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# Fourier Analysis of VRTB (Vestin Realty Mortgage II)

VRTB (Vestin Realty Mortgage II) appears to have interesting cyclic behaviour every 62 weeks (154.0394*cosine), 56 weeks (111.3873*cosine), and 28 weeks (83.4719*cosine).

VRTB (Vestin Realty Mortgage II) has an average price of 205.78 (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 5/1/2006 to 5/21/2018 for VRTB (Vestin Realty Mortgage II), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0205.7756   0
1376.7225 -102.9948 (1*2π)/618618 weeks
2313.588 -198.98 (2*2π)/618309 weeks
3224.528 -272.7563 (3*2π)/618206 weeks
4121.2554 -311.0862 (4*2π)/618155 weeks
519.21391 -311.2747 (5*2π)/618124 weeks
6-69.85421 -276.2305 (6*2π)/618103 weeks
7-135.7269 -213.9524 (7*2π)/61888 weeks
8-172.0284 -137.7366 (8*2π)/61877 weeks
9-177.0433 -61.54308 (9*2π)/61869 weeks
10-154.0394 4.41585 (10*2π)/61862 weeks
11-111.3873 50.50928 (11*2π)/61856 weeks
12-59.74732 72.42435 (12*2π)/61852 weeks
13-9.58325 70.20962 (13*2π)/61848 weeks
1429.65708 47.64318 (14*2π)/61844 weeks
1551.74321 12.88377 (15*2π)/61841 weeks
1655.02089 -25.27795 (16*2π)/61839 weeks
1740.83954 -57.84232 (17*2π)/61836 weeks
1814.14659 -78.4472 (18*2π)/61834 weeks
19-18.80228 -83.61245 (19*2π)/61833 weeks
20-49.79803 -73.89734 (20*2π)/61831 weeks
21-72.86108 -52.32722 (21*2π)/61829 weeks
22-83.47192 -23.62458 (22*2π)/61828 weeks
23-80.99519 5.94084 (23*2π)/61827 weeks
24-66.97939 30.83838 (24*2π)/61826 weeks
25-45.53077 46.32278 (25*2π)/61825 weeks
26-21.59948 50.51954 (26*2π)/61824 weeks
27-.23615 44.45581 (27*2π)/61823 weeks
2814.82924 30.57011 (28*2π)/61822 weeks
2921.06999 13.2654 (29*2π)/61821 weeks
3018.8928 -2.88269 (30*2π)/61821 weeks
319.37828 -14.47756 (31*2π)/61820 weeks
32-3.94506 -19.08853 (32*2π)/61819 weeks
33-17.16744 -16.59489 (33*2π)/61819 weeks
34-26.51254 -8.04797 (34*2π)/61818 weeks
35-30.09448 4.39141 (35*2π)/61818 weeks
36-27.67021 17.24593 (36*2π)/61817 weeks
37-19.54712 26.75939 (37*2π)/61817 weeks
38-8.01451 31.19151 (38*2π)/61816 weeks
394.47949 29.91759 (39*2π)/61816 weeks
4014.82259 23.5255 (40*2π)/61815 weeks
4120.49975 14.07698 (41*2π)/61815 weeks
4220.66678 3.64828 (42*2π)/61815 weeks
4315.76843 -5.38123 (43*2π)/61814 weeks
447.81259 -10.70335 (44*2π)/61814 weeks
45-1.20484 -10.94432 (45*2π)/61814 weeks
46-8.82123 -6.3868 (46*2π)/61813 weeks
47-13.24359 1.52917 (47*2π)/61813 weeks
48-13.24284 10.13466 (48*2π)/61813 weeks
49-8.39934 17.80069 (49*2π)/61813 weeks
50-.04795 22.4061 (50*2π)/61812 weeks
519.7602 22.66252 (51*2π)/61812 weeks
5218.63694 18.53392 (52*2π)/61812 weeks
5324.53575 10.56192 (53*2π)/61812 weeks
5426.3482 .61179 (54*2π)/61811 weeks
5523.92992 -9.12403 (55*2π)/61811 weeks
5617.48916 -16.26063 (56*2π)/61811 weeks
578.76196 -19.6455 (57*2π)/61811 weeks
58-.22413 -18.70934 (58*2π)/61811 weeks
59-7.46869 -13.7194 (59*2π)/61810 weeks
60-11.23802 -5.99886 (60*2π)/61810 weeks
61-11.11476 2.44738 (61*2π)/61810 weeks
62-6.99064 9.51588 (62*2π)/61810 weeks
63.07168 13.81785 (63*2π)/61810 weeks
648.22795 14.33839 (64*2π)/61810 weeks
6515.6146 10.83154 (65*2π)/61810 weeks
6620.55224 4.37363 (66*2π)/6189 weeks
6722.39549 -3.67287 (67*2π)/6189 weeks
6820.53421 -11.37011 (68*2π)/6189 weeks
6915.43968 -17.06326 (69*2π)/6189 weeks
708.38426 -20.20304 (70*2π)/6189 weeks
711.29553 -19.93151 (71*2π)/6189 weeks
72-4.25499 -16.8185 (72*2π)/6189 weeks
73-7.43506 -11.6074 (73*2π)/6188 weeks
74-7.82188 -5.81771 (74*2π)/6188 weeks
75-5.64709 -1.21334 (75*2π)/6188 weeks
76-1.7643 1.10601 (76*2π)/6188 weeks
772.92407 .91693 (77*2π)/6188 weeks
786.79844 -1.61269 (78*2π)/6188 weeks
798.74826 -5.60361 (79*2π)/6188 weeks
808.20928 -9.87093 (80*2π)/6188 weeks
815.14917 -13.40073 (81*2π)/6188 weeks
82.57556 -15.24848 (82*2π)/6188 weeks
83-4.41044 -14.74888 (83*2π)/6187 weeks
84-8.32759 -11.96688 (84*2π)/6187 weeks
85-10.48273 -7.59663 (85*2π)/6187 weeks
86-10.08445 -2.75322 (86*2π)/6187 weeks
87-7.37801 1.31557 (87*2π)/6187 weeks
88-3.04871 3.43292 (88*2π)/6187 weeks
891.96953 3.13965 (89*2π)/6187 weeks
906.09908 .29373 (90*2π)/6187 weeks
918.38286 -4.39513 (91*2π)/6187 weeks
927.89999 -10.04338 (92*2π)/6187 weeks
934.72918 -15.14816 (93*2π)/6187 weeks
94-.51259 -18.52063 (94*2π)/6187 weeks
95-6.85279 -19.23368 (95*2π)/6187 weeks
96-13.14513 -16.74583 (96*2π)/6186 weeks
97-18.07599 -11.77732 (97*2π)/6186 weeks
98-20.41737 -5.37036 (98*2π)/6186 weeks
99-19.71869 1.37389 (99*2π)/6186 weeks
100-16.11271 7.11648 (100*2π)/6186 weeks
101-10.71959 10.91076 (101*2π)/6186 weeks
102-4.6955 11.76272 (102*2π)/6186 weeks
103.64458 9.69969 (103*2π)/6186 weeks
1044.39808 5.38746 (104*2π)/6186 weeks
1055.76717 .15485 (105*2π)/6186 weeks
1064.47248 -4.70163 (106*2π)/6186 weeks
107.90908 -8.13538 (107*2π)/6186 weeks
108-3.95469 -9.33814 (108*2π)/6186 weeks
109-8.73432 -8.15677 (109*2π)/6186 weeks
110-12.4164 -4.78453 (110*2π)/6186 weeks
111-14.02125 -.12832 (111*2π)/6186 weeks
112-13.2162 4.64668 (112*2π)/6186 weeks
113-10.35658 8.56542 (113*2π)/6185 weeks
114-6.02208 10.70858 (114*2π)/6185 weeks
115-1.51211 10.61761 (115*2π)/6185 weeks
1162.27091 8.46677 (116*2π)/6185 weeks
1174.463 4.92937 (117*2π)/6185 weeks
1184.48694 1.15448 (118*2π)/6185 weeks
1192.53402 -1.99025 (119*2π)/6185 weeks
120-.86637 -3.63084 (120*2π)/6185 weeks
121-4.5902 -3.14375 (121*2π)/6185 weeks
122-7.52416 -.68011 (122*2π)/6185 weeks
123-8.90112 3.35795 (123*2π)/6185 weeks
124-8.0972 7.78367 (124*2π)/6185 weeks
125-5.20085 11.50743 (125*2π)/6185 weeks
126-.59422 13.50916 (126*2π)/6185 weeks
1274.729 13.14416 (127*2π)/6185 weeks
1289.72247 10.51454 (128*2π)/6185 weeks
12912.98496 6.00133 (129*2π)/6185 weeks
13013.70537 .44909 (130*2π)/6185 weeks
13111.93519 -5.09818 (131*2π)/6185 weeks
1328.03424 -9.29136 (132*2π)/6185 weeks
1332.7467 -11.12683 (133*2π)/6185 weeks
134-2.74865 -10.25295 (134*2π)/6185 weeks
135-7.27975 -6.92852 (135*2π)/6185 weeks
136-9.68382 -1.89962 (136*2π)/6185 weeks
137-9.55733 3.61592 (137*2π)/6185 weeks
138-6.70873 8.58417 (138*2π)/6184 weeks
139-2.01218 11.66979 (139*2π)/6184 weeks
1403.64718 12.25197 (140*2π)/6184 weeks
1419.08889 10.19833 (141*2π)/6184 weeks
14213.0764 5.93777 (142*2π)/6184 weeks
14314.73142 .48606 (143*2π)/6184 weeks
14413.75822 -5.06882 (144*2π)/6184 weeks
14510.52619 -9.55734 (145*2π)/6184 weeks
1465.78339 -12.00536 (146*2π)/6184 weeks
147.63118 -12.06744 (147*2π)/6184 weeks
148-3.78574 -9.82912 (148*2π)/6184 weeks
149-6.39887 -6.09803 (149*2π)/6184 weeks
150-6.79783 -1.68675 (150*2π)/6184 weeks
151-4.99638 2.21628 (151*2π)/6184 weeks
152-1.65125 4.66385 (152*2π)/6184 weeks
1532.38362 4.93418 (153*2π)/6184 weeks
1546.15749 3.04786 (154*2π)/6184 weeks
1558.50721 -.3734 (155*2π)/6184 weeks
1568.84416 -4.588 (156*2π)/6184 weeks
1577.07439 -8.61893 (157*2π)/6184 weeks
1583.52422 -11.32566 (158*2π)/6184 weeks
159-.90969 -12.07636 (159*2π)/6184 weeks
160-5.25195 -10.6883 (160*2π)/6184 weeks
161-8.34434 -7.37874 (161*2π)/6184 weeks
162-9.58621 -3.04054 (162*2π)/6184 weeks
163-8.59056 1.38987 (163*2π)/6184 weeks
164-5.58768 4.78075 (164*2π)/6184 weeks
165-1.3376 6.24405 (165*2π)/6184 weeks
1663.18621 5.50053 (166*2π)/6184 weeks
1676.91417 2.51704 (167*2π)/6184 weeks
1688.86729 -1.8592 (168*2π)/6184 weeks
1698.45785 -6.78513 (169*2π)/6184 weeks
1705.67733 -11.09154 (170*2π)/6184 weeks
1711.1622 -13.78652 (171*2π)/6184 weeks
172-4.12144 -14.19216 (172*2π)/6184 weeks
173-9.05291 -12.12584 (173*2π)/6184 weeks
174-12.6183 -7.95356 (174*2π)/6184 weeks
175-14.09329 -2.64528 (175*2π)/6184 weeks
176-13.06426 2.5454 (176*2π)/6184 weeks
177-9.79435 6.64619 (177*2π)/6183 weeks
178-5.04423 8.89219 (178*2π)/6183 weeks
179.02973 8.72334 (179*2π)/6183 weeks
1804.23037 6.2155 (180*2π)/6183 weeks
1816.75898 1.95466 (181*2π)/6183 weeks
1827.03009 -2.9631 (182*2π)/6183 weeks
1835.02893 -7.2985 (183*2π)/6183 weeks
1841.09351 -10.18688 (184*2π)/6183 weeks
185-3.80886 -10.93609 (185*2π)/6183 weeks
186-8.46322 -9.42564 (186*2π)/6183 weeks
187-11.88624 -5.99556 (187*2π)/6183 weeks
188-13.32517 -1.31053 (188*2π)/6183 weeks
189-12.52281 3.42807 (189*2π)/6183 weeks
190-9.76293 7.39319 (190*2π)/6183 weeks
191-5.69462 9.48763 (191*2π)/6183 weeks
192-1.22656 9.50623 (192*2π)/6183 weeks
1932.55805 7.56767 (193*2π)/6183 weeks
1944.85 4.13107 (194*2π)/6183 weeks
1955.16382 .19588 (195*2π)/6183 weeks
1963.55034 -3.25845 (196*2π)/6183 weeks
197.42439 -5.37182 (197*2π)/6183 weeks
198-3.33307 -5.59103 (198*2π)/6183 weeks
199-6.73879 -3.90123 (199*2π)/6183 weeks
200-8.91652 -.69834 (200*2π)/6183 weeks
201-9.32071 3.30145 (201*2π)/6183 weeks
202-7.77939 7.03272 (202*2π)/6183 weeks
203-4.55003 9.65043 (203*2π)/6183 weeks
204-.46914 10.48324 (204*2π)/6183 weeks
2053.65342 9.25845 (205*2π)/6183 weeks
2066.85026 6.39103 (206*2π)/6183 weeks
2078.24065 2.41503 (207*2π)/6183 weeks
2087.58428 -1.7104 (208*2π)/6183 weeks
2095.03338 -5.1462 (209*2π)/6183 weeks
2101.24695 -6.9104 (210*2π)/6183 weeks
211-2.90923 -6.61274 (211*2π)/6183 weeks
212-6.48984 -4.31941 (212*2π)/6183 weeks
213-8.64631 -.52119 (213*2π)/6183 weeks
214-8.67944 3.85615 (214*2π)/6183 weeks
215-6.63131 8.00365 (215*2π)/6183 weeks
216-2.87799 10.81935 (216*2π)/6183 weeks
2171.8155 11.70366 (217*2π)/6183 weeks
2186.48241 10.43507 (218*2π)/6183 weeks
21910.06675 7.20079 (219*2π)/6183 weeks
22011.89468 2.70852 (220*2π)/6183 weeks
22111.64333 -2.14668 (221*2π)/6183 weeks
2229.41102 -6.34462 (222*2π)/6183 weeks
2235.75526 -8.97957 (223*2π)/6183 weeks
2241.40972 -9.66794 (224*2π)/6183 weeks
225-2.65293 -8.34968 (225*2π)/6183 weeks
226-5.54026 -5.51284 (226*2π)/6183 weeks
227-6.63272 -1.85816 (227*2π)/6183 weeks
228-5.84312 1.8062 (228*2π)/6183 weeks
229-3.52001 4.59217 (229*2π)/6183 weeks
230-.26903 5.83401 (230*2π)/6183 weeks
2313.12508 5.28735 (231*2π)/6183 weeks
2325.86078 3.25419 (232*2π)/6183 weeks
2337.23604 .20597 (233*2π)/6183 weeks
2346.99856 -3.06445 (234*2π)/6183 weeks
2355.27183 -5.7975 (235*2π)/6183 weeks
2362.52361 -7.28683 (236*2π)/6183 weeks
237-.68705 -7.35014 (237*2π)/6183 weeks
238-3.28302 -5.9511 (238*2π)/6183 weeks
239-4.81514 -3.42811 (239*2π)/6183 weeks
240-4.92444 -.55183 (240*2π)/6183 weeks
241-3.58702 1.99487 (241*2π)/6183 weeks
242-1.11404 3.43481 (242*2π)/6183 weeks
2431.89762 3.41166 (243*2π)/6183 weeks
2444.58513 1.89643 (244*2π)/6183 weeks
2456.32976 -.73469 (245*2π)/6183 weeks
2466.49486 -3.99893 (246*2π)/6183 weeks
2475.08977 -7.19523 (247*2π)/6183 weeks
2482.34174 -9.53672 (248*2π)/6182 weeks
249-1.23409 -10.42885 (249*2π)/6182 weeks
250-4.84312 -9.65632 (250*2π)/6182 weeks
251-7.7983 -7.39501 (251*2π)/6182 weeks
252-9.48984 -4.07869 (252*2π)/6182 weeks
253-9.54761 -.41782 (253*2π)/6182 weeks
254-7.96411 2.76917 (254*2π)/6182 weeks
255-5.19006 4.95921 (255*2π)/6182 weeks
256-1.90587 5.64801 (256*2π)/6182 weeks
2571.11529 4.77628 (257*2π)/6182 weeks
2583.31037 2.52879 (258*2π)/6182 weeks
2594.2098 -.50613 (259*2π)/6182 weeks
2603.72785 -3.51701 (260*2π)/6182 weeks
2611.92262 -5.81904 (261*2π)/6182 weeks
262-.85271 -7.0057 (262*2π)/6182 weeks
263-3.81573 -6.87118 (263*2π)/6182 weeks
264-6.30165 -5.4621 (264*2π)/6182 weeks
265-7.83549 -3.06935 (265*2π)/6182 weeks
266-8.18108 -.35585 (266*2π)/6182 weeks
267-7.34844 2.07148 (267*2π)/6182 weeks
268-5.51149 3.71578 (268*2π)/6182 weeks
269-3.27605 4.3263 (269*2π)/6182 weeks
270-1.19377 3.92037 (270*2π)/6182 weeks
271.18729 2.58829 (271*2π)/6182 weeks
272.62508 .83121 (272*2π)/6182 weeks
273.14174 -.85764 (273*2π)/6182 weeks
274-1.17015 -1.92197 (274*2π)/6182 weeks
275-2.95079 -2.08784 (275*2π)/6182 weeks
276-4.6116 -1.39357 (276*2π)/6182 weeks
277-5.6831 .09358 (277*2π)/6182 weeks
278-5.81983 2.02155 (278*2π)/6182 weeks
279-5.0491 3.98849 (279*2π)/6182 weeks
280-3.54191 5.39608 (280*2π)/6182 weeks
281-1.54181 5.85483 (281*2π)/6182 weeks
282.457 5.30677 (282*2π)/6182 weeks
2832.08836 3.96403 (283*2π)/6182 weeks
2842.87289 2.0946 (284*2π)/6182 weeks
2852.65616 .23842 (285*2π)/6182 weeks
2861.48179 -1.28559 (286*2π)/6182 weeks
287-.26914 -2.16321 (287*2π)/6182 weeks
288-2.13033 -2.06341 (288*2π)/6182 weeks
289-3.59357 -.97001 (289*2π)/6182 weeks
290-4.4657 .86764 (290*2π)/6182 weeks
291-4.48695 2.82078 (291*2π)/6182 weeks
292-3.50581 4.59382 (292*2π)/6182 weeks
293-1.76924 5.70553 (293*2π)/6182 weeks
294.27369 6.05534 (294*2π)/6182 weeks
2952.20774 5.51072 (295*2π)/6182 weeks
2963.5206 4.13912 (296*2π)/6182 weeks
2974.17915 2.32704 (297*2π)/6182 weeks
2984.08659 .46856 (298*2π)/6182 weeks
2993.2499 -.86832 (299*2π)/6182 weeks
3001.90442 -1.551 (300*2π)/6182 weeks
301.49709 -1.56512 (301*2π)/6182 weeks
302-.56859 -.92329 (302*2π)/6182 weeks
303-1.00938 .15674 (303*2π)/6182 weeks
304-.87954 1.30898 (304*2π)/6182 weeks
305-.09947 2.08111 (305*2π)/6182 weeks
3061.05514 2.39175 (306*2π)/6182 weeks
3072.19094 2.06694 (307*2π)/6182 weeks
3083.05303 1.15425 (308*2π)/6182 weeks
3093.39659   (309*2π)/6182 weeks
3103.05303 -1.15425 (310*2π)/6182 weeks
3112.19094 -2.06694 (311*2π)/6182 weeks
3121.05514 -2.39175 (312*2π)/6182 weeks
313-.09947 -2.08111 (313*2π)/6182 weeks
314-.87954 -1.30898 (314*2π)/6182 weeks
315-1.00938 -.15674 (315*2π)/6182 weeks
316-.56859 .92329 (316*2π)/6182 weeks
317.49709 1.56512 (317*2π)/6182 weeks
3181.90442 1.551 (318*2π)/6182 weeks
3193.2499 .86832 (319*2π)/6182 weeks
3204.08659 -.46856 (320*2π)/6182 weeks
3214.17915 -2.32704 (321*2π)/6182 weeks
3223.5206 -4.13912 (322*2π)/6182 weeks
3232.20774 -5.51072 (323*2π)/6182 weeks
324.27369 -6.05534 (324*2π)/6182 weeks
325-1.76924 -5.70553 (325*2π)/6182 weeks
326-3.50581 -4.59382 (326*2π)/6182 weeks
327-4.48695 -2.82078 (327*2π)/6182 weeks
328-4.4657 -.86764 (328*2π)/6182 weeks
329-3.59357 .97001 (329*2π)/6182 weeks
330-2.13033 2.06341 (330*2π)/6182 weeks
331-.26914 2.16321 (331*2π)/6182 weeks
3321.48179 1.28559 (332*2π)/6182 weeks
3332.65616 -.23842 (333*2π)/6182 weeks
3342.87289 -2.0946 (334*2π)/6182 weeks
3352.08836 -3.96403 (335*2π)/6182 weeks
336.457 -5.30677 (336*2π)/6182 weeks
337-1.54181 -5.85483 (337*2π)/6182 weeks
338-3.54191 -5.39608 (338*2π)/6182 weeks
339-5.0491 -3.98849 (339*2π)/6182 weeks
340-5.81983 -2.02155 (340*2π)/6182 weeks
341-5.6831 -.09358 (341*2π)/6182 weeks
342-4.6116 1.39357 (342*2π)/6182 weeks
343-2.95079 2.08784 (343*2π)/6182 weeks
344-1.17015 1.92197 (344*2π)/6182 weeks
345.14174 .85764 (345*2π)/6182 weeks
346.62508 -.83121 (346*2π)/6182 weeks
347.18729 -2.58829 (347*2π)/6182 weeks
348-1.19377 -3.92037 (348*2π)/6182 weeks
349-3.27605 -4.3263 (349*2π)/6182 weeks
350-5.51149 -3.71578 (350*2π)/6182 weeks
351-7.34844 -2.07148 (351*2π)/6182 weeks
352-8.18108 .35585 (352*2π)/6182 weeks
353-7.83549 3.06935 (353*2π)/6182 weeks
354-6.30165 5.4621 (354*2π)/6182 weeks
355-3.81573 6.87118 (355*2π)/6182 weeks
356-.85271 7.0057 (356*2π)/6182 weeks
3571.92262 5.81904 (357*2π)/6182 weeks
3583.72785 3.51701 (358*2π)/6182 weeks
3594.2098 .50613 (359*2π)/6182 weeks
3603.31037 -2.52879 (360*2π)/6182 weeks
3611.11529 -4.77628 (361*2π)/6182 weeks
362-1.90587 -5.64801 (362*2π)/6182 weeks
363-5.19006 -4.95921 (363*2π)/6182 weeks
364-7.96411 -2.76917 (364*2π)/6182 weeks
365-9.54761 .41782 (365*2π)/6182 weeks
366-9.48984 4.07869 (366*2π)/6182 weeks
367-7.7983 7.39501 (367*2π)/6182 weeks
368-4.84312 9.65632 (368*2π)/6182 weeks
369-1.23409 10.42885 (369*2π)/6182 weeks
3702.34174 9.53672 (370*2π)/6182 weeks
3715.08977 7.19523 (371*2π)/6182 weeks
3726.49486 3.99893 (372*2π)/6182 weeks
3736.32976 .73469 (373*2π)/6182 weeks
3744.58513 -1.89643 (374*2π)/6182 weeks
3751.89762 -3.41166 (375*2π)/6182 weeks
376-1.11404 -3.43481 (376*2π)/6182 weeks
377-3.58702 -1.99487 (377*2π)/6182 weeks
378-4.92444 .55183 (378*2π)/6182 weeks
379-4.81514 3.42811 (379*2π)/6182 weeks
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