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# Fourier Analysis of EXPR (Express)

EXPR (Express) appears to have interesting cyclic behaviour every 42 weeks (.7784*cosine), 42 weeks (.7216*sine), and 14 weeks (.3749*cosine).

EXPR (Express) has an average price of 15.97 (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 5/13/2010 to 4/16/2018 for EXPR (Express), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
015.96935   0
1-2.72067 3.18058 (1*2π)/415415 weeks
2-1.97628 2.54219 (2*2π)/415208 weeks
3-.60201 2.43182 (3*2π)/415138 weeks
4-.00578 -1.40999 (4*2π)/415104 weeks
51.00033 .8967 (5*2π)/41583 weeks
6-.63008 .48693 (6*2π)/41569 weeks
7.10551 -.69207 (7*2π)/41559 weeks
8.59583 .10055 (8*2π)/41552 weeks
9.40361 .13361 (9*2π)/41546 weeks
10-.77838 .72165 (10*2π)/41542 weeks
11.12787 .15966 (11*2π)/41538 weeks
12.13007 .34878 (12*2π)/41535 weeks
13-.13688 .21069 (13*2π)/41532 weeks
14-.1156 .37596 (14*2π)/41530 weeks
15.10171 .49354 (15*2π)/41528 weeks
16.10313 .05948 (16*2π)/41526 weeks
17.04713 .24562 (17*2π)/41524 weeks
18-.0229 .71137 (18*2π)/41523 weeks
19-.29692 .32423 (19*2π)/41522 weeks
20-.11634 -.47929 (20*2π)/41521 weeks
21.30319 .18292 (21*2π)/41520 weeks
22-.01201 .26407 (22*2π)/41519 weeks
23.32735 .13584 (23*2π)/41518 weeks
24-.15493 -.12105 (24*2π)/41517 weeks
25-.05879 -.06488 (25*2π)/41517 weeks
26.0122 .18733 (26*2π)/41516 weeks
27.31084 -.085 (27*2π)/41515 weeks
28.0906 .05383 (28*2π)/41515 weeks
29-.22678 .03753 (29*2π)/41514 weeks
30-.37494 .10479 (30*2π)/41514 weeks
31-.06986 -.08437 (31*2π)/41513 weeks
32-.13504 -.14274 (32*2π)/41513 weeks
33.13524 -.03185 (33*2π)/41513 weeks
34.14453 .00256 (34*2π)/41512 weeks
35-.03195 .19328 (35*2π)/41512 weeks
36-.15096 .0019 (36*2π)/41512 weeks
37-.04653 .11093 (37*2π)/41511 weeks
38.02419 .05337 (38*2π)/41511 weeks
39.0461 .00474 (39*2π)/41511 weeks
40.22451 -.14031 (40*2π)/41510 weeks
41.28967 .34994 (41*2π)/41510 weeks
42.1239 .01039 (42*2π)/41510 weeks
43-.04302 .07098 (43*2π)/41510 weeks
44.06263 .10704 (44*2π)/4159 weeks
45.01176 .15432 (45*2π)/4159 weeks
46-.00334 -.02889 (46*2π)/4159 weeks
47.09784 -.10608 (47*2π)/4159 weeks
48.16696 .20022 (48*2π)/4159 weeks
49-.08584 -.06324 (49*2π)/4158 weeks
50.08916 .1752 (50*2π)/4158 weeks
51-.12934 -.105 (51*2π)/4158 weeks
52.13854 -.03323 (52*2π)/4158 weeks
53-.08759 .11881 (53*2π)/4158 weeks
54-.05715 -.00956 (54*2π)/4158 weeks
55.05779 .11268 (55*2π)/4158 weeks
56-.01855 .01045 (56*2π)/4157 weeks
57.02027 .11357 (57*2π)/4157 weeks
58-.20571 -.13767 (58*2π)/4157 weeks
59-.0454 .03036 (59*2π)/4157 weeks
60.09159 .00163 (60*2π)/4157 weeks
61.12626 -.07295 (61*2π)/4157 weeks
62-.00656 -.00404 (62*2π)/4157 weeks
63-.04997 .01587 (63*2π)/4157 weeks
64.10379 -.01471 (64*2π)/4156 weeks
65.10612 .03772 (65*2π)/4156 weeks
66-.00204 .13656 (66*2π)/4156 weeks
67.04036 -.12185 (67*2π)/4156 weeks
68.01644 .03308 (68*2π)/4156 weeks
69-.07942 -.00114 (69*2π)/4156 weeks
70.06625 -.05792 (70*2π)/4156 weeks
71.00066 -.01837 (71*2π)/4156 weeks
72.09488 .04483 (72*2π)/4156 weeks
73-.08766 -.07301 (73*2π)/4156 weeks
74.10858 .06472 (74*2π)/4156 weeks
75.00803 -.0357 (75*2π)/4156 weeks
76.02551 .00691 (76*2π)/4155 weeks
77.01511 -.07442 (77*2π)/4155 weeks
78.06728 .05056 (78*2π)/4155 weeks
79.08534 -.0257 (79*2π)/4155 weeks
80.09303 .02671 (80*2π)/4155 weeks
81.09857 .07946 (81*2π)/4155 weeks
82.02463 .10467 (82*2π)/4155 weeks
83.00733 -.04768 (83*2π)/4155 weeks
84.06659 .03392 (84*2π)/4155 weeks
85.07672 -.07212 (85*2π)/4155 weeks
86-.03902 .11387 (86*2π)/4155 weeks
87.05994 -.0459 (87*2π)/4155 weeks
88.12516 .10099 (88*2π)/4155 weeks
89-.00494 .08614 (89*2π)/4155 weeks
90-.0145 -.03433 (90*2π)/4155 weeks
91-.01189 .0256 (91*2π)/4155 weeks
92.00482 .11589 (92*2π)/4155 weeks
93.00289 .06145 (93*2π)/4154 weeks
94.08949 .0066 (94*2π)/4154 weeks
95.01109 .05809 (95*2π)/4154 weeks
96.07154 .02487 (96*2π)/4154 weeks
97-.00973 .1341 (97*2π)/4154 weeks
98.01741 .02644 (98*2π)/4154 weeks
99.11362 .0758 (99*2π)/4154 weeks
100-.00052 -.02482 (100*2π)/4154 weeks
101-.04196 .03546 (101*2π)/4154 weeks
102.03035 .08972 (102*2π)/4154 weeks
103-.02019 -.04731 (103*2π)/4154 weeks
104-.01816 .11228 (104*2π)/4154 weeks
105-.02985 -.04915 (105*2π)/4154 weeks
106.00721 -.06891 (106*2π)/4154 weeks
107.04238 .03901 (107*2π)/4154 weeks
108-.01975 .01749 (108*2π)/4154 weeks
109.04554 .02655 (109*2π)/4154 weeks
110-.03816 -.00346 (110*2π)/4154 weeks
111-.01366 .02879 (111*2π)/4154 weeks
112.05697 -.02971 (112*2π)/4154 weeks
113.06501 .03341 (113*2π)/4154 weeks
114-.05326 -.02447 (114*2π)/4154 weeks
115.03288 .03154 (115*2π)/4154 weeks
116-.05139 .0836 (116*2π)/4154 weeks
117.05058 -.00001 (117*2π)/4154 weeks
118.04644 .03347 (118*2π)/4154 weeks
119.09152 .09072 (119*2π)/4153 weeks
120-.03526 .01925 (120*2π)/4153 weeks
121.0058 .06101 (121*2π)/4153 weeks
122-.0017 .03912 (122*2π)/4153 weeks
123.07844 -.02092 (123*2π)/4153 weeks
124.01183 -.03319 (124*2π)/4153 weeks
125-.02394 .02396 (125*2π)/4153 weeks
126.02931 .00072 (126*2π)/4153 weeks
127.08137 -.01457 (127*2π)/4153 weeks
128.08357 .04093 (128*2π)/4153 weeks
129-.03458 -.04337 (129*2π)/4153 weeks
130.00853 .00394 (130*2π)/4153 weeks
131.05957 .07381 (131*2π)/4153 weeks
132-.016 .0097 (132*2π)/4153 weeks
133-.04594 -.01871 (133*2π)/4153 weeks
134-.02417 .01117 (134*2π)/4153 weeks
135.02228 -.003 (135*2π)/4153 weeks
136-.05991 -.007 (136*2π)/4153 weeks
137.00817 .06652 (137*2π)/4153 weeks
138.05855 -.02011 (138*2π)/4153 weeks
139-.00288 .02602 (139*2π)/4153 weeks
140-.01227 .00599 (140*2π)/4153 weeks
141.04412 -.02876 (141*2π)/4153 weeks
142.04718 .02303 (142*2π)/4153 weeks
143.04076 .03273 (143*2π)/4153 weeks
144.04713 .04831 (144*2π)/4153 weeks
145.01879 .0378 (145*2π)/4153 weeks
146.0659 -.05042 (146*2π)/4153 weeks
147.0027 -.02696 (147*2π)/4153 weeks
148.05708 .00643 (148*2π)/4153 weeks
149-.07743 .06036 (149*2π)/4153 weeks
150.03046 -.02084 (150*2π)/4153 weeks
151.01692 -.00062 (151*2π)/4153 weeks
152-.02506 -.02595 (152*2π)/4153 weeks
153.02503 .0286 (153*2π)/4153 weeks
154.0543 .03724 (154*2π)/4153 weeks
155.02631 .10211 (155*2π)/4153 weeks
156.0234 -.02116 (156*2π)/4153 weeks
157.03256 -.03242 (157*2π)/4153 weeks
158.00314 -.05153 (158*2π)/4153 weeks
159.06424 -.02216 (159*2π)/4153 weeks
160-.00376 .06047 (160*2π)/4153 weeks
161.06245 -.02697 (161*2π)/4153 weeks
162-.01726 .0405 (162*2π)/4153 weeks
163-.00155 -.02433 (163*2π)/4153 weeks
164.03229 .01984 (164*2π)/4153 weeks
165.05657 -.08571 (165*2π)/4153 weeks
166.06762 -.01847 (166*2π)/4153 weeks
167-.02128 .06986 (167*2π)/4152 weeks
168.01765 .02112 (168*2π)/4152 weeks
169.01758 .03701 (169*2π)/4152 weeks
170-.00708 -.00659 (170*2π)/4152 weeks
171.00109 -.02884 (171*2π)/4152 weeks
172.01158 .03289 (172*2π)/4152 weeks
173.03598 .02667 (173*2π)/4152 weeks
174.05413 -.01286 (174*2π)/4152 weeks
175.03896 -.05086 (175*2π)/4152 weeks
176-.02733 .07379 (176*2π)/4152 weeks
177-.00837 -.00646 (177*2π)/4152 weeks
178.02694 .08733 (178*2π)/4152 weeks
179.02038 .03774 (179*2π)/4152 weeks
180.07472 -.01472 (180*2π)/4152 weeks
181.00094 -.00383 (181*2π)/4152 weeks
182-.05529 .00714 (182*2π)/4152 weeks
183.01804 -.05696 (183*2π)/4152 weeks
184.08373 .05177 (184*2π)/4152 weeks
185.04673 -.01883 (185*2π)/4152 weeks
186.03429 -.02641 (186*2π)/4152 weeks
187-.0236 .02265 (187*2π)/4152 weeks
188.02482 .02173 (188*2π)/4152 weeks
189.0238 -.02506 (189*2π)/4152 weeks
190.03352 -.04845 (190*2π)/4152 weeks
191.0177 .06414 (191*2π)/4152 weeks
192.0164 -.04736 (192*2π)/4152 weeks
193.02982 .01121 (193*2π)/4152 weeks
194.03944 -.0226 (194*2π)/4152 weeks
195-.01345 .00467 (195*2π)/4152 weeks
196.02785 .01627 (196*2π)/4152 weeks
197.01006 .02024 (197*2π)/4152 weeks
198.04625 -.01066 (198*2π)/4152 weeks
199-.01093 -.0014 (199*2π)/4152 weeks
200.02803 .00498 (200*2π)/4152 weeks
201.03535 -.00505 (201*2π)/4152 weeks
202.04621 .00184 (202*2π)/4152 weeks
203.00726 -.02971 (203*2π)/4152 weeks
204.05298 -.07453 (204*2π)/4152 weeks
205-.002 .06365 (205*2π)/4152 weeks
206.0595 .02107 (206*2π)/4152 weeks
207.0257 .00026 (207*2π)/4152 weeks
208.0257 -.00026 (208*2π)/4152 weeks
209.0595 -.02107 (209*2π)/4152 weeks
210-.002 -.06365 (210*2π)/4152 weeks
211.05298 .07453 (211*2π)/4152 weeks
212.00726 .02971 (212*2π)/4152 weeks
213.04621 -.00184 (213*2π)/4152 weeks
214.03535 .00505 (214*2π)/4152 weeks
215.02803 -.00498 (215*2π)/4152 weeks
216-.01093 .0014 (216*2π)/4152 weeks
217.04625 .01066 (217*2π)/4152 weeks
218.01006 -.02024 (218*2π)/4152 weeks
219.02785 -.01627 (219*2π)/4152 weeks
220-.01345 -.00467 (220*2π)/4152 weeks
221.03944 .0226 (221*2π)/4152 weeks
222.02982 -.01121 (222*2π)/4152 weeks
223.0164 .04736 (223*2π)/4152 weeks
224.0177 -.06414 (224*2π)/4152 weeks
225.03352 .04845 (225*2π)/4152 weeks
226.0238 .02506 (226*2π)/4152 weeks
227.02482 -.02173 (227*2π)/4152 weeks
228-.0236 -.02265 (228*2π)/4152 weeks
229.03429 .02641 (229*2π)/4152 weeks
230.04673 .01883 (230*2π)/4152 weeks
231.08373 -.05177 (231*2π)/4152 weeks
232.01804 .05696 (232*2π)/4152 weeks
233-.05529 -.00714 (233*2π)/4152 weeks
234.00094 .00383 (234*2π)/4152 weeks
235.07472 .01472 (235*2π)/4152 weeks
236.02038 -.03774 (236*2π)/4152 weeks
237.02694 -.08733 (237*2π)/4152 weeks
238-.00837 .00646 (238*2π)/4152 weeks
239-.02733 -.07379 (239*2π)/4152 weeks
240.03896 .05086 (240*2π)/4152 weeks
241.05413 .01286 (241*2π)/4152 weeks
242.03598 -.02667 (242*2π)/4152 weeks
243.01158 -.03289 (243*2π)/4152 weeks
244.00109 .02884 (244*2π)/4152 weeks
245-.00708 .00659 (245*2π)/4152 weeks
246.01758 -.03701 (246*2π)/4152 weeks
247.01765 -.02112 (247*2π)/4152 weeks
248-.02128 -.06986 (248*2π)/4152 weeks
249.06762 .01847 (249*2π)/4152 weeks
250.05657 .08571 (250*2π)/4152 weeks
251.03229 -.01984 (251*2π)/4152 weeks
252-.00155 .02433 (252*2π)/4152 weeks
253-.01726 -.0405 (253*2π)/4152 weeks
254.06245 .02697 (254*2π)/4152 weeks
255-.00376 -.06047 (255*2π)/4152 weeks
256.06424 .02216 (256*2π)/4152 weeks
257.00314 .05153 (257*2π)/4152 weeks
258.03256 .03242 (258*2π)/4152 weeks
259.0234 .02116 (259*2π)/4152 weeks
260.02631 -.10211 (260*2π)/4152 weeks
261.0543 -.03724 (261*2π)/4152 weeks
262.02503 -.0286 (262*2π)/4152 weeks
263-.02506 .02595 (263*2π)/4152 weeks
264.01692 .00062 (264*2π)/4152 weeks
265.03046 .02084 (265*2π)/4152 weeks
266-.07743 -.06036 (266*2π)/4152 weeks
267.05708 -.00643 (267*2π)/4152 weeks
268.0027 .02696 (268*2π)/4152 weeks
269.0659 .05042 (269*2π)/4152 weeks
270.01879 -.0378 (270*2π)/4152 weeks
271.04713 -.04831 (271*2π)/4152 weeks
272.04076 -.03273 (272*2π)/4152 weeks
273.04718 -.02303 (273*2π)/4152 weeks
274.04412 .02876 (274*2π)/4152 weeks
275-.01227 -.00599 (275*2π)/4152 weeks
276-.00288 -.02602 (276*2π)/4152 weeks
277.05855 .02011 (277*2π)/4151 weeks
278.00817 -.06652 (278*2π)/4151 weeks
279-.05991 .007 (279*2π)/4151 weeks
280.02228 .003 (280*2π)/4151 weeks
281-.02417 -.01117 (281*2π)/4151 weeks
282-.04594 .01871 (282*2π)/4151 weeks
283-.016 -.0097 (283*2π)/4151 weeks
284.05957 -.07381 (284*2π)/4151 weeks
285.00853 -.00394 (285*2π)/4151 weeks
286-.03458 .04337 (286*2π)/4151 weeks
287.08357 -.04093 (287*2π)/4151 weeks
288.08137 .01457 (288*2π)/4151 weeks
289.02931 -.00072 (289*2π)/4151 weeks
290-.02394 -.02396 (290*2π)/4151 weeks
291.01183 .03319 (291*2π)/4151 weeks
292.07844 .02092 (292*2π)/4151 weeks
293-.0017 -.03912 (293*2π)/4151 weeks
294.0058 -.06101 (294*2π)/4151 weeks
295-.03526 -.01925 (295*2π)/4151 weeks
296.09152 -.09072 (296*2π)/4151 weeks
297.04644 -.03347 (297*2π)/4151 weeks
298.05058 .00001 (298*2π)/4151 weeks
299-.05139 -.0836 (299*2π)/4151 weeks
300.03288 -.03154 (300*2π)/4151 weeks
301-.05326 .02447 (301*2π)/4151 weeks
302.06501 -.03341 (302*2π)/4151 weeks
303.05697 .02971 (303*2π)/4151 weeks
304-.01366 -.02879 (304*2π)/4151 weeks
305-.03816 .00346 (305*2π)/4151 weeks
306.04554 -.02655 (306*2π)/4151 weeks
307-.01975 -.01749 (307*2π)/4151 weeks
308.04238 -.03901 (308*2π)/4151 weeks
309.00721 .06891 (309*2π)/4151 weeks
310-.02985 .04915 (310*2π)/4151 weeks
311-.01816 -.11228 (311*2π)/4151 weeks
312-.02019 .04731 (312*2π)/4151 weeks
313.03035 -.08972 (313*2π)/4151 weeks
314-.04196 -.03546 (314*2π)/4151 weeks
315-.00052 .02482 (315*2π)/4151 weeks
316.11362 -.0758 (316*2π)/4151 weeks
317.01741 -.02644 (317*2π)/4151 weeks
318-.00973 -.1341 (318*2π)/4151 weeks
319.07154 -.02487 (319*2π)/4151 weeks
320.01109 -.05809 (320*2π)/4151 weeks
321.08949 -.0066 (321*2π)/4151 weeks
322.00289 -.06145 (322*2π)/4151 weeks
323.00482 -.11589 (323*2π)/4151 weeks
324-.01189 -.0256 (324*2π)/4151 weeks
325-.0145 .03433 (325*2π)/4151 weeks
326-.00494 -.08614 (326*2π)/4151 weeks
327.12516 -.10099 (327*2π)/4151 weeks
328.05994 .0459 (328*2π)/4151 weeks
329-.03902 -.11387 (329*2π)/4151 weeks
330.07672 .07212 (330*2π)/4151 weeks
331.06659 -.03392 (331*2π)/4151 weeks
332.00733 .04768 (332*2π)/4151 weeks
333.02463 -.10467 (333*2π)/4151 weeks
334.09857 -.07946 (334*2π)/4151 weeks
335.09303 -.02671 (335*2π)/4151 weeks
336.08534 .0257 (336*2π)/4151 weeks
337.06728 -.05056 (337*2π)/4151 weeks
338.01511 .07442 (338*2π)/4151 weeks
339.02551 -.00691 (339*2π)/4151 weeks
340.00803 .0357 (340*2π)/4151 weeks
341.10858 -.06472 (341*2π)/4151 weeks
342-.08766 .07301 (342*2π)/4151 weeks
343.09488 -.04483 (343*2π)/4151 weeks
344.00066 .01837 (344*2π)/4151 weeks
345.06625 .05792 (345*2π)/4151 weeks
346-.07942 .00114 (346*2π)/4151 weeks
347.01644 -.03308 (347*2π)/4151 weeks
348.04036 .12185 (348*2π)/4151 weeks
349-.00204 -.13656 (349*2π)/4151 weeks
350.10612 -.03772 (350*2π)/4151 weeks
351.10379 .01471 (351*2π)/4151 weeks
352-.04997 -.01587 (352*2π)/4151 weeks
353-.00656 .00404 (353*2π)/4151 weeks
354.12626 .07295 (354*2π)/4151 weeks
355.09159 -.00163 (355*2π)/4151 weeks
356-.0454 -.03036 (356*2π)/4151 weeks
357-.20571 .13767 (357*2π)/4151 weeks
358.02027 -.11357 (358*2π)/4151 weeks
359-.01855 -.01045 (359*2π)/4151 weeks
360.05779 -.11268 (360*2π)/4151 weeks
361-.05715 .00956 (361*2π)/4151 weeks
362-.08759 -.11881 (362*2π)/4151 weeks
363.13854 .03323 (363*2π)/4151 weeks
364-.12934 .105 (364*2π)/4151 weeks
365.08916 -.1752 (365*2π)/4151 weeks
366-.08584 .06324 (366*2π)/4151 weeks
367.16696 -.20022 (367*2π)/4151 weeks
368.09784 .10608 (368*2π)/4151 weeks
369-.00334 .02889 (369*2π)/4151 weeks
370.01176 -.15432 (370*2π)/4151 weeks
371.06263 -.10704 (371*2π)/4151 weeks
372-.04302 -.07098 (372*2π)/4151 weeks
373.1239 -.01039 (373*2π)/4151 weeks
374.28967 -.34994 (374*2π)/4151 weeks
375.22451 .14031 (375*2π)/4151 weeks
376.0461 -.00474 (376*2π)/4151 weeks
377.02419 -.05337 (377*2π)/4151 weeks
378-.04653 -.11093 (378*2π)/4151 weeks
379-.15096 -.0019 (379*2π)/4151 weeks
380-.03195 -.19328 (380*2π)/4151 weeks
381.14453 -.00256 (381*2π)/4151 weeks
382.13524 .03185 (382*2π)/4151 weeks
383-.13504 .14274 (383*2π)/4151 weeks
384-.06986 .08437 (384*2π)/4151 weeks
385-.37494 -.10479 (385*2π)/4151 weeks
386-.22678 -.03753 (386*2π)/4151 weeks
387.0906 -.05383 (387*2π)/4151 weeks
388.31084 .085 (388*2π)/4151 weeks
389.0122 -.18733 (389*2π)/4151 weeks
390-.05879 .06488 (390*2π)/4151 weeks
391-.15493 .12105 (391*2π)/4151 weeks
392.32735 -.13584 (392*2π)/4151 weeks
393-.01201 -.26407 (393*2π)/4151 weeks
394.30319 -.18292 (394*2π)/4151 weeks
395-.11634 .47929 (395*2π)/4151 weeks
396-.29692 -.32423 (396*2π)/4151 weeks
397-.0229 -.71137 (397*2π)/4151 weeks
398.04713 -.24562 (398*2π)/4151 weeks
399.10313 -.05948 (399*2π)/4151 weeks
400.10171 -.49354 (400*2π)/4151 weeks
401-.1156 -.37596 (401*2π)/4151 weeks
402-.13688 -.21069 (402*2π)/4151 weeks
403.13007 -.34878 (403*2π)/4151 weeks
404.12787 -.15966 (404*2π)/4151 weeks
405-.77838 -.72165 (405*2π)/4151 weeks
406.40361 -.13361 (406*2π)/4151 weeks
407.59583 -.10055 (407*2π)/4151 weeks
408.10551 .69207 (408*2π)/4151 weeks
409-.63008 -.48693 (409*2π)/4151 weeks
4101.00033 -.8967 (410*2π)/4151 weeks
411-.00578 1.40999 (411*2π)/4151 weeks
412-.60201 -2.43182 (412*2π)/4151 weeks
413-1.97628 -2.54219 (413*2π)/4151 weeks