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Fourier Analysis of TWM (ProShares UltraShort Russell200)


TWM (ProShares UltraShort Russell200) appears to have interesting cyclic behaviour every 44 weeks (45.8045*sine), 48 weeks (41.8305*sine), and 53 weeks (28.3941*cosine).

TWM (ProShares UltraShort Russell200) has an average price of 321.14 (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 1/25/2007 to 3/20/2017 for TWM (ProShares UltraShort Russell200), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0321.1385   0 
1186.0114 366.9622 (1*2π)/531531 weeks
2-56.54184 224.2567 (2*2π)/531266 weeks
3-89.21186 57.25041 (3*2π)/531177 weeks
4-6.98037 -2.93259 (4*2π)/531133 weeks
540.14753 25.89055 (5*2π)/531106 weeks
622.60975 68.30641 (6*2π)/53189 weeks
7-25.81121 60.43942 (7*2π)/53176 weeks
8-27.51781 2.29329 (8*2π)/53166 weeks
916.11865 -4.4789 (9*2π)/53159 weeks
1028.39407 14.10128 (10*2π)/53153 weeks
1126.98714 41.83054 (11*2π)/53148 weeks
12-9.16626 45.80446 (12*2π)/53144 weeks
13-16.94821 18.20126 (13*2π)/53141 weeks
14-5.67381 7.16538 (14*2π)/53138 weeks
153.76533 8.91799 (15*2π)/53135 weeks
161.4511 11.05166 (16*2π)/53133 weeks
179.62828 7.32362 (17*2π)/53131 weeks
188.75321 16.99729 (18*2π)/53130 weeks
195.68817 14.85286 (19*2π)/53128 weeks
204.23289 17.59799 (20*2π)/53127 weeks
21-1.26628 15.60831 (21*2π)/53125 weeks
22-.89184 7.22231 (22*2π)/53124 weeks
238.28727 10.24788 (23*2π)/53123 weeks
248.25483 19.8847 (24*2π)/53122 weeks
25-6.30322 25.28496 (25*2π)/53121 weeks
26-16.15594 8.87421 (26*2π)/53120 weeks
27-8.44064 -6.07459 (27*2π)/53120 weeks
2812.1545 -8.23609 (28*2π)/53119 weeks
2920.90756 13.34088 (29*2π)/53118 weeks
301.97424 29.08811 (30*2π)/53118 weeks
31-19.15425 18.59678 (31*2π)/53117 weeks
32-17.95176 -7.53027 (32*2π)/53117 weeks
337.8109 -13.48695 (33*2π)/53116 weeks
3417.07813 4.42853 (34*2π)/53116 weeks
359.23769 16.39574 (35*2π)/53115 weeks
36-4.03826 14.50212 (36*2π)/53115 weeks
37-5.11504 4.52917 (37*2π)/53114 weeks
38.35082 .52533 (38*2π)/53114 weeks
396.5822 1.96649 (39*2π)/53114 weeks
406.84707 11.09796 (40*2π)/53113 weeks
41-2.33358 10.60241 (41*2π)/53113 weeks
42-.40829 4.72003 (42*2π)/53113 weeks
432.03694 4.9564 (43*2π)/53112 weeks
442.31586 8.92853 (44*2π)/53112 weeks
45-3.54122 8.4543 (45*2π)/53112 weeks
46-3.3884 2.766 (46*2π)/53112 weeks
47-.69415 .07674 (47*2π)/53111 weeks
483.17405 2.65822 (48*2π)/53111 weeks
492.51854 5.22609 (49*2π)/53111 weeks
50-1.01613 4.96642 (50*2π)/53111 weeks
51-.63093 1.59348 (51*2π)/53110 weeks
521.72313 .05607 (52*2π)/53110 weeks
536.63851 1.31209 (53*2π)/53110 weeks
545.84816 8.96019 (54*2π)/53110 weeks
55-2.89573 7.70066 (55*2π)/53110 weeks
56-2.59174 1.12907 (56*2π)/5319 weeks
572.73259 .2747 (57*2π)/5319 weeks
584.36922 3.99536 (58*2π)/5319 weeks
59-.2852 7.59621 (59*2π)/5319 weeks
60-4.60132 .7601 (60*2π)/5319 weeks
611.73819 -3.69196 (61*2π)/5319 weeks
628.15023 -1.16153 (62*2π)/5319 weeks
638.05168 6.66977 (63*2π)/5318 weeks
641.06125 8.41772 (64*2π)/5318 weeks
65.33555 4.16116 (65*2π)/5318 weeks
661.53391 2.61267 (66*2π)/5318 weeks
674.50453 5.65993 (67*2π)/5318 weeks
68-1.76335 9.63584 (68*2π)/5318 weeks
69-6.98008 2.22123 (69*2π)/5318 weeks
70-1.98669 -4.80445 (70*2π)/5318 weeks
716.63878 -4.46449 (71*2π)/5317 weeks
728.59737 4.96651 (72*2π)/5317 weeks
731.9158 6.8551 (73*2π)/5317 weeks
74-.60477 6.20494 (74*2π)/5317 weeks
75-4.68322 .01093 (75*2π)/5317 weeks
763.35167 -5.31627 (76*2π)/5317 weeks
778.82243 1.1509 (77*2π)/5317 weeks
786.93228 7.59843 (78*2π)/5317 weeks
79-.87941 8.84657 (79*2π)/5317 weeks
80-3.81796 2.39465 (80*2π)/5317 weeks
81-1.34555 -2.65864 (81*2π)/5317 weeks
826.51457 -4.03275 (82*2π)/5316 weeks
8310.09449 4.25957 (83*2π)/5316 weeks
844.37099 9.84568 (84*2π)/5316 weeks
85-2.44801 7.4664 (85*2π)/5316 weeks
86-2.65859 2.01033 (86*2π)/5316 weeks
87.83911 .60048 (87*2π)/5316 weeks
882.35333 2.40367 (88*2π)/5316 weeks
89.76534 3.90552 (89*2π)/5316 weeks
90-.83512 1.69129 (90*2π)/5316 weeks
911.9913 .50581 (91*2π)/5316 weeks
921.43975 2.91246 (92*2π)/5316 weeks
93-.47053 1.13199 (93*2π)/5316 weeks
941.09227 -1.76273 (94*2π)/5316 weeks
955.29129 -1.29377 (95*2π)/5316 weeks
966.72903 3.16073 (96*2π)/5316 weeks
972.75693 6.64559 (97*2π)/5315 weeks
98-2.09775 4.38372 (98*2π)/5315 weeks
99-1.44604 -1.86683 (99*2π)/5315 weeks
1005.40975 -2.89458 (100*2π)/5315 weeks
1018.50572 2.67858 (101*2π)/5315 weeks
1025.27816 8.477 (102*2π)/5315 weeks
103-1.22596 7.60996 (103*2π)/5315 weeks
104-4.35764 2.32317 (104*2π)/5315 weeks
105.0038 -3.5833 (105*2π)/5315 weeks
1066.90804 -.6088 (106*2π)/5315 weeks
1076.46922 6.40713 (107*2π)/5315 weeks
108.2742 8.16084 (108*2π)/5315 weeks
109-3.25662 4.62415 (109*2π)/5315 weeks
110-3.86419 -.21747 (110*2π)/5315 weeks
1111.53395 -3.56756 (111*2π)/5315 weeks
1125.338 .5339 (112*2π)/5315 weeks
1133.3459 4.0042 (113*2π)/5315 weeks
114.83755 4.31775 (114*2π)/5315 weeks
115-1.18992 2.32491 (115*2π)/5315 weeks
116.06676 -.59665 (116*2π)/5315 weeks
1173.94091 -1.12508 (117*2π)/5315 weeks
1185.53651 3.08842 (118*2π)/5315 weeks
1191.79238 6.05397 (119*2π)/5314 weeks
120-1.4577 3.28178 (120*2π)/5314 weeks
121-.82728 .59616 (121*2π)/5314 weeks
1221.16281 .01566 (122*2π)/5314 weeks
1232.17706 .72564 (123*2π)/5314 weeks
1242.88455 1.36661 (124*2π)/5314 weeks
1252.46383 2.65866 (125*2π)/5314 weeks
1261.16437 2.65048 (126*2π)/5314 weeks
1271.41439 1.20441 (127*2π)/5314 weeks
1283.16726 1.94846 (128*2π)/5314 weeks
1291.82018 4.16762 (129*2π)/5314 weeks
130-.47316 3.55448 (130*2π)/5314 weeks
131-1.68222 2.19233 (131*2π)/5314 weeks
132-.7551 -.38687 (132*2π)/5314 weeks
1331.32531 .02385 (133*2π)/5314 weeks
1341.09368 -.21336 (134*2π)/5314 weeks
1352.991 .0828 (135*2π)/5314 weeks
1362.91185 1.59413 (136*2π)/5314 weeks
1371.8726 3.49524 (137*2π)/5314 weeks
138-1.63077 1.78024 (138*2π)/5314 weeks
139.77787 -1.96275 (139*2π)/5314 weeks
1404.57083 .33779 (140*2π)/5314 weeks
1413.54491 3.98708 (141*2π)/5314 weeks
142-.33102 4.36796 (142*2π)/5314 weeks
143-1.6851 .33229 (143*2π)/5314 weeks
1441.07817 -1.33471 (144*2π)/5314 weeks
1453.93427 -.03926 (145*2π)/5314 weeks
1463.07617 3.89027 (146*2π)/5314 weeks
147-.34151 3.0766 (147*2π)/5314 weeks
148-.40341 1.22927 (148*2π)/5314 weeks
149.42022 .15811 (149*2π)/5314 weeks
1501.22933 .09832 (150*2π)/5314 weeks
1511.99432 .16415 (151*2π)/5314 weeks
1522.63285 1.56988 (152*2π)/5313 weeks
153.16969 2.44065 (153*2π)/5313 weeks
154.14963 .01287 (154*2π)/5313 weeks
1551.2273 .15188 (155*2π)/5313 weeks
1561.5672 -.08398 (156*2π)/5313 weeks
1572.61764 .25836 (157*2π)/5313 weeks
1582.92493 2.13614 (158*2π)/5313 weeks
159.1394 2.95964 (159*2π)/5313 weeks
160-1.32302 .75172 (160*2π)/5313 weeks
161-.28009 -2.2598 (161*2π)/5313 weeks
1623.53258 -2.35429 (162*2π)/5313 weeks
1635.06767 1.02247 (163*2π)/5313 weeks
1642.69622 3.69574 (164*2π)/5313 weeks
165-.07382 2.57229 (165*2π)/5313 weeks
166-.71623 .16105 (166*2π)/5313 weeks
1671.43938 -1.63863 (167*2π)/5313 weeks
1684.22615 -.31387 (168*2π)/5313 weeks
1694.15754 2.92149 (169*2π)/5313 weeks
1701.08901 4.32935 (170*2π)/5313 weeks
171-1.71126 2.35206 (171*2π)/5313 weeks
172-1.71185 -.97276 (172*2π)/5313 weeks
1731.65915 -2.83999 (173*2π)/5313 weeks
1744.48716 -.40985 (174*2π)/5313 weeks
1753.59955 3.1552 (175*2π)/5313 weeks
176-.10477 3.40754 (176*2π)/5313 weeks
177-1.20474 .37222 (177*2π)/5313 weeks
178.55153 -1.84664 (178*2π)/5313 weeks
1793.11396 -.56028 (179*2π)/5313 weeks
1802.52877 1.10743 (180*2π)/5313 weeks
1811.26593 1.87405 (181*2π)/5313 weeks
182-.18238 .17458 (182*2π)/5313 weeks
1831.64361 -1.66944 (183*2π)/5313 weeks
1843.49017 -.42385 (184*2π)/5313 weeks
1853.79391 1.36553 (185*2π)/5313 weeks
1862.35944 2.69687 (186*2π)/5313 weeks
1871.72888 2.7112 (187*2π)/5313 weeks
188-.77758 3.31387 (188*2π)/5313 weeks
189-1.79665 -.35175 (189*2π)/5313 weeks
190.07478 -1.21062 (190*2π)/5313 weeks
1911.43194 -1.47241 (191*2π)/5313 weeks
1922.0367 -.42597 (192*2π)/5313 weeks
1931.90268 -.45761 (193*2π)/5313 weeks
1942.25008 .59263 (194*2π)/5313 weeks
195.79244 -.52926 (195*2π)/5313 weeks
1962.79631 -.92257 (196*2π)/5313 weeks
1973.157 -.38509 (197*2π)/5313 weeks
1984.55338 1.22488 (198*2π)/5313 weeks
1992.33455 3.63277 (199*2π)/5313 weeks
200-.66896 2.11678 (200*2π)/5313 weeks
201-.20095 -.85538 (201*2π)/5313 weeks
2022.81534 -1.12678 (202*2π)/5313 weeks
2033.06415 1.80606 (203*2π)/5313 weeks
204.55894 2.1174 (204*2π)/5313 weeks
205-.74044 .53628 (205*2π)/5313 weeks
206-.07616 -2.22858 (206*2π)/5313 weeks
2073.83629 -2.50513 (207*2π)/5313 weeks
2085.05726 1.31684 (208*2π)/5313 weeks
2091.91742 3.6537 (209*2π)/5313 weeks
210-1.03483 1.17715 (210*2π)/5313 weeks
211.95723 -1.6867 (211*2π)/5313 weeks
2123.21535 .14235 (212*2π)/5313 weeks
2131.73066 1.72989 (213*2π)/5312 weeks
214.54901 .98597 (214*2π)/5312 weeks
215-.30761 -.12889 (215*2π)/5312 weeks
2161.14162 -2.54585 (216*2π)/5312 weeks
2174.20888 -1.00156 (217*2π)/5312 weeks
2183.33246 1.45823 (218*2π)/5312 weeks
2191.16706 2.02351 (219*2π)/5312 weeks
220.09625 -.54637 (220*2π)/5312 weeks
2212.56418 -1.36323 (221*2π)/5312 weeks
2223.83039 -.03362 (222*2π)/5312 weeks
2233.42868 1.96863 (223*2π)/5312 weeks
224.60633 2.4964 (224*2π)/5312 weeks
225-.50443 -.23781 (225*2π)/5312 weeks
2261.38968 -2.28642 (226*2π)/5312 weeks
2274.77278 -1.51833 (227*2π)/5312 weeks
2284.94314 2.4668 (228*2π)/5312 weeks
2291.86667 3.61067 (229*2π)/5312 weeks
230-.03668 2.64464 (230*2π)/5312 weeks
231-1.03251 -.46274 (231*2π)/5312 weeks
2321.86809 -.99478 (232*2π)/5312 weeks
2332.34072 -.07995 (233*2π)/5312 weeks
2342.4062 1.28657 (234*2π)/5312 weeks
235.98555 .925 (235*2π)/5312 weeks
2361.2848 .74194 (236*2π)/5312 weeks
237.32225 .14955 (237*2π)/5312 weeks
2381.52979 -1.33834 (238*2π)/5312 weeks
2393.27646 -.53375 (239*2π)/5312 weeks
2404.11622 1.38647 (240*2π)/5312 weeks
2411.64327 3.64675 (241*2π)/5312 weeks
242-1.35261 1.76998 (242*2π)/5312 weeks
243-.78285 -1.25228 (243*2π)/5312 weeks
2441.56045 -2.68897 (244*2π)/5312 weeks
2454.68279 -1.60235 (245*2π)/5312 weeks
2465.16284 2.55543 (246*2π)/5312 weeks
2471.90653 5.14342 (247*2π)/5312 weeks
248-3.00651 2.96086 (248*2π)/5312 weeks
249-2.12197 -2.32123 (249*2π)/5312 weeks
2501.90172 -3.32537 (250*2π)/5312 weeks
2515.10709 -1.09132 (251*2π)/5312 weeks
2523.96843 3.37954 (252*2π)/5312 weeks
253-.70557 3.5792 (253*2π)/5312 weeks
254-1.95026 -1.12826 (254*2π)/5312 weeks
2551.81728 -2.71019 (255*2π)/5312 weeks
2564.13907 -.58205 (256*2π)/5312 weeks
2573.79662 2.50578 (257*2π)/5312 weeks
258.90399 4.30632 (258*2π)/5312 weeks
259-3.03046 1.89535 (259*2π)/5312 weeks
260-1.62309 -3.11345 (260*2π)/5312 weeks
2612.88682 -2.78396 (261*2π)/5312 weeks
2623.47261 .29629 (262*2π)/5312 weeks
2632.12546 1.82323 (263*2π)/5312 weeks
264.83523 1.85651 (264*2π)/5312 weeks
265-1.0045 1.43481 (265*2π)/5312 weeks
266-1.0045 -1.43481 (266*2π)/5312 weeks
267.83523 -1.85651 (267*2π)/5312 weeks
2682.12546 -1.82323 (268*2π)/5312 weeks
2693.47261 -.29629 (269*2π)/5312 weeks
2702.88682 2.78396 (270*2π)/5312 weeks
271-1.62309 3.11345 (271*2π)/5312 weeks
272-3.03046 -1.89535 (272*2π)/5312 weeks
273.90399 -4.30632 (273*2π)/5312 weeks
2743.79662 -2.50578 (274*2π)/5312 weeks
2754.13907 .58205 (275*2π)/5312 weeks
2761.81728 2.71019 (276*2π)/5312 weeks
277-1.95026 1.12826 (277*2π)/5312 weeks
278-.70557 -3.5792 (278*2π)/5312 weeks
2793.96843 -3.37954 (279*2π)/5312 weeks
2805.10709 1.09132 (280*2π)/5312 weeks
2811.90172 3.32537 (281*2π)/5312 weeks
282-2.12197 2.32123 (282*2π)/5312 weeks
283-3.00651 -2.96086 (283*2π)/5312 weeks
2841.90653 -5.14342 (284*2π)/5312 weeks
2855.16284 -2.55543 (285*2π)/5312 weeks
2864.68279 1.60235 (286*2π)/5312 weeks
2871.56045 2.68897 (287*2π)/5312 weeks
288-.78285 1.25228 (288*2π)/5312 weeks
289-1.35261 -1.76998 (289*2π)/5312 weeks
2901.64327 -3.64675 (290*2π)/5312 weeks
2914.11622 -1.38647 (291*2π)/5312 weeks
2923.27646 .53375 (292*2π)/5312 weeks
2931.52979 1.33834 (293*2π)/5312 weeks
294.32225 -.14955 (294*2π)/5312 weeks
2951.2848 -.74194 (295*2π)/5312 weeks
296.98555 -.925 (296*2π)/5312 weeks
2972.4062 -1.28657 (297*2π)/5312 weeks
2982.34072 .07995 (298*2π)/5312 weeks
2991.86809 .99478 (299*2π)/5312 weeks
300-1.03251 .46274 (300*2π)/5312 weeks
301-.03668 -2.64464 (301*2π)/5312 weeks
3021.86667 -3.61067 (302*2π)/5312 weeks
3034.94314 -2.4668 (303*2π)/5312 weeks
3044.77278 1.51833 (304*2π)/5312 weeks
3051.38968 2.28642 (305*2π)/5312 weeks
306-.50443 .23781 (306*2π)/5312 weeks
307.60633 -2.4964 (307*2π)/5312 weeks
3083.42868 -1.96863 (308*2π)/5312 weeks
3093.83039 .03362 (309*2π)/5312 weeks
3102.56418 1.36323 (310*2π)/5312 weeks
311.09625 .54637 (311*2π)/5312 weeks
3121.16706 -2.02351 (312*2π)/5312 weeks
3133.33246 -1.45823 (313*2π)/5312 weeks
3144.20888 1.00156 (314*2π)/5312 weeks
3151.14162 2.54585 (315*2π)/5312 weeks
316-.30761 .12889 (316*2π)/5312 weeks
317.54901 -.98597 (317*2π)/5312 weeks
3181.73066 -1.72989 (318*2π)/5312 weeks
3193.21535 -.14235 (319*2π)/5312 weeks
320.95723 1.6867 (320*2π)/5312 weeks
321-1.03483 -1.17715 (321*2π)/5312 weeks
3221.91742 -3.6537 (322*2π)/5312 weeks
3235.05726 -1.31684 (323*2π)/5312 weeks
3243.83629 2.50513 (324*2π)/5312 weeks
325-.07616 2.22858 (325*2π)/5312 weeks
326-.74044 -.53628 (326*2π)/5312 weeks
327.55894 -2.1174 (327*2π)/5312 weeks
3283.06415 -1.80606 (328*2π)/5312 weeks
3292.81534 1.12678 (329*2π)/5312 weeks
330-.20095 .85538 (330*2π)/5312 weeks
331-.66896 -2.11678 (331*2π)/5312 weeks
3322.33455 -3.63277 (332*2π)/5312 weeks
3334.55338 -1.22488 (333*2π)/5312 weeks
3343.157 .38509 (334*2π)/5312 weeks
3352.79631 .92257 (335*2π)/5312 weeks
336.79244 .52926 (336*2π)/5312 weeks
3372.25008 -.59263 (337*2π)/5312 weeks
3381.90268 .45761 (338*2π)/5312 weeks
3392.0367 .42597 (339*2π)/5312 weeks
3401.43194 1.47241 (340*2π)/5312 weeks
341.07478 1.21062 (341*2π)/5312 weeks
342-1.79665 .35175 (342*2π)/5312 weeks
343-.77758 -3.31387 (343*2π)/5312 weeks
3441.72888 -2.7112 (344*2π)/5312 weeks
3452.35944 -2.69687 (345*2π)/5312 weeks
3463.79391 -1.36553 (346*2π)/5312 weeks
3473.49017 .42385 (347*2π)/5312 weeks
3481.64361 1.66944 (348*2π)/5312 weeks
349-.18238 -.17458 (349*2π)/5312 weeks
3501.26593 -1.87405 (350*2π)/5312 weeks
3512.52877 -1.10743 (351*2π)/5312 weeks
3523.11396 .56028 (352*2π)/5312 weeks
353.55153 1.84664 (353*2π)/5312 weeks
354-1.20474 -.37222 (354*2π)/5312 weeks
355-.10477 -3.40754 (355*2π)/5311 weeks
3563.59955 -3.1552 (356*2π)/5311 weeks
3574.48716 .40985 (357*2π)/5311 weeks
3581.65915 2.83999 (358*2π)/5311 weeks
359-1.71185 .97276 (359*2π)/5311 weeks
360-1.71126 -2.35206 (360*2π)/5311 weeks
3611.08901 -4.32935 (361*2π)/5311 weeks
3624.15754 -2.92149 (362*2π)/5311 weeks
3634.22615 .31387 (363*2π)/5311 weeks
3641.43938 1.63863 (364*2π)/5311 weeks
365-.71623 -.16105 (365*2π)/5311 weeks
366-.07382 -2.57229 (366*2π)/5311 weeks
3672.69622 -3.69574 (367*2π)/5311 weeks
3685.06767 -1.02247 (368*2π)/5311 weeks
3693.53258 2.35429 (369*2π)/5311 weeks
370-.28009 2.2598 (370*2π)/5311 weeks
371-1.32302 -.75172 (371*2π)/5311 weeks
372.1394 -2.95964 (372*2π)/5311 weeks
3732.92493 -2.13614 (373*2π)/5311 weeks
3742.61764 -.25836 (374*2π)/5311 weeks
3751.5672 .08398 (375*2π)/5311 weeks
3761.2273 -.15188 (376*2π)/5311 weeks
377.14963 -.01287 (377*2π)/5311 weeks
378.16969 -2.44065 (378*2π)/5311 weeks
3792.63285 -1.56988 (379*2π)/5311 weeks
3801.99432 -.16415 (380*2π)/5311 weeks
3811.22933 -.09832 (381*2π)/5311 weeks
382.42022 -.15811 (382*2π)/5311 weeks
383-.40341 -1.22927 (383*2π)/5311 weeks
384-.34151 -3.0766 (384*2π)/5311 weeks
3853.07617 -3.89027 (385*2π)/5311 weeks
3863.93427 .03926 (386*2π)/5311 weeks
3871.07817 1.33471 (387*2π)/5311 weeks
388-1.6851 -.33229 (388*2π)/5311 weeks
389-.33102 -4.36796 (389*2π)/5311 weeks
3903.54491 -3.98708 (390*2π)/5311 weeks
3914.57083 -.33779 (391*2π)/5311 weeks
392.77787 1.96275 (392*2π)/5311 weeks
393-1.63077 -1.78024 (393*2π)/5311 weeks
3941.8726 -3.49524 (394*2π)/5311 weeks
3952.91185 -1.59413 (395*2π)/5311 weeks
3962.991 -.0828 (396*2π)/5311 weeks
3971.09368 .21336 (397*2π)/5311 weeks
3981.32531 -.02385 (398*2π)/5311 weeks
399-.7551 .38687 (399*2π)/5311 weeks
400-1.68222 -2.19233 (400*2π)/5311 weeks
401-.47316 -3.55448 (401*2π)/5311 weeks
4021.82018 -4.16762 (402*2π)/5311 weeks
4033.16726 -1.94846 (403*2π)/5311 weeks
4041.41439 -1.20441 (404*2π)/5311 weeks
4051.16437 -2.65048 (405*2π)/5311 weeks
4062.46383 -2.65866 (406*2π)/5311 weeks
4072.88455 -1.36661 (407*2π)/5311 weeks
4082.17706 -.72564 (408*2π)/5311 weeks
4091.16281 -.01566 (409*2π)/5311 weeks
410-.82728 -.59616 (410*2π)/5311 weeks
411-1.4577 -3.28178 (411*2π)/5311 weeks
4121.79238 -6.05397 (412*2π)/5311 weeks
4135.53651 -3.08842 (413*2π)/5311 weeks
4143.94091 1.12508 (414*2π)/5311 weeks
415.06676 .59665 (415*2π)/5311 weeks
416-1.18992 -2.32491 (416*2π)/5311 weeks
417.83755 -4.31775 (417*2π)/5311 weeks
4183.3459 -4.0042 (418*2π)/5311 weeks
4195.338 -.5339 (419*2π)/5311 weeks
4201.53395 3.56756 (420*2π)/5311 weeks
421-3.86419 .21747 (421*2π)/5311 weeks
422-3.25662 -4.62415 (422*2π)/5311 weeks
423.2742 -8.16084 (423*2π)/5311 weeks
4246.46922 -6.40713 (424*2π)/5311 weeks
4256.90804 .6088 (425*2π)/5311 weeks
426.0038 3.5833 (426*2π)/5311 weeks
427-4.35764 -2.32317 (427*2π)/5311 weeks
428-1.22596 -7.60996 (428*2π)/5311 weeks
4295.27816 -8.477 (429*2π)/5311 weeks
4308.50572 -2.67858 (430*2π)/5311 weeks
4315.40975 2.89458 (431*2π)/5311 weeks
432-1.44604 1.86683 (432*2π)/5311 weeks
433-2.09775 -4.38372 (433*2π)/5311 weeks
4342.75693 -6.64559 (434*2π)/5311 weeks
4356.72903 -3.16073 (435*2π)/5311 weeks
4365.29129 1.29377 (436*2π)/5311 weeks
4371.09227 1.76273 (437*2π)/5311 weeks
438-.47053 -1.13199 (438*2π)/5311 weeks
4391.43975 -2.91246 (439*2π)/5311 weeks
4401.9913 -.50581 (440*2π)/5311 weeks
441-.83512 -1.69129 (441*2π)/5311 weeks
442.76534 -3.90552 (442*2π)/5311 weeks
4432.35333 -2.40367 (443*2π)/5311 weeks
444.83911 -.60048 (444*2π)/5311 weeks
445-2.65859 -2.01033 (445*2π)/5311 weeks
446-2.44801 -7.4664 (446*2π)/5311 weeks
4474.37099 -9.84568 (447*2π)/5311 weeks
44810.09449 -4.25957 (448*2π)/5311 weeks
4496.51457 4.03275 (449*2π)/5311 weeks
450-1.34555 2.65864 (450*2π)/5311 weeks
451-3.81796 -2.39465 (451*2π)/5311 weeks
452-.87941 -8.84657 (452*2π)/5311 weeks
4536.93228 -7.59843 (453*2π)/5311 weeks
4548.82243 -1.1509 (454*2π)/5311 weeks
4553.35167 5.31627 (455*2π)/5311 weeks
456-4.68322 -.01093 (456*2π)/5311 weeks
457-.60477 -6.20494 (457*2π)/5311 weeks
4581.9158 -6.8551 (458*2π)/5311 weeks
4598.59737 -4.96651 (459*2π)/5311 weeks
4606.63878 4.46449 (460*2π)/5311 weeks
461-1.98669 4.80445 (461*2π)/5311 weeks
462-6.98008 -2.22123 (462*2π)/5311 weeks
463-1.76335 -9.63584 (463*2π)/5311 weeks
4644.50453 -5.65993 (464*2π)/5311 weeks
4651.53391 -2.61267 (465*2π)/5311 weeks
466.33555 -4.16116 (466*2π)/5311 weeks
4671.06125 -8.41772 (467*2π)/5311 weeks
4688.05168 -6.66977 (468*2π)/5311 weeks
4698.15023 1.16153 (469*2π)/5311 weeks
4701.73819 3.69196 (470*2π)/5311 weeks
471-4.60132 -.7601 (471*2π)/5311 weeks
472-.2852 -7.59621 (472*2π)/5311 weeks
4734.36922 -3.99536 (473*2π)/5311 weeks
4742.73259 -.2747 (474*2π)/5311 weeks
475-2.59174 -1.12907 (475*2π)/5311 weeks
476-2.89573 -7.70066 (476*2π)/5311 weeks
4775.84816 -8.96019 (477*2π)/5311 weeks
4786.63851 -1.31209 (478*2π)/5311 weeks
4791.72313 -.05607 (479*2π)/5311 weeks
480-.63093 -1.59348 (480*2π)/5311 weeks
481-1.01613 -4.96642 (481*2π)/5311 weeks
4822.51854 -5.22609 (482*2π)/5311 weeks
4833.17405 -2.65822 (483*2π)/5311 weeks
484-.69415 -.07674 (484*2π)/5311 weeks
485-3.3884 -2.766 (485*2π)/5311 weeks
486-3.54122 -8.4543 (486*2π)/5311 weeks
4872.31586 -8.92853 (487*2π)/5311 weeks
4882.03694 -4.9564 (488*2π)/5311 weeks
489-.40829 -4.72003 (489*2π)/5311 weeks
490-2.33358 -10.60241 (490*2π)/5311 weeks
4916.84707 -11.09796 (491*2π)/5311 weeks
4926.5822 -1.96649 (492*2π)/5311 weeks
493.35082 -.52533 (493*2π)/5311 weeks
494-5.11504 -4.52917 (494*2π)/5311 weeks
495-4.03826 -14.50212 (495*2π)/5311 weeks
4969.23769 -16.39574 (496*2π)/5311 weeks
49717.07813 -4.42853 (497*2π)/5311 weeks
4987.8109 13.48695 (498*2π)/5311 weeks
499-17.95176 7.53027 (499*2π)/5311 weeks
500-19.15425 -18.59678 (500*2π)/5311 weeks
5011.97424 -29.08811 (501*2π)/5311 weeks
50220.90756 -13.34088 (502*2π)/5311 weeks
50312.1545 8.23609 (503*2π)/5311 weeks
504-8.44064 6.07459 (504*2π)/5311 weeks
505-16.15594 -8.87421 (505*2π)/5311 weeks
506-6.30322 -25.28496 (506*2π)/5311 weeks
5078.25483 -19.8847 (507*2π)/5311 weeks
5088.28727 -10.24788 (508*2π)/5311 weeks
509-.89184 -7.22231 (509*2π)/5311 weeks
510-1.26628 -15.60831 (510*2π)/5311 weeks
5114.23289 -17.59799 (511*2π)/5311 weeks
5125.68817 -14.85286 (512*2π)/5311 weeks
5138.75321 -16.99729 (513*2π)/5311 weeks
5149.62828 -7.32362 (514*2π)/5311 weeks
5151.4511 -11.05166 (515*2π)/5311 weeks
5163.76533 -8.91799 (516*2π)/5311 weeks
517-5.67381 -7.16538 (517*2π)/5311 weeks
518-16.94821 -18.20126 (518*2π)/5311 weeks
519-9.16626 -45.80446 (519*2π)/5311 weeks
52026.98714 -41.83054 (520*2π)/5311 weeks
52128.39407 -14.10128 (521*2π)/5311 weeks
52216.11865 4.4789 (522*2π)/5311 weeks
523-27.51781 -2.29329 (523*2π)/5311 weeks
524-25.81121 -60.43942 (524*2π)/5311 weeks
52522.60975 -68.30641 (525*2π)/5311 weeks
52640.14753 -25.89055 (526*2π)/5311 weeks
527-6.98037 2.93259 (527*2π)/5311 weeks
528-89.21186 -57.25041 (528*2π)/5311 weeks
529-56.54184 -224.2567 (529*2π)/5311 weeks

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