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# Fourier Analysis of DXD (ProShares UltraShort Dow30)

DXD (ProShares UltraShort Dow30) appears to have interesting cyclic behaviour every 62 weeks (10.37*sine), 56 weeks (5.4086*sine), and 17 weeks (3.7396*cosine).

DXD (ProShares UltraShort Dow30) has an average price of 79.22 (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 7/13/2006 to 4/23/2018 for DXD (ProShares UltraShort Dow30), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
079.21685   0
118.92692 78.16228 (1*2π)/616616 weeks
2-17.53474 28.86196 (2*2π)/616308 weeks
3-7.53738 1.94541 (3*2π)/616205 weeks
411.41083 2.49024 (4*2π)/616154 weeks
511.91708 14.78792 (5*2π)/616123 weeks
6.64014 17.35158 (6*2π)/616103 weeks
7-5.99219 7.90916 (7*2π)/61688 weeks
8-.10569 .71827 (8*2π)/61677 weeks
97.11417 5.51116 (9*2π)/61668 weeks
10.84322 10.37001 (10*2π)/61662 weeks
11-1.81584 5.40863 (11*2π)/61656 weeks
12-1.45808 3.92853 (12*2π)/61651 weeks
13.84048 1.52583 (13*2π)/61647 weeks
142.83372 3.5799 (14*2π)/61644 weeks
151.19954 4.52752 (15*2π)/61641 weeks
161.04931 3.70668 (16*2π)/61639 weeks
17.63852 3.42156 (17*2π)/61636 weeks
181.44461 3.4766 (18*2π)/61634 weeks
19-.72068 3.74901 (19*2π)/61632 weeks
20.52131 1.78321 (20*2π)/61631 weeks
211.24469 2.52393 (21*2π)/61629 weeks
221.74453 2.86241 (22*2π)/61628 weeks
231.1827 3.74117 (23*2π)/61627 weeks
24-.54187 3.73786 (24*2π)/61626 weeks
25-1.00583 1.99226 (25*2π)/61625 weeks
261.10833 1.57032 (26*2π)/61624 weeks
27.80042 2.86522 (27*2π)/61623 weeks
28-1.15392 3.14656 (28*2π)/61622 weeks
29-1.63772 .16882 (29*2π)/61621 weeks
301.57984 .023 (30*2π)/61621 weeks
312.56104 1.75701 (31*2π)/61620 weeks
321.48328 3.69567 (32*2π)/61619 weeks
33-1.60628 3.12793 (33*2π)/61619 weeks
34-1.68236 -.03152 (34*2π)/61618 weeks
351.55237 -.79303 (35*2π)/61618 weeks
363.73955 2.01159 (36*2π)/61617 weeks
371.02465 4.916 (37*2π)/61617 weeks
38-2.56289 2.66468 (38*2π)/61616 weeks
39-.99951 -.29793 (39*2π)/61616 weeks
401.17336 .23903 (40*2π)/61615 weeks
411.32251 1.88139 (41*2π)/61615 weeks
42.01408 2.00925 (42*2π)/61615 weeks
43-.11426 1.43396 (43*2π)/61614 weeks
44-.07643 1.12733 (44*2π)/61614 weeks
45.28551 .66152 (45*2π)/61614 weeks
46.82853 1.40258 (46*2π)/61613 weeks
47-.04702 1.21814 (47*2π)/61613 weeks
48.66924 .87457 (48*2π)/61613 weeks
49.14137 1.55231 (49*2π)/61613 weeks
50.04599 .83486 (50*2π)/61612 weeks
51.10314 .6561 (51*2π)/61612 weeks
52.66831 .33332 (52*2π)/61612 weeks
531.38101 1.18384 (53*2π)/61612 weeks
54.89087 1.54542 (54*2π)/61611 weeks
55.16581 1.78807 (55*2π)/61611 weeks
56-.21222 1.21779 (56*2π)/61611 weeks
57.19522 .54413 (57*2π)/61611 weeks
58.84267 1.02826 (58*2π)/61611 weeks
59.14023 1.4445 (59*2π)/61610 weeks
60-.46386 1.15697 (60*2π)/61610 weeks
61-.45221 .03847 (61*2π)/61610 weeks
621.05383 -.34924 (62*2π)/61610 weeks
631.82697 1.33192 (63*2π)/61610 weeks
64.22039 2.05183 (64*2π)/61610 weeks
65-.64097 .98706 (65*2π)/6169 weeks
66.00631 .11873 (66*2π)/6169 weeks
67.97851 .25291 (67*2π)/6169 weeks
68.86908 1.4624 (68*2π)/6169 weeks
69-.35451 1.13317 (69*2π)/6169 weeks
70.17901 .15215 (70*2π)/6169 weeks
71.84334 .32653 (71*2π)/6169 weeks
721.01493 1.21433 (72*2π)/6169 weeks
73.18615 1.41977 (73*2π)/6168 weeks
74-.17317 .48997 (74*2π)/6168 weeks
75.47085 .75494 (75*2π)/6168 weeks
76.42743 .57214 (76*2π)/6168 weeks
77.30734 1.04925 (77*2π)/6168 weeks
78.04424 .19113 (78*2π)/6168 weeks
791.11894 .40188 (79*2π)/6168 weeks
80.89702 1.58667 (80*2π)/6168 weeks
81-.36121 1.47761 (81*2π)/6168 weeks
82-.72619 .42769 (82*2π)/6168 weeks
83.42395 -.36535 (83*2π)/6167 weeks
841.1305 .60934 (84*2π)/6167 weeks
85.35112 1.09123 (85*2π)/6167 weeks
86.29977 1.03667 (86*2π)/6167 weeks
87-.53456 .53133 (87*2π)/6167 weeks
88.52397 -.49012 (88*2π)/6167 weeks
891.38743 .66494 (89*2π)/6167 weeks
90.67871 1.41681 (90*2π)/6167 weeks
91-.22152 1.31527 (91*2π)/6167 weeks
92-.46173 .2144 (92*2π)/6167 weeks
93.42084 -.0304 (93*2π)/6167 weeks
941.0369 .27696 (94*2π)/6167 weeks
95.94328 1.41013 (95*2π)/6166 weeks
96-.38244 1.34144 (96*2π)/6166 weeks
97-.45386 .26707 (97*2π)/6166 weeks
98.30681 -.25789 (98*2π)/6166 weeks
99.87125 .40546 (99*2π)/6166 weeks
100.60059 .99434 (100*2π)/6166 weeks
101-.03342 .81359 (101*2π)/6166 weeks
102.11926 .1341 (102*2π)/6166 weeks
103.63267 .3365 (103*2π)/6166 weeks
104.45642 .81332 (104*2π)/6166 weeks
105-.14586 .54806 (105*2π)/6166 weeks
106.39924 .03797 (106*2π)/6166 weeks
107.57909 .66763 (107*2π)/6166 weeks
108.11358 .6364 (108*2π)/6166 weeks
109.03477 .0476 (109*2π)/6166 weeks
110.66921 -.09044 (110*2π)/6166 weeks
1111.00706 .52557 (111*2π)/6166 weeks
112.43926 1.09062 (112*2π)/6166 weeks
113-.14043 .74329 (113*2π)/6165 weeks
114.06242 -.13407 (114*2π)/6165 weeks
115.90325 -.02974 (115*2π)/6165 weeks
1161.05536 .96744 (116*2π)/6165 weeks
117.07499 1.35662 (117*2π)/6165 weeks
118-.68709 .51467 (118*2π)/6165 weeks
119.00984 -.38501 (119*2π)/6165 weeks
120.76115 -.25871 (120*2π)/6165 weeks
1211.1063 .54295 (121*2π)/6165 weeks
122.37574 1.16706 (122*2π)/6165 weeks
123-.23393 .57756 (123*2π)/6165 weeks
124.05974 -.21669 (124*2π)/6165 weeks
125.83534 -.04578 (125*2π)/6165 weeks
126.94893 .63501 (126*2π)/6165 weeks
127.52567 1.05393 (127*2π)/6165 weeks
128-.29331 .83788 (128*2π)/6165 weeks
129-.12743 -.1053 (129*2π)/6165 weeks
130.61547 -.1717 (130*2π)/6165 weeks
131.85905 .47317 (131*2π)/6165 weeks
132.56634 .92789 (132*2π)/6165 weeks
133-.05485 .75769 (133*2π)/6165 weeks
134.03553 .0912 (134*2π)/6165 weeks
135.47857 -.00916 (135*2π)/6165 weeks
136.79634 .60665 (136*2π)/6165 weeks
137.20009 .97059 (137*2π)/6164 weeks
138-.36547 .41803 (138*2π)/6164 weeks
139.16736 -.19079 (139*2π)/6164 weeks
140.58472 .05507 (140*2π)/6164 weeks
141.50873 .46719 (141*2π)/6164 weeks
142.30391 .42158 (142*2π)/6164 weeks
143.32675 .39027 (143*2π)/6164 weeks
144.15734 .29504 (144*2π)/6164 weeks
145.31651 .04853 (145*2π)/6164 weeks
146.63749 .24055 (146*2π)/6164 weeks
147.34384 .5414 (147*2π)/6164 weeks
148.17895 .22949 (148*2π)/6164 weeks
149.5903 .07413 (149*2π)/6164 weeks
150.67897 .39949 (150*2π)/6164 weeks
151.4232 .53912 (151*2π)/6164 weeks
152.22116 .67586 (152*2π)/6164 weeks
153.01311 .30684 (153*2π)/6164 weeks
154.31863 .09523 (154*2π)/6164 weeks
155.28674 .17518 (155*2π)/6164 weeks
156.47167 .08811 (156*2π)/6164 weeks
157.63957 .36946 (157*2π)/6164 weeks
158.55446 .62844 (158*2π)/6164 weeks
159-.0311 .5993 (159*2π)/6164 weeks
160.11958 -.15262 (160*2π)/6164 weeks
161.72577 .16308 (161*2π)/6164 weeks
162.36737 .63828 (162*2π)/6164 weeks
163.14875 .38187 (163*2π)/6164 weeks
164.27301 .12365 (164*2π)/6164 weeks
165.51227 .19881 (165*2π)/6164 weeks
166.39573 .50372 (166*2π)/6164 weeks
167.22971 .43687 (167*2π)/6164 weeks
168.03054 .24538 (168*2π)/6164 weeks
169.33075 -.08069 (169*2π)/6164 weeks
170.60512 .32621 (170*2π)/6164 weeks
171.24641 .39284 (171*2π)/6164 weeks
172.2747 .22578 (172*2π)/6164 weeks
173.38627 .18753 (173*2π)/6164 weeks
174.43122 .37171 (174*2π)/6164 weeks
175.24643 .28491 (175*2π)/6164 weeks
176.3273 .21813 (176*2π)/6164 weeks
177.22285 .3814 (177*2π)/6163 weeks
178.25437 -.00414 (178*2π)/6163 weeks
179.55158 .29827 (179*2π)/6163 weeks
180.28508 .34459 (180*2π)/6163 weeks
181.34033 .17987 (181*2π)/6163 weeks
182.39796 .2639 (182*2π)/6163 weeks
183.33653 .32334 (183*2π)/6163 weeks
184.24917 .07685 (184*2π)/6163 weeks
185.48497 .17718 (185*2π)/6163 weeks
186.54835 .18919 (186*2π)/6163 weeks
187.51431 .55693 (187*2π)/6163 weeks
188.18447 .46579 (188*2π)/6163 weeks
189.16142 .23371 (189*2π)/6163 weeks
190.32005 .15131 (190*2π)/6163 weeks
191.40885 .29974 (191*2π)/6163 weeks
192.3 .30148 (192*2π)/6163 weeks
193.21777 .19309 (193*2π)/6163 weeks
194.37995 .20876 (194*2π)/6163 weeks
195.41784 .19961 (195*2π)/6163 weeks
196.48296 .33206 (196*2π)/6163 weeks
197.35482 .44025 (197*2π)/6163 weeks
198.15851 .44653 (198*2π)/6163 weeks
199-.00106 .2398 (199*2π)/6163 weeks
200.22297 -.09029 (200*2π)/6163 weeks
201.54046 .08163 (201*2π)/6163 weeks
202.50512 .38928 (202*2π)/6163 weeks
203.14897 .48219 (203*2π)/6163 weeks
204.01791 .04943 (204*2π)/6163 weeks
205.37449 -.00907 (205*2π)/6163 weeks
206.52855 .09533 (206*2π)/6163 weeks
207.42499 .42149 (207*2π)/6163 weeks
208.17594 .29218 (208*2π)/6163 weeks
209.24442 .23251 (209*2π)/6163 weeks
210.28381 .10702 (210*2π)/6163 weeks
211.36797 .27506 (211*2π)/6163 weeks
212.08049 .29256 (212*2π)/6163 weeks
213.16308 .03936 (213*2π)/6163 weeks
214.26357 -.04168 (214*2π)/6163 weeks
215.45255 -.02825 (215*2π)/6163 weeks
216.44748 .20518 (216*2π)/6163 weeks
217.49768 .16138 (217*2π)/6163 weeks
218.37944 .54853 (218*2π)/6163 weeks
219-.12161 .14974 (219*2π)/6163 weeks
220.29995 -.01541 (220*2π)/6163 weeks
221.28537 .05728 (221*2π)/6163 weeks
222.38886 .07154 (222*2π)/6163 weeks
223.33502 .13228 (223*2π)/6163 weeks
224.43276 .0232 (224*2π)/6163 weeks
225.36146 .29275 (225*2π)/6163 weeks
226.3564 .01775 (226*2π)/6163 weeks
227.55316 .39373 (227*2π)/6163 weeks
228.21404 .37162 (228*2π)/6163 weeks
229.18719 .35785 (229*2π)/6163 weeks
230-.10183 .06138 (230*2π)/6163 weeks
231.28185 -.32522 (231*2π)/6163 weeks
232.77495 .10371 (232*2π)/6163 weeks
233.4721 .59732 (233*2π)/6163 weeks
234-.1057 .46692 (234*2π)/6163 weeks
235-.09642 -.18324 (235*2π)/6163 weeks
236.56018 -.22516 (236*2π)/6163 weeks
237.6313 .25979 (237*2π)/6163 weeks
238.28513 .55538 (238*2π)/6163 weeks
239-.2899 .30027 (239*2π)/6163 weeks
240.0707 -.53104 (240*2π)/6163 weeks
241.77081 -.21333 (241*2π)/6163 weeks
242.68915 .40655 (242*2π)/6163 weeks
243.17346 .52277 (243*2π)/6163 weeks
244.02776 .10127 (244*2π)/6163 weeks
245.27836 -.01787 (245*2π)/6163 weeks
246.26252 .1019 (246*2π)/6163 weeks
247.2905 -.00955 (247*2π)/6162 weeks
248.47222 .04267 (248*2π)/6162 weeks
249.39308 .16968 (249*2π)/6162 weeks
250.48058 .23664 (250*2π)/6162 weeks
251.23494 .50928 (251*2π)/6162 weeks
252-.09576 .14821 (252*2π)/6162 weeks
253.19789 -.06832 (253*2π)/6162 weeks
254.44308 -.03057 (254*2π)/6162 weeks
255.38579 .3967 (255*2π)/6162 weeks
256-.146 .22496 (256*2π)/6162 weeks
257.0528 -.12306 (257*2π)/6162 weeks
258.2608 -.19716 (258*2π)/6162 weeks
259.57108 -.11475 (259*2π)/6162 weeks
260.42193 .29261 (260*2π)/6162 weeks
261.07139 .22159 (261*2π)/6162 weeks
262.02935 -.151 (262*2π)/6162 weeks
263.45083 -.33267 (263*2π)/6162 weeks
264.77634 .10598 (264*2π)/6162 weeks
265.38311 .55224 (265*2π)/6162 weeks
266-.07171 .26909 (266*2π)/6162 weeks
267-.01375 -.14079 (267*2π)/6162 weeks
268.50462 -.32258 (268*2π)/6162 weeks
269.54246 .22556 (269*2π)/6162 weeks
270.28144 .24731 (270*2π)/6162 weeks
271.08672 .20098 (271*2π)/6162 weeks
272.19004 -.15854 (272*2π)/6162 weeks
273.4007 .05626 (273*2π)/6162 weeks
274.27059 .0975 (274*2π)/6162 weeks
275.29821 .16397 (275*2π)/6162 weeks
276.06753 .12271 (276*2π)/6162 weeks
277.07579 -.24733 (277*2π)/6162 weeks
278.32424 -.17805 (278*2π)/6162 weeks
279.58498 -.14158 (279*2π)/6162 weeks
280.55677 .2579 (280*2π)/6162 weeks
281.11852 .3569 (281*2π)/6162 weeks
282-.06473 .04526 (282*2π)/6162 weeks
283.06571 -.32374 (283*2π)/6162 weeks
284.42718 -.39119 (284*2π)/6162 weeks
285.80302 -.06587 (285*2π)/6162 weeks
286.6308 .40817 (286*2π)/6162 weeks
287-.06817 .50993 (287*2π)/6162 weeks
288-.21547 -.30258 (288*2π)/6162 weeks
289.44573 -.4331 (289*2π)/6162 weeks
290.65781 -.06822 (290*2π)/6162 weeks
291.59833 .36228 (291*2π)/6162 weeks
292-.02426 .40658 (292*2π)/6162 weeks
293-.18974 -.28297 (293*2π)/6162 weeks
294.46212 -.57546 (294*2π)/6162 weeks
295.69701 .04023 (295*2π)/6162 weeks
296.38069 .27654 (296*2π)/6162 weeks
297.07307 .05351 (297*2π)/6162 weeks
298.17617 -.31528 (298*2π)/6162 weeks
299.49499 -.40413 (299*2π)/6162 weeks
300.9464 .01903 (300*2π)/6162 weeks
301.47299 .60167 (301*2π)/6162 weeks
302-.06687 .07585 (302*2π)/6162 weeks
303.21941 -.29691 (303*2π)/6162 weeks
304.52301 -.12736 (304*2π)/6162 weeks
305.59066 .15745 (305*2π)/6162 weeks
306.39678 .24496 (306*2π)/6162 weeks
307.22074 .31392 (307*2π)/6162 weeks
308-.15504   (308*2π)/6162 weeks
309.22074 -.31392 (309*2π)/6162 weeks
310.39678 -.24496 (310*2π)/6162 weeks
311.59066 -.15745 (311*2π)/6162 weeks
312.52301 .12736 (312*2π)/6162 weeks
313.21941 .29691 (313*2π)/6162 weeks
314-.06687 -.07585 (314*2π)/6162 weeks
315.47299 -.60167 (315*2π)/6162 weeks
316.9464 -.01903 (316*2π)/6162 weeks
317.49499 .40413 (317*2π)/6162 weeks
318.17617 .31528 (318*2π)/6162 weeks
319.07307 -.05351 (319*2π)/6162 weeks
320.38069 -.27654 (320*2π)/6162 weeks
321.69701 -.04023 (321*2π)/6162 weeks
322.46212 .57546 (322*2π)/6162 weeks
323-.18974 .28297 (323*2π)/6162 weeks
324-.02426 -.40658 (324*2π)/6162 weeks
325.59833 -.36228 (325*2π)/6162 weeks
326.65781 .06822 (326*2π)/6162 weeks
327.44573 .4331 (327*2π)/6162 weeks
328-.21547 .30258 (328*2π)/6162 weeks
329-.06817 -.50993 (329*2π)/6162 weeks
330.6308 -.40817 (330*2π)/6162 weeks
331.80302 .06587 (331*2π)/6162 weeks
332.42718 .39119 (332*2π)/6162 weeks
333.06571 .32374 (333*2π)/6162 weeks
334-.06473 -.04526 (334*2π)/6162 weeks
335.11852 -.3569 (335*2π)/6162 weeks
336.55677 -.2579 (336*2π)/6162 weeks
337.58498 .14158 (337*2π)/6162 weeks
338.32424 .17805 (338*2π)/6162 weeks
339.07579 .24733 (339*2π)/6162 weeks
340.06753 -.12271 (340*2π)/6162 weeks
341.29821 -.16397 (341*2π)/6162 weeks
342.27059 -.0975 (342*2π)/6162 weeks
343.4007 -.05626 (343*2π)/6162 weeks
344.19004 .15854 (344*2π)/6162 weeks
345.08672 -.20098 (345*2π)/6162 weeks
346.28144 -.24731 (346*2π)/6162 weeks
347.54246 -.22556 (347*2π)/6162 weeks
348.50462 .32258 (348*2π)/6162 weeks
349-.01375 .14079 (349*2π)/6162 weeks
350-.07171 -.26909 (350*2π)/6162 weeks
351.38311 -.55224 (351*2π)/6162 weeks
352.77634 -.10598 (352*2π)/6162 weeks
353.45083 .33267 (353*2π)/6162 weeks
354.02935 .151 (354*2π)/6162 weeks
355.07139 -.22159 (355*2π)/6162 weeks
356.42193 -.29261 (356*2π)/6162 weeks
357.57108 .11475 (357*2π)/6162 weeks
358.2608 .19716 (358*2π)/6162 weeks
359.0528 .12306 (359*2π)/6162 weeks
360-.146 -.22496 (360*2π)/6162 weeks
361.38579 -.3967 (361*2π)/6162 weeks
362.44308 .03057 (362*2π)/6162 weeks
363.19789 .06832 (363*2π)/6162 weeks
364-.09576 -.14821 (364*2π)/6162 weeks
365.23494 -.50928 (365*2π)/6162 weeks
366.48058 -.23664 (366*2π)/6162 weeks
367.39308 -.16968 (367*2π)/6162 weeks
368.47222 -.04267 (368*2π)/6162 weeks
369.2905 .00955 (369*2π)/6162 weeks
370.26252 -.1019 (370*2π)/6162 weeks
371.27836 .01787 (371*2π)/6162 weeks
372.02776 -.10127 (372*2π)/6162 weeks
373.17346 -.52277 (373*2π)/6162 weeks
374.68915 -.40655 (374*2π)/6162 weeks
375.77081 .21333 (375*2π)/6162 weeks
376.0707 .53104 (376*2π)/6162 weeks
377-.2899 -.30027 (377*2π)/6162 weeks
378.28513 -.55538 (378*2π)/6162 weeks
379.6313 -.25979 (379*2π)/6162 weeks
380.56018 .22516 (380*2π)/6162 weeks
381-.09642 .18324 (381*2π)/6162 weeks
382-.1057 -.46692 (382*2π)/6162 weeks
383.4721 -.59732 (383*2π)/6162 weeks
384.77495 -.10371 (384*2π)/6162 weeks
385.28185 .32522 (385*2π)/6162 weeks
386-.10183 -.06138 (386*2π)/6162 weeks
387.18719 -.35785 (387*2π)/6162 weeks
388.21404 -.37162 (388*2π)/6162 weeks
389.55316 -.39373 (389*2π)/6162 weeks
390.3564 -.01775 (390*2π)/6162 weeks
391.36146 -.29275 (391*2π)/6162 weeks
392.43276 -.0232 (392*2π)/6162 weeks
393.33502 -.13228 (393*2π)/6162 weeks
394.38886 -.07154 (394*2π)/6162 weeks
395.28537 -.05728 (395*2π)/6162 weeks
396.29995 .01541 (396*2π)/6162 weeks
397-.12161 -.14974 (397*2π)/6162 weeks
398.37944 -.54853 (398*2π)/6162 weeks
399.49768 -.16138 (399*2π)/6162 weeks
400.44748 -.20518 (400*2π)/6162 weeks
401.45255 .02825 (401*2π)/6162 weeks
402.26357 .04168 (402*2π)/6162 weeks
403.16308 -.03936 (403*2π)/6162 weeks
404.08049 -.29256 (404*2π)/6162 weeks
405.36797 -.27506 (405*2π)/6162 weeks
406.28381 -.10702 (406*2π)/6162 weeks
407.24442 -.23251 (407*2π)/6162 weeks
408.17594 -.29218 (408*2π)/6162 weeks
409.42499 -.42149 (409*2π)/6162 weeks
410.52855 -.09533 (410*2π)/6162 weeks
411.37449 .00907 (411*2π)/6161 weeks
412.01791 -.04943 (412*2π)/6161 weeks
413.14897 -.48219 (413*2π)/6161 weeks
414.50512 -.38928 (414*2π)/6161 weeks
415.54046 -.08163 (415*2π)/6161 weeks
416.22297 .09029 (416*2π)/6161 weeks
417-.00106 -.2398 (417*2π)/6161 weeks
418.15851 -.44653 (418*2π)/6161 weeks
419.35482 -.44025 (419*2π)/6161 weeks
420.48296 -.33206 (420*2π)/6161 weeks
421.41784 -.19961 (421*2π)/6161 weeks
422.37995 -.20876 (422*2π)/6161 weeks
423.21777 -.19309 (423*2π)/6161 weeks
424.3 -.30148 (424*2π)/6161 weeks
425.40885 -.29974 (425*2π)/6161 weeks
426.32005 -.15131 (426*2π)/6161 weeks
427.16142 -.23371 (427*2π)/6161 weeks
428.18447 -.46579 (428*2π)/6161 weeks
429.51431 -.55693 (429*2π)/6161 weeks
430.54835 -.18919 (430*2π)/6161 weeks
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