91*2π)/5896 weeks
92-3.62843 6.11485 (92*2π)/5896 weeks
93-3.20473 -.74645 (93*2π)/5896 weeks
942.69326 -2.38149 (94*2π)/5896 weeks
955.1122 2.22541 (95*2π)/5896 weeks
961.82397 4.89893 (96*2π)/5896 weeks
97-.48611 2.86809 (97*2π)/5896 weeks
98.79324 .80019 (98*2π)/5896 weeks
992.73607 1.76925 (99*2π)/5896 weeks
1001.52394 3.16371 (100*2π)/5896 weeks
1011.27264 1.65675 (101*2π)/5896 weeks
1021.97914 2.81504 (102*2π)/5896 weeks
103.01379 2.47441 (103*2π)/5896 weeks
104.09028 -.08371 (104*2π)/5896 weeks
1053.44824 -.98733 (105*2π)/5896 weeks
1065.61762 2.63433 (106*2π)/5896 weeks
1072.52466 5.96269 (107*2π)/5896 weeks
108-1.25625 3.66411 (108*2π)/5895 weeks
109-.03383 -.63688 (109*2π)/5895 weeks
1104.69321 -.00595 (110*2π)/5895 weeks
1114.45993 5.3802 (111*2π)/5895 weeks
112-.69417 6.24157 (112*2π)/5895 weeks
113-3.70111 1.29186 (113*2π)/5895 weeks
114.90125 -2.84788 (114*2π)/5895 weeks
1155.60785 -.40016 (115*2π)/5895 weeks
1164.72669 5.27927 (116*2π)/5895 weeks
117-1.56449 5.32229 (117*2π)/5895 weeks
118-2.3234 -.62698 (118*2π)/5895 weeks
1193.53404 -2.71599 (119*2π)/5895 weeks
1206.56308 2.35429 (120*2π)/5895 weeks
1213.12887 6.09538 (121*2π)/5895 weeks
122-1.52526 5.00848 (122*2π)/5895 weeks
123-1.95425 -.39417 (123*2π)/5895 weeks
1242.95512 -1.2962 (124*2π)/5895 weeks
1254.66498 2.35629 (125*2π)/5895 weeks
1262.48208 4.49372 (126*2π)/5895 weeks
127-.26039 3.60434 (127*2π)/5895 weeks
128-.31482 .65357 (128*2π)/5895 weeks
1292.33902 .09924 (129*2π)/5895 weeks
1303.56388 3.15534 (130*2π)/5895 weeks
131.21687 4.67785 (131*2π)/5894 weeks
132-2.02043 1.17678 (132*2π)/5894 weeks
1331.4241 -1.29057 (133*2π)/5894 weeks
1343.63753 .79032 (134*2π)/5894 weeks
1352.54626 3.21304 (135*2π)/5894 weeks
136.53596 3.06664 (136*2π)/5894 weeks
137-.15888 1.9856 (137*2π)/5894 weeks
138.08611 .2194 (138*2π)/5894 weeks
1392.03632 -.14562 (139*2π)/5894 weeks
1402.72347 1.6501 (140*2π)/5894 weeks
1411.09853 1.83288 (141*2π)/5894 weeks
1421.37966 .06673 (142*2π)/5894 weeks
1433.3744 1.126 (143*2π)/5894 weeks
1442.63028 3.14746 (144*2π)/5894 weeks
1451.04523 3.43002 (145*2π)/5894 weeks
146-.62431 1.68481 (146*2π)/5894 weeks
147.75944 -.15966 (147*2π)/5894 weeks
1481.75293 .50059 (148*2π)/5894 weeks
1492.60286 .46404 (149*2π)/5894 weeks
1503.02959 2.14636 (150*2π)/5894 weeks
1511.96021 2.84703 (151*2π)/5894 weeks
152-.05163 2.19921 (152*2π)/5894 weeks
1531.21716 -.6498 (153*2π)/5894 weeks
1543.82799 1.46708 (154*2π)/5894 weeks
1551.2724 3.74297 (155*2π)/5894 weeks
156-.35565 1.65862 (156*2π)/5894 weeks
157.98101 -.33834 (157*2π)/5894 weeks
1583.63805 .76668 (158*2π)/5894 weeks
1592.26922 3.51298 (159*2π)/5894 weeks
160-.14568 2.82579 (160*2π)/5894 weeks
161-.47585 .10436 (161*2π)/5894 weeks
1622.73787 -.45806 (162*2π)/5894 weeks
1632.7513 2.25648 (163*2π)/5894 weeks
1641.31233 2.28829 (164*2π)/5894 weeks
165.62467 1.62872 (165*2π)/5894 weeks
166.88619 .90336 (166*2π)/5894 weeks
1671.37933 .76987 (167*2π)/5894 weeks
1681.9736 1.12287 (168*2π)/5894 weeks
1691.53403 2.25129 (169*2π)/5893 weeks
170.09692 .9052 (170*2π)/5893 weeks
1711.76404 .15131 (171*2π)/5893 weeks
1721.9796 .82096 (172*2π)/5893 weeks
1732.43654 1.13777 (173*2π)/5893 weeks
1742.18007 2.24543 (174*2π)/5893 weeks
175.58659 2.29364 (175*2π)/5893 weeks
176.26755 .06552 (176*2π)/5893 weeks
1772.54952 -.16043 (177*2π)/5893 weeks
1783.60099 1.85655 (178*2π)/5893 weeks
1791.54088 3.93907 (179*2π)/5893 weeks
180-1.04974 2.14636 (180*2π)/5893 weeks
181-.05291 -.48916 (181*2π)/5893 weeks
1822.50842 -.24102 (182*2π)/5893 weeks
1832.62702 1.92844 (183*2π)/5893 weeks
184.83314 2.5589 (184*2π)/5893 weeks
185-.13553 .69196 (185*2π)/5893 weeks
1861.38249 -.70024 (186*2π)/5893 weeks
1873.37239 .42945 (187*2π)/5893 weeks
1882.89452 3.03799 (188*2π)/5893 weeks
189.18885 3.34865 (189*2π)/5893 weeks
190-1.11282 .97701 (190*2π)/5893 weeks
191.61831 -1.29416 (191*2π)/5893 weeks
1923.41254 -.08068 (192*2π)/5893 weeks
1932.72457 2.71129 (193*2π)/5893 weeks
194.05811 2.75604 (194*2π)/5893 weeks
195-.57429 .18139 (195*2π)/5893 weeks
1961.74719 -.69684 (196*2π)/5893 weeks
1972.94402 .79669 (197*2π)/5893 weeks
1981.61973 2.43833 (198*2π)/5893 weeks
199.45448 1.30203 (199*2π)/5893 weeks
200.87853 .57729 (200*2π)/5893 weeks
2012.11549 .70938 (201*2π)/5893 weeks
2021.61152 2.34525 (202*2π)/5893 weeks
203-.43904 1.81128 (203*2π)/5893 weeks
204-.28571 -.20248 (204*2π)/5893 weeks
2051.28892 -1.06135 (205*2π)/5893 weeks
2062.85067 -.07707 (206*2π)/5893 weeks
2072.73303 1.20469 (207*2π)/5893 weeks
2082.34905 2.72249 (208*2π)/5893 weeks
209-.73807 2.52909 (209*2π)/5893 weeks
210-.11922 -.45353 (210*2π)/5893 weeks
2111.45726 -.51366 (211*2π)/5893 weeks
2122.45444 .42592 (212*2π)/5893 weeks
2131.64227 1.31923 (213*2π)/5893 weeks
2141.40839 .65599 (214*2π)/5893 weeks
2151.48549 1.14954 (215*2π)/5893 weeks
2161.74849 .24911 (216*2π)/5893 weeks
2172.50927 1.9336 (217*2π)/5893 weeks
2181.11587 2.22486 (218*2π)/5893 weeks
219.06588 2.25794 (219*2π)/5893 weeks
220-.93287 -.09664 (220*2π)/5893 weeks
2211.75606 -1.33804 (221*2π)/5893 weeks
2223.26676 1.37405 (222*2π)/5893 weeks
223.85699 3.15342 (223*2π)/5893 weeks
224-1.47999 .75302 (224*2π)/5893 weeks
225.991 -1.73881 (225*2π)/5893 weeks
2263.29204 .61165 (226*2π)/5893 weeks
2271.55228 2.70863 (227*2π)/5893 weeks
228-.93736 1.89104 (228*2π)/5893 weeks
229-.92166 -1.54098 (229*2π)/5893 weeks
2302.90885 -1.61848 (230*2π)/5893 weeks
2313.50439 1.71435 (231*2π)/5893 weeks
232.43777 2.87717 (232*2π)/5893 weeks
233-.89601 -.03065 (233*2π)/5893 weeks
2341.82661 -1.1222 (234*2π)/5893 weeks
2352.38159 1.2689 (235*2π)/5893 weeks
236.51349 1.39723 (236*2π)/5892 weeks
237.56831 -.04013 (237*2π)/5892 weeks
2381.55431 -.39749 (238*2π)/5892 weeks
2392.98116 .81794 (239*2π)/5892 weeks
2401.3195 2.99583 (240*2π)/5892 weeks
241-.95206 1.35135 (241*2π)/5892 weeks
242-.07871 -.50122 (242*2π)/5892 weeks
2431.90097 -.38614 (243*2π)/5892 weeks
2441.33531 1.93899 (244*2π)/5892 weeks
245-.82396 .80411 (245*2π)/5892 weeks
246-.36734 -.96187 (246*2π)/5892 weeks
2471.45512 -1.59222 (247*2π)/5892 weeks
2482.97441 .24813 (248*2π)/5892 weeks
2491.25005 1.73201 (249*2π)/5892 weeks
250-.38101 .46092 (250*2π)/5892 weeks
251.46506 -1.67705 (251*2π)/5892 weeks
2523.30279 -1.06892 (252*2π)/5892 weeks
2532.99374 2.01865 (253*2π)/5892 weeks
254.22873 2.26066 (254*2π)/5892 weeks
255-.79314 .51786 (255*2π)/5892 weeks
256.19473 -1.85816 (256*2π)/5892 weeks
2572.67257 -.3977 (257*2π)/5892 weeks
2581.85499 .82837 (258*2π)/5892 weeks
259.83196 1.36145 (259*2π)/5892 weeks
260.10706 -.14143 (260*2π)/5892 weeks
2611.12034 -.33297 (261*2π)/5892 weeks
2621.46554 -.39025 (262*2π)/5892 weeks
2632.1953 .6131 (263*2π)/5892 weeks
264.61784 1.56011 (264*2π)/5892 weeks
265-.51134 -.09245 (265*2π)/5892 weeks
266.25814 -1.6594 (266*2π)/5892 weeks
2672.85564 -1.41954 (267*2π)/5892 weeks
2683.06556 1.3361 (268*2π)/5892 weeks
269.3854 2.0934 (269*2π)/5892 weeks
270-1.03748 .25231 (270*2π)/5892 weeks
271-.16907 -2.17441 (271*2π)/5892 weeks
2722.99533 -2.39926 (272*2π)/5892 weeks
2733.97973 1.1633 (273*2π)/5892 weeks
274.96869 3.37013 (274*2π)/5892 weeks
275-2.71592 .4907 (275*2π)/5892 weeks
276-.03249 -3.62846 (276*2π)/5892 weeks
2773.64585 -1.95177 (277*2π)/5892 weeks
2783.57777 1.38743 (278*2π)/5892 weeks
279-.11927 2.48708 (279*2π)/5892 weeks
280-1.95897 -1.27958 (280*2π)/5892 weeks
2811.58252 -3.95946 (281*2π)/5892 weeks
2824.5236 -.56545 (282*2π)/5892 weeks
2832.24679 1.94137 (283*2π)/5892 weeks
284-.3653 .76802 (284*2π)/5892 weeks
285.06077 -2.24625 (285*2π)/5892 weeks
2863.07435 -2.79701 (286*2π)/5892 weeks
2875.00129 .35836 (287*2π)/5892 weeks
2881.9704 3.18431 (288*2π)/5892 weeks
289-.75716 .36672 (289*2π)/5892 weeks
2901.31856 -1.72798 (290*2π)/5892 weeks
2912.86398 -.79855 (291*2π)/5892 weeks
2922.86989 .82498 (292*2π)/5892 weeks
2931.82527 1.74261 (293*2π)/5892 weeks
294-.32627 1.41577 (294*2π)/5892 weeks
295-.32627 -1.41577 (295*2π)/5892 weeks
2961.82527 -1.74261 (296*2π)/5892 weeks
2972.86989 -.82498 (297*2π)/5892 weeks
2982.86398 .79855 (298*2π)/5892 weeks
2991.31856 1.72798 (299*2π)/5892 weeks
300-.75716 -.36672 (300*2π)/5892 weeks
3011.9704 -3.18431 (301*2π)/5892 weeks
3025.00129 -.35836 (302*2π)/5892 weeks
3033.07435 2.79701 (303*2π)/5892 weeks
304.06077 2.24625 (304*2π)/5892 weeks
305-.3653 -.76802 (305*2π)/5892 weeks
3062.24679 -1.94137 (306*2π)/5892 weeks
3074.5236 .56545 (307*2π)/5892 weeks
3081.58252 3.95946 (308*2π)/5892 weeks
309-1.95897 1.27958 (309*2π)/5892 weeks
310-.11927 -2.48708 (310*2π)/5892 weeks
3113.57777 -1.38743 (311*2π)/5892 weeks
3123.64585 1.95177 (312*2π)/5892 weeks
313-.03249 3.62846 (313*2π)/5892 weeks
314-2.71592 -.4907 (314*2π)/5892 weeks
315.96869 -3.37013 (315*2π)/5892 weeks
3163.97973 -1.1633 (316*2π)/5892 weeks
3172.99533 2.39926 (317*2π)/5892 weeks
318-.16907 2.17441 (318*2π)/5892 weeks
319-1.03748 -.25231 (319*2π)/5892 weeks
320.3854 -2.0934 (320*2π)/5892 weeks
3213.06556 -1.3361 (321*2π)/5892 weeks
3222.85564 1.41954 (322*2π)/5892 weeks
323.25814 1.6594 (323*2π)/5892 weeks
324-.51134 .09245 (324*2π)/5892 weeks
325.61784 -1.56011 (325*2π)/5892 weeks
3262.1953 -.6131 (326*2π)/5892 weeks
3271.46554 .39025 (327*2π)/5892 weeks
3281.12034 .33297 (328*2π)/5892 weeks
329.10706 .14143 (329*2π)/5892 weeks
330.83196 -1.36145 (330*2π)/5892 weeks
3311.85499 -.82837 (331*2π)/5892 weeks
3322.67257 .3977 (332*2π)/5892 weeks
333.19473 1.85816 (333*2π)/5892 weeks
334-.79314 -.51786 (334*2π)/5892 weeks
335.22873 -2.26066 (335*2π)/5892 weeks
3362.99374 -2.01865 (336*2π)/5892 weeks
3373.30279 1.06892 (337*2π)/5892 weeks
338.46506 1.67705 (338*2π)/5892 weeks
339-.38101 -.46092 (339*2π)/5892 weeks
3401.25005 -1.73201 (340*2π)/5892 weeks
3412.97441 -.24813 (341*2π)/5892 weeks
3421.45512 1.59222 (342*2π)/5892 weeks
343-.36734 .96187 (343*2π)/5892 weeks
344-.82396 -.80411 (344*2π)/5892 weeks
3451.33531 -1.93899 (345*2π)/5892 weeks
3461.90097 .38614 (346*2π)/5892 weeks
347-.07871 .50122 (347*2π)/5892 weeks
348-.95206 -1.35135 (348*2π)/5892 weeks
3491.3195 -2.99583 (349*2π)/5892 weeks
3502.98116 -.81794 (350*2π)/5892 weeks
3511.55431 .39749 (351*2π)/5892 weeks
352.56831 .04013 (352*2π)/5892 weeks
353.51349 -1.39723 (353*2π)/5892 weeks
3542.38159 -1.2689 (354*2π)/5892 weeks
3551.82661 1.1222 (355*2π)/5892 weeks
356-.89601 .03065 (356*2π)/5892 weeks
357.43777 -2.87717 (357*2π)/5892 weeks
3583.50439 -1.71435 (358*2π)/5892 weeks
3592.90885 1.61848 (359*2π)/5892 weeks
360-.92166 1.54098 (360*2π)/5892 weeks
361-.93736 -1.89104 (361*2π)/5892 weeks
3621.55228 -2.70863 (362*2π)/5892 weeks
3633.29204 -.61165 (363*2π)/5892 weeks
364.991 1.73881 (364*2π)/5892 weeks
365-1.47999 -.75302 (365*2π)/5892 weeks
366.85699 -3.15342 (366*2π)/5892 weeks
3673.26676 -1.37405 (367*2π)/5892 weeks
3681.75606 1.33804 (368*2π)/5892 weeks
369-.93287 .09664 (369*2π)/5892 weeks
370.06588 -2.25794 (370*2π)/5892 weeks
3711.11587 -2.22486 (371*2π)/5892 weeks
3722.50927 -1.9336 (372*2π)/5892 weeks
3731.74849 -.24911 (373*2π)/5892 weeks
3741.48549 -1.14954 (374*2π)/5892 weeks
3751.40839 -.65599 (375*2π)/5892 weeks
3761.64227 -1.31923 (376*2π)/5892 weeks
3772.45444 -.42592 (377*2π)/5892 weeks
3781.45726 .51366 (378*2π)/5892 weeks
379-.11922 .45353 (379*2π)/5892 weeks
380-.73807 -2.52909 (380*2π)/5892 weeks
3812.34905 -2.72249 (381*2π)/5892 weeks
3822.73303 -1.20469 (382*2π)/5892 weeks
3832.85067 .07707 (383*2π)/5892 weeks
3841.28892 1.06135 (384*2π)/5892 weeks
385-.28571 .20248 (385*2π)/5892 weeks
386-.43904 -1.81128 (386*2π)/5892 weeks
3871.61152 -2.34525 (387*2π)/5892 weeks
3882.11549 -.70938 (388*2π)/5892 weeks
389.87853 -.57729 (389*2π)/5892 weeks
390.45448 -1.30203 (390*2π)/5892 weeks
3911.61973 -2.43833 (391*2π)/5892 weeks
3922.94402 -.79669 (392*2π)/5892 weeks
3931.74719 .69684 (393*2π)/5891 weeks
394-.57429 -.18139 (394*2π)/5891 weeks
395.05811 -2.75604 (395*2π)/5891 weeks
3962.72457 -2.71129 (396*2π)/5891 weeks
3973.41254 .08068 (397*2π)/5891 weeks
398.61831 1.29416 (398*2π)/5891 weeks
399-1.11282 -.97701 (399*2π)/5891 weeks
400.18885 -3.34865 (400*2π)/5891 weeks
4012.89452 -3.03799 (401*2π)/5891 weeks
4023.37239 -.42945 (402*2π)/5891 weeks
4031.38249 .70024 (403*2π)/5891 weeks
404-.13553 -.69196 (404*2π)/5891 weeks
405.83314 -2.5589 (405*2π)/5891 weeks
4062.62702 -1.92844 (406*2π)/5891 weeks
4072.50842 .24102 (407*2π)/5891 weeks
408-.05291 .48916 (408*2π)/5891 weeks
409-1.04974 -2.14636 (409*2π)/5891 weeks
4101.54088 -3.93907 (410*2π)/5891 weeks
4113.60099 -1.85655 (411*2π)/5891 weeks
4122.54952 .16043 (412*2π)/5891 weeks
413.26755 -.06552 (413*2π)/5891 weeks
414.58659 -2.29364 (414*2π)/5891 weeks
4152.18007 -2.24543 (415*2π)/5891 weeks
4162.43654 -1.13777 (416*2π)/5891 weeks
4171.9796 -.82096 (417*2π)/5891 weeks
4181.76404 -.15131 (418*2π)/5891 weeks
419.09692 -.9052 (419*2π)/5891 weeks
4201.53403 -2.25129 (420*2π)/5891 weeks
4211.9736 -1.12287 (421*2π)/5891 weeks
4221.37933 -.76987 (422*2π)/5891 weeks
423.88619 -.90336 (423*2π)/5891 weeks
424.62467 -1.62872 (424*2π)/5891 weeks
4251.31233 -2.28829 (425*2π)/5891 weeks
4262.7513 -2.25648 (426*2π)/5891 weeks
4272.73787 .45806 (427*2π)/5891 weeks
428-.47585 -.10436 (428*2π)/5891 weeks
429-.14568 -2.82579 (429*2π)/5891 weeks
4302.26922 -3.51298 (430*2π)/5891 weeks
4313.63805 -.76668 (431*2π)/5891 weeks
432.98101 .33834 (432*2π)/5891 weeks
433-.35565 -1.65862 (433*2π)/5891 weeks
4341.2724 -3.74297 (434*2π)/5891 weeks
4353.82799 -1.46708 (435*2π)/5891 weeks
4361.21716 .6498 (436*2π)/5891 weeks
437-.05163 -2.19921 (437*2π)/5891 weeks
4381.96021 -2.84703 (438*2π)/5891 weeks
4393.02959 -2.14636 (439*2π)/5891 weeks
4402.60286 -.46404 (440*2π)/5891 weeks
4411.75293 -.50059 (441*2π)/5891 weeks
442.75944 .15966 (442*2π)/5891 weeks
443-.62431 -1.68481 (443*2π)/5891 weeks
4441.04523 -3.43002 (444*2π)/5891 weeks
4452.63028 -3.14746 (445*2π)/5891 weeks
4463.3744 -1.126 (446*2π)/5891 weeks
4471.37966 -.06673 (447*2π)/5891 weeks
4481.09853 -1.83288 (448*2π)/5891 weeks
4492.72347 -1.6501 (449*2π)/5891 weeks
4502.03632 .14562 (450*2π)/5891 weeks
451.08611 -.2194 (451*2π)/5891 weeks
452-.15888 -1.9856 (452*2π)/5891 weeks
453.53596 -3.06664 (453*2π)/5891 weeks
4542.54626 -3.21304 (454*2π)/5891 weeks
4553.63753 -.79032 (455*2π)/5891 weeks
4561.4241 1.29057 (456*2π)/5891 weeks
457-2.02043 -1.17678 (457*2π)/5891 weeks
458.21687 -4.67785 (458*2π)/5891 weeks
4593.56388 -3.15534 (459*2π)/5891 weeks
4602.33902 -.09924 (460*2π)/5891 weeks
461-.31482 -.65357 (461*2π)/5891 weeks
462-.26039 -3.60434 (462*2π)/5891 weeks
4632.48208 -4.49372 (463*2π)/5891 weeks
4644.66498 -2.35629 (464*2π)/5891 weeks
4652.95512 1.2962 (465*2π)/5891 weeks
466-1.95425 .39417 (466*2π)/5891 weeks
467-1.52526 -5.00848 (467*2π)/5891 weeks
4683.12887 -6.09538 (468*2π)/5891 weeks
4696.56308 -2.35429 (469*2π)/5891 weeks
4703.53404 2.71599 (470*2π)/5891 weeks
471-2.3234 .62698 (471*2π)/5891 weeks
472-1.56449 -5.32229 (472*2π)/5891 weeks
4734.72669 -5.27927 (473*2π)/5891 weeks
4745.60785 .40016 (474*2π)/5891 weeks
475.90125 2.84788 (475*2π)/5891 weeks
476-3.70111 -1.29186 (476*2π)/5891 weeks
477-.69417 -6.24157 (477*2π)/5891 weeks
4784.45993 -5.3802 (478*2π)/5891 weeks
4794.69321 .00595 (479*2π)/5891 weeks
480-.03383 .63688 (480*2π)/5891 weeks
481-1.25625 -3.66411 (481*2π)/5891 weeks
4822.52466 -5.96269 (482*2π)/5891 weeks
4835.61762 -2.63433 (483*2π)/5891 weeks
4843.44824 .98733 (484*2π)/5891 weeks
485.09028 .08371 (485*2π)/5891 weeks
486.01379 -2.47441 (486*2π)/5891 weeks
4871.97914 -2.81504 (487*2π)/5891 weeks
4881.27264 -1.65675 (488*2π)/5891 weeks
4891.52394 -3.16371 (489*2π)/5891 weeks
4902.73607 -1.76925 (490*2π)/5891 weeks
491.79324 -.80019 (491*2π)/5891 weeks
492-.48611 -2.86809 (492*2π)/5891 weeks
4931.82397 -4.89893 (493*2π)/5891 weeks
4945.1122 -2.22541 (494*2π)/5891 weeks
4952.69326 2.38149 (495*2π)/5891 weeks
496-3.20473 .74645 (496*2π)/5891 weeks
497-3.62843 -6.11485 (497*2π)/5891 weeks
4983.73375 -7.79522 (498*2π)/5891 weeks
4995.61184 -1.40972 (499*2π)/5891 weeks
5001.65524 1.21089 (500*2π)/5891 weeks
501-3.28647 -.9485 (501*2π)/5891 weeks
502-1.57736 -7.30377 (502*2π)/5891 weeks
5034.43358 -6.82825 (503*2π)/5891 weeks
5046.5653 -1.3594 (504*2π)/5891 weeks
505.24915 2.3262 (505*2π)/5891 weeks
506-2.96113 -4.07705 (506*2π)/5891 weeks
5071.80094 -5.78395 (507*2π)/5891 weeks
5083.8743 -4.82749 (508*2π)/5891 weeks
5095.20184 .32522 (509*2π)/5891 weeks
510-2.43002 2.09521 (510*2π)/5891 weeks
511-4.56857 -5.39676 (511*2π)/5891 weeks
512.84113 -9.75577 (512*2π)/5891 weeks
5136.68879 -5.56376 (513*2π)/5891 weeks
5143.13232 -.17298 (514*2π)/5891 weeks
515.15213 -3.54245 (515*2π)/5891 weeks
5162.56924 -3.96597 (516*2π)/5891 weeks
5172.63863 -3.07531 (517*2π)/5891 weeks
518.73835 -.81236 (518*2π)/5891 weeks
519-1.7443 -5.08739 (519*2π)/5891 weeks
5202.73527 -7.98116 (520*2π)/5891 weeks
5215.66729 -4.19807 (521*2π)/5891 weeks
5224.01478 -.38737 (522*2π)/5891 weeks
523-.87186 -2.25949 (523*2π)/5891 weeks
5242.32657 -5.57497 (524*2π)/5891 weeks
5253.54495 -2.15158 (525*2π)/5891 weeks
526.59894 -.57345 (526*2π)/5891 weeks
527-2.77763 -4.39164 (527*2π)/5891 weeks
5281.34798 -8.95168 (528*2π)/5891 weeks
5297.67053 -3.95646 (529*2π)/5891 weeks
5302.3875 1.55369 (530*2π)/5891 weeks
531-2.45878 -1.82344 (531*2π)/5891 weeks
532-2.0371 -5.86916 (532*2π)/5891 weeks
5331.20114 -7.4187 (533*2π)/5891 weeks
5342.44534 -4.77654 (534*2π)/5891 weeks
535.58613 -4.99621 (535*2π)/5891 weeks
536.49701 -6.70091 (536*2π)/5891 weeks
5373.66454 -7.61052 (537*2π)/5891 weeks
5385.22175 -5.64302 (538*2π)/5891 weeks
5393.60076 -1.51464 (539*2π)/5891 weeks
540.03738 -3.17328 (540*2π)/5891 weeks
5411.1881 -5.47477 (541*2π)/5891 weeks
5421.84846 -4.759 (542*2π)/5891 weeks
543.69206 -3.83674 (543*2π)/5891 weeks
544-.58978 -7.76267 (544*2π)/5891 weeks
5455.68801 -8.3123 (545*2π)/5891 weeks
5464.57084 -1.7361 (546*2π)/5891 weeks
547-.83433 -1.21328 (547*2π)/5891 weeks
548-4.32678 -6.47183 (548*2π)/5891 weeks
549.87093 -13.41802 (549*2π)/5891 weeks
55010.4017 -7.6541 (550*2π)/5891 weeks
5516.41067 3.7633 (551*2π)/5891 weeks
552-9.72004 4.00541 (552*2π)/5891 weeks
553-13.89039 -16.76509 (553*2π)/5891 weeks
5547.40913 -23.3147 (554*2π)/5891 weeks
55516.73479 -4.90124 (555*2π)/5891 weeks
5562.46863 7.36016 (556*2π)/5891 weeks
557-12.86168 -5.02483 (557*2π)/5891 weeks
558-3.83599 -21.74075 (558*2π)/5891 weeks
55911.3719 -16.18119 (559*2π)/5891 weeks
56011.89558 -2.58404 (560*2π)/5891 weeks
561-2.73098 3.47076 (561*2π)/5891 weeks
562-8.67768 -10.44233 (562*2π)/5891 weeks
563-.29227 -16.24638 (563*2π)/5891 weeks
5645.66211 -12.4812 (564*2π)/5891 weeks
565.27543 -8.20388 (565*2π)/5891 weeks
566-1.56848 -13.07086 (566*2π)/5891 weeks
567.76502 -16.08515 (567*2π)/5891 weeks
5684.42356 -17.37764 (568*2π)/5891 weeks
56910.47917 -15.77982 (569*2π)/5891 weeks
5708.58128 -4.79808 (570*2π)/5891 weeks
571-2.67575 -7.94696 (571*2π)/5891 weeks
572-5.38635 -12.84356 (572*2π)/5891 weeks
573-5.7261 -23.18516 (573*2π)/5891 weeks
5746.42494 -29.16331 (574*2π)/5891 weeks
57518.90494 -20.97785 (575*2π)/5891 weeks
57613.36798 1.22131 (576*2π)/5891 weeks
577-18.36549 -5.96307 (577*2π)/5891 weeks
578-15.64636 -37.13873 (578*2π)/5891 weeks
5793.81572 -52.81525 (579*2π)/5891 weeks
58037.86427 -36.10984 (580*2π)/5891 weeks
58115.55377 4.02695 (581*2π)/5891 weeks
582-26.45037 -24.73059 (582*2π)/5891 weeks
583-4.38623 -77.30738 (583*2π)/5891 weeks
58450.91999 -69.66846 (584*2π)/5891 weeks
58553.29235 -9.34238 (585*2π)/5891 weeks
586-40.86338 -7.40177 (586*2π)/5891 weeks
587-66.67892 -154.933 (587*2π)/5891 weeks



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