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Fourier Analysis of SDP (ProShares UltraShort Utilities)


SDP (ProShares UltraShort Utilities) appears to have interesting cyclic behaviour every 37 weeks (9.3632*sine), 48 weeks (9.1923*sine), and 28 weeks (7.2731*cosine).

SDP (ProShares UltraShort Utilities) has an average price of 168.43 (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 3/14/2007 to 3/20/2017 for SDP (ProShares UltraShort Utilities), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0168.4313   0 
124.67755 142.1102 (1*2π)/524524 weeks
2-26.41542 58.56733 (2*2π)/524262 weeks
3-16.10589 14.58274 (3*2π)/524175 weeks
4.8571 5.21868 (4*2π)/524131 weeks
514.18047 12.76714 (5*2π)/524105 weeks
610.76962 23.38303 (6*2π)/52487 weeks
7-1.1753 21.42276 (7*2π)/52475 weeks
8-8.68316 10.3745 (8*2π)/52466 weeks
9-.64498 4.08757 (9*2π)/52458 weeks
101.49561 6.24731 (10*2π)/52452 weeks
11.33036 9.19226 (11*2π)/52448 weeks
121.68439 6.00496 (12*2π)/52444 weeks
13.20873 7.0476 (13*2π)/52440 weeks
14.57884 9.36317 (14*2π)/52437 weeks
15-2.78173 7.66514 (15*2π)/52435 weeks
16-3.70077 6.95279 (16*2π)/52433 weeks
17-6.54498 -1.60486 (17*2π)/52431 weeks
181.54023 -3.56071 (18*2π)/52429 weeks
197.27308 .64618 (19*2π)/52428 weeks
206.07927 6.05111 (20*2π)/52426 weeks
211.22424 8.58992 (21*2π)/52425 weeks
22-2.19025 4.76894 (22*2π)/52424 weeks
23-.8126 1.35541 (23*2π)/52423 weeks
243.23326 .63732 (24*2π)/52422 weeks
254.2998 4.15668 (25*2π)/52421 weeks
26.96858 5.65806 (26*2π)/52420 weeks
27-.61622 4.63977 (27*2π)/52419 weeks
28-2.37436 3.65327 (28*2π)/52419 weeks
29-1.13551 -1.13228 (29*2π)/52418 weeks
303.51546 -.78639 (30*2π)/52417 weeks
315.34857 3.82312 (31*2π)/52417 weeks
321.71212 6.37204 (32*2π)/52416 weeks
33-1.71073 4.21994 (33*2π)/52416 weeks
34.19034 1.6874 (34*2π)/52415 weeks
35.94204 1.58553 (35*2π)/52415 weeks
36-.20498 1.94593 (36*2π)/52415 weeks
371.90671 1.58415 (37*2π)/52414 weeks
381.47559 2.55462 (38*2π)/52414 weeks
39.50134 3.5634 (39*2π)/52413 weeks
40.8834 1.17672 (40*2π)/52413 weeks
41.23096 2.88247 (41*2π)/52413 weeks
42-.55669 2.17949 (42*2π)/52412 weeks
43-.19265 .40902 (43*2π)/52412 weeks
441.89526 .15422 (44*2π)/52412 weeks
454.1618 1.82807 (45*2π)/52412 weeks
462.46148 4.62748 (46*2π)/52411 weeks
47-.89044 4.27459 (47*2π)/52411 weeks
48-1.70618 1.8381 (48*2π)/52411 weeks
49.05305 -.95534 (49*2π)/52411 weeks
502.83161 .55199 (50*2π)/52410 weeks
513.65221 2.47877 (51*2π)/52410 weeks
522.06127 5.53339 (52*2π)/52410 weeks
53-1.3498 4.79464 (53*2π)/52410 weeks
54-3.6112 .81273 (54*2π)/52410 weeks
55-.56573 -1.44856 (55*2π)/52410 weeks
562.70763 -.36545 (56*2π)/5249 weeks
573.29594 2.71768 (57*2π)/5249 weeks
58.1685 3.51962 (58*2π)/5249 weeks
59-.34574 1.58697 (59*2π)/5249 weeks
60.49874 1.56744 (60*2π)/5249 weeks
61.155 1.30649 (61*2π)/5249 weeks
62.43859 1.91074 (62*2π)/5248 weeks
63-.34443 1.34048 (63*2π)/5248 weeks
641.03151 1.35944 (64*2π)/5248 weeks
65.24605 1.08504 (65*2π)/5248 weeks
66.78359 1.76811 (66*2π)/5248 weeks
67-.8825 1.71319 (67*2π)/5248 weeks
68-.79257 -.38225 (68*2π)/5248 weeks
69.87999 -.50802 (69*2π)/5248 weeks
702.20264 -.02565 (70*2π)/5247 weeks
712.07539 2.38249 (71*2π)/5247 weeks
72.54017 2.47759 (72*2π)/5247 weeks
73-.40083 2.14381 (73*2π)/5247 weeks
74-1.57877 .07179 (74*2π)/5247 weeks
75.7315 -1.16707 (75*2π)/5247 weeks
762.55523 .34606 (76*2π)/5247 weeks
771.8963 1.99032 (77*2π)/5247 weeks
78.47699 2.42803 (78*2π)/5247 weeks
79-.57558 1.12545 (79*2π)/5247 weeks
80-.57586 .05261 (80*2π)/5247 weeks
811.61388 -.93479 (81*2π)/5246 weeks
822.81743 1.09395 (82*2π)/5246 weeks
832.04022 3.18327 (83*2π)/5246 weeks
84-.59027 2.4361 (84*2π)/5246 weeks
85-.2431 .6401 (85*2π)/5246 weeks
86.4041 .15879 (86*2π)/5246 weeks
871.3345 .73251 (87*2π)/5246 weeks
88.77548 1.64308 (88*2π)/5246 weeks
89.19489 1.31177 (89*2π)/5246 weeks
90.59004 .50884 (90*2π)/5246 weeks
911.26744 1.41912 (91*2π)/5246 weeks
92.18208 1.99275 (92*2π)/5246 weeks
93-1.12132 1.0844 (93*2π)/5246 weeks
94-.44022 -.39396 (94*2π)/5246 weeks
951.16785 -.71697 (95*2π)/5246 weeks
962.13726 .62997 (96*2π)/5245 weeks
971.29992 2.43514 (97*2π)/5245 weeks
98-1.05283 2.60492 (98*2π)/5245 weeks
99-2.00432 -.05336 (99*2π)/5245 weeks
100.10946 -1.89937 (100*2π)/5245 weeks
1012.07835 -.60224 (101*2π)/5245 weeks
1022.29365 .4029 (102*2π)/5245 weeks
1031.82321 1.79869 (103*2π)/5245 weeks
104.13785 1.70694 (104*2π)/5245 weeks
105-.22651 .77624 (105*2π)/5245 weeks
106.45705 -.03165 (106*2π)/5245 weeks
1071.47148 .23928 (107*2π)/5245 weeks
1082.00597 .76704 (108*2π)/5245 weeks
1091.44553 1.56634 (109*2π)/5245 weeks
110.54443 2.1867 (110*2π)/5245 weeks
111-.90131 1.2919 (111*2π)/5245 weeks
112-.61015 .23298 (112*2π)/5245 weeks
113.15226 -.52007 (113*2π)/5245 weeks
1141.57154 -.17087 (114*2π)/5245 weeks
1151.89702 1.25602 (115*2π)/5245 weeks
116.75835 1.61591 (116*2π)/5245 weeks
117-.1397 1.47039 (117*2π)/5244 weeks
118.0483 .37713 (118*2π)/5244 weeks
119.08797 .43116 (119*2π)/5244 weeks
120.42641 .2607 (120*2π)/5244 weeks
1211.03153 .69153 (121*2π)/5244 weeks
1221.09484 1.22767 (122*2π)/5244 weeks
123-.27647 1.48511 (123*2π)/5244 weeks
124-.98189 .21136 (124*2π)/5244 weeks
125.22457 -.60164 (125*2π)/5244 weeks
126.86688 .24814 (126*2π)/5244 weeks
127.86705 -.03823 (127*2π)/5244 weeks
1281.28805 .23639 (128*2π)/5244 weeks
129.85907 .7707 (129*2π)/5244 weeks
130.48656 .75976 (130*2π)/5244 weeks
131.1541 .51746 (131*2π)/5244 weeks
132.32467 -.42077 (132*2π)/5244 weeks
1331.28686 -.44536 (133*2π)/5244 weeks
1341.99971 .50209 (134*2π)/5244 weeks
135.90112 2.03014 (135*2π)/5244 weeks
136-.39462 .77737 (136*2π)/5244 weeks
137.69069 -.22469 (137*2π)/5244 weeks
138.76531 .70794 (138*2π)/5244 weeks
139.51614 .44869 (139*2π)/5244 weeks
140.79435 .2808 (140*2π)/5244 weeks
1411.21686 .46832 (141*2π)/5244 weeks
1421.08733 1.02765 (142*2π)/5244 weeks
143.53145 1.43126 (143*2π)/5244 weeks
144-.45761 1.11453 (144*2π)/5244 weeks
145-.37352 -.75971 (145*2π)/5244 weeks
1461.17023 -.35181 (146*2π)/5244 weeks
1471.50779 .63155 (147*2π)/5244 weeks
148.74571 1.22754 (148*2π)/5244 weeks
149.05805 .77312 (149*2π)/5244 weeks
150.42999 .46357 (150*2π)/5243 weeks
151-.00725 .05455 (151*2π)/5243 weeks
1521.1216 -.43465 (152*2π)/5243 weeks
1531.44779 1.04516 (153*2π)/5243 weeks
154.2124 1.06926 (154*2π)/5243 weeks
155.25168 .23125 (155*2π)/5243 weeks
156.80721 .2664 (156*2π)/5243 weeks
157.36781 .59816 (157*2π)/5243 weeks
158.43955 .52808 (158*2π)/5243 weeks
159.0066 .43676 (159*2π)/5243 weeks
160.538 -.05786 (160*2π)/5243 weeks
161.71279 .00446 (161*2π)/5243 weeks
162.96425 .14554 (162*2π)/5243 weeks
163.37234 .56122 (163*2π)/5243 weeks
164.27671 -.06833 (164*2π)/5243 weeks
1651.04189 -.37719 (165*2π)/5243 weeks
1661.59847 .01677 (166*2π)/5243 weeks
1671.65495 .93109 (167*2π)/5243 weeks
168.55409 1.43304 (168*2π)/5243 weeks
169-.00092 .88795 (169*2π)/5243 weeks
170-.0698 .12784 (170*2π)/5243 weeks
171.58613 -.53203 (171*2π)/5243 weeks
1721.30556 .35448 (172*2π)/5243 weeks
1731.12475 .79146 (173*2π)/5243 weeks
174.08357 1.15533 (174*2π)/5243 weeks
175-.09709 .33171 (175*2π)/5243 weeks
176.20801 -.11037 (176*2π)/5243 weeks
177.87938 .02688 (177*2π)/5243 weeks
178.77743 .48609 (178*2π)/5243 weeks
179.5181 .51225 (179*2π)/5243 weeks
180.66342 .55122 (180*2π)/5243 weeks
181.15408 .5411 (181*2π)/5243 weeks
182-.18194 .37418 (182*2π)/5243 weeks
183.00406 -.2129 (183*2π)/5243 weeks
184.36536 -.66675 (184*2π)/5243 weeks
1851.05452 -.97261 (185*2π)/5243 weeks
1862.34724 .08804 (186*2π)/5243 weeks
1871.04779 1.14955 (187*2π)/5243 weeks
188.23401 .84095 (188*2π)/5243 weeks
189.25638 .10989 (189*2π)/5243 weeks
190.76085 -.24299 (190*2π)/5243 weeks
191.9305 .28385 (191*2π)/5243 weeks
1921.10829 .30364 (192*2π)/5243 weeks
193.83592 1.46511 (193*2π)/5243 weeks
194-.26658 .93564 (194*2π)/5243 weeks
195-.54735 .12932 (195*2π)/5243 weeks
196-.17833 -.64643 (196*2π)/5243 weeks
197.73958 -1.11698 (197*2π)/5243 weeks
1981.79377 -.15456 (198*2π)/5243 weeks
1991.48312 1.23194 (199*2π)/5243 weeks
200-.14864 1.37929 (200*2π)/5243 weeks
201-.51688 .01091 (201*2π)/5243 weeks
202.1738 -.76403 (202*2π)/5243 weeks
203.85391 -.59952 (203*2π)/5243 weeks
2041.5659 .28639 (204*2π)/5243 weeks
205.90103 .91849 (205*2π)/5243 weeks
206-.27995 .70781 (206*2π)/5243 weeks
207-.21434 -.25796 (207*2π)/5243 weeks
208.56541 -.51896 (208*2π)/5243 weeks
209.44333 -.17844 (209*2π)/5243 weeks
210.75286 -.58026 (210*2π)/5242 weeks
2111.38801 -.23494 (211*2π)/5242 weeks
212.90647 .51615 (212*2π)/5242 weeks
213.77275 .19239 (213*2π)/5242 weeks
214.58611 .36596 (214*2π)/5242 weeks
215.31389 .20733 (215*2π)/5242 weeks
216.29222 -.51696 (216*2π)/5242 weeks
2171.38361 -.90294 (217*2π)/5242 weeks
2181.67216 .50754 (218*2π)/5242 weeks
219.71955 1.06373 (219*2π)/5242 weeks
220.4194 .38483 (220*2π)/5242 weeks
221.24016 .11934 (221*2π)/5242 weeks
222.48686 -.38349 (222*2π)/5242 weeks
2231.11324 -.3804 (223*2π)/5242 weeks
2241.61096 .23629 (224*2π)/5242 weeks
2251.29705 .94207 (225*2π)/5242 weeks
226.42391 1.19426 (226*2π)/5242 weeks
227-.07558 .61454 (227*2π)/5242 weeks
228-.10807 -.00046 (228*2π)/5242 weeks
229.44691 -.13472 (229*2π)/5242 weeks
230.59646 -.29384 (230*2π)/5242 weeks
2311.00779 .44103 (231*2π)/5242 weeks
232.51131 .40673 (232*2π)/5242 weeks
233.36793 .52837 (233*2π)/5242 weeks
234-.16122 -.01946 (234*2π)/5242 weeks
235.19384 -.56602 (235*2π)/5242 weeks
236.92444 -.41299 (236*2π)/5242 weeks
2371.28973 -.09299 (237*2π)/5242 weeks
2381.08813 .84762 (238*2π)/5242 weeks
239.07339 .77613 (239*2π)/5242 weeks
240-.26002 .12291 (240*2π)/5242 weeks
241-.04042 -.59922 (241*2π)/5242 weeks
242.73381 -.8051 (242*2π)/5242 weeks
2431.27079 -.37715 (243*2π)/5242 weeks
2441.29458 .6046 (244*2π)/5242 weeks
245.44359 .90141 (245*2π)/5242 weeks
246-.17932 .21264 (246*2π)/5242 weeks
247-.23366 -.14077 (247*2π)/5242 weeks
248.29598 -1.11212 (248*2π)/5242 weeks
2491.24635 -.39731 (249*2π)/5242 weeks
2501.12377 .15929 (250*2π)/5242 weeks
251.2127 .18326 (251*2π)/5242 weeks
252.32324 -.30044 (252*2π)/5242 weeks
253.50735 -.46912 (253*2π)/5242 weeks
254.61088 -.62986 (254*2π)/5242 weeks
2551.50236 -.57252 (255*2π)/5242 weeks
2561.62982 .34782 (256*2π)/5242 weeks
257.60534 .5962 (257*2π)/5242 weeks
258.40885 .11898 (258*2π)/5242 weeks
259.26191 -.08414 (259*2π)/5242 weeks
260.35147 -.57507 (260*2π)/5242 weeks
2611.1937 -.93934 (261*2π)/5242 weeks
2621.91514   (262*2π)/5242 weeks
2631.1937 .93934 (263*2π)/5242 weeks
264.35147 .57507 (264*2π)/5242 weeks
265.26191 .08414 (265*2π)/5242 weeks
266.40885 -.11898 (266*2π)/5242 weeks
267.60534 -.5962 (267*2π)/5242 weeks
2681.62982 -.34782 (268*2π)/5242 weeks
2691.50236 .57252 (269*2π)/5242 weeks
270.61088 .62986 (270*2π)/5242 weeks
271.50735 .46912 (271*2π)/5242 weeks
272.32324 .30044 (272*2π)/5242 weeks
273.2127 -.18326 (273*2π)/5242 weeks
2741.12377 -.15929 (274*2π)/5242 weeks
2751.24635 .39731 (275*2π)/5242 weeks
276.29598 1.11212 (276*2π)/5242 weeks
277-.23366 .14077 (277*2π)/5242 weeks
278-.17932 -.21264 (278*2π)/5242 weeks
279.44359 -.90141 (279*2π)/5242 weeks
2801.29458 -.6046 (280*2π)/5242 weeks
2811.27079 .37715 (281*2π)/5242 weeks
282.73381 .8051 (282*2π)/5242 weeks
283-.04042 .59922 (283*2π)/5242 weeks
284-.26002 -.12291 (284*2π)/5242 weeks
285.07339 -.77613 (285*2π)/5242 weeks
2861.08813 -.84762 (286*2π)/5242 weeks
2871.28973 .09299 (287*2π)/5242 weeks
288.92444 .41299 (288*2π)/5242 weeks
289.19384 .56602 (289*2π)/5242 weeks
290-.16122 .01946 (290*2π)/5242 weeks
291.36793 -.52837 (291*2π)/5242 weeks
292.51131 -.40673 (292*2π)/5242 weeks
2931.00779 -.44103 (293*2π)/5242 weeks
294.59646 .29384 (294*2π)/5242 weeks
295.44691 .13472 (295*2π)/5242 weeks
296-.10807 .00046 (296*2π)/5242 weeks
297-.07558 -.61454 (297*2π)/5242 weeks
298.42391 -1.19426 (298*2π)/5242 weeks
2991.29705 -.94207 (299*2π)/5242 weeks
3001.61096 -.23629 (300*2π)/5242 weeks
3011.11324 .3804 (301*2π)/5242 weeks
302.48686 .38349 (302*2π)/5242 weeks
303.24016 -.11934 (303*2π)/5242 weeks
304.4194 -.38483 (304*2π)/5242 weeks
305.71955 -1.06373 (305*2π)/5242 weeks
3061.67216 -.50754 (306*2π)/5242 weeks
3071.38361 .90294 (307*2π)/5242 weeks
308.29222 .51696 (308*2π)/5242 weeks
309.31389 -.20733 (309*2π)/5242 weeks
310.58611 -.36596 (310*2π)/5242 weeks
311.77275 -.19239 (311*2π)/5242 weeks
312.90647 -.51615 (312*2π)/5242 weeks
3131.38801 .23494 (313*2π)/5242 weeks
314.75286 .58026 (314*2π)/5242 weeks
315.44333 .17844 (315*2π)/5242 weeks
316.56541 .51896 (316*2π)/5242 weeks
317-.21434 .25796 (317*2π)/5242 weeks
318-.27995 -.70781 (318*2π)/5242 weeks
319.90103 -.91849 (319*2π)/5242 weeks
3201.5659 -.28639 (320*2π)/5242 weeks
321.85391 .59952 (321*2π)/5242 weeks
322.1738 .76403 (322*2π)/5242 weeks
323-.51688 -.01091 (323*2π)/5242 weeks
324-.14864 -1.37929 (324*2π)/5242 weeks
3251.48312 -1.23194 (325*2π)/5242 weeks
3261.79377 .15456 (326*2π)/5242 weeks
327.73958 1.11698 (327*2π)/5242 weeks
328-.17833 .64643 (328*2π)/5242 weeks
329-.54735 -.12932 (329*2π)/5242 weeks
330-.26658 -.93564 (330*2π)/5242 weeks
331.83592 -1.46511 (331*2π)/5242 weeks
3321.10829 -.30364 (332*2π)/5242 weeks
333.9305 -.28385 (333*2π)/5242 weeks
334.76085 .24299 (334*2π)/5242 weeks
335.25638 -.10989 (335*2π)/5242 weeks
336.23401 -.84095 (336*2π)/5242 weeks
3371.04779 -1.14955 (337*2π)/5242 weeks
3382.34724 -.08804 (338*2π)/5242 weeks
3391.05452 .97261 (339*2π)/5242 weeks
340.36536 .66675 (340*2π)/5242 weeks
341.00406 .2129 (341*2π)/5242 weeks
342-.18194 -.37418 (342*2π)/5242 weeks
343.15408 -.5411 (343*2π)/5242 weeks
344.66342 -.55122 (344*2π)/5242 weeks
345.5181 -.51225 (345*2π)/5242 weeks
346.77743 -.48609 (346*2π)/5242 weeks
347.87938 -.02688 (347*2π)/5242 weeks
348.20801 .11037 (348*2π)/5242 weeks
349-.09709 -.33171 (349*2π)/5242 weeks
350.08357 -1.15533 (350*2π)/5241 weeks
3511.12475 -.79146 (351*2π)/5241 weeks
3521.30556 -.35448 (352*2π)/5241 weeks
353.58613 .53203 (353*2π)/5241 weeks
354-.0698 -.12784 (354*2π)/5241 weeks
355-.00092 -.88795 (355*2π)/5241 weeks
356.55409 -1.43304 (356*2π)/5241 weeks
3571.65495 -.93109 (357*2π)/5241 weeks
3581.59847 -.01677 (358*2π)/5241 weeks
3591.04189 .37719 (359*2π)/5241 weeks
360.27671 .06833 (360*2π)/5241 weeks
361.37234 -.56122 (361*2π)/5241 weeks
362.96425 -.14554 (362*2π)/5241 weeks
363.71279 -.00446 (363*2π)/5241 weeks
364.538 .05786 (364*2π)/5241 weeks
365.0066 -.43676 (365*2π)/5241 weeks
366.43955 -.52808 (366*2π)/5241 weeks
367.36781 -.59816 (367*2π)/5241 weeks
368.80721 -.2664 (368*2π)/5241 weeks
369.25168 -.23125 (369*2π)/5241 weeks
370.2124 -1.06926 (370*2π)/5241 weeks
3711.44779 -1.04516 (371*2π)/5241 weeks
3721.1216 .43465 (372*2π)/5241 weeks
373-.00725 -.05455 (373*2π)/5241 weeks
374.42999 -.46357 (374*2π)/5241 weeks
375.05805 -.77312 (375*2π)/5241 weeks
376.74571 -1.22754 (376*2π)/5241 weeks
3771.50779 -.63155 (377*2π)/5241 weeks
3781.17023 .35181 (378*2π)/5241 weeks
379-.37352 .75971 (379*2π)/5241 weeks
380-.45761 -1.11453 (380*2π)/5241 weeks
381.53145 -1.43126 (381*2π)/5241 weeks
3821.08733 -1.02765 (382*2π)/5241 weeks
3831.21686 -.46832 (383*2π)/5241 weeks
384.79435 -.2808 (384*2π)/5241 weeks
385.51614 -.44869 (385*2π)/5241 weeks
386.76531 -.70794 (386*2π)/5241 weeks
387.69069 .22469 (387*2π)/5241 weeks
388-.39462 -.77737 (388*2π)/5241 weeks
389.90112 -2.03014 (389*2π)/5241 weeks
3901.99971 -.50209 (390*2π)/5241 weeks
3911.28686 .44536 (391*2π)/5241 weeks
392.32467 .42077 (392*2π)/5241 weeks
393.1541 -.51746 (393*2π)/5241 weeks
394.48656 -.75976 (394*2π)/5241 weeks
395.85907 -.7707 (395*2π)/5241 weeks
3961.28805 -.23639 (396*2π)/5241 weeks
397.86705 .03823 (397*2π)/5241 weeks
398.86688 -.24814 (398*2π)/5241 weeks
399.22457 .60164 (399*2π)/5241 weeks
400-.98189 -.21136 (400*2π)/5241 weeks
401-.27647 -1.48511 (401*2π)/5241 weeks
4021.09484 -1.22767 (402*2π)/5241 weeks
4031.03153 -.69153 (403*2π)/5241 weeks
404.42641 -.2607 (404*2π)/5241 weeks
405.08797 -.43116 (405*2π)/5241 weeks
406.0483 -.37713 (406*2π)/5241 weeks
407-.1397 -1.47039 (407*2π)/5241 weeks
408.75835 -1.61591 (408*2π)/5241 weeks
4091.89702 -1.25602 (409*2π)/5241 weeks
4101.57154 .17087 (410*2π)/5241 weeks
411.15226 .52007 (411*2π)/5241 weeks
412-.61015 -.23298 (412*2π)/5241 weeks
413-.90131 -1.2919 (413*2π)/5241 weeks
414.54443 -2.1867 (414*2π)/5241 weeks
4151.44553 -1.56634 (415*2π)/5241 weeks
4162.00597 -.76704 (416*2π)/5241 weeks
4171.47148 -.23928 (417*2π)/5241 weeks
418.45705 .03165 (418*2π)/5241 weeks
419-.22651 -.77624 (419*2π)/5241 weeks
420.13785 -1.70694 (420*2π)/5241 weeks
4211.82321 -1.79869 (421*2π)/5241 weeks
4222.29365 -.4029 (422*2π)/5241 weeks
4232.07835 .60224 (423*2π)/5241 weeks
424.10946 1.89937 (424*2π)/5241 weeks
425-2.00432 .05336 (425*2π)/5241 weeks
426-1.05283 -2.60492 (426*2π)/5241 weeks
4271.29992 -2.43514 (427*2π)/5241 weeks
4282.13726 -.62997 (428*2π)/5241 weeks
4291.16785 .71697 (429*2π)/5241 weeks
430-.44022 .39396 (430*2π)/5241 weeks
431-1.12132 -1.0844 (431*2π)/5241 weeks
432.18208 -1.99275 (432*2π)/5241 weeks
4331.26744 -1.41912 (433*2π)/5241 weeks
434.59004 -.50884 (434*2π)/5241 weeks
435.19489 -1.31177 (435*2π)/5241 weeks
436.77548 -1.64308 (436*2π)/5241 weeks
4371.3345 -.73251 (437*2π)/5241 weeks
438.4041 -.15879 (438*2π)/5241 weeks
439-.2431 -.6401 (439*2π)/5241 weeks
440-.59027 -2.4361 (440*2π)/5241 weeks
4412.04022 -3.18327 (441*2π)/5241 weeks
4422.81743 -1.09395 (442*2π)/5241 weeks
4431.61388 .93479 (443*2π)/5241 weeks
444-.57586 -.05261 (444*2π)/5241 weeks
445-.57558 -1.12545 (445*2π)/5241 weeks
446.47699 -2.42803 (446*2π)/5241 weeks
4471.8963 -1.99032 (447*2π)/5241 weeks
4482.55523 -.34606 (448*2π)/5241 weeks
449.7315 1.16707 (449*2π)/5241 weeks
450-1.57877 -.07179 (450*2π)/5241 weeks
451-.40083 -2.14381 (451*2π)/5241 weeks
452.54017 -2.47759 (452*2π)/5241 weeks
4532.07539 -2.38249 (453*2π)/5241 weeks
4542.20264 .02565 (454*2π)/5241 weeks
455.87999 .50802 (455*2π)/5241 weeks
456-.79257 .38225 (456*2π)/5241 weeks
457-.8825 -1.71319 (457*2π)/5241 weeks
458.78359 -1.76811 (458*2π)/5241 weeks
459.24605 -1.08504 (459*2π)/5241 weeks
4601.03151 -1.35944 (460*2π)/5241 weeks
461-.34443 -1.34048 (461*2π)/5241 weeks
462.43859 -1.91074 (462*2π)/5241 weeks
463.155 -1.30649 (463*2π)/5241 weeks
464.49874 -1.56744 (464*2π)/5241 weeks
465-.34574 -1.58697 (465*2π)/5241 weeks
466.1685 -3.51962 (466*2π)/5241 weeks
4673.29594 -2.71768 (467*2π)/5241 weeks
4682.70763 .36545 (468*2π)/5241 weeks
469-.56573 1.44856 (469*2π)/5241 weeks
470-3.6112 -.81273 (470*2π)/5241 weeks
471-1.3498 -4.79464 (471*2π)/5241 weeks
4722.06127 -5.53339 (472*2π)/5241 weeks
4733.65221 -2.47877 (473*2π)/5241 weeks
4742.83161 -.55199 (474*2π)/5241 weeks
475.05305 .95534 (475*2π)/5241 weeks
476-1.70618 -1.8381 (476*2π)/5241 weeks
477-.89044 -4.27459 (477*2π)/5241 weeks
4782.46148 -4.62748 (478*2π)/5241 weeks
4794.1618 -1.82807 (479*2π)/5241 weeks
4801.89526 -.15422 (480*2π)/5241 weeks
481-.19265 -.40902 (481*2π)/5241 weeks
482-.55669 -2.17949 (482*2π)/5241 weeks
483.23096 -2.88247 (483*2π)/5241 weeks
484.8834 -1.17672 (484*2π)/5241 weeks
485.50134 -3.5634 (485*2π)/5241 weeks
4861.47559 -2.55462 (486*2π)/5241 weeks
4871.90671 -1.58415 (487*2π)/5241 weeks
488-.20498 -1.94593 (488*2π)/5241 weeks
489.94204 -1.58553 (489*2π)/5241 weeks
490.19034 -1.6874 (490*2π)/5241 weeks
491-1.71073 -4.21994 (491*2π)/5241 weeks
4921.71212 -6.37204 (492*2π)/5241 weeks
4935.34857 -3.82312 (493*2π)/5241 weeks
4943.51546 .78639 (494*2π)/5241 weeks
495-1.13551 1.13228 (495*2π)/5241 weeks
496-2.37436 -3.65327 (496*2π)/5241 weeks
497-.61622 -4.63977 (497*2π)/5241 weeks
498.96858 -5.65806 (498*2π)/5241 weeks
4994.2998 -4.15668 (499*2π)/5241 weeks
5003.23326 -.63732 (500*2π)/5241 weeks
501-.8126 -1.35541 (501*2π)/5241 weeks
502-2.19025 -4.76894 (502*2π)/5241 weeks
5031.22424 -8.58992 (503*2π)/5241 weeks
5046.07927 -6.05111 (504*2π)/5241 weeks
5057.27308 -.64618 (505*2π)/5241 weeks
5061.54023 3.56071 (506*2π)/5241 weeks
507-6.54498 1.60486 (507*2π)/5241 weeks
508-3.70077 -6.95279 (508*2π)/5241 weeks
509-2.78173 -7.66514 (509*2π)/5241 weeks
510.57884 -9.36317 (510*2π)/5241 weeks
511.20873 -7.0476 (511*2π)/5241 weeks
5121.68439 -6.00496 (512*2π)/5241 weeks
513.33036 -9.19226 (513*2π)/5241 weeks
5141.49561 -6.24731 (514*2π)/5241 weeks
515-.64498 -4.08757 (515*2π)/5241 weeks
516-8.68316 -10.3745 (516*2π)/5241 weeks
517-1.1753 -21.42276 (517*2π)/5241 weeks
51810.76962 -23.38303 (518*2π)/5241 weeks
51914.18047 -12.76714 (519*2π)/5241 weeks
520.8571 -5.21868 (520*2π)/5241 weeks
521-16.10589 -14.58274 (521*2π)/5241 weeks
522-26.41542 -58.56733 (522*2π)/5241 weeks

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