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# Fourier Analysis of VXZ (iPath® S&P 500 VIX Mid-Term Futures™ ETN)

VXZ (iPath® S&P 500 VIX Mid-Term Futures™ ETN) appears to have interesting cyclic behaviour every 32 weeks (13.7831*sine), 34 weeks (13.6329*sine), and 44 weeks (11.0594*sine).

VXZ (iPath® S&P 500 VIX Mid-Term Futures™ ETN) has an average price of 140.66 (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 2/20/2009 to 4/16/2018 for VXZ (iPath® S&P 500 VIX Mid-Term Futures™ ETN), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0140.6587   0
156.12826 126.8436 (1*2π)/479479 weeks
2-6.94054 55.46468 (2*2π)/479240 weeks
310.37584 37.39795 (3*2π)/479160 weeks
4.24806 33.31324 (4*2π)/479120 weeks
52.32399 12.34782 (5*2π)/47996 weeks
616.92567 16.12604 (6*2π)/47980 weeks
79.45461 26.7102 (7*2π)/47968 weeks
8-.2533 24.71369 (8*2π)/47960 weeks
9-5.52457 13.01087 (9*2π)/47953 weeks
101.21292 7.13139 (10*2π)/47948 weeks
114.42815 11.05939 (11*2π)/47944 weeks
122.9491 8.01712 (12*2π)/47940 weeks
137.02619 9.04731 (13*2π)/47937 weeks
146.53916 13.63291 (14*2π)/47934 weeks
15-.27012 13.78313 (15*2π)/47932 weeks
16-1.0092 8.17518 (16*2π)/47930 weeks
172.05172 8.21796 (17*2π)/47928 weeks
18.59552 8.33998 (18*2π)/47927 weeks
19.13442 6.46758 (19*2π)/47925 weeks
201.44129 6.34754 (20*2π)/47924 weeks
213.31328 5.82112 (21*2π)/47923 weeks
222.11806 8.40711 (22*2π)/47922 weeks
23-.45389 7.95825 (23*2π)/47921 weeks
24-.30882 6.32349 (24*2π)/47920 weeks
25.77443 5.6494 (25*2π)/47919 weeks
26-.59573 5.4797 (26*2π)/47918 weeks
27-.60836 4.19604 (27*2π)/47918 weeks
281.56326 4.20126 (28*2π)/47917 weeks
291.89305 4.74909 (29*2π)/47917 weeks
30.36746 5.77697 (30*2π)/47916 weeks
31-.22143 5.22238 (31*2π)/47915 weeks
32-.85547 4.29633 (32*2π)/47915 weeks
33-.3685 2.96999 (33*2π)/47915 weeks
34.35831 3.59159 (34*2π)/47914 weeks
35.24319 1.84699 (35*2π)/47914 weeks
363.15903 3.18905 (36*2π)/47913 weeks
37.44087 6.19638 (37*2π)/47913 weeks
38-1.36441 3.2336 (38*2π)/47913 weeks
391.4424 2.38728 (39*2π)/47912 weeks
40.73713 4.57406 (40*2π)/47912 weeks
41-1.83107 3.77181 (41*2π)/47912 weeks
42.18139 .9293 (42*2π)/47911 weeks
43.54138 1.75158 (43*2π)/47911 weeks
44.78229 1.6149 (44*2π)/47911 weeks
451.77455 2.26415 (45*2π)/47911 weeks
461.3909 2.14066 (46*2π)/47910 weeks
471.33509 2.50743 (47*2π)/47910 weeks
48.67185 2.74315 (48*2π)/47910 weeks
491.04735 2.34707 (49*2π)/47910 weeks
501.23452 2.06323 (50*2π)/47910 weeks
51.60295 2.33594 (51*2π)/4799 weeks
521.55039 1.52978 (52*2π)/4799 weeks
531.60511 2.83683 (53*2π)/4799 weeks
54.59501 2.87124 (54*2π)/4799 weeks
55.61371 2.30399 (55*2π)/4799 weeks
56.44771 1.87125 (56*2π)/4799 weeks
571.04732 1.37895 (57*2π)/4798 weeks
58.9589 1.51569 (58*2π)/4798 weeks
592.02233 1.9946 (59*2π)/4798 weeks
601.61059 2.82226 (60*2π)/4798 weeks
61.31602 2.80086 (61*2π)/4798 weeks
62.34837 2.15731 (62*2π)/4798 weeks
63.72123 1.66224 (63*2π)/4798 weeks
64.24144 2.08129 (64*2π)/4797 weeks
65-.10716 1.10425 (65*2π)/4797 weeks
661.34511 -.19946 (66*2π)/4797 weeks
673.11294 1.75809 (67*2π)/4797 weeks
681.17334 3.38235 (68*2π)/4797 weeks
69.31889 2.14487 (69*2π)/4797 weeks
70.60317 1.84903 (70*2π)/4797 weeks
71.10753 1.63995 (71*2π)/4797 weeks
72.32338 .39933 (72*2π)/4797 weeks
732.20923 .75653 (73*2π)/4797 weeks
741.93812 2.38262 (74*2π)/4796 weeks
75.56526 2.20486 (75*2π)/4796 weeks
761.02624 1.59881 (76*2π)/4796 weeks
77.76541 1.6377 (77*2π)/4796 weeks
78.96777 1.57836 (78*2π)/4796 weeks
791.1837 1.7172 (79*2π)/4796 weeks
801.16907 1.62357 (80*2π)/4796 weeks
811.09339 1.85269 (81*2π)/4796 weeks
82.1317 2.06032 (82*2π)/4796 weeks
83.30056 .91085 (83*2π)/4796 weeks
841.16349 .99821 (84*2π)/4796 weeks
85.96155 1.34239 (85*2π)/4796 weeks
86.89062 1.31885 (86*2π)/4796 weeks
871.02576 1.08562 (87*2π)/4796 weeks
881.01905 1.56671 (88*2π)/4795 weeks
89.83088 1.26464 (89*2π)/4795 weeks
90.98202 .70006 (90*2π)/4795 weeks
911.66793 1.23763 (91*2π)/4795 weeks
92.74894 1.66363 (92*2π)/4795 weeks
931.20791 1.01086 (93*2π)/4795 weeks
941.45212 1.31452 (94*2π)/4795 weeks
95.94177 1.70883 (95*2π)/4795 weeks
96.70321 1.66514 (96*2π)/4795 weeks
97.55368 1.11251 (97*2π)/4795 weeks
98.92045 .64841 (98*2π)/4795 weeks
991.4686 1.26857 (99*2π)/4795 weeks
100.73922 1.82633 (100*2π)/4795 weeks
101.7646 .86947 (101*2π)/4795 weeks
102.78268 .92484 (102*2π)/4795 weeks
103.86417 1.00213 (103*2π)/4795 weeks
1041.44688 .99305 (104*2π)/4795 weeks
1051.28348 1.18022 (105*2π)/4795 weeks
106.93437 1.12901 (106*2π)/4795 weeks
1071.31982 1.23346 (107*2π)/4794 weeks
1081.09213 1.88795 (108*2π)/4794 weeks
109.56783 1.17197 (109*2π)/4794 weeks
110.77391 1.10215 (110*2π)/4794 weeks
111.75342 1.47959 (111*2π)/4794 weeks
112.38324 1.19443 (112*2π)/4794 weeks
113.63409 .62506 (113*2π)/4794 weeks
1141.21194 .85074 (114*2π)/4794 weeks
115.97286 1.2005 (115*2π)/4794 weeks
116.68132 1.18866 (116*2π)/4794 weeks
117.92037 1.09992 (117*2π)/4794 weeks
118.65515 .77461 (118*2π)/4794 weeks
119.96976 .72052 (119*2π)/4794 weeks
1201.16776 1.13222 (120*2π)/4794 weeks
121.68048 1.0811 (121*2π)/4794 weeks
122.83268 .56884 (122*2π)/4794 weeks
1231.31357 1.17837 (123*2π)/4794 weeks
124.85614 1.61867 (124*2π)/4794 weeks
125.63331 1.15432 (125*2π)/4794 weeks
126.36246 .89064 (126*2π)/4794 weeks
127.44446 .80857 (127*2π)/4794 weeks
128.80496 .81168 (128*2π)/4794 weeks
129.71521 .52499 (129*2π)/4794 weeks
130.90939 .99799 (130*2π)/4794 weeks
131.57262 1.11181 (131*2π)/4794 weeks
132.22706 .51575 (132*2π)/4794 weeks
133.78562 .18208 (133*2π)/4794 weeks
134.89003 .5665 (134*2π)/4794 weeks
135.80187 .54145 (135*2π)/4794 weeks
1361.1105 .3431 (136*2π)/4794 weeks
1371.34368 .6108 (137*2π)/4793 weeks
1381.02896 1.19131 (138*2π)/4793 weeks
139.48606 .91062 (139*2π)/4793 weeks
140.48058 .36966 (140*2π)/4793 weeks
1411.09822 .31975 (141*2π)/4793 weeks
1421.09652 .71741 (142*2π)/4793 weeks
1431.21462 .76751 (143*2π)/4793 weeks
144.72395 .92794 (144*2π)/4793 weeks
145.71125 .50779 (145*2π)/4793 weeks
146.89347 .49212 (146*2π)/4793 weeks
147.9442 .53336 (147*2π)/4793 weeks
1481.12606 .66706 (148*2π)/4793 weeks
149.92041 .79652 (149*2π)/4793 weeks
1501.13034 .85993 (150*2π)/4793 weeks
151.65847 1.00652 (151*2π)/4793 weeks
152.52453 .77384 (152*2π)/4793 weeks
153.74635 .61518 (153*2π)/4793 weeks
154.67308 .56765 (154*2π)/4793 weeks
155.78434 .68331 (155*2π)/4793 weeks
156.62525 .71954 (156*2π)/4793 weeks
157.70106 .49235 (157*2π)/4793 weeks
158.86206 .64258 (158*2π)/4793 weeks
159.54773 .40808 (159*2π)/4793 weeks
160.95741 .33086 (160*2π)/4793 weeks
1611.06748 .55713 (161*2π)/4793 weeks
1621.05923 .66764 (162*2π)/4793 weeks
163.76256 .89791 (163*2π)/4793 weeks
164.61059 .71696 (164*2π)/4793 weeks
165.53622 .65123 (165*2π)/4793 weeks
166.69223 .52178 (166*2π)/4793 weeks
167.60899 .3924 (167*2π)/4793 weeks
168.79489 .0129 (168*2π)/4793 weeks
1691.4462 .31871 (169*2π)/4793 weeks
1701.41926 1.26017 (170*2π)/4793 weeks
171.39866 1.18193 (171*2π)/4793 weeks
172.39736 .53938 (172*2π)/4793 weeks
173.48236 .81622 (173*2π)/4793 weeks
174.30814 .50809 (174*2π)/4793 weeks
175.39441 .00665 (175*2π)/4793 weeks
1761.17052 .24726 (176*2π)/4793 weeks
177.76591 1.08392 (177*2π)/4793 weeks
178-.11125 .60326 (178*2π)/4793 weeks
179.23582 .21709 (179*2π)/4793 weeks
180.47179 .01809 (180*2π)/4793 weeks
181.38321 -.00901 (181*2π)/4793 weeks
182.73864 -.31709 (182*2π)/4793 weeks
1831.18544 .05439 (183*2π)/4793 weeks
184.77961 .58066 (184*2π)/4793 weeks
185.51402 .40927 (185*2π)/4793 weeks
186.38453 .04105 (186*2π)/4793 weeks
187.52721 .09115 (187*2π)/4793 weeks
188.40969 -.27699 (188*2π)/4793 weeks
189.72265 -.60512 (189*2π)/4793 weeks
1901.48587 -.26049 (190*2π)/4793 weeks
1911.2916 .30134 (191*2π)/4793 weeks
1921.04193 .45719 (192*2π)/4792 weeks
193.82381 .71681 (193*2π)/4792 weeks
194.17666 .34628 (194*2π)/4792 weeks
195.24608 -.476 (195*2π)/4792 weeks
1961.21915 -.44111 (196*2π)/4792 weeks
1971.0468 .17271 (197*2π)/4792 weeks
198.95475 .03315 (198*2π)/4792 weeks
1991.10376 .13472 (199*2π)/4792 weeks
200.93261 .33204 (200*2π)/4792 weeks
201.58868 .31348 (201*2π)/4792 weeks
202.78436 -.01796 (202*2π)/4792 weeks
203.93958 .05112 (203*2π)/4792 weeks
204.85913 .18747 (204*2π)/4792 weeks
205.73213 .02372 (205*2π)/4792 weeks
206.91255 -.178 (206*2π)/4792 weeks
2071.25922 .20472 (207*2π)/4792 weeks
208.40502 .43623 (208*2π)/4792 weeks
209.66736 -.34117 (209*2π)/4792 weeks
2101.11266 -.00488 (210*2π)/4792 weeks
211.58584 -.09067 (211*2π)/4792 weeks
2121.07889 -.42924 (212*2π)/4792 weeks
2131.51777 .05508 (213*2π)/4792 weeks
214.91811 .48921 (214*2π)/4792 weeks
215.70027 .21883 (215*2π)/4792 weeks
216.93782 -.03216 (216*2π)/4792 weeks
217.81127 .21589 (217*2π)/4792 weeks
218.67359 -.02199 (218*2π)/4792 weeks
219.74079 -.08443 (219*2π)/4792 weeks
220.72337 -.27226 (220*2π)/4792 weeks
2211.29492 -.36389 (221*2π)/4792 weeks
222.8731 .03216 (222*2π)/4792 weeks
2231.05215 -.29774 (223*2π)/4792 weeks
2241.36206 .0621 (224*2π)/4792 weeks
225.8985 .28939 (225*2π)/4792 weeks
226.54967 -.35358 (226*2π)/4792 weeks
2271.23627 -.3568 (227*2π)/4792 weeks
2281.45296 -.06771 (228*2π)/4792 weeks
2291.50899 .13618 (229*2π)/4792 weeks
2301.20264 .39998 (230*2π)/4792 weeks
231.78729 .50495 (231*2π)/4792 weeks
232.50782 .24896 (232*2π)/4792 weeks
233.50444 -.37627 (233*2π)/4792 weeks
2341.13143 -.56168 (234*2π)/4792 weeks
2351.4631 -.01411 (235*2π)/4792 weeks
2361.15124 .27937 (236*2π)/4792 weeks
2371.09017 -.05552 (237*2π)/4792 weeks
2381.20038 .40355 (238*2π)/4792 weeks
239.38243 .52991 (239*2π)/4792 weeks
240.38243 -.52991 (240*2π)/4792 weeks
2411.20038 -.40355 (241*2π)/4792 weeks
2421.09017 .05552 (242*2π)/4792 weeks
2431.15124 -.27937 (243*2π)/4792 weeks
2441.4631 .01411 (244*2π)/4792 weeks
2451.13143 .56168 (245*2π)/4792 weeks
246.50444 .37627 (246*2π)/4792 weeks
247.50782 -.24896 (247*2π)/4792 weeks
248.78729 -.50495 (248*2π)/4792 weeks
2491.20264 -.39998 (249*2π)/4792 weeks
2501.50899 -.13618 (250*2π)/4792 weeks
2511.45296 .06771 (251*2π)/4792 weeks
2521.23627 .3568 (252*2π)/4792 weeks
253.54967 .35358 (253*2π)/4792 weeks
254.8985 -.28939 (254*2π)/4792 weeks
2551.36206 -.0621 (255*2π)/4792 weeks
2561.05215 .29774 (256*2π)/4792 weeks
257.8731 -.03216 (257*2π)/4792 weeks
2581.29492 .36389 (258*2π)/4792 weeks
259.72337 .27226 (259*2π)/4792 weeks
260.74079 .08443 (260*2π)/4792 weeks
261.67359 .02199 (261*2π)/4792 weeks
262.81127 -.21589 (262*2π)/4792 weeks
263.93782 .03216 (263*2π)/4792 weeks
264.70027 -.21883 (264*2π)/4792 weeks
265.91811 -.48921 (265*2π)/4792 weeks
2661.51777 -.05508 (266*2π)/4792 weeks
2671.07889 .42924 (267*2π)/4792 weeks
268.58584 .09067 (268*2π)/4792 weeks
2691.11266 .00488 (269*2π)/4792 weeks
270.66736 .34117 (270*2π)/4792 weeks
271.40502 -.43623 (271*2π)/4792 weeks
2721.25922 -.20472 (272*2π)/4792 weeks
273.91255 .178 (273*2π)/4792 weeks
274.73213 -.02372 (274*2π)/4792 weeks
275.85913 -.18747 (275*2π)/4792 weeks
276.93958 -.05112 (276*2π)/4792 weeks
277.78436 .01796 (277*2π)/4792 weeks
278.58868 -.31348 (278*2π)/4792 weeks
279.93261 -.33204 (279*2π)/4792 weeks
2801.10376 -.13472 (280*2π)/4792 weeks
281.95475 -.03315 (281*2π)/4792 weeks
2821.0468 -.17271 (282*2π)/4792 weeks
2831.21915 .44111 (283*2π)/4792 weeks
284.24608 .476 (284*2π)/4792 weeks
285.17666 -.34628 (285*2π)/4792 weeks
286.82381 -.71681 (286*2π)/4792 weeks
2871.04193 -.45719 (287*2π)/4792 weeks
2881.2916 -.30134 (288*2π)/4792 weeks
2891.48587 .26049 (289*2π)/4792 weeks
290.72265 .60512 (290*2π)/4792 weeks
291.40969 .27699 (291*2π)/4792 weeks
292.52721 -.09115 (292*2π)/4792 weeks
293.38453 -.04105 (293*2π)/4792 weeks
294.51402 -.40927 (294*2π)/4792 weeks
295.77961 -.58066 (295*2π)/4792 weeks
2961.18544 -.05439 (296*2π)/4792 weeks
297.73864 .31709 (297*2π)/4792 weeks
298.38321 .00901 (298*2π)/4792 weeks
299.47179 -.01809 (299*2π)/4792 weeks
300.23582 -.21709 (300*2π)/4792 weeks
301-.11125 -.60326 (301*2π)/4792 weeks
302.76591 -1.08392 (302*2π)/4792 weeks
3031.17052 -.24726 (303*2π)/4792 weeks
304.39441 -.00665 (304*2π)/4792 weeks
305.30814 -.50809 (305*2π)/4792 weeks
306.48236 -.81622 (306*2π)/4792 weeks
307.39736 -.53938 (307*2π)/4792 weeks
308.39866 -1.18193 (308*2π)/4792 weeks
3091.41926 -1.26017 (309*2π)/4792 weeks
3101.4462 -.31871 (310*2π)/4792 weeks
311.79489 -.0129 (311*2π)/4792 weeks
312.60899 -.3924 (312*2π)/4792 weeks
313.69223 -.52178 (313*2π)/4792 weeks
314.53622 -.65123 (314*2π)/4792 weeks
315.61059 -.71696 (315*2π)/4792 weeks
316.76256 -.89791 (316*2π)/4792 weeks
3171.05923 -.66764 (317*2π)/4792 weeks
3181.06748 -.55713 (318*2π)/4792 weeks
319.95741 -.33086 (319*2π)/4792 weeks
320.54773 -.40808 (320*2π)/4791 weeks
321.86206 -.64258 (321*2π)/4791 weeks
322.70106 -.49235 (322*2π)/4791 weeks
323.62525 -.71954 (323*2π)/4791 weeks
324.78434 -.68331 (324*2π)/4791 weeks
325.67308 -.56765 (325*2π)/4791 weeks
326.74635 -.61518 (326*2π)/4791 weeks
327.52453 -.77384 (327*2π)/4791 weeks
328.65847 -1.00652 (328*2π)/4791 weeks
3291.13034 -.85993 (329*2π)/4791 weeks
330.92041 -.79652 (330*2π)/4791 weeks
3311.12606 -.66706 (331*2π)/4791 weeks
332.9442 -.53336 (332*2π)/4791 weeks
333.89347 -.49212 (333*2π)/4791 weeks
334.71125 -.50779 (334*2π)/4791 weeks
335.72395 -.92794 (335*2π)/4791 weeks
3361.21462 -.76751 (336*2π)/4791 weeks
3371.09652 -.71741 (337*2π)/4791 weeks
3381.09822 -.31975 (338*2π)/4791 weeks
339.48058 -.36966 (339*2π)/4791 weeks
340.48606 -.91062 (340*2π)/4791 weeks
3411.02896 -1.19131 (341*2π)/4791 weeks
3421.34368 -.6108 (342*2π)/4791 weeks
3431.1105 -.3431 (343*2π)/4791 weeks
344.80187 -.54145 (344*2π)/4791 weeks
345.89003 -.5665 (345*2π)/4791 weeks
346.78562 -.18208 (346*2π)/4791 weeks
347.22706 -.51575 (347*2π)/4791 weeks
348.57262 -1.11181 (348*2π)/4791 weeks
349.90939 -.99799 (349*2π)/4791 weeks
350.71521 -.52499 (350*2π)/4791 weeks
351.80496 -.81168 (351*2π)/4791 weeks
352.44446 -.80857 (352*2π)/4791 weeks
353.36246 -.89064 (353*2π)/4791 weeks
354.63331 -1.15432 (354*2π)/4791 weeks
355.85614 -1.61867 (355*2π)/4791 weeks
3561.31357 -1.17837 (356*2π)/4791 weeks
357.83268 -.56884 (357*2π)/4791 weeks
358.68048 -1.0811 (358*2π)/4791 weeks
3591.16776 -1.13222 (359*2π)/4791 weeks
360.96976 -.72052 (360*2π)/4791 weeks
361.65515 -.77461 (361*2π)/4791 weeks
362.92037 -1.09992 (362*2π)/4791 weeks
363.68132 -1.18866 (363*2π)/4791 weeks
364.97286 -1.2005 (364*2π)/4791 weeks
3651.21194 -.85074 (365*2π)/4791 weeks
366.63409 -.62506 (366*2π)/4791 weeks
367.38324 -1.19443 (367*2π)/4791 weeks
368.75342 -1.47959 (368*2π)/4791 weeks
369.77391 -1.10215 (369*2π)/4791 weeks
370.56783 -1.17197 (370*2π)/4791 weeks
3711.09213 -1.88795 (371*2π)/4791 weeks
3721.31982 -1.23346 (372*2π)/4791 weeks
373.93437 -1.12901 (373*2π)/4791 weeks
3741.28348 -1.18022 (374*2π)/4791 weeks
3751.44688 -.99305 (375*2π)/4791 weeks
376.86417 -1.00213 (376*2π)/4791 weeks
377.78268 -.92484 (377*2π)/4791 weeks
378.7646 -.86947 (378*2π)/4791 weeks
379.73922 -1.82633 (379*2π)/4791 weeks
3801.4686 -1.26857 (380*2π)/4791 weeks
381.92045 -.64841 (381*2π)/4791 weeks
382.55368 -1.11251 (382*2π)/4791 weeks
383.70321 -1.66514 (383*2π)/4791 weeks
384.94177 -1.70883 (384*2π)/4791 weeks
3851.45212 -1.31452 (385*2π)/4791 weeks
3861.20791 -1.01086 (386*2π)/4791 weeks
387.74894 -1.66363 (387*2π)/4791 weeks
3881.66793 -1.23763 (388*2π)/4791 weeks
389.98202 -.70006 (389*2π)/4791 weeks
390.83088 -1.26464 (390*2π)/4791 weeks
3911.01905 -1.56671 (391*2π)/4791 weeks
3921.02576 -1.08562 (392*2π)/4791 weeks
393.89062 -1.31885 (393*2π)/4791 weeks
394.96155 -1.34239 (394*2π)/4791 weeks
3951.16349 -.99821 (395*2π)/4791 weeks
396.30056 -.91085 (396*2π)/4791 weeks
397.1317 -2.06032 (397*2π)/4791 weeks
3981.09339 -1.85269 (398*2π)/4791 weeks
3991.16907 -1.62357 (399*2π)/4791 weeks
4001.1837 -1.7172 (400*2π)/4791 weeks
401.96777 -1.57836 (401*2π)/4791 weeks
402.76541 -1.6377 (402*2π)/4791 weeks
4031.02624 -1.59881 (403*2π)/4791 weeks
404.56526 -2.20486 (404*2π)/4791 weeks
4051.93812 -2.38262 (405*2π)/4791 weeks
4062.20923 -.75653 (406*2π)/4791 weeks
407.32338 -.39933 (407*2π)/4791 weeks
408.10753 -1.63995 (408*2π)/4791 weeks
409.60317 -1.84903 (409*2π)/4791 weeks
410.31889 -2.14487 (410*2π)/4791 weeks
4111.17334 -3.38235 (411*2π)/4791 weeks
4123.11294 -1.75809 (412*2π)/4791 weeks
4131.34511 .19946 (413*2π)/4791 weeks
414-.10716 -1.10425 (414*2π)/4791 weeks
415.24144 -2.08129 (415*2π)/4791 weeks
416.72123 -1.66224 (416*2π)/4791 weeks
417.34837 -2.15731 (417*2π)/4791 weeks
418.31602 -2.80086 (418*2π)/4791 weeks
4191.61059 -2.82226 (419*2π)/4791 weeks
4202.02233 -1.9946 (420*2π)/4791 weeks
421.9589 -1.51569 (421*2π)/4791 weeks
4221.04732 -1.37895 (422*2π)/4791 weeks
423.44771 -1.87125 (423*2π)/4791 weeks
424.61371 -2.30399 (424*2π)/4791 weeks
425.59501 -2.87124 (425*2π)/4791 weeks
4261.60511 -2.83683 (426*2π)/4791 weeks
4271.55039 -1.52978 (427*2π)/4791 weeks
428.60295 -2.33594 (428*2π)/4791 weeks
4291.23452 -2.06323 (429*2π)/4791 weeks
4301.04735 -2.34707 (430*2π)/4791 weeks
431.67185 -2.74315 (431*2π)/4791 weeks
4321.33509 -2.50743 (432*2π)/4791 weeks
4331.3909 -2.14066 (433*2π)/4791 weeks
4341.77455 -2.26415 (434*2π)/4791 weeks
435.78229 -1.6149 (435*2π)/4791 weeks
436.54138 -1.75158 (436*2π)/4791 weeks
437.18139 -.9293 (437*2π)/4791 weeks
438-1.83107 -3.77181 (438*2π)/4791 weeks
439.73713 -4.57406 (439*2π)/4791 weeks
4401.4424 -2.38728 (440*2π)/4791 weeks
441-1.36441 -3.2336 (441*2π)/4791 weeks
442.44087 -6.19638 (442*2π)/4791 weeks
4433.15903 -3.18905 (443*2π)/4791 weeks
444.24319 -1.84699 (444*2π)/4791 weeks
445.35831 -3.59159 (445*2π)/4791 weeks
446-.3685 -2.96999 (446*2π)/4791 weeks
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449.36746 -5.77697 (449*2π)/4791 weeks
4501.89305 -4.74909 (450*2π)/4791 weeks
4511.56326 -4.20126 (451*2π)/4791 weeks
452-.60836 -4.19604 (452*2π)/4791 weeks
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456-.45389 -7.95825 (456*2π)/4791 weeks
4572.11806 -8.40711 (457*2π)/4791 weeks
4583.31328 -5.82112 (458*2π)/4791 weeks
4591.44129 -6.34754 (459*2π)/4791 weeks
460.13442 -6.46758 (460*2π)/4791 weeks
461.59552 -8.33998 (461*2π)/4791 weeks
4622.05172 -8.21796 (462*2π)/4791 weeks
463-1.0092 -8.17518 (463*2π)/4791 weeks
464-.27012 -13.78313 (464*2π)/4791 weeks
4656.53916 -13.63291 (465*2π)/4791 weeks
4667.02619 -9.04731 (466*2π)/4791 weeks
4672.9491 -8.01712 (467*2π)/4791 weeks
4684.42815 -11.05939 (468*2π)/4791 weeks
4691.21292 -7.13139 (469*2π)/4791 weeks
470-5.52457 -13.01087 (470*2π)/4791 weeks
471-.2533 -24.71369 (471*2π)/4791 weeks
4729.45461 -26.7102 (472*2π)/4791 weeks
47316.92567 -16.12604 (473*2π)/4791 weeks
4742.32399 -12.34782 (474*2π)/4791 weeks
475.24806 -33.31324 (475*2π)/4791 weeks
47610.37584 -37.39795 (476*2π)/4791 weeks
477-6.94054 -55.46468 (477*2π)/4791 weeks