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# Fourier Analysis of SDS (ProShares UltraShort S&P500)

SDS (ProShares UltraShort S&P500) appears to have interesting cyclic behaviour every 62 weeks (52.2043*sine), 57 weeks (33.6228*sine), and 45 weeks (18.521*cosine).

SDS (ProShares UltraShort S&P500) has an average price of 377.48 (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 7/13/2006 to 6/18/2018 for SDS (ProShares UltraShort S&P500), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0377.4755   0
1103.7549 395.8591 (1*2π)/624624 weeks
2-86.62464 154.9403 (2*2π)/624312 weeks
3-55.26525 12.87634 (3*2π)/624208 weeks
447.35353 -3.28614 (4*2π)/624156 weeks
564.28897 61.23633 (5*2π)/624125 weeks
610.48297 85.7606 (6*2π)/624104 weeks
7-31.8441 47.11121 (7*2π)/62489 weeks
8-10.61436 -1.55892 (8*2π)/62478 weeks
938.24218 14.43681 (9*2π)/62469 weeks
1015.05748 52.20425 (10*2π)/62462 weeks
11-9.18765 33.62278 (11*2π)/62457 weeks
12-11.3814 22.17445 (12*2π)/62452 weeks
13-3.22746 2.41053 (13*2π)/62448 weeks
1418.52095 10.36023 (14*2π)/62445 weeks
1511.2625 25.34306 (15*2π)/62442 weeks
162.14235 22.55641 (16*2π)/62439 weeks
17-1.56045 16.98952 (17*2π)/62437 weeks
182.67038 13.04 (18*2π)/62435 weeks
19-1.587 16.34385 (19*2π)/62433 weeks
202.54954 6.33921 (20*2π)/62431 weeks
217.46565 11.68827 (21*2π)/62430 weeks
227.20969 12.64077 (22*2π)/62428 weeks
235.79182 16.69084 (23*2π)/62427 weeks
24.48943 18.85429 (24*2π)/62426 weeks
25-5.13718 12.63219 (25*2π)/62425 weeks
262.20883 5.13433 (26*2π)/62424 weeks
274.41545 13.07075 (27*2π)/62423 weeks
28-1.70564 16.69026 (28*2π)/62422 weeks
29-10.13589 7.08111 (29*2π)/62422 weeks
303.24252 -4.60098 (30*2π)/62421 weeks
3111.5863 5.07162 (31*2π)/62420 weeks
329.72648 15.1758 (32*2π)/62420 weeks
33-3.66552 20.03627 (33*2π)/62419 weeks
34-11.28401 5.10198 (34*2π)/62418 weeks
352.32559 -6.76596 (35*2π)/62418 weeks
3616.27643 1.78601 (36*2π)/62417 weeks
3712.41638 20.93323 (37*2π)/62417 weeks
38-8.40228 21.83552 (38*2π)/62416 weeks
39-11.41045 1.66728 (39*2π)/62416 weeks
402.61327 -3.00112 (40*2π)/62416 weeks
418.63935 4.63231 (41*2π)/62415 weeks
423.85153 11.72556 (42*2π)/62415 weeks
43-1.14075 8.46817 (43*2π)/62415 weeks
44-.95434 5.17145 (44*2π)/62414 weeks
45.69919 3.67048 (45*2π)/62414 weeks
464.56906 3.7158 (46*2π)/62414 weeks
472.15961 9.60779 (47*2π)/62413 weeks
48-1.22794 4.76937 (48*2π)/62413 weeks
492.80512 4.91452 (49*2π)/62413 weeks
50.13092 5.90885 (50*2π)/62412 weeks
51.54565 4.61087 (51*2π)/62412 weeks
52.12286 2.27648 (52*2π)/62412 weeks
534.52538 .84847 (53*2π)/62412 weeks
545.39256 6.47493 (54*2π)/62412 weeks
554.00142 7.70373 (55*2π)/62411 weeks
56.21383 7.6547 (56*2π)/62411 weeks
57-.75185 4.85359 (57*2π)/62411 weeks
581.94532 3.04186 (58*2π)/62411 weeks
593.42035 6.31622 (59*2π)/62411 weeks
60.26835 6.90446 (60*2π)/62410 weeks
61-2.75942 4.65328 (61*2π)/62410 weeks
62-1.4691 -.80694 (62*2π)/62410 weeks
635.93234 -.80104 (63*2π)/62410 weeks
646.95068 7.99314 (64*2π)/62410 weeks
65-.4789 8.42681 (65*2π)/62410 weeks
66-2.56552 3.079 (66*2π)/6249 weeks
671.09884 .30098 (67*2π)/6249 weeks
684.86557 2.07726 (68*2π)/6249 weeks
692.88222 6.8644 (69*2π)/6249 weeks
70-1.42474 3.47079 (70*2π)/6249 weeks
712.64527 .6908 (71*2π)/6249 weeks
724.8593 2.84463 (72*2π)/6249 weeks
734.06951 7.03882 (73*2π)/6249 weeks
74-.7517 6.48341 (74*2π)/6248 weeks
75-.82288 1.16864 (75*2π)/6248 weeks
762.84842 3.10384 (76*2π)/6248 weeks
772.48478 3.14706 (77*2π)/6248 weeks
781.3349 5.43182 (78*2π)/6248 weeks
79-.43167 1.06536 (79*2π)/6248 weeks
805.48306 1.37151 (80*2π)/6248 weeks
814.98919 7.46143 (81*2π)/6248 weeks
82-1.24639 8.24119 (82*2π)/6248 weeks
83-4.51573 3.20218 (83*2π)/6248 weeks
84.63785 -2.47224 (84*2π)/6247 weeks
855.52634 2.09403 (85*2π)/6247 weeks
862.34706 5.10109 (86*2π)/6247 weeks
871.89185 5.51471 (87*2π)/6247 weeks
88-3.5379 4.05822 (88*2π)/6247 weeks
89.33782 -3.31855 (89*2π)/6247 weeks
907.1944 1.24624 (90*2π)/6247 weeks
914.75864 6.70536 (91*2π)/6247 weeks
92-.61014 7.5726 (92*2π)/6247 weeks
93-3.3148 1.89245 (93*2π)/6247 weeks
941.47037 -.83008 (94*2π)/6247 weeks
954.52575 .66556 (95*2π)/6247 weeks
965.78907 5.86272 (96*2π)/6247 weeks
97-1.33301 8.16159 (97*2π)/6246 weeks
98-4.14187 1.53107 (98*2π)/6246 weeks
99.06572 -2.39998 (99*2π)/6246 weeks
1005.13697 .16892 (100*2π)/6246 weeks
1014.42801 4.51154 (101*2π)/6246 weeks
102.31238 5.04687 (102*2π)/6246 weeks
103-1.01617 1.67054 (103*2π)/6246 weeks
1041.81824 .61368 (104*2π)/6246 weeks
1052.92962 2.89436 (105*2π)/6246 weeks
106.30108 3.93237 (106*2π)/6246 weeks
107.37948 .48182 (107*2π)/6246 weeks
1083.04801 2.30046 (108*2π)/6246 weeks
109.55599 3.28961 (109*2π)/6246 weeks
110-.58942 1.42705 (110*2π)/6246 weeks
1111.49221 -.93693 (111*2π)/6246 weeks
1124.87026 .90066 (112*2π)/6246 weeks
1134.00102 4.7933 (113*2π)/6246 weeks
114-.02517 4.73221 (114*2π)/6245 weeks
115-1.70511 1.2824 (115*2π)/6245 weeks
1162.01738 -1.31831 (116*2π)/6245 weeks
1175.86903 1.84621 (117*2π)/6245 weeks
1183.22985 6.52089 (118*2π)/6245 weeks
119-2.0527 5.97112 (119*2π)/6245 weeks
120-3.79459 -.16318 (120*2π)/6245 weeks
1211.11344 -2.72251 (121*2π)/6245 weeks
1225.49104 -.65447 (122*2π)/6245 weeks
1235.0293 4.68931 (123*2π)/6245 weeks
124-.69426 5.28673 (124*2π)/6245 weeks
125-2.26666 .4756 (125*2π)/6245 weeks
1262.35302 -2.42174 (126*2π)/6245 weeks
1275.77472 .96602 (127*2π)/6245 weeks
1284.16857 4.74344 (128*2π)/6245 weeks
129.26776 5.91051 (129*2π)/6245 weeks
130-2.83621 1.63054 (130*2π)/6245 weeks
1311.00934 -1.94893 (131*2π)/6245 weeks
1324.69449 .17591 (132*2π)/6245 weeks
1333.76083 3.48433 (133*2π)/6245 weeks
1341.00769 4.69604 (134*2π)/6245 weeks
135-1.27432 2.11044 (135*2π)/6245 weeks
1361.15954 -.41498 (136*2π)/6245 weeks
1373.74781 .47754 (137*2π)/6245 weeks
1383.33919 4.15584 (138*2π)/6245 weeks
139-.37588 4.62473 (139*2π)/6244 weeks
140-2.11683 .7673 (140*2π)/6244 weeks
1411.48907 -1.18356 (141*2π)/6244 weeks
1423.37103 .51977 (142*2π)/6244 weeks
1432.22472 2.61133 (143*2π)/6244 weeks
1441.06428 2.13116 (144*2π)/6244 weeks
1451.24572 1.94896 (145*2π)/6244 weeks
146.33901 1.15098 (146*2π)/6244 weeks
1471.44218 -.23123 (147*2π)/6244 weeks
1483.23724 .9989 (148*2π)/6244 weeks
1491.73863 2.39631 (149*2π)/6244 weeks
150.95297 1.05202 (150*2π)/6244 weeks
1512.97342 .71272 (151*2π)/6244 weeks
1522.84891 2.27897 (152*2π)/6244 weeks
1531.77675 2.42318 (153*2π)/6244 weeks
154.76435 3.08149 (154*2π)/6244 weeks
155.02177 .98736 (155*2π)/6244 weeks
1561.77822 .53001 (156*2π)/6244 weeks
1571.05533 1.11021 (157*2π)/6244 weeks
1582.00705 .1958 (158*2π)/6244 weeks
1592.94701 1.51515 (159*2π)/6244 weeks
1602.8432 2.60088 (160*2π)/6244 weeks
161.08124 3.02991 (161*2π)/6244 weeks
162.31416 -.65145 (162*2π)/6244 weeks
1633.46711 .70645 (163*2π)/6244 weeks
1641.82925 3.35649 (164*2π)/6244 weeks
165.35118 1.87193 (165*2π)/6244 weeks
166.81893 .22806 (166*2π)/6244 weeks
1672.63386 .44927 (167*2π)/6244 weeks
1682.54932 2.73947 (168*2π)/6244 weeks
169.70283 2.49524 (169*2π)/6244 weeks
170-.2536 1.24225 (170*2π)/6244 weeks
1711.15695 -1.0089 (171*2π)/6244 weeks
1723.82013 1.28504 (172*2π)/6244 weeks
1731.30873 2.87203 (173*2π)/6244 weeks
174.73857 1.43525 (174*2π)/6244 weeks
1751.15657 .64017 (175*2π)/6244 weeks
1762.09686 .99693 (176*2π)/6244 weeks
1771.44528 1.63237 (177*2π)/6244 weeks
1781.3135 1.25916 (178*2π)/6244 weeks
1791.37146 1.73402 (179*2π)/6243 weeks
180.47758 .20735 (180*2π)/6243 weeks
1812.99993 .37662 (181*2π)/6243 weeks
1821.85216 2.06535 (182*2π)/6243 weeks
1831.23176 1.14582 (183*2π)/6243 weeks
1841.74942 1.11904 (184*2π)/6243 weeks
1851.58614 1.37521 (185*2π)/6243 weeks
186.72289 .95351 (186*2π)/6243 weeks
1872.06726 .21059 (187*2π)/6243 weeks
1882.47468 .8121 (188*2π)/6243 weeks
1893.09588 2.13391 (189*2π)/6243 weeks
1901.05864 2.98029 (190*2π)/6243 weeks
191-.00645 1.32565 (191*2π)/6243 weeks
1921.05131 .0814 (192*2π)/6243 weeks
1932.30708 .86659 (193*2π)/6243 weeks
1941.55615 1.90128 (194*2π)/6243 weeks
195.52219 1.58535 (195*2π)/6243 weeks
196.88494 -.00297 (196*2π)/6243 weeks
1971.93077 .09451 (197*2π)/6243 weeks
1982.80356 .92296 (198*2π)/6243 weeks
1992.32209 2.52051 (199*2π)/6243 weeks
200.73483 2.63734 (200*2π)/6243 weeks
201-.34293 1.38656 (201*2π)/6243 weeks
202-.03177 -.43344 (202*2π)/6243 weeks
2032.47454 -.65358 (203*2π)/6243 weeks
2043.08112 1.55832 (204*2π)/6243 weeks
2051.59828 2.76607 (205*2π)/6243 weeks
206-.42446 1.77818 (206*2π)/6243 weeks
207.42699 -.6207 (207*2π)/6243 weeks
2082.24327 -.11431 (208*2π)/6243 weeks
2093.02871 1.28607 (209*2π)/6243 weeks
2101.30399 2.46942 (210*2π)/6243 weeks
211.4709 1.10897 (211*2π)/6243 weeks
212.72085 .5102 (212*2π)/6243 weeks
2132.22306 .21523 (213*2π)/6243 weeks
2142.21105 2.22033 (214*2π)/6243 weeks
215-.14495 1.96326 (215*2π)/6243 weeks
216-.11553 .22101 (216*2π)/6243 weeks
217.95041 -.95765 (217*2π)/6243 weeks
2182.86201 -.4599 (218*2π)/6243 weeks
2192.58254 1.16656 (219*2π)/6243 weeks
2202.66624 1.6549 (220*2π)/6243 weeks
221.73927 3.25343 (221*2π)/6243 weeks
222-1.0057 .00146 (222*2π)/6243 weeks
2231.32072 -.49236 (223*2π)/6243 weeks
2241.78282 -.03703 (224*2π)/6243 weeks
2252.06461 .77026 (225*2π)/6243 weeks
2261.25057 .77971 (226*2π)/6243 weeks
2271.94042 .00419 (227*2π)/6243 weeks
2281.55965 1.1097 (228*2π)/6243 weeks
2292.24724 -.10074 (229*2π)/6243 weeks
2302.66687 2.44611 (230*2π)/6243 weeks
231.5769 1.92928 (231*2π)/6243 weeks
232.42839 1.79256 (232*2π)/6243 weeks
233-.89682 -.09803 (233*2π)/6243 weeks
2341.55677 -2.02709 (234*2π)/6243 weeks
2354.05265 .62604 (235*2π)/6243 weeks
2362.16842 3.13276 (236*2π)/6243 weeks
237-.92693 2.24843 (237*2π)/6243 weeks
238-.54825 -1.26125 (238*2π)/6243 weeks
2392.93592 -1.07829 (239*2π)/6243 weeks
2402.95268 1.56651 (240*2π)/6243 weeks
241.95526 2.72356 (241*2π)/6243 weeks
242-1.57181 1.26404 (242*2π)/6243 weeks
243.15958 -2.81782 (243*2π)/6243 weeks
2443.87007 -1.21614 (244*2π)/6243 weeks
2453.65908 2.19493 (245*2π)/6243 weeks
246.58897 2.95226 (246*2π)/6243 weeks
247-.51817 .1585 (247*2π)/6243 weeks
2481.57832 -.64746 (248*2π)/6243 weeks
2491.84368 .88203 (249*2π)/6243 weeks
250.97074 .53696 (250*2π)/6242 weeks
2511.60507 -.1084 (251*2π)/6242 weeks
2521.91957 .50922 (252*2π)/6242 weeks
2532.44325 .79181 (253*2π)/6242 weeks
2541.7436 2.6856 (254*2π)/6242 weeks
255-.86529 1.49838 (255*2π)/6242 weeks
256.2122 -.70424 (256*2π)/6242 weeks
2571.70112 -.7514 (257*2π)/6242 weeks
2582.56639 1.40208 (258*2π)/6242 weeks
259-.18715 2.07603 (259*2π)/6242 weeks
260-.4797 -.38677 (260*2π)/6242 weeks
261.67002 -1.34239 (261*2π)/6242 weeks
2622.19317 -1.25713 (262*2π)/6242 weeks
2632.81371 .95304 (263*2π)/6242 weeks
264.91261 1.61449 (264*2π)/6242 weeks
265-.19333 -.01094 (265*2π)/6242 weeks
2661.04877 -1.80446 (266*2π)/6242 weeks
2673.67744 -.93813 (267*2π)/6242 weeks
2683.4237 2.11348 (268*2π)/6242 weeks
269.45904 2.52251 (269*2π)/6242 weeks
270-.62792 .52757 (270*2π)/6242 weeks
271.10576 -1.72584 (271*2π)/6242 weeks
2723.28974 -.67908 (272*2π)/6242 weeks
2732.27526 1.22815 (273*2π)/6242 weeks
2741.31834 1.62744 (274*2π)/6242 weeks
275-.30535 .40265 (275*2π)/6242 weeks
2761.30232 -.76832 (276*2π)/6242 weeks
2771.69625 .1252 (277*2π)/6242 weeks
2781.81071 .34159 (278*2π)/6242 weeks
2791.13181 1.39025 (279*2π)/6242 weeks
280-.30102 .49777 (280*2π)/6242 weeks
281.6903 -1.09897 (281*2π)/6242 weeks
2821.43541 -1.34939 (282*2π)/6242 weeks
2833.1178 -.36452 (283*2π)/6242 weeks
2842.46111 1.82108 (284*2π)/6242 weeks
285.07522 1.59225 (285*2π)/6242 weeks
286-.62652 -.19947 (286*2π)/6242 weeks
287.49752 -1.83476 (287*2π)/6242 weeks
2882.62351 -2.16656 (288*2π)/6242 weeks
2894.1862 .52758 (289*2π)/6242 weeks
2902.46814 3.0995 (290*2π)/6242 weeks
291-1.75916 2.22768 (291*2π)/6242 weeks
292-1.18353 -2.52581 (292*2π)/6242 weeks
2932.66997 -2.39617 (293*2π)/6242 weeks
2943.67988 -.01646 (294*2π)/6242 weeks
2952.37604 2.64068 (295*2π)/6242 weeks
296-1.31889 1.73601 (296*2π)/6242 weeks
297-1.07164 -2.24985 (297*2π)/6242 weeks
2982.97032 -3.06398 (298*2π)/6242 weeks
2993.6685 .53025 (299*2π)/6242 weeks
3001.5293 1.73764 (300*2π)/6242 weeks
301-.22334 .297 (301*2π)/6242 weeks
302.69497 -1.91515 (302*2π)/6242 weeks
3032.73513 -2.24183 (303*2π)/6242 weeks
3044.83639 .45463 (304*2π)/6242 weeks
3051.90541 3.35558 (305*2π)/6242 weeks
306-.89323 .46 (306*2π)/6242 weeks
307.88497 -1.7958 (307*2π)/6242 weeks
3082.5397 -1.04042 (308*2π)/6242 weeks
3093.18384 .66347 (309*2π)/6242 weeks
3102.16148 1.47531 (310*2π)/6242 weeks
311.78072 2.01399 (311*2π)/6242 weeks
312-1.24537   (312*2π)/6242 weeks
313.78072 -2.01399 (313*2π)/6242 weeks
3142.16148 -1.47531 (314*2π)/6242 weeks
3153.18384 -.66347 (315*2π)/6242 weeks
3162.5397 1.04042 (316*2π)/6242 weeks
317.88497 1.7958 (317*2π)/6242 weeks
318-.89323 -.46 (318*2π)/6242 weeks
3191.90541 -3.35558 (319*2π)/6242 weeks
3204.83639 -.45463 (320*2π)/6242 weeks
3212.73513 2.24183 (321*2π)/6242 weeks
322.69497 1.91515 (322*2π)/6242 weeks
323-.22334 -.297 (323*2π)/6242 weeks
3241.5293 -1.73764 (324*2π)/6242 weeks
3253.6685 -.53025 (325*2π)/6242 weeks
3262.97032 3.06398 (326*2π)/6242 weeks
327-1.07164 2.24985 (327*2π)/6242 weeks
328-1.31889 -1.73601 (328*2π)/6242 weeks
3292.37604 -2.64068 (329*2π)/6242 weeks
3303.67988 .01646 (330*2π)/6242 weeks
3312.66997 2.39617 (331*2π)/6242 weeks
332-1.18353 2.52581 (332*2π)/6242 weeks
333-1.75916 -2.22768 (333*2π)/6242 weeks
3342.46814 -3.0995 (334*2π)/6242 weeks
3354.1862 -.52758 (335*2π)/6242 weeks
3362.62351 2.16656 (336*2π)/6242 weeks
337.49752 1.83476 (337*2π)/6242 weeks
338-.62652 .19947 (338*2π)/6242 weeks
339.07522 -1.59225 (339*2π)/6242 weeks
3402.46111 -1.82108 (340*2π)/6242 weeks
3413.1178 .36452 (341*2π)/6242 weeks
3421.43541 1.34939 (342*2π)/6242 weeks
343.6903 1.09897 (343*2π)/6242 weeks
344-.30102 -.49777 (344*2π)/6242 weeks
3451.13181 -1.39025 (345*2π)/6242 weeks
3461.81071 -.34159 (346*2π)/6242 weeks
3471.69625 -.1252 (347*2π)/6242 weeks
3481.30232 .76832 (348*2π)/6242 weeks
349-.30535 -.40265 (349*2π)/6242 weeks
3501.31834 -1.62744 (350*2π)/6242 weeks
3512.27526 -1.22815 (351*2π)/6242 weeks
3523.28974 .67908 (352*2π)/6242 weeks
353.10576 1.72584 (353*2π)/6242 weeks
354-.62792 -.52757 (354*2π)/6242 weeks
355.45904 -2.52251 (355*2π)/6242 weeks
3563.4237 -2.11348 (356*2π)/6242 weeks
3573.67744 .93813 (357*2π)/6242 weeks
3581.04877 1.80446 (358*2π)/6242 weeks
359-.19333 .01094 (359*2π)/6242 weeks
360.91261 -1.61449 (360*2π)/6242 weeks
3612.81371 -.95304 (361*2π)/6242 weeks
3622.19317 1.25713 (362*2π)/6242 weeks
363.67002 1.34239 (363*2π)/6242 weeks
364-.4797 .38677 (364*2π)/6242 weeks
365-.18715 -2.07603 (365*2π)/6242 weeks
3662.56639 -1.40208 (366*2π)/6242 weeks
3671.70112 .7514 (367*2π)/6242 weeks
368.2122 .70424 (368*2π)/6242 weeks
369-.86529 -1.49838 (369*2π)/6242 weeks
3701.7436 -2.6856 (370*2π)/6242 weeks
3712.44325 -.79181 (371*2π)/6242 weeks
3721.91957 -.50922 (372*2π)/6242 weeks
3731.60507 .1084 (373*2π)/6242 weeks
374.97074 -.53696 (374*2π)/6242 weeks
3751.84368 -.88203 (375*2π)/6242 weeks
3761.57832 .64746 (376*2π)/6242 weeks
377-.51817 -.1585 (377*2π)/6242 weeks
378.58897 -2.95226 (378*2π)/6242 weeks
3793.65908 -2.19493 (379*2π)/6242 weeks
3803.87007 1.21614 (380*2π)/6242 weeks
381.15958 2.81782 (381*2π)/6242 weeks
382-1.57181 -1.26404 (382*2π)/6242 weeks
383.95526 -2.72356 (383*2π)/6242 weeks
3842.95268 -1.56651 (384*2π)/6242 weeks
3852.93592 1.07829 (385*2π)/6242 weeks
386-.54825 1.26125 (386*2π)/6242 weeks
387-.92693 -2.24843 (387*2π)/6242 weeks
3882.16842 -3.13276 (388*2π)/6242 weeks
3894.05265 -.62604 (389*2π)/6242 weeks
3901.55677 2.02709 (390*2π)/6242 weeks
391-.89682 .09803 (391*2π)/6242 weeks
392.42839 -1.79256 (392*2π)/6242 weeks
393.5769 -1.92928 (393*2π)/6242 weeks
3942.66687 -2.44611 (394*2π)/6242 weeks
3952.24724 .10074 (395*2π)/6242 weeks
3961.55965 -1.1097 (396*2π)/6242 weeks
3971.94042 -.00419 (397*2π)/6242 weeks
3981.25057 -.77971 (398*2π)/6242 weeks
3992.06461 -.77026 (399*2π)/6242 weeks
4001.78282 .03703 (400*2π)/6242 weeks
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