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# Fourier Analysis of SDP (ProShares UltraShort Utilities)

SDP (ProShares UltraShort Utilities) appears to have interesting cyclic behaviour every 48 weeks (8.476*sine), 36 weeks (8.0209*sine), and 41 weeks (7.5393*sine).

SDP (ProShares UltraShort Utilities) has an average price of 155.26 (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.

## Fourier Analysis

Using data from 3/14/2007 to 4/16/2018 for SDP (ProShares UltraShort Utilities), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0155.2565   0
136.56091 140.2409 (1*2π)/580580 weeks
2-20.64971 66.44224 (2*2π)/580290 weeks
3-19.8682 22.64733 (3*2π)/580193 weeks
4-3.47359 7.99497 (4*2π)/580145 weeks
59.86288 5.36525 (5*2π)/580116 weeks
612.39939 15.02011 (6*2π)/58097 weeks
74.92006 22.93675 (7*2π)/58083 weeks
8-2.69872 19.53069 (8*2π)/58073 weeks
9-6.74964 8.20532 (9*2π)/58064 weeks
10-.16914 3.89102 (10*2π)/58058 weeks
111.23113 5.72154 (11*2π)/58053 weeks
121.35702 8.47601 (12*2π)/58048 weeks
13.68264 5.34544 (13*2π)/58045 weeks
141.19062 7.53932 (14*2π)/58041 weeks
152.06079 6.86904 (15*2π)/58039 weeks
16-1.15741 8.02087 (16*2π)/58036 weeks
17-2.66085 5.80594 (17*2π)/58034 weeks
18-5.07975 5.7103 (18*2π)/58032 weeks
19-4.46616 -2.80389 (19*2π)/58031 weeks
201.7866 -3.25583 (20*2π)/58029 weeks
216.54559 .40646 (21*2π)/58028 weeks
225.80366 5.02536 (22*2π)/58026 weeks
232.4234 7.78077 (23*2π)/58025 weeks
24-1.64994 5.5708 (24*2π)/58024 weeks
25-1.63539 2.1007 (25*2π)/58023 weeks
26.44687 .12944 (26*2π)/58022 weeks
273.53083 1.98897 (27*2π)/58021 weeks
283.27379 5.09514 (28*2π)/58021 weeks
29.56776 5.08286 (29*2π)/58020 weeks
30-.70025 4.16557 (30*2π)/58019 weeks
31-2.27091 3.32915 (31*2π)/58019 weeks
32-1.46031 -.73734 (32*2π)/58018 weeks
332.55158 -.98774 (33*2π)/58018 weeks
345.11179 2.09082 (34*2π)/58017 weeks
352.98617 5.46593 (35*2π)/58017 weeks
36-.42252 5.30927 (36*2π)/58016 weeks
37-1.47797 2.1162 (37*2π)/58016 weeks
38.24812 1.88411 (38*2π)/58015 weeks
391.21939 1.92988 (39*2π)/58015 weeks
40.00063 1.39998 (40*2π)/58015 weeks
411.83567 1.58265 (41*2π)/58014 weeks
421.40564 2.36808 (42*2π)/58014 weeks
43.93424 3.21713 (43*2π)/58013 weeks
44.02459 1.2614 (44*2π)/58013 weeks
451.13629 2.761 (45*2π)/58013 weeks
46.19528 2.23437 (46*2π)/58013 weeks
47-.41073 1.05492 (47*2π)/58012 weeks
48.55619 -.26345 (48*2π)/58012 weeks
492.03653 .06558 (49*2π)/58012 weeks
503.67557 2.33749 (50*2π)/58012 weeks
512.02366 4.37363 (51*2π)/58011 weeks
52-.7763 4.01051 (52*2π)/58011 weeks
53-1.51432 2.01856 (53*2π)/58011 weeks
54-.6676 -.43604 (54*2π)/58011 weeks
552.28824 -.13664 (55*2π)/58011 weeks
563.0607 1.31312 (56*2π)/58010 weeks
573.09306 3.59666 (57*2π)/58010 weeks
58.14248 5.17679 (58*2π)/58010 weeks
59-2.21645 4.0862 (59*2π)/58010 weeks
60-2.73086 -.10564 (60*2π)/58010 weeks
61-.23303 -1.45846 (61*2π)/58010 weeks
622.44257 -.3207 (62*2π)/5809 weeks
633.08252 2.16354 (63*2π)/5809 weeks
64.53136 3.42908 (64*2π)/5809 weeks
65-.56396 1.8945 (65*2π)/5809 weeks
66.2357 1.28427 (66*2π)/5809 weeks
67.16902 1.62481 (67*2π)/5809 weeks
68.60572 1.23166 (68*2π)/5809 weeks
69.14094 1.67803 (69*2π)/5808 weeks
70-.18487 .7836 (70*2π)/5808 weeks
71.83251 1.49909 (71*2π)/5808 weeks
72.30901 .97664 (72*2π)/5808 weeks
73.7424 1.54429 (73*2π)/5808 weeks
74-.64159 1.74671 (74*2π)/5808 weeks
75-1.05616 .12865 (75*2π)/5808 weeks
76.49443 -.54005 (76*2π)/5808 weeks
771.46488 -.27768 (77*2π)/5808 weeks
782.59713 1.01229 (78*2π)/5807 weeks
791.23909 2.38689 (79*2π)/5807 weeks
80.2379 2.21762 (80*2π)/5807 weeks
81-.59197 1.91227 (81*2π)/5807 weeks
82-1.28388 -.18378 (82*2π)/5807 weeks
83.67275 -1.05813 (83*2π)/5807 weeks
842.30549 .0925 (84*2π)/5807 weeks
851.93057 1.62128 (85*2π)/5807 weeks
86.83409 2.22699 (86*2π)/5807 weeks
87-.4734 1.7042 (87*2π)/5807 weeks
88-.39457 .67405 (88*2π)/5807 weeks
89.00163 -.75372 (89*2π)/5807 weeks
902.07939 -.44899 (90*2π)/5806 weeks
912.43874 1.34599 (91*2π)/5806 weeks
921.47313 3.1175 (92*2π)/5806 weeks
93-.57214 2.20472 (93*2π)/5806 weeks
94-.31785 .61718 (94*2π)/5806 weeks
95.1591 .23526 (95*2π)/5806 weeks
961.06078 .45206 (96*2π)/5806 weeks
971.08393 1.36156 (97*2π)/5806 weeks
98.39096 1.32064 (98*2π)/5806 weeks
99.09219 .797 (99*2π)/5806 weeks
100.90555 .56289 (100*2π)/5806 weeks
101.99839 1.59003 (101*2π)/5806 weeks
102.03287 1.81016 (102*2π)/5806 weeks
103-1.0161 .86791 (103*2π)/5806 weeks
104-.43151 -.33555 (104*2π)/5806 weeks
105.84378 -.73187 (105*2π)/5806 weeks
1061.85512 .26814 (106*2π)/5805 weeks
1071.75037 1.86787 (107*2π)/5805 weeks
108.22373 2.63605 (108*2π)/5805 weeks
109-1.6993 1.31878 (109*2π)/5805 weeks
110-1.33324 -.98436 (110*2π)/5805 weeks
111.83813 -1.66977 (111*2π)/5805 weeks
1121.90156 -.28145 (112*2π)/5805 weeks
1132.13326 .50417 (113*2π)/5805 weeks
1141.68689 1.65701 (114*2π)/5805 weeks
115.23653 1.71669 (115*2π)/5805 weeks
116-.1202 .95597 (116*2π)/5805 weeks
117.22472 .05698 (117*2π)/5805 weeks
1181.01276 -.17792 (118*2π)/5805 weeks
1191.29518 .29952 (119*2π)/5805 weeks
1201.54745 1.31329 (120*2π)/5805 weeks
1211.20019 1.75522 (121*2π)/5805 weeks
122.23163 2.07799 (122*2π)/5805 weeks
123-.81148 .97582 (123*2π)/5805 weeks
124-.58539 .17832 (124*2π)/5805 weeks
125.04463 -.43921 (125*2π)/5805 weeks
1261.29748 -.35102 (126*2π)/5805 weeks
1271.83296 .65824 (127*2π)/5805 weeks
128.91993 1.51986 (128*2π)/5805 weeks
129.33253 1.53672 (129*2π)/5804 weeks
130-.34205 .82582 (130*2π)/5804 weeks
131.27056 .45436 (131*2π)/5804 weeks
132.21249 .20861 (132*2π)/5804 weeks
133.47186 .12792 (133*2π)/5804 weeks
134.9313 .66533 (134*2π)/5804 weeks
1351.03107 1.08757 (135*2π)/5804 weeks
136-.09784 1.4639 (136*2π)/5804 weeks
137-.83345 .62425 (137*2π)/5804 weeks
138-.07694 -.50862 (138*2π)/5804 weeks
139.90412 -.29949 (139*2π)/5804 weeks
140.50364 .05033 (140*2π)/5804 weeks
141.85022 .06915 (141*2π)/5804 weeks
1421.16253 .54339 (142*2π)/5804 weeks
143.73066 .74593 (143*2π)/5804 weeks
144.41636 .70899 (144*2π)/5804 weeks
145.13979 .51239 (145*2π)/5804 weeks
146.18901 -.26834 (146*2π)/5804 weeks
147.9626 -.37237 (147*2π)/5804 weeks
1481.68199 .2148 (148*2π)/5804 weeks
1491.60994 1.53804 (149*2π)/5804 weeks
150-.05341 1.44002 (150*2π)/5804 weeks
151-.15616 .11587 (151*2π)/5804 weeks
152.98297 .12075 (152*2π)/5804 weeks
153.57067 .59335 (153*2π)/5804 weeks
154.46256 .34191 (154*2π)/5804 weeks
155.72601 .23586 (155*2π)/5804 weeks
1561.0971 .36363 (156*2π)/5804 weeks
1571.03728 .83773 (157*2π)/5804 weeks
158.68193 1.1981 (158*2π)/5804 weeks
159-.0764 1.17306 (159*2π)/5804 weeks
160-.80574 .16178 (160*2π)/5804 weeks
161.60306 -.79232 (161*2π)/5804 weeks
1621.27788 -.13265 (162*2π)/5804 weeks
1631.25857 .75076 (163*2π)/5804 weeks
164.56672 1.05887 (164*2π)/5804 weeks
165.08571 .62162 (165*2π)/5804 weeks
166.43665 .39686 (166*2π)/5803 weeks
167.01984 .16721 (167*2π)/5803 weeks
168.73771 -.48199 (168*2π)/5803 weeks
1691.54363 .44846 (169*2π)/5803 weeks
170.58981 1.13298 (170*2π)/5803 weeks
171.02578 .51505 (171*2π)/5803 weeks
172.4051 .16485 (172*2π)/5803 weeks
173.76222 .51179 (173*2π)/5803 weeks
174.31797 .46853 (174*2π)/5803 weeks
175.35884 .50498 (175*2π)/5803 weeks
176-.01212 .40382 (176*2π)/5803 weeks
177.44641 -.08349 (177*2π)/5803 weeks
178.56992 -.02225 (178*2π)/5803 weeks
179.69863 .05657 (179*2π)/5803 weeks
180.62861 .59648 (180*2π)/5803 weeks
181.17405 .17471 (181*2π)/5803 weeks
182.3796 -.35305 (182*2π)/5803 weeks
1831.01739 -.2101 (183*2π)/5803 weeks
1841.47265 .24761 (184*2π)/5803 weeks
1851.40315 1.0235 (185*2π)/5803 weeks
186.43458 1.29927 (186*2π)/5803 weeks
187-.00104 .8367 (187*2π)/5803 weeks
188-.12172 .20447 (188*2π)/5803 weeks
189.23076 -.36185 (189*2π)/5803 weeks
1901.19946 -.01196 (190*2π)/5803 weeks
1911.00348 .5561 (191*2π)/5803 weeks
192.78282 1.1249 (192*2π)/5803 weeks
193-.08168 .68952 (193*2π)/5803 weeks
194-.00311 .14315 (194*2π)/5803 weeks
195.30035 -.17146 (195*2π)/5803 weeks
196.83144 .08014 (196*2π)/5803 weeks
197.73417 .4576 (197*2π)/5803 weeks
198.52696 .49729 (198*2π)/5803 weeks
199.61141 .40265 (199*2π)/5803 weeks
200.24829 .63538 (200*2π)/5803 weeks
201.10192 .47892 (201*2π)/5803 weeks
202-.13888 -.06096 (202*2π)/5803 weeks
203.0217 -.3493 (203*2π)/5803 weeks
204.44207 -.6085 (204*2π)/5803 weeks
2051.19789 -.80878 (205*2π)/5803 weeks
2062.11612 .3893 (206*2π)/5803 weeks
207.94362 1.0705 (207*2π)/5803 weeks
208.26004 .84291 (208*2π)/5803 weeks
209.16224 .20133 (209*2π)/5803 weeks
210.4308 -.12373 (210*2π)/5803 weeks
211.91191 .23067 (211*2π)/5803 weeks
212.82733 .3163 (212*2π)/5803 weeks
2131.22876 .6752 (213*2π)/5803 weeks
214.234 1.33188 (214*2π)/5803 weeks
215-.33279 .71726 (215*2π)/5803 weeks
216-.47445 .00592 (216*2π)/5803 weeks
217-.13713 -.61534 (217*2π)/5803 weeks
218.59645 -1.0057 (218*2π)/5803 weeks
2191.58428 -.30363 (219*2π)/5803 weeks
2201.5847 .81226 (220*2π)/5803 weeks
221.40874 1.42225 (221*2π)/5803 weeks
222-.5436 .49448 (222*2π)/5803 weeks
223-.25641 -.36696 (223*2π)/5803 weeks
224.55009 -.65635 (224*2π)/5803 weeks
2251.05283 -.55445 (225*2π)/5803 weeks
2261.35767 .45099 (226*2π)/5803 weeks
227.81475 .87542 (227*2π)/5803 weeks
228-.20211 .65828 (228*2π)/5803 weeks
229-.19541 -.15205 (229*2π)/5803 weeks
230.39544 -.53682 (230*2π)/5803 weeks
231.57018 -.12658 (231*2π)/5803 weeks
232.51316 -.44614 (232*2π)/5803 weeks
2331.01918 -.45369 (233*2π)/5802 weeks
2341.31125 .21657 (234*2π)/5802 weeks
235.65476 .3862 (235*2π)/5802 weeks
236.73184 .24724 (236*2π)/5802 weeks
237.50287 .33611 (237*2π)/5802 weeks
238.29357 .19827 (238*2π)/5802 weeks
239.24803 -.40266 (239*2π)/5802 weeks
240.9842 -.84153 (240*2π)/5802 weeks
2411.6738 .23769 (241*2π)/5802 weeks
2421.10235 .91143 (242*2π)/5802 weeks
243.27442 .53077 (243*2π)/5802 weeks
244.30031 .32033 (244*2π)/5802 weeks
245.22558 -.05959 (245*2π)/5802 weeks
246.58471 -.41908 (246*2π)/5802 weeks
2471.08853 -.32253 (247*2π)/5802 weeks
2481.45584 .25902 (248*2π)/5802 weeks
2491.18775 .82713 (249*2π)/5802 weeks
250.49486 1.10636 (250*2π)/5802 weeks
251-.02631 .67136 (251*2π)/5802 weeks
252-.10964 .20378 (252*2π)/5802 weeks
253.28704 -.23757 (253*2π)/5802 weeks
254.44721 -.1208 (254*2π)/5802 weeks
255.90384 -.2319 (255*2π)/5802 weeks
256.711 .47736 (256*2π)/5802 weeks
257.47678 .34108 (257*2π)/5802 weeks
258.31614 .47809 (258*2π)/5802 weeks
259-.1026 -.02463 (259*2π)/5802 weeks
260.17193 -.45649 (260*2π)/5802 weeks
261.83532 -.46288 (261*2π)/5802 weeks
2621.07195 -.22483 (262*2π)/5802 weeks
2631.24595 .44086 (263*2π)/5802 weeks
264.48107 .91481 (264*2π)/5802 weeks
265-.09513 .48599 (265*2π)/5802 weeks
266-.22437 -.07708 (266*2π)/5802 weeks
267.10787 -.63243 (267*2π)/5802 weeks
268.75844 -.68859 (268*2π)/5802 weeks
2691.16525 -.31819 (269*2π)/5802 weeks
2701.21992 .50706 (270*2π)/5802 weeks
271.53182 .821 (271*2π)/5802 weeks
272-.18566 .4189 (272*2π)/5802 weeks
273-.1316 .00312 (273*2π)/5802 weeks
274-.22989 -.66848 (274*2π)/5802 weeks
275.82636 -.92893 (275*2π)/5802 weeks
2761.01372 -.15814 (276*2π)/5802 weeks
277.86825 .35532 (277*2π)/5802 weeks
278.15933 .03926 (278*2π)/5802 weeks
279.27814 -.29989 (279*2π)/5802 weeks
280.43297 -.44658 (280*2π)/5802 weeks
281.54586 -.54613 (281*2π)/5802 weeks
2821.22594 -.74819 (282*2π)/5802 weeks
2831.52023 -.05115 (283*2π)/5802 weeks
284.91648 .68901 (284*2π)/5802 weeks
285.38957 .3228 (285*2π)/5802 weeks
286.39646 .07905 (286*2π)/5802 weeks
287.27078 -.22589 (287*2π)/5802 weeks
288.43079 -.66062 (288*2π)/5802 weeks
2891.2341 -.83305 (289*2π)/5802 weeks
2901.7902   (290*2π)/5802 weeks
2911.2341 .83305 (291*2π)/5802 weeks
292.43079 .66062 (292*2π)/5802 weeks
293.27078 .22589 (293*2π)/5802 weeks
294.39646 -.07905 (294*2π)/5802 weeks
295.38957 -.3228 (295*2π)/5802 weeks
296.91648 -.68901 (296*2π)/5802 weeks
2971.52023 .05115 (297*2π)/5802 weeks
2981.22594 .74819 (298*2π)/5802 weeks
299.54586 .54613 (299*2π)/5802 weeks
300.43297 .44658 (300*2π)/5802 weeks
301.27814 .29989 (301*2π)/5802 weeks
302.15933 -.03926 (302*2π)/5802 weeks
303.86825 -.35532 (303*2π)/5802 weeks
3041.01372 .15814 (304*2π)/5802 weeks
305.82636 .92893 (305*2π)/5802 weeks
306-.22989 .66848 (306*2π)/5802 weeks
307-.1316 -.00312 (307*2π)/5802 weeks
308-.18566 -.4189 (308*2π)/5802 weeks
309.53182 -.821 (309*2π)/5802 weeks
3101.21992 -.50706 (310*2π)/5802 weeks
3111.16525 .31819 (311*2π)/5802 weeks
312.75844 .68859 (312*2π)/5802 weeks
313.10787 .63243 (313*2π)/5802 weeks
314-.22437 .07708 (314*2π)/5802 weeks
315-.09513 -.48599 (315*2π)/5802 weeks
316.48107 -.91481 (316*2π)/5802 weeks
3171.24595 -.44086 (317*2π)/5802 weeks
3181.07195 .22483 (318*2π)/5802 weeks
319.83532 .46288 (319*2π)/5802 weeks
320.17193 .45649 (320*2π)/5802 weeks
321-.1026 .02463 (321*2π)/5802 weeks
322.31614 -.47809 (322*2π)/5802 weeks
323.47678 -.34108 (323*2π)/5802 weeks
324.711 -.47736 (324*2π)/5802 weeks
325.90384 .2319 (325*2π)/5802 weeks
326.44721 .1208 (326*2π)/5802 weeks
327.28704 .23757 (327*2π)/5802 weeks
328-.10964 -.20378 (328*2π)/5802 weeks
329-.02631 -.67136 (329*2π)/5802 weeks
330.49486 -1.10636 (330*2π)/5802 weeks
3311.18775 -.82713 (331*2π)/5802 weeks
3321.45584 -.25902 (332*2π)/5802 weeks
3331.08853 .32253 (333*2π)/5802 weeks
334.58471 .41908 (334*2π)/5802 weeks
335.22558 .05959 (335*2π)/5802 weeks
336.30031 -.32033 (336*2π)/5802 weeks
337.27442 -.53077 (337*2π)/5802 weeks
3381.10235 -.91143 (338*2π)/5802 weeks
3391.6738 -.23769 (339*2π)/5802 weeks
340.9842 .84153 (340*2π)/5802 weeks
341.24803 .40266 (341*2π)/5802 weeks
342.29357 -.19827 (342*2π)/5802 weeks
343.50287 -.33611 (343*2π)/5802 weeks
344.73184 -.24724 (344*2π)/5802 weeks
345.65476 -.3862 (345*2π)/5802 weeks
3461.31125 -.21657 (346*2π)/5802 weeks
3471.01918 .45369 (347*2π)/5802 weeks
348.51316 .44614 (348*2π)/5802 weeks
349.57018 .12658 (349*2π)/5802 weeks
350.39544 .53682 (350*2π)/5802 weeks
351-.19541 .15205 (351*2π)/5802 weeks
352-.20211 -.65828 (352*2π)/5802 weeks
353.81475 -.87542 (353*2π)/5802 weeks
3541.35767 -.45099 (354*2π)/5802 weeks
3551.05283 .55445 (355*2π)/5802 weeks
356.55009 .65635 (356*2π)/5802 weeks
357-.25641 .36696 (357*2π)/5802 weeks
358-.5436 -.49448 (358*2π)/5802 weeks
359.40874 -1.42225 (359*2π)/5802 weeks
3601.5847 -.81226 (360*2π)/5802 weeks
3611.58428 .30363 (361*2π)/5802 weeks
362.59645 1.0057 (362*2π)/5802 weeks
363-.13713 .61534 (363*2π)/5802 weeks
364-.47445 -.00592 (364*2π)/5802 weeks
365-.33279 -.71726 (365*2π)/5802 weeks
366.234 -1.33188 (366*2π)/5802 weeks
3671.22876 -.6752 (367*2π)/5802 weeks
368.82733 -.3163 (368*2π)/5802 weeks
369.91191 -.23067 (369*2π)/5802 weeks
370.4308 .12373 (370*2π)/5802 weeks
371.16224 -.20133 (371*2π)/5802 weeks
372.26004 -.84291 (372*2π)/5802 weeks
373.94362 -1.0705 (373*2π)/5802 weeks
3742.11612 -.3893 (374*2π)/5802 weeks
3751.19789 .80878 (375*2π)/5802 weeks
376.44207 .6085 (376*2π)/5802 weeks
377.0217 .3493 (377*2π)/5802 weeks
378-.13888 .06096 (378*2π)/5802 weeks
379.10192 -.47892 (379*2π)/5802 weeks
380.24829 -.63538 (380*2π)/5802 weeks
381.61141 -.40265 (381*2π)/5802 weeks
382.52696 -.49729 (382*2π)/5802 weeks
383.73417 -.4576 (383*2π)/5802 weeks
384.83144 -.08014 (384*2π)/5802 weeks
385.30035 .17146 (385*2π)/5802 weeks
386-.00311 -.14315 (386*2π)/5802 weeks
387-.08168 -.68952 (387*2π)/5801 weeks
388.78282 -1.1249 (388*2π)/5801 weeks
3891.00348 -.5561 (389*2π)/5801 weeks
3901.19946 .01196 (390*2π)/5801 weeks
391.23076 .36185 (391*2π)/5801 weeks
392-.12172 -.20447 (392*2π)/5801 weeks
393-.00104 -.8367 (393*2π)/5801 weeks
394.43458 -1.29927 (394*2π)/5801 weeks
3951.40315 -1.0235 (395*2π)/5801 weeks
3961.47265 -.24761 (396*2π)/5801 weeks
3971.01739 .2101 (397*2π)/5801 weeks
398.3796 .35305 (398*2π)/5801 weeks
399.17405 -.17471 (399*2π)/5801 weeks
400.62861 -.59648 (400*2π)/5801 weeks
401.69863 -.05657 (401*2π)/5801 weeks
402.56992 .02225 (402*2π)/5801 weeks
403.44641 .08349 (403*2π)/5801 weeks
404-.01212 -.40382 (404*2π)/5801 weeks
405.35884 -.50498 (405*2π)/5801 weeks
406.31797 -.46853 (406*2π)/5801 weeks
407.76222 -.51179 (407*2π)/5801 weeks
408.4051 -.16485 (408*2π)/5801 weeks
409.02578 -.51505 (409*2π)/5801 weeks
410.58981 -1.13298 (410*2π)/5801 weeks
4111.54363 -.44846 (411*2π)/5801 weeks
412.73771 .48199 (412*2π)/5801 weeks
413.01984 -.16721 (413*2π)/5801 weeks
414.43665 -.39686 (414*2π)/5801 weeks
415.08571 -.62162 (415*2π)/5801 weeks
416.56672 -1.05887 (416*2π)/5801 weeks
4171.25857 -.75076 (417*2π)/5801 weeks
4181.27788 .13265 (418*2π)/5801 weeks
419.60306 .79232 (419*2π)/5801 weeks
420-.80574 -.16178 (420*2π)/5801 weeks
421-.0764 -1.17306 (421*2π)/5801 weeks
422.68193 -1.1981 (422*2π)/5801 weeks
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