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# Fourier Analysis of SSG (ProShares UltraShort Semiconductors)

SSG (ProShares UltraShort Semiconductors) appears to have interesting cyclic behaviour every 45 weeks (84.3365*sine), 49 weeks (75.0488*cosine), and 53 weeks (41.7033*cosine).

SSG (ProShares UltraShort Semiconductors) has an average price of 403.62 (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 2/1/2007 to 4/16/2018 for SSG (ProShares UltraShort Semiconductors), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0403.6243   0
1260.0757 459.0229 (1*2π)/586586 weeks
2-39.74668 343.4115 (2*2π)/586293 weeks
3-161.3971 121.5052 (3*2π)/586195 weeks
4-69.65058 -25.06271 (4*2π)/586147 weeks
551.48908 -45.17198 (5*2π)/586117 weeks
6103.0705 44.04057 (6*2π)/58698 weeks
746.40107 113.2567 (7*2π)/58684 weeks
8-37.98483 100.5508 (8*2π)/58673 weeks
9-57.10592 10.6448 (9*2π)/58665 weeks
10.03809 -21.1777 (10*2π)/58659 weeks
1141.70327 -16.02286 (11*2π)/58653 weeks
1275.04877 33.6742 (12*2π)/58649 weeks
1336.73954 84.33649 (13*2π)/58645 weeks
14-17.72912 74.89776 (14*2π)/58642 weeks
15-34.74039 39.36005 (15*2π)/58639 weeks
16-28.75095 10.87709 (16*2π)/58637 weeks
17-6.5829 -6.12301 (17*2π)/58634 weeks
1812.66903 -2.78243 (18*2π)/58633 weeks
1926.36651 16.16084 (19*2π)/58631 weeks
2011.49289 33.54727 (20*2π)/58629 weeks
21-1.6551 26.40878 (21*2π)/58628 weeks
22-3.94804 17.90501 (22*2π)/58627 weeks
23-.28505 10.58689 (23*2π)/58625 weeks
246.50018 10.98619 (24*2π)/58624 weeks
2514.96563 19.49483 (25*2π)/58623 weeks
261.95047 28.16773 (26*2π)/58623 weeks
27-4.97757 22.71143 (27*2π)/58622 weeks
28-14.13977 20.46193 (28*2π)/58621 weeks
29-11.40705 3.71045 (29*2π)/58620 weeks
30-4.18782 -1.66266 (30*2π)/58620 weeks
319.63052 -5.36072 (31*2π)/58619 weeks
3221.42772 7.98958 (32*2π)/58618 weeks
3315.5437 27.24091 (33*2π)/58618 weeks
34-3.18698 32.43522 (34*2π)/58617 weeks
35-20.88702 19.27818 (35*2π)/58617 weeks
36-17.14992 -6.63997 (36*2π)/58616 weeks
377.16884 -9.74882 (37*2π)/58616 weeks
3815.59273 5.87314 (38*2π)/58615 weeks
3910.31758 16.55064 (39*2π)/58615 weeks
40-.01919 19.53883 (40*2π)/58615 weeks
41-7.50598 12.96584 (41*2π)/58614 weeks
42-8.39866 3.36292 (42*2π)/58614 weeks
431.27466 -4.3125 (43*2π)/58614 weeks
4411.80136 5.5939 (44*2π)/58613 weeks
455.5389 13.71904 (45*2π)/58613 weeks
46-.24907 10.55936 (46*2π)/58613 weeks
47-1.81742 7.81134 (47*2π)/58612 weeks
482.81297 4.48385 (48*2π)/58612 weeks
495.93228 10.80546 (49*2π)/58612 weeks
50-2.29974 15.10741 (50*2π)/58612 weeks
51-6.11743 9.82592 (51*2π)/58611 weeks
52-9.03251 3.75549 (52*2π)/58611 weeks
53-4.02111 -2.79849 (53*2π)/58611 weeks
543.4629 -1.58693 (54*2π)/58611 weeks
554.8983 2.98953 (55*2π)/58611 weeks
563.42861 4.66274 (56*2π)/58610 weeks
571.50888 5.56365 (57*2π)/58610 weeks
58-1.29251 2.06984 (58*2π)/58610 weeks
594.43447 -1.96928 (59*2π)/58610 weeks
608.91789 5.42059 (60*2π)/58610 weeks
614.40969 7.08588 (61*2π)/58610 weeks
622.38592 7.83991 (62*2π)/5869 weeks
63.64168 5.26112 (63*2π)/5869 weeks
642.11455 4.94518 (64*2π)/5869 weeks
651.01256 5.91484 (65*2π)/5869 weeks
66-1.9941 4.25441 (66*2π)/5869 weeks
67-.1518 -1.03885 (67*2π)/5869 weeks
684.77362 -2.45989 (68*2π)/5869 weeks
6910.77533 1.72032 (69*2π)/5868 weeks
708.60466 8.98265 (70*2π)/5868 weeks
711.84712 9.15524 (71*2π)/5868 weeks
721.04807 6.32253 (72*2π)/5868 weeks
73.49608 3.46936 (73*2π)/5868 weeks
746.48181 2.36751 (74*2π)/5868 weeks
757.38341 9.90166 (75*2π)/5868 weeks
76-.57133 13.84632 (76*2π)/5868 weeks
77-8.67044 7.16311 (77*2π)/5868 weeks
78-5.99566 -3.27562 (78*2π)/5868 weeks
794.55302 -4.85122 (79*2π)/5867 weeks
808.64692 1.88093 (80*2π)/5867 weeks
815.95582 6.16637 (81*2π)/5867 weeks
823.23931 9.08182 (82*2π)/5867 weeks
83-3.33609 6.3583 (83*2π)/5867 weeks
84-1.55051 -1.47754 (84*2π)/5867 weeks
855.65596 -1.56672 (85*2π)/5867 weeks
869.57612 3.40879 (86*2π)/5867 weeks
877.09477 11.66092 (87*2π)/5867 weeks
88-1.7165 11.4234 (88*2π)/5867 weeks
89-5.94031 7.52438 (89*2π)/5867 weeks
90-7.80699 -1.51181 (90*2π)/5867 weeks
911.44335 -6.70582 (91*2π)/5866 weeks
929.52969 -3.33366 (92*2π)/5866 weeks
9311.81437 6.69639 (93*2π)/5866 weeks
943.06375 12.61389 (94*2π)/5866 weeks
95-4.89918 8.50092 (95*2π)/5866 weeks
96-4.83454 -.26467 (96*2π)/5866 weeks
972.41754 -3.3322 (97*2π)/5866 weeks
987.74495 1.02351 (98*2π)/5866 weeks
995.49477 7.91123 (99*2π)/5866 weeks
100-1.06633 7.35249 (100*2π)/5866 weeks
101-1.73708 3.99297 (101*2π)/5866 weeks
102-2.14137 1.73375 (102*2π)/5866 weeks
103-.38514 .27625 (103*2π)/5866 weeks
104-.25169 -1.26882 (104*2π)/5866 weeks
1053.83414 -3.45684 (105*2π)/5866 weeks
1067.99695 -.08562 (106*2π)/5866 weeks
1076.97703 5.5591 (107*2π)/5865 weeks
1082.99534 7.51685 (108*2π)/5865 weeks
109-1.25835 5.37694 (109*2π)/5865 weeks
110-2.43933 .40657 (110*2π)/5865 weeks
1111.59635 -3.09192 (111*2π)/5865 weeks
1128.12015 -2.02513 (112*2π)/5865 weeks
1139.29154 6.10203 (113*2π)/5865 weeks
1143.93723 9.62486 (114*2π)/5865 weeks
115-2.81242 8.12677 (115*2π)/5865 weeks
116-6.1904 1.61422 (116*2π)/5865 weeks
117-1.29017 -5.68844 (117*2π)/5865 weeks
1188.53406 -4.97923 (118*2π)/5865 weeks
11911.12049 3.43381 (119*2π)/5865 weeks
1207.12991 10.17344 (120*2π)/5865 weeks
121-.9266 11.52646 (121*2π)/5865 weeks
122-7.65654 4.72211 (122*2π)/5865 weeks
123-3.78879 -4.77294 (123*2π)/5865 weeks
1245.03379 -4.86064 (124*2π)/5865 weeks
1258.15322 1.51371 (125*2π)/5865 weeks
1264.91986 6.50241 (126*2π)/5865 weeks
127.04877 5.88048 (127*2π)/5865 weeks
128-1.71942 2.27822 (128*2π)/5865 weeks
129-.85191 -1.98049 (129*2π)/5865 weeks
1305.24385 -3.1416 (130*2π)/5865 weeks
1318.4975 2.03348 (131*2π)/5864 weeks
1324.81514 7.80707 (132*2π)/5864 weeks
133-.37979 5.64422 (133*2π)/5864 weeks
134-1.40551 1.69082 (134*2π)/5864 weeks
1351.25837 -.70885 (135*2π)/5864 weeks
1363.67582 .76604 (136*2π)/5864 weeks
1374.32895 2.10369 (137*2π)/5864 weeks
1383.04383 3.68134 (138*2π)/5864 weeks
1391.2787 3.3377 (139*2π)/5864 weeks
140.05713 .95744 (140*2π)/5864 weeks
1412.74541 -1.65949 (141*2π)/5864 weeks
1426.94795 .61127 (142*2π)/5864 weeks
1436.50005 4.84673 (143*2π)/5864 weeks
1443.55897 6.37053 (144*2π)/5864 weeks
145-.11959 6.27822 (145*2π)/5864 weeks
146-1.33944 2.22591 (146*2π)/5864 weeks
1472.31293 .65465 (147*2π)/5864 weeks
1482.4838 3.16342 (148*2π)/5864 weeks
149.78191 3.07415 (149*2π)/5864 weeks
150-.07633 1.56021 (150*2π)/5864 weeks
1511.98881 -.80101 (151*2π)/5864 weeks
1525.31981 2.12315 (152*2π)/5864 weeks
1532.56252 4.47537 (153*2π)/5864 weeks
154.63398 3.14154 (154*2π)/5864 weeks
155.28411 1.79459 (155*2π)/5864 weeks
1561.92294 .51357 (156*2π)/5864 weeks
1573.32385 2.05142 (157*2π)/5864 weeks
1582.12558 2.92912 (158*2π)/5864 weeks
1591.5626 3.45235 (159*2π)/5864 weeks
160-.79992 2.26236 (160*2π)/5864 weeks
161.93445 -.37999 (161*2π)/5864 weeks
1622.09509 .73803 (162*2π)/5864 weeks
1632.82843 -.20343 (163*2π)/5864 weeks
1644.20431 1.93968 (164*2π)/5864 weeks
1652.54408 2.8409 (165*2π)/5864 weeks
1661.71241 2.34778 (166*2π)/5864 weeks
1671.99444 1.37586 (167*2π)/5864 weeks
1683.50729 1.04648 (168*2π)/5863 weeks
1693.93837 3.89799 (169*2π)/5863 weeks
170.89885 4.08537 (170*2π)/5863 weeks
171.88676 2.93723 (171*2π)/5863 weeks
172.17216 2.59596 (172*2π)/5863 weeks
173-.09541 .85862 (173*2π)/5863 weeks
1741.23696 -.41227 (174*2π)/5863 weeks
1754.06586 .73784 (175*2π)/5863 weeks
1763.11634 3.4575 (176*2π)/5863 weeks
1771.45934 4.19864 (177*2π)/5863 weeks
178-1.43554 3.32207 (178*2π)/5863 weeks
179-1.98487 -.56563 (179*2π)/5863 weeks
1801.52333 -2.4841 (180*2π)/5863 weeks
1814.28209 -.58918 (181*2π)/5863 weeks
1824.11713 1.95976 (182*2π)/5863 weeks
1833.00347 3.03757 (183*2π)/5863 weeks
1841.2897 3.50163 (184*2π)/5863 weeks
185-.99978 2.08097 (185*2π)/5863 weeks
186-.47055 -1.45505 (186*2π)/5863 weeks
1873.80929 -2.39172 (187*2π)/5863 weeks
1886.12257 .88165 (188*2π)/5863 weeks
1894.96405 4.27113 (189*2π)/5863 weeks
1901.78348 6.12512 (190*2π)/5863 weeks
191-1.67132 4.33948 (191*2π)/5863 weeks
192-2.56036 .52859 (192*2π)/5863 weeks
193-.04696 -2.24694 (193*2π)/5863 weeks
1943.51514 -1.99627 (194*2π)/5863 weeks
1954.73858 .7401 (195*2π)/5863 weeks
1964.10606 3.11037 (196*2π)/5863 weeks
1971.90783 3.51782 (197*2π)/5863 weeks
1981.04104 3.2294 (198*2π)/5863 weeks
199-.63296 1.75557 (199*2π)/5863 weeks
200.97361 .37845 (200*2π)/5863 weeks
2011.33998 .82948 (201*2π)/5863 weeks
2021.99936 .80945 (202*2π)/5863 weeks
2031.77373 2.2852 (203*2π)/5863 weeks
204-.26558 1.7432 (204*2π)/5863 weeks
205.03465 -.16815 (205*2π)/5863 weeks
206.91564 -1.85355 (206*2π)/5863 weeks
2074.90827 -2.04431 (207*2π)/5863 weeks
2086.34206 3.35065 (208*2π)/5863 weeks
2091.86074 5.5961 (209*2π)/5863 weeks
210-1.26527 4.01596 (210*2π)/5863 weeks
211-2.67477 .5356 (211*2π)/5863 weeks
212.22655 -2.06366 (212*2π)/5863 weeks
2132.52294 -.61005 (213*2π)/5863 weeks
2143.02426 -.17303 (214*2π)/5863 weeks
2153.25865 3.26594 (215*2π)/5863 weeks
216-1.19505 2.80876 (216*2π)/5863 weeks
217-1.32725 -.15023 (217*2π)/5863 weeks
218-.91268 -2.64499 (218*2π)/5863 weeks
2193.41972 -4.24397 (219*2π)/5863 weeks
2206.96199 -.64802 (220*2π)/5863 weeks
2215.10485 4.3062 (221*2π)/5863 weeks
222.55292 4.89573 (222*2π)/5863 weeks
223-2.74984 1.11106 (223*2π)/5863 weeks
224.23875 -3.15024 (224*2π)/5863 weeks
2254.14111 -1.81765 (225*2π)/5863 weeks
2265.11389 1.09168 (226*2π)/5863 weeks
2273.38671 4.12265 (227*2π)/5863 weeks
228-1.49065 3.72009 (228*2π)/5863 weeks
229-2.01814 -1.00882 (229*2π)/5863 weeks
2301.26939 -3.70124 (230*2π)/5863 weeks
2315.60007 -2.07358 (231*2π)/5863 weeks
2325.52148 2.68307 (232*2π)/5863 weeks
2331.52014 4.1571 (233*2π)/5863 weeks
234-.07598 .89282 (234*2π)/5863 weeks
2351.96536 -.47418 (235*2π)/5862 weeks
2363.17522 1.02135 (236*2π)/5862 weeks
2372.93756 2.93454 (237*2π)/5862 weeks
238.05764 4.06686 (238*2π)/5862 weeks
239-2.78545 1.35396 (239*2π)/5862 weeks
240-1.16356 -2.69313 (240*2π)/5862 weeks
2411.87361 -2.73754 (241*2π)/5862 weeks
2424.63542 -1.29361 (242*2π)/5862 weeks
2434.03162 2.38146 (243*2π)/5862 weeks
2441.06307 2.98389 (244*2π)/5862 weeks
245-.97318 1.37391 (245*2π)/5862 weeks
246-.95378 -1.45459 (246*2π)/5862 weeks
2472.49506 -2.98721 (247*2π)/5862 weeks
2485.26416 -.06085 (248*2π)/5862 weeks
2493.41933 3.51666 (249*2π)/5862 weeks
250-.8847 3.76504 (250*2π)/5862 weeks
251-2.80319 -.43371 (251*2π)/5862 weeks
252-.42254 -3.59096 (252*2π)/5862 weeks
2532.96 -3.50414 (253*2π)/5862 weeks
2545.56466 -1.5489 (254*2π)/5862 weeks
2554.62966 3.1774 (255*2π)/5862 weeks
256.45235 2.65014 (256*2π)/5862 weeks
257-.11377 .78414 (257*2π)/5862 weeks
258.05678 -1.17625 (258*2π)/5862 weeks
2591.75331 -1.22344 (259*2π)/5862 weeks
2602.22629 -.90984 (260*2π)/5862 weeks
2612.82206 -.6688 (261*2π)/5862 weeks
2623.05162 .80642 (262*2π)/5862 weeks
2631.30249 1.38479 (263*2π)/5862 weeks
264.69545 .30334 (264*2π)/5862 weeks
265.213 -1.26752 (265*2π)/5862 weeks
2661.95139 -2.71483 (266*2π)/5862 weeks
2675.36336 -1.86521 (267*2π)/5862 weeks
2685.59026 2.75463 (268*2π)/5862 weeks
2691.60176 4.9161 (269*2π)/5862 weeks
270-2.55287 3.0841 (270*2π)/5862 weeks
271-4.40277 -1.8892 (271*2π)/5862 weeks
272-.4486 -6.46817 (272*2π)/5862 weeks
2735.62548 -6.24764 (273*2π)/5862 weeks
2748.88122 -.22647 (274*2π)/5862 weeks
2755.12511 5.08666 (275*2π)/5862 weeks
276-.40775 4.08817 (276*2π)/5862 weeks
277-2.42166 .13315 (277*2π)/5862 weeks
278-.4963 -3.60808 (278*2π)/5862 weeks
2793.5089 -4.25617 (279*2π)/5862 weeks
2806.65897 -.5817 (280*2π)/5862 weeks
2814.07831 2.86737 (281*2π)/5862 weeks
282.88791 3.08292 (282*2π)/5862 weeks
283-1.70366 .37744 (283*2π)/5862 weeks
284-.23084 -2.83059 (284*2π)/5862 weeks
2852.7329 -4.62946 (285*2π)/5862 weeks
2866.62942 -1.87141 (286*2π)/5862 weeks
2874.9482 3.30524 (287*2π)/5862 weeks
288.26115 2.72452 (288*2π)/5862 weeks
289-.40262 -.61766 (289*2π)/5862 weeks
290.55215 -2.93554 (290*2π)/5862 weeks
2913.1406 -3.26297 (291*2π)/5862 weeks
2924.9538 -2.74517 (292*2π)/5862 weeks
2936.99402   (293*2π)/5862 weeks
2944.9538 2.74517 (294*2π)/5862 weeks
2953.1406 3.26297 (295*2π)/5862 weeks
296.55215 2.93554 (296*2π)/5862 weeks
297-.40262 .61766 (297*2π)/5862 weeks
298.26115 -2.72452 (298*2π)/5862 weeks
2994.9482 -3.30524 (299*2π)/5862 weeks
3006.62942 1.87141 (300*2π)/5862 weeks
3012.7329 4.62946 (301*2π)/5862 weeks
302-.23084 2.83059 (302*2π)/5862 weeks
303-1.70366 -.37744 (303*2π)/5862 weeks
304.88791 -3.08292 (304*2π)/5862 weeks
3054.07831 -2.86737 (305*2π)/5862 weeks
3066.65897 .5817 (306*2π)/5862 weeks
3073.5089 4.25617 (307*2π)/5862 weeks
308-.4963 3.60808 (308*2π)/5862 weeks
309-2.42166 -.13315 (309*2π)/5862 weeks
310-.40775 -4.08817 (310*2π)/5862 weeks
3115.12511 -5.08666 (311*2π)/5862 weeks
3128.88122 .22647 (312*2π)/5862 weeks
3135.62548 6.24764 (313*2π)/5862 weeks
314-.4486 6.46817 (314*2π)/5862 weeks
315-4.40277 1.8892 (315*2π)/5862 weeks
316-2.55287 -3.0841 (316*2π)/5862 weeks
3171.60176 -4.9161 (317*2π)/5862 weeks
3185.59026 -2.75463 (318*2π)/5862 weeks
3195.36336 1.86521 (319*2π)/5862 weeks
3201.95139 2.71483 (320*2π)/5862 weeks
321.213 1.26752 (321*2π)/5862 weeks
322.69545 -.30334 (322*2π)/5862 weeks
3231.30249 -1.38479 (323*2π)/5862 weeks
3243.05162 -.80642 (324*2π)/5862 weeks
3252.82206 .6688 (325*2π)/5862 weeks
3262.22629 .90984 (326*2π)/5862 weeks
3271.75331 1.22344 (327*2π)/5862 weeks
328.05678 1.17625 (328*2π)/5862 weeks
329-.11377 -.78414 (329*2π)/5862 weeks
330.45235 -2.65014 (330*2π)/5862 weeks
3314.62966 -3.1774 (331*2π)/5862 weeks
3325.56466 1.5489 (332*2π)/5862 weeks
3332.96 3.50414 (333*2π)/5862 weeks
334-.42254 3.59096 (334*2π)/5862 weeks
335-2.80319 .43371 (335*2π)/5862 weeks
336-.8847 -3.76504 (336*2π)/5862 weeks
3373.41933 -3.51666 (337*2π)/5862 weeks
3385.26416 .06085 (338*2π)/5862 weeks
3392.49506 2.98721 (339*2π)/5862 weeks
340-.95378 1.45459 (340*2π)/5862 weeks
341-.97318 -1.37391 (341*2π)/5862 weeks
3421.06307 -2.98389 (342*2π)/5862 weeks
3434.03162 -2.38146 (343*2π)/5862 weeks
3444.63542 1.29361 (344*2π)/5862 weeks
3451.87361 2.73754 (345*2π)/5862 weeks
346-1.16356 2.69313 (346*2π)/5862 weeks
347-2.78545 -1.35396 (347*2π)/5862 weeks
348.05764 -4.06686 (348*2π)/5862 weeks
3492.93756 -2.93454 (349*2π)/5862 weeks
3503.17522 -1.02135 (350*2π)/5862 weeks
3511.96536 .47418 (351*2π)/5862 weeks
352-.07598 -.89282 (352*2π)/5862 weeks
3531.52014 -4.1571 (353*2π)/5862 weeks
3545.52148 -2.68307 (354*2π)/5862 weeks
3555.60007 2.07358 (355*2π)/5862 weeks
3561.26939 3.70124 (356*2π)/5862 weeks
357-2.01814 1.00882 (357*2π)/5862 weeks
358-1.49065 -3.72009 (358*2π)/5862 weeks
3593.38671 -4.12265 (359*2π)/5862 weeks
3605.11389 -1.09168 (360*2π)/5862 weeks
3614.14111 1.81765 (361*2π)/5862 weeks
362.23875 3.15024 (362*2π)/5862 weeks
363-2.74984 -1.11106 (363*2π)/5862 weeks
364.55292 -4.89573 (364*2π)/5862 weeks
3655.10485 -4.3062 (365*2π)/5862 weeks
3666.96199 .64802 (366*2π)/5862 weeks
3673.41972 4.24397 (367*2π)/5862 weeks
368-.91268 2.64499 (368*2π)/5862 weeks
369-1.32725 .15023 (369*2π)/5862 weeks
370-1.19505 -2.80876 (370*2π)/5862 weeks
3713.25865 -3.26594 (371*2π)/5862 weeks
3723.02426 .17303 (372*2π)/5862 weeks
3732.52294 .61005 (373*2π)/5862 weeks
374.22655 2.06366 (374*2π)/5862 weeks
375-2.67477 -.5356 (375*2π)/5862 weeks
376-1.26527 -4.01596 (376*2π)/5862 weeks
3771.86074 -5.5961 (377*2π)/5862 weeks
3786.34206 -3.35065 (378*2π)/5862 weeks
3794.90827 2.04431 (379*2π)/5862 weeks
380.91564 1.85355 (380*2π)/5862 weeks
381.03465 .16815 (381*2π)/5862 weeks
382-.26558 -1.7432 (382*2π)/5862 weeks
3831.77373 -2.2852 (383*2π)/5862 weeks
3841.99936 -.80945 (384*2π)/5862 weeks
3851.33998 -.82948 (385*2π)/5862 weeks
386.97361 -.37845 (386*2π)/5862 weeks
387-.63296 -1.75557 (387*2π)/5862 weeks
3881.04104 -3.2294 (388*2π)/5862 weeks
3891.90783 -3.51782 (389*2π)/5862 weeks
3904.10606 -3.11037 (390*2π)/5862 weeks
3914.73858 -.7401 (391*2π)/5861 weeks
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