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Fourier Analysis of TMV (Direxion Daily 20-Year Treasury)


TMV (Direxion Daily 20-Year Treasury) appears to have interesting cyclic behaviour every 37 weeks (14.9511*sine), 41 weeks (14.3968*sine), and 34 weeks (3.6226*cosine).

TMV (Direxion Daily 20-Year Treasury) has an average price of 110.83 (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 4/16/2009 to 1/17/2017 for TMV (Direxion Daily 20-Year Treasury), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0110.8258   0 
161.75793 89.20827 (1*2π)/406406 weeks
27.03389 72.42361 (2*2π)/406203 weeks
31.85603 26.43337 (3*2π)/406135 weeks
47.2186 32.45309 (4*2π)/406102 weeks
5-.57644 29.85233 (5*2π)/40681 weeks
6-8.79952 13.93332 (6*2π)/40668 weeks
73.70018 3.27153 (7*2π)/40658 weeks
811.17744 10.60377 (8*2π)/40651 weeks
96.50588 18.3899 (9*2π)/40645 weeks
102.79479 14.39678 (10*2π)/40641 weeks
11.56748 14.95107 (11*2π)/40637 weeks
12-3.62256 11.65355 (12*2π)/40634 weeks
13-1.14413 8.49379 (13*2π)/40631 weeks
14.24649 8.6004 (14*2π)/40629 weeks
15-2.16784 8.50265 (15*2π)/40627 weeks
16-1.93561 5.63192 (16*2π)/40625 weeks
17-1.58774 6.01962 (17*2π)/40624 weeks
18.55192 6.01611 (18*2π)/40623 weeks
19-2.59975 7.00897 (19*2π)/40621 weeks
20-1.44179 3.11124 (20*2π)/40620 weeks
21-.09231 3.73332 (21*2π)/40619 weeks
22-.8091 3.80614 (22*2π)/40618 weeks
23-.28875 2.34891 (23*2π)/40618 weeks
242.47939 3.32259 (24*2π)/40617 weeks
251.37866 5.73713 (25*2π)/40616 weeks
26-1.2762 4.79263 (26*2π)/40616 weeks
27-.93842 4.06756 (27*2π)/40615 weeks
28-.54404 3.65027 (28*2π)/40615 weeks
29-1.38468 3.19556 (29*2π)/40614 weeks
30.05065 1.42358 (30*2π)/40614 weeks
31.87514 2.54894 (31*2π)/40613 weeks
32.52357 4.6781 (32*2π)/40613 weeks
33-.60344 2.90104 (33*2π)/40612 weeks
34.26877 3.0274 (34*2π)/40612 weeks
35-.66975 3.96903 (35*2π)/40612 weeks
36-1.75652 3.00293 (36*2π)/40611 weeks
37-1.40828 1.12648 (37*2π)/40611 weeks
38-.54261 1.09658 (38*2π)/40611 weeks
39.03911 1.6134 (39*2π)/40610 weeks
40-.39463 1.61761 (40*2π)/40610 weeks
41-.47986 .55376 (41*2π)/40610 weeks
42.35616 .59476 (42*2π)/40610 weeks
43.67147 1.06688 (43*2π)/4069 weeks
44.78047 1.09278 (44*2π)/4069 weeks
451.11615 .97251 (45*2π)/4069 weeks
461.59909 .9085 (46*2π)/4069 weeks
471.05797 1.47336 (47*2π)/4069 weeks
481.16437 2.06661 (48*2π)/4068 weeks
49.67555 2.08143 (49*2π)/4068 weeks
50.16209 1.74959 (50*2π)/4068 weeks
51.21377 .76617 (51*2π)/4068 weeks
52.70461 .94968 (52*2π)/4068 weeks
531.08024 .54308 (53*2π)/4068 weeks
541.33934 .2686 (54*2π)/4068 weeks
552.63917 .86432 (55*2π)/4067 weeks
562.6243 3.07158 (56*2π)/4067 weeks
57.40022 2.70039 (57*2π)/4067 weeks
58.51241 1.74651 (58*2π)/4067 weeks
591.24102 1.96864 (59*2π)/4067 weeks
60.51495 2.04828 (60*2π)/4067 weeks
611.07354 1.57906 (61*2π)/4067 weeks
62.54743 2.44347 (62*2π)/4067 weeks
63.32934 1.92364 (63*2π)/4066 weeks
64.27209 1.40588 (64*2π)/4066 weeks
65.62705 1.42467 (65*2π)/4066 weeks
66.89404 1.81344 (66*2π)/4066 weeks
67.25244 1.96138 (67*2π)/4066 weeks
68.34236 2.00808 (68*2π)/4066 weeks
69-.22813 1.98322 (69*2π)/4066 weeks
70-.37006 1.10732 (70*2π)/4066 weeks
71.35298 1.1466 (71*2π)/4066 weeks
72.23254 1.43865 (72*2π)/4066 weeks
73.0635 1.04813 (73*2π)/4066 weeks
74.30107 1.02374 (74*2π)/4065 weeks
75.34249 1.39874 (75*2π)/4065 weeks
76-.05394 1.3152 (76*2π)/4065 weeks
77.1366 .77616 (77*2π)/4065 weeks
78.31187 1.43134 (78*2π)/4065 weeks
79.0386 1.10668 (79*2π)/4065 weeks
80-.28584 1.03483 (80*2π)/4065 weeks
81-.22187 .3588 (81*2π)/4065 weeks
82.29335 .51946 (82*2π)/4065 weeks
83.23314 .37123 (83*2π)/4065 weeks
84.48286 .62158 (84*2π)/4065 weeks
85.33284 .89898 (85*2π)/4065 weeks
86.02056 .74722 (86*2π)/4065 weeks
87-.16668 .37735 (87*2π)/4065 weeks
88.1262 -.06514 (88*2π)/4065 weeks
89.5604 .2205 (89*2π)/4065 weeks
90.53601 .2744 (90*2π)/4065 weeks
91.33656 .27243 (91*2π)/4064 weeks
92.46641 -.13603 (92*2π)/4064 weeks
93.8204 -.29095 (93*2π)/4064 weeks
941.55946 .35447 (94*2π)/4064 weeks
951.37812 .53471 (95*2π)/4064 weeks
96.81342 1.0693 (96*2π)/4064 weeks
97.57977 .58306 (97*2π)/4064 weeks
98.97576 .55165 (98*2π)/4064 weeks
991.28581 1.27634 (99*2π)/4064 weeks
100.62356 1.57386 (100*2π)/4064 weeks
101-.09094 1.26354 (101*2π)/4064 weeks
102.16662 .45854 (102*2π)/4064 weeks
103.48202 .88171 (103*2π)/4064 weeks
104.14185 .64878 (104*2π)/4064 weeks
105-.02183 .19391 (105*2π)/4064 weeks
106.45105 .20606 (106*2π)/4064 weeks
107.67449 .28733 (107*2π)/4064 weeks
108.52634 .53385 (108*2π)/4064 weeks
109.65423 .19068 (109*2π)/4064 weeks
110.4104 .64172 (110*2π)/4064 weeks
111.38397 .21773 (111*2π)/4064 weeks
112.76038 .1279 (112*2π)/4064 weeks
113.77434 .60633 (113*2π)/4064 weeks
114.5306 .4329 (114*2π)/4064 weeks
115.76367 .61674 (115*2π)/4064 weeks
116.54679 .50644 (116*2π)/4064 weeks
117-.08998 .4189 (117*2π)/4063 weeks
118.22077 -.32751 (118*2π)/4063 weeks
119.96598 -.25555 (119*2π)/4063 weeks
1201.04435 .07372 (120*2π)/4063 weeks
1211.08481 .36998 (121*2π)/4063 weeks
122.74735 .22976 (122*2π)/4063 weeks
1231.34196 .27013 (123*2π)/4063 weeks
1241.17296 .92435 (124*2π)/4063 weeks
125.65424 .63943 (125*2π)/4063 weeks
126.58453 1.03666 (126*2π)/4063 weeks
127.41355 .64625 (127*2π)/4063 weeks
128.36645 .42057 (128*2π)/4063 weeks
129.50613 .21372 (129*2π)/4063 weeks
130.70118 .42652 (130*2π)/4063 weeks
131.63684 .72468 (131*2π)/4063 weeks
132.47816 .52011 (132*2π)/4063 weeks
133.20808 .61038 (133*2π)/4063 weeks
134.25559 .43514 (134*2π)/4063 weeks
135-.01791 .23003 (135*2π)/4063 weeks
136.03023 .18241 (136*2π)/4063 weeks
137-.07231 -.16982 (137*2π)/4063 weeks
138.62848 -.3781 (138*2π)/4063 weeks
139.44928 -.01276 (139*2π)/4063 weeks
140.37398 .02268 (140*2π)/4063 weeks
141.36023 -.41687 (141*2π)/4063 weeks
142.77856 .05962 (142*2π)/4063 weeks
143.20303 -.40151 (143*2π)/4063 weeks
144.75767 -.66168 (144*2π)/4063 weeks
1451.13536 -.58393 (145*2π)/4063 weeks
1461.12823 -.16894 (146*2π)/4063 weeks
1471.34071 -.3878 (147*2π)/4063 weeks
1481.57379 .06756 (148*2π)/4063 weeks
1491.25756 .40179 (149*2π)/4063 weeks
150.88008 .08591 (150*2π)/4063 weeks
1511.24214 .21387 (151*2π)/4063 weeks
1521.28728 .17223 (152*2π)/4063 weeks
1531.01182 .46543 (153*2π)/4063 weeks
154.98714 .25903 (154*2π)/4063 weeks
155.85374 .39178 (155*2π)/4063 weeks
156.93123 .19314 (156*2π)/4063 weeks
1571.22752 -.10493 (157*2π)/4063 weeks
1581.48129 .45682 (158*2π)/4063 weeks
1591.03572 .78086 (159*2π)/4063 weeks
1601.22641 .68084 (160*2π)/4063 weeks
161.96277 .87136 (161*2π)/4063 weeks
162.57411 1.01178 (162*2π)/4063 weeks
163-.05601 .55686 (163*2π)/4062 weeks
164.22215 -.04119 (164*2π)/4062 weeks
165.8056 -.26949 (165*2π)/4062 weeks
1661.10127 .51672 (166*2π)/4062 weeks
167.55781 .20426 (167*2π)/4062 weeks
168.81319 .3117 (168*2π)/4062 weeks
169.65906 .63249 (169*2π)/4062 weeks
170.34102 .3118 (170*2π)/4062 weeks
171.39547 .08648 (171*2π)/4062 weeks
172.51011 -.04894 (172*2π)/4062 weeks
173.79017 -.09218 (173*2π)/4062 weeks
174.75351 .23957 (174*2π)/4062 weeks
175.6741 -.15585 (175*2π)/4062 weeks
176.85394 -.043 (176*2π)/4062 weeks
1771.26192 -.23379 (177*2π)/4062 weeks
1781.11675 .3949 (178*2π)/4062 weeks
179.75262 .15469 (179*2π)/4062 weeks
1801.26641 -.17241 (180*2π)/4062 weeks
1811.77121 .28437 (181*2π)/4062 weeks
1821.62711 .85468 (182*2π)/4062 weeks
1831.15122 1.11341 (183*2π)/4062 weeks
184.86754 1.09434 (184*2π)/4062 weeks
185.74104 1.3172 (185*2π)/4062 weeks
186.39602 .9311 (186*2π)/4062 weeks
187-.19831 .80221 (187*2π)/4062 weeks
188.33542 .42681 (188*2π)/4062 weeks
189.27 .42813 (189*2π)/4062 weeks
190.38597 .49757 (190*2π)/4062 weeks
191.30576 .72744 (191*2π)/4062 weeks
192-.20422 .35054 (192*2π)/4062 weeks
193.0657 -.11847 (193*2π)/4062 weeks
194.55431 .05698 (194*2π)/4062 weeks
195.15269 .35002 (195*2π)/4062 weeks
196.01594 .10279 (196*2π)/4062 weeks
197.64698 -.27012 (197*2π)/4062 weeks
198.47212 .4763 (198*2π)/4062 weeks
199-.11502 .20075 (199*2π)/4062 weeks
200-.01388 -.21335 (200*2π)/4062 weeks
201.24326 -.21497 (201*2π)/4062 weeks
202.40517 -.44493 (202*2π)/4062 weeks
2031.12288   (203*2π)/4062 weeks
204.40517 .44493 (204*2π)/4062 weeks
205.24326 .21497 (205*2π)/4062 weeks
206-.01388 .21335 (206*2π)/4062 weeks
207-.11502 -.20075 (207*2π)/4062 weeks
208.47212 -.4763 (208*2π)/4062 weeks
209.64698 .27012 (209*2π)/4062 weeks
210.01594 -.10279 (210*2π)/4062 weeks
211.15269 -.35002 (211*2π)/4062 weeks
212.55431 -.05698 (212*2π)/4062 weeks
213.0657 .11847 (213*2π)/4062 weeks
214-.20422 -.35054 (214*2π)/4062 weeks
215.30576 -.72744 (215*2π)/4062 weeks
216.38597 -.49757 (216*2π)/4062 weeks
217.27 -.42813 (217*2π)/4062 weeks
218.33542 -.42681 (218*2π)/4062 weeks
219-.19831 -.80221 (219*2π)/4062 weeks
220.39602 -.9311 (220*2π)/4062 weeks
221.74104 -1.3172 (221*2π)/4062 weeks
222.86754 -1.09434 (222*2π)/4062 weeks
2231.15122 -1.11341 (223*2π)/4062 weeks
2241.62711 -.85468 (224*2π)/4062 weeks
2251.77121 -.28437 (225*2π)/4062 weeks
2261.26641 .17241 (226*2π)/4062 weeks
227.75262 -.15469 (227*2π)/4062 weeks
2281.11675 -.3949 (228*2π)/4062 weeks
2291.26192 .23379 (229*2π)/4062 weeks
230.85394 .043 (230*2π)/4062 weeks
231.6741 .15585 (231*2π)/4062 weeks
232.75351 -.23957 (232*2π)/4062 weeks
233.79017 .09218 (233*2π)/4062 weeks
234.51011 .04894 (234*2π)/4062 weeks
235.39547 -.08648 (235*2π)/4062 weeks
236.34102 -.3118 (236*2π)/4062 weeks
237.65906 -.63249 (237*2π)/4062 weeks
238.81319 -.3117 (238*2π)/4062 weeks
239.55781 -.20426 (239*2π)/4062 weeks
2401.10127 -.51672 (240*2π)/4062 weeks
241.8056 .26949 (241*2π)/4062 weeks
242.22215 .04119 (242*2π)/4062 weeks
243-.05601 -.55686 (243*2π)/4062 weeks
244.57411 -1.01178 (244*2π)/4062 weeks
245.96277 -.87136 (245*2π)/4062 weeks
2461.22641 -.68084 (246*2π)/4062 weeks
2471.03572 -.78086 (247*2π)/4062 weeks
2481.48129 -.45682 (248*2π)/4062 weeks
2491.22752 .10493 (249*2π)/4062 weeks
250.93123 -.19314 (250*2π)/4062 weeks
251.85374 -.39178 (251*2π)/4062 weeks
252.98714 -.25903 (252*2π)/4062 weeks
2531.01182 -.46543 (253*2π)/4062 weeks
2541.28728 -.17223 (254*2π)/4062 weeks
2551.24214 -.21387 (255*2π)/4062 weeks
256.88008 -.08591 (256*2π)/4062 weeks
2571.25756 -.40179 (257*2π)/4062 weeks
2581.57379 -.06756 (258*2π)/4062 weeks
2591.34071 .3878 (259*2π)/4062 weeks
2601.12823 .16894 (260*2π)/4062 weeks
2611.13536 .58393 (261*2π)/4062 weeks
262.75767 .66168 (262*2π)/4062 weeks
263.20303 .40151 (263*2π)/4062 weeks
264.77856 -.05962 (264*2π)/4062 weeks
265.36023 .41687 (265*2π)/4062 weeks
266.37398 -.02268 (266*2π)/4062 weeks
267.44928 .01276 (267*2π)/4062 weeks
268.62848 .3781 (268*2π)/4062 weeks
269-.07231 .16982 (269*2π)/4062 weeks
270.03023 -.18241 (270*2π)/4062 weeks
271-.01791 -.23003 (271*2π)/4061 weeks
272.25559 -.43514 (272*2π)/4061 weeks
273.20808 -.61038 (273*2π)/4061 weeks
274.47816 -.52011 (274*2π)/4061 weeks
275.63684 -.72468 (275*2π)/4061 weeks
276.70118 -.42652 (276*2π)/4061 weeks
277.50613 -.21372 (277*2π)/4061 weeks
278.36645 -.42057 (278*2π)/4061 weeks
279.41355 -.64625 (279*2π)/4061 weeks
280.58453 -1.03666 (280*2π)/4061 weeks
281.65424 -.63943 (281*2π)/4061 weeks
2821.17296 -.92435 (282*2π)/4061 weeks
2831.34196 -.27013 (283*2π)/4061 weeks
284.74735 -.22976 (284*2π)/4061 weeks
2851.08481 -.36998 (285*2π)/4061 weeks
2861.04435 -.07372 (286*2π)/4061 weeks
287.96598 .25555 (287*2π)/4061 weeks
288.22077 .32751 (288*2π)/4061 weeks
289-.08998 -.4189 (289*2π)/4061 weeks
290.54679 -.50644 (290*2π)/4061 weeks
291.76367 -.61674 (291*2π)/4061 weeks
292.5306 -.4329 (292*2π)/4061 weeks
293.77434 -.60633 (293*2π)/4061 weeks
294.76038 -.1279 (294*2π)/4061 weeks
295.38397 -.21773 (295*2π)/4061 weeks
296.4104 -.64172 (296*2π)/4061 weeks
297.65423 -.19068 (297*2π)/4061 weeks
298.52634 -.53385 (298*2π)/4061 weeks
299.67449 -.28733 (299*2π)/4061 weeks
300.45105 -.20606 (300*2π)/4061 weeks
301-.02183 -.19391 (301*2π)/4061 weeks
302.14185 -.64878 (302*2π)/4061 weeks
303.48202 -.88171 (303*2π)/4061 weeks
304.16662 -.45854 (304*2π)/4061 weeks
305-.09094 -1.26354 (305*2π)/4061 weeks
306.62356 -1.57386 (306*2π)/4061 weeks
3071.28581 -1.27634 (307*2π)/4061 weeks
308.97576 -.55165 (308*2π)/4061 weeks
309.57977 -.58306 (309*2π)/4061 weeks
310.81342 -1.0693 (310*2π)/4061 weeks
3111.37812 -.53471 (311*2π)/4061 weeks
3121.55946 -.35447 (312*2π)/4061 weeks
313.8204 .29095 (313*2π)/4061 weeks
314.46641 .13603 (314*2π)/4061 weeks
315.33656 -.27243 (315*2π)/4061 weeks
316.53601 -.2744 (316*2π)/4061 weeks
317.5604 -.2205 (317*2π)/4061 weeks
318.1262 .06514 (318*2π)/4061 weeks
319-.16668 -.37735 (319*2π)/4061 weeks
320.02056 -.74722 (320*2π)/4061 weeks
321.33284 -.89898 (321*2π)/4061 weeks
322.48286 -.62158 (322*2π)/4061 weeks
323.23314 -.37123 (323*2π)/4061 weeks
324.29335 -.51946 (324*2π)/4061 weeks
325-.22187 -.3588 (325*2π)/4061 weeks
326-.28584 -1.03483 (326*2π)/4061 weeks
327.0386 -1.10668 (327*2π)/4061 weeks
328.31187 -1.43134 (328*2π)/4061 weeks
329.1366 -.77616 (329*2π)/4061 weeks
330-.05394 -1.3152 (330*2π)/4061 weeks
331.34249 -1.39874 (331*2π)/4061 weeks
332.30107 -1.02374 (332*2π)/4061 weeks
333.0635 -1.04813 (333*2π)/4061 weeks
334.23254 -1.43865 (334*2π)/4061 weeks
335.35298 -1.1466 (335*2π)/4061 weeks
336-.37006 -1.10732 (336*2π)/4061 weeks
337-.22813 -1.98322 (337*2π)/4061 weeks
338.34236 -2.00808 (338*2π)/4061 weeks
339.25244 -1.96138 (339*2π)/4061 weeks
340.89404 -1.81344 (340*2π)/4061 weeks
341.62705 -1.42467 (341*2π)/4061 weeks
342.27209 -1.40588 (342*2π)/4061 weeks
343.32934 -1.92364 (343*2π)/4061 weeks
344.54743 -2.44347 (344*2π)/4061 weeks
3451.07354 -1.57906 (345*2π)/4061 weeks
346.51495 -2.04828 (346*2π)/4061 weeks
3471.24102 -1.96864 (347*2π)/4061 weeks
348.51241 -1.74651 (348*2π)/4061 weeks
349.40022 -2.70039 (349*2π)/4061 weeks
3502.6243 -3.07158 (350*2π)/4061 weeks
3512.63917 -.86432 (351*2π)/4061 weeks
3521.33934 -.2686 (352*2π)/4061 weeks
3531.08024 -.54308 (353*2π)/4061 weeks
354.70461 -.94968 (354*2π)/4061 weeks
355.21377 -.76617 (355*2π)/4061 weeks
356.16209 -1.74959 (356*2π)/4061 weeks
357.67555 -2.08143 (357*2π)/4061 weeks
3581.16437 -2.06661 (358*2π)/4061 weeks
3591.05797 -1.47336 (359*2π)/4061 weeks
3601.59909 -.9085 (360*2π)/4061 weeks
3611.11615 -.97251 (361*2π)/4061 weeks
362.78047 -1.09278 (362*2π)/4061 weeks
363.67147 -1.06688 (363*2π)/4061 weeks
364.35616 -.59476 (364*2π)/4061 weeks
365-.47986 -.55376 (365*2π)/4061 weeks
366-.39463 -1.61761 (366*2π)/4061 weeks
367.03911 -1.6134 (367*2π)/4061 weeks
368-.54261 -1.09658 (368*2π)/4061 weeks
369-1.40828 -1.12648 (369*2π)/4061 weeks
370-1.75652 -3.00293 (370*2π)/4061 weeks
371-.66975 -3.96903 (371*2π)/4061 weeks
372.26877 -3.0274 (372*2π)/4061 weeks
373-.60344 -2.90104 (373*2π)/4061 weeks
374.52357 -4.6781 (374*2π)/4061 weeks
375.87514 -2.54894 (375*2π)/4061 weeks
376.05065 -1.42358 (376*2π)/4061 weeks
377-1.38468 -3.19556 (377*2π)/4061 weeks
378-.54404 -3.65027 (378*2π)/4061 weeks
379-.93842 -4.06756 (379*2π)/4061 weeks
380-1.2762 -4.79263 (380*2π)/4061 weeks
3811.37866 -5.73713 (381*2π)/4061 weeks
3822.47939 -3.32259 (382*2π)/4061 weeks
383-.28875 -2.34891 (383*2π)/4061 weeks
384-.8091 -3.80614 (384*2π)/4061 weeks
385-.09231 -3.73332 (385*2π)/4061 weeks
386-1.44179 -3.11124 (386*2π)/4061 weeks
387-2.59975 -7.00897 (387*2π)/4061 weeks
388.55192 -6.01611 (388*2π)/4061 weeks
389-1.58774 -6.01962 (389*2π)/4061 weeks
390-1.93561 -5.63192 (390*2π)/4061 weeks
391-2.16784 -8.50265 (391*2π)/4061 weeks
392.24649 -8.6004 (392*2π)/4061 weeks
393-1.14413 -8.49379 (393*2π)/4061 weeks
394-3.62256 -11.65355 (394*2π)/4061 weeks
395.56748 -14.95107 (395*2π)/4061 weeks
3962.79479 -14.39678 (396*2π)/4061 weeks
3976.50588 -18.3899 (397*2π)/4061 weeks
39811.17744 -10.60377 (398*2π)/4061 weeks
3993.70018 -3.27153 (399*2π)/4061 weeks
400-8.79952 -13.93332 (400*2π)/4061 weeks
401-.57644 -29.85233 (401*2π)/4061 weeks
4027.2186 -32.45309 (402*2π)/4061 weeks
4031.85603 -26.43337 (403*2π)/4061 weeks
4047.03389 -72.42361 (404*2π)/4061 weeks

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