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Fourier Analysis of TWM (PROSHARES ULTRASHORT RUSSELL2000 PROSHARES ULTRASHORT RUSSELL2000)


TWM (PROSHARES ULTRASHORT RUSSELL2000 PROSHARES ULTRASHORT RUSSELL2000) appears to have interesting cyclic behaviour every 44 weeks (42.3061*sine), 48 weeks (41.5211*sine), and 52 weeks (27.97*cosine).

TWM (PROSHARES ULTRASHORT RUSSELL2000 PROSHARES ULTRASHORT RUSSELL2000) has an average price of 299.95 (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 1/16/2018 for TWM (PROSHARES ULTRASHORT RUSSELL2000 PROSHARES ULTRASHORT RUSSELL2000), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0299.9495   0 
1203.2504 343.3285 (1*2π)/574574 weeks
2-34.6731 233.9684 (2*2π)/574287 weeks
3-91.63959 88.14708 (3*2π)/574191 weeks
4-29.08069 3.5583 (4*2π)/574144 weeks
527.8967 10.33593 (5*2π)/574115 weeks
637.61444 48.91303 (6*2π)/57496 weeks
71.28098 65.66895 (7*2π)/57482 weeks
8-35.51356 34.87821 (8*2π)/57472 weeks
9-12.46743 -6.52721 (9*2π)/57464 weeks
1019.42307 1.70985 (10*2π)/57457 weeks
1127.97 16.25459 (11*2π)/57452 weeks
1222.82588 41.52113 (12*2π)/57448 weeks
13-8.8836 42.30613 (13*2π)/57444 weeks
14-16.07991 18.53321 (14*2π)/57441 weeks
15-6.81889 7.79873 (15*2π)/57438 weeks
162.3484 7.30966 (16*2π)/57436 weeks
172.78727 11.01738 (17*2π)/57434 weeks
185.2224 5.3623 (18*2π)/57432 weeks
1910.99207 12.86546 (19*2π)/57430 weeks
204.78166 15.34004 (20*2π)/57429 weeks
215.18599 15.1503 (21*2π)/57427 weeks
221.75202 16.72774 (22*2π)/57426 weeks
23-2.03907 12.99816 (23*2π)/57425 weeks
241.62388 5.74029 (24*2π)/57424 weeks
258.22689 10.67393 (25*2π)/57423 weeks
267.27958 19.39106 (26*2π)/57422 weeks
27-5.58317 23.77105 (27*2π)/57421 weeks
28-15.27315 9.75009 (28*2π)/57421 weeks
29-10.05829 -3.8237 (29*2π)/57420 weeks
305.86475 -9.50919 (30*2π)/57419 weeks
3119.50151 5.50198 (31*2π)/57419 weeks
3211.17567 24.94942 (32*2π)/57418 weeks
33-9.28427 24.72366 (33*2π)/57417 weeks
34-20.94764 6.30363 (34*2π)/57417 weeks
35-8.55765 -13.44928 (35*2π)/57416 weeks
3612.52219 -8.12753 (36*2π)/57416 weeks
3715.00304 7.48568 (37*2π)/57416 weeks
386.67178 16.22346 (38*2π)/57415 weeks
39-4.37617 12.83214 (39*2π)/57415 weeks
40-4.79343 4.27258 (40*2π)/57414 weeks
41-.09201 .64833 (41*2π)/57414 weeks
425.24259 1.38329 (42*2π)/57414 weeks
437.74382 8.65409 (43*2π)/57413 weeks
44.10334 11.66808 (44*2π)/57413 weeks
45-1.9396 5.13383 (45*2π)/57413 weeks
46.84457 4.37652 (46*2π)/57412 weeks
472.87981 5.92114 (47*2π)/57412 weeks
48-.00336 9.29206 (48*2π)/57412 weeks
49-4.35415 6.11891 (49*2π)/57412 weeks
50-2.63102 2.25739 (50*2π)/57411 weeks
51.33668 -.0463 (51*2π)/57411 weeks
522.9517 2.76598 (52*2π)/57411 weeks
532.38562 4.93782 (53*2π)/57411 weeks
54-.71744 4.82878 (54*2π)/57411 weeks
55-.76155 1.83711 (55*2π)/57410 weeks
561.03581 .32815 (56*2π)/57410 weeks
574.73078 .06552 (57*2π)/57410 weeks
586.86317 5.74912 (58*2π)/57410 weeks
59.15619 9.57055 (59*2π)/57410 weeks
60-3.32689 4.00904 (60*2π)/57410 weeks
61-.2471 -.11022 (61*2π)/5749 weeks
623.47056 1.50273 (62*2π)/5749 weeks
633.74177 5.03495 (63*2π)/5749 weeks
64-1.73061 6.48822 (64*2π)/5749 weeks
65-3.77761 -.37768 (65*2π)/5749 weeks
662.00019 -3.3399 (66*2π)/5749 weeks
677.4557 -1.10147 (67*2π)/5749 weeks
687.82966 5.68155 (68*2π)/5748 weeks
692.14599 8.36123 (69*2π)/5748 weeks
70.05243 4.33854 (70*2π)/5748 weeks
71.85721 3.05508 (71*2π)/5748 weeks
723.66714 3.26838 (72*2π)/5748 weeks
732.19277 8.29619 (73*2π)/5748 weeks
74-5.18321 6.59091 (74*2π)/5748 weeks
75-5.6596 -1.19537 (75*2π)/5748 weeks
76.35096 -5.09197 (76*2π)/5748 weeks
777.85235 -2.381 (77*2π)/5747 weeks
787.10809 5.79645 (78*2π)/5747 weeks
791.51406 6.23806 (79*2π)/5747 weeks
80-.61996 5.76801 (80*2π)/5747 weeks
81-4.41112 .63177 (81*2π)/5747 weeks
821.75664 -5.0073 (82*2π)/5747 weeks
838.03461 -.35504 (83*2π)/5747 weeks
847.55278 5.40198 (84*2π)/5747 weeks
851.98597 9.02961 (85*2π)/5747 weeks
86-3.46193 5.01442 (86*2π)/5747 weeks
87-2.80528 -.10762 (87*2π)/5747 weeks
881.07904 -3.98419 (88*2π)/5747 weeks
898.38897 -1.58617 (89*2π)/5746 weeks
908.62125 6.06547 (90*2π)/5746 weeks
912.8419 9.42995 (91*2π)/5746 weeks
92-2.54898 6.38235 (92*2π)/5746 weeks
93-2.37393 1.79612 (93*2π)/5746 weeks
94.69011 .59536 (94*2π)/5746 weeks
952.23508 2.04289 (95*2π)/5746 weeks
961.30228 3.5974 (96*2π)/5746 weeks
97-.60956 2.36453 (97*2π)/5746 weeks
98.83548 .07898 (98*2π)/5746 weeks
992.20238 1.9799 (99*2π)/5746 weeks
100.00443 2.22421 (100*2π)/5746 weeks
101-.3363 -.16354 (101*2π)/5746 weeks
1022.32566 -1.9783 (102*2π)/5746 weeks
1035.76157 -.17178 (103*2π)/5746 weeks
1045.98916 3.96813 (104*2π)/5746 weeks
1051.94505 6.20245 (105*2π)/5745 weeks
106-2.1085 3.82019 (106*2π)/5745 weeks
107-1.41592 -1.59497 (107*2π)/5745 weeks
1084.46819 -2.94928 (108*2π)/5745 weeks
1097.82235 1.48873 (109*2π)/5745 weeks
1106.2665 6.83852 (110*2π)/5745 weeks
111.38701 8.04841 (111*2π)/5745 weeks
112-3.36822 4.75476 (112*2π)/5745 weeks
113-2.80318 -1.23615 (113*2π)/5745 weeks
1143.57831 -3.11597 (114*2π)/5745 weeks
1157.22843 1.87225 (115*2π)/5745 weeks
1164.38775 7.21364 (116*2π)/5745 weeks
117-.87636 7.05004 (117*2π)/5745 weeks
118-3.23488 3.8068 (118*2π)/5745 weeks
119-3.39762 -.60059 (119*2π)/5745 weeks
1201.46936 -3.26836 (120*2π)/5745 weeks
1214.90627 .20517 (121*2π)/5745 weeks
1223.54593 3.57969 (122*2π)/5745 weeks
1231.41747 4.13036 (123*2π)/5745 weeks
124-.61607 2.9719 (124*2π)/5745 weeks
125-.60724 .14457 (125*2π)/5745 weeks
1261.73952 -1.4928 (126*2π)/5745 weeks
1274.96291 .6366 (127*2π)/5745 weeks
1284.22965 4.57965 (128*2π)/5744 weeks
129.14383 5.28271 (129*2π)/5744 weeks
130-1.33042 2.32293 (130*2π)/5744 weeks
131-.41396 .2207 (131*2π)/5744 weeks
1321.23012 .00874 (132*2π)/5744 weeks
1332.05555 .68231 (133*2π)/5744 weeks
1342.6976 1.25009 (134*2π)/5744 weeks
1352.41397 2.41721 (135*2π)/5744 weeks
1361.28148 2.60718 (136*2π)/5744 weeks
137.91328 1.34654 (137*2π)/5744 weeks
1382.35601 1.17874 (138*2π)/5744 weeks
1392.56404 3.41409 (139*2π)/5744 weeks
140.50531 4.07904 (140*2π)/5744 weeks
141-.72251 2.96217 (141*2π)/5744 weeks
142-1.6677 1.05706 (142*2π)/5744 weeks
143-.06831 -.64825 (143*2π)/5744 weeks
1441.17297 .25037 (144*2π)/5744 weeks
1451.25479 -.3369 (145*2π)/5744 weeks
1462.92568 .25621 (146*2π)/5744 weeks
1472.72897 1.54393 (147*2π)/5744 weeks
1481.93441 3.18028 (148*2π)/5744 weeks
149-1.23073 2.41267 (149*2π)/5744 weeks
150-.17796 -1.34339 (150*2π)/5744 weeks
1513.80616 -.86866 (151*2π)/5744 weeks
1524.23042 2.49277 (152*2π)/5744 weeks
1531.4536 4.40596 (153*2π)/5744 weeks
154-1.69866 2.60874 (154*2π)/5744 weeks
155-.63026 -.70227 (155*2π)/5744 weeks
1561.88532 -1.22916 (156*2π)/5744 weeks
1574.07673 .76426 (157*2π)/5744 weeks
1582.25687 3.87923 (158*2π)/5744 weeks
159-.41091 2.68139 (159*2π)/5744 weeks
160-.39153 1.15704 (160*2π)/5744 weeks
161.31879 .14399 (161*2π)/5744 weeks
1621.07615 .02043 (162*2π)/5744 weeks
1631.65469 .05883 (163*2π)/5744 weeks
1642.41082 .94993 (164*2π)/5744 weeks
1651.20761 2.63906 (165*2π)/5743 weeks
166-.42781 .8719 (166*2π)/5743 weeks
167.87162 -.08726 (167*2π)/5743 weeks
1681.1929 .09816 (168*2π)/5743 weeks
1691.81515 -.07806 (169*2π)/5743 weeks
1702.71255 .61586 (170*2π)/5743 weeks
1712.45485 2.48402 (171*2π)/5743 weeks
172-.14948 2.58395 (172*2π)/5743 weeks
173-1.25272 .57841 (173*2π)/5743 weeks
174-.33373 -2.04078 (174*2π)/5743 weeks
1752.97195 -2.38643 (175*2π)/5743 weeks
1764.7733 .3291 (176*2π)/5743 weeks
1773.36902 3.14414 (177*2π)/5743 weeks
178.53454 3.03745 (178*2π)/5743 weeks
179-.60374 1.21784 (179*2π)/5743 weeks
180.19742 -1.05766 (180*2π)/5743 weeks
1812.64646 -1.46613 (181*2π)/5743 weeks
1824.2689 .75081 (182*2π)/5743 weeks
1833.17928 3.44328 (183*2π)/5743 weeks
184.31861 3.92164 (184*2π)/5743 weeks
185-1.71618 1.78483 (185*2π)/5743 weeks
186-1.46249 -1.10115 (186*2π)/5743 weeks
1871.50884 -2.62657 (187*2π)/5743 weeks
1884.06369 -.638 (188*2π)/5743 weeks
1893.76853 2.48167 (189*2π)/5743 weeks
190.71076 3.4871 (190*2π)/5743 weeks
191-1.18184 1.17554 (191*2π)/5743 weeks
192-.44016 -1.04555 (192*2π)/5743 weeks
1932.1123 -1.44986 (193*2π)/5743 weeks
1942.78437 .53263 (194*2π)/5743 weeks
1952.08873 1.34766 (195*2π)/5743 weeks
196.56811 1.51814 (196*2π)/5743 weeks
197.02138 -.43762 (197*2π)/5743 weeks
1982.0333 -1.47992 (198*2π)/5743 weeks
1993.34388 -.22215 (199*2π)/5743 weeks
2003.5163 1.32709 (200*2π)/5743 weeks
2012.28181 2.50147 (201*2π)/5743 weeks
2021.64524 2.36411 (202*2π)/5743 weeks
203.00718 3.25483 (203*2π)/5743 weeks
204-2.03345 .69038 (204*2π)/5743 weeks
205-.28299 -1.00914 (205*2π)/5743 weeks
206.68419 -1.35266 (206*2π)/5743 weeks
2071.86794 -.89165 (207*2π)/5743 weeks
2081.74549 -.27424 (208*2π)/5743 weeks
2092.12317 -.40431 (209*2π)/5743 weeks
2101.64162 .72149 (210*2π)/5743 weeks
2111.02842 -.9292 (211*2π)/5743 weeks
2122.69614 -.69124 (212*2π)/5743 weeks
2132.98383 -.34114 (213*2π)/5743 weeks
2144.226 1.04383 (214*2π)/5743 weeks
2152.51006 3.27862 (215*2π)/5743 weeks
216-.30368 2.47158 (216*2π)/5743 weeks
217-.58324 -.17072 (217*2π)/5743 weeks
2181.66765 -1.45078 (218*2π)/5743 weeks
2193.30642 .61114 (219*2π)/5743 weeks
2201.58782 2.31091 (220*2π)/5743 weeks
221-.07134 1.46474 (221*2π)/5743 weeks
222-.77773 -.37248 (222*2π)/5743 weeks
223.82406 -2.68056 (223*2π)/5743 weeks
2244.21163 -1.70403 (224*2π)/5743 weeks
2254.51336 1.72991 (225*2π)/5743 weeks
2261.55671 3.38678 (226*2π)/5743 weeks
227-.92214 1.14375 (227*2π)/5743 weeks
228.61895 -1.46786 (228*2π)/5743 weeks
2292.91218 -.26821 (229*2π)/5743 weeks
2302.04781 1.50979 (230*2π)/5742 weeks
231.71056 1.1394 (231*2π)/5742 weeks
232.10065 .50381 (232*2π)/5742 weeks
233-.00406 -1.44547 (233*2π)/5742 weeks
2342.71303 -2.27157 (234*2π)/5742 weeks
2353.88776 .26329 (235*2π)/5742 weeks
2362.61903 1.66321 (236*2π)/5742 weeks
237.54462 1.49183 (237*2π)/5742 weeks
238.40637 -.94505 (238*2π)/5742 weeks
2392.5491 -1.13683 (239*2π)/5742 weeks
2403.56855 .03161 (240*2π)/5742 weeks
2413.23274 1.70982 (241*2π)/5742 weeks
242.90501 2.47203 (242*2π)/5742 weeks
243-.52932 .35926 (243*2π)/5742 weeks
244.64952 -1.71268 (244*2π)/5742 weeks
2453.34558 -2.09516 (245*2π)/5742 weeks
2465.17692 .77241 (246*2π)/5742 weeks
2473.19967 3.31418 (247*2π)/5742 weeks
248.89589 2.98614 (248*2π)/5742 weeks
249-.70055 1.93025 (249*2π)/5742 weeks
250-.13736 -1.11351 (250*2π)/5742 weeks
2511.96735 -.61572 (251*2π)/5742 weeks
2522.26931 -.00065 (252*2π)/5742 weeks
2532.17563 1.23971 (253*2π)/5742 weeks
254.94101 .88278 (254*2π)/5742 weeks
2551.26094 .64375 (255*2π)/5742 weeks
256.46168 .45935 (256*2π)/5742 weeks
2571.01396 -1.03798 (257*2π)/5742 weeks
2582.73 -.90548 (258*2π)/5742 weeks
2593.60904 .2863 (259*2π)/5742 weeks
2603.0698 2.77505 (260*2π)/5742 weeks
261.04424 3.04484 (261*2π)/5742 weeks
262-1.38117 .41188 (262*2π)/5742 weeks
263-.19326 -1.70435 (263*2π)/5742 weeks
2642.13373 -2.51326 (264*2π)/5742 weeks
2654.74968 -1.043 (265*2π)/5742 weeks
2664.6582 2.62336 (266*2π)/5742 weeks
2671.78387 4.7794 (267*2π)/5742 weeks
268-2.55172 3.11516 (268*2π)/5742 weeks
269-2.4376 -1.6365 (269*2π)/5742 weeks
2701.02152 -3.24016 (270*2π)/5742 weeks
2713.99349 -2.07184 (271*2π)/5742 weeks
2724.72535 1.79937 (272*2π)/5742 weeks
2731.3021 3.98983 (273*2π)/5742 weeks
274-2.08838 1.56308 (274*2π)/5742 weeks
275-.51146 -2.25265 (275*2π)/5742 weeks
2762.71168 -2.10108 (276*2π)/5742 weeks
2774.1286 .1199 (277*2π)/5742 weeks
2783.25579 2.74606 (278*2π)/5742 weeks
279.43983 4.08745 (279*2π)/5742 weeks
280-2.89694 1.69199 (280*2π)/5742 weeks
281-1.77809 -2.75765 (281*2π)/5742 weeks
2822.25926 -2.95606 (282*2π)/5742 weeks
2833.43017 -.16567 (283*2π)/5742 weeks
2842.56367 1.51323 (284*2π)/5742 weeks
2851.19028 1.81095 (285*2π)/5742 weeks
286-.03808 1.83996 (286*2π)/5742 weeks
287-1.53821   (287*2π)/5742 weeks
288-.03808 -1.83996 (288*2π)/5742 weeks
2891.19028 -1.81095 (289*2π)/5742 weeks
2902.56367 -1.51323 (290*2π)/5742 weeks
2913.43017 .16567 (291*2π)/5742 weeks
2922.25926 2.95606 (292*2π)/5742 weeks
293-1.77809 2.75765 (293*2π)/5742 weeks
294-2.89694 -1.69199 (294*2π)/5742 weeks
295.43983 -4.08745 (295*2π)/5742 weeks
2963.25579 -2.74606 (296*2π)/5742 weeks
2974.1286 -.1199 (297*2π)/5742 weeks
2982.71168 2.10108 (298*2π)/5742 weeks
299-.51146 2.25265 (299*2π)/5742 weeks
300-2.08838 -1.56308 (300*2π)/5742 weeks
3011.3021 -3.98983 (301*2π)/5742 weeks
3024.72535 -1.79937 (302*2π)/5742 weeks
3033.99349 2.07184 (303*2π)/5742 weeks
3041.02152 3.24016 (304*2π)/5742 weeks
305-2.4376 1.6365 (305*2π)/5742 weeks
306-2.55172 -3.11516 (306*2π)/5742 weeks
3071.78387 -4.7794 (307*2π)/5742 weeks
3084.6582 -2.62336 (308*2π)/5742 weeks
3094.74968 1.043 (309*2π)/5742 weeks
3102.13373 2.51326 (310*2π)/5742 weeks
311-.19326 1.70435 (311*2π)/5742 weeks
312-1.38117 -.41188 (312*2π)/5742 weeks
313.04424 -3.04484 (313*2π)/5742 weeks
3143.0698 -2.77505 (314*2π)/5742 weeks
3153.60904 -.2863 (315*2π)/5742 weeks
3162.73 .90548 (316*2π)/5742 weeks
3171.01396 1.03798 (317*2π)/5742 weeks
318.46168 -.45935 (318*2π)/5742 weeks
3191.26094 -.64375 (319*2π)/5742 weeks
320.94101 -.88278 (320*2π)/5742 weeks
3212.17563 -1.23971 (321*2π)/5742 weeks
3222.26931 .00065 (322*2π)/5742 weeks
3231.96735 .61572 (323*2π)/5742 weeks
324-.13736 1.11351 (324*2π)/5742 weeks
325-.70055 -1.93025 (325*2π)/5742 weeks
326.89589 -2.98614 (326*2π)/5742 weeks
3273.19967 -3.31418 (327*2π)/5742 weeks
3285.17692 -.77241 (328*2π)/5742 weeks
3293.34558 2.09516 (329*2π)/5742 weeks
330.64952 1.71268 (330*2π)/5742 weeks
331-.52932 -.35926 (331*2π)/5742 weeks
332.90501 -2.47203 (332*2π)/5742 weeks
3333.23274 -1.70982 (333*2π)/5742 weeks
3343.56855 -.03161 (334*2π)/5742 weeks
3352.5491 1.13683 (335*2π)/5742 weeks
336.40637 .94505 (336*2π)/5742 weeks
337.54462 -1.49183 (337*2π)/5742 weeks
3382.61903 -1.66321 (338*2π)/5742 weeks
3393.88776 -.26329 (339*2π)/5742 weeks
3402.71303 2.27157 (340*2π)/5742 weeks
341-.00406 1.44547 (341*2π)/5742 weeks
342.10065 -.50381 (342*2π)/5742 weeks
343.71056 -1.1394 (343*2π)/5742 weeks
3442.04781 -1.50979 (344*2π)/5742 weeks
3452.91218 .26821 (345*2π)/5742 weeks
346.61895 1.46786 (346*2π)/5742 weeks
347-.92214 -1.14375 (347*2π)/5742 weeks
3481.55671 -3.38678 (348*2π)/5742 weeks
3494.51336 -1.72991 (349*2π)/5742 weeks
3504.21163 1.70403 (350*2π)/5742 weeks
351.82406 2.68056 (351*2π)/5742 weeks
352-.77773 .37248 (352*2π)/5742 weeks
353-.07134 -1.46474 (353*2π)/5742 weeks
3541.58782 -2.31091 (354*2π)/5742 weeks
3553.30642 -.61114 (355*2π)/5742 weeks
3561.66765 1.45078 (356*2π)/5742 weeks
357-.58324 .17072 (357*2π)/5742 weeks
358-.30368 -2.47158 (358*2π)/5742 weeks
3592.51006 -3.27862 (359*2π)/5742 weeks
3604.226 -1.04383 (360*2π)/5742 weeks
3612.98383 .34114 (361*2π)/5742 weeks
3622.69614 .69124 (362*2π)/5742 weeks
3631.02842 .9292 (363*2π)/5742 weeks
3641.64162 -.72149 (364*2π)/5742 weeks
3652.12317 .40431 (365*2π)/5742 weeks
3661.74549 .27424 (366*2π)/5742 weeks
3671.86794 .89165 (367*2π)/5742 weeks
368.68419 1.35266 (368*2π)/5742 weeks
369-.28299 1.00914 (369*2π)/5742 weeks
370-2.03345 -.69038 (370*2π)/5742 weeks
371.00718 -3.25483 (371*2π)/5742 weeks
3721.64524 -2.36411 (372*2π)/5742 weeks
3732.28181 -2.50147 (373*2π)/5742 weeks
3743.5163 -1.32709 (374*2π)/5742 weeks
3753.34388 .22215 (375*2π)/5742 weeks
3762.0333 1.47992 (376*2π)/5742 weeks
377.02138 .43762 (377*2π)/5742 weeks
378.56811 -1.51814 (378*2π)/5742 weeks
3792.08873 -1.34766 (379*2π)/5742 weeks
3802.78437 -.53263 (380*2π)/5742 weeks
3812.1123 1.44986 (381*2π)/5742 weeks
382-.44016 1.04555 (382*2π)/5742 weeks
383-1.18184 -1.17554 (383*2π)/5741 weeks
384.71076 -3.4871 (384*2π)/5741 weeks
3853.76853 -2.48167 (385*2π)/5741 weeks
3864.06369 .638 (386*2π)/5741 weeks
3871.50884 2.62657 (387*2π)/5741 weeks
388-1.46249 1.10115 (388*2π)/5741 weeks
389-1.71618 -1.78483 (389*2π)/5741 weeks
390.31861 -3.92164 (390*2π)/5741 weeks
3913.17928 -3.44328 (391*2π)/5741 weeks
3924.2689 -.75081 (392*2π)/5741 weeks
3932.64646 1.46613 (393*2π)/5741 weeks
394.19742 1.05766 (394*2π)/5741 weeks
395-.60374 -1.21784 (395*2π)/5741 weeks
396.53454 -3.03745 (396*2π)/5741 weeks
3973.36902 -3.14414 (397*2π)/5741 weeks
3984.7733 -.3291 (398*2π)/5741 weeks
3992.97195 2.38643 (399*2π)/5741 weeks
400-.33373 2.04078 (400*2π)/5741 weeks
401-1.25272 -.57841 (401*2π)/5741 weeks
402-.14948 -2.58395 (402*2π)/5741 weeks
4032.45485 -2.48402 (403*2π)/5741 weeks
4042.71255 -.61586 (404*2π)/5741 weeks
4051.81515 .07806 (405*2π)/5741 weeks
4061.1929 -.09816 (406*2π)/5741 weeks
407.87162 .08726 (407*2π)/5741 weeks
408-.42781 -.8719 (408*2π)/5741 weeks
4091.20761 -2.63906 (409*2π)/5741 weeks
4102.41082 -.94993 (410*2π)/5741 weeks
4111.65469 -.05883 (411*2π)/5741 weeks
4121.07615 -.02043 (412*2π)/5741 weeks
413.31879 -.14399 (413*2π)/5741 weeks
414-.39153 -1.15704 (414*2π)/5741 weeks
415-.41091 -2.68139 (415*2π)/5741 weeks
4162.25687 -3.87923 (416*2π)/5741 weeks
4174.07673 -.76426 (417*2π)/5741 weeks
4181.88532 1.22916 (418*2π)/5741 weeks
419-.63026 .70227 (419*2π)/5741 weeks
420-1.69866 -2.60874 (420*2π)/5741 weeks
4211.4536 -4.40596 (421*2π)/5741 weeks
4224.23042 -2.49277 (422*2π)/5741 weeks
4233.80616 .86866 (423*2π)/5741 weeks
424-.17796 1.34339 (424*2π)/5741 weeks
425-1.23073 -2.41267 (425*2π)/5741 weeks
4261.93441 -3.18028 (426*2π)/5741 weeks
4272.72897 -1.54393 (427*2π)/5741 weeks
4282.92568 -.25621 (428*2π)/5741 weeks
4291.25479 .3369 (429*2π)/5741 weeks
4301.17297 -.25037 (430*2π)/5741 weeks
431-.06831 .64825 (431*2π)/5741 weeks
432-1.6677 -1.05706 (432*2π)/5741 weeks
433-.72251 -2.96217 (433*2π)/5741 weeks
434.50531 -4.07904 (434*2π)/5741 weeks
4352.56404 -3.41409 (435*2π)/5741 weeks
4362.35601 -1.17874 (436*2π)/5741 weeks
437.91328 -1.34654 (437*2π)/5741 weeks
4381.28148 -2.60718 (438*2π)/5741 weeks
4392.41397 -2.41721 (439*2π)/5741 weeks
4402.6976 -1.25009 (440*2π)/5741 weeks
4412.05555 -.68231 (441*2π)/5741 weeks
4421.23012 -.00874 (442*2π)/5741 weeks
443-.41396 -.2207 (443*2π)/5741 weeks
444-1.33042 -2.32293 (444*2π)/5741 weeks
445.14383 -5.28271 (445*2π)/5741 weeks
4464.22965 -4.57965 (446*2π)/5741 weeks
4474.96291 -.6366 (447*2π)/5741 weeks
4481.73952 1.4928 (448*2π)/5741 weeks
449-.60724 -.14457 (449*2π)/5741 weeks
450-.61607 -2.9719 (450*2π)/5741 weeks
4511.41747 -4.13036 (451*2π)/5741 weeks
4523.54593 -3.57969 (452*2π)/5741 weeks
4534.90627 -.20517 (453*2π)/5741 weeks
4541.46936 3.26836 (454*2π)/5741 weeks
455-3.39762 .60059 (455*2π)/5741 weeks
456-3.23488 -3.8068 (456*2π)/5741 weeks
457-.87636 -7.05004 (457*2π)/5741 weeks
4584.38775 -7.21364 (458*2π)/5741 weeks
4597.22843 -1.87225 (459*2π)/5741 weeks
4603.57831 3.11597 (460*2π)/5741 weeks
461-2.80318 1.23615 (461*2π)/5741 weeks
462-3.36822 -4.75476 (462*2π)/5741 weeks
463.38701 -8.04841 (463*2π)/5741 weeks
4646.2665 -6.83852 (464*2π)/5741 weeks
4657.82235 -1.48873 (465*2π)/5741 weeks
4664.46819 2.94928 (466*2π)/5741 weeks
467-1.41592 1.59497 (467*2π)/5741 weeks
468-2.1085 -3.82019 (468*2π)/5741 weeks
4691.94505 -6.20245 (469*2π)/5741 weeks
4705.98916 -3.96813 (470*2π)/5741 weeks
4715.76157 .17178 (471*2π)/5741 weeks
4722.32566 1.9783 (472*2π)/5741 weeks
473-.3363 .16354 (473*2π)/5741 weeks
474.00443 -2.22421 (474*2π)/5741 weeks
4752.20238 -1.9799 (475*2π)/5741 weeks
476.83548 -.07898 (476*2π)/5741 weeks
477-.60956 -2.36453 (477*2π)/5741 weeks
4781.30228 -3.5974 (478*2π)/5741 weeks
4792.23508 -2.04289 (479*2π)/5741 weeks
480.69011 -.59536 (480*2π)/5741 weeks
481-2.37393 -1.79612 (481*2π)/5741 weeks
482-2.54898 -6.38235 (482*2π)/5741 weeks
4832.8419 -9.42995 (483*2π)/5741 weeks
4848.62125 -6.06547 (484*2π)/5741 weeks
4858.38897 1.58617 (485*2π)/5741 weeks
4861.07904 3.98419 (486*2π)/5741 weeks
487-2.80528 .10762 (487*2π)/5741 weeks
488-3.46193 -5.01442 (488*2π)/5741 weeks
4891.98597 -9.02961 (489*2π)/5741 weeks
4907.55278 -5.40198 (490*2π)/5741 weeks
4918.03461 .35504 (491*2π)/5741 weeks
4921.75664 5.0073 (492*2π)/5741 weeks
493-4.41112 -.63177 (493*2π)/5741 weeks
494-.61996 -5.76801 (494*2π)/5741 weeks
4951.51406 -6.23806 (495*2π)/5741 weeks
4967.10809 -5.79645 (496*2π)/5741 weeks
4977.85235 2.381 (497*2π)/5741 weeks
498.35096 5.09197 (498*2π)/5741 weeks
499-5.6596 1.19537 (499*2π)/5741 weeks
500-5.18321 -6.59091 (500*2π)/5741 weeks
5012.19277 -8.29619 (501*2π)/5741 weeks
5023.66714 -3.26838 (502*2π)/5741 weeks
503.85721 -3.05508 (503*2π)/5741 weeks
504.05243 -4.33854 (504*2π)/5741 weeks
5052.14599 -8.36123 (505*2π)/5741 weeks
5067.82966 -5.68155 (506*2π)/5741 weeks
5077.4557 1.10147 (507*2π)/5741 weeks
5082.00019 3.3399 (508*2π)/5741 weeks
509-3.77761 .37768 (509*2π)/5741 weeks
510-1.73061 -6.48822 (510*2π)/5741 weeks
5113.74177 -5.03495 (511*2π)/5741 weeks
5123.47056 -1.50273 (512*2π)/5741 weeks
513-.2471 .11022 (513*2π)/5741 weeks
514-3.32689 -4.00904 (514*2π)/5741 weeks
515.15619 -9.57055 (515*2π)/5741 weeks
5166.86317 -5.74912 (516*2π)/5741 weeks
5174.73078 -.06552 (517*2π)/5741 weeks
5181.03581 -.32815 (518*2π)/5741 weeks
519-.76155 -1.83711 (519*2π)/5741 weeks
520-.71744 -4.82878 (520*2π)/5741 weeks
5212.38562 -4.93782 (521*2π)/5741 weeks
5222.9517 -2.76598 (522*2π)/5741 weeks
523.33668 .0463 (523*2π)/5741 weeks
524-2.63102 -2.25739 (524*2π)/5741 weeks
525-4.35415 -6.11891 (525*2π)/5741 weeks
526-.00336 -9.29206 (526*2π)/5741 weeks
5272.87981 -5.92114 (527*2π)/5741 weeks
528.84457 -4.37652 (528*2π)/5741 weeks
529-1.9396 -5.13383 (529*2π)/5741 weeks
530.10334 -11.66808 (530*2π)/5741 weeks
5317.74382 -8.65409 (531*2π)/5741 weeks
5325.24259 -1.38329 (532*2π)/5741 weeks
533-.09201 -.64833 (533*2π)/5741 weeks
534-4.79343 -4.27258 (534*2π)/5741 weeks
535-4.37617 -12.83214 (535*2π)/5741 weeks
5366.67178 -16.22346 (536*2π)/5741 weeks
53715.00304 -7.48568 (537*2π)/5741 weeks
53812.52219 8.12753 (538*2π)/5741 weeks
539-8.55765 13.44928 (539*2π)/5741 weeks
540-20.94764 -6.30363 (540*2π)/5741 weeks
541-9.28427 -24.72366 (541*2π)/5741 weeks
54211.17567 -24.94942 (542*2π)/5741 weeks
54319.50151 -5.50198 (543*2π)/5741 weeks
5445.86475 9.50919 (544*2π)/5741 weeks
545-10.05829 3.8237 (545*2π)/5741 weeks
546-15.27315 -9.75009 (546*2π)/5741 weeks
547-5.58317 -23.77105 (547*2π)/5741 weeks
5487.27958 -19.39106 (548*2π)/5741 weeks
5498.22689 -10.67393 (549*2π)/5741 weeks
5501.62388 -5.74029 (550*2π)/5741 weeks
551-2.03907 -12.99816 (551*2π)/5741 weeks
5521.75202 -16.72774 (552*2π)/5741 weeks
5535.18599 -15.1503 (553*2π)/5741 weeks
5544.78166 -15.34004 (554*2π)/5741 weeks
55510.99207 -12.86546 (555*2π)/5741 weeks
5565.2224 -5.3623 (556*2π)/5741 weeks
5572.78727 -11.01738 (557*2π)/5741 weeks
5582.3484 -7.30966 (558*2π)/5741 weeks
559-6.81889 -7.79873 (559*2π)/5741 weeks
560-16.07991 -18.53321 (560*2π)/5741 weeks
561-8.8836 -42.30613 (561*2π)/5741 weeks
56222.82588 -41.52113 (562*2π)/5741 weeks
56327.97 -16.25459 (563*2π)/5741 weeks
56419.42307 -1.70985 (564*2π)/5741 weeks
565-12.46743 6.52721 (565*2π)/5741 weeks
566-35.51356 -34.87821 (566*2π)/5741 weeks
5671.28098 -65.66895 (567*2π)/5741 weeks
56837.61444 -48.91303 (568*2π)/5741 weeks
56927.8967 -10.33593 (569*2π)/5741 weeks
570-29.08069 -3.5583 (570*2π)/5741 weeks
571-91.63959 -88.14708 (571*2π)/5741 weeks
572-34.6731 -233.9684 (572*2π)/5741 weeks



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