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Fourier Analysis of EMM (SPDR DJ Wilshire Mid Cap ETF)


EMM (SPDR DJ Wilshire Mid Cap ETF) appears to have interesting cyclic behaviour every 100 weeks (68.6327*sine), 91 weeks (58.9789*sine), and 83 weeks (25.4076*cosine).

EMM (SPDR DJ Wilshire Mid Cap ETF) has an average price of 94.56 (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 1/29/1988 to 3/20/2017 for EMM (SPDR DJ Wilshire Mid Cap ETF), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
094.56097   0 
1101.7667 89.21865 (1*2π)/997997 weeks
257.16212 92.38849 (2*2π)/997499 weeks
3-6.75321 75.46098 (3*2π)/997332 weeks
4-8.70402 22.73522 (4*2π)/997249 weeks
5-1.63689 .69545 (5*2π)/997199 weeks
636.74061 -7.66561 (6*2π)/997166 weeks
749.48125 5.17159 (7*2π)/997142 weeks
862.71246 38.64909 (8*2π)/997125 weeks
937.19025 62.11427 (9*2π)/997111 weeks
1013.85944 68.63274 (10*2π)/997100 weeks
11-20.32179 58.97888 (11*2π)/99791 weeks
12-25.40761 29.83382 (12*2π)/99783 weeks
13-22.77764 15.50886 (13*2π)/99777 weeks
14-11.63499 1.94684 (14*2π)/99771 weeks
151.16296 4.36069 (15*2π)/99766 weeks
163.80623 9.47648 (16*2π)/99762 weeks
171.91987 15.22103 (17*2π)/99759 weeks
18-.45864 14.61245 (18*2π)/99755 weeks
19-10.16106 16.39393 (19*2π)/99752 weeks
20-11.29039 5.86817 (20*2π)/99750 weeks
21-11.85388 .8004 (21*2π)/99747 weeks
22-6.80124 -7.77451 (22*2π)/99745 weeks
23.93447 -5.69106 (23*2π)/99743 weeks
241.3093 -5.15511 (24*2π)/99742 weeks
251.40708 -7.24163 (25*2π)/99740 weeks
266.3628 -8.77968 (26*2π)/99738 weeks
2710.33426 -10.81712 (27*2π)/99737 weeks
2817.96288 -5.32018 (28*2π)/99736 weeks
2917.93993 1.50086 (29*2π)/99734 weeks
3014.67994 5.25845 (30*2π)/99733 weeks
3110.71419 9.49813 (31*2π)/99732 weeks
323.2053 5.72728 (32*2π)/99731 weeks
331.80349 -.83489 (33*2π)/99730 weeks
345.07942 -6.95076 (34*2π)/99729 weeks
3513.35094 -9.81455 (35*2π)/99728 weeks
3620.75573 -7.29909 (36*2π)/99728 weeks
3725.39686 3.41312 (37*2π)/99727 weeks
3821.22567 9.70494 (38*2π)/99726 weeks
3914.15409 14.6297 (39*2π)/99726 weeks
406.20845 10.04176 (40*2π)/99725 weeks
415.67884 4.93735 (41*2π)/99724 weeks
426.8808 -2.00643 (42*2π)/99724 weeks
4315.29255 -4.63529 (43*2π)/99723 weeks
4421.9648 1.11392 (44*2π)/99723 weeks
4522.16741 7.65296 (45*2π)/99722 weeks
4618.88725 11.34905 (46*2π)/99722 weeks
4715.80488 13.79942 (47*2π)/99721 weeks
4812.20159 12.05881 (48*2π)/99721 weeks
4911.95913 9.59965 (49*2π)/99720 weeks
5014.03613 8.80215 (50*2π)/99720 weeks
5117.42723 10.94256 (51*2π)/99720 weeks
5215.88873 15.56976 (52*2π)/99719 weeks
5312.68179 17.4148 (53*2π)/99719 weeks
5410.3479 16.48257 (54*2π)/99718 weeks
5510.13019 15.33423 (55*2π)/99718 weeks
5611.64853 17.69934 (56*2π)/99718 weeks
578.9207 21.45812 (57*2π)/99717 weeks
583.12668 22.29227 (58*2π)/99717 weeks
59-1.8494 18.69058 (59*2π)/99717 weeks
60-1.19747 13.99887 (60*2π)/99717 weeks
61-.52378 11.97577 (61*2π)/99716 weeks
621.47054 12.02483 (62*2π)/99716 weeks
632.16578 12.96335 (63*2π)/99716 weeks
64.04091 14.37497 (64*2π)/99716 weeks
65-2.34577 14.50586 (65*2π)/99715 weeks
66-5.01012 11.6378 (66*2π)/99715 weeks
67-5.2849 8.43824 (67*2π)/99715 weeks
68-4.59122 6.40897 (68*2π)/99715 weeks
69-2.37604 3.92442 (69*2π)/99714 weeks
70-1.02846 4.29831 (70*2π)/99714 weeks
71.49433 4.84635 (71*2π)/99714 weeks
72-.48526 5.34894 (72*2π)/99714 weeks
73-1.54308 3.83156 (73*2π)/99714 weeks
74.78209 1.98554 (74*2π)/99713 weeks
751.97742 2.0453 (75*2π)/99713 weeks
763.63298 3.29568 (76*2π)/99713 weeks
773.38889 4.14965 (77*2π)/99713 weeks
782.73398 4.88029 (78*2π)/99713 weeks
79.97694 3.34421 (79*2π)/99713 weeks
803.37916 .99884 (80*2π)/99712 weeks
815.73078 .64817 (81*2π)/99712 weeks
829.33103 2.83073 (82*2π)/99712 weeks
8310.02354 6.81377 (83*2π)/99712 weeks
848.64363 10.78536 (84*2π)/99712 weeks
853.22623 13.71343 (85*2π)/99712 weeks
86-2.61406 9.84913 (86*2π)/99712 weeks
87-2.15885 3.68735 (87*2π)/99711 weeks
881.75931 -.1529 (88*2π)/99711 weeks
898.34033 1.69256 (89*2π)/99711 weeks
909.49595 6.46806 (90*2π)/99711 weeks
918.01956 10.6629 (91*2π)/99711 weeks
924.89543 12.29717 (92*2π)/99711 weeks
93.9147 13.45264 (93*2π)/99711 weeks
94-2.80806 9.2718 (94*2π)/99711 weeks
95-2.04176 6.64253 (95*2π)/99710 weeks
96-.95858 3.47653 (96*2π)/99710 weeks
973.35721 4.4267 (97*2π)/99710 weeks
982.03829 6.19053 (98*2π)/99710 weeks
992.17618 7.30156 (99*2π)/99710 weeks
100.57596 6.5462 (100*2π)/99710 weeks
101-.22658 5.82117 (101*2π)/99710 weeks
102.39236 4.15405 (102*2π)/99710 weeks
1032.48295 4.20442 (103*2π)/99710 weeks
1041.85873 4.5551 (104*2π)/99710 weeks
1052.99971 6.56575 (105*2π)/9979 weeks
106.30764 5.4902 (106*2π)/9979 weeks
107.37774 4.01512 (107*2π)/9979 weeks
1082.27554 2.95304 (108*2π)/9979 weeks
1093.16545 3.01872 (109*2π)/9979 weeks
1104.91107 3.20142 (110*2π)/9979 weeks
1116.58555 5.70336 (111*2π)/9979 weeks
1126.28989 7.0605 (112*2π)/9979 weeks
1135.39737 11.49103 (113*2π)/9979 weeks
114-.01868 11.5553 (114*2π)/9979 weeks
115-1.74329 7.65232 (115*2π)/9979 weeks
116-1.97468 6.13493 (116*2π)/9979 weeks
117.9904 2.34475 (117*2π)/9979 weeks
1184.20934 4.3466 (118*2π)/9978 weeks
1195.58133 7.04889 (119*2π)/9978 weeks
1204.93831 11.10541 (120*2π)/9978 weeks
121.88151 12.90546 (121*2π)/9978 weeks
122-3.73242 11.98562 (122*2π)/9978 weeks
123-4.24002 9.20756 (123*2π)/9978 weeks
124-6.67896 6.14665 (124*2π)/9978 weeks
125-3.8432 3.16535 (125*2π)/9978 weeks
126-1.71755 2.94668 (126*2π)/9978 weeks
127.27485 3.66196 (127*2π)/9978 weeks
128.15606 6.74962 (128*2π)/9978 weeks
129-2.80691 8.0481 (129*2π)/9978 weeks
130-5.79061 4.62703 (130*2π)/9978 weeks
131-4.86563 2.59202 (131*2π)/9978 weeks
132-3.16593 -.37512 (132*2π)/9978 weeks
133-.13845 .78249 (133*2π)/9977 weeks
134-.19682 1.87035 (134*2π)/9977 weeks
135.15182 2.1319 (135*2π)/9977 weeks
136-.12782 3.30755 (136*2π)/9977 weeks
137-1.74205 2.08813 (137*2π)/9977 weeks
138-.95157 .70665 (138*2π)/9977 weeks
139.75207 .10328 (139*2π)/9977 weeks
1402.63423 -.07894 (140*2π)/9977 weeks
1413.6415 3.46933 (141*2π)/9977 weeks
1421.78814 4.43286 (142*2π)/9977 weeks
143.76666 3.48856 (143*2π)/9977 weeks
144-.78242 3.59333 (144*2π)/9977 weeks
1451.21875 1.14921 (145*2π)/9977 weeks
1461.42003 1.3898 (146*2π)/9977 weeks
1473.57322 1.58497 (147*2π)/9977 weeks
1485.13787 4.58683 (148*2π)/9977 weeks
1492.58848 6.17486 (149*2π)/9977 weeks
150.61336 6.92107 (150*2π)/9977 weeks
151-.78003 5.05734 (151*2π)/9977 weeks
152-.57552 3.34949 (152*2π)/9977 weeks
153.72279 3.3222 (153*2π)/9977 weeks
1541.1661 3.73892 (154*2π)/9976 weeks
1551.71488 4.05207 (155*2π)/9976 weeks
1561.18599 6.15888 (156*2π)/9976 weeks
157-1.00151 5.65595 (157*2π)/9976 weeks
158-1.35067 4.18031 (158*2π)/9976 weeks
159-.72861 3.55269 (159*2π)/9976 weeks
160.13752 3.87264 (160*2π)/9976 weeks
161-.71796 4.83721 (161*2π)/9976 weeks
162-2.17245 3.97815 (162*2π)/9976 weeks
163-1.2789 2.09187 (163*2π)/9976 weeks
164.14559 2.54175 (164*2π)/9976 weeks
165.43627 3.44186 (165*2π)/9976 weeks
166.26357 5.02443 (166*2π)/9976 weeks
167-2.62564 5.26243 (167*2π)/9976 weeks
168-3.09356 2.71314 (168*2π)/9976 weeks
169-2.87253 1.96459 (169*2π)/9976 weeks
170-2.21383 .51069 (170*2π)/9976 weeks
171.03004 -.42824 (171*2π)/9976 weeks
172.77614 1.21321 (172*2π)/9976 weeks
1732.22314 2.49995 (173*2π)/9976 weeks
174.12783 4.51481 (174*2π)/9976 weeks
175-1.85323 3.45393 (175*2π)/9976 weeks
176-1.94974 2.95804 (176*2π)/9976 weeks
177-2.58996 .61576 (177*2π)/9976 weeks
178-1.37729 -.70127 (178*2π)/9976 weeks
1792.2782 -.1897 (179*2π)/9976 weeks
1801.23366 1.71427 (180*2π)/9976 weeks
1812.06224 2.70655 (181*2π)/9976 weeks
182.22854 3.65748 (182*2π)/9975 weeks
183-.05832 2.89709 (183*2π)/9975 weeks
184-1.30157 3.81736 (184*2π)/9975 weeks
185-1.85746 1.06277 (185*2π)/9975 weeks
186-.66549 .51234 (186*2π)/9975 weeks
1871.06776 1.22041 (187*2π)/9975 weeks
188.6272 1.89196 (188*2π)/9975 weeks
189.59781 2.62819 (189*2π)/9975 weeks
190-.80286 3.15558 (190*2π)/9975 weeks
191-.49991 1.49524 (191*2π)/9975 weeks
192-1.21871 2.71078 (192*2π)/9975 weeks
193-1.39481 .29718 (193*2π)/9975 weeks
194.04489 1.22293 (194*2π)/9975 weeks
195-.46576 .19932 (195*2π)/9975 weeks
1961.02526 1.19559 (196*2π)/9975 weeks
197.3789 1.63846 (197*2π)/9975 weeks
198-.30264 2.21766 (198*2π)/9975 weeks
199-1.34649 .72999 (199*2π)/9975 weeks
200-.19792 -.23236 (200*2π)/9975 weeks
201.72011 -.77294 (201*2π)/9975 weeks
2022.40714 .55031 (202*2π)/9975 weeks
2031.83928 .90159 (203*2π)/9975 weeks
2042.25909 2.00707 (204*2π)/9975 weeks
2051.62138 2.79359 (205*2π)/9975 weeks
206.76732 2.69903 (206*2π)/9975 weeks
207-.61957 2.19163 (207*2π)/9975 weeks
208.63163 .78973 (208*2π)/9975 weeks
2091.60422 .76258 (209*2π)/9975 weeks
2102.55326 1.89906 (210*2π)/9975 weeks
2112.1091 3.94029 (211*2π)/9975 weeks
212.67567 3.80623 (212*2π)/9975 weeks
213-.52705 3.75948 (213*2π)/9975 weeks
214-1.15581 2.45608 (214*2π)/9975 weeks
215-.14548 1.70857 (215*2π)/9975 weeks
216.46691 1.19353 (216*2π)/9975 weeks
2171.73411 3.12823 (217*2π)/9975 weeks
218.15535 4.56298 (218*2π)/9975 weeks
219-1.85315 3.66009 (219*2π)/9975 weeks
220-2.14051 2.9543 (220*2π)/9975 weeks
221-2.3291 1.72952 (221*2π)/9975 weeks
222-2.80219 .90039 (222*2π)/9974 weeks
223-1.3997 -1.09744 (223*2π)/9974 weeks
2241.32592 -.76172 (224*2π)/9974 weeks
2251.81098 1.76883 (225*2π)/9974 weeks
226.57861 4.14546 (226*2π)/9974 weeks
227-1.91339 2.40545 (227*2π)/9974 weeks
228-2.7936 2.89805 (228*2π)/9974 weeks
229-3.41415 -.25213 (229*2π)/9974 weeks
230-2.29115 -2.04617 (230*2π)/9974 weeks
231.22989 -2.99256 (231*2π)/9974 weeks
2323.53885 -.98727 (232*2π)/9974 weeks
2332.68709 1.6268 (233*2π)/9974 weeks
234.6599 3.63276 (234*2π)/9974 weeks
235-.87511 1.83248 (235*2π)/9974 weeks
236-1.28436 .72132 (236*2π)/9974 weeks
237-.19061 .30059 (237*2π)/9974 weeks
238.31333 .48569 (238*2π)/9974 weeks
239-.27692 .11845 (239*2π)/9974 weeks
240.82527 .52667 (240*2π)/9974 weeks
241.59717 .50811 (241*2π)/9974 weeks
242.98698 .54796 (242*2π)/9974 weeks
243.37633 1.28446 (243*2π)/9974 weeks
2441.52639 .89453 (244*2π)/9974 weeks
245.57407 1.68328 (245*2π)/9974 weeks
246.20047 2.53482 (246*2π)/9974 weeks
247-1.0287 1.56682 (247*2π)/9974 weeks
248-.64512 .49325 (248*2π)/9974 weeks
249-.98657 .41121 (249*2π)/9974 weeks
250.60081 -.02071 (250*2π)/9974 weeks
251-.24817 .01507 (251*2π)/9974 weeks
252.82549 -.14185 (252*2π)/9974 weeks
2531.47226 .05407 (253*2π)/9974 weeks
2541.96669 1.18134 (254*2π)/9974 weeks
2551.27314 2.3881 (255*2π)/9974 weeks
256.24832 3.07927 (256*2π)/9974 weeks
257-2.33239 2.41594 (257*2π)/9974 weeks
258-2.18095 .11164 (258*2π)/9974 weeks
259-1.921 -1.60257 (259*2π)/9974 weeks
2601.15514 -3.0495 (260*2π)/9974 weeks
2613.26625 -.32089 (261*2π)/9974 weeks
2622.67525 1.466 (262*2π)/9974 weeks
2631.4792 2.55681 (263*2π)/9974 weeks
264-.13859 2.73684 (264*2π)/9974 weeks
265-1.11518 2.06054 (265*2π)/9974 weeks
266-1.91527 .42987 (266*2π)/9974 weeks
267-1.7036 -1.52799 (267*2π)/9974 weeks
2681.92527 -1.75688 (268*2π)/9974 weeks
2691.65782 .19453 (269*2π)/9974 weeks
2701.36865 .5247 (270*2π)/9974 weeks
2711.18851 1.27982 (271*2π)/9974 weeks
272.95091 .65157 (272*2π)/9974 weeks
273.36472 1.55129 (273*2π)/9974 weeks
274.23289 .87102 (274*2π)/9974 weeks
275-.49438 .46852 (275*2π)/9974 weeks
276.59852 -.15663 (276*2π)/9974 weeks
277-.05756 -.20679 (277*2π)/9974 weeks
2781.54423 -.90784 (278*2π)/9974 weeks
2791.89801 .1812 (279*2π)/9974 weeks
2802.51225 .34248 (280*2π)/9974 weeks
2811.87214 2.17421 (281*2π)/9974 weeks
2821.16327 1.85353 (282*2π)/9974 weeks
283.55052 1.57093 (283*2π)/9974 weeks
284.54522 1.60481 (284*2π)/9974 weeks
285.13986 1.1839 (285*2π)/9973 weeks
286.54526 .47148 (286*2π)/9973 weeks
2871.64083 .49884 (287*2π)/9973 weeks
2881.8397 1.91447 (288*2π)/9973 weeks
2891.49551 2.90057 (289*2π)/9973 weeks
290-.07437 2.52168 (290*2π)/9973 weeks
291.21429 2.68692 (291*2π)/9973 weeks
292-.7252 2.76266 (292*2π)/9973 weeks
293-.80119 1.97046 (293*2π)/9973 weeks
294-1.58976 1.95994 (294*2π)/9973 weeks
295-.59422 1.33911 (295*2π)/9973 weeks
296-.92132 1.81303 (296*2π)/9973 weeks
297-1.48239 2.16927 (297*2π)/9973 weeks
298-2.26699 1.72683 (298*2π)/9973 weeks
299-2.40346 .76789 (299*2π)/9973 weeks
300-2.0795 .38236 (300*2π)/9973 weeks
301-2.14134 .72877 (301*2π)/9973 weeks
302-2.53136 .39554 (302*2π)/9973 weeks
303-3.39017 -.55134 (303*2π)/9973 weeks
304-2.87699 -1.57442 (304*2π)/9973 weeks
305-1.86168 -2.59059 (305*2π)/9973 weeks
306-.64272 -2.54667 (306*2π)/9973 weeks
307-.12473 -1.26886 (307*2π)/9973 weeks
308-.33548 -.83501 (308*2π)/9973 weeks
309-1.45425 -.97344 (309*2π)/9973 weeks
310-1.46848 -1.37216 (310*2π)/9973 weeks
311-1.63701 -2.29004 (311*2π)/9973 weeks
312-1.16095 -3.46091 (312*2π)/9973 weeks
313.60656 -3.64185 (313*2π)/9973 weeks
3141.30527 -2.74262 (314*2π)/9973 weeks
3151.63061 -2.0686 (315*2π)/9973 weeks
3161.50845 -1.70223 (316*2π)/9973 weeks
3171.34429 -1.02743 (317*2π)/9973 weeks
3181.01229 -.83303 (318*2π)/9973 weeks
319.3299 -1.33414 (319*2π)/9973 weeks
320.29795 -2.16433 (320*2π)/9973 weeks
3212.07649 -2.32139 (321*2π)/9973 weeks
3222.36249 -1.59662 (322*2π)/9973 weeks
3232.20147 -.33299 (323*2π)/9973 weeks
3241.89961 -.42033 (324*2π)/9973 weeks
3251.55507 .15908 (325*2π)/9973 weeks
3261.2196 -.03858 (326*2π)/9973 weeks
327.42242 .32632 (327*2π)/9973 weeks
328.46356 -.94966 (328*2π)/9973 weeks
3291.01265 -.77688 (329*2π)/9973 weeks
3301.54657 -.99715 (330*2π)/9973 weeks
3311.38505 .93346 (331*2π)/9973 weeks
332.45917 -.04533 (332*2π)/9973 weeks
333-.54093 .13403 (333*2π)/9973 weeks
334.20653 -1.47288 (334*2π)/9973 weeks
335.99966 -1.01665 (335*2π)/9973 weeks
3361.34687 -.54437 (336*2π)/9973 weeks
337.84011 .66641 (337*2π)/9973 weeks
338-.28148 .40707 (338*2π)/9973 weeks
339-1.45122 .1546 (339*2π)/9973 weeks
340-1.57594 -2.28869 (340*2π)/9973 weeks
341-.10569 -2.47546 (341*2π)/9973 weeks
342.51329 -2.37122 (342*2π)/9973 weeks
3431.4171 -2.3311 (343*2π)/9973 weeks
3441.15087 -1.30341 (344*2π)/9973 weeks
3451.52239 -.34758 (345*2π)/9973 weeks
346-.67116 -.20334 (346*2π)/9973 weeks
347-1.8172 -2.10838 (347*2π)/9973 weeks
348-.49792 -3.8283 (348*2π)/9973 weeks
3491.50376 -4.35086 (349*2π)/9973 weeks
3502.23443 -3.50778 (350*2π)/9973 weeks
3512.9786 -2.04874 (351*2π)/9973 weeks
3522.94866 -1.79207 (352*2π)/9973 weeks
3531.82935 -.45665 (353*2π)/9973 weeks
354.38459 -.67938 (354*2π)/9973 weeks
355.15869 -2.87265 (355*2π)/9973 weeks
356.91523 -4.2819 (356*2π)/9973 weeks
3573.50143 -3.92153 (357*2π)/9973 weeks
3584.90715 -2.83312 (358*2π)/9973 weeks
3593.93019 -.45073 (359*2π)/9973 weeks
3603.12815 .05406 (360*2π)/9973 weeks
3611.77601 -.60532 (361*2π)/9973 weeks
3621.23993 -1.55085 (362*2π)/9973 weeks
3632.85068 -2.27289 (363*2π)/9973 weeks
3643.20083 -1.99778 (364*2π)/9973 weeks
3653.41131 -.56993 (365*2π)/9973 weeks
3662.76565 -.97594 (366*2π)/9973 weeks
3672.61066 -1.36069 (367*2π)/9973 weeks
3683.44131 -1.09006 (368*2π)/9973 weeks
3694.00354 -.6324 (369*2π)/9973 weeks
3702.44624 .29308 (370*2π)/9973 weeks
3713.06497 -.2566 (371*2π)/9973 weeks
3722.54926 -.10686 (372*2π)/9973 weeks
3731.80287 -.06069 (373*2π)/9973 weeks
3741.94965 -.55509 (374*2π)/9973 weeks
3752.1317 -2.08304 (375*2π)/9973 weeks
3763.3593 -1.60493 (376*2π)/9973 weeks
3774.79503 -.36509 (377*2π)/9973 weeks
3783.45401 .55419 (378*2π)/9973 weeks
3792.88544 .88813 (379*2π)/9973 weeks
3802.46582 1.01738 (380*2π)/9973 weeks
3811.99655 .47258 (381*2π)/9973 weeks
382.72813 .3935 (382*2π)/9973 weeks
3831.45433 -1.20294 (383*2π)/9973 weeks
3842.68701 -1.84998 (384*2π)/9973 weeks
3853.18085 -.50613 (385*2π)/9973 weeks
3863.28497 .04758 (386*2π)/9973 weeks
3872.83154 .12171 (387*2π)/9973 weeks
3882.13294 .42153 (388*2π)/9973 weeks
3892.26624 .39759 (389*2π)/9973 weeks
3901.31696 -.32906 (390*2π)/9973 weeks
3911.79949 -1.12745 (391*2π)/9973 weeks
3922.6601 -.68237 (392*2π)/9973 weeks
3932.34726 -1.33321 (393*2π)/9973 weeks
3943.18724 -.38888 (394*2π)/9973 weeks
3952.48433 -.8262 (395*2π)/9973 weeks
3962.90573 -.76945 (396*2π)/9973 weeks
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