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Fourier Analysis of EEV (ProShares UltraShort MSCI Emerg)


EEV (ProShares UltraShort MSCI Emerg) appears to have interesting cyclic behaviour every 41 weeks (20.8545*sine), 45 weeks (18.7458*sine), and 49 weeks (14.2954*sine).

EEV (ProShares UltraShort MSCI Emerg) has an average price of 85.4 (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 11/1/2007 to 3/20/2017 for EEV (ProShares UltraShort MSCI Emerg), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
085.40417   0 
194.3875 64.38081 (1*2π)/491491 weeks
247.67379 80.62131 (2*2π)/491246 weeks
35.84409 73.25912 (3*2π)/491164 weeks
4-17.86879 50.66785 (4*2π)/491123 weeks
5-23.56895 26.90353 (5*2π)/49198 weeks
6-15.84403 5.83386 (6*2π)/49182 weeks
7-.81532 -1.04498 (7*2π)/49170 weeks
89.26473 2.27709 (8*2π)/49161 weeks
912.60199 7.24315 (9*2π)/49155 weeks
1012.78207 14.2954 (10*2π)/49149 weeks
117.45556 18.74575 (11*2π)/49145 weeks
123.30789 20.85451 (12*2π)/49141 weeks
13-3.62609 18.31236 (13*2π)/49138 weeks
14-6.95203 14.65622 (14*2π)/49135 weeks
15-9.47613 11.00443 (15*2π)/49133 weeks
16-9.44836 4.15538 (16*2π)/49131 weeks
17-6.23935 .24516 (17*2π)/49129 weeks
18-1.81886 -2.7878 (18*2π)/49127 weeks
192.68271 -2.21862 (19*2π)/49126 weeks
206.45919 1.11827 (20*2π)/49125 weeks
217.02289 6.57888 (21*2π)/49123 weeks
223.7139 10.10222 (22*2π)/49122 weeks
23-1.03464 10.38504 (23*2π)/49121 weeks
24-4.64107 5.95814 (24*2π)/49120 weeks
25-4.8884 1.48318 (25*2π)/49120 weeks
26-2.17538 -2.72464 (26*2π)/49119 weeks
272.63031 -3.23755 (27*2π)/49118 weeks
286.74167 -1.0335 (28*2π)/49118 weeks
298.65576 3.90329 (29*2π)/49117 weeks
306.35531 8.51524 (30*2π)/49116 weeks
312.3876 9.37627 (31*2π)/49116 weeks
32-1.03866 8.63466 (32*2π)/49115 weeks
33-3.15427 5.83548 (33*2π)/49115 weeks
34-3.44653 3.34994 (34*2π)/49114 weeks
35-2.83322 .75695 (35*2π)/49114 weeks
36-.34225 -1.05637 (36*2π)/49114 weeks
372.16669 -.16306 (37*2π)/49113 weeks
382.76441 .69988 (38*2π)/49113 weeks
393.55249 2.07473 (39*2π)/49113 weeks
403.28472 3.5701 (40*2π)/49112 weeks
412.6086 4.70548 (41*2π)/49112 weeks
421.00669 4.8611 (42*2π)/49112 weeks
43-.18968 3.74913 (43*2π)/49111 weeks
44-1.03258 2.92056 (44*2π)/49111 weeks
45-.30584 1.50955 (45*2π)/49111 weeks
46.43458 .90891 (46*2π)/49111 weeks
471.83521 .48143 (47*2π)/49110 weeks
483.20876 1.06097 (48*2π)/49110 weeks
493.93607 2.74513 (49*2π)/49110 weeks
503.74439 4.50879 (50*2π)/49110 weeks
511.71393 5.85954 (51*2π)/49110 weeks
52-.33307 5.79177 (52*2π)/4919 weeks
53-1.82468 4.31379 (53*2π)/4919 weeks
54-2.33955 2.38005 (54*2π)/4919 weeks
55-1.06619 .57818 (55*2π)/4919 weeks
56.31723 .43025 (56*2π)/4919 weeks
571.45044 .73771 (57*2π)/4919 weeks
582.04259 1.8371 (58*2π)/4918 weeks
591.67744 2.69302 (59*2π)/4918 weeks
601.5693 3.43689 (60*2π)/4918 weeks
61.53956 3.91988 (61*2π)/4918 weeks
62-.0801 3.95886 (62*2π)/4918 weeks
63-1.60171 4.00503 (63*2π)/4918 weeks
64-2.99112 2.60637 (64*2π)/4918 weeks
65-3.11392 .42802 (65*2π)/4918 weeks
66-1.9593 -1.74141 (66*2π)/4917 weeks
67.54884 -2.36813 (67*2π)/4917 weeks
682.60509 -1.37847 (68*2π)/4917 weeks
693.86201 -.09085 (69*2π)/4917 weeks
704.2837 2.66135 (70*2π)/4917 weeks
712.18034 4.51114 (71*2π)/4917 weeks
72.03381 4.62189 (72*2π)/4917 weeks
73-2.28499 3.49148 (73*2π)/4917 weeks
74-2.52448 .76936 (74*2π)/4917 weeks
75-1.52333 -1.01082 (75*2π)/4917 weeks
76.46906 -2.28016 (76*2π)/4916 weeks
773.01409 -1.50825 (77*2π)/4916 weeks
784.37303 .32172 (78*2π)/4916 weeks
794.21728 2.72561 (79*2π)/4916 weeks
802.55265 4.62158 (80*2π)/4916 weeks
81.2432 4.82051 (81*2π)/4916 weeks
82-1.45767 3.85038 (82*2π)/4916 weeks
83-2.05493 2.14794 (83*2π)/4916 weeks
84-1.59629 .7155 (84*2π)/4916 weeks
85-1.04327 -.11557 (85*2π)/4916 weeks
86.25879 -.70515 (86*2π)/4916 weeks
871.42731 -.59914 (87*2π)/4916 weeks
882.25739 .27798 (88*2π)/4916 weeks
892.39606 1.53592 (89*2π)/4916 weeks
901.72286 2.69268 (90*2π)/4915 weeks
91.61918 3.37397 (91*2π)/4915 weeks
92-.65113 3.3004 (92*2π)/4915 weeks
93-1.68698 2.21876 (93*2π)/4915 weeks
94-1.938 .6982 (94*2π)/4915 weeks
95-1.33294 -.8271 (95*2π)/4915 weeks
96-.09216 -1.646 (96*2π)/4915 weeks
971.64163 -1.53215 (97*2π)/4915 weeks
982.93114 -.27881 (98*2π)/4915 weeks
993.31222 1.56075 (99*2π)/4915 weeks
1002.35697 3.02424 (100*2π)/4915 weeks
101.84491 3.47111 (101*2π)/4915 weeks
102-.82228 3.17943 (102*2π)/4915 weeks
103-1.87071 1.54549 (103*2π)/4915 weeks
104-1.62915 .03908 (104*2π)/4915 weeks
105-.50582 -.89769 (105*2π)/4915 weeks
106.92191 -1.05988 (106*2π)/4915 weeks
1072.11668 -.2375 (107*2π)/4915 weeks
1082.46261 1.00372 (108*2π)/4915 weeks
1091.88285 2.28632 (109*2π)/4915 weeks
110.50701 2.75318 (110*2π)/4914 weeks
111-.64241 2.01737 (111*2π)/4914 weeks
112-1.08659 1.18225 (112*2π)/4914 weeks
113-.7359 .15748 (113*2π)/4914 weeks
114.08146 .01905 (114*2π)/4914 weeks
115.45669 .16266 (115*2π)/4914 weeks
116.68017 .43024 (116*2π)/4914 weeks
117.63489 .81666 (117*2π)/4914 weeks
118.25517 .91828 (118*2π)/4914 weeks
119-.11583 .49358 (119*2π)/4914 weeks
120-.07011 -.0269 (120*2π)/4914 weeks
121.35447 -.13809 (121*2π)/4914 weeks
122.90423 -.1431 (122*2π)/4914 weeks
1231.2521 .43079 (123*2π)/4914 weeks
124.80136 .70015 (124*2π)/4914 weeks
125.58895 .52743 (125*2π)/4914 weeks
126.55081 .42677 (126*2π)/4914 weeks
127.70587 .26887 (127*2π)/4914 weeks
128.74712 .61322 (128*2π)/4914 weeks
129.40573 .56233 (129*2π)/4914 weeks
130.47622 .27921 (130*2π)/4914 weeks
131.54908 .02639 (131*2π)/4914 weeks
1321.00866 -.29324 (132*2π)/4914 weeks
1331.41197 .10291 (133*2π)/4914 weeks
1341.6477 .49274 (134*2π)/4914 weeks
1351.46753 1.21466 (135*2π)/4914 weeks
136.87135 1.43594 (136*2π)/4914 weeks
137.4557 1.36263 (137*2π)/4914 weeks
138-.05301 1.08844 (138*2π)/4914 weeks
139-.20633 .48839 (139*2π)/4914 weeks
140-.08681 -.17237 (140*2π)/4914 weeks
141.42039 -.68254 (141*2π)/4913 weeks
1421.41627 -.47878 (142*2π)/4913 weeks
1431.70241 .07341 (143*2π)/4913 weeks
1441.92618 .61257 (144*2π)/4913 weeks
1451.76984 1.36207 (145*2π)/4913 weeks
1461.05318 1.93614 (146*2π)/4913 weeks
147-.05687 1.86586 (147*2π)/4913 weeks
148-.78597 1.11324 (148*2π)/4913 weeks
149-.88804 .03626 (149*2π)/4913 weeks
150-.26255 -.84832 (150*2π)/4913 weeks
151.62604 -1.06892 (151*2π)/4913 weeks
1521.56312 -.88241 (152*2π)/4913 weeks
1532.13127 -.13317 (153*2π)/4913 weeks
1542.18991 .96846 (154*2π)/4913 weeks
1551.58593 1.70114 (155*2π)/4913 weeks
156.62566 2.00606 (156*2π)/4913 weeks
157-.36785 1.55366 (157*2π)/4913 weeks
158-.97772 .68715 (158*2π)/4913 weeks
159-.94773 -.50148 (159*2π)/4913 weeks
160-.10796 -1.35035 (160*2π)/4913 weeks
161.98568 -1.56133 (161*2π)/4913 weeks
1622.03055 -1.0812 (162*2π)/4913 weeks
1632.55199 -.09646 (163*2π)/4913 weeks
1642.42891 .80104 (164*2π)/4913 weeks
1651.69525 1.51767 (165*2π)/4913 weeks
166.85916 1.58574 (166*2π)/4913 weeks
167.12502 1.1856 (167*2π)/4913 weeks
168-.07061 .28732 (168*2π)/4913 weeks
169.48214 -.37159 (169*2π)/4913 weeks
1701.17823 -.66585 (170*2π)/4913 weeks
1711.97678 -.35297 (171*2π)/4913 weeks
1722.42708 .48155 (172*2π)/4913 weeks
1732.48901 1.40088 (173*2π)/4913 weeks
1741.78104 2.37504 (174*2π)/4913 weeks
175.48131 2.35337 (175*2π)/4913 weeks
176-.35869 1.84762 (176*2π)/4913 weeks
177-.78246 .92632 (177*2π)/4913 weeks
178-.45696 .04801 (178*2π)/4913 weeks
179.11592 -.37477 (179*2π)/4913 weeks
1801.04883 -.64843 (180*2π)/4913 weeks
1811.79301 .06316 (181*2π)/4913 weeks
1821.89449 .70546 (182*2π)/4913 weeks
1831.80152 1.63449 (183*2π)/4913 weeks
184.85257 2.31266 (184*2π)/4913 weeks
185-.29538 2.20694 (185*2π)/4913 weeks
186-1.10132 1.3592 (186*2π)/4913 weeks
187-1.09055 .13682 (187*2π)/4913 weeks
188-.42443 -.54801 (188*2π)/4913 weeks
189.44027 -.80362 (189*2π)/4913 weeks
1901.19814 -.47105 (190*2π)/4913 weeks
1911.52884 .4942 (191*2π)/4913 weeks
1921.29477 1.00921 (192*2π)/4913 weeks
193.6309 1.38556 (193*2π)/4913 weeks
194.08555 1.14724 (194*2π)/4913 weeks
195-.17376 1.03767 (195*2π)/4913 weeks
196-.46548 .81539 (196*2π)/4913 weeks
197-.71609 .25164 (197*2π)/4912 weeks
198-.5777 -.47377 (198*2π)/4912 weeks
199.01622 -.88951 (199*2π)/4912 weeks
200.59872 -.98696 (200*2π)/4912 weeks
2011.40476 -.71757 (201*2π)/4912 weeks
2021.78538 .1127 (202*2π)/4912 weeks
2031.55962 1.06162 (203*2π)/4912 weeks
204.7274 1.72624 (204*2π)/4912 weeks
205-.34381 1.45184 (205*2π)/4912 weeks
206-1.04524 .65222 (206*2π)/4912 weeks
207-1.21219 -.44645 (207*2π)/4912 weeks
208-.65191 -1.42196 (208*2π)/4912 weeks
209.46603 -1.87776 (209*2π)/4912 weeks
2101.6685 -1.72233 (210*2π)/4912 weeks
2112.58055 -.7329 (211*2π)/4912 weeks
2122.65496 .52932 (212*2π)/4912 weeks
2131.99903 1.66157 (213*2π)/4912 weeks
214.62838 2.19369 (214*2π)/4912 weeks
215-.52788 1.65945 (215*2π)/4912 weeks
216-1.24405 .72621 (216*2π)/4912 weeks
217-1.09818 -.75368 (217*2π)/4912 weeks
218-.14961 -1.61051 (218*2π)/4912 weeks
2191.00163 -1.88295 (219*2π)/4912 weeks
2202.35013 -1.34175 (220*2π)/4912 weeks
2213.10636 .10577 (221*2π)/4912 weeks
2222.89792 1.56486 (222*2π)/4912 weeks
2231.72213 2.76329 (223*2π)/4912 weeks
224.06764 2.98769 (224*2π)/4912 weeks
225-1.3761 2.2159 (225*2π)/4912 weeks
226-2.26104 .79613 (226*2π)/4912 weeks
227-2.0813 -.81858 (227*2π)/4912 weeks
228-1.12276 -1.99212 (228*2π)/4912 weeks
229.53373 -2.56147 (229*2π)/4912 weeks
2302.20597 -1.78725 (230*2π)/4912 weeks
2312.83397 -.30109 (231*2π)/4912 weeks
2322.62218 1.19938 (232*2π)/4912 weeks
2331.34488 2.34683 (233*2π)/4912 weeks
234-.46089 2.28577 (234*2π)/4912 weeks
235-1.78943 .98141 (235*2π)/4912 weeks
236-1.90965 -.59809 (236*2π)/4912 weeks
237-1.04304 -1.95936 (237*2π)/4912 weeks
238.40468 -2.46945 (238*2π)/4912 weeks
2392.17396 -2.26466 (239*2π)/4912 weeks
2403.29165 -.75503 (240*2π)/4912 weeks
2413.03557 .99424 (241*2π)/4912 weeks
2421.96581 2.12368 (242*2π)/4912 weeks
243.44884 2.58356 (243*2π)/4912 weeks
244-.86802 2.12176 (244*2π)/4912 weeks
245-1.94747 .87778 (245*2π)/4912 weeks
246-1.94747 -.87778 (246*2π)/4912 weeks
247-.86802 -2.12176 (247*2π)/4912 weeks
248.44884 -2.58356 (248*2π)/4912 weeks
2491.96581 -2.12368 (249*2π)/4912 weeks
2503.03557 -.99424 (250*2π)/4912 weeks
2513.29165 .75503 (251*2π)/4912 weeks
2522.17396 2.26466 (252*2π)/4912 weeks
253.40468 2.46945 (253*2π)/4912 weeks
254-1.04304 1.95936 (254*2π)/4912 weeks
255-1.90965 .59809 (255*2π)/4912 weeks
256-1.78943 -.98141 (256*2π)/4912 weeks
257-.46089 -2.28577 (257*2π)/4912 weeks
2581.34488 -2.34683 (258*2π)/4912 weeks
2592.62218 -1.19938 (259*2π)/4912 weeks
2602.83397 .30109 (260*2π)/4912 weeks
2612.20597 1.78725 (261*2π)/4912 weeks
262.53373 2.56147 (262*2π)/4912 weeks
263-1.12276 1.99212 (263*2π)/4912 weeks
264-2.0813 .81858 (264*2π)/4912 weeks
265-2.26104 -.79613 (265*2π)/4912 weeks
266-1.3761 -2.2159 (266*2π)/4912 weeks
267.06764 -2.98769 (267*2π)/4912 weeks
2681.72213 -2.76329 (268*2π)/4912 weeks
2692.89792 -1.56486 (269*2π)/4912 weeks
2703.10636 -.10577 (270*2π)/4912 weeks
2712.35013 1.34175 (271*2π)/4912 weeks
2721.00163 1.88295 (272*2π)/4912 weeks
273-.14961 1.61051 (273*2π)/4912 weeks
274-1.09818 .75368 (274*2π)/4912 weeks
275-1.24405 -.72621 (275*2π)/4912 weeks
276-.52788 -1.65945 (276*2π)/4912 weeks
277.62838 -2.19369 (277*2π)/4912 weeks
2781.99903 -1.66157 (278*2π)/4912 weeks
2792.65496 -.52932 (279*2π)/4912 weeks
2802.58055 .7329 (280*2π)/4912 weeks
2811.6685 1.72233 (281*2π)/4912 weeks
282.46603 1.87776 (282*2π)/4912 weeks
283-.65191 1.42196 (283*2π)/4912 weeks
284-1.21219 .44645 (284*2π)/4912 weeks
285-1.04524 -.65222 (285*2π)/4912 weeks
286-.34381 -1.45184 (286*2π)/4912 weeks
287.7274 -1.72624 (287*2π)/4912 weeks
2881.55962 -1.06162 (288*2π)/4912 weeks
2891.78538 -.1127 (289*2π)/4912 weeks
2901.40476 .71757 (290*2π)/4912 weeks
291.59872 .98696 (291*2π)/4912 weeks
292.01622 .88951 (292*2π)/4912 weeks
293-.5777 .47377 (293*2π)/4912 weeks
294-.71609 -.25164 (294*2π)/4912 weeks
295-.46548 -.81539 (295*2π)/4912 weeks
296-.17376 -1.03767 (296*2π)/4912 weeks
297.08555 -1.14724 (297*2π)/4912 weeks
298.6309 -1.38556 (298*2π)/4912 weeks
2991.29477 -1.00921 (299*2π)/4912 weeks
3001.52884 -.4942 (300*2π)/4912 weeks
3011.19814 .47105 (301*2π)/4912 weeks
302.44027 .80362 (302*2π)/4912 weeks
303-.42443 .54801 (303*2π)/4912 weeks
304-1.09055 -.13682 (304*2π)/4912 weeks
305-1.10132 -1.3592 (305*2π)/4912 weeks
306-.29538 -2.20694 (306*2π)/4912 weeks
307.85257 -2.31266 (307*2π)/4912 weeks
3081.80152 -1.63449 (308*2π)/4912 weeks
3091.89449 -.70546 (309*2π)/4912 weeks
3101.79301 -.06316 (310*2π)/4912 weeks
3111.04883 .64843 (311*2π)/4912 weeks
312.11592 .37477 (312*2π)/4912 weeks
313-.45696 -.04801 (313*2π)/4912 weeks
314-.78246 -.92632 (314*2π)/4912 weeks
315-.35869 -1.84762 (315*2π)/4912 weeks
316.48131 -2.35337 (316*2π)/4912 weeks
3171.78104 -2.37504 (317*2π)/4912 weeks
3182.48901 -1.40088 (318*2π)/4912 weeks
3192.42708 -.48155 (319*2π)/4912 weeks
3201.97678 .35297 (320*2π)/4912 weeks
3211.17823 .66585 (321*2π)/4912 weeks
322.48214 .37159 (322*2π)/4912 weeks
323-.07061 -.28732 (323*2π)/4912 weeks
324.12502 -1.1856 (324*2π)/4912 weeks
325.85916 -1.58574 (325*2π)/4912 weeks
3261.69525 -1.51767 (326*2π)/4912 weeks
3272.42891 -.80104 (327*2π)/4912 weeks
3282.55199 .09646 (328*2π)/4911 weeks
3292.03055 1.0812 (329*2π)/4911 weeks
330.98568 1.56133 (330*2π)/4911 weeks
331-.10796 1.35035 (331*2π)/4911 weeks
332-.94773 .50148 (332*2π)/4911 weeks
333-.97772 -.68715 (333*2π)/4911 weeks
334-.36785 -1.55366 (334*2π)/4911 weeks
335.62566 -2.00606 (335*2π)/4911 weeks
3361.58593 -1.70114 (336*2π)/4911 weeks
3372.18991 -.96846 (337*2π)/4911 weeks
3382.13127 .13317 (338*2π)/4911 weeks
3391.56312 .88241 (339*2π)/4911 weeks
340.62604 1.06892 (340*2π)/4911 weeks
341-.26255 .84832 (341*2π)/4911 weeks
342-.88804 -.03626 (342*2π)/4911 weeks
343-.78597 -1.11324 (343*2π)/4911 weeks
344-.05687 -1.86586 (344*2π)/4911 weeks
3451.05318 -1.93614 (345*2π)/4911 weeks
3461.76984 -1.36207 (346*2π)/4911 weeks
3471.92618 -.61257 (347*2π)/4911 weeks
3481.70241 -.07341 (348*2π)/4911 weeks
3491.41627 .47878 (349*2π)/4911 weeks
350.42039 .68254 (350*2π)/4911 weeks
351-.08681 .17237 (351*2π)/4911 weeks
352-.20633 -.48839 (352*2π)/4911 weeks
353-.05301 -1.08844 (353*2π)/4911 weeks
354.4557 -1.36263 (354*2π)/4911 weeks
355.87135 -1.43594 (355*2π)/4911 weeks
3561.46753 -1.21466 (356*2π)/4911 weeks
3571.6477 -.49274 (357*2π)/4911 weeks
3581.41197 -.10291 (358*2π)/4911 weeks
3591.00866 .29324 (359*2π)/4911 weeks
360.54908 -.02639 (360*2π)/4911 weeks
361.47622 -.27921 (361*2π)/4911 weeks
362.40573 -.56233 (362*2π)/4911 weeks
363.74712 -.61322 (363*2π)/4911 weeks
364.70587 -.26887 (364*2π)/4911 weeks
365.55081 -.42677 (365*2π)/4911 weeks
366.58895 -.52743 (366*2π)/4911 weeks
367.80136 -.70015 (367*2π)/4911 weeks
3681.2521 -.43079 (368*2π)/4911 weeks
369.90423 .1431 (369*2π)/4911 weeks
370.35447 .13809 (370*2π)/4911 weeks
371-.07011 .0269 (371*2π)/4911 weeks
372-.11583 -.49358 (372*2π)/4911 weeks
373.25517 -.91828 (373*2π)/4911 weeks
374.63489 -.81666 (374*2π)/4911 weeks
375.68017 -.43024 (375*2π)/4911 weeks
376.45669 -.16266 (376*2π)/4911 weeks
377.08146 -.01905 (377*2π)/4911 weeks
378-.7359 -.15748 (378*2π)/4911 weeks
379-1.08659 -1.18225 (379*2π)/4911 weeks
380-.64241 -2.01737 (380*2π)/4911 weeks
381.50701 -2.75318 (381*2π)/4911 weeks
3821.88285 -2.28632 (382*2π)/4911 weeks
3832.46261 -1.00372 (383*2π)/4911 weeks
3842.11668 .2375 (384*2π)/4911 weeks
385.92191 1.05988 (385*2π)/4911 weeks
386-.50582 .89769 (386*2π)/4911 weeks
387-1.62915 -.03908 (387*2π)/4911 weeks
388-1.87071 -1.54549 (388*2π)/4911 weeks
389-.82228 -3.17943 (389*2π)/4911 weeks
390.84491 -3.47111 (390*2π)/4911 weeks
3912.35697 -3.02424 (391*2π)/4911 weeks
3923.31222 -1.56075 (392*2π)/4911 weeks
3932.93114 .27881 (393*2π)/4911 weeks
3941.64163 1.53215 (394*2π)/4911 weeks
395-.09216 1.646 (395*2π)/4911 weeks
396-1.33294 .8271 (396*2π)/4911 weeks
397-1.938 -.6982 (397*2π)/4911 weeks
398-1.68698 -2.21876 (398*2π)/4911 weeks
399-.65113 -3.3004 (399*2π)/4911 weeks
400.61918 -3.37397 (400*2π)/4911 weeks
4011.72286 -2.69268 (401*2π)/4911 weeks
4022.39606 -1.53592 (402*2π)/4911 weeks
4032.25739 -.27798 (403*2π)/4911 weeks
4041.42731 .59914 (404*2π)/4911 weeks
405.25879 .70515 (405*2π)/4911 weeks
406-1.04327 .11557 (406*2π)/4911 weeks
407-1.59629 -.7155 (407*2π)/4911 weeks
408-2.05493 -2.14794 (408*2π)/4911 weeks
409-1.45767 -3.85038 (409*2π)/4911 weeks
410.2432 -4.82051 (410*2π)/4911 weeks
4112.55265 -4.62158 (411*2π)/4911 weeks
4124.21728 -2.72561 (412*2π)/4911 weeks
4134.37303 -.32172 (413*2π)/4911 weeks
4143.01409 1.50825 (414*2π)/4911 weeks
415.46906 2.28016 (415*2π)/4911 weeks
416-1.52333 1.01082 (416*2π)/4911 weeks
417-2.52448 -.76936 (417*2π)/4911 weeks
418-2.28499 -3.49148 (418*2π)/4911 weeks
419.03381 -4.62189 (419*2π)/4911 weeks
4202.18034 -4.51114 (420*2π)/4911 weeks
4214.2837 -2.66135 (421*2π)/4911 weeks
4223.86201 .09085 (422*2π)/4911 weeks
4232.60509 1.37847 (423*2π)/4911 weeks
424.54884 2.36813 (424*2π)/4911 weeks
425-1.9593 1.74141 (425*2π)/4911 weeks
426-3.11392 -.42802 (426*2π)/4911 weeks
427-2.99112 -2.60637 (427*2π)/4911 weeks
428-1.60171 -4.00503 (428*2π)/4911 weeks
429-.0801 -3.95886 (429*2π)/4911 weeks
430.53956 -3.91988 (430*2π)/4911 weeks
4311.5693 -3.43689 (431*2π)/4911 weeks
4321.67744 -2.69302 (432*2π)/4911 weeks
4332.04259 -1.8371 (433*2π)/4911 weeks
4341.45044 -.73771 (434*2π)/4911 weeks
435.31723 -.43025 (435*2π)/4911 weeks
436-1.06619 -.57818 (436*2π)/4911 weeks
437-2.33955 -2.38005 (437*2π)/4911 weeks
438-1.82468 -4.31379 (438*2π)/4911 weeks
439-.33307 -5.79177 (439*2π)/4911 weeks
4401.71393 -5.85954 (440*2π)/4911 weeks
4413.74439 -4.50879 (441*2π)/4911 weeks
4423.93607 -2.74513 (442*2π)/4911 weeks
4433.20876 -1.06097 (443*2π)/4911 weeks
4441.83521 -.48143 (444*2π)/4911 weeks
445.43458 -.90891 (445*2π)/4911 weeks
446-.30584 -1.50955 (446*2π)/4911 weeks
447-1.03258 -2.92056 (447*2π)/4911 weeks
448-.18968 -3.74913 (448*2π)/4911 weeks
4491.00669 -4.8611 (449*2π)/4911 weeks
4502.6086 -4.70548 (450*2π)/4911 weeks
4513.28472 -3.5701 (451*2π)/4911 weeks
4523.55249 -2.07473 (452*2π)/4911 weeks
4532.76441 -.69988 (453*2π)/4911 weeks
4542.16669 .16306 (454*2π)/4911 weeks
455-.34225 1.05637 (455*2π)/4911 weeks
456-2.83322 -.75695 (456*2π)/4911 weeks
457-3.44653 -3.34994 (457*2π)/4911 weeks
458-3.15427 -5.83548 (458*2π)/4911 weeks
459-1.03866 -8.63466 (459*2π)/4911 weeks
4602.3876 -9.37627 (460*2π)/4911 weeks
4616.35531 -8.51524 (461*2π)/4911 weeks
4628.65576 -3.90329 (462*2π)/4911 weeks
4636.74167 1.0335 (463*2π)/4911 weeks
4642.63031 3.23755 (464*2π)/4911 weeks
465-2.17538 2.72464 (465*2π)/4911 weeks
466-4.8884 -1.48318 (466*2π)/4911 weeks
467-4.64107 -5.95814 (467*2π)/4911 weeks
468-1.03464 -10.38504 (468*2π)/4911 weeks
4693.7139 -10.10222 (469*2π)/4911 weeks
4707.02289 -6.57888 (470*2π)/4911 weeks
4716.45919 -1.11827 (471*2π)/4911 weeks
4722.68271 2.21862 (472*2π)/4911 weeks
473-1.81886 2.7878 (473*2π)/4911 weeks
474-6.23935 -.24516 (474*2π)/4911 weeks
475-9.44836 -4.15538 (475*2π)/4911 weeks
476-9.47613 -11.00443 (476*2π)/4911 weeks
477-6.95203 -14.65622 (477*2π)/4911 weeks
478-3.62609 -18.31236 (478*2π)/4911 weeks
4793.30789 -20.85451 (479*2π)/4911 weeks
4807.45556 -18.74575 (480*2π)/4911 weeks
48112.78207 -14.2954 (481*2π)/4911 weeks
48212.60199 -7.24315 (482*2π)/4911 weeks
4839.26473 -2.27709 (483*2π)/4911 weeks
484-.81532 1.04498 (484*2π)/4911 weeks
485-15.84403 -5.83386 (485*2π)/4911 weeks
486-23.56895 -26.90353 (486*2π)/4911 weeks
487-17.86879 -50.66785 (487*2π)/4911 weeks
4885.84409 -73.25912 (488*2π)/4911 weeks
48947.67379 -80.62131 (489*2π)/4911 weeks

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