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Fourier Analysis of MZZ (ProShares UltraShort MidCap400)


MZZ (ProShares UltraShort MidCap400) appears to have interesting cyclic behaviour every 55 weeks (44.2572*sine), 39 weeks (30.9944*sine), and 50 weeks (23.2213*cosine).

MZZ (ProShares UltraShort MidCap400) has an average price of 302.27 (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 1/17/2017 for MZZ (ProShares UltraShort MidCap400), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0302.2732   0 
1115.7902 337.2792 (1*2π)/550550 weeks
2-77.67568 136.888 (2*2π)/550275 weeks
3-17.90895 -8.94262 (3*2π)/550183 weeks
466.68086 28.44905 (4*2π)/550138 weeks
534.46308 84.90256 (5*2π)/550110 weeks
6-25.90437 61.75272 (6*2π)/55092 weeks
7-12.28761 2.40958 (7*2π)/55079 weeks
840.89398 16.50911 (8*2π)/55069 weeks
918.60028 57.5272 (9*2π)/55061 weeks
10-11.6797 44.2572 (10*2π)/55055 weeks
11-23.22132 13.96163 (11*2π)/55050 weeks
129.69597 -3.91518 (12*2π)/55046 weeks
1320.7465 21.06865 (13*2π)/55042 weeks
146.75863 30.99435 (14*2π)/55039 weeks
15-6.48712 23.58262 (15*2π)/55037 weeks
16-4.9177 12.61877 (16*2π)/55034 weeks
17-1.81683 6.42487 (17*2π)/55032 weeks
1811.63109 8.11122 (18*2π)/55031 weeks
198.15036 18.47041 (19*2π)/55029 weeks
203.01245 18.29691 (20*2π)/55028 weeks
21-.42196 16.0268 (21*2π)/55026 weeks
22-1.6043 11.05278 (22*2π)/55025 weeks
235.31449 9.70458 (23*2π)/55024 weeks
241.89834 16.78232 (24*2π)/55023 weeks
25-7.72691 13.9804 (25*2π)/55022 weeks
26-5.70218 -1.92687 (26*2π)/55021 weeks
2712.03292 1.60507 (27*2π)/55020 weeks
2812.32841 16.96047 (28*2π)/55020 weeks
29-5.17819 22.73057 (29*2π)/55019 weeks
30-13.03211 2.76282 (30*2π)/55018 weeks
316.92977 -6.8018 (31*2π)/55018 weeks
3218.39988 11.34109 (32*2π)/55017 weeks
33-.1997 26.32805 (33*2π)/55017 weeks
34-17.01489 7.3979 (34*2π)/55016 weeks
35-1.15844 -7.17445 (35*2π)/55016 weeks
3610.98735 2.20109 (36*2π)/55015 weeks
375.62881 14.04174 (37*2π)/55015 weeks
38-4.21003 9.47295 (38*2π)/55014 weeks
39-2.16239 2.08016 (39*2π)/55014 weeks
403.98358 1.3366 (40*2π)/55014 weeks
416.58088 8.10278 (41*2π)/55013 weeks
42-.53722 8.33387 (42*2π)/55013 weeks
43.94468 4.07417 (43*2π)/55013 weeks
441.98588 5.14269 (44*2π)/55013 weeks
45.83828 5.71144 (45*2π)/55012 weeks
46.67883 2.43993 (46*2π)/55012 weeks
475.53896 2.63697 (47*2π)/55012 weeks
484.77694 6.73359 (48*2π)/55011 weeks
491.86337 8.46293 (49*2π)/55011 weeks
50.51317 5.93701 (50*2π)/55011 weeks
511.72435 4.52817 (51*2π)/55011 weeks
522.38897 7.24195 (52*2π)/55011 weeks
53-1.58928 6.9329 (53*2π)/55010 weeks
54-2.85167 2.66843 (54*2π)/55010 weeks
551.73932 -1.71599 (55*2π)/55010 weeks
568.15754 3.91586 (56*2π)/55010 weeks
571.05859 9.45097 (57*2π)/55010 weeks
58-2.97784 3.83166 (58*2π)/5509 weeks
591.45412 .61431 (59*2π)/5509 weeks
604.1554 3.15074 (60*2π)/5509 weeks
61.66162 5.79686 (61*2π)/5509 weeks
62.50852 .22394 (62*2π)/5509 weeks
635.68227 2.23207 (63*2π)/5509 weeks
645.26524 6.95841 (64*2π)/5509 weeks
65-.79675 7.38875 (65*2π)/5508 weeks
66-1.07121 1.60436 (66*2π)/5508 weeks
672.99281 2.77151 (67*2π)/5508 weeks
682.81071 3.88693 (68*2π)/5508 weeks
69.3401 4.19467 (69*2π)/5508 weeks
703.02056 .13407 (70*2π)/5508 weeks
717.04837 6.13372 (71*2π)/5508 weeks
72.03517 10.23034 (72*2π)/5508 weeks
73-5.29067 4.44517 (73*2π)/5508 weeks
74-.3508 -3.10757 (74*2π)/5507 weeks
756.06822 2.00442 (75*2π)/5507 weeks
763.02214 5.40594 (76*2π)/5507 weeks
77-.19107 6.67381 (77*2π)/5507 weeks
78-2.92524 .03932 (78*2π)/5507 weeks
795.30756 -1.42145 (79*2π)/5507 weeks
806.03543 5.80786 (80*2π)/5507 weeks
81.10917 8.50892 (81*2π)/5507 weeks
82-3.98348 2.33801 (82*2π)/5507 weeks
831.20707 -1.37692 (83*2π)/5507 weeks
845.8424 1.22276 (84*2π)/5507 weeks
853.78257 8.40116 (85*2π)/5506 weeks
86-4.30656 5.7751 (86*2π)/5506 weeks
87-2.60212 -1.63068 (87*2π)/5506 weeks
884.2011 -1.62051 (88*2π)/5506 weeks
894.89464 3.88869 (89*2π)/5506 weeks
90.67487 4.68804 (90*2π)/5506 weeks
91-.18529 1.66162 (91*2π)/5506 weeks
922.20895 .83518 (92*2π)/5506 weeks
932.46963 3.06301 (93*2π)/5506 weeks
94.84776 2.18216 (94*2π)/5506 weeks
952.25196 2.44181 (95*2π)/5506 weeks
96.26905 2.98974 (96*2π)/5506 weeks
97-.16463 .26214 (97*2π)/5506 weeks
983.43542 -1.13177 (98*2π)/5506 weeks
995.95533 2.9005 (99*2π)/5506 weeks
1002.15175 6.38938 (100*2π)/5506 weeks
101-1.62837 3.17055 (101*2π)/5505 weeks
1021.09196 -1.15156 (102*2π)/5505 weeks
1035.93627 1.64514 (103*2π)/5505 weeks
1042.8187 6.85064 (104*2π)/5505 weeks
105-2.90471 4.94503 (105*2π)/5505 weeks
106-2.15976 -2.0331 (106*2π)/5505 weeks
1074.17682 -2.16495 (107*2π)/5505 weeks
1086.26968 3.77445 (108*2π)/5505 weeks
109.03964 6.80044 (109*2π)/5505 weeks
110-2.9585 .57761 (110*2π)/5505 weeks
1112.9057 -3.1783 (111*2π)/5505 weeks
1127.03156 2.14378 (112*2π)/5505 weeks
1133.23772 6.51522 (113*2π)/5505 weeks
114-1.98038 4.94128 (114*2π)/5505 weeks
115-1.37093 -1.17841 (115*2π)/5505 weeks
1164.00126 -.7631 (116*2π)/5505 weeks
1174.37681 3.51523 (117*2π)/5505 weeks
1181.36502 4.89186 (118*2π)/5505 weeks
119-.90607 2.58209 (119*2π)/5505 weeks
1201.08187 .03384 (120*2π)/5505 weeks
1213.9657 1.66063 (121*2π)/5505 weeks
1221.75723 4.99228 (122*2π)/5505 weeks
123-2.0697 2.59895 (123*2π)/5504 weeks
124.57522 -1.48537 (124*2π)/5504 weeks
1253.70347 .44326 (125*2π)/5504 weeks
1262.84528 3.35441 (126*2π)/5504 weeks
127.5612 3.2428 (127*2π)/5504 weeks
128-.21886 2.00137 (128*2π)/5504 weeks
129.32448 .0299 (129*2π)/5504 weeks
1302.52672 .13687 (130*2π)/5504 weeks
1312.39538 2.22453 (131*2π)/5504 weeks
132.87372 1.40598 (132*2π)/5504 weeks
1332.74371 .07273 (133*2π)/5504 weeks
1343.6372 2.3937 (134*2π)/5504 weeks
1351.81034 3.46319 (135*2π)/5504 weeks
136-.41039 2.76369 (136*2π)/5504 weeks
137.13713 .10908 (137*2π)/5504 weeks
1381.87733 .48128 (138*2π)/5504 weeks
1392.53859 .39482 (139*2π)/5504 weeks
1403.3073 2.10944 (140*2π)/5504 weeks
1412.10898 3.00603 (141*2π)/5504 weeks
142-.14955 2.15898 (142*2π)/5504 weeks
1431.89901 -.7312 (143*2π)/5504 weeks
1444.01812 2.40004 (144*2π)/5504 weeks
145.50339 3.47796 (145*2π)/5504 weeks
146-.20579 .80624 (146*2π)/5504 weeks
1472.3065 -.49076 (147*2π)/5504 weeks
1483.73821 2.64631 (148*2π)/5504 weeks
149.79058 3.60994 (149*2π)/5504 weeks
150-.83981 1.25449 (150*2π)/5504 weeks
1511.85524 -1.0303 (151*2π)/5504 weeks
1523.30849 1.94425 (152*2π)/5504 weeks
1531.49219 2.46536 (153*2π)/5504 weeks
154.6821 1.80046 (154*2π)/5504 weeks
155.94848 .96598 (155*2π)/5504 weeks
1561.49676 .80892 (156*2π)/5504 weeks
1572.13017 1.28289 (157*2π)/5504 weeks
1581.16459 2.438 (158*2π)/5503 weeks
159.42346 .31545 (159*2π)/5503 weeks
1602.12427 .55164 (160*2π)/5503 weeks
1612.22201 .86813 (161*2π)/5503 weeks
1622.65379 1.73204 (162*2π)/5503 weeks
1631.42532 2.70462 (163*2π)/5503 weeks
164-.14344 1.12609 (164*2π)/5503 weeks
1652.02623 -.42982 (165*2π)/5503 weeks
1663.77165 1.33273 (166*2π)/5503 weeks
1672.20643 4.08379 (167*2π)/5503 weeks
168-1.03593 2.59279 (168*2π)/5503 weeks
169-.12245 -.49856 (169*2π)/5503 weeks
1702.76032 -.16562 (170*2π)/5503 weeks
1712.62581 2.23769 (171*2π)/5503 weeks
172.44667 2.53142 (172*2π)/5503 weeks
173.07155 .226 (173*2π)/5503 weeks
1742.3195 -.64398 (174*2π)/5503 weeks
1753.87654 1.58017 (175*2π)/5503 weeks
1761.75385 3.82418 (176*2π)/5503 weeks
177-.96334 2.36039 (177*2π)/5503 weeks
178-.471 -.71907 (178*2π)/5503 weeks
1792.93816 -.9398 (179*2π)/5503 weeks
1803.41838 2.37211 (180*2π)/5503 weeks
181.49605 3.22431 (181*2π)/5503 weeks
182-.74442 .48571 (182*2π)/5503 weeks
1831.78452 -.76389 (183*2π)/5503 weeks
1843.14263 .95823 (184*2π)/5503 weeks
1851.44302 2.5745 (185*2π)/5503 weeks
186.54339 1.14519 (186*2π)/5503 weeks
1871.14021 .39804 (187*2π)/5503 weeks
1882.40615 1.34792 (188*2π)/5503 weeks
189.80363 2.70201 (189*2π)/5503 weeks
190-.72396 .80289 (190*2π)/5503 weeks
191.47156 -.90571 (191*2π)/5503 weeks
1922.55485 -.71818 (192*2π)/5503 weeks
1932.99623 1.0156 (193*2π)/5503 weeks
1942.82748 2.36077 (194*2π)/5503 weeks
195-.26304 3.18374 (195*2π)/5503 weeks
196-.38795 -.36965 (196*2π)/5503 weeks
1971.50882 -.56745 (197*2π)/5503 weeks
1982.61158 .52327 (198*2π)/5503 weeks
1991.6141 1.37284 (199*2π)/5503 weeks
2001.66412 .66872 (200*2π)/5503 weeks
2011.33442 1.0811 (201*2π)/5503 weeks
2022.53476 .47419 (202*2π)/5503 weeks
2031.92402 2.47527 (203*2π)/5503 weeks
204.8321 2.33357 (204*2π)/5503 weeks
205-1.03972 1.43084 (205*2π)/5503 weeks
206.53786 -1.41749 (206*2π)/5503 weeks
2073.54726 .31466 (207*2π)/5503 weeks
2081.79261 3.22231 (208*2π)/5503 weeks
209-1.47387 1.51438 (209*2π)/5503 weeks
210.61989 -1.84127 (210*2π)/5503 weeks
2113.52445 .51636 (211*2π)/5503 weeks
2121.54633 2.91293 (212*2π)/5503 weeks
213-1.23899 1.72778 (213*2π)/5503 weeks
214-.35046 -2.19567 (214*2π)/5503 weeks
2153.70805 -.96569 (215*2π)/5503 weeks
2162.93721 2.74537 (216*2π)/5503 weeks
217-.71565 2.17455 (217*2π)/5503 weeks
218.13415 -1.23857 (218*2π)/5503 weeks
2192.89471 .12183 (219*2π)/5503 weeks
2201.26773 1.87182 (220*2π)/5503 weeks
221.28565 .3522 (221*2π)/5502 weeks
2221.33015 -.36656 (222*2π)/5502 weeks
2233.03846 .37396 (223*2π)/5502 weeks
2241.82133 3.10343 (224*2π)/5502 weeks
225-.98849 1.5752 (225*2π)/5502 weeks
226-.03843 -.56923 (226*2π)/5502 weeks
2272.20576 -.19446 (227*2π)/5502 weeks
228.92789 2.22034 (228*2π)/5502 weeks
229-.90115 .31863 (229*2π)/5502 weeks
230.08712 -1.48732 (230*2π)/5502 weeks
2312.41637 -1.39845 (231*2π)/5502 weeks
2322.53974 1.36881 (232*2π)/5502 weeks
233.12949 1.4493 (233*2π)/5502 weeks
234-.31983 -.92877 (234*2π)/5502 weeks
2352.57696 -1.8992 (235*2π)/5502 weeks
2363.7326 1.41985 (236*2π)/5502 weeks
237.71164 2.70242 (237*2π)/5502 weeks
238-.81305 .801 (238*2π)/5502 weeks
239.00662 -1.89804 (239*2π)/5502 weeks
2402.85154 -.3767 (240*2π)/5502 weeks
2411.9206 .92922 (241*2π)/5502 weeks
242.5523 1.35793 (242*2π)/5502 weeks
243.39009 -.45775 (243*2π)/5502 weeks
2441.22101 -.30703 (244*2π)/5502 weeks
2451.93631 -.29032 (245*2π)/5502 weeks
2461.80005 1.44574 (246*2π)/5502 weeks
247-.40274 .99864 (247*2π)/5502 weeks
248-.242 -1.02685 (248*2π)/5502 weeks
2492.11804 -2.13397 (249*2π)/5502 weeks
2503.57743 .60888 (250*2π)/5502 weeks
251.95918 2.41757 (251*2π)/5502 weeks
252-1.03167 .58036 (252*2π)/5502 weeks
253-.33336 -2.19911 (253*2π)/5502 weeks
2543.2237 -2.52915 (254*2π)/5502 weeks
2554.08491 1.53282 (255*2π)/5502 weeks
256.26054 3.56843 (256*2π)/5502 weeks
257-2.93281 -.81305 (257*2π)/5502 weeks
2581.45473 -3.898 (258*2π)/5502 weeks
2594.24849 -.78251 (259*2π)/5502 weeks
2602.39533 2.70389 (260*2π)/5502 weeks
261-1.83273 1.02174 (261*2π)/5502 weeks
262-.4097 -3.62229 (262*2π)/5502 weeks
2634.58779 -2.30823 (263*2π)/5502 weeks
2643.29764 1.71561 (264*2π)/5502 weeks
265.01797 1.31119 (265*2π)/5502 weeks
266-.27764 -2.05054 (266*2π)/5502 weeks
2673.02763 -3.04822 (267*2π)/5502 weeks
2685.30721 .39598 (268*2π)/5502 weeks
2691.69751 3.34932 (269*2π)/5502 weeks
270-.71175 -.19165 (270*2π)/5502 weeks
2711.96488 -1.68985 (271*2π)/5502 weeks
2723.31083 -.33075 (272*2π)/5502 weeks
2732.72177 1.26971 (273*2π)/5502 weeks
2741.11826 2.05014 (274*2π)/5502 weeks
275-.94755   (275*2π)/5502 weeks
2761.11826 -2.05014 (276*2π)/5502 weeks
2772.72177 -1.26971 (277*2π)/5502 weeks
2783.31083 .33075 (278*2π)/5502 weeks
2791.96488 1.68985 (279*2π)/5502 weeks
280-.71175 .19165 (280*2π)/5502 weeks
2811.69751 -3.34932 (281*2π)/5502 weeks
2825.30721 -.39598 (282*2π)/5502 weeks
2833.02763 3.04822 (283*2π)/5502 weeks
284-.27764 2.05054 (284*2π)/5502 weeks
285.01797 -1.31119 (285*2π)/5502 weeks
2863.29764 -1.71561 (286*2π)/5502 weeks
2874.58779 2.30823 (287*2π)/5502 weeks
288-.4097 3.62229 (288*2π)/5502 weeks
289-1.83273 -1.02174 (289*2π)/5502 weeks
2902.39533 -2.70389 (290*2π)/5502 weeks
2914.24849 .78251 (291*2π)/5502 weeks
2921.45473 3.898 (292*2π)/5502 weeks
293-2.93281 .81305 (293*2π)/5502 weeks
294.26054 -3.56843 (294*2π)/5502 weeks
2954.08491 -1.53282 (295*2π)/5502 weeks
2963.2237 2.52915 (296*2π)/5502 weeks
297-.33336 2.19911 (297*2π)/5502 weeks
298-1.03167 -.58036 (298*2π)/5502 weeks
299.95918 -2.41757 (299*2π)/5502 weeks
3003.57743 -.60888 (300*2π)/5502 weeks
3012.11804 2.13397 (301*2π)/5502 weeks
302-.242 1.02685 (302*2π)/5502 weeks
303-.40274 -.99864 (303*2π)/5502 weeks
3041.80005 -1.44574 (304*2π)/5502 weeks
3051.93631 .29032 (305*2π)/5502 weeks
3061.22101 .30703 (306*2π)/5502 weeks
307.39009 .45775 (307*2π)/5502 weeks
308.5523 -1.35793 (308*2π)/5502 weeks
3091.9206 -.92922 (309*2π)/5502 weeks
3102.85154 .3767 (310*2π)/5502 weeks
311.00662 1.89804 (311*2π)/5502 weeks
312-.81305 -.801 (312*2π)/5502 weeks
313.71164 -2.70242 (313*2π)/5502 weeks
3143.7326 -1.41985 (314*2π)/5502 weeks
3152.57696 1.8992 (315*2π)/5502 weeks
316-.31983 .92877 (316*2π)/5502 weeks
317.12949 -1.4493 (317*2π)/5502 weeks
3182.53974 -1.36881 (318*2π)/5502 weeks
3192.41637 1.39845 (319*2π)/5502 weeks
320.08712 1.48732 (320*2π)/5502 weeks
321-.90115 -.31863 (321*2π)/5502 weeks
322.92789 -2.22034 (322*2π)/5502 weeks
3232.20576 .19446 (323*2π)/5502 weeks
324-.03843 .56923 (324*2π)/5502 weeks
325-.98849 -1.5752 (325*2π)/5502 weeks
3261.82133 -3.10343 (326*2π)/5502 weeks
3273.03846 -.37396 (327*2π)/5502 weeks
3281.33015 .36656 (328*2π)/5502 weeks
329.28565 -.3522 (329*2π)/5502 weeks
3301.26773 -1.87182 (330*2π)/5502 weeks
3312.89471 -.12183 (331*2π)/5502 weeks
332.13415 1.23857 (332*2π)/5502 weeks
333-.71565 -2.17455 (333*2π)/5502 weeks
3342.93721 -2.74537 (334*2π)/5502 weeks
3353.70805 .96569 (335*2π)/5502 weeks
336-.35046 2.19567 (336*2π)/5502 weeks
337-1.23899 -1.72778 (337*2π)/5502 weeks
3381.54633 -2.91293 (338*2π)/5502 weeks
3393.52445 -.51636 (339*2π)/5502 weeks
340.61989 1.84127 (340*2π)/5502 weeks
341-1.47387 -1.51438 (341*2π)/5502 weeks
3421.79261 -3.22231 (342*2π)/5502 weeks
3433.54726 -.31466 (343*2π)/5502 weeks
344.53786 1.41749 (344*2π)/5502 weeks
345-1.03972 -1.43084 (345*2π)/5502 weeks
346.8321 -2.33357 (346*2π)/5502 weeks
3471.92402 -2.47527 (347*2π)/5502 weeks
3482.53476 -.47419 (348*2π)/5502 weeks
3491.33442 -1.0811 (349*2π)/5502 weeks
3501.66412 -.66872 (350*2π)/5502 weeks
3511.6141 -1.37284 (351*2π)/5502 weeks
3522.61158 -.52327 (352*2π)/5502 weeks
3531.50882 .56745 (353*2π)/5502 weeks
354-.38795 .36965 (354*2π)/5502 weeks
355-.26304 -3.18374 (355*2π)/5502 weeks
3562.82748 -2.36077 (356*2π)/5502 weeks
3572.99623 -1.0156 (357*2π)/5502 weeks
3582.55485 .71818 (358*2π)/5502 weeks
359.47156 .90571 (359*2π)/5502 weeks
360-.72396 -.80289 (360*2π)/5502 weeks
361.80363 -2.70201 (361*2π)/5502 weeks
3622.40615 -1.34792 (362*2π)/5502 weeks
3631.14021 -.39804 (363*2π)/5502 weeks
364.54339 -1.14519 (364*2π)/5502 weeks
3651.44302 -2.5745 (365*2π)/5502 weeks
3663.14263 -.95823 (366*2π)/5502 weeks
3671.78452 .76389 (367*2π)/5501 weeks
368-.74442 -.48571 (368*2π)/5501 weeks
369.49605 -3.22431 (369*2π)/5501 weeks
3703.41838 -2.37211 (370*2π)/5501 weeks
3712.93816 .9398 (371*2π)/5501 weeks
372-.471 .71907 (372*2π)/5501 weeks
373-.96334 -2.36039 (373*2π)/5501 weeks
3741.75385 -3.82418 (374*2π)/5501 weeks
3753.87654 -1.58017 (375*2π)/5501 weeks
3762.3195 .64398 (376*2π)/5501 weeks
377.07155 -.226 (377*2π)/5501 weeks
378.44667 -2.53142 (378*2π)/5501 weeks
3792.62581 -2.23769 (379*2π)/5501 weeks
3802.76032 .16562 (380*2π)/5501 weeks
381-.12245 .49856 (381*2π)/5501 weeks
382-1.03593 -2.59279 (382*2π)/5501 weeks
3832.20643 -4.08379 (383*2π)/5501 weeks
3843.77165 -1.33273 (384*2π)/5501 weeks
3852.02623 .42982 (385*2π)/5501 weeks
386-.14344 -1.12609 (386*2π)/5501 weeks
3871.42532 -2.70462 (387*2π)/5501 weeks
3882.65379 -1.73204 (388*2π)/5501 weeks
3892.22201 -.86813 (389*2π)/5501 weeks
3902.12427 -.55164 (390*2π)/5501 weeks
391.42346 -.31545 (391*2π)/5501 weeks
3921.16459 -2.438 (392*2π)/5501 weeks
3932.13017 -1.28289 (393*2π)/5501 weeks
3941.49676 -.80892 (394*2π)/5501 weeks
395.94848 -.96598 (395*2π)/5501 weeks
396.6821 -1.80046 (396*2π)/5501 weeks
3971.49219 -2.46536 (397*2π)/5501 weeks
3983.30849 -1.94425 (398*2π)/5501 weeks
3991.85524 1.0303 (399*2π)/5501 weeks
400-.83981 -1.25449 (400*2π)/5501 weeks
401.79058 -3.60994 (401*2π)/5501 weeks
4023.73821 -2.64631 (402*2π)/5501 weeks
4032.3065 .49076 (403*2π)/5501 weeks
404-.20579 -.80624 (404*2π)/5501 weeks
405.50339 -3.47796 (405*2π)/5501 weeks
4064.01812 -2.40004 (406*2π)/5501 weeks
4071.89901 .7312 (407*2π)/5501 weeks
408-.14955 -2.15898 (408*2π)/5501 weeks
4092.10898 -3.00603 (409*2π)/5501 weeks
4103.3073 -2.10944 (410*2π)/5501 weeks
4112.53859 -.39482 (411*2π)/5501 weeks
4121.87733 -.48128 (412*2π)/5501 weeks
413.13713 -.10908 (413*2π)/5501 weeks
414-.41039 -2.76369 (414*2π)/5501 weeks
4151.81034 -3.46319 (415*2π)/5501 weeks
4163.6372 -2.3937 (416*2π)/5501 weeks
4172.74371 -.07273 (417*2π)/5501 weeks
418.87372 -1.40598 (418*2π)/5501 weeks
4192.39538 -2.22453 (419*2π)/5501 weeks
4202.52672 -.13687 (420*2π)/5501 weeks
421.32448 -.0299 (421*2π)/5501 weeks
422-.21886 -2.00137 (422*2π)/5501 weeks
423.5612 -3.2428 (423*2π)/5501 weeks
4242.84528 -3.35441 (424*2π)/5501 weeks
4253.70347 -.44326 (425*2π)/5501 weeks
426.57522 1.48537 (426*2π)/5501 weeks
427-2.0697 -2.59895 (427*2π)/5501 weeks
4281.75723 -4.99228 (428*2π)/5501 weeks
4293.9657 -1.66063 (429*2π)/5501 weeks
4301.08187 -.03384 (430*2π)/5501 weeks
431-.90607 -2.58209 (431*2π)/5501 weeks
4321.36502 -4.89186 (432*2π)/5501 weeks
4334.37681 -3.51523 (433*2π)/5501 weeks
4344.00126 .7631 (434*2π)/5501 weeks
435-1.37093 1.17841 (435*2π)/5501 weeks
436-1.98038 -4.94128 (436*2π)/5501 weeks
4373.23772 -6.51522 (437*2π)/5501 weeks
4387.03156 -2.14378 (438*2π)/5501 weeks
4392.9057 3.1783 (439*2π)/5501 weeks
440-2.9585 -.57761 (440*2π)/5501 weeks
441.03964 -6.80044 (441*2π)/5501 weeks
4426.26968 -3.77445 (442*2π)/5501 weeks
4434.17682 2.16495 (443*2π)/5501 weeks
444-2.15976 2.0331 (444*2π)/5501 weeks
445-2.90471 -4.94503 (445*2π)/5501 weeks
4462.8187 -6.85064 (446*2π)/5501 weeks
4475.93627 -1.64514 (447*2π)/5501 weeks
4481.09196 1.15156 (448*2π)/5501 weeks
449-1.62837 -3.17055 (449*2π)/5501 weeks
4502.15175 -6.38938 (450*2π)/5501 weeks
4515.95533 -2.9005 (451*2π)/5501 weeks
4523.43542 1.13177 (452*2π)/5501 weeks
453-.16463 -.26214 (453*2π)/5501 weeks
454.26905 -2.98974 (454*2π)/5501 weeks
4552.25196 -2.44181 (455*2π)/5501 weeks
456.84776 -2.18216 (456*2π)/5501 weeks
4572.46963 -3.06301 (457*2π)/5501 weeks
4582.20895 -.83518 (458*2π)/5501 weeks
459-.18529 -1.66162 (459*2π)/5501 weeks
460.67487 -4.68804 (460*2π)/5501 weeks
4614.89464 -3.88869 (461*2π)/5501 weeks
4624.2011 1.62051 (462*2π)/5501 weeks
463-2.60212 1.63068 (463*2π)/5501 weeks
464-4.30656 -5.7751 (464*2π)/5501 weeks
4653.78257 -8.40116 (465*2π)/5501 weeks
4665.8424 -1.22276 (466*2π)/5501 weeks
4671.20707 1.37692 (467*2π)/5501 weeks
468-3.98348 -2.33801 (468*2π)/5501 weeks
469.10917 -8.50892 (469*2π)/5501 weeks
4706.03543 -5.80786 (470*2π)/5501 weeks
4715.30756 1.42145 (471*2π)/5501 weeks
472-2.92524 -.03932 (472*2π)/5501 weeks
473-.19107 -6.67381 (473*2π)/5501 weeks
4743.02214 -5.40594 (474*2π)/5501 weeks
4756.06822 -2.00442 (475*2π)/5501 weeks
476-.3508 3.10757 (476*2π)/5501 weeks
477-5.29067 -4.44517 (477*2π)/5501 weeks
478.03517 -10.23034 (478*2π)/5501 weeks
4797.04837 -6.13372 (479*2π)/5501 weeks
4803.02056 -.13407 (480*2π)/5501 weeks
481.3401 -4.19467 (481*2π)/5501 weeks
4822.81071 -3.88693 (482*2π)/5501 weeks
4832.99281 -2.77151 (483*2π)/5501 weeks
484-1.07121 -1.60436 (484*2π)/5501 weeks
485-.79675 -7.38875 (485*2π)/5501 weeks
4865.26524 -6.95841 (486*2π)/5501 weeks
4875.68227 -2.23207 (487*2π)/5501 weeks
488.50852 -.22394 (488*2π)/5501 weeks
489.66162 -5.79686 (489*2π)/5501 weeks
4904.1554 -3.15074 (490*2π)/5501 weeks
4911.45412 -.61431 (491*2π)/5501 weeks
492-2.97784 -3.83166 (492*2π)/5501 weeks
4931.05859 -9.45097 (493*2π)/5501 weeks
4948.15754 -3.91586 (494*2π)/5501 weeks
4951.73932 1.71599 (495*2π)/5501 weeks
496-2.85167 -2.66843 (496*2π)/5501 weeks
497-1.58928 -6.9329 (497*2π)/5501 weeks
4982.38897 -7.24195 (498*2π)/5501 weeks
4991.72435 -4.52817 (499*2π)/5501 weeks
500.51317 -5.93701 (500*2π)/5501 weeks
5011.86337 -8.46293 (501*2π)/5501 weeks
5024.77694 -6.73359 (502*2π)/5501 weeks
5035.53896 -2.63697 (503*2π)/5501 weeks
504.67883 -2.43993 (504*2π)/5501 weeks
505.83828 -5.71144 (505*2π)/5501 weeks
5061.98588 -5.14269 (506*2π)/5501 weeks
507.94468 -4.07417 (507*2π)/5501 weeks
508-.53722 -8.33387 (508*2π)/5501 weeks
5096.58088 -8.10278 (509*2π)/5501 weeks
5103.98358 -1.3366 (510*2π)/5501 weeks
511-2.16239 -2.08016 (511*2π)/5501 weeks
512-4.21003 -9.47295 (512*2π)/5501 weeks
5135.62881 -14.04174 (513*2π)/5501 weeks
51410.98735 -2.20109 (514*2π)/5501 weeks
515-1.15844 7.17445 (515*2π)/5501 weeks
516-17.01489 -7.3979 (516*2π)/5501 weeks
517-.1997 -26.32805 (517*2π)/5501 weeks
51818.39988 -11.34109 (518*2π)/5501 weeks
5196.92977 6.8018 (519*2π)/5501 weeks
520-13.03211 -2.76282 (520*2π)/5501 weeks
521-5.17819 -22.73057 (521*2π)/5501 weeks
52212.32841 -16.96047 (522*2π)/5501 weeks
52312.03292 -1.60507 (523*2π)/5501 weeks
524-5.70218 1.92687 (524*2π)/5501 weeks
525-7.72691 -13.9804 (525*2π)/5501 weeks
5261.89834 -16.78232 (526*2π)/5501 weeks
5275.31449 -9.70458 (527*2π)/5501 weeks
528-1.6043 -11.05278 (528*2π)/5501 weeks
529-.42196 -16.0268 (529*2π)/5501 weeks
5303.01245 -18.29691 (530*2π)/5501 weeks
5318.15036 -18.47041 (531*2π)/5501 weeks
53211.63109 -8.11122 (532*2π)/5501 weeks
533-1.81683 -6.42487 (533*2π)/5501 weeks
534-4.9177 -12.61877 (534*2π)/5501 weeks
535-6.48712 -23.58262 (535*2π)/5501 weeks
5366.75863 -30.99435 (536*2π)/5501 weeks
53720.7465 -21.06865 (537*2π)/5501 weeks
5389.69597 3.91518 (538*2π)/5501 weeks
539-23.22132 -13.96163 (539*2π)/5501 weeks
540-11.6797 -44.2572 (540*2π)/5501 weeks
54118.60028 -57.5272 (541*2π)/5501 weeks
54240.89398 -16.50911 (542*2π)/5501 weeks
543-12.28761 -2.40958 (543*2π)/5501 weeks
544-25.90437 -61.75272 (544*2π)/5501 weeks
54534.46308 -84.90256 (545*2π)/5501 weeks
54666.68086 -28.44905 (546*2π)/5501 weeks
547-17.90895 8.94262 (547*2π)/5501 weeks
548-77.67568 -136.888 (548*2π)/5501 weeks

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