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Fourier Analysis of MZZ (PROSHARES ULTRASHORT MIDCAP400 PROSHARES ULTRASHORT MIDCAP400)


MZZ (PROSHARES ULTRASHORT MIDCAP400 PROSHARES ULTRASHORT MIDCAP400) appears to have interesting cyclic behaviour every 60 weeks (53.2766*sine), 55 weeks (40.1366*sine), and 50 weeks (21.7532*cosine).

MZZ (PROSHARES ULTRASHORT MIDCAP400 PROSHARES ULTRASHORT MIDCAP400) has an average price of 278.91 (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 1/16/2018 for MZZ (PROSHARES ULTRASHORT MIDCAP400 PROSHARES ULTRASHORT MIDCAP400), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0278.9055   0 
1140.1685 317.8896 (1*2π)/602602 weeks
2-62.78705 159.6541 (2*2π)/602301 weeks
3-46.23677 13.68379 (3*2π)/602201 weeks
447.87259 4.46118 (4*2π)/602151 weeks
554.32073 63.37918 (5*2π)/602120 weeks
63.05677 78.46166 (6*2π)/602100 weeks
7-27.71506 32.35173 (7*2π)/60286 weeks
85.39348 -4.28252 (8*2π)/60275 weeks
938.82749 26.6716 (9*2π)/60267 weeks
1011.34663 53.27663 (10*2π)/60260 weeks
11-11.4352 40.13663 (11*2π)/60255 weeks
12-21.75323 14.52697 (12*2π)/60250 weeks
134.26482 -4.56444 (13*2π)/60246 weeks
1420.11704 15.10624 (14*2π)/60243 weeks
1510.54303 27.79262 (15*2π)/60240 weeks
16-2.40755 26.62487 (16*2π)/60238 weeks
17-6.33793 15.73926 (17*2π)/60235 weeks
18-2.95412 10.04902 (18*2π)/60233 weeks
192.72701 3.31245 (19*2π)/60232 weeks
2011.72308 10.96689 (20*2π)/60230 weeks
216.18887 17.28939 (21*2π)/60229 weeks
222.23187 16.86189 (22*2π)/60227 weeks
23-.49596 14.73437 (23*2π)/60226 weeks
24-1.50726 10.6053 (24*2π)/60225 weeks
253.82112 8.10632 (25*2π)/60224 weeks
263.35759 14.99281 (26*2π)/60223 weeks
27-3.94023 15.50259 (27*2π)/60222 weeks
28-8.83169 4.83228 (28*2π)/60222 weeks
294.49951 -3.77211 (29*2π)/60221 weeks
3013.27324 6.97751 (30*2π)/60220 weeks
317.7183 19.23816 (31*2π)/60219 weeks
32-9.1439 17.80054 (32*2π)/60219 weeks
33-10.61907 -.44427 (33*2π)/60218 weeks
347.62286 -5.65504 (34*2π)/60218 weeks
3516.93233 9.93792 (35*2π)/60217 weeks
362.4558 24.08354 (36*2π)/60217 weeks
37-15.38063 11.78579 (37*2π)/60216 weeks
38-6.45318 -5.61982 (38*2π)/60216 weeks
397.75323 -2.19224 (39*2π)/60215 weeks
409.55063 9.07134 (40*2π)/60215 weeks
41-.31506 12.71868 (41*2π)/60215 weeks
42-4.16264 5.66193 (42*2π)/60214 weeks
43-.43514 1.04652 (43*2π)/60214 weeks
444.70715 1.88148 (44*2π)/60214 weeks
455.39737 8.32725 (45*2π)/60213 weeks
46-.59321 7.58552 (46*2π)/60213 weeks
47.62919 3.77916 (47*2π)/60213 weeks
481.80687 4.65841 (48*2π)/60213 weeks
491.27328 5.3742 (49*2π)/60212 weeks
50-.04659 3.41268 (50*2π)/60212 weeks
513.0368 1.43163 (51*2π)/60212 weeks
525.39329 5.14368 (52*2π)/60212 weeks
533.95425 7.09969 (53*2π)/60211 weeks
54.71763 7.0284 (54*2π)/60211 weeks
55.543 5.18311 (55*2π)/60211 weeks
562.00652 4.32324 (56*2π)/60211 weeks
571.99908 6.86557 (57*2π)/60211 weeks
58-1.36951 6.41094 (58*2π)/60210 weeks
59-2.64252 2.92556 (59*2π)/60210 weeks
60.21961 -1.2276 (60*2π)/60210 weeks
616.65956 1.15197 (61*2π)/60210 weeks
624.02719 8.72592 (62*2π)/60210 weeks
63-1.98951 6.46099 (63*2π)/60210 weeks
64-1.13267 1.12636 (64*2π)/6029 weeks
652.62262 1.21092 (65*2π)/6029 weeks
663.71699 4.17034 (66*2π)/6029 weeks
67-.29289 4.59157 (67*2π)/6029 weeks
681.28533 -.07442 (68*2π)/6029 weeks
695.25816 2.26707 (69*2π)/6029 weeks
704.95312 6.17921 (70*2π)/6029 weeks
71-.06189 7.30001 (71*2π)/6028 weeks
72-1.6668 2.64958 (72*2π)/6028 weeks
732.49458 1.61974 (73*2π)/6028 weeks
742.43927 3.21288 (74*2π)/6028 weeks
751.83758 4.45795 (75*2π)/6028 weeks
76.16211 1.92626 (76*2π)/6028 weeks
775.17034 1.01258 (77*2π)/6028 weeks
785.49745 7.55625 (78*2π)/6028 weeks
79-1.32054 8.92646 (79*2π)/6028 weeks
80-4.96444 3.37075 (80*2π)/6028 weeks
81-.25449 -2.82687 (81*2π)/6027 weeks
825.581 1.28775 (82*2π)/6027 weeks
833.17706 4.94285 (83*2π)/6027 weeks
841.15909 5.99628 (84*2π)/6027 weeks
85-3.21674 2.81132 (85*2π)/6027 weeks
861.4109 -2.46357 (86*2π)/6027 weeks
876.53127 2.1947 (87*2π)/6027 weeks
883.90081 7.02588 (88*2π)/6027 weeks
89-1.97918 6.83237 (89*2π)/6027 weeks
90-3.01292 .6063 (90*2π)/6027 weeks
911.76828 -1.14524 (91*2π)/6027 weeks
925.52762 1.46316 (92*2π)/6027 weeks
933.7134 7.60749 (93*2π)/6026 weeks
94-3.405 6.19011 (94*2π)/6026 weeks
95-3.33699 -.46073 (95*2π)/6026 weeks
962.19757 -2.49097 (96*2π)/6026 weeks
975.04689 1.73954 (97*2π)/6026 weeks
982.24902 4.84612 (98*2π)/6026 weeks
99-.34428 3.24128 (99*2π)/6026 weeks
100.48869 .95584 (100*2π)/6026 weeks
1012.57076 1.32382 (101*2π)/6026 weeks
1021.94149 3.04047 (102*2π)/6026 weeks
103.92221 1.83274 (103*2π)/6026 weeks
1042.09177 2.2858 (104*2π)/6026 weeks
105.40074 2.86459 (105*2π)/6026 weeks
106-.30126 .74096 (106*2π)/6026 weeks
1072.17246 -1.11828 (107*2π)/6026 weeks
1085.36275 1.09199 (108*2π)/6026 weeks
1094.0906 5.13873 (109*2π)/6026 weeks
110-.31626 4.90139 (110*2π)/6025 weeks
111-1.3314 .87542 (111*2π)/6025 weeks
1122.68747 -1.0269 (112*2π)/6025 weeks
1135.54538 3.05885 (113*2π)/6025 weeks
1141.76247 6.49287 (114*2π)/6025 weeks
115-2.87382 4.23353 (115*2π)/6025 weeks
116-2.08441 -1.71984 (116*2π)/6025 weeks
1173.30371 -2.22379 (117*2π)/6025 weeks
1186.06911 2.26947 (118*2π)/6025 weeks
1192.16431 6.4557 (119*2π)/6025 weeks
120-2.71872 2.89882 (120*2π)/6025 weeks
121-.49895 -2.43257 (121*2π)/6025 weeks
1225.32621 -1.32035 (122*2π)/6025 weeks
1235.6966 4.14436 (123*2π)/6025 weeks
1241.59663 6.18595 (124*2π)/6025 weeks
125-2.3802 3.53745 (125*2π)/6025 weeks
126-.6229 -1.43605 (126*2π)/6025 weeks
1273.77166 -.59487 (127*2π)/6025 weeks
1284.16922 3.07558 (128*2π)/6025 weeks
1291.77789 4.5447 (129*2π)/6025 weeks
130-.55088 3.09463 (130*2π)/6025 weeks
131.12969 .32514 (131*2π)/6025 weeks
1322.73512 .29672 (132*2π)/6025 weeks
1333.25179 3.50368 (133*2π)/6025 weeks
134-.2085 4.42654 (134*2π)/6024 weeks
135-1.89356 .76339 (135*2π)/6024 weeks
1361.63394 -1.18214 (136*2π)/6024 weeks
1373.60212 .89944 (137*2π)/6024 weeks
1382.45623 3.16557 (138*2π)/6024 weeks
139.53048 3.00756 (139*2π)/6024 weeks
140-.13281 1.97716 (140*2π)/6024 weeks
141.03028 .28836 (141*2π)/6024 weeks
1421.87379 -.19667 (142*2π)/6024 weeks
1432.74139 1.44024 (143*2π)/6024 weeks
1441.19474 1.9171 (144*2π)/6024 weeks
1451.07204 .28665 (145*2π)/6024 weeks
1463.19116 .81291 (146*2π)/6024 weeks
1472.92994 2.87801 (147*2π)/6024 weeks
1481.39107 3.29774 (148*2π)/6024 weeks
149-.51991 2.22308 (149*2π)/6024 weeks
150.21356 .0515 (150*2π)/6024 weeks
1511.74031 .4026 (151*2π)/6024 weeks
1522.20321 .34153 (152*2π)/6024 weeks
1533.19064 1.50065 (153*2π)/6024 weeks
1542.20668 2.54112 (154*2π)/6024 weeks
155.58739 2.7969 (155*2π)/6024 weeks
156-.00976 .17596 (156*2π)/6024 weeks
1573.24599 .19475 (157*2π)/6024 weeks
1582.81876 3.44943 (158*2π)/6024 weeks
159-.00417 2.6238 (159*2π)/6024 weeks
160.06771 .32873 (160*2π)/6024 weeks
1612.44019 -.37047 (161*2π)/6024 weeks
1623.45164 2.45802 (162*2π)/6024 weeks
163.94663 3.40893 (163*2π)/6024 weeks
164-.71919 1.68789 (164*2π)/6024 weeks
165.69202 -.8565 (165*2π)/6024 weeks
1663.2811 .79619 (166*2π)/6024 weeks
1671.93468 2.4741 (167*2π)/6024 weeks
168.9939 2.151 (168*2π)/6024 weeks
169.66293 1.3112 (169*2π)/6024 weeks
1701.09677 .79929 (170*2π)/6024 weeks
1711.56495 .73144 (171*2π)/6024 weeks
1722.01503 1.32399 (172*2π)/6024 weeks
173.94045 2.2346 (173*2π)/6023 weeks
174.33809 .35947 (174*2π)/6023 weeks
1751.91379 .38484 (175*2π)/6023 weeks
1761.96957 .80752 (176*2π)/6023 weeks
1772.43583 1.2866 (177*2π)/6023 weeks
1781.94113 2.34701 (178*2π)/6023 weeks
179.36319 2.09101 (179*2π)/6023 weeks
180.50281 -.13936 (180*2π)/6023 weeks
1812.66737 -.04327 (181*2π)/6023 weeks
1823.51205 2.00812 (182*2π)/6023 weeks
1831.35261 3.86518 (183*2π)/6023 weeks
184-1.04118 2.01848 (184*2π)/6023 weeks
185-.03451 -.48426 (185*2π)/6023 weeks
1862.43093 -.26479 (186*2π)/6023 weeks
1872.62326 1.82703 (187*2π)/6023 weeks
188.95083 2.53393 (188*2π)/6023 weeks
189-.16632 .84149 (189*2π)/6023 weeks
1901.11703 -.63574 (190*2π)/6023 weeks
1913.13978 .16699 (191*2π)/6023 weeks
1923.1332 2.66608 (192*2π)/6023 weeks
193.63446 3.44786 (193*2π)/6023 weeks
194-1.06343 1.46901 (194*2π)/6023 weeks
195-.00299 -.99079 (195*2π)/6023 weeks
1962.89328 -.6881 (196*2π)/6023 weeks
1973.16228 2.13908 (197*2π)/6023 weeks
198.75222 3.05207 (198*2π)/6023 weeks
199-.7538 .99701 (199*2π)/6023 weeks
200.95311 -.83094 (200*2π)/6023 weeks
2012.62364 .1743 (201*2π)/6023 weeks
2022.37715 2.14241 (202*2π)/6023 weeks
203.58508 1.85787 (203*2π)/6023 weeks
204.73281 .80152 (204*2π)/6023 weeks
2051.51179 .30581 (205*2π)/6023 weeks
2062.14856 1.64755 (206*2π)/6023 weeks
207.45997 2.43554 (207*2π)/6023 weeks
208-.63712 .66387 (208*2π)/6023 weeks
209.36403 -.78084 (209*2π)/6023 weeks
2102.12858 -.8217 (210*2π)/6023 weeks
2112.86958 .64851 (211*2π)/6023 weeks
2122.71465 1.58693 (212*2π)/6023 weeks
2131.27163 3.22197 (213*2π)/6023 weeks
214-1.15109 1.09121 (214*2π)/6023 weeks
215.58262 -.60154 (215*2π)/6023 weeks
2161.82644 -.35993 (216*2π)/6023 weeks
2172.32099 .90014 (217*2π)/6023 weeks
2181.35575 1.1815 (218*2π)/6023 weeks
2191.62126 .65799 (219*2π)/6023 weeks
2201.24253 1.00284 (220*2π)/6023 weeks
2212.1639 .32387 (221*2π)/6023 weeks
2222.12216 2.1685 (222*2π)/6023 weeks
223.97637 2.14638 (223*2π)/6023 weeks
224-.266 2.08569 (224*2π)/6023 weeks
225-.67816 -.48248 (225*2π)/6023 weeks
2262.09913 -1.17562 (226*2π)/6023 weeks
2273.09311 1.63163 (227*2π)/6023 weeks
228.58249 3.06217 (228*2π)/6023 weeks
229-1.43947 .52647 (229*2π)/6023 weeks
2301.09665 -1.69798 (230*2π)/6023 weeks
2313.22106 .63641 (231*2π)/6023 weeks
2321.54741 2.64395 (232*2π)/6023 weeks
233-.85015 1.91857 (233*2π)/6023 weeks
234-1.04381 -1.33405 (234*2π)/6023 weeks
2352.63465 -1.77001 (235*2π)/6023 weeks
2363.57268 1.36509 (236*2π)/6023 weeks
237.82583 2.92349 (237*2π)/6023 weeks
238-1.00104 .42555 (238*2π)/6023 weeks
2391.31738 -1.26806 (239*2π)/6023 weeks
2402.55604 .85857 (240*2π)/6023 weeks
241.80461 1.59299 (241*2π)/6022 weeks
242.34954 .18988 (242*2π)/6022 weeks
2431.24056 -.31791 (243*2π)/6022 weeks
2442.68238 .19788 (244*2π)/6022 weeks
2452.15514 2.59659 (245*2π)/6022 weeks
246-.59023 2.13627 (246*2π)/6022 weeks
247-.50485 -.09235 (247*2π)/6022 weeks
2481.12893 -.79863 (248*2π)/6022 weeks
2492.06392 1.17834 (249*2π)/6022 weeks
250-.30067 1.65909 (250*2π)/6022 weeks
251-.66487 -.29429 (251*2π)/6022 weeks
252.57206 -1.54935 (252*2π)/6022 weeks
2532.53581 -1.01031 (253*2π)/6022 weeks
2542.2107 1.33493 (254*2π)/6022 weeks
255.18005 1.35765 (255*2π)/6022 weeks
256-.37872 -.57038 (256*2π)/6022 weeks
2571.7211 -1.90401 (257*2π)/6022 weeks
2583.65687 .32533 (258*2π)/6022 weeks
2591.81654 2.56993 (259*2π)/6022 weeks
260-.35663 1.58066 (260*2π)/6022 weeks
261-.84695 -.25534 (261*2π)/6022 weeks
2621.42139 -1.91073 (262*2π)/6022 weeks
2632.4422 .28456 (263*2π)/6022 weeks
2641.67312 .95541 (264*2π)/6022 weeks
265.33268 1.11293 (265*2π)/6022 weeks
266.40621 -.43148 (266*2π)/6022 weeks
2671.11864 -.27718 (267*2π)/6022 weeks
2681.62092 -.34715 (268*2π)/6022 weeks
2692.01672 .95215 (269*2π)/6022 weeks
270.25622 1.42512 (270*2π)/6022 weeks
271-.42673 -.32855 (271*2π)/6022 weeks
272.50775 -1.80916 (272*2π)/6022 weeks
2732.98215 -1.14369 (273*2π)/6022 weeks
2742.8551 1.51583 (274*2π)/6022 weeks
275.2404 1.97649 (275*2π)/6022 weeks
276-1.02839 .15628 (276*2π)/6022 weeks
277-.11806 -2.15833 (277*2π)/6022 weeks
2782.92455 -2.35313 (278*2π)/6022 weeks
2793.9339 1.05621 (279*2π)/6022 weeks
2801.15616 3.27716 (280*2π)/6022 weeks
281-2.56417 .83938 (281*2π)/6022 weeks
282-.45218 -3.42475 (282*2π)/6022 weeks
2833.36227 -2.26242 (283*2π)/6022 weeks
2843.71444 .92293 (284*2π)/6022 weeks
285.50986 2.63845 (285*2π)/6022 weeks
286-2.01166 -.44464 (286*2π)/6022 weeks
287.58573 -3.7519 (287*2π)/6022 weeks
2884.40993 -1.52432 (288*2π)/6022 weeks
2892.94242 1.63501 (289*2π)/6022 weeks
290.15164 1.31679 (290*2π)/6022 weeks
291-.50704 -1.46347 (291*2π)/6022 weeks
2922.02797 -2.89226 (292*2π)/6022 weeks
2934.76389 -.97579 (293*2π)/6022 weeks
2943.47024 2.65563 (294*2π)/6022 weeks
295-.42063 1.74205 (295*2π)/6022 weeks
296.19891 -1.4027 (296*2π)/6022 weeks
2972.33126 -1.20578 (297*2π)/6022 weeks
2983.08069 .18962 (298*2π)/6022 weeks
2992.3516 1.34568 (299*2π)/6022 weeks
300.8237 1.90143 (300*2π)/6022 weeks
301-.88035   (301*2π)/6022 weeks
302.8237 -1.90143 (302*2π)/6022 weeks
3032.3516 -1.34568 (303*2π)/6022 weeks
3043.08069 -.18962 (304*2π)/6022 weeks
3052.33126 1.20578 (305*2π)/6022 weeks
306.19891 1.4027 (306*2π)/6022 weeks
307-.42063 -1.74205 (307*2π)/6022 weeks
3083.47024 -2.65563 (308*2π)/6022 weeks
3094.76389 .97579 (309*2π)/6022 weeks
3102.02797 2.89226 (310*2π)/6022 weeks
311-.50704 1.46347 (311*2π)/6022 weeks
312.15164 -1.31679 (312*2π)/6022 weeks
3132.94242 -1.63501 (313*2π)/6022 weeks
3144.40993 1.52432 (314*2π)/6022 weeks
315.58573 3.7519 (315*2π)/6022 weeks
316-2.01166 .44464 (316*2π)/6022 weeks
317.50986 -2.63845 (317*2π)/6022 weeks
3183.71444 -.92293 (318*2π)/6022 weeks
3193.36227 2.26242 (319*2π)/6022 weeks
320-.45218 3.42475 (320*2π)/6022 weeks
321-2.56417 -.83938 (321*2π)/6022 weeks
3221.15616 -3.27716 (322*2π)/6022 weeks
3233.9339 -1.05621 (323*2π)/6022 weeks
3242.92455 2.35313 (324*2π)/6022 weeks
325-.11806 2.15833 (325*2π)/6022 weeks
326-1.02839 -.15628 (326*2π)/6022 weeks
327.2404 -1.97649 (327*2π)/6022 weeks
3282.8551 -1.51583 (328*2π)/6022 weeks
3292.98215 1.14369 (329*2π)/6022 weeks
330.50775 1.80916 (330*2π)/6022 weeks
331-.42673 .32855 (331*2π)/6022 weeks
332.25622 -1.42512 (332*2π)/6022 weeks
3332.01672 -.95215 (333*2π)/6022 weeks
3341.62092 .34715 (334*2π)/6022 weeks
3351.11864 .27718 (335*2π)/6022 weeks
336.40621 .43148 (336*2π)/6022 weeks
337.33268 -1.11293 (337*2π)/6022 weeks
3381.67312 -.95541 (338*2π)/6022 weeks
3392.4422 -.28456 (339*2π)/6022 weeks
3401.42139 1.91073 (340*2π)/6022 weeks
341-.84695 .25534 (341*2π)/6022 weeks
342-.35663 -1.58066 (342*2π)/6022 weeks
3431.81654 -2.56993 (343*2π)/6022 weeks
3443.65687 -.32533 (344*2π)/6022 weeks
3451.7211 1.90401 (345*2π)/6022 weeks
346-.37872 .57038 (346*2π)/6022 weeks
347.18005 -1.35765 (347*2π)/6022 weeks
3482.2107 -1.33493 (348*2π)/6022 weeks
3492.53581 1.01031 (349*2π)/6022 weeks
350.57206 1.54935 (350*2π)/6022 weeks
351-.66487 .29429 (351*2π)/6022 weeks
352-.30067 -1.65909 (352*2π)/6022 weeks
3532.06392 -1.17834 (353*2π)/6022 weeks
3541.12893 .79863 (354*2π)/6022 weeks
355-.50485 .09235 (355*2π)/6022 weeks
356-.59023 -2.13627 (356*2π)/6022 weeks
3572.15514 -2.59659 (357*2π)/6022 weeks
3582.68238 -.19788 (358*2π)/6022 weeks
3591.24056 .31791 (359*2π)/6022 weeks
360.34954 -.18988 (360*2π)/6022 weeks
361.80461 -1.59299 (361*2π)/6022 weeks
3622.55604 -.85857 (362*2π)/6022 weeks
3631.31738 1.26806 (363*2π)/6022 weeks
364-1.00104 -.42555 (364*2π)/6022 weeks
365.82583 -2.92349 (365*2π)/6022 weeks
3663.57268 -1.36509 (366*2π)/6022 weeks
3672.63465 1.77001 (367*2π)/6022 weeks
368-1.04381 1.33405 (368*2π)/6022 weeks
369-.85015 -1.91857 (369*2π)/6022 weeks
3701.54741 -2.64395 (370*2π)/6022 weeks
3713.22106 -.63641 (371*2π)/6022 weeks
3721.09665 1.69798 (372*2π)/6022 weeks
373-1.43947 -.52647 (373*2π)/6022 weeks
374.58249 -3.06217 (374*2π)/6022 weeks
3753.09311 -1.63163 (375*2π)/6022 weeks
3762.09913 1.17562 (376*2π)/6022 weeks
377-.67816 .48248 (377*2π)/6022 weeks
378-.266 -2.08569 (378*2π)/6022 weeks
379.97637 -2.14638 (379*2π)/6022 weeks
3802.12216 -2.1685 (380*2π)/6022 weeks
3812.1639 -.32387 (381*2π)/6022 weeks
3821.24253 -1.00284 (382*2π)/6022 weeks
3831.62126 -.65799 (383*2π)/6022 weeks
3841.35575 -1.1815 (384*2π)/6022 weeks
3852.32099 -.90014 (385*2π)/6022 weeks
3861.82644 .35993 (386*2π)/6022 weeks
387.58262 .60154 (387*2π)/6022 weeks
388-1.15109 -1.09121 (388*2π)/6022 weeks
3891.27163 -3.22197 (389*2π)/6022 weeks
3902.71465 -1.58693 (390*2π)/6022 weeks
3912.86958 -.64851 (391*2π)/6022 weeks
3922.12858 .8217 (392*2π)/6022 weeks
393.36403 .78084 (393*2π)/6022 weeks
394-.63712 -.66387 (394*2π)/6022 weeks
395.45997 -2.43554 (395*2π)/6022 weeks
3962.14856 -1.64755 (396*2π)/6022 weeks
3971.51179 -.30581 (397*2π)/6022 weeks
398.73281 -.80152 (398*2π)/6022 weeks
399.58508 -1.85787 (399*2π)/6022 weeks
4002.37715 -2.14241 (400*2π)/6022 weeks
4012.62364 -.1743 (401*2π)/6022 weeks
402.95311 .83094 (402*2π)/6021 weeks
403-.7538 -.99701 (403*2π)/6021 weeks
404.75222 -3.05207 (404*2π)/6021 weeks
4053.16228 -2.13908 (405*2π)/6021 weeks
4062.89328 .6881 (406*2π)/6021 weeks
407-.00299 .99079 (407*2π)/6021 weeks
408-1.06343 -1.46901 (408*2π)/6021 weeks
409.63446 -3.44786 (409*2π)/6021 weeks
4103.1332 -2.66608 (410*2π)/6021 weeks
4113.13978 -.16699 (411*2π)/6021 weeks
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413-.16632 -.84149 (413*2π)/6021 weeks
414.95083 -2.53393 (414*2π)/6021 weeks
4152.62326 -1.82703 (415*2π)/6021 weeks
4162.43093 .26479 (416*2π)/6021 weeks
417-.03451 .48426 (417*2π)/6021 weeks
418-1.04118 -2.01848 (418*2π)/6021 weeks
4191.35261 -3.86518 (419*2π)/6021 weeks
4203.51205 -2.00812 (420*2π)/6021 weeks
4212.66737 .04327 (421*2π)/6021 weeks
422.50281 .13936 (422*2π)/6021 weeks
423.36319 -2.09101 (423*2π)/6021 weeks
4241.94113 -2.34701 (424*2π)/6021 weeks
4252.43583 -1.2866 (425*2π)/6021 weeks
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429.94045 -2.2346 (429*2π)/6021 weeks
4302.01503 -1.32399 (430*2π)/6021 weeks
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433.66293 -1.3112 (433*2π)/6021 weeks
434.9939 -2.151 (434*2π)/6021 weeks
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438-.71919 -1.68789 (438*2π)/6021 weeks
439.94663 -3.40893 (439*2π)/6021 weeks
4403.45164 -2.45802 (440*2π)/6021 weeks
4412.44019 .37047 (441*2π)/6021 weeks
442.06771 -.32873 (442*2π)/6021 weeks
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4442.81876 -3.44943 (444*2π)/6021 weeks
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446-.00976 -.17596 (446*2π)/6021 weeks
447.58739 -2.7969 (447*2π)/6021 weeks
4482.20668 -2.54112 (448*2π)/6021 weeks
4493.19064 -1.50065 (449*2π)/6021 weeks
4502.20321 -.34153 (450*2π)/6021 weeks
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453-.51991 -2.22308 (453*2π)/6021 weeks
4541.39107 -3.29774 (454*2π)/6021 weeks
4552.92994 -2.87801 (455*2π)/6021 weeks
4563.19116 -.81291 (456*2π)/6021 weeks
4571.07204 -.28665 (457*2π)/6021 weeks
4581.19474 -1.9171 (458*2π)/6021 weeks
4592.74139 -1.44024 (459*2π)/6021 weeks
4601.87379 .19667 (460*2π)/6021 weeks
461.03028 -.28836 (461*2π)/6021 weeks
462-.13281 -1.97716 (462*2π)/6021 weeks
463.53048 -3.00756 (463*2π)/6021 weeks
4642.45623 -3.16557 (464*2π)/6021 weeks
4653.60212 -.89944 (465*2π)/6021 weeks
4661.63394 1.18214 (466*2π)/6021 weeks
467-1.89356 -.76339 (467*2π)/6021 weeks
468-.2085 -4.42654 (468*2π)/6021 weeks
4693.25179 -3.50368 (469*2π)/6021 weeks
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471.12969 -.32514 (471*2π)/6021 weeks
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4731.77789 -4.5447 (473*2π)/6021 weeks
4744.16922 -3.07558 (474*2π)/6021 weeks
4753.77166 .59487 (475*2π)/6021 weeks
476-.6229 1.43605 (476*2π)/6021 weeks
477-2.3802 -3.53745 (477*2π)/6021 weeks
4781.59663 -6.18595 (478*2π)/6021 weeks
4795.6966 -4.14436 (479*2π)/6021 weeks
4805.32621 1.32035 (480*2π)/6021 weeks
481-.49895 2.43257 (481*2π)/6021 weeks
482-2.71872 -2.89882 (482*2π)/6021 weeks
4832.16431 -6.4557 (483*2π)/6021 weeks
4846.06911 -2.26947 (484*2π)/6021 weeks
4853.30371 2.22379 (485*2π)/6021 weeks
486-2.08441 1.71984 (486*2π)/6021 weeks
487-2.87382 -4.23353 (487*2π)/6021 weeks
4881.76247 -6.49287 (488*2π)/6021 weeks
4895.54538 -3.05885 (489*2π)/6021 weeks
4902.68747 1.0269 (490*2π)/6021 weeks
491-1.3314 -.87542 (491*2π)/6021 weeks
492-.31626 -4.90139 (492*2π)/6021 weeks
4934.0906 -5.13873 (493*2π)/6021 weeks
4945.36275 -1.09199 (494*2π)/6021 weeks
4952.17246 1.11828 (495*2π)/6021 weeks
496-.30126 -.74096 (496*2π)/6021 weeks
497.40074 -2.86459 (497*2π)/6021 weeks
4982.09177 -2.2858 (498*2π)/6021 weeks
499.92221 -1.83274 (499*2π)/6021 weeks
5001.94149 -3.04047 (500*2π)/6021 weeks
5012.57076 -1.32382 (501*2π)/6021 weeks
502.48869 -.95584 (502*2π)/6021 weeks
503-.34428 -3.24128 (503*2π)/6021 weeks
5042.24902 -4.84612 (504*2π)/6021 weeks
5055.04689 -1.73954 (505*2π)/6021 weeks
5062.19757 2.49097 (506*2π)/6021 weeks
507-3.33699 .46073 (507*2π)/6021 weeks
508-3.405 -6.19011 (508*2π)/6021 weeks
5093.7134 -7.60749 (509*2π)/6021 weeks
5105.52762 -1.46316 (510*2π)/6021 weeks
5111.76828 1.14524 (511*2π)/6021 weeks
512-3.01292 -.6063 (512*2π)/6021 weeks
513-1.97918 -6.83237 (513*2π)/6021 weeks
5143.90081 -7.02588 (514*2π)/6021 weeks
5156.53127 -2.1947 (515*2π)/6021 weeks
5161.4109 2.46357 (516*2π)/6021 weeks
517-3.21674 -2.81132 (517*2π)/6021 weeks
5181.15909 -5.99628 (518*2π)/6021 weeks
5193.17706 -4.94285 (519*2π)/6021 weeks
5205.581 -1.28775 (520*2π)/6021 weeks
521-.25449 2.82687 (521*2π)/6021 weeks
522-4.96444 -3.37075 (522*2π)/6021 weeks
523-1.32054 -8.92646 (523*2π)/6021 weeks
5245.49745 -7.55625 (524*2π)/6021 weeks
5255.17034 -1.01258 (525*2π)/6021 weeks
526.16211 -1.92626 (526*2π)/6021 weeks
5271.83758 -4.45795 (527*2π)/6021 weeks
5282.43927 -3.21288 (528*2π)/6021 weeks
5292.49458 -1.61974 (529*2π)/6021 weeks
530-1.6668 -2.64958 (530*2π)/6021 weeks
531-.06189 -7.30001 (531*2π)/6021 weeks
5324.95312 -6.17921 (532*2π)/6021 weeks
5335.25816 -2.26707 (533*2π)/6021 weeks
5341.28533 .07442 (534*2π)/6021 weeks
535-.29289 -4.59157 (535*2π)/6021 weeks
5363.71699 -4.17034 (536*2π)/6021 weeks
5372.62262 -1.21092 (537*2π)/6021 weeks
538-1.13267 -1.12636 (538*2π)/6021 weeks
539-1.98951 -6.46099 (539*2π)/6021 weeks
5404.02719 -8.72592 (540*2π)/6021 weeks
5416.65956 -1.15197 (541*2π)/6021 weeks
542.21961 1.2276 (542*2π)/6021 weeks
543-2.64252 -2.92556 (543*2π)/6021 weeks
544-1.36951 -6.41094 (544*2π)/6021 weeks
5451.99908 -6.86557 (545*2π)/6021 weeks
5462.00652 -4.32324 (546*2π)/6021 weeks
547.543 -5.18311 (547*2π)/6021 weeks
548.71763 -7.0284 (548*2π)/6021 weeks
5493.95425 -7.09969 (549*2π)/6021 weeks
5505.39329 -5.14368 (550*2π)/6021 weeks
5513.0368 -1.43163 (551*2π)/6021 weeks
552-.04659 -3.41268 (552*2π)/6021 weeks
5531.27328 -5.3742 (553*2π)/6021 weeks
5541.80687 -4.65841 (554*2π)/6021 weeks
555.62919 -3.77916 (555*2π)/6021 weeks
556-.59321 -7.58552 (556*2π)/6021 weeks
5575.39737 -8.32725 (557*2π)/6021 weeks
5584.70715 -1.88148 (558*2π)/6021 weeks
559-.43514 -1.04652 (559*2π)/6021 weeks
560-4.16264 -5.66193 (560*2π)/6021 weeks
561-.31506 -12.71868 (561*2π)/6021 weeks
5629.55063 -9.07134 (562*2π)/6021 weeks
5637.75323 2.19224 (563*2π)/6021 weeks
564-6.45318 5.61982 (564*2π)/6021 weeks
565-15.38063 -11.78579 (565*2π)/6021 weeks
5662.4558 -24.08354 (566*2π)/6021 weeks
56716.93233 -9.93792 (567*2π)/6021 weeks
5687.62286 5.65504 (568*2π)/6021 weeks
569-10.61907 .44427 (569*2π)/6021 weeks
570-9.1439 -17.80054 (570*2π)/6021 weeks
5717.7183 -19.23816 (571*2π)/6021 weeks
57213.27324 -6.97751 (572*2π)/6021 weeks
5734.49951 3.77211 (573*2π)/6021 weeks
574-8.83169 -4.83228 (574*2π)/6021 weeks
575-3.94023 -15.50259 (575*2π)/6021 weeks
5763.35759 -14.99281 (576*2π)/6021 weeks
5773.82112 -8.10632 (577*2π)/6021 weeks
578-1.50726 -10.6053 (578*2π)/6021 weeks
579-.49596 -14.73437 (579*2π)/6021 weeks
5802.23187 -16.86189 (580*2π)/6021 weeks
5816.18887 -17.28939 (581*2π)/6021 weeks
58211.72308 -10.96689 (582*2π)/6021 weeks
5832.72701 -3.31245 (583*2π)/6021 weeks
584-2.95412 -10.04902 (584*2π)/6021 weeks
585-6.33793 -15.73926 (585*2π)/6021 weeks
586-2.40755 -26.62487 (586*2π)/6021 weeks
58710.54303 -27.79262 (587*2π)/6021 weeks
58820.11704 -15.10624 (588*2π)/6021 weeks
5894.26482 4.56444 (589*2π)/6021 weeks
590-21.75323 -14.52697 (590*2π)/6021 weeks
591-11.4352 -40.13663 (591*2π)/6021 weeks
59211.34663 -53.27663 (592*2π)/6021 weeks
59338.82749 -26.6716 (593*2π)/6021 weeks
5945.39348 4.28252 (594*2π)/6021 weeks
595-27.71506 -32.35173 (595*2π)/6021 weeks
5963.05677 -78.46166 (596*2π)/6021 weeks
59754.32073 -63.37918 (597*2π)/6021 weeks
59847.87259 -4.46118 (598*2π)/6021 weeks
599-46.23677 -13.68379 (599*2π)/6021 weeks
600-62.78705 -159.6541 (600*2π)/6021 weeks



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