groupProj. UProj. WSCorr. UCorr. WS BLLCMPos. angler MU MP

11520 645.85 3424.67 342.89 1819.54 -16.18 83.67 -3.83 169.77 0.3609 331.8 15.8


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SDO HMI 2012-07-12 04:59:10 UT

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spotProj. UProj. WSCorr. UCorr. WSBLLCMPos. angler MU MP

1 2.54 3.63 1.34 1.92 -12.80 98.66 11.16 213.12 0.3468 941.5 725.8
2 0.00 1.27 0.00 0.68 -15.13 98.32 10.82 208.92 0.3764 1038.0 816.2
3 0.00 1.09 0.00 0.58 -15.87 98.01 10.51 207.26 0.3845 797.0 683.0
4 0.00 1.18 0.00 0.63 -15.80 97.68 10.18 206.62 0.3811 911.0 743.1
5 0.00 1.18 0.00 0.64 -16.55 97.69 10.19 205.75 0.3919 688.0 531.8
6 0.00 2.09 0.00 1.12 -15.38 97.50 10.00 206.74 0.3737 993.0 839.5
7 0.00 1.00 0.00 0.54 -16.38 97.20 9.70 204.85 0.3861 684.0 509.8
8 0.00 2.45 0.00 1.34 -19.53 96.59 9.09 200.41 0.4285 325.0 282.9
9 0.00 4.18 0.00 2.28 -19.36 96.22 8.72 199.79 0.4240 896.0 764.4
10 0.00 1.09 0.00 0.57 -14.10 95.53 8.03 203.50 0.3412 790.0 648.1
11 0.00 1.36 0.00 0.72 -13.91 95.34 7.83 203.22 0.3370 891.0 658.4
12 0.00 1.27 0.00 0.67 -13.84 95.02 7.51 202.45 0.3340 779.0 686.3
13 0.00 0.73 0.00 0.39 -18.22 94.86 7.36 197.79 0.3999 634.0 509.8
14 29.34 240.80 15.52 127.23 -15.15 94.49 6.99 199.63 0.3510 1179.2 395.1
15 11.90 -14.00 6.28 -14.00 -14.89 93.97 6.47 198.53 0.3441 1205.9 999999
16 0.00 2.27 0.00 1.21 -16.87 93.65 6.15 196.01 0.3734 1036.0 813.9
17 4.09 -14.00 2.16 -14.00 -15.21 93.57 6.07 197.16 0.3471 933.2 999999
18 0.00 1.45 0.00 0.78 -18.01 92.89 5.38 193.35 0.3881 747.0 507.1
19 0.00 1.73 0.00 0.92 -16.89 92.82 5.32 193.92 0.3703 534.0 505.3
20 1.36 1.91 0.72 1.01 -16.60 92.75 5.25 193.94 0.3654 1000.7 860.8
21 0.00 2.63 0.00 1.40 -16.83 92.59 5.09 193.39 0.3684 954.0 719.6
22 0.00 2.72 0.00 1.45 -16.53 92.46 4.96 193.24 0.3632 772.0 676.4
23 1.27 3.00 0.67 1.57 -14.72 92.35 4.85 194.24 0.3339 795.1 671.1
24 0.00 1.00 0.00 0.54 -18.73 92.13 4.63 191.16 0.3968 755.0 581.9
25 0.00 2.63 0.00 1.42 -18.93 92.01 4.51 190.77 0.3996 789.0 630.3
26 0.00 1.18 0.00 0.61 -12.95 91.78 4.28 193.94 0.3032 -672.0 -593.3
27 0.00 7.81 0.00 4.11 -15.07 91.60 4.10 191.88 0.3367 -1062.0 -812.5
28 0.00 1.45 0.00 0.76 -15.16 91.38 3.88 191.20 0.3375 -985.0 -777.2
29 0.00 1.45 0.00 0.75 -11.68 90.64 3.14 191.16 0.2781 -829.0 -646.5
30 0.00 1.45 0.00 0.75 -11.64 89.98 2.48 188.89 0.2757 -911.0 -656.5
31 0.00 1.36 0.00 0.71 -13.87 89.97 2.47 187.73 0.3126 -681.0 -576.0
32 0.00 2.82 0.00 1.46 -12.40 89.90 2.39 188.18 0.2881 -871.0 -844.5
33 0.00 1.27 0.00 0.66 -12.69 89.84 2.34 187.84 0.2927 -785.0 -662.9
34 0.00 0.73 0.00 0.39 -16.59 89.85 2.35 186.34 0.3568 574.0 694.5
35 0.00 2.00 0.00 1.03 -12.02 89.77 2.27 187.94 0.2814 -787.0 -692.5
36 0.00 0.36 0.00 0.19 -14.87 89.76 2.26 186.70 0.3285 -364.0 -393.0
37 0.00 4.18 0.00 2.22 -16.85 89.75 2.25 186.01 0.3609 582.0 593.3
38 0.00 3.09 0.00 1.59 -11.64 89.67 2.17 187.79 0.2749 -972.0 -683.9
39 0.00 1.36 0.00 0.73 -18.22 89.68 2.17 185.42 0.3830 671.0 529.9
40 0.00 1.54 0.00 0.81 -14.77 89.61 2.10 186.27 0.3266 -867.0 -612.0
41 0.00 1.27 0.00 0.66 -12.40 89.52 2.02 186.91 0.2873 -763.0 -638.5
42 0.00 1.00 0.00 0.54 -18.26 89.48 1.98 184.94 0.3833 961.0 751.2
43 0.00 3.09 0.00 1.59 -11.67 89.33 1.83 186.56 0.2747 -740.0 -631.1
44 0.00 3.18 0.00 1.67 -14.83 89.35 1.85 185.50 0.3273 -933.0 -642.7
45 0.00 0.64 0.00 0.34 -16.75 89.21 1.71 184.59 0.3584 561.0 538.7
46 0.00 1.91 0.00 1.03 -18.85 89.17 1.67 184.04 0.3924 821.0 685.2
47 0.00 1.54 0.00 0.79 -11.07 89.01 1.51 185.66 0.2640 -954.0 -726.2
48 0.00 1.00 0.00 0.54 -18.19 88.97 1.47 183.67 0.3816 905.0 753.1
49 0.00 4.63 0.00 2.49 -18.92 88.40 0.89 182.16 0.3928 802.0 653.4
50 0.00 1.09 0.00 0.56 -11.77 88.30 0.80 182.87 0.2748 -715.0 -581.5
51 0.00 1.18 0.00 0.61 -12.31 88.30 0.80 182.78 0.2839 -598.0 -492.6
52 0.00 3.27 0.00 1.75 -17.89 88.29 0.79 182.01 0.3762 1037.0 682.3
53 1.73 21.80 0.90 11.38 -14.35 88.19 0.68 182.09 0.3180 -1077.3 -641.9
54 0.00 1.27 0.00 0.66 -12.94 88.18 0.68 182.26 0.2945 -750.0 -560.2
55 12.99 97.74 6.81 51.32 -15.09 88.00 0.50 181.46 0.3301 -1153.4 -392.5
56 2.82 -53.00 1.47 -53.00 -14.41 87.90 0.40 181.22 0.3189 -1212.3 999999
57 0.00 1.36 0.00 0.77 -24.68 87.83 0.33 180.62 0.4834 -751.0 -573.0
58 0.00 2.72 0.00 1.42 -13.87 87.74 0.24 180.76 0.3098 -869.0 -665.9
59 2.54 3.27 1.33 1.71 -14.83 87.68 0.18 180.54 0.3258 -1022.2 -936.1
60 0.00 1.00 0.00 0.52 -14.61 87.68 0.18 180.55 0.3220 -1075.0 -900.8
61 6.72 57.22 3.53 30.12 -15.22 87.56 0.05 180.16 0.3322 -1061.9 -360.9
62 2.72 -61.00 1.43 -61.00 -15.64 87.30 -0.20 179.43 0.3391 -938.0 999999
63 6.36 -61.00 3.34 -61.00 -15.45 87.18 -0.32 179.07 0.3360 -1046.9 999999
64 1.09 7.99 0.57 4.18 -14.90 87.15 -0.36 178.95 0.3269 -954.6 -733.7
65 0.00 2.27 0.00 1.17 -11.67 87.15 -0.35 178.74 0.2729 -983.0 -654.0
66 0.00 1.09 0.00 0.58 -17.33 87.05 -0.46 178.81 0.3670 849.0 597.3
67 0.00 2.09 0.00 1.09 -14.38 87.05 -0.45 178.63 0.3184 -832.0 -581.5
68 0.00 0.91 0.00 0.51 -24.72 86.89 -0.61 178.85 0.4840 -746.0 -633.2
69 0.00 1.00 0.00 0.54 -20.25 86.68 -0.82 178.13 0.4141 -790.0 -661.4
70 0.00 1.09 0.00 0.58 -17.43 86.47 -1.03 177.32 0.3689 725.0 605.5
71 0.00 1.45 0.00 0.81 -23.06 86.23 -1.27 177.45 0.4587 647.0 467.4
72 0.00 1.18 0.00 0.67 -25.14 86.08 -1.42 177.36 0.4908 -731.0 -642.3
73 0.00 1.00 0.00 0.52 -14.96 86.11 -1.40 175.88 0.3287 -634.0 -487.2
74 0.00 1.18 0.00 0.65 -21.33 85.73 -1.78 176.15 0.4320 -835.0 -546.6
75 0.00 1.54 0.00 0.84 -20.52 85.67 -1.83 175.89 0.4193 738.0 468.2
76 10.90 314.37 5.84 169.22 -18.29 85.53 -1.97 175.11 0.3838 1277.8 385.0
77 0.82 -76.00 0.44 -76.00 -17.99 85.51 -2.00 174.97 0.3790 1107.2 999999
78 24.89 96.83 12.82 49.84 -11.70 85.53 -1.97 172.95 0.2755 -1160.9 -515.9
79 20.16 -76.00 10.83 -76.00 -18.55 85.24 -2.26 174.46 0.3885 1247.9 999999
80 0.00 1.63 0.00 0.88 -18.13 84.86 -2.64 173.40 0.3822 772.0 528.7
81 13.17 -76.00 7.08 -76.00 -18.62 84.76 -2.74 173.30 0.3904 1079.6 999999
82 1.73 -76.00 0.93 -76.00 -19.25 84.68 -2.82 173.32 0.4006 709.9 999999
83 0.00 2.09 0.00 1.15 -21.26 84.58 -2.92 173.67 0.4326 833.0 641.4
84 2.63 -76.00 1.42 -76.00 -19.12 84.52 -2.98 172.90 0.3988 703.3 999999
85 2.91 -76.00 1.57 -76.00 -18.89 84.50 -3.01 172.76 0.3952 786.7 999999
86 120.26 2067.16 63.61 1099.76 -16.20 84.48 -3.02 171.69 0.3519 1609.5 79.4
87 0.00 1.18 0.00 0.63 -18.56 84.37 -3.13 172.35 0.3901 613.0 534.0
88 0.00 1.54 0.00 0.84 -20.43 83.62 -3.88 171.30 0.4214 765.0 609.9
89 0.00 1.00 0.00 0.52 -11.81 83.79 -3.72 166.96 0.2823 -890.0 -726.9
90 1.18 -86.00 0.62 -86.00 -15.46 83.63 -3.87 169.00 0.3422 918.0 999999
91 0.00 1.91 0.00 1.04 -19.76 83.54 -3.96 170.86 0.4111 770.0 532.0
92 0.00 1.63 0.00 0.89 -20.56 83.42 -4.08 170.92 0.4240 657.0 532.2
93 1.00 -86.00 0.53 -86.00 -16.27 83.49 -4.01 169.07 0.3557 1249.0 999999
94 0.00 1.91 0.00 0.98 -11.18 83.36 -4.14 164.93 0.2737 -807.0 -706.7
95 0.00 1.27 0.00 0.66 -12.99 83.08 -4.42 165.64 0.3043 -898.0 -645.2
96 0.00 2.54 0.00 1.32 -12.48 83.03 -4.48 165.03 0.2963 -1069.0 -765.9
97 0.00 1.45 0.00 0.75 -12.03 82.81 -4.69 163.94 0.2901 -870.0 -677.8
98 0.00 1.18 0.00 0.61 -12.64 82.80 -4.70 164.47 0.2998 -968.0 -815.5
99 173.67 -86.00 92.55 -86.00 -16.96 82.61 -4.89 167.20 0.3697 1447.2 999999
100 0.00 1.54 0.00 0.80 -13.08 82.70 -4.80 164.56 0.3075 -880.0 -624.2
101 0.00 1.09 0.00 0.57 -12.80 82.61 -4.89 164.02 0.3033 -843.0 -617.9
102 0.00 1.00 0.00 0.56 -23.18 82.08 -5.42 169.26 0.4680 -853.0 -676.5
103 0.00 0.54 0.00 0.29 -15.50 82.30 -5.20 165.38 0.3477 271.0 371.2
104 1.54 -86.00 0.81 -86.00 -15.14 82.28 -5.22 165.05 0.3422 392.0 999999
105 0.00 2.18 0.00 1.12 -9.99 82.16 -5.34 159.34 0.2608 -949.0 -733.9
106 2.45 -86.00 1.30 -86.00 -16.15 81.93 -5.57 164.91 0.3595 1077.6 999999
107 0.00 1.63 0.00 0.85 -13.70 82.00 -5.51 163.02 0.3205 631.0 383.5
108 3.18 -86.00 1.69 -86.00 -16.44 81.89 -5.61 165.02 0.3643 829.9 999999
109 0.00 1.00 0.00 0.52 -12.10 82.00 -5.50 161.40 0.2952 -871.0 -687.7
110 0.91 -86.00 0.49 -86.00 -18.11 81.65 -5.85 165.60 0.3915 197.9 999999
111 1.18 -86.00 0.63 -86.00 -17.42 81.54 -5.96 164.87 0.3812 807.2 999999
112 5.18 -86.00 2.75 -86.00 -16.35 81.54 -5.96 164.06 0.3643 900.5 999999
113 3.72 -86.00 1.99 -86.00 -16.87 81.40 -6.10 164.11 0.3731 968.5 999999
114 3.63 -86.00 1.94 -86.00 -17.20 81.16 -6.34 163.79 0.3793 712.8 999999
115 2.72 -86.00 1.46 -86.00 -17.39 81.16 -6.34 163.92 0.3824 440.3 999999
116 1.09 -86.00 0.58 -86.00 -16.45 81.12 -6.38 163.09 0.3678 708.4 999999
117 2.18 -86.00 1.17 -86.00 -17.36 81.09 -6.41 163.74 0.3822 -208.8 999999
118 0.91 -86.00 0.48 -86.00 -14.51 80.33 -7.17 159.22 0.3421 -1154.6 999999
119 5.36 -86.00 2.87 -86.00 -16.75 80.12 -7.38 160.90 0.3775 668.2 999999
120 31.88 -86.00 17.01 -86.00 -16.36 80.01 -7.49 160.27 0.3722 -1272.3 999999
121 0.00 27.52 0.00 14.47 -14.00 79.93 -7.57 157.60 0.3368 -705.0 -667.0
122 2.72 -86.00 1.45 -86.00 -15.97 79.80 -7.70 159.38 0.3675 -1226.8 999999
123 1.54 -86.00 0.82 -86.00 -15.00 79.84 -7.67 158.46 0.3525 -1005.3 999999
124 5.09 -86.00 2.69 -86.00 -15.13 79.61 -7.89 158.03 0.3559 -1166.1 999999
125 2.72 -86.00 1.44 -86.00 -14.62 79.59 -7.91 157.42 0.3482 -1067.2 999999
126 1.36 -86.00 0.73 -86.00 -15.84 79.52 -7.99 158.56 0.3672 -1245.1 999999
127 2.72 -86.00 1.46 -86.00 -16.30 79.43 -8.07 158.83 0.3746 -739.8 999999
128 2.27 -86.00 1.23 -86.00 -18.33 79.34 -8.16 160.52 0.4056 -826.6 999999
129 1.18 -86.00 0.63 -86.00 -16.59 79.39 -8.11 159.01 0.3792 914.0 999999
130 1.91 -86.00 1.01 -86.00 -14.84 79.46 -8.04 157.33 0.3524 -1001.9 999999
131 0.00 5.27 0.00 2.86 -18.76 79.26 -8.25 160.70 0.4125 -642.0 -627.7
132 2.36 -86.00 1.26 -86.00 -16.04 79.35 -8.15 158.36 0.3712 -817.4 999999
133 0.00 1.18 0.00 0.65 -19.73 79.17 -8.33 161.32 0.4273 873.0 667.9
134 0.00 1.09 0.00 0.59 -19.09 79.14 -8.36 160.73 0.4181 -842.0 -696.2
135 1.63 -86.00 0.86 -86.00 -14.55 79.28 -8.22 156.54 0.3493 -974.5 999999
136 0.00 1.45 0.00 0.76 -13.66 79.28 -8.22 155.44 0.3358 -1050.0 -896.8
137 2.63 -86.00 1.41 -86.00 -16.37 79.11 -8.39 158.13 0.3775 251.1 999999
138 1.82 2.09 0.95 1.10 -13.47 79.10 -8.41 154.72 0.3343 -1001.7 -982.3
139 10.81 -86.00 5.79 -86.00 -16.44 78.91 -8.59 157.74 0.3797 -576.4 999999
140 0.00 0.73 0.00 0.39 -18.57 78.81 -8.69 159.57 0.4120 427.0 333.4
141 4.27 -86.00 2.29 -86.00 -16.86 78.86 -8.64 158.06 0.3863 -559.0 999999
142 2.18 -86.00 1.16 -86.00 -15.33 78.83 -8.67 156.34 0.3638 -1027.4 999999
143 0.00 3.27 0.00 1.72 -13.98 78.89 -8.61 154.84 0.3434 -937.0 -768.1
144 0.00 1.73 0.00 0.91 -13.72 78.87 -8.64 154.45 0.3397 -1051.0 -794.4
145 0.54 2.27 0.29 1.20 -14.50 78.74 -8.76 155.12 0.3520 -1022.7 -875.6
146 1.18 -86.00 0.63 -86.00 -15.95 78.61 -8.89 156.52 0.3744 -938.4 999999
147 0.00 6.72 0.00 3.53 -13.31 78.69 -8.81 153.45 0.3349 -976.0 -933.7
148 0.00 0.82 0.00 0.44 -16.73 78.48 -9.02 157.06 0.3868 -825.0 -708.8
149 0.00 1.82 0.00 0.96 -14.37 78.55 -8.95 154.50 0.3515 -793.0 -636.7
150 0.00 7.99 0.00 4.34 -18.47 78.36 -9.14 158.52 0.4132 -361.0 -430.1
151 0.00 4.00 0.00 2.17 -18.08 78.32 -9.19 158.05 0.4077 -725.0 -732.9
152 0.00 1.00 0.00 0.53 -13.60 78.52 -8.98 153.41 0.3404 -705.0 -612.4
153 0.00 1.09 0.00 0.58 -15.53 78.44 -9.06 155.63 0.3693 -994.0 -594.8
154 0.00 4.45 0.00 2.41 -17.78 78.30 -9.20 157.72 0.4034 -417.0 -453.6
155 0.00 3.72 0.00 2.01 -17.56 78.08 -9.42 157.03 0.4014 -830.0 -765.8
156 0.00 1.45 0.00 0.76 -13.35 78.28 -9.23 152.44 0.3385 -1032.0 -806.5
157 0.00 1.36 0.00 0.74 -18.05 78.03 -9.48 157.40 0.4090 -1031.0 -943.5
158 0.00 1.18 0.00 0.62 -14.12 78.21 -9.29 153.33 0.3502 -910.0 -708.8
159 1.54 54.32 0.83 29.20 -16.28 78.08 -9.42 155.66 0.3827 -1005.3 -711.9
160 7.81 -159.00 4.21 -159.00 -17.00 77.95 -9.55 156.16 0.3941 -992.3 999999
161 0.36 4.18 0.19 2.20 -13.41 78.08 -9.42 152.04 0.3410 -1047.2 -846.6
162 0.00 2.27 0.00 1.23 -17.92 77.87 -9.63 156.94 0.4081 -1078.0 -858.0
163 0.00 1.36 0.00 0.72 -13.99 77.96 -9.54 152.55 0.3502 -860.0 -678.3
164 2.45 -159.00 1.32 -159.00 -16.38 77.79 -9.71 155.11 0.3862 -1010.2 999999
165 1.27 -159.00 0.68 -159.00 -16.71 77.77 -9.73 155.44 0.3911 -1002.6 999999
166 0.00 1.09 0.00 0.59 -18.09 77.70 -9.80 156.74 0.4116 -660.0 -560.8
167 0.00 1.82 0.00 0.97 -14.89 77.70 -9.80 153.11 0.3653 -965.0 -732.9
168 0.00 1.82 0.00 0.99 -17.83 77.55 -9.95 156.16 0.4087 -1015.0 -834.0
169 0.00 1.18 0.00 0.63 -16.03 77.65 -9.86 154.38 0.3820 -857.0 -739.3
170 3.63 -159.00 1.96 -159.00 -16.71 77.58 -9.92 155.02 0.3924 -958.2 999999
171 0.00 1.82 0.00 0.95 -11.07 77.73 -9.77 147.40 0.3106 -1019.0 -838.4
172 0.00 1.00 0.00 0.54 -16.00 77.36 -10.14 153.70 0.3836 -1074.0 -922.9
173 0.00 3.18 0.00 1.69 -14.61 77.39 -10.11 152.01 0.3635 -706.0 -683.6
174 2.00 2.54 1.08 1.37 -16.59 77.26 -10.24 154.18 0.3928 -717.3 -602.5
175 0.00 1.45 0.00 0.77 -13.65 77.37 -10.13 150.63 0.3499 -774.0 -659.9
176 0.00 1.45 0.00 0.77 -14.84 77.32 -10.18 152.14 0.3673 -772.0 -680.4
177 0.00 1.09 0.00 0.60 -20.12 76.95 -10.55 157.19 0.4455 -808.0 -691.8
178 0.00 2.54 0.00 1.36 -15.94 77.17 -10.33 153.20 0.3841 -1006.0 -801.8
179 0.00 0.91 0.00 0.49 -16.16 77.16 -10.35 153.45 0.3875 -903.0 -823.8
180 0.00 3.00 0.00 1.60 -15.00 77.09 -10.41 151.82 0.3714 -966.0 -866.5
181 0.00 4.45 0.00 2.38 -15.45 77.06 -10.44 152.36 0.3780 -694.0 -788.5
182 2.36 8.99 1.27 4.83 -16.30 76.92 -10.58 153.10 0.3911 -753.1 -626.5
183 0.00 1.27 0.00 0.68 -15.81 76.85 -10.65 152.34 0.3847 -896.0 -721.9
184 0.00 0.91 0.00 0.49 -16.66 76.71 -10.79 153.07 0.3977 -644.0 -506.9
185 40.33 170.13 21.27 89.72 -12.95 76.86 -10.64 148.35 0.3444 -1237.1 -379.8
186 4.54 9.99 2.43 5.36 -15.52 76.55 -10.96 151.30 0.3830 -881.1 -631.7
187 3.91 -185.00 2.07 -185.00 -13.50 76.58 -10.92 148.53 0.3544 -747.0 999999
188 0.00 2.27 0.00 1.22 -16.08 76.32 -11.18 151.53 0.3925 -720.0 -629.6
189 0.00 1.09 0.00 0.58 -15.21 76.01 -11.49 149.72 0.3828 -744.0 -610.5
190 0.00 1.09 0.00 0.59 -16.51 75.61 -11.89 150.60 0.4040 -932.0 -661.0
191 0.00 0.91 0.00 0.49 -15.08 72.19 -15.31 141.97 0.4156 -658.0 -516.9


  • Proj. U -  Projected umbra area in millionths of solar disc, negative values indicate
    that the umbra consists of fragmented regions which cannot be separated without losing umbral area.
    In this way several spots (intensity minima in the umbra) have a common umbra, e.g. -2 means that
    the given spot shares an umbra with spot No.2, and the common U value is indicated at spot No.2.
  • Proj. WS -  Projected whole spot area in millionths of solar disc, negative values indicate
    that several umbras have a common penumbra, e.g. -7 means that the given umbra shares
    a penumbra with umbra No.7, and the WS value is indicated at No.7.
  • Corr. U -  Corrected umbra area in millionths of solar hemisphere, for negative values see above
  • Corr. WS -  Corrected whole spot area in millionths of solar hemisphere, for negative values see above
  • B -  Heliographic latitude B; positive: North, negative: South
  • L -  Heliographic longitude L
  • LCM -  Longitudinal distance from the Sun's central meridian
  • Pos. angle -  Position angle
  • r -  Distance from the centre of Sun's disc in terms of Sun's radius
  • MU -  Mean magnetic field within the umbra contour averaged the pixel values with sign.
  • MP -  Mean magnetic field within the penumbra contour averaged the pixel values with sign.