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Fourier Analysis of EEV (ProShares UltraShort MSCI Emerg)


EEV (ProShares UltraShort MSCI Emerg) appears to have interesting cyclic behaviour every 40 weeks (21.5446*sine), 44 weeks (19.1244*sine), and 48 weeks (16.0674*sine).

EEV (ProShares UltraShort MSCI Emerg) has an average price of 86.89 (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 1/9/2017 for EEV (ProShares UltraShort MSCI Emerg), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
086.89487   0 
195.49014 66.35941 (1*2π)/481481 weeks
247.06548 82.47009 (2*2π)/481241 weeks
34.23926 73.31439 (3*2π)/481160 weeks
4-19.2155 49.04127 (4*2π)/481120 weeks
5-24.30592 24.6284 (5*2π)/48196 weeks
6-14.61722 4.1557 (6*2π)/48180 weeks
7.81284 -.86225 (7*2π)/48169 weeks
810.24215 3.68295 (8*2π)/48160 weeks
913.62959 8.80617 (9*2π)/48153 weeks
1012.60552 16.06742 (10*2π)/48148 weeks
116.80271 19.12442 (11*2π)/48144 weeks
121.30823 21.54464 (12*2π)/48140 weeks
13-4.42524 17.70508 (13*2π)/48137 weeks
14-7.46109 13.67319 (14*2π)/48134 weeks
15-10.4403 8.96678 (15*2π)/48132 weeks
16-8.53958 2.4768 (16*2π)/48130 weeks
17-5.27067 -1.02207 (17*2π)/48128 weeks
18.27353 -2.6306 (18*2π)/48127 weeks
195.00034 -1.41337 (19*2π)/48125 weeks
207.81359 2.86482 (20*2π)/48124 weeks
216.00047 8.03623 (21*2π)/48123 weeks
221.36222 10.29284 (22*2π)/48122 weeks
23-4.1268 8.74004 (23*2π)/48121 weeks
24-5.45539 4.07069 (24*2π)/48120 weeks
25-4.17647 -.58394 (25*2π)/48119 weeks
26.69632 -3.29215 (26*2π)/48119 weeks
275.38569 -2.34031 (27*2π)/48118 weeks
288.76259 1.50913 (28*2π)/48117 weeks
297.98746 6.84701 (29*2π)/48117 weeks
303.65239 9.36183 (30*2π)/48116 weeks
31.05965 9.23575 (31*2π)/48116 weeks
32-2.95137 6.97794 (32*2π)/48115 weeks
33-3.55926 4.18188 (33*2π)/48115 weeks
34-3.31294 1.5629 (34*2π)/48114 weeks
35-1.27388 -.80495 (35*2π)/48114 weeks
361.73376 -.57823 (36*2π)/48113 weeks
372.55173 .6896 (37*2π)/48113 weeks
383.59752 1.85515 (38*2π)/48113 weeks
393.5598 3.42775 (39*2π)/48112 weeks
402.92651 4.52042 (40*2π)/48112 weeks
411.2227 4.92529 (41*2π)/48112 weeks
42-.23772 3.97359 (42*2π)/48111 weeks
43-.97901 3.23164 (43*2π)/48111 weeks
44-.37178 1.60336 (44*2π)/48111 weeks
45.40608 .96652 (45*2π)/48111 weeks
461.80757 .46158 (46*2π)/48110 weeks
473.23817 1.04475 (47*2π)/48110 weeks
484.01371 2.78936 (48*2π)/48110 weeks
493.80301 4.64123 (49*2π)/48110 weeks
501.67051 5.97881 (50*2π)/48110 weeks
51-.47851 5.84428 (51*2π)/4819 weeks
52-1.93884 4.2608 (52*2π)/4819 weeks
53-2.3625 2.18572 (53*2π)/4819 weeks
54-.86056 .52607 (54*2π)/4819 weeks
55.50495 .45623 (55*2π)/4819 weeks
561.6889 .89164 (56*2π)/4819 weeks
572.11728 2.0745 (57*2π)/4818 weeks
581.70146 2.76077 (58*2π)/4818 weeks
591.40109 3.68976 (59*2π)/4818 weeks
60.32185 3.93404 (60*2π)/4818 weeks
61-.36395 4.17162 (61*2π)/4818 weeks
62-2.10709 3.76084 (62*2π)/4818 weeks
63-3.28068 1.93488 (63*2π)/4818 weeks
64-3.00433 -.29863 (64*2π)/4818 weeks
65-1.09924 -2.28583 (65*2π)/4817 weeks
661.45524 -2.27541 (66*2π)/4817 weeks
673.06667 -.93243 (67*2π)/4817 weeks
684.42539 .88926 (68*2π)/4817 weeks
693.5892 3.85186 (69*2π)/4817 weeks
701.18352 4.75241 (70*2π)/4817 weeks
71-1.06096 4.44669 (71*2π)/4817 weeks
72-2.86037 2.01527 (72*2π)/4817 weeks
73-2.18015 -.23638 (73*2π)/4817 weeks
74-.70642 -1.86051 (74*2π)/4817 weeks
752.03491 -2.18525 (75*2π)/4816 weeks
763.87805 -.55306 (76*2π)/4816 weeks
774.50192 1.93623 (77*2π)/4816 weeks
783.45584 4.23181 (78*2π)/4816 weeks
791.10106 5.1022 (79*2π)/4816 weeks
80-.88475 4.37956 (80*2π)/4816 weeks
81-1.99233 2.67828 (81*2π)/4816 weeks
82-1.85858 1.0089 (82*2π)/4816 weeks
83-1.22586 .12377 (83*2π)/4816 weeks
84-.11672 -.7798 (84*2π)/4816 weeks
851.05841 -.73498 (85*2π)/4816 weeks
862.0812 .10027 (86*2π)/4816 weeks
872.43385 1.40066 (87*2π)/4816 weeks
881.93524 2.6873 (88*2π)/4815 weeks
89.90905 3.44217 (89*2π)/4815 weeks
90-.40317 3.40845 (90*2π)/4815 weeks
91-1.60942 2.35953 (91*2π)/4815 weeks
92-1.99044 .79951 (92*2π)/4815 weeks
93-1.46056 -.78822 (93*2π)/4815 weeks
94-.18299 -1.65843 (94*2π)/4815 weeks
951.6268 -1.58686 (95*2π)/4815 weeks
962.98368 -.30091 (96*2π)/4815 weeks
973.36114 1.61591 (97*2π)/4815 weeks
982.3368 3.12702 (98*2π)/4815 weeks
99.77054 3.55858 (99*2π)/4815 weeks
100-.96987 3.16896 (100*2π)/4815 weeks
101-1.89459 1.39626 (101*2π)/4815 weeks
102-1.55172 -.16575 (102*2π)/4815 weeks
103-.34998 -1.02848 (103*2π)/4815 weeks
1041.14084 -1.03227 (104*2π)/4815 weeks
1052.23915 -.01124 (105*2π)/4815 weeks
1062.45849 1.33705 (106*2π)/4815 weeks
1071.63496 2.57605 (107*2π)/4814 weeks
108.15337 2.78274 (108*2π)/4814 weeks
109-.72018 1.86045 (109*2π)/4814 weeks
110-1.07422 .84175 (110*2π)/4814 weeks
111-.44328 -.0528 (111*2π)/4814 weeks
112.21342 .03077 (112*2π)/4814 weeks
113.55493 .21806 (113*2π)/4814 weeks
114.70679 .54305 (114*2π)/4814 weeks
115.45705 .89998 (115*2π)/4814 weeks
116-.01288 .87265 (116*2π)/4814 weeks
117-.12621 .36776 (117*2π)/4814 weeks
118.25101 -.14345 (118*2π)/4814 weeks
119.61195 -.28518 (119*2π)/4814 weeks
1201.15238 .00233 (120*2π)/4814 weeks
121.98474 .69363 (121*2π)/4814 weeks
122.61432 .66378 (122*2π)/4814 weeks
123.57815 .51929 (123*2π)/4814 weeks
124.59939 .34993 (124*2π)/4814 weeks
125.88945 .49769 (125*2π)/4814 weeks
126.58208 .65 (126*2π)/4814 weeks
127.45284 .29007 (127*2π)/4814 weeks
128.49239 .09066 (128*2π)/4814 weeks
129.74819 -.25841 (129*2π)/4814 weeks
1301.37813 .00955 (130*2π)/4814 weeks
1311.61457 .37039 (131*2π)/4814 weeks
1321.64907 1.0823 (132*2π)/4814 weeks
1331.04851 1.4503 (133*2π)/4814 weeks
134.56802 1.37642 (134*2π)/4814 weeks
135.04093 1.18032 (135*2π)/4814 weeks
136-.21821 .56318 (136*2π)/4814 weeks
137-.1723 -.0918 (137*2π)/4814 weeks
138.31034 -.62567 (138*2π)/4813 weeks
1391.36894 -.57271 (139*2π)/4813 weeks
1401.71422 .02571 (140*2π)/4813 weeks
1411.95057 .56365 (141*2π)/4813 weeks
1421.81559 1.34249 (142*2π)/4813 weeks
1431.08821 1.95905 (143*2π)/4813 weeks
144-.0624 1.90435 (144*2π)/4813 weeks
145-.81805 1.11795 (145*2π)/4813 weeks
146-.90356 -.00535 (146*2π)/4813 weeks
147-.2205 -.90204 (147*2π)/4813 weeks
148.69741 -1.10247 (148*2π)/4813 weeks
1491.67503 -.84394 (149*2π)/4813 weeks
1502.22161 -.04497 (150*2π)/4813 weeks
1512.13918 1.10643 (151*2π)/4813 weeks
1521.45458 1.82554 (152*2π)/4813 weeks
153.40475 2.04649 (153*2π)/4813 weeks
154-.52612 1.46676 (154*2π)/4813 weeks
155-1.04919 .45969 (155*2π)/4813 weeks
156-.79685 -.79093 (156*2π)/4813 weeks
157.18465 -1.50712 (157*2π)/4813 weeks
1581.34614 -1.55644 (158*2π)/4813 weeks
1592.29444 -.86796 (159*2π)/4813 weeks
1602.56072 .22444 (160*2π)/4813 weeks
1612.30236 1.17233 (161*2π)/4813 weeks
1621.42315 1.62559 (162*2π)/4813 weeks
163.58468 1.50372 (163*2π)/4813 weeks
164-.06168 .82242 (164*2π)/4813 weeks
165.07761 -.11997 (165*2π)/4813 weeks
166.71198 -.53143 (166*2π)/4813 weeks
1671.6122 -.56753 (167*2π)/4813 weeks
1682.35859 .00966 (168*2π)/4813 weeks
1692.53462 .87594 (169*2π)/4813 weeks
1702.21196 1.97764 (170*2π)/4813 weeks
171.94761 2.61543 (171*2π)/4813 weeks
172-.02743 2.21335 (172*2π)/4813 weeks
173-.68232 1.40447 (173*2π)/4813 weeks
174-.62948 .34416 (174*2π)/4813 weeks
175-.0526 -.26984 (175*2π)/4813 weeks
176.65367 -.69922 (176*2π)/4813 weeks
1771.67423 -.23396 (177*2π)/4813 weeks
1781.86056 .55036 (178*2π)/4813 weeks
1791.93912 1.38947 (179*2π)/4813 weeks
1801.16313 2.28634 (180*2π)/4813 weeks
181-.01746 2.36552 (181*2π)/4813 weeks
182-.98758 1.61514 (182*2π)/4813 weeks
183-1.20979 .355 (183*2π)/4813 weeks
184-.5659 -.47567 (184*2π)/4813 weeks
185.28745 -.82716 (185*2π)/4813 weeks
1861.11512 -.53421 (186*2π)/4813 weeks
1871.60358 .39996 (187*2π)/4813 weeks
1881.33811 .95929 (188*2π)/4813 weeks
189.68359 1.41085 (189*2π)/4813 weeks
190.0882 1.19209 (190*2π)/4813 weeks
191-.17163 1.06932 (191*2π)/4813 weeks
192-.47753 .83592 (192*2π)/4813 weeks
193-.73963 .25128 (193*2π)/4812 weeks
194-.57996 -.50173 (194*2π)/4812 weeks
195.04778 -.91278 (195*2π)/4812 weeks
196.66279 -1.01179 (196*2π)/4812 weeks
1971.49602 -.66609 (197*2π)/4812 weeks
1981.82754 .21866 (198*2π)/4812 weeks
1991.49341 1.18379 (199*2π)/4812 weeks
200.50539 1.79404 (200*2π)/4812 weeks
201-.53185 1.40826 (201*2π)/4812 weeks
202-1.14586 .50169 (202*2π)/4812 weeks
203-1.14159 -.68984 (203*2π)/4812 weeks
204-.42068 -1.64663 (204*2π)/4812 weeks
205.76543 -1.92522 (205*2π)/4812 weeks
2062.03159 -1.52661 (206*2π)/4812 weeks
2072.743 -.31586 (207*2π)/4812 weeks
2082.60713 .98503 (208*2π)/4812 weeks
2091.69128 2.01677 (209*2π)/4812 weeks
210.17318 2.0859 (210*2π)/4812 weeks
211-.82823 1.33404 (211*2π)/4812 weeks
212-1.41957 .08562 (212*2π)/4812 weeks
213-.77289 -1.21786 (213*2π)/4812 weeks
214.35929 -1.79451 (214*2π)/4812 weeks
2151.74189 -1.80283 (215*2π)/4812 weeks
2162.95749 -.78945 (216*2π)/4812 weeks
2173.1049 .81105 (217*2π)/4812 weeks
2182.39202 2.3382 (218*2π)/4812 weeks
219.7953 3.07247 (219*2π)/4812 weeks
220-.90127 2.71358 (220*2π)/4812 weeks
221-2.06485 1.54868 (221*2π)/4812 weeks
222-2.28382 -.18637 (222*2π)/4812 weeks
223-1.5062 -1.63832 (223*2π)/4812 weeks
224-.0704 -2.5804 (224*2π)/4812 weeks
2251.80623 -2.26463 (225*2π)/4812 weeks
2262.80467 -.8143 (226*2π)/4812 weeks
2272.80231 .74202 (227*2π)/4812 weeks
2281.75362 2.16227 (228*2π)/4812 weeks
229-.10138 2.4766 (229*2π)/4812 weeks
230-1.6871 1.42363 (230*2π)/4812 weeks
231-1.9871 -.24242 (231*2π)/4812 weeks
232-1.26013 -1.77696 (232*2π)/4812 weeks
233.22404 -2.48768 (233*2π)/4812 weeks
2341.97842 -2.4707 (234*2π)/4812 weeks
2353.27756 -1.00497 (235*2π)/4812 weeks
2363.14939 .86993 (236*2π)/4812 weeks
2372.08592 2.1135 (237*2π)/4812 weeks
238.54265 2.65113 (238*2π)/4812 weeks
239-.84629 2.18624 (239*2π)/4812 weeks
240-1.98654 .91248 (240*2π)/4812 weeks
241-1.98654 -.91248 (241*2π)/4812 weeks
242-.84629 -2.18624 (242*2π)/4812 weeks
243.54265 -2.65113 (243*2π)/4812 weeks
2442.08592 -2.1135 (244*2π)/4812 weeks
2453.14939 -.86993 (245*2π)/4812 weeks
2463.27756 1.00497 (246*2π)/4812 weeks
2471.97842 2.4707 (247*2π)/4812 weeks
248.22404 2.48768 (248*2π)/4812 weeks
249-1.26013 1.77696 (249*2π)/4812 weeks
250-1.9871 .24242 (250*2π)/4812 weeks
251-1.6871 -1.42363 (251*2π)/4812 weeks
252-.10138 -2.4766 (252*2π)/4812 weeks
2531.75362 -2.16227 (253*2π)/4812 weeks
2542.80231 -.74202 (254*2π)/4812 weeks
2552.80467 .8143 (255*2π)/4812 weeks
2561.80623 2.26463 (256*2π)/4812 weeks
257-.0704 2.5804 (257*2π)/4812 weeks
258-1.5062 1.63832 (258*2π)/4812 weeks
259-2.28382 .18637 (259*2π)/4812 weeks
260-2.06485 -1.54868 (260*2π)/4812 weeks
261-.90127 -2.71358 (261*2π)/4812 weeks
262.7953 -3.07247 (262*2π)/4812 weeks
2632.39202 -2.3382 (263*2π)/4812 weeks
2643.1049 -.81105 (264*2π)/4812 weeks
2652.95749 .78945 (265*2π)/4812 weeks
2661.74189 1.80283 (266*2π)/4812 weeks
267.35929 1.79451 (267*2π)/4812 weeks
268-.77289 1.21786 (268*2π)/4812 weeks
269-1.41957 -.08562 (269*2π)/4812 weeks
270-.82823 -1.33404 (270*2π)/4812 weeks
271.17318 -2.0859 (271*2π)/4812 weeks
2721.69128 -2.01677 (272*2π)/4812 weeks
2732.60713 -.98503 (273*2π)/4812 weeks
2742.743 .31586 (274*2π)/4812 weeks
2752.03159 1.52661 (275*2π)/4812 weeks
276.76543 1.92522 (276*2π)/4812 weeks
277-.42068 1.64663 (277*2π)/4812 weeks
278-1.14159 .68984 (278*2π)/4812 weeks
279-1.14586 -.50169 (279*2π)/4812 weeks
280-.53185 -1.40826 (280*2π)/4812 weeks
281.50539 -1.79404 (281*2π)/4812 weeks
2821.49341 -1.18379 (282*2π)/4812 weeks
2831.82754 -.21866 (283*2π)/4812 weeks
2841.49602 .66609 (284*2π)/4812 weeks
285.66279 1.01179 (285*2π)/4812 weeks
286.04778 .91278 (286*2π)/4812 weeks
287-.57996 .50173 (287*2π)/4812 weeks
288-.73963 -.25128 (288*2π)/4812 weeks
289-.47753 -.83592 (289*2π)/4812 weeks
290-.17163 -1.06932 (290*2π)/4812 weeks
291.0882 -1.19209 (291*2π)/4812 weeks
292.68359 -1.41085 (292*2π)/4812 weeks
2931.33811 -.95929 (293*2π)/4812 weeks
2941.60358 -.39996 (294*2π)/4812 weeks
2951.11512 .53421 (295*2π)/4812 weeks
296.28745 .82716 (296*2π)/4812 weeks
297-.5659 .47567 (297*2π)/4812 weeks
298-1.20979 -.355 (298*2π)/4812 weeks
299-.98758 -1.61514 (299*2π)/4812 weeks
300-.01746 -2.36552 (300*2π)/4812 weeks
3011.16313 -2.28634 (301*2π)/4812 weeks
3021.93912 -1.38947 (302*2π)/4812 weeks
3031.86056 -.55036 (303*2π)/4812 weeks
3041.67423 .23396 (304*2π)/4812 weeks
305.65367 .69922 (305*2π)/4812 weeks
306-.0526 .26984 (306*2π)/4812 weeks
307-.62948 -.34416 (307*2π)/4812 weeks
308-.68232 -1.40447 (308*2π)/4812 weeks
309-.02743 -2.21335 (309*2π)/4812 weeks
310.94761 -2.61543 (310*2π)/4812 weeks
3112.21196 -1.97764 (311*2π)/4812 weeks
3122.53462 -.87594 (312*2π)/4812 weeks
3132.35859 -.00966 (313*2π)/4812 weeks
3141.6122 .56753 (314*2π)/4812 weeks
315.71198 .53143 (315*2π)/4812 weeks
316.07761 .11997 (316*2π)/4812 weeks
317-.06168 -.82242 (317*2π)/4812 weeks
318.58468 -1.50372 (318*2π)/4812 weeks
3191.42315 -1.62559 (319*2π)/4812 weeks
3202.30236 -1.17233 (320*2π)/4812 weeks
3212.56072 -.22444 (321*2π)/4811 weeks
3222.29444 .86796 (322*2π)/4811 weeks
3231.34614 1.55644 (323*2π)/4811 weeks
324.18465 1.50712 (324*2π)/4811 weeks
325-.79685 .79093 (325*2π)/4811 weeks
326-1.04919 -.45969 (326*2π)/4811 weeks
327-.52612 -1.46676 (327*2π)/4811 weeks
328.40475 -2.04649 (328*2π)/4811 weeks
3291.45458 -1.82554 (329*2π)/4811 weeks
3302.13918 -1.10643 (330*2π)/4811 weeks
3312.22161 .04497 (331*2π)/4811 weeks
3321.67503 .84394 (332*2π)/4811 weeks
333.69741 1.10247 (333*2π)/4811 weeks
334-.2205 .90204 (334*2π)/4811 weeks
335-.90356 .00535 (335*2π)/4811 weeks
336-.81805 -1.11795 (336*2π)/4811 weeks
337-.0624 -1.90435 (337*2π)/4811 weeks
3381.08821 -1.95905 (338*2π)/4811 weeks
3391.81559 -1.34249 (339*2π)/4811 weeks
3401.95057 -.56365 (340*2π)/4811 weeks
3411.71422 -.02571 (341*2π)/4811 weeks
3421.36894 .57271 (342*2π)/4811 weeks
343.31034 .62567 (343*2π)/4811 weeks
344-.1723 .0918 (344*2π)/4811 weeks
345-.21821 -.56318 (345*2π)/4811 weeks
346.04093 -1.18032 (346*2π)/4811 weeks
347.56802 -1.37642 (347*2π)/4811 weeks
3481.04851 -1.4503 (348*2π)/4811 weeks
3491.64907 -1.0823 (349*2π)/4811 weeks
3501.61457 -.37039 (350*2π)/4811 weeks
3511.37813 -.00955 (351*2π)/4811 weeks
352.74819 .25841 (352*2π)/4811 weeks
353.49239 -.09066 (353*2π)/4811 weeks
354.45284 -.29007 (354*2π)/4811 weeks
355.58208 -.65 (355*2π)/4811 weeks
356.88945 -.49769 (356*2π)/4811 weeks
357.59939 -.34993 (357*2π)/4811 weeks
358.57815 -.51929 (358*2π)/4811 weeks
359.61432 -.66378 (359*2π)/4811 weeks
360.98474 -.69363 (360*2π)/4811 weeks
3611.15238 -.00233 (361*2π)/4811 weeks
362.61195 .28518 (362*2π)/4811 weeks
363.25101 .14345 (363*2π)/4811 weeks
364-.12621 -.36776 (364*2π)/4811 weeks
365-.01288 -.87265 (365*2π)/4811 weeks
366.45705 -.89998 (366*2π)/4811 weeks
367.70679 -.54305 (367*2π)/4811 weeks
368.55493 -.21806 (368*2π)/4811 weeks
369.21342 -.03077 (369*2π)/4811 weeks
370-.44328 .0528 (370*2π)/4811 weeks
371-1.07422 -.84175 (371*2π)/4811 weeks
372-.72018 -1.86045 (372*2π)/4811 weeks
373.15337 -2.78274 (373*2π)/4811 weeks
3741.63496 -2.57605 (374*2π)/4811 weeks
3752.45849 -1.33705 (375*2π)/4811 weeks
3762.23915 .01124 (376*2π)/4811 weeks
3771.14084 1.03227 (377*2π)/4811 weeks
378-.34998 1.02848 (378*2π)/4811 weeks
379-1.55172 .16575 (379*2π)/4811 weeks
380-1.89459 -1.39626 (380*2π)/4811 weeks
381-.96987 -3.16896 (381*2π)/4811 weeks
382.77054 -3.55858 (382*2π)/4811 weeks
3832.3368 -3.12702 (383*2π)/4811 weeks
3843.36114 -1.61591 (384*2π)/4811 weeks
3852.98368 .30091 (385*2π)/4811 weeks
3861.6268 1.58686 (386*2π)/4811 weeks
387-.18299 1.65843 (387*2π)/4811 weeks
388-1.46056 .78822 (388*2π)/4811 weeks
389-1.99044 -.79951 (389*2π)/4811 weeks
390-1.60942 -2.35953 (390*2π)/4811 weeks
391-.40317 -3.40845 (391*2π)/4811 weeks
392.90905 -3.44217 (392*2π)/4811 weeks
3931.93524 -2.6873 (393*2π)/4811 weeks
3942.43385 -1.40066 (394*2π)/4811 weeks
3952.0812 -.10027 (395*2π)/4811 weeks
3961.05841 .73498 (396*2π)/4811 weeks
397-.11672 .7798 (397*2π)/4811 weeks
398-1.22586 -.12377 (398*2π)/4811 weeks
399-1.85858 -1.0089 (399*2π)/4811 weeks
400-1.99233 -2.67828 (400*2π)/4811 weeks
401-.88475 -4.37956 (401*2π)/4811 weeks
4021.10106 -5.1022 (402*2π)/4811 weeks
4033.45584 -4.23181 (403*2π)/4811 weeks
4044.50192 -1.93623 (404*2π)/4811 weeks
4053.87805 .55306 (405*2π)/4811 weeks
4062.03491 2.18525 (406*2π)/4811 weeks
407-.70642 1.86051 (407*2π)/4811 weeks
408-2.18015 .23638 (408*2π)/4811 weeks
409-2.86037 -2.01527 (409*2π)/4811 weeks
410-1.06096 -4.44669 (410*2π)/4811 weeks
4111.18352 -4.75241 (411*2π)/4811 weeks
4123.5892 -3.85186 (412*2π)/4811 weeks
4134.42539 -.88926 (413*2π)/4811 weeks
4143.06667 .93243 (414*2π)/4811 weeks
4151.45524 2.27541 (415*2π)/4811 weeks
416-1.09924 2.28583 (416*2π)/4811 weeks
417-3.00433 .29863 (417*2π)/4811 weeks
418-3.28068 -1.93488 (418*2π)/4811 weeks
419-2.10709 -3.76084 (419*2π)/4811 weeks
420-.36395 -4.17162 (420*2π)/4811 weeks
421.32185 -3.93404 (421*2π)/4811 weeks
4221.40109 -3.68976 (422*2π)/4811 weeks
4231.70146 -2.76077 (423*2π)/4811 weeks
4242.11728 -2.0745 (424*2π)/4811 weeks
4251.6889 -.89164 (425*2π)/4811 weeks
426.50495 -.45623 (426*2π)/4811 weeks
427-.86056 -.52607 (427*2π)/4811 weeks
428-2.3625 -2.18572 (428*2π)/4811 weeks
429-1.93884 -4.2608 (429*2π)/4811 weeks
430-.47851 -5.84428 (430*2π)/4811 weeks
4311.67051 -5.97881 (431*2π)/4811 weeks
4323.80301 -4.64123 (432*2π)/4811 weeks
4334.01371 -2.78936 (433*2π)/4811 weeks
4343.23817 -1.04475 (434*2π)/4811 weeks
4351.80757 -.46158 (435*2π)/4811 weeks
436.40608 -.96652 (436*2π)/4811 weeks
437-.37178 -1.60336 (437*2π)/4811 weeks
438-.97901 -3.23164 (438*2π)/4811 weeks
439-.23772 -3.97359 (439*2π)/4811 weeks
4401.2227 -4.92529 (440*2π)/4811 weeks
4412.92651 -4.52042 (441*2π)/4811 weeks
4423.5598 -3.42775 (442*2π)/4811 weeks
4433.59752 -1.85515 (443*2π)/4811 weeks
4442.55173 -.6896 (444*2π)/4811 weeks
4451.73376 .57823 (445*2π)/4811 weeks
446-1.27388 .80495 (446*2π)/4811 weeks
447-3.31294 -1.5629 (447*2π)/4811 weeks
448-3.55926 -4.18188 (448*2π)/4811 weeks
449-2.95137 -6.97794 (449*2π)/4811 weeks
450.05965 -9.23575 (450*2π)/4811 weeks
4513.65239 -9.36183 (451*2π)/4811 weeks
4527.98746 -6.84701 (452*2π)/4811 weeks
4538.76259 -1.50913 (453*2π)/4811 weeks
4545.38569 2.34031 (454*2π)/4811 weeks
455.69632 3.29215 (455*2π)/4811 weeks
456-4.17647 .58394 (456*2π)/4811 weeks
457-5.45539 -4.07069 (457*2π)/4811 weeks
458-4.1268 -8.74004 (458*2π)/4811 weeks
4591.36222 -10.29284 (459*2π)/4811 weeks
4606.00047 -8.03623 (460*2π)/4811 weeks
4617.81359 -2.86482 (461*2π)/4811 weeks
4625.00034 1.41337 (462*2π)/4811 weeks
463.27353 2.6306 (463*2π)/4811 weeks
464-5.27067 1.02207 (464*2π)/4811 weeks
465-8.53958 -2.4768 (465*2π)/4811 weeks
466-10.4403 -8.96678 (466*2π)/4811 weeks
467-7.46109 -13.67319 (467*2π)/4811 weeks
468-4.42524 -17.70508 (468*2π)/4811 weeks
4691.30823 -21.54464 (469*2π)/4811 weeks
4706.80271 -19.12442 (470*2π)/4811 weeks
47112.60552 -16.06742 (471*2π)/4811 weeks
47213.62959 -8.80617 (472*2π)/4811 weeks
47310.24215 -3.68295 (473*2π)/4811 weeks
474.81284 .86225 (474*2π)/4811 weeks
475-14.61722 -4.1557 (475*2π)/4811 weeks
476-24.30592 -24.6284 (476*2π)/4811 weeks
477-19.2155 -49.04127 (477*2π)/4811 weeks
4784.23926 -73.31439 (478*2π)/4811 weeks
47947.06548 -82.47009 (479*2π)/4811 weeks

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