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Fourier Analysis of UFPIX (UltraShort Latin America ProFun)


UFPIX (UltraShort Latin America ProFun) appears to have interesting cyclic behaviour every 44 weeks (15.5123*sine), 40 weeks (15.3825*sine), and 48 weeks (14.4068*sine).

UFPIX (UltraShort Latin America ProFun) has an average price of 52.33 (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 10/16/2007 to 1/9/2017 for UFPIX (UltraShort Latin America ProFun), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
052.32749   0 
158.94374 32.91776 (1*2π)/483483 weeks
226.79844 44.40588 (2*2π)/483242 weeks
31.21279 38.88416 (3*2π)/483161 weeks
4-11.67764 24.73466 (4*2π)/483121 weeks
5-10.84449 11.03896 (5*2π)/48397 weeks
6-1.86983 1.34288 (6*2π)/48381 weeks
77.63779 1.03467 (7*2π)/48369 weeks
812.19085 6.35532 (8*2π)/48360 weeks
912.49628 10.19058 (9*2π)/48354 weeks
109.12609 14.40678 (10*2π)/48348 weeks
112.99227 15.51226 (11*2π)/48344 weeks
12-2.39496 15.38253 (12*2π)/48340 weeks
13-5.5076 11.02645 (13*2π)/48337 weeks
14-6.30737 6.56096 (14*2π)/48335 weeks
15-5.62782 3.03986 (15*2π)/48332 weeks
16-2.30257 .00514 (16*2π)/48330 weeks
17.48022 -.42055 (17*2π)/48328 weeks
183.94435 .80357 (18*2π)/48327 weeks
195.3634 2.61622 (19*2π)/48325 weeks
204.67375 5.27742 (20*2π)/48324 weeks
211.643 6.96651 (21*2π)/48323 weeks
22-1.68514 6.05123 (22*2π)/48322 weeks
23-3.74869 3.46858 (23*2π)/48321 weeks
24-2.38195 .93454 (24*2π)/48320 weeks
25.16755 -.36377 (25*2π)/48319 weeks
263.19842 .10185 (26*2π)/48319 weeks
274.61735 1.81056 (27*2π)/48318 weeks
284.62241 4.14011 (28*2π)/48317 weeks
292.6669 5.65404 (29*2π)/48317 weeks
30-.09259 5.20196 (30*2π)/48316 weeks
31-1.42533 3.90705 (31*2π)/48316 weeks
32-1.86973 2.10935 (32*2π)/48315 weeks
33-1.36154 .93398 (33*2π)/48315 weeks
34-.28082 -.04582 (34*2π)/48314 weeks
351.48947 -.4697 (35*2π)/48314 weeks
363.07031 .30129 (36*2π)/48313 weeks
373.23336 1.48773 (37*2π)/48313 weeks
383.35898 2.961 (38*2π)/48313 weeks
392.53656 4.09338 (39*2π)/48312 weeks
401.27395 4.57847 (40*2π)/48312 weeks
41-.26952 3.96442 (41*2π)/48312 weeks
42-.99329 2.65952 (42*2π)/48312 weeks
43-1.06555 1.63959 (43*2π)/48311 weeks
44.18516 .83202 (44*2π)/48311 weeks
451.23649 .67736 (45*2π)/48311 weeks
462.27788 1.07779 (46*2π)/48311 weeks
472.69758 2.32936 (47*2π)/48310 weeks
481.96667 3.78796 (48*2π)/48310 weeks
49.60229 4.55547 (49*2π)/48310 weeks
50-1.3338 3.88255 (50*2π)/48310 weeks
51-2.31913 2.35987 (51*2π)/4839 weeks
52-2.03577 .62185 (52*2π)/4839 weeks
53-.91124 -.5713 (53*2π)/4839 weeks
54.66709 -.4224 (54*2π)/4839 weeks
551.37295 .21699 (55*2π)/4839 weeks
561.83639 .8826 (56*2π)/4839 weeks
571.5763 1.6232 (57*2π)/4838 weeks
581.01861 1.94646 (58*2π)/4838 weeks
59.23998 2.31503 (59*2π)/4838 weeks
60-.49681 1.82733 (60*2π)/4838 weeks
61-.92835 1.16025 (61*2π)/4838 weeks
62-1.04589 -.19149 (62*2π)/4838 weeks
63-.1163 -1.45632 (63*2π)/4838 weeks
641.42356 -1.57503 (64*2π)/4838 weeks
652.96945 -.68874 (65*2π)/4837 weeks
663.3102 .9328 (66*2π)/4837 weeks
672.72048 2.25731 (67*2π)/4837 weeks
681.79377 3.23538 (68*2π)/4837 weeks
69-.04996 3.18666 (69*2π)/4837 weeks
70-1.02169 1.88138 (70*2π)/4837 weeks
71-.95005 .40567 (71*2π)/4837 weeks
72.04982 -.97224 (72*2π)/4837 weeks
731.49853 -.76361 (73*2π)/4837 weeks
742.52417 .03238 (74*2π)/4837 weeks
752.92509 1.41084 (75*2π)/4836 weeks
762.05906 2.62698 (76*2π)/4836 weeks
77.64637 3.1691 (77*2π)/4836 weeks
78-.6376 2.69891 (78*2π)/4836 weeks
79-1.21711 1.49253 (79*2π)/4836 weeks
80-.87419 .25437 (80*2π)/4836 weeks
81-.00958 -.59898 (81*2π)/4836 weeks
82.92551 -.67564 (82*2π)/4836 weeks
831.69134 -.33917 (83*2π)/4836 weeks
842.38902 .24212 (84*2π)/4836 weeks
852.26652 1.09072 (85*2π)/4836 weeks
861.56616 2.06137 (86*2π)/4836 weeks
87.62023 2.44349 (87*2π)/4836 weeks
88-.26994 2.10937 (88*2π)/4835 weeks
89-.69891 1.36712 (89*2π)/4835 weeks
90-.46545 .32653 (90*2π)/4835 weeks
91.30054 -.55523 (91*2π)/4835 weeks
921.31412 -.72718 (92*2π)/4835 weeks
932.1233 -.13645 (93*2π)/4835 weeks
942.27182 .91136 (94*2π)/4835 weeks
951.81505 1.95041 (95*2π)/4835 weeks
96.69121 2.4919 (96*2π)/4835 weeks
97-.33836 2.17288 (97*2π)/4835 weeks
98-.88442 1.15452 (98*2π)/4835 weeks
99-.65598 .03174 (99*2π)/4835 weeks
100.06094 -.81829 (100*2π)/4835 weeks
1011.33058 -1.0233 (101*2π)/4835 weeks
1022.03086 -.38027 (102*2π)/4835 weeks
1032.17169 .60053 (103*2π)/4835 weeks
1041.82515 1.45792 (104*2π)/4835 weeks
1051.04841 1.79422 (105*2π)/4835 weeks
106.37858 1.56031 (106*2π)/4835 weeks
107-.00279 .97592 (107*2π)/4835 weeks
108.20509 .36182 (108*2π)/4834 weeks
109.80933 .17611 (109*2π)/4834 weeks
1101.17519 .166 (110*2π)/4834 weeks
1111.3512 .45177 (111*2π)/4834 weeks
1121.2439 .63418 (112*2π)/4834 weeks
1131.2705 .69443 (113*2π)/4834 weeks
1141.33014 .87991 (114*2π)/4834 weeks
1151.21283 1.15587 (115*2π)/4834 weeks
1161.08611 1.3995 (116*2π)/4834 weeks
117.91165 1.68034 (117*2π)/4834 weeks
118.5032 1.74569 (118*2π)/4834 weeks
119.02498 1.29966 (119*2π)/4834 weeks
120-.23853 .81021 (120*2π)/4834 weeks
121-.0865 .17659 (121*2π)/4834 weeks
122.60481 .00056 (122*2π)/4834 weeks
1231.11201 .3435 (123*2π)/4834 weeks
1241.25523 .8599 (124*2π)/4834 weeks
125.90635 1.34086 (125*2π)/4834 weeks
126.54221 1.33706 (126*2π)/4834 weeks
127.26752 1.26685 (127*2π)/4834 weeks
128-.04551 1.01165 (128*2π)/4834 weeks
129-.14056 .75139 (129*2π)/4834 weeks
130-.25856 .50412 (130*2π)/4834 weeks
131-.04543 .06269 (131*2π)/4834 weeks
132.25219 -.17089 (132*2π)/4834 weeks
133.78722 -.17652 (133*2π)/4834 weeks
1341.1257 .21586 (134*2π)/4834 weeks
1351.10597 .64529 (135*2π)/4834 weeks
136.85922 .97689 (136*2π)/4834 weeks
137.40322 1.03659 (137*2π)/4834 weeks
138-.07215 .9398 (138*2π)/4834 weeks
139-.34145 .60705 (139*2π)/4833 weeks
140-.24394 -.10893 (140*2π)/4833 weeks
141.20909 -.47199 (141*2π)/4833 weeks
142.64095 -.57833 (142*2π)/4833 weeks
1431.12598 -.46169 (143*2π)/4833 weeks
1441.552 -.05466 (144*2π)/4833 weeks
1451.59653 .63288 (145*2π)/4833 weeks
1461.18945 1.17007 (146*2π)/4833 weeks
147.48194 1.36421 (147*2π)/4833 weeks
148-.10291 1.01992 (148*2π)/4833 weeks
149-.32109 .44052 (149*2π)/4833 weeks
150-.22766 -.2814 (150*2π)/4833 weeks
151.28566 -.67589 (151*2π)/4833 weeks
1521.10059 -.48487 (152*2π)/4833 weeks
1531.64772 .05145 (153*2π)/4833 weeks
1541.68348 .85617 (154*2π)/4833 weeks
1551.1847 1.41696 (155*2π)/4833 weeks
156.38167 1.62208 (156*2π)/4833 weeks
157-.50209 1.2241 (157*2π)/4833 weeks
158-.89097 .38873 (158*2π)/4833 weeks
159-.70773 -.4281 (159*2π)/4833 weeks
160-.00066 -.87475 (160*2π)/4833 weeks
161.7695 -.74602 (161*2π)/4833 weeks
1621.28675 -.32407 (162*2π)/4833 weeks
1631.20427 .27922 (163*2π)/4833 weeks
164.78048 .70818 (164*2π)/4833 weeks
165.09179 .7653 (165*2π)/4833 weeks
166-.51811 .24724 (166*2π)/4833 weeks
167-.60537 -.43706 (167*2π)/4833 weeks
168-.09751 -1.21978 (168*2π)/4833 weeks
169.78507 -1.64329 (169*2π)/4833 weeks
1701.64468 -1.44214 (170*2π)/4833 weeks
1712.36203 -.70009 (171*2π)/4833 weeks
1722.36758 .54419 (172*2π)/4833 weeks
1731.70493 1.297 (173*2π)/4833 weeks
174.69334 1.45264 (174*2π)/4833 weeks
175-.13767 .87319 (175*2π)/4833 weeks
176-.31029 -.03225 (176*2π)/4833 weeks
177-.00229 -.90052 (177*2π)/4833 weeks
1781.03061 -1.35931 (178*2π)/4833 weeks
1791.86086 -1.02448 (179*2π)/4833 weeks
1802.46156 -.28638 (180*2π)/4833 weeks
1812.51184 .84238 (181*2π)/4833 weeks
1821.83011 1.76867 (182*2π)/4833 weeks
183.76654 2.06643 (183*2π)/4833 weeks
184-.27981 1.46227 (184*2π)/4833 weeks
185-.59547 .42653 (185*2π)/4833 weeks
186-.27593 -.50897 (186*2π)/4833 weeks
187.47751 -.94223 (187*2π)/4833 weeks
1881.40407 -.67555 (188*2π)/4833 weeks
1891.79908 -.13769 (189*2π)/4833 weeks
1901.69042 .59281 (190*2π)/4833 weeks
1911.2205 .99418 (191*2π)/4833 weeks
192.80717 1.16975 (192*2π)/4833 weeks
193.39948 1.16276 (193*2π)/4833 weeks
194-.0287 .83214 (194*2π)/4832 weeks
195-.27192 .2166 (195*2π)/4832 weeks
196-.04072 -.34703 (196*2π)/4832 weeks
197.39272 -.67114 (197*2π)/4832 weeks
1981.03481 -.73929 (198*2π)/4832 weeks
1991.58487 -.31943 (199*2π)/4832 weeks
2001.66831 .43677 (200*2π)/4832 weeks
2011.26154 1.24922 (201*2π)/4832 weeks
202.52118 1.47179 (202*2π)/4832 weeks
203-.21268 1.15629 (203*2π)/4832 weeks
204-.65786 .39993 (204*2π)/4832 weeks
205-.63349 -.48023 (205*2π)/4832 weeks
206-.12508 -1.11573 (206*2π)/4832 weeks
207.73325 -1.35636 (207*2π)/4832 weeks
2081.55808 -1.01263 (208*2π)/4832 weeks
2092.00635 -.24747 (209*2π)/4832 weeks
2101.92506 .64165 (210*2π)/4832 weeks
2111.17281 1.20205 (211*2π)/4832 weeks
212.32649 1.17387 (212*2π)/4832 weeks
213-.45052 .66381 (213*2π)/4832 weeks
214-.55931 -.27942 (214*2π)/4832 weeks
215-.10985 -1.04258 (215*2π)/4832 weeks
216.73322 -1.54611 (216*2π)/4832 weeks
2171.78706 -1.37652 (217*2π)/4832 weeks
2182.43164 -.48307 (218*2π)/4832 weeks
2192.48372 .71515 (219*2π)/4832 weeks
2201.71334 1.64482 (220*2π)/4832 weeks
221.58264 1.95222 (221*2π)/4832 weeks
222-.48024 1.57249 (222*2π)/4832 weeks
223-1.07132 .55839 (223*2π)/4832 weeks
224-.85914 -.63006 (224*2π)/4832 weeks
225-.11461 -1.57039 (225*2π)/4832 weeks
2261.15479 -1.76902 (226*2π)/4832 weeks
2272.12779 -1.04016 (227*2π)/4832 weeks
2282.48208 .02349 (228*2π)/4832 weeks
2292.06552 1.22171 (229*2π)/4832 weeks
230.86144 1.84789 (230*2π)/4832 weeks
231-.47884 1.53713 (231*2π)/4832 weeks
232-1.07963 .5006 (232*2π)/4832 weeks
233-.88187 -.73412 (233*2π)/4832 weeks
234.04888 -1.58315 (234*2π)/4832 weeks
2351.33752 -1.85691 (235*2π)/4832 weeks
2362.44345 -1.02811 (236*2π)/4832 weeks
2372.62761 .34442 (237*2π)/4832 weeks
2381.9709 1.39634 (238*2π)/4832 weeks
239.82619 1.98562 (239*2π)/4832 weeks
240-.31654 1.73208 (240*2π)/4832 weeks
241-1.26798 .72961 (241*2π)/4832 weeks
242-1.26798 -.72961 (242*2π)/4832 weeks
243-.31654 -1.73208 (243*2π)/4832 weeks
244.82619 -1.98562 (244*2π)/4832 weeks
2451.9709 -1.39634 (245*2π)/4832 weeks
2462.62761 -.34442 (246*2π)/4832 weeks
2472.44345 1.02811 (247*2π)/4832 weeks
2481.33752 1.85691 (248*2π)/4832 weeks
249.04888 1.58315 (249*2π)/4832 weeks
250-.88187 .73412 (250*2π)/4832 weeks
251-1.07963 -.5006 (251*2π)/4832 weeks
252-.47884 -1.53713 (252*2π)/4832 weeks
253.86144 -1.84789 (253*2π)/4832 weeks
2542.06552 -1.22171 (254*2π)/4832 weeks
2552.48208 -.02349 (255*2π)/4832 weeks
2562.12779 1.04016 (256*2π)/4832 weeks
2571.15479 1.76902 (257*2π)/4832 weeks
258-.11461 1.57039 (258*2π)/4832 weeks
259-.85914 .63006 (259*2π)/4832 weeks
260-1.07132 -.55839 (260*2π)/4832 weeks
261-.48024 -1.57249 (261*2π)/4832 weeks
262.58264 -1.95222 (262*2π)/4832 weeks
2631.71334 -1.64482 (263*2π)/4832 weeks
2642.48372 -.71515 (264*2π)/4832 weeks
2652.43164 .48307 (265*2π)/4832 weeks
2661.78706 1.37652 (266*2π)/4832 weeks
267.73322 1.54611 (267*2π)/4832 weeks
268-.10985 1.04258 (268*2π)/4832 weeks
269-.55931 .27942 (269*2π)/4832 weeks
270-.45052 -.66381 (270*2π)/4832 weeks
271.32649 -1.17387 (271*2π)/4832 weeks
2721.17281 -1.20205 (272*2π)/4832 weeks
2731.92506 -.64165 (273*2π)/4832 weeks
2742.00635 .24747 (274*2π)/4832 weeks
2751.55808 1.01263 (275*2π)/4832 weeks
276.73325 1.35636 (276*2π)/4832 weeks
277-.12508 1.11573 (277*2π)/4832 weeks
278-.63349 .48023 (278*2π)/4832 weeks
279-.65786 -.39993 (279*2π)/4832 weeks
280-.21268 -1.15629 (280*2π)/4832 weeks
281.52118 -1.47179 (281*2π)/4832 weeks
2821.26154 -1.24922 (282*2π)/4832 weeks
2831.66831 -.43677 (283*2π)/4832 weeks
2841.58487 .31943 (284*2π)/4832 weeks
2851.03481 .73929 (285*2π)/4832 weeks
286.39272 .67114 (286*2π)/4832 weeks
287-.04072 .34703 (287*2π)/4832 weeks
288-.27192 -.2166 (288*2π)/4832 weeks
289-.0287 -.83214 (289*2π)/4832 weeks
290.39948 -1.16276 (290*2π)/4832 weeks
291.80717 -1.16975 (291*2π)/4832 weeks
2921.2205 -.99418 (292*2π)/4832 weeks
2931.69042 -.59281 (293*2π)/4832 weeks
2941.79908 .13769 (294*2π)/4832 weeks
2951.40407 .67555 (295*2π)/4832 weeks
296.47751 .94223 (296*2π)/4832 weeks
297-.27593 .50897 (297*2π)/4832 weeks
298-.59547 -.42653 (298*2π)/4832 weeks
299-.27981 -1.46227 (299*2π)/4832 weeks
300.76654 -2.06643 (300*2π)/4832 weeks
3011.83011 -1.76867 (301*2π)/4832 weeks
3022.51184 -.84238 (302*2π)/4832 weeks
3032.46156 .28638 (303*2π)/4832 weeks
3041.86086 1.02448 (304*2π)/4832 weeks
3051.03061 1.35931 (305*2π)/4832 weeks
306-.00229 .90052 (306*2π)/4832 weeks
307-.31029 .03225 (307*2π)/4832 weeks
308-.13767 -.87319 (308*2π)/4832 weeks
309.69334 -1.45264 (309*2π)/4832 weeks
3101.70493 -1.297 (310*2π)/4832 weeks
3112.36758 -.54419 (311*2π)/4832 weeks
3122.36203 .70009 (312*2π)/4832 weeks
3131.64468 1.44214 (313*2π)/4832 weeks
314.78507 1.64329 (314*2π)/4832 weeks
315-.09751 1.21978 (315*2π)/4832 weeks
316-.60537 .43706 (316*2π)/4832 weeks
317-.51811 -.24724 (317*2π)/4832 weeks
318.09179 -.7653 (318*2π)/4832 weeks
319.78048 -.70818 (319*2π)/4832 weeks
3201.20427 -.27922 (320*2π)/4832 weeks
3211.28675 .32407 (321*2π)/4832 weeks
322.7695 .74602 (322*2π)/4832 weeks
323-.00066 .87475 (323*2π)/4831 weeks
324-.70773 .4281 (324*2π)/4831 weeks
325-.89097 -.38873 (325*2π)/4831 weeks
326-.50209 -1.2241 (326*2π)/4831 weeks
327.38167 -1.62208 (327*2π)/4831 weeks
3281.1847 -1.41696 (328*2π)/4831 weeks
3291.68348 -.85617 (329*2π)/4831 weeks
3301.64772 -.05145 (330*2π)/4831 weeks
3311.10059 .48487 (331*2π)/4831 weeks
332.28566 .67589 (332*2π)/4831 weeks
333-.22766 .2814 (333*2π)/4831 weeks
334-.32109 -.44052 (334*2π)/4831 weeks
335-.10291 -1.01992 (335*2π)/4831 weeks
336.48194 -1.36421 (336*2π)/4831 weeks
3371.18945 -1.17007 (337*2π)/4831 weeks
3381.59653 -.63288 (338*2π)/4831 weeks
3391.552 .05466 (339*2π)/4831 weeks
3401.12598 .46169 (340*2π)/4831 weeks
341.64095 .57833 (341*2π)/4831 weeks
342.20909 .47199 (342*2π)/4831 weeks
343-.24394 .10893 (343*2π)/4831 weeks
344-.34145 -.60705 (344*2π)/4831 weeks
345-.07215 -.9398 (345*2π)/4831 weeks
346.40322 -1.03659 (346*2π)/4831 weeks
347.85922 -.97689 (347*2π)/4831 weeks
3481.10597 -.64529 (348*2π)/4831 weeks
3491.1257 -.21586 (349*2π)/4831 weeks
350.78722 .17652 (350*2π)/4831 weeks
351.25219 .17089 (351*2π)/4831 weeks
352-.04543 -.06269 (352*2π)/4831 weeks
353-.25856 -.50412 (353*2π)/4831 weeks
354-.14056 -.75139 (354*2π)/4831 weeks
355-.04551 -1.01165 (355*2π)/4831 weeks
356.26752 -1.26685 (356*2π)/4831 weeks
357.54221 -1.33706 (357*2π)/4831 weeks
358.90635 -1.34086 (358*2π)/4831 weeks
3591.25523 -.8599 (359*2π)/4831 weeks
3601.11201 -.3435 (360*2π)/4831 weeks
361.60481 -.00056 (361*2π)/4831 weeks
362-.0865 -.17659 (362*2π)/4831 weeks
363-.23853 -.81021 (363*2π)/4831 weeks
364.02498 -1.29966 (364*2π)/4831 weeks
365.5032 -1.74569 (365*2π)/4831 weeks
366.91165 -1.68034 (366*2π)/4831 weeks
3671.08611 -1.3995 (367*2π)/4831 weeks
3681.21283 -1.15587 (368*2π)/4831 weeks
3691.33014 -.87991 (369*2π)/4831 weeks
3701.2705 -.69443 (370*2π)/4831 weeks
3711.2439 -.63418 (371*2π)/4831 weeks
3721.3512 -.45177 (372*2π)/4831 weeks
3731.17519 -.166 (373*2π)/4831 weeks
374.80933 -.17611 (374*2π)/4831 weeks
375.20509 -.36182 (375*2π)/4831 weeks
376-.00279 -.97592 (376*2π)/4831 weeks
377.37858 -1.56031 (377*2π)/4831 weeks
3781.04841 -1.79422 (378*2π)/4831 weeks
3791.82515 -1.45792 (379*2π)/4831 weeks
3802.17169 -.60053 (380*2π)/4831 weeks
3812.03086 .38027 (381*2π)/4831 weeks
3821.33058 1.0233 (382*2π)/4831 weeks
383.06094 .81829 (383*2π)/4831 weeks
384-.65598 -.03174 (384*2π)/4831 weeks
385-.88442 -1.15452 (385*2π)/4831 weeks
386-.33836 -2.17288 (386*2π)/4831 weeks
387.69121 -2.4919 (387*2π)/4831 weeks
3881.81505 -1.95041 (388*2π)/4831 weeks
3892.27182 -.91136 (389*2π)/4831 weeks
3902.1233 .13645 (390*2π)/4831 weeks
3911.31412 .72718 (391*2π)/4831 weeks
392.30054 .55523 (392*2π)/4831 weeks
393-.46545 -.32653 (393*2π)/4831 weeks
394-.69891 -1.36712 (394*2π)/4831 weeks
395-.26994 -2.10937 (395*2π)/4831 weeks
396.62023 -2.44349 (396*2π)/4831 weeks
3971.56616 -2.06137 (397*2π)/4831 weeks
3982.26652 -1.09072 (398*2π)/4831 weeks
3992.38902 -.24212 (399*2π)/4831 weeks
4001.69134 .33917 (400*2π)/4831 weeks
401.92551 .67564 (401*2π)/4831 weeks
402-.00958 .59898 (402*2π)/4831 weeks
403-.87419 -.25437 (403*2π)/4831 weeks
404-1.21711 -1.49253 (404*2π)/4831 weeks
405-.6376 -2.69891 (405*2π)/4831 weeks
406.64637 -3.1691 (406*2π)/4831 weeks
4072.05906 -2.62698 (407*2π)/4831 weeks
4082.92509 -1.41084 (408*2π)/4831 weeks
4092.52417 -.03238 (409*2π)/4831 weeks
4101.49853 .76361 (410*2π)/4831 weeks
411.04982 .97224 (411*2π)/4831 weeks
412-.95005 -.40567 (412*2π)/4831 weeks
413-1.02169 -1.88138 (413*2π)/4831 weeks
414-.04996 -3.18666 (414*2π)/4831 weeks
4151.79377 -3.23538 (415*2π)/4831 weeks
4162.72048 -2.25731 (416*2π)/4831 weeks
4173.3102 -.9328 (417*2π)/4831 weeks
4182.96945 .68874 (418*2π)/4831 weeks
4191.42356 1.57503 (419*2π)/4831 weeks
420-.1163 1.45632 (420*2π)/4831 weeks
421-1.04589 .19149 (421*2π)/4831 weeks
422-.92835 -1.16025 (422*2π)/4831 weeks
423-.49681 -1.82733 (423*2π)/4831 weeks
424.23998 -2.31503 (424*2π)/4831 weeks
4251.01861 -1.94646 (425*2π)/4831 weeks
4261.5763 -1.6232 (426*2π)/4831 weeks
4271.83639 -.8826 (427*2π)/4831 weeks
4281.37295 -.21699 (428*2π)/4831 weeks
429.66709 .4224 (429*2π)/4831 weeks
430-.91124 .5713 (430*2π)/4831 weeks
431-2.03577 -.62185 (431*2π)/4831 weeks
432-2.31913 -2.35987 (432*2π)/4831 weeks
433-1.3338 -3.88255 (433*2π)/4831 weeks
434.60229 -4.55547 (434*2π)/4831 weeks
4351.96667 -3.78796 (435*2π)/4831 weeks
4362.69758 -2.32936 (436*2π)/4831 weeks
4372.27788 -1.07779 (437*2π)/4831 weeks
4381.23649 -.67736 (438*2π)/4831 weeks
439.18516 -.83202 (439*2π)/4831 weeks
440-1.06555 -1.63959 (440*2π)/4831 weeks
441-.99329 -2.65952 (441*2π)/4831 weeks
442-.26952 -3.96442 (442*2π)/4831 weeks
4431.27395 -4.57847 (443*2π)/4831 weeks
4442.53656 -4.09338 (444*2π)/4831 weeks
4453.35898 -2.961 (445*2π)/4831 weeks
4463.23336 -1.48773 (446*2π)/4831 weeks
4473.07031 -.30129 (447*2π)/4831 weeks
4481.48947 .4697 (448*2π)/4831 weeks
449-.28082 .04582 (449*2π)/4831 weeks
450-1.36154 -.93398 (450*2π)/4831 weeks
451-1.86973 -2.10935 (451*2π)/4831 weeks
452-1.42533 -3.90705 (452*2π)/4831 weeks
453-.09259 -5.20196 (453*2π)/4831 weeks
4542.6669 -5.65404 (454*2π)/4831 weeks
4554.62241 -4.14011 (455*2π)/4831 weeks
4564.61735 -1.81056 (456*2π)/4831 weeks
4573.19842 -.10185 (457*2π)/4831 weeks
458.16755 .36377 (458*2π)/4831 weeks
459-2.38195 -.93454 (459*2π)/4831 weeks
460-3.74869 -3.46858 (460*2π)/4831 weeks
461-1.68514 -6.05123 (461*2π)/4831 weeks
4621.643 -6.96651 (462*2π)/4831 weeks
4634.67375 -5.27742 (463*2π)/4831 weeks
4645.3634 -2.61622 (464*2π)/4831 weeks
4653.94435 -.80357 (465*2π)/4831 weeks
466.48022 .42055 (466*2π)/4831 weeks
467-2.30257 -.00514 (467*2π)/4831 weeks
468-5.62782 -3.03986 (468*2π)/4831 weeks
469-6.30737 -6.56096 (469*2π)/4831 weeks
470-5.5076 -11.02645 (470*2π)/4831 weeks
471-2.39496 -15.38253 (471*2π)/4831 weeks
4722.99227 -15.51226 (472*2π)/4831 weeks
4739.12609 -14.40678 (473*2π)/4831 weeks
47412.49628 -10.19058 (474*2π)/4831 weeks
47512.19085 -6.35532 (475*2π)/4831 weeks
4767.63779 -1.03467 (476*2π)/4831 weeks
477-1.86983 -1.34288 (477*2π)/4831 weeks
478-10.84449 -11.03896 (478*2π)/4831 weeks
479-11.67764 -24.73466 (479*2π)/4831 weeks
4801.21279 -38.88416 (480*2π)/4831 weeks
48126.79844 -44.40588 (481*2π)/4831 weeks

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