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Fourier Analysis of TWM (ProShares UltraShort Russell2000)


TWM (ProShares UltraShort Russell2000) appears to have interesting cyclic behaviour every 45 weeks (45.9142*sine), 49 weeks (33.908*sine), and 49 weeks (27.2377*cosine).

TWM (ProShares UltraShort Russell2000) has an average price of 293.24 (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 4/16/2018 for TWM (ProShares UltraShort Russell2000), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0293.244   0 
1206.4316 335.4981 (1*2π)/587587 weeks
2-28.63351 235.1535 (2*2π)/587294 weeks
3-89.98292 95.93355 (3*2π)/587196 weeks
4-34.42955 6.28139 (4*2π)/587147 weeks
523.47151 6.74897 (5*2π)/587117 weeks
638.58851 42.12098 (6*2π)/58798 weeks
77.07729 64.29347 (7*2π)/58784 weeks
8-31.68399 43.91161 (8*2π)/58773 weeks
9-19.738 -1.8401 (9*2π)/58765 weeks
1015.42252 -2.60222 (10*2π)/58759 weeks
1125.1368 12.15214 (11*2π)/58753 weeks
1227.23774 33.90795 (12*2π)/58749 weeks
13-.31667 45.9142 (13*2π)/58745 weeks
14-16.55037 24.76424 (14*2π)/58742 weeks
15-9.46362 9.69398 (15*2π)/58739 weeks
16-.24772 5.87649 (16*2π)/58737 weeks
173.75184 9.73367 (17*2π)/58735 weeks
181.5507 7.37284 (18*2π)/58733 weeks
1910.32508 8.4763 (19*2π)/58731 weeks
207.33646 15.99243 (20*2π)/58729 weeks
215.07598 13.8315 (21*2π)/58728 weeks
224.00259 15.83193 (22*2π)/58727 weeks
23-.55548 14.8675 (23*2π)/58726 weeks
24-2.35448 9.11537 (24*2π)/58724 weeks
255.90017 6.72727 (25*2π)/58723 weeks
268.68809 13.30657 (26*2π)/58723 weeks
273.20555 21.97319 (27*2π)/58722 weeks
28-11.69996 19.73451 (28*2π)/58721 weeks
29-14.18802 4.6907 (29*2π)/58720 weeks
30-5.59316 -6.76525 (30*2π)/58720 weeks
3112.0898 -6.80528 (31*2π)/58719 weeks
3219.22283 11.15127 (32*2π)/58718 weeks
335.14125 26.35722 (33*2π)/58718 weeks
34-13.48266 21.41146 (34*2π)/58717 weeks
35-19.83254 1.04824 (35*2π)/58717 weeks
36-3.40429 -14.38456 (36*2π)/58716 weeks
3714.11383 -5.09442 (37*2π)/58716 weeks
3813.84474 9.08389 (38*2π)/58715 weeks
394.86903 16.22793 (39*2π)/58715 weeks
40-4.87751 11.44399 (40*2π)/58715 weeks
41-4.35953 3.61368 (41*2π)/58714 weeks
42.26264 .5425 (42*2π)/58714 weeks
435.37041 1.49019 (43*2π)/58714 weeks
447.44213 8.6661 (44*2π)/58713 weeks
45.07146 11.38733 (45*2π)/58713 weeks
46-1.96811 5.09089 (46*2π)/58713 weeks
47.75133 4.281 (47*2π)/58712 weeks
482.74616 5.56575 (48*2π)/58712 weeks
49.47519 9.02745 (49*2π)/58712 weeks
50-4.01533 6.59187 (50*2π)/58712 weeks
51-2.7575 2.37868 (51*2π)/58712 weeks
52-.45094 .02903 (52*2π)/58711 weeks
532.8945 2.17626 (53*2π)/58711 weeks
542.59763 4.30221 (54*2π)/58711 weeks
55-.13818 5.16488 (55*2π)/58711 weeks
56-1.11519 2.3371 (56*2π)/58710 weeks
57.41532 .64486 (57*2π)/58710 weeks
583.18901 -.23673 (58*2π)/58710 weeks
596.86177 3.59987 (59*2π)/58710 weeks
603.11239 9.45387 (60*2π)/58710 weeks
61-2.98342 5.8818 (61*2π)/58710 weeks
62-1.94217 .79806 (62*2π)/5879 weeks
632.39933 .34596 (63*2π)/5879 weeks
643.87415 3.25061 (64*2π)/5879 weeks
651.19171 6.84689 (65*2π)/5879 weeks
66-4.05974 3.26206 (66*2π)/5879 weeks
67-.83398 -2.84612 (67*2π)/5879 weeks
684.61483 -2.82681 (68*2π)/5879 weeks
698.60881 2.04602 (69*2π)/5879 weeks
705.67432 7.52382 (70*2π)/5878 weeks
71.03564 6.47701 (71*2π)/5878 weeks
72.49743 3.65597 (72*2π)/5878 weeks
731.53687 2.41399 (73*2π)/5878 weeks
744.07218 4.86508 (74*2π)/5878 weeks
75-.28363 8.8564 (75*2π)/5878 weeks
76-6.11785 4.07547 (76*2π)/5878 weeks
77-4.08416 -3.0175 (77*2π)/5878 weeks
782.25138 -5.20953 (78*2π)/5878 weeks
798.53891 -.25676 (79*2π)/5877 weeks
805.44076 6.60637 (80*2π)/5877 weeks
811.06448 5.70468 (81*2π)/5877 weeks
82-1.51544 5.47129 (82*2π)/5877 weeks
83-4.01373 -.7436 (83*2π)/5877 weeks
842.95956 -4.81566 (84*2π)/5877 weeks
857.9719 .40259 (85*2π)/5877 weeks
867.10222 5.80371 (86*2π)/5877 weeks
871.3881 8.78596 (87*2π)/5877 weeks
88-3.48066 4.58785 (88*2π)/5877 weeks
89-2.70264 -.21668 (89*2π)/5877 weeks
901.08058 -3.89503 (90*2π)/5877 weeks
918.10523 -1.64068 (91*2π)/5876 weeks
928.54845 5.68894 (92*2π)/5876 weeks
933.14074 9.18204 (93*2π)/5876 weeks
94-2.30127 6.67868 (94*2π)/5876 weeks
95-2.53444 2.18425 (95*2π)/5876 weeks
96.39234 .5469 (96*2π)/5876 weeks
972.15652 1.69801 (97*2π)/5876 weeks
981.62392 3.30714 (98*2π)/5876 weeks
99-.4278 2.70881 (99*2π)/5876 weeks
100.09321 .25528 (100*2π)/5876 weeks
1012.20987 1.39287 (101*2π)/5876 weeks
102.51729 2.6074 (102*2π)/5876 weeks
103-.46433 .6222 (103*2π)/5876 weeks
1041.25515 -1.67701 (104*2π)/5876 weeks
1054.75521 -1.19256 (105*2π)/5876 weeks
1066.18919 2.38513 (106*2π)/5876 weeks
1073.58014 5.90517 (107*2π)/5875 weeks
108-.66056 5.25279 (108*2π)/5875 weeks
109-2.39944 .5583 (109*2π)/5875 weeks
1101.65413 -3.29186 (110*2π)/5875 weeks
1116.70939 -.85622 (111*2π)/5875 weeks
1127.46876 4.26603 (112*2π)/5875 weeks
1133.38938 8.23893 (113*2π)/5875 weeks
114-1.53199 6.57825 (114*2π)/5875 weeks
115-3.92763 1.98723 (115*2π)/5875 weeks
116-.49857 -3.00725 (116*2π)/5875 weeks
1175.62831 -1.42158 (117*2π)/5875 weeks
1186.78809 4.26324 (118*2π)/5875 weeks
1192.31491 7.61409 (119*2π)/5875 weeks
120-2.01092 5.82742 (120*2π)/5875 weeks
121-3.5753 2.59891 (121*2π)/5875 weeks
122-2.37112 -1.91661 (122*2π)/5875 weeks
1232.93768 -2.62037 (123*2π)/5875 weeks
1244.86651 1.22251 (124*2π)/5875 weeks
1252.88079 3.67919 (125*2π)/5875 weeks
126.85044 3.96944 (126*2π)/5875 weeks
127-.90377 2.5029 (127*2π)/5875 weeks
128-.30857 -.14136 (128*2π)/5875 weeks
1292.28097 -1.46946 (129*2π)/5875 weeks
1304.99433 1.07383 (130*2π)/5875 weeks
1313.80903 4.76379 (131*2π)/5874 weeks
132-.13786 4.99715 (132*2π)/5874 weeks
133-1.28291 2.1501 (133*2π)/5874 weeks
134-.33891 .17957 (134*2π)/5874 weeks
1351.21271 .01612 (135*2π)/5874 weeks
1362.00343 .66975 (136*2π)/5874 weeks
1372.61901 1.18874 (137*2π)/5874 weeks
1382.40689 2.31728 (138*2π)/5874 weeks
1391.33789 2.58355 (139*2π)/5874 weeks
140.79712 1.4628 (140*2π)/5874 weeks
1412.09495 1.08986 (141*2π)/5874 weeks
1422.75863 3.06915 (142*2π)/5874 weeks
143.91598 4.02637 (143*2π)/5874 weeks
144-.54217 3.00356 (144*2π)/5874 weeks
145-1.64606 1.59221 (145*2π)/5874 weeks
146-.56304 -.43516 (146*2π)/5874 weeks
1471.20095 -.0555 (147*2π)/5874 weeks
148.95395 -.09792 (148*2π)/5874 weeks
1492.42679 -.26207 (149*2π)/5874 weeks
1502.69318 1.31563 (150*2π)/5874 weeks
1512.50726 2.56807 (151*2π)/5874 weeks
152.00483 3.31577 (152*2π)/5874 weeks
153-1.15776 -.21867 (153*2π)/5874 weeks
1542.21605 -1.87658 (154*2π)/5874 weeks
1554.2884 1.03486 (155*2π)/5874 weeks
1562.87416 3.89907 (156*2π)/5874 weeks
157-.3765 3.96068 (157*2π)/5874 weeks
158-1.66406 .58204 (158*2π)/5874 weeks
159.54292 -1.15608 (159*2π)/5874 weeks
1603.00066 -.68544 (160*2π)/5874 weeks
1613.88002 2.39296 (161*2π)/5874 weeks
162.81429 3.69318 (162*2π)/5874 weeks
163-.50747 1.79545 (163*2π)/5874 weeks
164-.32723 .64745 (164*2π)/5874 weeks
165.54886 .08843 (165*2π)/5874 weeks
1661.20787 .10684 (166*2π)/5874 weeks
1671.93008 .20885 (167*2π)/5874 weeks
1682.41947 1.40095 (168*2π)/5873 weeks
169.45995 2.43742 (169*2π)/5873 weeks
170-.23065 .34449 (170*2π)/5873 weeks
1711.00379 -.00728 (171*2π)/5873 weeks
1721.20459 .03131 (172*2π)/5873 weeks
1731.90748 -.04341 (173*2π)/5873 weeks
1742.71506 .80598 (174*2π)/5873 weeks
1752.13856 2.65891 (175*2π)/5873 weeks
176-.33706 2.35716 (176*2π)/5873 weeks
177-1.24961 .37427 (177*2π)/5873 weeks
178-.18111 -2.1174 (178*2π)/5873 weeks
1792.9998 -2.27601 (179*2π)/5873 weeks
1804.65216 .36561 (180*2π)/5873 weeks
1813.30242 3.05744 (181*2π)/5873 weeks
182.57532 3.0135 (182*2π)/5873 weeks
183-.56875 1.29719 (183*2π)/5873 weeks
184.028 -.91691 (184*2π)/5873 weeks
1852.3019 -1.49834 (185*2π)/5873 weeks
1864.09571 .42959 (186*2π)/5873 weeks
1873.42953 3.09212 (187*2π)/5873 weeks
188.78293 3.93138 (188*2π)/5873 weeks
189-1.51297 2.23996 (189*2π)/5873 weeks
190-1.71261 -.4532 (190*2π)/5873 weeks
191.65215 -2.50674 (191*2π)/5873 weeks
1923.5972 -1.27877 (192*2π)/5873 weeks
1934.11418 1.61489 (193*2π)/5873 weeks
1941.64895 3.50416 (194*2π)/5873 weeks
195-.95955 2.05923 (195*2π)/5873 weeks
196-.8377 -.30232 (196*2π)/5873 weeks
1971.14432 -1.69246 (197*2π)/5873 weeks
1982.86895 -.20277 (198*2π)/5873 weeks
1992.26997 1.01838 (199*2π)/5873 weeks
2001.30686 1.67578 (200*2π)/5873 weeks
201-.08977 .56646 (201*2π)/5873 weeks
202.84112 -1.30627 (202*2π)/5873 weeks
2032.84919 -.85346 (203*2π)/5873 weeks
2043.48226 .50081 (204*2π)/5873 weeks
2053.07418 2.03395 (205*2π)/5873 weeks
2061.71697 2.33054 (206*2π)/5873 weeks
2071.35987 2.79485 (207*2π)/5873 weeks
208-1.14521 2.69551 (208*2π)/5873 weeks
209-1.43893 -.445 (209*2π)/5873 weeks
210.06698 -1.04661 (210*2π)/5873 weeks
2111.11107 -1.34906 (211*2π)/5873 weeks
2121.89526 -.56173 (212*2π)/5873 weeks
2131.66198 -.30396 (213*2π)/5873 weeks
2142.28368 -.11898 (214*2π)/5873 weeks
2151.17862 .59065 (215*2π)/5873 weeks
2161.45054 -1.18171 (216*2π)/5873 weeks
2172.69399 -.49903 (217*2π)/5873 weeks
2183.11235 -.31868 (218*2π)/5873 weeks
2194.11033 1.45398 (219*2π)/5873 weeks
2202.09927 3.29099 (220*2π)/5873 weeks
221-.45908 2.14726 (221*2π)/5873 weeks
222-.45921 -.36483 (222*2π)/5873 weeks
2231.80834 -1.38962 (223*2π)/5873 weeks
2243.22258 .69635 (224*2π)/5873 weeks
2251.51583 2.2526 (225*2π)/5873 weeks
226-.05768 1.4318 (226*2π)/5873 weeks
227-.75649 -.30547 (227*2π)/5873 weeks
228.65352 -2.5495 (228*2π)/5873 weeks
2293.94951 -1.87146 (229*2π)/5873 weeks
2304.54565 1.38288 (230*2π)/5873 weeks
2311.92812 3.30509 (231*2π)/5873 weeks
232-.7883 1.57231 (232*2π)/5873 weeks
233.14923 -1.22837 (233*2π)/5873 weeks
2342.67029 -.68222 (234*2π)/5873 weeks
2352.34306 1.29108 (235*2π)/5872 weeks
236.87707 1.29135 (236*2π)/5872 weeks
237.31575 .66614 (237*2π)/5872 weeks
238-.24546 -.79537 (238*2π)/5872 weeks
2391.71912 -2.40587 (239*2π)/5872 weeks
2403.87245 -.57671 (240*2π)/5872 weeks
2413.00711 1.31136 (241*2π)/5872 weeks
2421.30382 1.86989 (242*2π)/5872 weeks
243.00784 .01367 (243*2π)/5872 weeks
2441.79443 -1.4436 (244*2π)/5872 weeks
2453.09703 -.6067 (245*2π)/5872 weeks
2463.40395 .97326 (246*2π)/5872 weeks
2472.18 2.5229 (247*2π)/5872 weeks
248-.10501 1.59634 (248*2π)/5872 weeks
249-.13117 -.80496 (249*2π)/5872 weeks
2501.72813 -2.18186 (250*2π)/5872 weeks
2514.48612 -1.19633 (251*2π)/5872 weeks
2524.57185 2.11355 (252*2π)/5872 weeks
2532.05134 3.3233 (253*2π)/5872 weeks
254.3603 2.58827 (254*2π)/5872 weeks
255-1.16582 .85643 (255*2π)/5872 weeks
256.81298 -1.26538 (256*2π)/5872 weeks
2572.01361 -.26904 (257*2π)/5872 weeks
2582.41312 .25706 (258*2π)/5872 weeks
2591.75235 1.37959 (259*2π)/5872 weeks
260.97508 .60636 (260*2π)/5872 weeks
2611.15685 .6995 (261*2π)/5872 weeks
262.33163 .13701 (262*2π)/5872 weeks
2631.25387 -1.13854 (263*2π)/5872 weeks
2642.82945 -.69739 (264*2π)/5872 weeks
2653.63777 .52725 (265*2π)/5872 weeks
2662.72389 2.91479 (266*2π)/5872 weeks
267-.18956 2.83364 (267*2π)/5872 weeks
268-1.31849 .22174 (268*2π)/5872 weeks
269-.11322 -1.72826 (269*2π)/5872 weeks
2702.14056 -2.45108 (270*2π)/5872 weeks
2714.63571 -1.02591 (271*2π)/5872 weeks
2724.59577 2.49049 (272*2π)/5872 weeks
2731.93045 4.61131 (273*2π)/5872 weeks
274-2.27782 3.31882 (274*2π)/5872 weeks
275-2.60901 -1.26752 (275*2π)/5872 weeks
276.61353 -3.17874 (276*2π)/5872 weeks
2773.50889 -2.31668 (277*2π)/5872 weeks
2784.82492 1.15022 (278*2π)/5872 weeks
2792.03391 3.84418 (279*2π)/5872 weeks
280-1.61435 2.34077 (280*2π)/5872 weeks
281-1.21612 -1.71168 (281*2π)/5872 weeks
2821.98156 -2.40049 (282*2π)/5872 weeks
2833.81066 -.54779 (283*2π)/5872 weeks
2843.66773 2.07009 (284*2π)/5872 weeks
2851.54982 3.79633 (285*2π)/5872 weeks
286-2.03517 2.87598 (286*2π)/5872 weeks
287-2.82461 -1.33106 (287*2π)/5872 weeks
288.84444 -3.34244 (288*2π)/5872 weeks
2893.42681 -1.20709 (289*2π)/5872 weeks
2903.0178 .82334 (290*2π)/5872 weeks
2911.65101 1.73678 (291*2π)/5872 weeks
292.61276 1.77013 (292*2π)/5872 weeks
293-1.06238 1.24056 (293*2π)/5872 weeks
294-1.06238 -1.24056 (294*2π)/5872 weeks
295.61276 -1.77013 (295*2π)/5872 weeks
2961.65101 -1.73678 (296*2π)/5872 weeks
2973.0178 -.82334 (297*2π)/5872 weeks
2983.42681 1.20709 (298*2π)/5872 weeks
299.84444 3.34244 (299*2π)/5872 weeks
300-2.82461 1.33106 (300*2π)/5872 weeks
301-2.03517 -2.87598 (301*2π)/5872 weeks
3021.54982 -3.79633 (302*2π)/5872 weeks
3033.66773 -2.07009 (303*2π)/5872 weeks
3043.81066 .54779 (304*2π)/5872 weeks
3051.98156 2.40049 (305*2π)/5872 weeks
306-1.21612 1.71168 (306*2π)/5872 weeks
307-1.61435 -2.34077 (307*2π)/5872 weeks
3082.03391 -3.84418 (308*2π)/5872 weeks
3094.82492 -1.15022 (309*2π)/5872 weeks
3103.50889 2.31668 (310*2π)/5872 weeks
311.61353 3.17874 (311*2π)/5872 weeks
312-2.60901 1.26752 (312*2π)/5872 weeks
313-2.27782 -3.31882 (313*2π)/5872 weeks
3141.93045 -4.61131 (314*2π)/5872 weeks
3154.59577 -2.49049 (315*2π)/5872 weeks
3164.63571 1.02591 (316*2π)/5872 weeks
3172.14056 2.45108 (317*2π)/5872 weeks
318-.11322 1.72826 (318*2π)/5872 weeks
319-1.31849 -.22174 (319*2π)/5872 weeks
320-.18956 -2.83364 (320*2π)/5872 weeks
3212.72389 -2.91479 (321*2π)/5872 weeks
3223.63777 -.52725 (322*2π)/5872 weeks
3232.82945 .69739 (323*2π)/5872 weeks
3241.25387 1.13854 (324*2π)/5872 weeks
325.33163 -.13701 (325*2π)/5872 weeks
3261.15685 -.6995 (326*2π)/5872 weeks
327.97508 -.60636 (327*2π)/5872 weeks
3281.75235 -1.37959 (328*2π)/5872 weeks
3292.41312 -.25706 (329*2π)/5872 weeks
3302.01361 .26904 (330*2π)/5872 weeks
331.81298 1.26538 (331*2π)/5872 weeks
332-1.16582 -.85643 (332*2π)/5872 weeks
333.3603 -2.58827 (333*2π)/5872 weeks
3342.05134 -3.3233 (334*2π)/5872 weeks
3354.57185 -2.11355 (335*2π)/5872 weeks
3364.48612 1.19633 (336*2π)/5872 weeks
3371.72813 2.18186 (337*2π)/5872 weeks
338-.13117 .80496 (338*2π)/5872 weeks
339-.10501 -1.59634 (339*2π)/5872 weeks
3402.18 -2.5229 (340*2π)/5872 weeks
3413.40395 -.97326 (341*2π)/5872 weeks
3423.09703 .6067 (342*2π)/5872 weeks
3431.79443 1.4436 (343*2π)/5872 weeks
344.00784 -.01367 (344*2π)/5872 weeks
3451.30382 -1.86989 (345*2π)/5872 weeks
3463.00711 -1.31136 (346*2π)/5872 weeks
3473.87245 .57671 (347*2π)/5872 weeks
3481.71912 2.40587 (348*2π)/5872 weeks
349-.24546 .79537 (349*2π)/5872 weeks
350.31575 -.66614 (350*2π)/5872 weeks
351.87707 -1.29135 (351*2π)/5872 weeks
3522.34306 -1.29108 (352*2π)/5872 weeks
3532.67029 .68222 (353*2π)/5872 weeks
354.14923 1.22837 (354*2π)/5872 weeks
355-.7883 -1.57231 (355*2π)/5872 weeks
3561.92812 -3.30509 (356*2π)/5872 weeks
3574.54565 -1.38288 (357*2π)/5872 weeks
3583.94951 1.87146 (358*2π)/5872 weeks
359.65352 2.5495 (359*2π)/5872 weeks
360-.75649 .30547 (360*2π)/5872 weeks
361-.05768 -1.4318 (361*2π)/5872 weeks
3621.51583 -2.2526 (362*2π)/5872 weeks
3633.22258 -.69635 (363*2π)/5872 weeks
3641.80834 1.38962 (364*2π)/5872 weeks
365-.45921 .36483 (365*2π)/5872 weeks
366-.45908 -2.14726 (366*2π)/5872 weeks
3672.09927 -3.29099 (367*2π)/5872 weeks
3684.11033 -1.45398 (368*2π)/5872 weeks
3693.11235 .31868 (369*2π)/5872 weeks
3702.69399 .49903 (370*2π)/5872 weeks
3711.45054 1.18171 (371*2π)/5872 weeks
3721.17862 -.59065 (372*2π)/5872 weeks
3732.28368 .11898 (373*2π)/5872 weeks
3741.66198 .30396 (374*2π)/5872 weeks
3751.89526 .56173 (375*2π)/5872 weeks
3761.11107 1.34906 (376*2π)/5872 weeks
377.06698 1.04661 (377*2π)/5872 weeks
378-1.43893 .445 (378*2π)/5872 weeks
379-1.14521 -2.69551 (379*2π)/5872 weeks
3801.35987 -2.79485 (380*2π)/5872 weeks
3811.71697 -2.33054 (381*2π)/5872 weeks
3823.07418 -2.03395 (382*2π)/5872 weeks
3833.48226 -.50081 (383*2π)/5872 weeks
3842.84919 .85346 (384*2π)/5872 weeks
385.84112 1.30627 (385*2π)/5872 weeks
386-.08977 -.56646 (386*2π)/5872 weeks
3871.30686 -1.67578 (387*2π)/5872 weeks
3882.26997 -1.01838 (388*2π)/5872 weeks
3892.86895 .20277 (389*2π)/5872 weeks
3901.14432 1.69246 (390*2π)/5872 weeks
391-.8377 .30232 (391*2π)/5872 weeks
392-.95955 -2.05923 (392*2π)/5871 weeks
3931.64895 -3.50416 (393*2π)/5871 weeks
3944.11418 -1.61489 (394*2π)/5871 weeks
3953.5972 1.27877 (395*2π)/5871 weeks
396.65215 2.50674 (396*2π)/5871 weeks
397-1.71261 .4532 (397*2π)/5871 weeks
398-1.51297 -2.23996 (398*2π)/5871 weeks
399.78293 -3.93138 (399*2π)/5871 weeks
4003.42953 -3.09212 (400*2π)/5871 weeks
4014.09571 -.42959 (401*2π)/5871 weeks
4022.3019 1.49834 (402*2π)/5871 weeks
403.028 .91691 (403*2π)/5871 weeks
404-.56875 -1.29719 (404*2π)/5871 weeks
405.57532 -3.0135 (405*2π)/5871 weeks
4063.30242 -3.05744 (406*2π)/5871 weeks
4074.65216 -.36561 (407*2π)/5871 weeks
4082.9998 2.27601 (408*2π)/5871 weeks
409-.18111 2.1174 (409*2π)/5871 weeks
410-1.24961 -.37427 (410*2π)/5871 weeks
411-.33706 -2.35716 (411*2π)/5871 weeks
4122.13856 -2.65891 (412*2π)/5871 weeks
4132.71506 -.80598 (413*2π)/5871 weeks
4141.90748 .04341 (414*2π)/5871 weeks
4151.20459 -.03131 (415*2π)/5871 weeks
4161.00379 .00728 (416*2π)/5871 weeks
417-.23065 -.34449 (417*2π)/5871 weeks
418.45995 -2.43742 (418*2π)/5871 weeks
4192.41947 -1.40095 (419*2π)/5871 weeks
4201.93008 -.20885 (420*2π)/5871 weeks
4211.20787 -.10684 (421*2π)/5871 weeks
422.54886 -.08843 (422*2π)/5871 weeks
423-.32723 -.64745 (423*2π)/5871 weeks
424-.50747 -1.79545 (424*2π)/5871 weeks
425.81429 -3.69318 (425*2π)/5871 weeks
4263.88002 -2.39296 (426*2π)/5871 weeks
4273.00066 .68544 (427*2π)/5871 weeks
428.54292 1.15608 (428*2π)/5871 weeks
429-1.66406 -.58204 (429*2π)/5871 weeks
430-.3765 -3.96068 (430*2π)/5871 weeks
4312.87416 -3.89907 (431*2π)/5871 weeks
4324.2884 -1.03486 (432*2π)/5871 weeks
4332.21605 1.87658 (433*2π)/5871 weeks
434-1.15776 .21867 (434*2π)/5871 weeks
435.00483 -3.31577 (435*2π)/5871 weeks
4362.50726 -2.56807 (436*2π)/5871 weeks
4372.69318 -1.31563 (437*2π)/5871 weeks
4382.42679 .26207 (438*2π)/5871 weeks
439.95395 .09792 (439*2π)/5871 weeks
4401.20095 .0555 (440*2π)/5871 weeks
441-.56304 .43516 (441*2π)/5871 weeks
442-1.64606 -1.59221 (442*2π)/5871 weeks
443-.54217 -3.00356 (443*2π)/5871 weeks
444.91598 -4.02637 (444*2π)/5871 weeks
4452.75863 -3.06915 (445*2π)/5871 weeks
4462.09495 -1.08986 (446*2π)/5871 weeks
447.79712 -1.4628 (447*2π)/5871 weeks
4481.33789 -2.58355 (448*2π)/5871 weeks
4492.40689 -2.31728 (449*2π)/5871 weeks
4502.61901 -1.18874 (450*2π)/5871 weeks
4512.00343 -.66975 (451*2π)/5871 weeks
4521.21271 -.01612 (452*2π)/5871 weeks
453-.33891 -.17957 (453*2π)/5871 weeks
454-1.28291 -2.1501 (454*2π)/5871 weeks
455-.13786 -4.99715 (455*2π)/5871 weeks
4563.80903 -4.76379 (456*2π)/5871 weeks
4574.99433 -1.07383 (457*2π)/5871 weeks
4582.28097 1.46946 (458*2π)/5871 weeks
459-.30857 .14136 (459*2π)/5871 weeks
460-.90377 -2.5029 (460*2π)/5871 weeks
461.85044 -3.96944 (461*2π)/5871 weeks
4622.88079 -3.67919 (462*2π)/5871 weeks
4634.86651 -1.22251 (463*2π)/5871 weeks
4642.93768 2.62037 (464*2π)/5871 weeks
465-2.37112 1.91661 (465*2π)/5871 weeks
466-3.5753 -2.59891 (466*2π)/5871 weeks
467-2.01092 -5.82742 (467*2π)/5871 weeks
4682.31491 -7.61409 (468*2π)/5871 weeks
4696.78809 -4.26324 (469*2π)/5871 weeks
4705.62831 1.42158 (470*2π)/5871 weeks
471-.49857 3.00725 (471*2π)/5871 weeks
472-3.92763 -1.98723 (472*2π)/5871 weeks
473-1.53199 -6.57825 (473*2π)/5871 weeks
4743.38938 -8.23893 (474*2π)/5871 weeks
4757.46876 -4.26603 (475*2π)/5871 weeks
4766.70939 .85622 (476*2π)/5871 weeks
4771.65413 3.29186 (477*2π)/5871 weeks
478-2.39944 -.5583 (478*2π)/5871 weeks
479-.66056 -5.25279 (479*2π)/5871 weeks
4803.58014 -5.90517 (480*2π)/5871 weeks
4816.18919 -2.38513 (481*2π)/5871 weeks
4824.75521 1.19256 (482*2π)/5871 weeks
4831.25515 1.67701 (483*2π)/5871 weeks
484-.46433 -.6222 (484*2π)/5871 weeks
485.51729 -2.6074 (485*2π)/5871 weeks
4862.20987 -1.39287 (486*2π)/5871 weeks
487.09321 -.25528 (487*2π)/5871 weeks
488-.4278 -2.70881 (488*2π)/5871 weeks
4891.62392 -3.30714 (489*2π)/5871 weeks
4902.15652 -1.69801 (490*2π)/5871 weeks
491.39234 -.5469 (491*2π)/5871 weeks
492-2.53444 -2.18425 (492*2π)/5871 weeks
493-2.30127 -6.67868 (493*2π)/5871 weeks
4943.14074 -9.18204 (494*2π)/5871 weeks
4958.54845 -5.68894 (495*2π)/5871 weeks
4968.10523 1.64068 (496*2π)/5871 weeks
4971.08058 3.89503 (497*2π)/5871 weeks
498-2.70264 .21668 (498*2π)/5871 weeks
499-3.48066 -4.58785 (499*2π)/5871 weeks
5001.3881 -8.78596 (500*2π)/5871 weeks
5017.10222 -5.80371 (501*2π)/5871 weeks
5027.9719 -.40259 (502*2π)/5871 weeks
5032.95956 4.81566 (503*2π)/5871 weeks
504-4.01373 .7436 (504*2π)/5871 weeks
505-1.51544 -5.47129 (505*2π)/5871 weeks
5061.06448 -5.70468 (506*2π)/5871 weeks
5075.44076 -6.60637 (507*2π)/5871 weeks
5088.53891 .25676 (508*2π)/5871 weeks
5092.25138 5.20953 (509*2π)/5871 weeks
510-4.08416 3.0175 (510*2π)/5871 weeks
511-6.11785 -4.07547 (511*2π)/5871 weeks
512-.28363 -8.8564 (512*2π)/5871 weeks
5134.07218 -4.86508 (513*2π)/5871 weeks
5141.53687 -2.41399 (514*2π)/5871 weeks
515.49743 -3.65597 (515*2π)/5871 weeks
516.03564 -6.47701 (516*2π)/5871 weeks
5175.67432 -7.52382 (517*2π)/5871 weeks
5188.60881 -2.04602 (518*2π)/5871 weeks
5194.61483 2.82681 (519*2π)/5871 weeks
520-.83398 2.84612 (520*2π)/5871 weeks
521-4.05974 -3.26206 (521*2π)/5871 weeks
5221.19171 -6.84689 (522*2π)/5871 weeks
5233.87415 -3.25061 (523*2π)/5871 weeks
5242.39933 -.34596 (524*2π)/5871 weeks
525-1.94217 -.79806 (525*2π)/5871 weeks
526-2.98342 -5.8818 (526*2π)/5871 weeks
5273.11239 -9.45387 (527*2π)/5871 weeks
5286.86177 -3.59987 (528*2π)/5871 weeks
5293.18901 .23673 (529*2π)/5871 weeks
530.41532 -.64486 (530*2π)/5871 weeks
531-1.11519 -2.3371 (531*2π)/5871 weeks
532-.13818 -5.16488 (532*2π)/5871 weeks
5332.59763 -4.30221 (533*2π)/5871 weeks
5342.8945 -2.17626 (534*2π)/5871 weeks
535-.45094 -.02903 (535*2π)/5871 weeks
536-2.7575 -2.37868 (536*2π)/5871 weeks
537-4.01533 -6.59187 (537*2π)/5871 weeks
538.47519 -9.02745 (538*2π)/5871 weeks
5392.74616 -5.56575 (539*2π)/5871 weeks
540.75133 -4.281 (540*2π)/5871 weeks
541-1.96811 -5.09089 (541*2π)/5871 weeks
542.07146 -11.38733 (542*2π)/5871 weeks
5437.44213 -8.6661 (543*2π)/5871 weeks
5445.37041 -1.49019 (544*2π)/5871 weeks
545.26264 -.5425 (545*2π)/5871 weeks
546-4.35953 -3.61368 (546*2π)/5871 weeks
547-4.87751 -11.44399 (547*2π)/5871 weeks
5484.86903 -16.22793 (548*2π)/5871 weeks
54913.84474 -9.08389 (549*2π)/5871 weeks
55014.11383 5.09442 (550*2π)/5871 weeks
551-3.40429 14.38456 (551*2π)/5871 weeks
552-19.83254 -1.04824 (552*2π)/5871 weeks
553-13.48266 -21.41146 (553*2π)/5871 weeks
5545.14125 -26.35722 (554*2π)/5871 weeks
55519.22283 -11.15127 (555*2π)/5871 weeks
55612.0898 6.80528 (556*2π)/5871 weeks
557-5.59316 6.76525 (557*2π)/5871 weeks
558-14.18802 -4.6907 (558*2π)/5871 weeks
559-11.69996 -19.73451 (559*2π)/5871 weeks
5603.20555 -21.97319 (560*2π)/5871 weeks
5618.68809 -13.30657 (561*2π)/5871 weeks
5625.90017 -6.72727 (562*2π)/5871 weeks
563-2.35448 -9.11537 (563*2π)/5871 weeks
564-.55548 -14.8675 (564*2π)/5871 weeks
5654.00259 -15.83193 (565*2π)/5871 weeks
5665.07598 -13.8315 (566*2π)/5871 weeks
5677.33646 -15.99243 (567*2π)/5871 weeks
56810.32508 -8.4763 (568*2π)/5871 weeks
5691.5507 -7.37284 (569*2π)/5871 weeks
5703.75184 -9.73367 (570*2π)/5871 weeks
571-.24772 -5.87649 (571*2π)/5871 weeks
572-9.46362 -9.69398 (572*2π)/5871 weeks
573-16.55037 -24.76424 (573*2π)/5871 weeks
574-.31667 -45.9142 (574*2π)/5871 weeks
57527.23774 -33.90795 (575*2π)/5871 weeks
57625.1368 -12.15214 (576*2π)/5871 weeks
57715.42252 2.60222 (577*2π)/5871 weeks
578-19.738 1.8401 (578*2π)/5871 weeks
579-31.68399 -43.91161 (579*2π)/5871 weeks
5807.07729 -64.29347 (580*2π)/5871 weeks
58138.58851 -42.12098 (581*2π)/5871 weeks
58223.47151 -6.74897 (582*2π)/5871 weeks
583-34.42955 -6.28139 (583*2π)/5871 weeks
584-89.98292 -95.93355 (584*2π)/5871 weeks
585-28.63351 -235.1535 (585*2π)/5871 weeks



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