Back to list of Stocks    See Also: Seasonal Analysis of EFUGenetic Algorithms Stock Portfolio Generator, and Fourier Calculator

Fourier Analysis of EFU (ProShares UltraShort MSCI EAFE)


EFU (ProShares UltraShort MSCI EAFE) appears to have interesting cyclic behaviour every 48 weeks (14.1045*sine), 44 weeks (8.9357*sine), and 17 weeks (7.4027*cosine).

EFU (ProShares UltraShort MSCI EAFE) has an average price of 126.02 (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 10/25/2007 to 1/17/2017 for EFU (ProShares UltraShort MSCI EAFE), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0126.0221   0 
159.74827 102.3337 (1*2π)/483483 weeks
28.80687 74.8186 (2*2π)/483242 weeks
3-27.61515 47.46392 (3*2π)/483161 weeks
4-26.92717 17.29826 (4*2π)/483121 weeks
5-20.50272 -2.92157 (5*2π)/48397 weeks
6.59886 -13.00715 (6*2π)/48381 weeks
716.88578 1.14093 (7*2π)/48369 weeks
812.24058 15.60174 (8*2π)/48360 weeks
94.0563 13.84949 (9*2π)/48354 weeks
10-.19836 14.10452 (10*2π)/48348 weeks
11-4.3284 8.9357 (11*2π)/48344 weeks
12-2.8976 8.30776 (12*2π)/48340 weeks
13-3.03545 4.38738 (13*2π)/48337 weeks
14-.59118 5.68842 (14*2π)/48335 weeks
15-5.72495 6.20947 (15*2π)/48332 weeks
16-4.57146 1.24801 (16*2π)/48330 weeks
17-3.40069 -.47962 (17*2π)/48328 weeks
18.58155 -1.24153 (18*2π)/48327 weeks
192.13619 -.99222 (19*2π)/48325 weeks
205.71414 1.47832 (20*2π)/48324 weeks
213.2527 6.0674 (21*2π)/48323 weeks
22-1.15098 7.761 (22*2π)/48322 weeks
23-6.9774 3.73982 (23*2π)/48321 weeks
24-4.15659 -1.75766 (24*2π)/48320 weeks
25-1.87965 -3.79658 (25*2π)/48319 weeks
264.38719 -3.91788 (26*2π)/48319 weeks
277.13436 .22768 (27*2π)/48318 weeks
287.4027 4.52904 (28*2π)/48317 weeks
293.37384 8.84333 (29*2π)/48317 weeks
30-3.37028 7.22305 (30*2π)/48316 weeks
31-3.87901 2.33205 (31*2π)/48316 weeks
32-2.14387 .04448 (32*2π)/48315 weeks
33.23508 .18394 (33*2π)/48315 weeks
34.02719 .26586 (34*2π)/48314 weeks
351.46714 -.21132 (35*2π)/48314 weeks
363.05141 2.22733 (36*2π)/48313 weeks
37-.12457 2.74198 (37*2π)/48313 weeks
38.6178 1.22982 (38*2π)/48313 weeks
39.69474 2.00753 (39*2π)/48312 weeks
401.14255 1.8062 (40*2π)/48312 weeks
41.70778 2.54669 (41*2π)/48312 weeks
42-.18135 1.29724 (42*2π)/48312 weeks
43.04225 2.23373 (43*2π)/48311 weeks
44-.19416 1.87323 (44*2π)/48311 weeks
45-.6154 1.07752 (45*2π)/48311 weeks
46.64271 .15627 (46*2π)/48311 weeks
471.47772 .26095 (47*2π)/48310 weeks
482.50778 1.61366 (48*2π)/48310 weeks
491.77862 3.37504 (49*2π)/48310 weeks
50-.61247 3.47837 (50*2π)/48310 weeks
51-1.98524 2.40854 (51*2π)/4839 weeks
52-1.527 .6846 (52*2π)/4839 weeks
53-1.13711 -.25299 (53*2π)/4839 weeks
54.98893 -.86685 (54*2π)/4839 weeks
551.28982 1.01364 (55*2π)/4839 weeks
561.0638 1.1252 (56*2π)/4839 weeks
57.57514 1.71132 (57*2π)/4838 weeks
58-.143 1.06387 (58*2π)/4838 weeks
59.77183 1.3832 (59*2π)/4838 weeks
60.41408 1.32911 (60*2π)/4838 weeks
61.57955 2.29334 (61*2π)/4838 weeks
62-1.23375 2.56485 (62*2π)/4838 weeks
63-2.66612 .88485 (63*2π)/4838 weeks
64-1.88643 -1.34474 (64*2π)/4838 weeks
65.30114 -2.48566 (65*2π)/4837 weeks
662.54456 -1.41904 (66*2π)/4837 weeks
672.38745 .35 (67*2π)/4837 weeks
683.73941 1.30173 (68*2π)/4837 weeks
691.82547 4.29364 (69*2π)/4837 weeks
70-1.31738 3.46555 (70*2π)/4837 weeks
71-2.36948 2.05656 (71*2π)/4837 weeks
72-2.58608 -.7899 (72*2π)/4837 weeks
73-.28779 -1.43081 (73*2π)/4837 weeks
74.65998 -1.84501 (74*2π)/4837 weeks
753.06389 -.69673 (75*2π)/4836 weeks
762.98924 1.6665 (76*2π)/4836 weeks
771.81459 3.32365 (77*2π)/4836 weeks
78-.16096 3.14123 (78*2π)/4836 weeks
79-1.58485 1.9615 (79*2π)/4836 weeks
80-1.34553 .14748 (80*2π)/4836 weeks
81-.31829 -.36034 (81*2π)/4836 weeks
82.43334 .01543 (82*2π)/4836 weeks
83.00611 .84359 (83*2π)/4836 weeks
84-.17151 -.05442 (84*2π)/4836 weeks
85.25228 -.226 (85*2π)/4836 weeks
86.9937 .0009 (86*2π)/4836 weeks
871.33091 .84783 (87*2π)/4836 weeks
881.17089 1.56612 (88*2π)/4835 weeks
89.50348 2.1752 (89*2π)/4835 weeks
90-.6053 1.86816 (90*2π)/4835 weeks
91-1.45964 .58085 (91*2π)/4835 weeks
92-1.11132 -.44943 (92*2π)/4835 weeks
93-.09781 -1.43669 (93*2π)/4835 weeks
94.87323 -1.14254 (94*2π)/4835 weeks
952.19612 -.50076 (95*2π)/4835 weeks
962.40686 1.52202 (96*2π)/4835 weeks
971.2562 2.44516 (97*2π)/4835 weeks
98-.08114 2.45809 (98*2π)/4835 weeks
99-.97718 1.616 (99*2π)/4835 weeks
100-1.71677 .84988 (100*2π)/4835 weeks
101-1.19545 -1.04846 (101*2π)/4835 weeks
102.06405 -1.20661 (102*2π)/4835 weeks
1031.03569 -.55798 (103*2π)/4835 weeks
1041.56058 -.03415 (104*2π)/4835 weeks
1051.41378 1.09322 (105*2π)/4835 weeks
106.83044 1.45886 (106*2π)/4835 weeks
107-.10864 1.56477 (107*2π)/4835 weeks
108-1.02198 .97439 (108*2π)/4834 weeks
109-.65009 -.32169 (109*2π)/4834 weeks
110-.24964 -.39822 (110*2π)/4834 weeks
111.08564 -.30232 (111*2π)/4834 weeks
112.36058 -.04468 (112*2π)/4834 weeks
113.37486 -.26353 (113*2π)/4834 weeks
114.95951 -.1282 (114*2π)/4834 weeks
115.47991 .60278 (115*2π)/4834 weeks
116.20096 .21053 (116*2π)/4834 weeks
117.58267 -.22465 (117*2π)/4834 weeks
118.94469 -.15898 (118*2π)/4834 weeks
119.80019 .19371 (119*2π)/4834 weeks
120.94489 .60623 (120*2π)/4834 weeks
121.2592 1.15896 (121*2π)/4834 weeks
122-.12342 .26502 (122*2π)/4834 weeks
123.33157 .00168 (123*2π)/4834 weeks
124.82759 -.31971 (124*2π)/4834 weeks
1251.15202 .63788 (125*2π)/4834 weeks
126.18327 .56702 (126*2π)/4834 weeks
127.5707 -.13257 (127*2π)/4834 weeks
128.76721 .3609 (128*2π)/4834 weeks
129.78906 .55513 (129*2π)/4834 weeks
130.61994 1.05479 (130*2π)/4834 weeks
131.21537 .68919 (131*2π)/4834 weeks
132-.00522 .95928 (132*2π)/4834 weeks
133-.59243 .02956 (133*2π)/4834 weeks
134.32016 -.51883 (134*2π)/4834 weeks
135.74712 -.06622 (135*2π)/4834 weeks
136.68685 .26998 (136*2π)/4834 weeks
137.43536 .2491 (137*2π)/4834 weeks
138.73058 .22194 (138*2π)/4834 weeks
139.90069 1.00068 (139*2π)/4833 weeks
140-.23225 .7954 (140*2π)/4833 weeks
141.15931 .19911 (141*2π)/4833 weeks
142.29619 .42213 (142*2π)/4833 weeks
143.06532 .51315 (143*2π)/4833 weeks
144-.45679 .05546 (144*2π)/4833 weeks
145.2511 -.27552 (145*2π)/4833 weeks
146.28972 -.43596 (146*2π)/4833 weeks
1471.12373 -.24566 (147*2π)/4833 weeks
1481.14628 .50067 (148*2π)/4833 weeks
149.92426 .91253 (149*2π)/4833 weeks
150.23465 1.20484 (150*2π)/4833 weeks
151-.53209 .94412 (151*2π)/4833 weeks
152-.46367 .1564 (152*2π)/4833 weeks
153-.51986 -.56229 (153*2π)/4833 weeks
154.35312 -1.09588 (154*2π)/4833 weeks
1551.00694 -.92261 (155*2π)/4833 weeks
1561.63153 -.34249 (156*2π)/4833 weeks
1571.79565 .74765 (157*2π)/4833 weeks
1581.01523 1.22221 (158*2π)/4833 weeks
159.38132 1.3923 (159*2π)/4833 weeks
160-.31653 .94365 (160*2π)/4833 weeks
161-.2365 .36746 (161*2π)/4833 weeks
162-.20682 -.14133 (162*2π)/4833 weeks
163.31311 -.26169 (163*2π)/4833 weeks
164.58581 -.20052 (164*2π)/4833 weeks
1651.18163 .28365 (165*2π)/4833 weeks
166.7435 1.08234 (166*2π)/4833 weeks
167.31638 .81051 (167*2π)/4833 weeks
168-.03405 1.09389 (168*2π)/4833 weeks
169-.61388 .5053 (169*2π)/4833 weeks
170-.42008 .4637 (170*2π)/4833 weeks
171-.93189 -.1327 (171*2π)/4833 weeks
172.11894 -1.03309 (172*2π)/4833 weeks
173.5307 -.5764 (173*2π)/4833 weeks
1741.03743 -.38487 (174*2π)/4833 weeks
175.90635 .4079 (175*2π)/4833 weeks
176.45448 .2253 (176*2π)/4833 weeks
177.68411 .87328 (177*2π)/4833 weeks
178-.57162 .75975 (178*2π)/4833 weeks
179-.34875 .17059 (179*2π)/4833 weeks
180-.9855 -.23777 (180*2π)/4833 weeks
181-.44245 -1.46129 (181*2π)/4833 weeks
182.94195 -1.6571 (182*2π)/4833 weeks
1831.93615 -.9206 (183*2π)/4833 weeks
1842.20512 .47159 (184*2π)/4833 weeks
1851.26358 1.45229 (185*2π)/4833 weeks
186.21581 1.55126 (186*2π)/4833 weeks
187-.73416 1.15924 (187*2π)/4833 weeks
188-1.19058 -.40159 (188*2π)/4833 weeks
189-.23862 -1.02347 (189*2π)/4833 weeks
190.58427 -1.17204 (190*2π)/4833 weeks
1911.35141 -.40844 (191*2π)/4833 weeks
192.98126 .24103 (192*2π)/4833 weeks
193.70018 .00137 (193*2π)/4833 weeks
194.93921 .05686 (194*2π)/4832 weeks
195.91153 .49345 (195*2π)/4832 weeks
196.65849 .51944 (196*2π)/4832 weeks
197.68196 .76657 (197*2π)/4832 weeks
198-.09107 .95585 (198*2π)/4832 weeks
199-.38115 .3209 (199*2π)/4832 weeks
200-.54022 -.28229 (200*2π)/4832 weeks
201.38106 -1.113 (201*2π)/4832 weeks
202.99116 -.59532 (202*2π)/4832 weeks
2031.21799 -.18967 (203*2π)/4832 weeks
2041.28262 .39949 (204*2π)/4832 weeks
205.90669 .90262 (205*2π)/4832 weeks
206.37246 1.01908 (206*2π)/4832 weeks
207-.12348 .90875 (207*2π)/4832 weeks
208-.48714 .35773 (208*2π)/4832 weeks
209-.4354 .08694 (209*2π)/4832 weeks
210-.55364 -.5772 (210*2π)/4832 weeks
211.37003 -.58818 (211*2π)/4832 weeks
212.44966 -.60733 (212*2π)/4832 weeks
2131.20685 -.30071 (213*2π)/4832 weeks
214.92561 .25666 (214*2π)/4832 weeks
215.84396 .4768 (215*2π)/4832 weeks
216.25594 1.10033 (216*2π)/4832 weeks
217-.60202 .60958 (217*2π)/4832 weeks
218-.59449 -.01787 (218*2π)/4832 weeks
219-.65797 -.79603 (219*2π)/4832 weeks
220.117 -1.32783 (220*2π)/4832 weeks
221.87652 -1.23277 (221*2π)/4832 weeks
2221.51417 -.91688 (222*2π)/4832 weeks
2231.86226 -.14653 (223*2π)/4832 weeks
2241.59982 .57989 (224*2π)/4832 weeks
2251.35749 1.43807 (225*2π)/4832 weeks
226-.18377 1.58028 (226*2π)/4832 weeks
227-.62261 .56281 (227*2π)/4832 weeks
228-.79446 .23041 (228*2π)/4832 weeks
229-.5904 -.88197 (229*2π)/4832 weeks
230.55435 -1.36843 (230*2π)/4832 weeks
2311.70863 -.7509 (231*2π)/4832 weeks
2321.69958 .13701 (232*2π)/4832 weeks
2331.43481 .79322 (233*2π)/4832 weeks
234.86186 1.23141 (234*2π)/4832 weeks
235-.12533 1.78645 (235*2π)/4832 weeks
236-1.42379 .68651 (236*2π)/4832 weeks
237-.8909 -.64002 (237*2π)/4832 weeks
238-.29671 -.95121 (238*2π)/4832 weeks
239.46978 -1.21235 (239*2π)/4832 weeks
240.84001 -.9196 (240*2π)/4832 weeks
2411.56247 -.58015 (241*2π)/4832 weeks
2421.56247 .58015 (242*2π)/4832 weeks
243.84001 .9196 (243*2π)/4832 weeks
244.46978 1.21235 (244*2π)/4832 weeks
245-.29671 .95121 (245*2π)/4832 weeks
246-.8909 .64002 (246*2π)/4832 weeks
247-1.42379 -.68651 (247*2π)/4832 weeks
248-.12533 -1.78645 (248*2π)/4832 weeks
249.86186 -1.23141 (249*2π)/4832 weeks
2501.43481 -.79322 (250*2π)/4832 weeks
2511.69958 -.13701 (251*2π)/4832 weeks
2521.70863 .7509 (252*2π)/4832 weeks
253.55435 1.36843 (253*2π)/4832 weeks
254-.5904 .88197 (254*2π)/4832 weeks
255-.79446 -.23041 (255*2π)/4832 weeks
256-.62261 -.56281 (256*2π)/4832 weeks
257-.18377 -1.58028 (257*2π)/4832 weeks
2581.35749 -1.43807 (258*2π)/4832 weeks
2591.59982 -.57989 (259*2π)/4832 weeks
2601.86226 .14653 (260*2π)/4832 weeks
2611.51417 .91688 (261*2π)/4832 weeks
262.87652 1.23277 (262*2π)/4832 weeks
263.117 1.32783 (263*2π)/4832 weeks
264-.65797 .79603 (264*2π)/4832 weeks
265-.59449 .01787 (265*2π)/4832 weeks
266-.60202 -.60958 (266*2π)/4832 weeks
267.25594 -1.10033 (267*2π)/4832 weeks
268.84396 -.4768 (268*2π)/4832 weeks
269.92561 -.25666 (269*2π)/4832 weeks
2701.20685 .30071 (270*2π)/4832 weeks
271.44966 .60733 (271*2π)/4832 weeks
272.37003 .58818 (272*2π)/4832 weeks
273-.55364 .5772 (273*2π)/4832 weeks
274-.4354 -.08694 (274*2π)/4832 weeks
275-.48714 -.35773 (275*2π)/4832 weeks
276-.12348 -.90875 (276*2π)/4832 weeks
277.37246 -1.01908 (277*2π)/4832 weeks
278.90669 -.90262 (278*2π)/4832 weeks
2791.28262 -.39949 (279*2π)/4832 weeks
2801.21799 .18967 (280*2π)/4832 weeks
281.99116 .59532 (281*2π)/4832 weeks
282.38106 1.113 (282*2π)/4832 weeks
283-.54022 .28229 (283*2π)/4832 weeks
284-.38115 -.3209 (284*2π)/4832 weeks
285-.09107 -.95585 (285*2π)/4832 weeks
286.68196 -.76657 (286*2π)/4832 weeks
287.65849 -.51944 (287*2π)/4832 weeks
288.91153 -.49345 (288*2π)/4832 weeks
289.93921 -.05686 (289*2π)/4832 weeks
290.70018 -.00137 (290*2π)/4832 weeks
291.98126 -.24103 (291*2π)/4832 weeks
2921.35141 .40844 (292*2π)/4832 weeks
293.58427 1.17204 (293*2π)/4832 weeks
294-.23862 1.02347 (294*2π)/4832 weeks
295-1.19058 .40159 (295*2π)/4832 weeks
296-.73416 -1.15924 (296*2π)/4832 weeks
297.21581 -1.55126 (297*2π)/4832 weeks
2981.26358 -1.45229 (298*2π)/4832 weeks
2992.20512 -.47159 (299*2π)/4832 weeks
3001.93615 .9206 (300*2π)/4832 weeks
301.94195 1.6571 (301*2π)/4832 weeks
302-.44245 1.46129 (302*2π)/4832 weeks
303-.9855 .23777 (303*2π)/4832 weeks
304-.34875 -.17059 (304*2π)/4832 weeks
305-.57162 -.75975 (305*2π)/4832 weeks
306.68411 -.87328 (306*2π)/4832 weeks
307.45448 -.2253 (307*2π)/4832 weeks
308.90635 -.4079 (308*2π)/4832 weeks
3091.03743 .38487 (309*2π)/4832 weeks
310.5307 .5764 (310*2π)/4832 weeks
311.11894 1.03309 (311*2π)/4832 weeks
312-.93189 .1327 (312*2π)/4832 weeks
313-.42008 -.4637 (313*2π)/4832 weeks
314-.61388 -.5053 (314*2π)/4832 weeks
315-.03405 -1.09389 (315*2π)/4832 weeks
316.31638 -.81051 (316*2π)/4832 weeks
317.7435 -1.08234 (317*2π)/4832 weeks
3181.18163 -.28365 (318*2π)/4832 weeks
319.58581 .20052 (319*2π)/4832 weeks
320.31311 .26169 (320*2π)/4832 weeks
321-.20682 .14133 (321*2π)/4832 weeks
322-.2365 -.36746 (322*2π)/4832 weeks
323-.31653 -.94365 (323*2π)/4831 weeks
324.38132 -1.3923 (324*2π)/4831 weeks
3251.01523 -1.22221 (325*2π)/4831 weeks
3261.79565 -.74765 (326*2π)/4831 weeks
3271.63153 .34249 (327*2π)/4831 weeks
3281.00694 .92261 (328*2π)/4831 weeks
329.35312 1.09588 (329*2π)/4831 weeks
330-.51986 .56229 (330*2π)/4831 weeks
331-.46367 -.1564 (331*2π)/4831 weeks
332-.53209 -.94412 (332*2π)/4831 weeks
333.23465 -1.20484 (333*2π)/4831 weeks
334.92426 -.91253 (334*2π)/4831 weeks
3351.14628 -.50067 (335*2π)/4831 weeks
3361.12373 .24566 (336*2π)/4831 weeks
337.28972 .43596 (337*2π)/4831 weeks
338.2511 .27552 (338*2π)/4831 weeks
339-.45679 -.05546 (339*2π)/4831 weeks
340.06532 -.51315 (340*2π)/4831 weeks
341.29619 -.42213 (341*2π)/4831 weeks
342.15931 -.19911 (342*2π)/4831 weeks
343-.23225 -.7954 (343*2π)/4831 weeks
344.90069 -1.00068 (344*2π)/4831 weeks
345.73058 -.22194 (345*2π)/4831 weeks
346.43536 -.2491 (346*2π)/4831 weeks
347.68685 -.26998 (347*2π)/4831 weeks
348.74712 .06622 (348*2π)/4831 weeks
349.32016 .51883 (349*2π)/4831 weeks
350-.59243 -.02956 (350*2π)/4831 weeks
351-.00522 -.95928 (351*2π)/4831 weeks
352.21537 -.68919 (352*2π)/4831 weeks
353.61994 -1.05479 (353*2π)/4831 weeks
354.78906 -.55513 (354*2π)/4831 weeks
355.76721 -.3609 (355*2π)/4831 weeks
356.5707 .13257 (356*2π)/4831 weeks
357.18327 -.56702 (357*2π)/4831 weeks
3581.15202 -.63788 (358*2π)/4831 weeks
359.82759 .31971 (359*2π)/4831 weeks
360.33157 -.00168 (360*2π)/4831 weeks
361-.12342 -.26502 (361*2π)/4831 weeks
362.2592 -1.15896 (362*2π)/4831 weeks
363.94489 -.60623 (363*2π)/4831 weeks
364.80019 -.19371 (364*2π)/4831 weeks
365.94469 .15898 (365*2π)/4831 weeks
366.58267 .22465 (366*2π)/4831 weeks
367.20096 -.21053 (367*2π)/4831 weeks
368.47991 -.60278 (368*2π)/4831 weeks
369.95951 .1282 (369*2π)/4831 weeks
370.37486 .26353 (370*2π)/4831 weeks
371.36058 .04468 (371*2π)/4831 weeks
372.08564 .30232 (372*2π)/4831 weeks
373-.24964 .39822 (373*2π)/4831 weeks
374-.65009 .32169 (374*2π)/4831 weeks
375-1.02198 -.97439 (375*2π)/4831 weeks
376-.10864 -1.56477 (376*2π)/4831 weeks
377.83044 -1.45886 (377*2π)/4831 weeks
3781.41378 -1.09322 (378*2π)/4831 weeks
3791.56058 .03415 (379*2π)/4831 weeks
3801.03569 .55798 (380*2π)/4831 weeks
381.06405 1.20661 (381*2π)/4831 weeks
382-1.19545 1.04846 (382*2π)/4831 weeks
383-1.71677 -.84988 (383*2π)/4831 weeks
384-.97718 -1.616 (384*2π)/4831 weeks
385-.08114 -2.45809 (385*2π)/4831 weeks
3861.2562 -2.44516 (386*2π)/4831 weeks
3872.40686 -1.52202 (387*2π)/4831 weeks
3882.19612 .50076 (388*2π)/4831 weeks
389.87323 1.14254 (389*2π)/4831 weeks
390-.09781 1.43669 (390*2π)/4831 weeks
391-1.11132 .44943 (391*2π)/4831 weeks
392-1.45964 -.58085 (392*2π)/4831 weeks
393-.6053 -1.86816 (393*2π)/4831 weeks
394.50348 -2.1752 (394*2π)/4831 weeks
3951.17089 -1.56612 (395*2π)/4831 weeks
3961.33091 -.84783 (396*2π)/4831 weeks
397.9937 -.0009 (397*2π)/4831 weeks
398.25228 .226 (398*2π)/4831 weeks
399-.17151 .05442 (399*2π)/4831 weeks
400.00611 -.84359 (400*2π)/4831 weeks
401.43334 -.01543 (401*2π)/4831 weeks
402-.31829 .36034 (402*2π)/4831 weeks
403-1.34553 -.14748 (403*2π)/4831 weeks
404-1.58485 -1.9615 (404*2π)/4831 weeks
405-.16096 -3.14123 (405*2π)/4831 weeks
4061.81459 -3.32365 (406*2π)/4831 weeks
4072.98924 -1.6665 (407*2π)/4831 weeks
4083.06389 .69673 (408*2π)/4831 weeks
409.65998 1.84501 (409*2π)/4831 weeks
410-.28779 1.43081 (410*2π)/4831 weeks
411-2.58608 .7899 (411*2π)/4831 weeks
412-2.36948 -2.05656 (412*2π)/4831 weeks
413-1.31738 -3.46555 (413*2π)/4831 weeks
4141.82547 -4.29364 (414*2π)/4831 weeks
4153.73941 -1.30173 (415*2π)/4831 weeks
4162.38745 -.35 (416*2π)/4831 weeks
4172.54456 1.41904 (417*2π)/4831 weeks
418.30114 2.48566 (418*2π)/4831 weeks
419-1.88643 1.34474 (419*2π)/4831 weeks
420-2.66612 -.88485 (420*2π)/4831 weeks
421-1.23375 -2.56485 (421*2π)/4831 weeks
422.57955 -2.29334 (422*2π)/4831 weeks
423.41408 -1.32911 (423*2π)/4831 weeks
424.77183 -1.3832 (424*2π)/4831 weeks
425-.143 -1.06387 (425*2π)/4831 weeks
426.57514 -1.71132 (426*2π)/4831 weeks
4271.0638 -1.1252 (427*2π)/4831 weeks
4281.28982 -1.01364 (428*2π)/4831 weeks
429.98893 .86685 (429*2π)/4831 weeks
430-1.13711 .25299 (430*2π)/4831 weeks
431-1.527 -.6846 (431*2π)/4831 weeks
432-1.98524 -2.40854 (432*2π)/4831 weeks
433-.61247 -3.47837 (433*2π)/4831 weeks
4341.77862 -3.37504 (434*2π)/4831 weeks
4352.50778 -1.61366 (435*2π)/4831 weeks
4361.47772 -.26095 (436*2π)/4831 weeks
437.64271 -.15627 (437*2π)/4831 weeks
438-.6154 -1.07752 (438*2π)/4831 weeks
439-.19416 -1.87323 (439*2π)/4831 weeks
440.04225 -2.23373 (440*2π)/4831 weeks
441-.18135 -1.29724 (441*2π)/4831 weeks
442.70778 -2.54669 (442*2π)/4831 weeks
4431.14255 -1.8062 (443*2π)/4831 weeks
444.69474 -2.00753 (444*2π)/4831 weeks
445.6178 -1.22982 (445*2π)/4831 weeks
446-.12457 -2.74198 (446*2π)/4831 weeks
4473.05141 -2.22733 (447*2π)/4831 weeks
4481.46714 .21132 (448*2π)/4831 weeks
449.02719 -.26586 (449*2π)/4831 weeks
450.23508 -.18394 (450*2π)/4831 weeks
451-2.14387 -.04448 (451*2π)/4831 weeks
452-3.87901 -2.33205 (452*2π)/4831 weeks
453-3.37028 -7.22305 (453*2π)/4831 weeks
4543.37384 -8.84333 (454*2π)/4831 weeks
4557.4027 -4.52904 (455*2π)/4831 weeks
4567.13436 -.22768 (456*2π)/4831 weeks
4574.38719 3.91788 (457*2π)/4831 weeks
458-1.87965 3.79658 (458*2π)/4831 weeks
459-4.15659 1.75766 (459*2π)/4831 weeks
460-6.9774 -3.73982 (460*2π)/4831 weeks
461-1.15098 -7.761 (461*2π)/4831 weeks
4623.2527 -6.0674 (462*2π)/4831 weeks
4635.71414 -1.47832 (463*2π)/4831 weeks
4642.13619 .99222 (464*2π)/4831 weeks
465.58155 1.24153 (465*2π)/4831 weeks
466-3.40069 .47962 (466*2π)/4831 weeks
467-4.57146 -1.24801 (467*2π)/4831 weeks
468-5.72495 -6.20947 (468*2π)/4831 weeks
469-.59118 -5.68842 (469*2π)/4831 weeks
470-3.03545 -4.38738 (470*2π)/4831 weeks
471-2.8976 -8.30776 (471*2π)/4831 weeks
472-4.3284 -8.9357 (472*2π)/4831 weeks
473-.19836 -14.10452 (473*2π)/4831 weeks
4744.0563 -13.84949 (474*2π)/4831 weeks
47512.24058 -15.60174 (475*2π)/4831 weeks
47616.88578 -1.14093 (476*2π)/4831 weeks
477.59886 13.00715 (477*2π)/4831 weeks
478-20.50272 2.92157 (478*2π)/4831 weeks
479-26.92717 -17.29826 (479*2π)/4831 weeks
480-27.61515 -47.46392 (480*2π)/4831 weeks
4818.80687 -74.8186 (481*2π)/4831 weeks

Problems, Comments, Suggestions? Click here to contact Greg Thatcher

Please read my Disclaimer





Copyright (c) 2013 Thatcher Development Software, LLC. All rights reserved. No claim to original U.S. Gov't works.