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Fourier Analysis of AMRN (Amarin Corporation plc)


AMRN (Amarin Corporation plc) appears to have interesting cyclic behaviour every 104 weeks (54.9008*sine), 113 weeks (54.0217*sine), and 125 weeks (47.0229*sine).

AMRN (Amarin Corporation plc) has an average price of 176.81 (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 4/5/1993 to 2/13/2017 for AMRN (Amarin Corporation plc), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0176.8089   0 
1224.731 181.2041 (1*2π)/12451,245 weeks
288.82811 191.6331 (2*2π)/1245623 weeks
3-2.3564 156.0732 (3*2π)/1245415 weeks
4-44.62697 75.20641 (4*2π)/1245311 weeks
52.81747 6.58067 (5*2π)/1245249 weeks
640.03579 31.04208 (6*2π)/1245208 weeks
734.28094 43.82538 (7*2π)/1245178 weeks
832.70136 54.05714 (8*2π)/1245156 weeks
914.94842 63.13504 (9*2π)/1245138 weeks
103.9301 47.02285 (10*2π)/1245125 weeks
119.55297 54.02166 (11*2π)/1245113 weeks
12-15.78189 54.90078 (12*2π)/1245104 weeks
13-24.38622 24.14502 (13*2π)/124596 weeks
14-4.62362 13.23017 (14*2π)/124589 weeks
151.45427 14.97218 (15*2π)/124583 weeks
1616.19488 20.1981 (16*2π)/124578 weeks
176.94042 39.65187 (17*2π)/124573 weeks
18-11.92101 31.31541 (18*2π)/124569 weeks
19-8.49377 19.84635 (19*2π)/124566 weeks
20-4.76079 20.75611 (20*2π)/124562 weeks
21-7.34281 17.60212 (21*2π)/124559 weeks
22-2.77342 15.44051 (22*2π)/124557 weeks
23-6.6666 18.26533 (23*2π)/124554 weeks
24-5.57655 13.80455 (24*2π)/124552 weeks
25-5.29557 14.34942 (25*2π)/124550 weeks
26-5.93931 11.01537 (26*2π)/124548 weeks
27-2.66531 8.1334 (27*2π)/124546 weeks
28.55391 11.74158 (28*2π)/124544 weeks
29-1.85357 12.36734 (29*2π)/124543 weeks
30-.33382 11.10128 (30*2π)/124542 weeks
31.75935 14.20552 (31*2π)/124540 weeks
32-1.90402 16.51586 (32*2π)/124539 weeks
33-5.54696 17.46693 (33*2π)/124538 weeks
34-10.27477 14.05972 (34*2π)/124537 weeks
35-10.8346 8.47585 (35*2π)/124536 weeks
36-6.45749 4.84364 (36*2π)/124535 weeks
37-3.22527 8.25817 (37*2π)/124534 weeks
38-6.2647 9.45105 (38*2π)/124533 weeks
39-7.34339 7.89322 (39*2π)/124532 weeks
40-9.10753 5.71419 (40*2π)/124531 weeks
41-7.44937 2.55873 (41*2π)/124530 weeks
42-4.65075 1.72743 (42*2π)/124530 weeks
43-5.35511 3.5571 (43*2π)/124529 weeks
44-6.24376 -.88936 (44*2π)/124528 weeks
45-2.72493 -2.40328 (45*2π)/124528 weeks
462.58434 -3.58351 (46*2π)/124527 weeks
476.93537 1.52157 (47*2π)/124526 weeks
485.33515 7.97329 (48*2π)/124526 weeks
49-.81503 7.72123 (49*2π)/124525 weeks
50.33356 3.98292 (50*2π)/124525 weeks
513.52755 4.8704 (51*2π)/124524 weeks
523.80828 10.35152 (52*2π)/124524 weeks
53-1.52631 14.04867 (53*2π)/124523 weeks
54-8.97428 11.59453 (54*2π)/124523 weeks
55-10.99395 3.25997 (55*2π)/124523 weeks
56-6.16355 -1.89897 (56*2π)/124522 weeks
57-.69392 -1.21067 (57*2π)/124522 weeks
581.47427 2.66743 (58*2π)/124521 weeks
59-1.10304 5.20041 (59*2π)/124521 weeks
60-4.01989 3.28274 (60*2π)/124521 weeks
61-1.46877 .77242 (61*2π)/124520 weeks
62-.11347 2.96099 (62*2π)/124520 weeks
63-1.24278 3.63756 (63*2π)/124520 weeks
64-3.96478 2.83194 (64*2π)/124519 weeks
65-3.29131 -1.24213 (65*2π)/124519 weeks
661.56338 -2.22206 (66*2π)/124519 weeks
673.57976 1.07364 (67*2π)/124519 weeks
683.7202 2.6896 (68*2π)/124518 weeks
693.07789 5.71821 (69*2π)/124518 weeks
701.05903 6.90861 (70*2π)/124518 weeks
71-1.59242 6.7343 (71*2π)/124518 weeks
72-3.55052 5.553 (72*2π)/124517 weeks
73-4.89232 2.84204 (73*2π)/124517 weeks
74-2.90865 -.12096 (74*2π)/124517 weeks
75.26903 .11414 (75*2π)/124517 weeks
76.74763 2.1299 (76*2π)/124516 weeks
77.07379 3.63992 (77*2π)/124516 weeks
78-2.06931 3.33075 (78*2π)/124516 weeks
79-2.978 .64551 (79*2π)/124516 weeks
80.12379 -1.14886 (80*2π)/124516 weeks
811.45378 1.29811 (81*2π)/124515 weeks
821.10113 1.58067 (82*2π)/124515 weeks
832.19112 1.45251 (83*2π)/124515 weeks
842.27263 3.9161 (84*2π)/124515 weeks
85.73873 3.80956 (85*2π)/124515 weeks
86.47153 4.74135 (86*2π)/124514 weeks
87-1.38088 4.26408 (87*2π)/124514 weeks
88-1.1776 2.4356 (88*2π)/124514 weeks
89.14168 3.54963 (89*2π)/124514 weeks
90-1.17945 3.64808 (90*2π)/124514 weeks
91-.89377 4.02146 (91*2π)/124514 weeks
92-2.99546 4.50388 (92*2π)/124514 weeks
93-4.58878 2.44551 (93*2π)/124513 weeks
94-3.66978 .64709 (94*2π)/124513 weeks
95-3.56559 .1227 (95*2π)/124513 weeks
96-3.29762 -2.0629 (96*2π)/124513 weeks
97-.19179 -3.10045 (97*2π)/124513 weeks
981.35258 -1.78408 (98*2π)/124513 weeks
992.68948 -.5826 (99*2π)/124513 weeks
1001.98053 1.56854 (100*2π)/124512 weeks
101-.00062 1.82451 (101*2π)/124512 weeks
102-.13979 -.85587 (102*2π)/124512 weeks
1033.31748 -.90108 (103*2π)/124512 weeks
1044.29796 2.50793 (104*2π)/124512 weeks
1051.75392 4.55639 (105*2π)/124512 weeks
106-.33937 4.80675 (106*2π)/124512 weeks
107-3.10154 2.64838 (107*2π)/124512 weeks
108-1.64414 -1.15632 (108*2π)/124512 weeks
1091.94889 -.34111 (109*2π)/124511 weeks
1101.35314 2.17416 (110*2π)/124511 weeks
111.64609 2.71075 (111*2π)/124511 weeks
112-1.87251 2.72841 (112*2π)/124511 weeks
113-2.7305 -1.09252 (113*2π)/124511 weeks
1141.14132 -2.92708 (114*2π)/124511 weeks
1153.0564 -.60883 (115*2π)/124511 weeks
1163.30461 .572 (116*2π)/124511 weeks
1173.12658 2.33202 (117*2π)/124511 weeks
118.86407 2.50776 (118*2π)/124511 weeks
1192.14922 .25778 (119*2π)/124510 weeks
1203.32053 2.76042 (120*2π)/124510 weeks
1211.63383 3.38475 (121*2π)/124510 weeks
1221.06388 3.38211 (122*2π)/124510 weeks
123-.24424 3.36986 (123*2π)/124510 weeks
124-.51107 .288 (124*2π)/124510 weeks
1253.05566 .39292 (125*2π)/124510 weeks
1262.95757 3.38145 (126*2π)/124510 weeks
1271.51673 3.58276 (127*2π)/124510 weeks
1281.50479 3.87136 (128*2π)/124510 weeks
129.11879 3.53038 (129*2π)/124510 weeks
1301.00701 2.76945 (130*2π)/124510 weeks
1311.23163 4.0885 (131*2π)/124510 weeks
132.17596 4.58856 (132*2π)/12459 weeks
133-.59134 4.51329 (133*2π)/12459 weeks
134-1.61245 4.17007 (134*2π)/12459 weeks
135-2.13952 3.19255 (135*2π)/12459 weeks
136-2.01656 2.26066 (136*2π)/12459 weeks
137-1.79143 1.64389 (137*2π)/12459 weeks
138-.82304 1.33055 (138*2π)/12459 weeks
139-.15058 1.96278 (139*2π)/12459 weeks
140-.49761 3.14445 (140*2π)/12459 weeks
141-2.01698 2.71876 (141*2π)/12459 weeks
142-2.46945 1.74581 (142*2π)/12459 weeks
143-1.43496 .4127 (143*2π)/12459 weeks
144-.24577 1.78145 (144*2π)/12459 weeks
145-1.57112 2.64292 (145*2π)/12459 weeks
146-2.86845 1.53802 (146*2π)/12459 weeks
147-2.59643 .02834 (147*2π)/12458 weeks
148-1.19681 -.75946 (148*2π)/12458 weeks
149.01238 .22728 (149*2π)/12458 weeks
150-.42161 1.54695 (150*2π)/12458 weeks
151-2.14534 1.20258 (151*2π)/12458 weeks
152-1.73744 -.50305 (152*2π)/12458 weeks
153-.70816 -.38845 (153*2π)/12458 weeks
154-.42339 -.2163 (154*2π)/12458 weeks
155.05942 .51129 (155*2π)/12458 weeks
156-1.50914 .83704 (156*2π)/12458 weeks
157-1.29827 -1.17268 (157*2π)/12458 weeks
158.50592 -.48655 (158*2π)/12458 weeks
159-.509 .55299 (159*2π)/12458 weeks
160-.45942 -.37451 (160*2π)/12458 weeks
161-.74516 .27998 (161*2π)/12458 weeks
162-1.32765 -1.47713 (162*2π)/12458 weeks
163.90013 -1.53572 (163*2π)/12458 weeks
164.12198 .28675 (164*2π)/12458 weeks
165-1.10497 -1.32295 (165*2π)/12458 weeks
166.1169 -2.57979 (166*2π)/12458 weeks
1671.32064 -3.14293 (167*2π)/12457 weeks
1684.16736 -2.92983 (168*2π)/12457 weeks
1695.22015 1.12654 (169*2π)/12457 weeks
1702.01197 2.39481 (170*2π)/12457 weeks
1711.12592 .61611 (171*2π)/12457 weeks
1722.05774 .57973 (172*2π)/12457 weeks
1731.89471 .79617 (173*2π)/12457 weeks
1742.56829 1.34513 (174*2π)/12457 weeks
1751.63955 2.32492 (175*2π)/12457 weeks
176.33333 1.44249 (176*2π)/12457 weeks
1771.49077 .5126 (177*2π)/12457 weeks
1781.46994 1.42926 (178*2π)/12457 weeks
1791.70402 1.16862 (179*2π)/12457 weeks
1801.89739 1.6352 (180*2π)/12457 weeks
1811.66691 2.4128 (181*2π)/12457 weeks
1821.04257 2.35518 (182*2π)/12457 weeks
183.72428 2.74898 (183*2π)/12457 weeks
184-.20342 2.21915 (184*2π)/12457 weeks
185-.00309 1.19712 (185*2π)/12457 weeks
186.8551 1.5376 (186*2π)/12457 weeks
187.63922 1.8349 (187*2π)/12457 weeks
188.78991 2.20877 (188*2π)/12457 weeks
189.1881 2.66724 (189*2π)/12457 weeks
190-.57557 2.30007 (190*2π)/12457 weeks
191-.22774 2.17561 (191*2π)/12457 weeks
192-1.04735 2.63452 (192*2π)/12456 weeks
193-2.16498 1.69056 (193*2π)/12456 weeks
194-1.77505 .26569 (194*2π)/12456 weeks
195-.93978 -.02801 (195*2π)/12456 weeks
196-.28655 .23029 (196*2π)/12456 weeks
197-.37883 .54442 (197*2π)/12456 weeks
198-.8652 .67816 (198*2π)/12456 weeks
199-1.08409 -.54998 (199*2π)/12456 weeks
200.35895 -.85215 (200*2π)/12456 weeks
201.91071 .40419 (201*2π)/12456 weeks
202-.14315 .88931 (202*2π)/12456 weeks
203-.41564 .51589 (203*2π)/12456 weeks
204-.981 -.04591 (204*2π)/12456 weeks
205-.48523 -1.38914 (205*2π)/12456 weeks
206.96073 -1.12896 (206*2π)/12456 weeks
207.82811 -.48008 (207*2π)/12456 weeks
2081.21888 -.68219 (208*2π)/12456 weeks
2091.66218 -.43932 (209*2π)/12456 weeks
2102.06837 .21299 (210*2π)/12456 weeks
2111.81832 1.22565 (211*2π)/12456 weeks
212.5432 1.55439 (212*2π)/12456 weeks
213-.0518 .33065 (213*2π)/12456 weeks
214.86103 -.46363 (214*2π)/12456 weeks
2151.47109 .05942 (215*2π)/12456 weeks
2161.78095 .29325 (216*2π)/12456 weeks
2171.67171 1.22408 (217*2π)/12456 weeks
218.77067 1.00304 (218*2π)/12456 weeks
2191.37174 .17123 (219*2π)/12456 weeks
2201.93569 1.3816 (220*2π)/12456 weeks
221.619 1.32057 (221*2π)/12456 weeks
222.96015 .52639 (222*2π)/12456 weeks
2231.38367 .6939 (223*2π)/12456 weeks
2241.71383 .36121 (224*2π)/12456 weeks
2252.92401 1.29789 (225*2π)/12456 weeks
2262.01241 2.60386 (226*2π)/12456 weeks
2271.36898 2.65159 (227*2π)/12455 weeks
2281.00858 2.83021 (228*2π)/12455 weeks
229.20274 2.69554 (229*2π)/12455 weeks
230.18171 2.19128 (230*2π)/12455 weeks
231.23066 2.24026 (231*2π)/12455 weeks
232.11084 2.54284 (232*2π)/12455 weeks
233-.38009 2.36534 (233*2π)/12455 weeks
234-.89446 2.09806 (234*2π)/12455 weeks
235-.76813 1.55019 (235*2π)/12455 weeks
236-.66463 1.68704 (236*2π)/12455 weeks
237-.90132 1.56677 (237*2π)/12455 weeks
238-.90224 .9219 (238*2π)/12455 weeks
239-.64868 1.04912 (239*2π)/12455 weeks
240-.55369 .86018 (240*2π)/12455 weeks
241-.17093 1.06056 (241*2π)/12455 weeks
242-.29043 1.60273 (242*2π)/12455 weeks
243-.86058 1.66495 (243*2π)/12455 weeks
244-1.76862 1.7757 (244*2π)/12455 weeks
245-2.22011 .23313 (245*2π)/12455 weeks
246-1.28311 -.4647 (246*2π)/12455 weeks
247-.47354 -.30609 (247*2π)/12455 weeks
248-.43177 .02252 (248*2π)/12455 weeks
249-.31922 .43383 (249*2π)/12455 weeks
250-1.11287 .35893 (250*2π)/12455 weeks
251-1.04833 -.62202 (251*2π)/12455 weeks
252.13262 -.45968 (252*2π)/12455 weeks
253-.43316 .08467 (253*2π)/12455 weeks
254-.04731 -.51965 (254*2π)/12455 weeks
255.10996 -.03805 (255*2π)/12455 weeks
256-.13434 .07413 (256*2π)/12455 weeks
257.16852 .05274 (257*2π)/12455 weeks
258-.45847 .64989 (258*2π)/12455 weeks
259-.97946 -.44553 (259*2π)/12455 weeks
260-.23063 -.89948 (260*2π)/12455 weeks
261.15208 -.64852 (261*2π)/12455 weeks
262.55527 -.80527 (262*2π)/12455 weeks
263.72452 -.02832 (263*2π)/12455 weeks
264.2419 -.01567 (264*2π)/12455 weeks
265.44994 -.14333 (265*2π)/12455 weeks
266.46136 .31195 (266*2π)/12455 weeks
267-.03826 .12732 (267*2π)/12455 weeks
268-.24716 -.07617 (268*2π)/12455 weeks
269-.00596 -.62598 (269*2π)/12455 weeks
270.47261 -.52163 (270*2π)/12455 weeks
271.55481 -.17247 (271*2π)/12455 weeks
272.3333 -.21264 (272*2π)/12455 weeks
273.36584 -.18088 (273*2π)/12455 weeks
274.50468 -.27397 (274*2π)/12455 weeks
275.18792 -.08358 (275*2π)/12455 weeks
276.50907 -.5346 (276*2π)/12455 weeks
277.67776 -.04965 (277*2π)/12454 weeks
278.27 .05784 (278*2π)/12454 weeks
279.04426 -.46614 (279*2π)/12454 weeks
280.39939 -.55729 (280*2π)/12454 weeks
281.53933 -.34879 (281*2π)/12454 weeks
282.26365 -.51068 (282*2π)/12454 weeks
283.35242 -.84351 (283*2π)/12454 weeks
284.52201 -1.49376 (284*2π)/12454 weeks
2851.75096 -1.21427 (285*2π)/12454 weeks
2861.85772 -.45488 (286*2π)/12454 weeks
2871.87872 -.1418 (287*2π)/12454 weeks
2881.71349 .57728 (288*2π)/12454 weeks
289.73505 .56215 (289*2π)/12454 weeks
290.84442 -.02215 (290*2π)/12454 weeks
291.98461 -.09258 (291*2π)/12454 weeks
2921.09397 -.23358 (292*2π)/12454 weeks
2931.56651 .1457 (293*2π)/12454 weeks
294.97228 .63067 (294*2π)/12454 weeks
295.68233 .13699 (295*2π)/12454 weeks
296.98088 -.17353 (296*2π)/12454 weeks
297.97437 .04027 (297*2π)/12454 weeks
2981.2122 -.2496 (298*2π)/12454 weeks
2991.28556 .16966 (299*2π)/12454 weeks
3001.17419 -.05392 (300*2π)/12454 weeks
3011.75193 .02217 (301*2π)/12454 weeks
3021.56559 .90976 (302*2π)/12454 weeks
303.99869 .71282 (303*2π)/12454 weeks
304.82598 .61594 (304*2π)/12454 weeks
305.63966 .45841 (305*2π)/12454 weeks
306.58879 -.23041 (306*2π)/12454 weeks
3071.54724 -.20651 (307*2π)/12454 weeks
3081.63085 .3345 (308*2π)/12454 weeks
3091.54692 .81964 (309*2π)/12454 weeks
310.94452 1.07756 (310*2π)/12454 weeks
311.46977 .32404 (311*2π)/12454 weeks
3121.20385 .18492 (312*2π)/12454 weeks
313.99531 .62575 (313*2π)/12454 weeks
314.72636 .42443 (314*2π)/12454 weeks
3151.00748 .03251 (315*2π)/12454 weeks
3161.15516 .02437 (316*2π)/12454 weeks
3171.6753 -.08833 (317*2π)/12454 weeks
3182.12548 .71081 (318*2π)/12454 weeks
3191.3927 1.3195 (319*2π)/12454 weeks
3201.30142 .66902 (320*2π)/12454 weeks
3211.57618 1.29788 (321*2π)/12454 weeks
322.91489 1.26542 (322*2π)/12454 weeks
3231.39222 .84149 (323*2π)/12454 weeks
3241.64735 2.10787 (324*2π)/12454 weeks
325.24637 2.39797 (325*2π)/12454 weeks
326-.48353 2.06639 (326*2π)/12454 weeks
327-1.51881 1.20505 (327*2π)/12454 weeks
328-1.42863 -.83395 (328*2π)/12454 weeks
329.72762 -1.5658 (329*2π)/12454 weeks
3301.79798 -.33281 (330*2π)/12454 weeks
3311.75305 .55886 (331*2π)/12454 weeks
3321.46108 1.22491 (332*2π)/12454 weeks
333.48585 1.39616 (333*2π)/12454 weeks
334.23677 .74412 (334*2π)/12454 weeks
335.52856 .45414 (335*2π)/12454 weeks
336.72866 .89525 (336*2π)/12454 weeks
337.20807 .74979 (337*2π)/12454 weeks
338.39961 .3478 (338*2π)/12454 weeks
339.68999 .51871 (339*2π)/12454 weeks
340.36275 .6173 (340*2π)/12454 weeks
341.39396 .47781 (341*2π)/12454 weeks
342.25884 .355 (342*2π)/12454 weeks
343.41303 -.09577 (343*2π)/12454 weeks
3441.2852 -.02999 (344*2π)/12454 weeks
345.96779 .94188 (345*2π)/12454 weeks
346.42374 .62159 (346*2π)/12454 weeks
347.37496 .35511 (347*2π)/12454 weeks
348.45847 -.20544 (348*2π)/12454 weeks
3491.61948 -.32323 (349*2π)/12454 weeks
3501.73774 1.05008 (350*2π)/12454 weeks
351.9991 1.18079 (351*2π)/12454 weeks
352.89415 1.23251 (352*2π)/12454 weeks
353.31592 1.28418 (353*2π)/12454 weeks
354.23537 .7039 (354*2π)/12454 weeks
355.29772 .77512 (355*2π)/12454 weeks
356.11009 .56844 (356*2π)/12453 weeks
357.314 -.08008 (357*2π)/12453 weeks
3581.31147 .35301 (358*2π)/12453 weeks
359.81863 1.04881 (359*2π)/12453 weeks
360.47827 .9272 (360*2π)/12453 weeks
361.27251 .88227 (361*2π)/12453 weeks
362-.00581 .40292 (362*2π)/12453 weeks
363.82163 .16946 (363*2π)/12453 weeks
364.81645 .97326 (364*2π)/12453 weeks
365.11617 .95732 (365*2π)/12453 weeks
366.08754 .42464 (366*2π)/12453 weeks
367.28764 .33816 (367*2π)/12453 weeks
368.56092 .18353 (368*2π)/12453 weeks
369.66326 .57353 (369*2π)/12453 weeks
370.32929 .62835 (370*2π)/12453 weeks
371.30809 .36437 (371*2π)/12453 weeks
372.49549 .24482 (372*2π)/12453 weeks
373.65392 .28764 (373*2π)/12453 weeks
374.8358 .40303 (374*2π)/12453 weeks
375.83346 .76669 (375*2π)/12453 weeks
376.58622 .92235 (376*2π)/12453 weeks
377.19567 .88327 (377*2π)/12453 weeks
378.13534 .70793 (378*2π)/12453 weeks
379-.07851 .3188 (379*2π)/12453 weeks
380.57217 .0272 (380*2π)/12453 weeks
381.78003 .39149 (381*2π)/12453 weeks
382.77858 .82733 (382*2π)/12453 weeks
383.45056 1.13307 (383*2π)/12453 weeks
384-.23627 1.18382 (384*2π)/12453 weeks
385-.66349 .38237 (385*2π)/12453 weeks
386-.23352 -.30074 (386*2π)/12453 weeks
387.40956 -.23219 (387*2π)/12453 weeks
388.72298 -.11989 (388*2π)/12453 weeks
389.99586 .43997 (389*2π)/12453 weeks
390.41478 .88604 (390*2π)/12453 weeks
391.06422 .49061 (391*2π)/12453 weeks
392.32446 .3534 (392*2π)/12453 weeks
393.34655 .48211 (393*2π)/12453 weeks
394.02721 .64723 (394*2π)/12453 weeks
395-.22966 .36366 (395*2π)/12453 weeks
396-.22418 .00262 (396*2π)/12453 weeks
397-.10851 -.21843 (397*2π)/12453 weeks
398.1432 -.51848 (398*2π)/12453 weeks
399.25655 -.46378 (399*2π)/12453 weeks
400.80887 -.84849 (400*2π)/12453 weeks
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