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# Fourier Analysis of EXD (Eaton Vance Tax-Advantaged Bond and Option Strategies Fund)

EXD (Eaton Vance Tax-Advantaged Bond and Option Strategies Fund) appears to have interesting cyclic behaviour every 30 weeks (.0966*sine), 42 weeks (.0802*sine), and 23 weeks (.074*cosine).

EXD (Eaton Vance Tax-Advantaged Bond and Option Strategies Fund) has an average price of 9.46 (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 6/25/2010 to 6/18/2018 for EXD (Eaton Vance Tax-Advantaged Bond and Option Strategies Fund), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
09.46491   0
1-.09869 -.4608 (1*2π)/418418 weeks
2-.28826 -.63137 (2*2π)/418209 weeks
3.1747 -.34284 (3*2π)/418139 weeks
4.05692 .06477 (4*2π)/418105 weeks
5-.13767 -.11429 (5*2π)/41884 weeks
6.014 .01444 (6*2π)/41870 weeks
7-.01152 .11515 (7*2π)/41860 weeks
8.03886 .03523 (8*2π)/41852 weeks
9.11392 .09281 (9*2π)/41846 weeks
10.02217 .08016 (10*2π)/41842 weeks
11.01965 -.01807 (11*2π)/41838 weeks
12-.0275 .02207 (12*2π)/41835 weeks
13-.03935 -.06186 (13*2π)/41832 weeks
14.00746 -.09656 (14*2π)/41830 weeks
15-.02963 -.03677 (15*2π)/41828 weeks
16-.03286 -.06107 (16*2π)/41826 weeks
17.03713 -.02992 (17*2π)/41825 weeks
18-.07405 -.03867 (18*2π)/41823 weeks
19-.01036 -.03848 (19*2π)/41822 weeks
20-.02344 -.00306 (20*2π)/41821 weeks
21-.04662 .00709 (21*2π)/41820 weeks
22.02316 -.02752 (22*2π)/41819 weeks
23-.02375 .01612 (23*2π)/41818 weeks
24.05124 -.0547 (24*2π)/41817 weeks
25-.01487 .01518 (25*2π)/41817 weeks
26-.00509 -.00601 (26*2π)/41816 weeks
27-.01593 .04136 (27*2π)/41815 weeks
28-.02263 .00913 (28*2π)/41815 weeks
29-.00874 .01168 (29*2π)/41814 weeks
30-.02834 -.00756 (30*2π)/41814 weeks
31.02094 -.01255 (31*2π)/41813 weeks
32-.00518 .05151 (32*2π)/41813 weeks
33.0045 -.02953 (33*2π)/41813 weeks
34-.00348 .01214 (34*2π)/41812 weeks
35-.01769 .01041 (35*2π)/41812 weeks
36.0015 -.03306 (36*2π)/41812 weeks
37-.04549 -.01315 (37*2π)/41811 weeks
38.00049 -.01125 (38*2π)/41811 weeks
39-.00031 .00418 (39*2π)/41811 weeks
40-.01777 .00923 (40*2π)/41810 weeks
41.00068 -.00161 (41*2π)/41810 weeks
42-.01102 -.01083 (42*2π)/41810 weeks
43-.00081 .00128 (43*2π)/41810 weeks
44.00588 .03698 (44*2π)/41810 weeks
45.02024 .01278 (45*2π)/4189 weeks
46-.00634 .02336 (46*2π)/4189 weeks
47.0036 .0178 (47*2π)/4189 weeks
48.00166 -.00343 (48*2π)/4189 weeks
49-.02953 .00158 (49*2π)/4189 weeks
50-.00046 .01112 (50*2π)/4188 weeks
51-.00351 -.00375 (51*2π)/4188 weeks
52-.00148 -.00517 (52*2π)/4188 weeks
53.0032 .0003 (53*2π)/4188 weeks
54-.00616 .00445 (54*2π)/4188 weeks
55-.00564 -.001 (55*2π)/4188 weeks
56.00567 -.00694 (56*2π)/4187 weeks
57-.00423 -.00957 (57*2π)/4187 weeks
58.00041 -.01355 (58*2π)/4187 weeks
59-.00194 -.00355 (59*2π)/4187 weeks
60.00389 .00969 (60*2π)/4187 weeks
61.01181 -.00867 (61*2π)/4187 weeks
62-.00467 .00064 (62*2π)/4187 weeks
63-.01758 .00978 (63*2π)/4187 weeks
64-.00388 .02117 (64*2π)/4187 weeks
65-.0042 .01967 (65*2π)/4186 weeks
66.00376 .00834 (66*2π)/4186 weeks
67.00829 .01319 (67*2π)/4186 weeks
68.01477 -.00152 (68*2π)/4186 weeks
69.00076 .00603 (69*2π)/4186 weeks
70.00837 .0029 (70*2π)/4186 weeks
71.00125 -.00777 (71*2π)/4186 weeks
72-.00335 -.00654 (72*2π)/4186 weeks
73-.00498 -.01233 (73*2π)/4186 weeks
74-.00407 -.00234 (74*2π)/4186 weeks
75.00275 -.00686 (75*2π)/4186 weeks
76-.00317 .00257 (76*2π)/4186 weeks
77.00256 .00313 (77*2π)/4185 weeks
78-.00287 -.00677 (78*2π)/4185 weeks
79.00058 .01 (79*2π)/4185 weeks
80.00667 .00905 (80*2π)/4185 weeks
81.00952 .00064 (81*2π)/4185 weeks
82.00307 .00564 (82*2π)/4185 weeks
83-.00652 .00762 (83*2π)/4185 weeks
84-.00243 -.00743 (84*2π)/4185 weeks
85-.0037 .00644 (85*2π)/4185 weeks
86-.00303 .00626 (86*2π)/4185 weeks
87.00524 -.00549 (87*2π)/4185 weeks
88-.00975 -.00134 (88*2π)/4185 weeks
89.00067 .01236 (89*2π)/4185 weeks
90.00397 -.00418 (90*2π)/4185 weeks
91.00349 .00538 (91*2π)/4185 weeks
92.00637 -.0015 (92*2π)/4185 weeks
93.00206 -.00395 (93*2π)/4184 weeks
94.00352 -.01092 (94*2π)/4184 weeks
95-.00574 .00105 (95*2π)/4184 weeks
96.00939 .0084 (96*2π)/4184 weeks
97-.00895 -.0044 (97*2π)/4184 weeks
98.00741 -.00376 (98*2π)/4184 weeks
99-.00707 .00027 (99*2π)/4184 weeks
100.00613 .00532 (100*2π)/4184 weeks
101.01388 .00506 (101*2π)/4184 weeks
102-.00122 -.00737 (102*2π)/4184 weeks
103.01098 .00039 (103*2π)/4184 weeks
104.00719 .00037 (104*2π)/4184 weeks
105.00978 .00268 (105*2π)/4184 weeks
106.00598 .00881 (106*2π)/4184 weeks
107.00331 -.00337 (107*2π)/4184 weeks
108.00208 -.00952 (108*2π)/4184 weeks
109-.00206 -.00122 (109*2π)/4184 weeks
110.0081 -.00945 (110*2π)/4184 weeks
111-.00016 -.01023 (111*2π)/4184 weeks
112-.0035 -.0066 (112*2π)/4184 weeks
113.00269 .00446 (113*2π)/4184 weeks
114.00423 -.01264 (114*2π)/4184 weeks
115-.00249 -.00191 (115*2π)/4184 weeks
116.01264 -.0059 (116*2π)/4184 weeks
117.00195 -.01018 (117*2π)/4184 weeks
118.00506 -.01051 (118*2π)/4184 weeks
119.00137 .00253 (119*2π)/4184 weeks
120.01408 .0056 (120*2π)/4183 weeks
121-.00663 -.00072 (121*2π)/4183 weeks
122.0014 .00737 (122*2π)/4183 weeks
123-.0122 -.01452 (123*2π)/4183 weeks
124-.01053 .00069 (124*2π)/4183 weeks
125.00093 -.00042 (125*2π)/4183 weeks
126-.00185 .00824 (126*2π)/4183 weeks
127.00019 -.00193 (127*2π)/4183 weeks
128-.01318 -.00343 (128*2π)/4183 weeks
129.00697 -.00007 (129*2π)/4183 weeks
130-.00874 -.00365 (130*2π)/4183 weeks
131-.00386 .00496 (131*2π)/4183 weeks
132.00668 -.005 (132*2π)/4183 weeks
133.00773 .00633 (133*2π)/4183 weeks
134-.00308 -.00797 (134*2π)/4183 weeks
135-.00296 -.00801 (135*2π)/4183 weeks
136.00121 .00052 (136*2π)/4183 weeks
137-.00699 -.0066 (137*2π)/4183 weeks
138-.00518 -.00666 (138*2π)/4183 weeks
139-.0109 -.00249 (139*2π)/4183 weeks
140-.0105 -.00179 (140*2π)/4183 weeks
141-.00269 -.00021 (141*2π)/4183 weeks
142-.00635 .00132 (142*2π)/4183 weeks
143-.0043 .00037 (143*2π)/4183 weeks
144-.00614 -.00186 (144*2π)/4183 weeks
145-.00729 -.00453 (145*2π)/4183 weeks
146.00305 -.00346 (146*2π)/4183 weeks
147-.01073 .00892 (147*2π)/4183 weeks
148-.01431 .00416 (148*2π)/4183 weeks
149-.00004 .00218 (149*2π)/4183 weeks
150-.0045 .00128 (150*2π)/4183 weeks
151.00424 -.01073 (151*2π)/4183 weeks
152.00286 .01055 (152*2π)/4183 weeks
153.00406 .00047 (153*2π)/4183 weeks
154.00074 -.00658 (154*2π)/4183 weeks
155.00098 .00033 (155*2π)/4183 weeks
156-.00335 -.00332 (156*2π)/4183 weeks
157.00278 .00212 (157*2π)/4183 weeks
158-.0069 -.00564 (158*2π)/4183 weeks
159-.00387 .00244 (159*2π)/4183 weeks
160-.01405 .00199 (160*2π)/4183 weeks
161-.01243 .00244 (161*2π)/4183 weeks
162.00695 -.00049 (162*2π)/4183 weeks
163.00098 .00259 (163*2π)/4183 weeks
164-.0013 -.00053 (164*2π)/4183 weeks
165.01381 .00114 (165*2π)/4183 weeks
166.00473 .01202 (166*2π)/4183 weeks
167.01089 -.00309 (167*2π)/4183 weeks
168.01265 .00062 (168*2π)/4182 weeks
169-.00214 .00083 (169*2π)/4182 weeks
170.00199 -.00723 (170*2π)/4182 weeks
171-.0092 .00687 (171*2π)/4182 weeks
172-.0023 -.00719 (172*2π)/4182 weeks
173-.00456 .00709 (173*2π)/4182 weeks
174-.005 -.00217 (174*2π)/4182 weeks
175-.00315 -.00037 (175*2π)/4182 weeks
176-.00093 .01371 (176*2π)/4182 weeks
177-.00119 .00287 (177*2π)/4182 weeks
178.00636 .00745 (178*2π)/4182 weeks
179.00907 .00903 (179*2π)/4182 weeks
180.0001 .00827 (180*2π)/4182 weeks
181-.00096 -.00116 (181*2π)/4182 weeks
182-.00488 .0101 (182*2π)/4182 weeks
183.00254 .00291 (183*2π)/4182 weeks
184.00092 .0115 (184*2π)/4182 weeks
185-.00671 .0095 (185*2π)/4182 weeks
186.00248 -.00649 (186*2π)/4182 weeks
187-.00287 .00189 (187*2π)/4182 weeks
188.00166 -.00286 (188*2π)/4182 weeks
189.00387 -.00102 (189*2π)/4182 weeks
190.00774 -.00932 (190*2π)/4182 weeks
191-.00963 -.01081 (191*2π)/4182 weeks
192.00624 -.00549 (192*2π)/4182 weeks
193.00004 -.0013 (193*2π)/4182 weeks
194-.00156 -.0037 (194*2π)/4182 weeks
195.00496 -.00196 (195*2π)/4182 weeks
196-.00262 -.00158 (196*2π)/4182 weeks
197-.00102 .00304 (197*2π)/4182 weeks
198.00121 .01032 (198*2π)/4182 weeks
199-.00032 -.00377 (199*2π)/4182 weeks
200.00516 .00528 (200*2π)/4182 weeks
201-.0138 -.00095 (201*2π)/4182 weeks
202.00443 -.00383 (202*2π)/4182 weeks
203.00279 .00739 (203*2π)/4182 weeks
204-.00356 -.00497 (204*2π)/4182 weeks
205.0092 -.00027 (205*2π)/4182 weeks
206-.0015 -.00041 (206*2π)/4182 weeks
207.0061 -.00008 (207*2π)/4182 weeks
208.00133 .00085 (208*2π)/4182 weeks
209-.00418   (209*2π)/4182 weeks
210.00133 -.00085 (210*2π)/4182 weeks
211.0061 .00008 (211*2π)/4182 weeks
212-.0015 .00041 (212*2π)/4182 weeks
213.0092 .00027 (213*2π)/4182 weeks
214-.00356 .00497 (214*2π)/4182 weeks
215.00279 -.00739 (215*2π)/4182 weeks
216.00443 .00383 (216*2π)/4182 weeks
217-.0138 .00095 (217*2π)/4182 weeks
218.00516 -.00528 (218*2π)/4182 weeks
219-.00032 .00377 (219*2π)/4182 weeks
220.00121 -.01032 (220*2π)/4182 weeks
221-.00102 -.00304 (221*2π)/4182 weeks
222-.00262 .00158 (222*2π)/4182 weeks
223.00496 .00196 (223*2π)/4182 weeks
224-.00156 .0037 (224*2π)/4182 weeks
225.00004 .0013 (225*2π)/4182 weeks
226.00624 .00549 (226*2π)/4182 weeks
227-.00963 .01081 (227*2π)/4182 weeks
228.00774 .00932 (228*2π)/4182 weeks
229.00387 .00102 (229*2π)/4182 weeks
230.00166 .00286 (230*2π)/4182 weeks
231-.00287 -.00189 (231*2π)/4182 weeks
232.00248 .00649 (232*2π)/4182 weeks
233-.00671 -.0095 (233*2π)/4182 weeks
234.00092 -.0115 (234*2π)/4182 weeks
235.00254 -.00291 (235*2π)/4182 weeks
236-.00488 -.0101 (236*2π)/4182 weeks
237-.00096 .00116 (237*2π)/4182 weeks
238.0001 -.00827 (238*2π)/4182 weeks
239.00907 -.00903 (239*2π)/4182 weeks
240.00636 -.00745 (240*2π)/4182 weeks
241-.00119 -.00287 (241*2π)/4182 weeks
242-.00093 -.01371 (242*2π)/4182 weeks
243-.00315 .00037 (243*2π)/4182 weeks
244-.005 .00217 (244*2π)/4182 weeks
245-.00456 -.00709 (245*2π)/4182 weeks
246-.0023 .00719 (246*2π)/4182 weeks
247-.0092 -.00687 (247*2π)/4182 weeks
248.00199 .00723 (248*2π)/4182 weeks
249-.00214 -.00083 (249*2π)/4182 weeks
250.01265 -.00062 (250*2π)/4182 weeks
251.01089 .00309 (251*2π)/4182 weeks
252.00473 -.01202 (252*2π)/4182 weeks
253.01381 -.00114 (253*2π)/4182 weeks
254-.0013 .00053 (254*2π)/4182 weeks
255.00098 -.00259 (255*2π)/4182 weeks
256.00695 .00049 (256*2π)/4182 weeks
257-.01243 -.00244 (257*2π)/4182 weeks
258-.01405 -.00199 (258*2π)/4182 weeks
259-.00387 -.00244 (259*2π)/4182 weeks
260-.0069 .00564 (260*2π)/4182 weeks
261.00278 -.00212 (261*2π)/4182 weeks
262-.00335 .00332 (262*2π)/4182 weeks
263.00098 -.00033 (263*2π)/4182 weeks
264.00074 .00658 (264*2π)/4182 weeks
265.00406 -.00047 (265*2π)/4182 weeks
266.00286 -.01055 (266*2π)/4182 weeks
267.00424 .01073 (267*2π)/4182 weeks
268-.0045 -.00128 (268*2π)/4182 weeks
269-.00004 -.00218 (269*2π)/4182 weeks
270-.01431 -.00416 (270*2π)/4182 weeks
271-.01073 -.00892 (271*2π)/4182 weeks
272.00305 .00346 (272*2π)/4182 weeks
273-.00729 .00453 (273*2π)/4182 weeks
274-.00614 .00186 (274*2π)/4182 weeks
275-.0043 -.00037 (275*2π)/4182 weeks
276-.00635 -.00132 (276*2π)/4182 weeks
277-.00269 .00021 (277*2π)/4182 weeks
278-.0105 .00179 (278*2π)/4182 weeks
279-.0109 .00249 (279*2π)/4181 weeks
280-.00518 .00666 (280*2π)/4181 weeks
281-.00699 .0066 (281*2π)/4181 weeks
282.00121 -.00052 (282*2π)/4181 weeks
283-.00296 .00801 (283*2π)/4181 weeks
284-.00308 .00797 (284*2π)/4181 weeks
285.00773 -.00633 (285*2π)/4181 weeks
286.00668 .005 (286*2π)/4181 weeks
287-.00386 -.00496 (287*2π)/4181 weeks
288-.00874 .00365 (288*2π)/4181 weeks
289.00697 .00007 (289*2π)/4181 weeks
290-.01318 .00343 (290*2π)/4181 weeks
291.00019 .00193 (291*2π)/4181 weeks
292-.00185 -.00824 (292*2π)/4181 weeks
293.00093 .00042 (293*2π)/4181 weeks
294-.01053 -.00069 (294*2π)/4181 weeks
295-.0122 .01452 (295*2π)/4181 weeks
296.0014 -.00737 (296*2π)/4181 weeks
297-.00663 .00072 (297*2π)/4181 weeks
298.01408 -.0056 (298*2π)/4181 weeks
299.00137 -.00253 (299*2π)/4181 weeks
300.00506 .01051 (300*2π)/4181 weeks
301.00195 .01018 (301*2π)/4181 weeks
302.01264 .0059 (302*2π)/4181 weeks
303-.00249 .00191 (303*2π)/4181 weeks
304.00423 .01264 (304*2π)/4181 weeks
305.00269 -.00446 (305*2π)/4181 weeks
306-.0035 .0066 (306*2π)/4181 weeks
307-.00016 .01023 (307*2π)/4181 weeks
308.0081 .00945 (308*2π)/4181 weeks
309-.00206 .00122 (309*2π)/4181 weeks
310.00208 .00952 (310*2π)/4181 weeks
311.00331 .00337 (311*2π)/4181 weeks
312.00598 -.00881 (312*2π)/4181 weeks
313.00978 -.00268 (313*2π)/4181 weeks
314.00719 -.00037 (314*2π)/4181 weeks
315.01098 -.00039 (315*2π)/4181 weeks
316-.00122 .00737 (316*2π)/4181 weeks
317.01388 -.00506 (317*2π)/4181 weeks
318.00613 -.00532 (318*2π)/4181 weeks
319-.00707 -.00027 (319*2π)/4181 weeks
320.00741 .00376 (320*2π)/4181 weeks
321-.00895 .0044 (321*2π)/4181 weeks
322.00939 -.0084 (322*2π)/4181 weeks
323-.00574 -.00105 (323*2π)/4181 weeks
324.00352 .01092 (324*2π)/4181 weeks
325.00206 .00395 (325*2π)/4181 weeks
326.00637 .0015 (326*2π)/4181 weeks
327.00349 -.00538 (327*2π)/4181 weeks
328.00397 .00418 (328*2π)/4181 weeks
329.00067 -.01236 (329*2π)/4181 weeks
330-.00975 .00134 (330*2π)/4181 weeks
331.00524 .00549 (331*2π)/4181 weeks
332-.00303 -.00626 (332*2π)/4181 weeks
333-.0037 -.00644 (333*2π)/4181 weeks
334-.00243 .00743 (334*2π)/4181 weeks
335-.00652 -.00762 (335*2π)/4181 weeks
336.00307 -.00564 (336*2π)/4181 weeks
337.00952 -.00064 (337*2π)/4181 weeks
338.00667 -.00905 (338*2π)/4181 weeks
339.00058 -.01 (339*2π)/4181 weeks
340-.00287 .00677 (340*2π)/4181 weeks
341.00256 -.00313 (341*2π)/4181 weeks
342-.00317 -.00257 (342*2π)/4181 weeks
343.00275 .00686 (343*2π)/4181 weeks
344-.00407 .00234 (344*2π)/4181 weeks
345-.00498 .01233 (345*2π)/4181 weeks
346-.00335 .00654 (346*2π)/4181 weeks
347.00125 .00777 (347*2π)/4181 weeks
348.00837 -.0029 (348*2π)/4181 weeks
349.00076 -.00603 (349*2π)/4181 weeks
350.01477 .00152 (350*2π)/4181 weeks
351.00829 -.01319 (351*2π)/4181 weeks
352.00376 -.00834 (352*2π)/4181 weeks
353-.0042 -.01967 (353*2π)/4181 weeks
354-.00388 -.02117 (354*2π)/4181 weeks
355-.01758 -.00978 (355*2π)/4181 weeks
356-.00467 -.00064 (356*2π)/4181 weeks
357.01181 .00867 (357*2π)/4181 weeks
358.00389 -.00969 (358*2π)/4181 weeks
359-.00194 .00355 (359*2π)/4181 weeks
360.00041 .01355 (360*2π)/4181 weeks
361-.00423 .00957 (361*2π)/4181 weeks
362.00567 .00694 (362*2π)/4181 weeks
363-.00564 .001 (363*2π)/4181 weeks
364-.00616 -.00445 (364*2π)/4181 weeks
365.0032 -.0003 (365*2π)/4181 weeks
366-.00148 .00517 (366*2π)/4181 weeks
367-.00351 .00375 (367*2π)/4181 weeks
368-.00046 -.01112 (368*2π)/4181 weeks
369-.02953 -.00158 (369*2π)/4181 weeks
370.00166 .00343 (370*2π)/4181 weeks
371.0036 -.0178 (371*2π)/4181 weeks
372-.00634 -.02336 (372*2π)/4181 weeks
373.02024 -.01278 (373*2π)/4181 weeks
374.00588 -.03698 (374*2π)/4181 weeks
375-.00081 -.00128 (375*2π)/4181 weeks
376-.01102 .01083 (376*2π)/4181 weeks
377.00068 .00161 (377*2π)/4181 weeks
378-.01777 -.00923 (378*2π)/4181 weeks
379-.00031 -.00418 (379*2π)/4181 weeks
380.00049 .01125 (380*2π)/4181 weeks
381-.04549 .01315 (381*2π)/4181 weeks
382.0015 .03306 (382*2π)/4181 weeks
383-.01769 -.01041 (383*2π)/4181 weeks
384-.00348 -.01214 (384*2π)/4181 weeks
385.0045 .02953 (385*2π)/4181 weeks
386-.00518 -.05151 (386*2π)/4181 weeks
387.02094 .01255 (387*2π)/4181 weeks
388-.02834 .00756 (388*2π)/4181 weeks
389-.00874 -.01168 (389*2π)/4181 weeks
390-.02263 -.00913 (390*2π)/4181 weeks
391-.01593 -.04136 (391*2π)/4181 weeks
392-.00509 .00601 (392*2π)/4181 weeks
393-.01487 -.01518 (393*2π)/4181 weeks
394.05124 .0547 (394*2π)/4181 weeks
395-.02375 -.01612 (395*2π)/4181 weeks
396.02316 .02752 (396*2π)/4181 weeks
397-.04662 -.00709 (397*2π)/4181 weeks
398-.02344 .00306 (398*2π)/4181 weeks
399-.01036 .03848 (399*2π)/4181 weeks
400-.07405 .03867 (400*2π)/4181 weeks
401.03713 .02992 (401*2π)/4181 weeks
402-.03286 .06107 (402*2π)/4181 weeks
403-.02963 .03677 (403*2π)/4181 weeks
404.00746 .09656 (404*2π)/4181 weeks
405-.03935 .06186 (405*2π)/4181 weeks
406-.0275 -.02207 (406*2π)/4181 weeks
407.01965 .01807 (407*2π)/4181 weeks
408.02217 -.08016 (408*2π)/4181 weeks
409.11392 -.09281 (409*2π)/4181 weeks
410.03886 -.03523 (410*2π)/4181 weeks
411-.01152 -.11515 (411*2π)/4181 weeks
412.014 -.01444 (412*2π)/4181 weeks
413-.13767 .11429 (413*2π)/4181 weeks
414.05692 -.06477 (414*2π)/4181 weeks
415.1747 .34284 (415*2π)/4181 weeks
416-.28826 .63137 (416*2π)/4181 weeks