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# Fourier Analysis of MLPI (UBS ETRACS Alerian MLP Infras ETN)

MLPI (UBS ETRACS Alerian MLP Infras ETN) appears to have interesting cyclic behaviour every 42 weeks (.3816*sine), 28 weeks (.3722*cosine), and 23 weeks (.2829*cosine).

MLPI (UBS ETRACS Alerian MLP Infras ETN) has an average price of 25.06 (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 4/1/2010 to 4/16/2018 for MLPI (UBS ETRACS Alerian MLP Infras ETN), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
025.05971   0
1-5.26926 -1.53543 (1*2π)/421421 weeks
21.82682 -.77233 (2*2π)/421211 weeks
3-1.47404 -2.07621 (3*2π)/421140 weeks
4-1.18578 .56873 (4*2π)/421105 weeks
5.52631 -.07139 (5*2π)/42184 weeks
6-.21833 -.41076 (6*2π)/42170 weeks
7-.4082 -.90201 (7*2π)/42160 weeks
8.19964 .09998 (8*2π)/42153 weeks
9.4683 -.56893 (9*2π)/42147 weeks
10-.35821 -.38162 (10*2π)/42142 weeks
11-.33902 -.07972 (11*2π)/42138 weeks
12-.33431 -.21682 (12*2π)/42135 weeks
13.3011 -.09624 (13*2π)/42132 weeks
14.0228 -.22868 (14*2π)/42130 weeks
15-.37224 -.17605 (15*2π)/42128 weeks
16.03686 -.11996 (16*2π)/42126 weeks
17-.04496 -.17451 (17*2π)/42125 weeks
18-.28287 .03132 (18*2π)/42123 weeks
19-.03052 -.01279 (19*2π)/42122 weeks
20.08909 -.04348 (20*2π)/42121 weeks
21-.12196 -.0362 (21*2π)/42120 weeks
22-.0493 -.02907 (22*2π)/42119 weeks
23-.01794 -.04442 (23*2π)/42118 weeks
24-.0234 -.01349 (24*2π)/42118 weeks
25.18164 .00847 (25*2π)/42117 weeks
26.03169 .02196 (26*2π)/42116 weeks
27.09337 .0193 (27*2π)/42116 weeks
28.05616 -.03331 (28*2π)/42115 weeks
29.07075 -.01518 (29*2π)/42115 weeks
30.04359 .03173 (30*2π)/42114 weeks
31.15083 -.09283 (31*2π)/42114 weeks
32.10279 .13433 (32*2π)/42113 weeks
33.01045 -.13952 (33*2π)/42113 weeks
34-.05623 -.12974 (34*2π)/42112 weeks
35.03627 .00486 (35*2π)/42112 weeks
36-.05876 -.19486 (36*2π)/42112 weeks
37-.1235 .03899 (37*2π)/42111 weeks
38.0963 -.05854 (38*2π)/42111 weeks
39-.04733 -.01921 (39*2π)/42111 weeks
40.00608 .05691 (40*2π)/42111 weeks
41-.0725 -.01649 (41*2π)/42110 weeks
42.14648 -.03329 (42*2π)/42110 weeks
43-.04439 -.15982 (43*2π)/42110 weeks
44-.07981 .00882 (44*2π)/42110 weeks
45.00959 -.05726 (45*2π)/4219 weeks
46.07561 -.0541 (46*2π)/4219 weeks
47-.08299 -.00725 (47*2π)/4219 weeks
48-.10033 .0723 (48*2π)/4219 weeks
49.06455 -.06519 (49*2π)/4219 weeks
50-.11257 -.05339 (50*2π)/4218 weeks
51.03533 .05373 (51*2π)/4218 weeks
52.06196 .07749 (52*2π)/4218 weeks
53.0294 -.01907 (53*2π)/4218 weeks
54.02748 -.10851 (54*2π)/4218 weeks
55-.01902 .02764 (55*2π)/4218 weeks
56.05225 -.04354 (56*2π)/4218 weeks
57-.02761 -.00445 (57*2π)/4217 weeks
58-.03425 .01959 (58*2π)/4217 weeks
59-.0475 -.0293 (59*2π)/4217 weeks
60-.0034 -.00266 (60*2π)/4217 weeks
61.06681 -.06643 (61*2π)/4217 weeks
62.00168 -.07368 (62*2π)/4217 weeks
63.04691 .02106 (63*2π)/4217 weeks
64.02635 -.12617 (64*2π)/4217 weeks
65-.07981 .01617 (65*2π)/4216 weeks
66.00064 -.08604 (66*2π)/4216 weeks
67-.01917 -.02787 (67*2π)/4216 weeks
68-.00964 -.02601 (68*2π)/4216 weeks
69-.00283 -.0953 (69*2π)/4216 weeks
70-.0163 -.05733 (70*2π)/4216 weeks
71-.07936 -.07471 (71*2π)/4216 weeks
72-.01431 .02546 (72*2π)/4216 weeks
73.08432 -.08544 (73*2π)/4216 weeks
74-.08416 -.08156 (74*2π)/4216 weeks
75-.05147 -.00542 (75*2π)/4216 weeks
76.02397 -.00502 (76*2π)/4216 weeks
77-.00948 -.09755 (77*2π)/4215 weeks
78-.06389 -.01406 (78*2π)/4215 weeks
79.01578 .03601 (79*2π)/4215 weeks
80-.00433 -.07372 (80*2π)/4215 weeks
81-.06494 -.11163 (81*2π)/4215 weeks
82-.03053 .06263 (82*2π)/4215 weeks
83.00403 .00814 (83*2π)/4215 weeks
84-.01215 -.01627 (84*2π)/4215 weeks
85-.01467 .04053 (85*2π)/4215 weeks
86.01052 -.01807 (86*2π)/4215 weeks
87-.01842 -.02648 (87*2π)/4215 weeks
88.00237 -.10292 (88*2π)/4215 weeks
89-.04716 .04065 (89*2π)/4215 weeks
90.07513 -.06163 (90*2π)/4215 weeks
91-.02598 -.03587 (91*2π)/4215 weeks
92-.00461 -.063 (92*2π)/4215 weeks
93-.03738 -.03332 (93*2π)/4215 weeks
94-.02446 -.0161 (94*2π)/4214 weeks
95-.06799 -.08235 (95*2π)/4214 weeks
96-.06678 .05839 (96*2π)/4214 weeks
97.10458 -.01955 (97*2π)/4214 weeks
98-.03914 -.02776 (98*2π)/4214 weeks
99-.01981 .00673 (99*2π)/4214 weeks
100-.0333 .01672 (100*2π)/4214 weeks
101.02629 -.01386 (101*2π)/4214 weeks
102-.03286 -.08969 (102*2π)/4214 weeks
103-.08158 .00241 (103*2π)/4214 weeks
104.02321 -.01147 (104*2π)/4214 weeks
105-.01363 -.08827 (105*2π)/4214 weeks
106-.02521 -.01336 (106*2π)/4214 weeks
107.00572 .04721 (107*2π)/4214 weeks
108.01285 -.0732 (108*2π)/4214 weeks
109-.04696 -.02447 (109*2π)/4214 weeks
110-.06332 .00205 (110*2π)/4214 weeks
111.01006 .01292 (111*2π)/4214 weeks
112.00779 -.03837 (112*2π)/4214 weeks
113-.01596 -.01483 (113*2π)/4214 weeks
114-.01046 -.02948 (114*2π)/4214 weeks
115-.03592 -.03247 (115*2π)/4214 weeks
116-.0174 -.00509 (116*2π)/4214 weeks
117-.02862 .0598 (117*2π)/4214 weeks
118.0169 -.0442 (118*2π)/4214 weeks
119.00679 -.01772 (119*2π)/4214 weeks
120-.02609 .00821 (120*2π)/4214 weeks
121-.00578 -.02186 (121*2π)/4213 weeks
122.00036 -.00694 (122*2π)/4213 weeks
123-.02477 -.0003 (123*2π)/4213 weeks
124.03914 -.04704 (124*2π)/4213 weeks
125-.05074 -.02884 (125*2π)/4213 weeks
126-.04647 .05023 (126*2π)/4213 weeks
127-.00876 -.03792 (127*2π)/4213 weeks
128-.02056 .01858 (128*2π)/4213 weeks
129.01601 -.02368 (129*2π)/4213 weeks
130-.00268 -.00797 (130*2π)/4213 weeks
131-.01106 -.03941 (131*2π)/4213 weeks
132-.05352 .03525 (132*2π)/4213 weeks
133.05629 -.00905 (133*2π)/4213 weeks
134-.00817 -.07168 (134*2π)/4213 weeks
135-.02209 -.00762 (135*2π)/4213 weeks
136.01076 -.00137 (136*2π)/4213 weeks
137.03086 .00373 (137*2π)/4213 weeks
138.00041 -.04018 (138*2π)/4213 weeks
139-.0388 -.04393 (139*2π)/4213 weeks
140-.00406 -.02229 (140*2π)/4213 weeks
141-.01966 -.03757 (141*2π)/4213 weeks
142-.00724 -.03295 (142*2π)/4213 weeks
143.012 .00595 (143*2π)/4213 weeks
144-.01262 -.00494 (144*2π)/4213 weeks
145-.02886 -.00815 (145*2π)/4213 weeks
146-.00766 -.04644 (146*2π)/4213 weeks
147-.04362 -.01759 (147*2π)/4213 weeks
148-.02595 -.01155 (148*2π)/4213 weeks
149-.00458 -.00827 (149*2π)/4213 weeks
150-.02996 -.01623 (150*2π)/4213 weeks
151-.05297 -.02021 (151*2π)/4213 weeks
152-.03331 .03791 (152*2π)/4213 weeks
153-.05143 -.01034 (153*2π)/4213 weeks
154.00528 -.00948 (154*2π)/4213 weeks
155-.02781 .05477 (155*2π)/4213 weeks
156-.00475 -.00181 (156*2π)/4213 weeks
157-.01956 -.01891 (157*2π)/4213 weeks
158-.02414 .03735 (158*2π)/4213 weeks
159.00097 -.013 (159*2π)/4213 weeks
160-.05958 .00651 (160*2π)/4213 weeks
161-.001 .01694 (161*2π)/4213 weeks
162.00409 -.01955 (162*2π)/4213 weeks
163-.02782 -.00589 (163*2π)/4213 weeks
164-.0059 -.02395 (164*2π)/4213 weeks
165-.02039 .01059 (165*2π)/4213 weeks
166-.02886 .01248 (166*2π)/4213 weeks
167-.01339 .03411 (167*2π)/4213 weeks
168-.01528 -.01173 (168*2π)/4213 weeks
169-.04605 -.00664 (169*2π)/4212 weeks
170-.00232 .00608 (170*2π)/4212 weeks
171-.07169 -.04034 (171*2π)/4212 weeks
172-.03677 .01422 (172*2π)/4212 weeks
173.00124 .00822 (173*2π)/4212 weeks
174-.00257 -.01587 (174*2π)/4212 weeks
175-.06827 .00804 (175*2π)/4212 weeks
176.01144 .00869 (176*2π)/4212 weeks
177-.00418 -.05508 (177*2π)/4212 weeks
178-.06897 .01328 (178*2π)/4212 weeks
179-.01575 -.00197 (179*2π)/4212 weeks
180-.04537 .01785 (180*2π)/4212 weeks
181-.03022 -.02218 (181*2π)/4212 weeks
182-.05422 .00335 (182*2π)/4212 weeks
183.01479 -.02824 (183*2π)/4212 weeks
184-.01192 -.01545 (184*2π)/4212 weeks
185-.00302 .05815 (185*2π)/4212 weeks
186-.04916 -.04678 (186*2π)/4212 weeks
187-.03965 .01439 (187*2π)/4212 weeks
188.04269 .00905 (188*2π)/4212 weeks
189-.05666 -.06886 (189*2π)/4212 weeks
190-.01883 .04055 (190*2π)/4212 weeks
191-.04487 .0042 (191*2π)/4212 weeks
192-.00085 .00214 (192*2π)/4212 weeks
193-.01478 -.00459 (193*2π)/4212 weeks
194-.0498 .02469 (194*2π)/4212 weeks
195.02334 -.01391 (195*2π)/4212 weeks
196-.03565 .00037 (196*2π)/4212 weeks
197.02435 .01083 (197*2π)/4212 weeks
198-.02896 -.03625 (198*2π)/4212 weeks
199-.03985 .0114 (199*2π)/4212 weeks
200.04162 -.01589 (200*2π)/4212 weeks
201-.06109 -.06083 (201*2π)/4212 weeks
202-.02268 .01912 (202*2π)/4212 weeks
203.00931 .00231 (203*2π)/4212 weeks
204.00109 -.0303 (204*2π)/4212 weeks
205-.01641 -.01528 (205*2π)/4212 weeks
206-.03067 .00011 (206*2π)/4212 weeks
207.01952 -.0325 (207*2π)/4212 weeks
208-.03645 .00104 (208*2π)/4212 weeks
209-.01724 -.00509 (209*2π)/4212 weeks
210.00416 -.0038 (210*2π)/4212 weeks
211.00416 .0038 (211*2π)/4212 weeks
212-.01724 .00509 (212*2π)/4212 weeks
213-.03645 -.00104 (213*2π)/4212 weeks
214.01952 .0325 (214*2π)/4212 weeks
215-.03067 -.00011 (215*2π)/4212 weeks
216-.01641 .01528 (216*2π)/4212 weeks
217.00109 .0303 (217*2π)/4212 weeks
218.00931 -.00231 (218*2π)/4212 weeks
219-.02268 -.01912 (219*2π)/4212 weeks
220-.06109 .06083 (220*2π)/4212 weeks
221.04162 .01589 (221*2π)/4212 weeks
222-.03985 -.0114 (222*2π)/4212 weeks
223-.02896 .03625 (223*2π)/4212 weeks
224.02435 -.01083 (224*2π)/4212 weeks
225-.03565 -.00037 (225*2π)/4212 weeks
226.02334 .01391 (226*2π)/4212 weeks
227-.0498 -.02469 (227*2π)/4212 weeks
228-.01478 .00459 (228*2π)/4212 weeks
229-.00085 -.00214 (229*2π)/4212 weeks
230-.04487 -.0042 (230*2π)/4212 weeks
231-.01883 -.04055 (231*2π)/4212 weeks
232-.05666 .06886 (232*2π)/4212 weeks
233.04269 -.00905 (233*2π)/4212 weeks
234-.03965 -.01439 (234*2π)/4212 weeks
235-.04916 .04678 (235*2π)/4212 weeks
236-.00302 -.05815 (236*2π)/4212 weeks
237-.01192 .01545 (237*2π)/4212 weeks
238.01479 .02824 (238*2π)/4212 weeks
239-.05422 -.00335 (239*2π)/4212 weeks
240-.03022 .02218 (240*2π)/4212 weeks
241-.04537 -.01785 (241*2π)/4212 weeks
242-.01575 .00197 (242*2π)/4212 weeks
243-.06897 -.01328 (243*2π)/4212 weeks
244-.00418 .05508 (244*2π)/4212 weeks
245.01144 -.00869 (245*2π)/4212 weeks
246-.06827 -.00804 (246*2π)/4212 weeks
247-.00257 .01587 (247*2π)/4212 weeks
248.00124 -.00822 (248*2π)/4212 weeks
249-.03677 -.01422 (249*2π)/4212 weeks
250-.07169 .04034 (250*2π)/4212 weeks
251-.00232 -.00608 (251*2π)/4212 weeks
252-.04605 .00664 (252*2π)/4212 weeks
253-.01528 .01173 (253*2π)/4212 weeks
254-.01339 -.03411 (254*2π)/4212 weeks
255-.02886 -.01248 (255*2π)/4212 weeks
256-.02039 -.01059 (256*2π)/4212 weeks
257-.0059 .02395 (257*2π)/4212 weeks
258-.02782 .00589 (258*2π)/4212 weeks
259.00409 .01955 (259*2π)/4212 weeks
260-.001 -.01694 (260*2π)/4212 weeks
261-.05958 -.00651 (261*2π)/4212 weeks
262.00097 .013 (262*2π)/4212 weeks
263-.02414 -.03735 (263*2π)/4212 weeks
264-.01956 .01891 (264*2π)/4212 weeks
265-.00475 .00181 (265*2π)/4212 weeks
266-.02781 -.05477 (266*2π)/4212 weeks
267.00528 .00948 (267*2π)/4212 weeks
268-.05143 .01034 (268*2π)/4212 weeks
269-.03331 -.03791 (269*2π)/4212 weeks
270-.05297 .02021 (270*2π)/4212 weeks
271-.02996 .01623 (271*2π)/4212 weeks
272-.00458 .00827 (272*2π)/4212 weeks
273-.02595 .01155 (273*2π)/4212 weeks
274-.04362 .01759 (274*2π)/4212 weeks
275-.00766 .04644 (275*2π)/4212 weeks
276-.02886 .00815 (276*2π)/4212 weeks
277-.01262 .00494 (277*2π)/4212 weeks
278.012 -.00595 (278*2π)/4212 weeks
279-.00724 .03295 (279*2π)/4212 weeks
280-.01966 .03757 (280*2π)/4212 weeks
281-.00406 .02229 (281*2π)/4211 weeks
282-.0388 .04393 (282*2π)/4211 weeks
283.00041 .04018 (283*2π)/4211 weeks
284.03086 -.00373 (284*2π)/4211 weeks
285.01076 .00137 (285*2π)/4211 weeks
286-.02209 .00762 (286*2π)/4211 weeks
287-.00817 .07168 (287*2π)/4211 weeks
288.05629 .00905 (288*2π)/4211 weeks
289-.05352 -.03525 (289*2π)/4211 weeks
290-.01106 .03941 (290*2π)/4211 weeks
291-.00268 .00797 (291*2π)/4211 weeks
292.01601 .02368 (292*2π)/4211 weeks
293-.02056 -.01858 (293*2π)/4211 weeks
294-.00876 .03792 (294*2π)/4211 weeks
295-.04647 -.05023 (295*2π)/4211 weeks
296-.05074 .02884 (296*2π)/4211 weeks
297.03914 .04704 (297*2π)/4211 weeks
298-.02477 .0003 (298*2π)/4211 weeks
299.00036 .00694 (299*2π)/4211 weeks
300-.00578 .02186 (300*2π)/4211 weeks
301-.02609 -.00821 (301*2π)/4211 weeks
302.00679 .01772 (302*2π)/4211 weeks
303.0169 .0442 (303*2π)/4211 weeks
304-.02862 -.0598 (304*2π)/4211 weeks
305-.0174 .00509 (305*2π)/4211 weeks
306-.03592 .03247 (306*2π)/4211 weeks
307-.01046 .02948 (307*2π)/4211 weeks
308-.01596 .01483 (308*2π)/4211 weeks
309.00779 .03837 (309*2π)/4211 weeks
310.01006 -.01292 (310*2π)/4211 weeks
311-.06332 -.00205 (311*2π)/4211 weeks
312-.04696 .02447 (312*2π)/4211 weeks
313.01285 .0732 (313*2π)/4211 weeks
314.00572 -.04721 (314*2π)/4211 weeks
315-.02521 .01336 (315*2π)/4211 weeks
316-.01363 .08827 (316*2π)/4211 weeks
317.02321 .01147 (317*2π)/4211 weeks
318-.08158 -.00241 (318*2π)/4211 weeks
319-.03286 .08969 (319*2π)/4211 weeks
320.02629 .01386 (320*2π)/4211 weeks
321-.0333 -.01672 (321*2π)/4211 weeks
322-.01981 -.00673 (322*2π)/4211 weeks
323-.03914 .02776 (323*2π)/4211 weeks
324.10458 .01955 (324*2π)/4211 weeks
325-.06678 -.05839 (325*2π)/4211 weeks
326-.06799 .08235 (326*2π)/4211 weeks
327-.02446 .0161 (327*2π)/4211 weeks
328-.03738 .03332 (328*2π)/4211 weeks
329-.00461 .063 (329*2π)/4211 weeks
330-.02598 .03587 (330*2π)/4211 weeks
331.07513 .06163 (331*2π)/4211 weeks
332-.04716 -.04065 (332*2π)/4211 weeks
333.00237 .10292 (333*2π)/4211 weeks
334-.01842 .02648 (334*2π)/4211 weeks
335.01052 .01807 (335*2π)/4211 weeks
336-.01467 -.04053 (336*2π)/4211 weeks
337-.01215 .01627 (337*2π)/4211 weeks
338.00403 -.00814 (338*2π)/4211 weeks
339-.03053 -.06263 (339*2π)/4211 weeks
340-.06494 .11163 (340*2π)/4211 weeks
341-.00433 .07372 (341*2π)/4211 weeks
342.01578 -.03601 (342*2π)/4211 weeks
343-.06389 .01406 (343*2π)/4211 weeks
344-.00948 .09755 (344*2π)/4211 weeks
345.02397 .00502 (345*2π)/4211 weeks
346-.05147 .00542 (346*2π)/4211 weeks
347-.08416 .08156 (347*2π)/4211 weeks
348.08432 .08544 (348*2π)/4211 weeks
349-.01431 -.02546 (349*2π)/4211 weeks
350-.07936 .07471 (350*2π)/4211 weeks
351-.0163 .05733 (351*2π)/4211 weeks
352-.00283 .0953 (352*2π)/4211 weeks
353-.00964 .02601 (353*2π)/4211 weeks
354-.01917 .02787 (354*2π)/4211 weeks
355.00064 .08604 (355*2π)/4211 weeks
356-.07981 -.01617 (356*2π)/4211 weeks
357.02635 .12617 (357*2π)/4211 weeks
358.04691 -.02106 (358*2π)/4211 weeks
359.00168 .07368 (359*2π)/4211 weeks
360.06681 .06643 (360*2π)/4211 weeks
361-.0034 .00266 (361*2π)/4211 weeks
362-.0475 .0293 (362*2π)/4211 weeks
363-.03425 -.01959 (363*2π)/4211 weeks
364-.02761 .00445 (364*2π)/4211 weeks
365.05225 .04354 (365*2π)/4211 weeks
366-.01902 -.02764 (366*2π)/4211 weeks
367.02748 .10851 (367*2π)/4211 weeks
368.0294 .01907 (368*2π)/4211 weeks
369.06196 -.07749 (369*2π)/4211 weeks
370.03533 -.05373 (370*2π)/4211 weeks
371-.11257 .05339 (371*2π)/4211 weeks
372.06455 .06519 (372*2π)/4211 weeks
373-.10033 -.0723 (373*2π)/4211 weeks
374-.08299 .00725 (374*2π)/4211 weeks
375.07561 .0541 (375*2π)/4211 weeks
376.00959 .05726 (376*2π)/4211 weeks
377-.07981 -.00882 (377*2π)/4211 weeks
378-.04439 .15982 (378*2π)/4211 weeks
379.14648 .03329 (379*2π)/4211 weeks
380-.0725 .01649 (380*2π)/4211 weeks
381.00608 -.05691 (381*2π)/4211 weeks
382-.04733 .01921 (382*2π)/4211 weeks
383.0963 .05854 (383*2π)/4211 weeks
384-.1235 -.03899 (384*2π)/4211 weeks
385-.05876 .19486 (385*2π)/4211 weeks
386.03627 -.00486 (386*2π)/4211 weeks
387-.05623 .12974 (387*2π)/4211 weeks
388.01045 .13952 (388*2π)/4211 weeks
389.10279 -.13433 (389*2π)/4211 weeks
390.15083 .09283 (390*2π)/4211 weeks
391.04359 -.03173 (391*2π)/4211 weeks
392.07075 .01518 (392*2π)/4211 weeks
393.05616 .03331 (393*2π)/4211 weeks
394.09337 -.0193 (394*2π)/4211 weeks
395.03169 -.02196 (395*2π)/4211 weeks
396.18164 -.00847 (396*2π)/4211 weeks
397-.0234 .01349 (397*2π)/4211 weeks
398-.01794 .04442 (398*2π)/4211 weeks
399-.0493 .02907 (399*2π)/4211 weeks
400-.12196 .0362 (400*2π)/4211 weeks
401.08909 .04348 (401*2π)/4211 weeks
402-.03052 .01279 (402*2π)/4211 weeks
403-.28287 -.03132 (403*2π)/4211 weeks
404-.04496 .17451 (404*2π)/4211 weeks
405.03686 .11996 (405*2π)/4211 weeks
406-.37224 .17605 (406*2π)/4211 weeks
407.0228 .22868 (407*2π)/4211 weeks
408.3011 .09624 (408*2π)/4211 weeks
409-.33431 .21682 (409*2π)/4211 weeks
410-.33902 .07972 (410*2π)/4211 weeks
411-.35821 .38162 (411*2π)/4211 weeks
412.4683 .56893 (412*2π)/4211 weeks
413.19964 -.09998 (413*2π)/4211 weeks
414-.4082 .90201 (414*2π)/4211 weeks
415-.21833 .41076 (415*2π)/4211 weeks
416.52631 .07139 (416*2π)/4211 weeks
417-1.18578 -.56873 (417*2π)/4211 weeks
418-1.47404 2.07621 (418*2π)/4211 weeks
4191.82682 .77233 (419*2π)/4211 weeks