Nice orthogonal matrices

I will define a nice orthogonal matrix as one where all entries have at most one or two (mabye three) digits beyond the decimal point.

In this document, we will look at

1. 2 × 2 non-real complex matrices
2. 3 × 3 non-real complex matrices
3. 4 × 4 non-real complex matrices
4. 5 × 4 non-real complex matrices

From these, you can construct nice matrices that have integer singular values.

Orthogonal 2 × 2 matrices

There are only few:

 1, 0
 0, 1

 0.8,  0.6
 0.6, -0.8

 0.96,  0.28
 0.28, -0.96

 0.936,  0.352
 0.352, -0.936 

 0.8432,  0.5376
 0.5376, -0.8432

Orthogonal 3 × 3 matrices

We can create an orthogonal matrix by taking a two $2 \times 2$ orthogonal matrices and placing it on the diagonal:

 1, 0, 0
 0, 1, 0
 0, 0, 1

 1, 0,   0
 0, a11, a12
 0, a21, a22

This is the only $3 \times 3$ full matrix that is both nice and orthogonal:

 0.8, -0.36,  0.48
 0.6,  0.48, -0.64
 0,    0.8,   0.6 

These have up to thee digits beyond the decimal place:

 0.96,  -0.168,  0.224
 0.28,   0.576, -0.768
 0,      0.8,    0.6

 0.8,   -0.168,  0.576
 0.6,    0.224, -0.768
 0,      0.96,   0.28

 0.768, -0.424,  0.48
 0.64,   0.48,  -0.6
 0.024,  0.768,  0.64

 0.928,  0.096, -0.36
 0.36,  -0.48,   0.8
 0.096,  0.872,  0.48

 0.864, -0.352,  0.36
 0.48,   0.36,  -0.8
 0.152,  0.864,  0.48

 0.856,  0.192, -0.48
 0.48,  -0.64,   0.6
 0.192,  0.744,  0.64

 0.96,   -0.0784,  0.2688
 0.28,    0.2688, -0.9216
 0,       0.96,    0.28

 0.96,    0.0784, -0.2688
 0.28,   -0.2688,  0 .9216
 0,       0.96,    0.28

 0.936,  -0.2112,  0.2816
 0.352,   0.5616, -0.7488
 0,       0.8,     0.6

 0.936,   0.2112, -0.2816
 0.352,  -0.5616,  0.7488
 0,       0.8,     0.6

 0.8,    -0.2112,  0.5616
 0.6,     0.2816, -0.7488
 0,       0.936,   0.352

 0.8,     0.2112, -0.5616
 0.6,    -0.2816,  0.7488
 0,       0.936,   0.352

 0.9856,  0.0192, -0.168
 0.168,  -0.224,   0.96
 0.0192,  0.9744,  0.224

 0.9984,  0.024,  -0.0512
 0.0512, -0.768,   0.6384
 0.024,   0.64,    0.768

 0.9728,  0.1296, -0.192
 0.2304, -0.6272,  0.744
 0.024,   0.768,   0.64

 0.768,   0.1296, -0.6272
 0.64,   -0.192,   0.744
 0.024,   0.9728,  0.2304

 0.9792,  0.1344, -0.152
 0.192,  -0.856,   0.48
 0.0656,  0.4992,  0.864

 0.864,  -0.152,   0.48
 0.4992,  0.1344, -0.856
 0.0656,  0.9792,  0.192

 0.9024,  0.152,  -0.4032
 0.424,  -0.48,    0.768
 0.0768,  0.864,   0.4976

 0.864,   0.152,  -0.48
 0.4976, -0.4032,  0.768
 0.0768,  0.9024,  0.424

 0.9856,  0.096,  -0.1392
 0.1392, -0.928,   0.3456
 0.096,   0.36,    0.928

 0.9584,  0.192,  -0.2112
 0.2688, -0.856,   0.4416
 0.096,   0.48,    0.872

 0.928,  -0.2304,  0.2928
 0.36,    0.352,  -0.864
 0.096,   0.9072,  0.4096

 0.9072, -0.2304,  0.352
 0.4096,  0.2928, -0.864
 0.096,   0.928,   0.36

 0.872,  -0.2112,  0.4416
 0.48,    0.192,  -0.856
 0.096,   0.9584,  0.2688

 0.872,  -0.3264,  0.3648
 0.48,    0.424,  -0.768
 0.096,   0.8448,  0.5264

 0.8448, -0.3264,  0.424
 0.5264,  0.3648, -0.768
 0.096,   0.872,   0.48

 0.8688,  0.224,  -0.4416
 0.48,   -0.6,     0.64
 0.1216,  0.768,   0.6288

 0.768,   0.224,  -0.6
 0.6288, -0.4416,  0.64
 0.1216,  0.8688,  0.48

 0.864,  -0.36,    0.352
 0.4752,  0.352,  -0.8064
 0.1664,  0.864,   0.4752

 0.96,    0.168,  -0.224
 0.224,  -0.9408,  0.2544
 0.168,   0.2944,  0.9408

 0.9024,  0.2368, -0.36
 0.3968, -0.7824,  0.48
 0.168,   0.576,   0.8

 0.8,    -0.36,    0.48
 0.576,   0.2368, -0.7824
 0.168,   0.9024,  0.3968

 0.8,     0.36,   -0.48
 0.576,  -0.6848,  0.4464
 0.168,   0.6336,  0.7552

 0.7552, -0.48,    0.4464
 0.6336,  0.36,   -0.6848
 0.168,   0.8,     0.576

 0.768,   0.28,   -0.576
 0.6144, -0.576,   0.5392
 0.1808,  0.768,   0.6144

 0.8976,  0.192,  -0.3968
 0.3968, -0.744,   0.5376
 0.192,   0.64,    0.744

 0.768,   0.2928, -0.5696
 0.6,    -0.64,    0.48
 0.224,   0.7104,  0.6672

 0.7104,  0.2928, -0.64
 0.6672, -0.5696,  0.48
 0.224,   0.768,   0.6

 0.768,  -0.5392,  0.3456
 0.576,   0.3456, -0.7408
 0.28,    0.768,   0.576

Orthogonal 4 × 4 matrices

We can create an orthogonal matrix by taking one or two $2 \times 2$ orthogonal matrices or a $3 \times 3$ orthogonal matrix and placing them on the diagonal:

 1, 0, 0, 0
 0, 1, 0, 0
 0, 0, 1, 0
 0, 0, 0, 1

 1, 0, 0,   0
 0, 1, 0,   0
 0, 0, a11, a12
 0, 0, a21, a22

 1, 0,   0,   0
 0, a11, a12, a13
 0, a21, a22, a23
 0, a31, a32, a33

 a11, a12, 0,   0
 a21, a22, 0,   0
 0,   0,   b11, b12
 0,   0,   b21, b22

Here are five other full matrices:

 0.7, -0.7, -0.1,  0.1
 0.7,  0.7, -0.1, -0.1
 0.1, -0.1,  0.7, -0.7
 0.1,  0.1,  0.7,  0.7

 0.7, -0.1, -0.5,  0.5
 0.7, -0.1,  0.5, -0.5
 0.1,  0.7, -0.5, -0.5
 0.1,  0.7,  0.5,  0.5

 0.9, -0.3, -0.3,  0.1
 0.3,  0.9, -0.1, -0.3
 0.3, -0.1,  0.9, -0.3
 0.1,  0.3,  0.3,  0.9

 0.8, -0.4, -0.4,  0.2
 0.4,  0.8, -0.2, -0.4
 0.4, -0.2,  0.8, -0.4
 0.2,  0.4,  0.4,  0.8

 0.5, -0.5, -0.5,  0.5
 0.5, -0.5,  0.5, -0.5
 0.5,  0.5, -0.5, -0.5
 0.5,  0.5,  0.5,  0.5

  0.8,   0,    -0.48,  0.36
  0.6,   0,     0.64, -0.48
  0,    -0.8,   0.36,  0.48
  0,     0.6,   0.48,  0.64

  0.8,  -0.48,  0.36,  0
  0.48,  0.8,   0,    -0.36
  0.36,  0,    -0.8,   0.48
  0,     0.36,  0.48,  0.8

  0.8,   0,    -0.6,   0
  0.48, -0.36,  0.64,  0.48
  0.36,  0.48,  0.48, -0.64
  0,     0.8,   0,     0.6

  0.64, -0.6,   0.48,  0
  0.6,   0.64,  0,    -0.48
  0.48,  0,    -0.64,  0.6
  0,     0.48,  0.6,   0.64

  0.94, -0.34,  0.02, -0.02
  0.34,  0.94, -0.02, -0.02
  0.02, -0.02, -0.94,  0.34
  0.02,  0.02,  0.34,  0.94

  0.94, -0.02,  0.26, -0.22
  0.34, -0.02, -0.74,  0.58
  0.02,  0.94, -0.22, -0.26
  0.02,  0.34,  0.58,  0.74

  0.94,  0.14,  0.22, -0.22
  0.34, -0.46, -0.58,  0.58
  0.02,  0.62, -0.74, -0.26
  0.02,  0.62,  0.26,  0.74

  0.86, -0.5,   0.1,  -0.02
  0.5,   0.86, -0.02, -0.1
  0.1,  -0.02, -0.86,  0.5
  0.02,  0.1,   0.5,   0.86

  0.86, -0.02,  0.46, -0.22
  0.5,  -0.1,  -0.7,   0.5
  0.1,   0.5,  -0.5,  -0.7
  0.02,  0.86,  0.22,  0.46

  0.86, -0.02, -0.38,  0.34
  0.5,   0.1,   0.5,  -0.7
  0.1,  -0.5,   0.7,   0.5
  0.02,  0.86,  0.34,  0.38

  0.86,  0.26, -0.22, -0.38
  0.5,  -0.5,   0.5,   0.5
  0.1,   0.1,  -0.7,   0.7
  0.02,  0.82,  0.46,  0.34

  0.98, -0.14, -0.14,  0.02
  0.14,  0.98, -0.02, -0.14
  0.14, -0.02,  0.98, -0.14
  0.02,  0.14,  0.14,  0.98

  0.98, -0.14, -0.1,   0.1
  0.14,  0.98, -0.1,  -0.1
  0.14, -0.02,  0.7,  -0.7
  0.02,  0.14,  0.7,  0.7

  0.98,  0.14, -0.14, -0.02
  0.14, -0.98, -0.02,  0.14
  0.14, -0.02,  0.98, -0.14
  0.02,  0.14,  0.14,  0.98

  0.98, -0.14, -0.1,   0.1
  0.14, -0.02,  0.7,  -0.7
  0.14,  0.98, -0.1,  -0.1
  0.02,  0.14,  0.7,   0.7

  0.7,  -0.7,   0.14, -0.02
  0.7,   0.7,  -0.02, -0.14
  0.14, -0.02, -0.7,   0.7
  0.02,  0.14,  0.7,   0.7

  0.7,  -0.7,  -0.1,   0.1
  0.7,   0.7,  -0.1,  -0.1
  0.14, -0.02,  0.98, -0.14
  0.02,  0.14,  0.14,  0.98

  0.7,  -0.1,  -0.5,   0.5
  0.7,  -0.1,   0.5,  -0.5
  0.14,  0.98, -0.1,  -0.1
  0.02,  0.14,  0.7,   0.7

  0.94, -0.26,  0.22, -0.02
  0.26,  0.94, -0.02, -0.22
  0.22, -0.02, -0.94,  0.26
  0.02,  0.22,  0.26,  0.94

  0.94,  0.22,  0.14, -0.22
  0.26, -0.02, -0.74,  0.62
  0.22, -0.94,  0.22,  0.14
  0.02,  0.26,  0.62,  0.74

  0.94, -0.02,  0.34, -0.02
  0.26,  0.22, -0.74, -0.58
  0.22, -0.26, -0.58,  0.74
  0.02,  0.94,  0.02,  0.34

  0.94, -0.02, -0.22,  0.26
  0.26, -0.58,  0.62, -0.46
  0.22,  0.74,  0.14, -0.62
  0.02,  0.34,  0.74,  0.58

  0.86, -0.46,  0.22, -0.02
  0.46,  0.86, -0.02, -0.22
  0.22, -0.02, -0.86,  0.46
  0.02,  0.22,  0.46,  0.86

  0.86, -0.22, -0.38,  0.26
  0.46, -0.02,  0.82, -0.34
  0.22,  0.86, -0.26, -0.38
  0.02,  0.46,  0.34,  0.82

  0.86, -0.02,  0.5,  -0.1
  0.46, -0.22, -0.7,   0.5
  0.22,  0.46, -0.5,  -0.7
  0.02,  0.86,  0.1,   0.5

  0.86, -0.02, -0.38,  0.34
  0.46, -0.22,  0.82, -0.26
  0.22,  0.46, -0.26, -0.82
  0.02,  0.86,  0.34,  0.38

  0.74, -0.26, -0.22,  0.58
  0.62,  0.62,  0.14, -0.46
  0.26, -0.74,  0.22, -0.58
  0.02,  0.02,  0.94,  0.34

  0.74, -0.62,  0.26, -0.02
  0.62,  0.74, -0.02, -0.26
  0.26, -0.02, -0.74,  0.62
  0.02,  0.26,  0.62,  0.74

  0.74,  0.62,  0.14, -0.22
  0.62, -0.74,  0.22,  0.14
  0.26, -0.02, -0.94,  0.22
  0.02,  0.26,  0.22,  0.94

  0.74, -0.02,  0.58, -0.34
  0.62, -0.26, -0.46,  0.58
  0.26,  0.62, -0.58, -0.46
  0.02,  0.74,  0.34,  0.58

  0.86, -0.38,  0.34, -0.02
  0.38,  0.86, -0.02, -0.34
  0.34, -0.02, -0.86,  0.38
  0.02,  0.34,  0.38,  0.86

  0.86, -0.38, -0.22,  0.26
  0.38,  0.86, -0.26, -0.22
  0.34, -0.02,  0.82, -0.46
  0.02,  0.34,  0.46,  0.82

  0.86,  0.38, -0.34, -0.02
  0.38, -0.86, -0.02,  0.34
  0.34, -0.02,  0.86, -0.38
  0.02,  0.34,  0.38,  0.86

  0.86, -0.02, -0.5,   0.1
  0.38,  0.34,  0.5,  -0.7
  0.34, -0.38,  0.7,   0.5
  0.02,  0.86,  0.1,   0.5

  0.86, -0.02,  0.46, -0.22
  0.38,  0.34, -0.82, -0.26
  0.34, -0.38, -0.26,  0.82
  0.02,  0.86,  0.22,  0.46

  0.82, -0.46,  0.34, -0.02
  0.46,  0.82, -0.02, -0.34
  0.34, -0.02, -0.82,  0.46
  0.02,  0.34,  0.46,  0.82

  0.82, -0.46, -0.22,  0.26
  0.46,  0.82, -0.26, -0.22
  0.34, -0.02,  0.86, -0.38
  0.02,  0.34,  0.38,  0.86

  0.82,  0.1,   0.26, -0.5
  0.46, -0.7,  -0.22,  0.5
  0.34,  0.7,  -0.38,  0.5
  0.02,  0.1,   0.86,  0.5

  0.74, -0.58,  0.34, -0.02
  0.58,  0.74, -0.02, -0.34
  0.34, -0.02, -0.74,  0.58
  0.02,  0.34,  0.58,  0.74

  0.74,  0.58, -0.34, -0.02
  0.58, -0.74, -0.02,  0.34
  0.34, -0.02,  0.74, -0.58
  0.02,  0.34,  0.58,  0.74

  0.74, -0.02,  0.62, -0.26
  0.58, -0.34, -0.46,  0.58
  0.34,  0.58, -0.58, -0.46
  0.02,  0.74,  0.26,  0.62

  0.98, -0.18,  0.06, -0.06
  0.18,  0.98, -0.06, -0.06
  0.06, -0.06, -0.98,  0.18
  0.06,  0.06,  0.18,  0.98

  0.98, -0.06, -0.18,  0.06
  0.18, -0.06,  0.82, -0.54
  0.06,  0.98, -0.06, -0.18
  0.06,  0.18,  0.54,  0.82

  0.98, -0.06,  0.18, -0.06
  0.18, -0.06, -0.82,  0.54
  0.06,  0.18, -0.54, -0.82
  0.06,  0.98,  0.06,  0.18

  0.98, -0.06,  0.06, -0.18
  0.18,  0.54, -0.54,  0.62
  0.06, -0.82, -0.18,  0.54
  0.06,  0.18,  0.82,  0.54

  0.78, -0.62,  0.06, -0.06
  0.62,  0.78, -0.06, -0.06
  0.06, -0.06, -0.78,  0.62
  0.06,  0.06,  0.62,  0.78

  0.78,  0.06,  0.46, -0.42
  0.62, -0.06, -0.66,  0.42
  0.06, -0.78,  0.42,  0.46
  0.06,  0.62,  0.42,  0.66

  0.78,  0.3,  -0.3,   0.46
  0.62, -0.3,   0.3,  -0.66
  0.06, -0.9,  -0.1,   0.42
  0.06,  0.1,   0.9,   0.42

  0.9,  -0.1,  -0.3,   0.3
  0.42,  0.42,  0.46, -0.66
  0.1,  -0.9,   0.3,  -0.3
  0.06,  0.06,  0.78,  0.62

  0.9,  -0.42,  0.1,  -0.06
  0.42,  0.9,  -0.06, -0.1
  0.1,  -0.06, -0.9,   0.42
  0.06,  0.1,   0.42,  0.9

  0.9,   0.42, -0.1,  -0.06
  0.42, -0.9,  -0.06,  0.1
  0.1,  -0.06,  0.9,  -0.42
  0.06,  0.1,   0.42,  0.9

  0.9,  -0.1,   0.3,  -0.3
  0.42, -0.06, -0.66,  0.62
  0.1,   0.9,  -0.3,  -0.3
  0.06,  0.42,  0.62,  0.66

  0.9,   0.1,   0.3,  -0.3
  0.42, -0.06, -0.78,  0.46
  0.1,  -0.9,   0.3,   0.3
  0.06,  0.42,  0.46,  0.78

  0.82, -0.54,  0.18, -0.06
  0.54,  0.82, -0.06, -0.18
  0.18, -0.06, -0.82,  0.54
  0.06,  0.18,  0.54,  0.82

  0.82,  0.54, -0.18, -0.06
  0.54, -0.82, -0.06,  0.18
  0.18, -0.06,  0.82, -0.54
  0.06,  0.18,  0.54,  0.82

  0.82, -0.06, -0.54,  0.18
  0.54,  0.18,  0.62, -0.54
  0.18, -0.54,  0.54,  0.62
  0.06,  0.82,  0.18,  0.54

  0.78, -0.46,  0.42, -0.06
  0.46,  0.78, -0.06, -0.42
  0.42, -0.06, -0.78,  0.46
  0.06,  0.42,  0.46,  0.78

  0.78,  0.46, -0.42, -0.06
  0.46, -0.78, -0.06,  0.42
  0.42, -0.06,  0.78, -0.46
  0.06,  0.42,  0.46,  0.78

  0.78,  0.46,  0.06, -0.42
  0.46, -0.78,  0.42,  0.06
  0.42, -0.06, -0.66,  0.62
  0.06,  0.42,  0.62,  0.66

  0.78,  0.46,  0.3,  -0.3
  0.46, -0.78,  0.3,   0.3
  0.42, -0.06, -0.9,   0.1
  0.06,  0.42,  0.1,   0.9

  0.78, -0.06, -0.62,  0.06
  0.46, -0.42,  0.66,  0.42
  0.42,  0.46,  0.42, -0.66
  0.06,  0.78,  0.06,  0.62

  0.66, -0.62,  0.42, -0.06
  0.62,  0.66, -0.06, -0.42
  0.42, -0.06, -0.66,  0.62
  0.06,  0.42,  0.62,  0.66

  0.66,  0.62, -0.42, -0.06
  0.62, -0.66, -0.06,  0.42
  0.42, -0.06,  0.66, -0.62
  0.06,  0.42,  0.62,  0.66

  0.66,  0.62, -0.3,  -0.3
  0.62, -0.66, -0.3,   0.3
  0.42, -0.06,  0.9,  -0.1
  0.06,  0.42,  0.1,   0.9

  0.76, -0.64,  0.08, -0.08
  0.64,  0.76, -0.08, -0.08
  0.08, -0.08, -0.76,  0.64
  0.08,  0.08,  0.64,  0.76

  0.76,  0.64, -0.08, -0.08
  0.64, -0.76, -0.08,  0.08
  0.08, -0.08,  0.76, -0.64
  0.08,  0.08,  0.64,  0.76

  0.76,  0.08, -0.56,  0.32
  0.64, -0.08,  0.56, -0.52
  0.08, -0.76,  0.32,  0.56
  0.08,  0.64,  0.52,  0.56

  0.76, -0.08, -0.56,  0.32
  0.64,  0.08,  0.56, -0.52
  0.08, -0.64,  0.52,  0.56
  0.08,  0.76,  0.32,  0.56

  0.76,  0.4,  -0.4,   0.32
  0.64, -0.4,   0.4,  -0.52
  0.08, -0.8,  -0.2,   0.56
  0.08,  0.2,   0.8,   0.56

  0.96, -0.24,  0.12, -0.08
  0.24,  0.96, -0.08, -0.12
  0.12, -0.08, -0.96,  0.24
  0.08,  0.12,  0.24,  0.96

  0.96,  0.24, -0.12, -0.08
  0.24, -0.96, -0.08,  0.12
  0.12, -0.08,  0.96, -0.24
  0.08,  0.12,  0.24,  0.96

  0.96, -0.12, -0.24,  0.08
  0.24, -0.08,  0.84, -0.48
  0.12,  0.96, -0.08, -0.24
  0.08,  0.24,  0.48,  0.84

  0.96, -0.08,  0.24, -0.12
  0.24, -0.12, -0.64,  0.72
  0.12,  0.24, -0.72, -0.64
  0.08,  0.96,  0.12,  0.24

  0.96,  0.08, -0.12, -0.24
  0.24, -0.48,  0.72,  0.44
  0.12, -0.24, -0.64,  0.72
  0.08,  0.84,  0.24,  0.48

  0.88, -0.44, -0.16,  0.08
  0.44,  0.88, -0.08, -0.16
  0.16, -0.08,  0.88, -0.44
  0.08,  0.16,  0.44,  0.88

  0.88, -0.44,  0.16, -0.08
  0.44,  0.88, -0.08, -0.16
  0.16, -0.08, -0.88,  0.44
  0.08,  0.16,  0.44,  0.88

  0.88,  0.44, -0.16, -0.08
  0.44, -0.88, -0.08,  0.16
  0.16, -0.08,  0.88, -0.44
  0.08,  0.16,  0.44,  0.88

  0.88, -0.16, -0.4,   0.2
  0.44, -0.08,  0.8,  -0.4
  0.16,  0.88, -0.2,  -0.4
  0.08,  0.44,  0.4,   0.8

  0.88, -0.16,  0.4,  -0.2
  0.44, -0.08, -0.8,   0.4
  0.16,  0.88, -0.2,  -0.4
  0.08,  0.44,  0.4,   0.8

  0.8,  -0.2,  -0.4,   0.4
  0.56,  0.56,  0.32, -0.52
  0.2,  -0.8,   0.4,  -0.4
  0.08,  0.08,  0.76,  0.64

  0.8,  -0.56,  0.2,  -0.08
  0.56,  0.8,  -0.08, -0.2
  0.2,  -0.08, -0.8,   0.56
  0.08,  0.2,   0.56,  0.8

  0.8,   0.56, -0.2,  -0.08
  0.56, -0.8,  -0.08,  0.2
  0.2,  -0.08,  0.8,  -0.56
  0.08,  0.2,   0.56,  0.8

  0.8,  -0.2,  -0.4,   0.4
  0.56, -0.08,  0.64, -0.52
  0.2,   0.8,  -0.4,  -0.4
  0.08,  0.56,  0.52,  0.64

  0.8,   0.2,   0.4,  -0.4
  0.56, -0.08, -0.76,  0.32
  0.2,  -0.8,   0.4,   0.4
  0.08,  0.56,  0.32,  0.76

  0.84, -0.48,  0.24, -0.08
  0.48,  0.84, -0.08, -0.24
  0.24, -0.08, -0.84,  0.48
  0.08,  0.24,  0.48,  0.84

  0.84,  0.48, -0.24, -0.08
  0.48, -0.84, -0.08,  0.24
  0.24, -0.08,  0.84, -0.48
  0.08,  0.24,  0.48,  0.84

  0.84, -0.08, -0.48,  0.24
  0.48,  0.24,  0.44, -0.72
  0.24, -0.48,  0.72,  0.44
  0.08,  0.84,  0.24,  0.48

  0.76, -0.56,  0.32, -0.08
  0.56,  0.76, -0.08, -0.32
  0.32, -0.08, -0.76,  0.56
  0.08,  0.32,  0.56,  0.76

  0.76,  0.56, -0.32, -0.08
  0.56, -0.76, -0.08,  0.32
  0.32, -0.08,  0.76, -0.56
  0.08,  0.32,  0.56,  0.76

  0.76,  0.32, -0.56,  0.08
  0.56, -0.08,  0.64, -0.52
  0.32, -0.76,  0.08,  0.56
  0.08,  0.56,  0.52,  0.64

  0.76,  0.32,  0.4,  -0.4
  0.56, -0.08, -0.8,   0.2
  0.32, -0.76,  0.4,   0.4
  0.08,  0.56,  0.2,   0.8

  0.76, -0.08, -0.64,  0.08
  0.56,  0.32,  0.56, -0.52
  0.32, -0.56,  0.52,  0.56
  0.08,  0.76,  0.08,  0.64

  0.8,  -0.44,  0.4,  -0.08
  0.44,  0.8,  -0.08, -0.4
  0.4,  -0.08, -0.8,   0.44
  0.08,  0.4,   0.44,  0.8

  0.8,   0.44, -0.4,  -0.08
  0.44, -0.8,  -0.08,  0.4
  0.4,  -0.08,  0.8,  -0.44
  0.08,  0.4,   0.44,  0.8

  0.8,  -0.4,  -0.4,   0.2
  0.44, -0.08,  0.88, -0.16
  0.4,   0.8,  -0.2,  -0.4
  0.08,  0.44,  0.16,  0.88

  0.8,   0.4,  -0.4,  -0.2
  0.44, -0.08,  0.88, -0.16
  0.4,  -0.8,  -0.2,   0.4
  0.08,  0.44,  0.16,  0.88

  0.8,   0.4,   0.2,  -0.4
  0.44, -0.08, -0.8,   0.4
  0.4,  -0.8,   0.4,   0.2
  0.08,  0.44,  0.4,   0.8

  0.64, -0.56,  0.52, -0.08
  0.56,  0.64, -0.08, -0.52
  0.52, -0.08, -0.64,  0.56
  0.08,  0.52,  0.56,  0.64

  0.64,  0.56, -0.52, -0.08
  0.56, -0.64, -0.08,  0.52
  0.52, -0.08,  0.64, -0.56
  0.08,  0.52,  0.56,  0.64

  0.64, -0.52, -0.4,   0.4
  0.56, -0.08,  0.8,  -0.2
  0.52,  0.64, -0.4,  -0.4
  0.08,  0.56,  0.2,   0.8

  0.98, -0.14,  0.1,  -0.1
  0.14,  0.98, -0.1,  -0.1
  0.1,  -0.1,  -0.98,  0.14
  0.1,   0.1,   0.14,  0.98

  0.98,  0.14, -0.1,  -0.1
  0.14, -0.98, -0.1,   0.1
  0.1,  -0.1,   0.98, -0.14
  0.1,   0.1,   0.14,  0.98

  0.7,  -0.7,  -0.1,   0.1
  0.7,   0.7,  -0.1,  -0.1
  0.1,  -0.1,   0.7,  -0.7
  0.1,   0.1,   0.7,   0.7

  0.7,   0.7,  -0.1,  -0.1
  0.7,  -0.7,  -0.1,   0.1
  0.1,  -0.1,   0.7,  -0.7
  0.1,   0.1,   0.7,   0.7

  0.7,  -0.1,  -0.62,  0.34
  0.7,  -0.1,   0.62, -0.34
  0.1,   0.7,  -0.34, -0.62
  0.1,   0.7,   0.34,  0.62

  0.7,  -0.1,   0.62, -0.34
  0.7,  -0.1,  -0.62,  0.34
  0.1,   0.7,  -0.34, -0.62
  0.1,   0.7,   0.34,  0.62

  0.7,  -0.1,  -0.5,   0.5
  0.7,  -0.1,   0.5,  -0.5
  0.1,   0.7,  -0.5,  -0.5
  0.1,   0.7,   0.5,   0.5

  0.7,  -0.1,  -0.62,  0.34
  0.7,   0.1,   0.5,  -0.5
  0.1,  -0.7,   0.5,   0.5
  0.1,   0.7,   0.34,  0.62

  0.7,  -0.1,   0.5,  -0.5
  0.7,   0.1,  -0.62,  0.34
  0.1,  -0.7,   0.34,  0.62
  0.1,   0.7,   0.5,   0.5

  0.7,   0.1,   0.5,  -0.5
  0.7,  -0.1,  -0.62,  0.34
  0.1,  -0.7,   0.5,   0.5
  0.1,   0.7,   0.34,  0.62

  0.7,   0.1,  -0.62,  0.34
  0.7,  -0.1,   0.5,  -0.5
  0.1,  -0.7,   0.34,  0.62
  0.1,   0.7,   0.5,   0.5

  0.82, -0.5,   0.26, -0.1
  0.5,   0.82, -0.1,  -0.26
  0.26, -0.1,  -0.82,  0.5
  0.1,   0.26,  0.5,   0.82

  0.82,  0.5,  -0.26, -0.1
  0.5,  -0.82, -0.1,   0.26
  0.26, -0.1,   0.82, -0.5
  0.1,   0.26,  0.5,   0.82

  0.82, -0.26, -0.38,  0.34
  0.5,  -0.1,   0.7,  -0.5
  0.26,  0.82, -0.34, -0.38
  0.1,   0.5,   0.5,   0.7

  0.82,  0.26,  0.22, -0.46
  0.5,  -0.1,  -0.7,   0.5
  0.26, -0.82,  0.46,  0.22
  0.1,   0.5,   0.5,   0.7

  0.9,  -0.3,  -0.3,   0.1
  0.3,   0.9,  -0.1,  -0.3
  0.3,  -0.1,   0.9,  -0.3
  0.1,   0.3,   0.3,   0.9

  0.9,  -0.3,   0.3,  -0.1
  0.3,   0.9,  -0.1,  -0.3
  0.3,  -0.1,  -0.9,   0.3
  0.1,   0.3,   0.3,   0.9

  0.9,  -0.3,  -0.26,  0.18
  0.3,   0.9,  -0.18, -0.26
  0.3,  -0.1,   0.78, -0.54
  0.1,   0.3,   0.54,  0.78

  0.9,  -0.3,   0.26, -0.18
  0.3,   0.9,  -0.18, -0.26
  0.3,  -0.1,  -0.78,  0.54
  0.1,   0.3,   0.54,  0.78

  0.9,   0.3,  -0.3,  -0.1
  0.3,  -0.9,  -0.1,   0.3
  0.3,  -0.1,   0.9,  -0.3
  0.1,   0.3,   0.3,   0.9

  0.9,   0.3,   0.1,  -0.3
  0.3,  -0.9,   0.3,   0.1
  0.3,  -0.1,  -0.78,  0.54
  0.1,   0.3,   0.54,  0.78

  0.9,   0.3,   0.18, -0.26
  0.3,  -0.9,   0.26,  0.18
  0.3,  -0.1,  -0.9,   0.3
  0.1,   0.3,   0.3,   0.9

  0.9,  -0.3,  -0.26,  0.18
  0.3,  -0.1,   0.78, -0.54
  0.3,   0.9,  -0.18, -0.26
  0.1,   0.3,   0.54,  0.78

  0.9,  -0.3,   0.26, -0.18
  0.3,  -0.1,  -0.78,  0.54
  0.3,   0.9,  -0.18, -0.26
  0.1,   0.3,   0.54,  0.78

  0.9,   0.3,   0.1,  -0.3
  0.3,  -0.1,  -0.78,  0.54
  0.3,  -0.9,   0.3,   0.1
  0.1,   0.3,   0.54,  0.78

  0.9,   0.3,   0.18, -0.26
  0.3,  -0.1,  -0.9,   0.3
  0.3,  -0.9,   0.26,  0.18
  0.1,   0.3,   0.3,   0.9

  0.78, -0.54,  0.3,  -0.1
  0.54,  0.78, -0.1,  -0.3
  0.3,  -0.1,  -0.78,  0.54
  0.1,   0.3,   0.54,  0.78

  0.78, -0.54, -0.26,  0.18
  0.54,  0.78, -0.18, -0.26
  0.3,  -0.1,   0.9,  -0.3
  0.1,   0.3,   0.3,   0.9

  0.78,  0.54, -0.3,  -0.1
  0.54, -0.78, -0.1,   0.3
  0.3,  -0.1,   0.78, -0.54
  0.1,   0.3,   0.54,  0.78

  0.78,  0.54, -0.26, -0.18
  0.54, -0.78, -0.18,  0.26
  0.3,  -0.1,   0.9,  -0.3
  0.1,   0.3,   0.3,   0.9

  0.7,   0.7,  -0.1,  -0.1
  0.62, -0.62, -0.34,  0.34
  0.34, -0.34,  0.62, -0.62
  0.1,   0.1,   0.7,   0.7

  0.7,  -0.62,  0.34, -0.1
  0.62,  0.7,  -0.1,  -0.34
  0.34, -0.1,  -0.7,   0.62
  0.1,   0.34,  0.62,  0.7

  0.7,   0.62, -0.34, -0.1
  0.62, -0.7,  -0.1,   0.34
  0.34, -0.1,   0.7,  -0.62
  0.1,   0.34,  0.62,  0.7

  0.7,  -0.1,  -0.7,   0.1
  0.62,  0.34,  0.5,  -0.5
  0.34, -0.62,  0.5,   0.5
  0.1,   0.7,   0.1,   0.7

  0.7,  -0.1,   0.5,  -0.5
  0.62,  0.34, -0.7,   0.1
  0.34, -0.62,  0.1,   0.7
  0.1,   0.7,   0.5,   0.5

  0.7,   0.7,  -0.1,  -0.1
  0.5,  -0.5,  -0.5,   0.5
  0.5,  -0.5,   0.5,  -0.5
  0.1,   0.1,   0.7,   0.7

  0.7,  -0.5,   0.5,  -0.1
  0.5,   0.7,  -0.1,  -0.5
  0.5,  -0.1,  -0.7,   0.5
  0.1,   0.5,   0.5,   0.7

  0.7,  -0.5,  -0.38,  0.34
  0.5,   0.7,  -0.34, -0.38
  0.5,  -0.1,   0.82, -0.26
  0.1,   0.5,   0.26,  0.82

  0.7,   0.5,  -0.5,  -0.1
  0.5,  -0.7,  -0.1,   0.5
  0.5,  -0.1,   0.7,  -0.5
  0.1,   0.5,   0.5,   0.7

  0.7,   0.5,   0.22, -0.46
  0.5,  -0.7,   0.46,  0.22
  0.5,  -0.1,  -0.82,  0.26
  0.1,   0.5,   0.26,  0.82

  0.7,  -0.5,  -0.38,  0.34
  0.5,  -0.1,   0.82, -0.26
  0.5,   0.7,  -0.34, -0.38
  0.1,   0.5,   0.26,  0.82

  0.7,   0.5,   0.22, -0.46
  0.5,  -0.1,  -0.82,  0.26
  0.5,  -0.7,   0.46,  0.22
  0.1,   0.5,   0.26,  0.82

  0.72, -0.64,  0.24, -0.12
  0.64,  0.72, -0.12, -0.24
  0.24, -0.12, -0.72,  0.64
  0.12,  0.24,  0.64,  0.72

  0.72,  0.64, -0.24, -0.12
  0.64, -0.72, -0.12,  0.24
  0.24, -0.12,  0.72, -0.64
  0.12,  0.24,  0.64,  0.72

  0.72,  0.24,  0.44, -0.48
  0.64, -0.12, -0.72,  0.24
  0.24, -0.72,  0.48,  0.44
  0.12,  0.64,  0.24,  0.72

  0.94, -0.22,  0.22, -0.14
  0.22,  0.94, -0.14, -0.22
  0.22, -0.14, -0.94,  0.22
  0.14,  0.22,  0.22,  0.94

  0.94,  0.22, -0.22, -0.14
  0.22, -0.94, -0.14,  0.22
  0.22, -0.14,  0.94, -0.22
  0.14,  0.22,  0.22,  0.94

  0.74, -0.62,  0.22, -0.14
  0.62,  0.74, -0.14, -0.22
  0.22, -0.14, -0.74,  0.62
  0.14,  0.22,  0.62,  0.74

  0.74,  0.62, -0.22, -0.14
  0.62, -0.74, -0.14,  0.22
  0.22, -0.14,  0.74, -0.62
  0.14,  0.22,  0.62,  0.74

  0.74,  0.22,  0.26, -0.58
  0.62, -0.14, -0.62,  0.46
  0.22, -0.74,  0.58,  0.26
  0.14,  0.62,  0.46,  0.62

  0.62, -0.62,  0.46, -0.14
  0.62,  0.62, -0.14, -0.46
  0.46, -0.14, -0.62,  0.62
  0.14,  0.46,  0.62,  0.62

  0.62,  0.62, -0.46, -0.14
  0.62, -0.62, -0.14,  0.46
  0.46, -0.14,  0.62, -0.62
  0.14,  0.46,  0.62,  0.62

  0.62,  0.46,  0.26, -0.58
  0.62, -0.14, -0.74,  0.22
  0.46, -0.62,  0.58,  0.26
  0.14,  0.62,  0.22,  0.74

  0.62, -0.14, -0.74,  0.22
  0.62,  0.46,  0.26, -0.58
  0.46, -0.62,  0.58,  0.26
  0.14,  0.62,  0.22,  0.74

  0.92, -0.32,  0.16, -0.16
  0.32,  0.92, -0.16, -0.16
  0.16, -0.16, -0.92,  0.32
  0.16,  0.16,  0.32,  0.92

  0.92,  0.32, -0.16, -0.16
  0.32, -0.92, -0.16,  0.16
  0.16, -0.16,  0.92, -0.32
  0.16,  0.16,  0.32,  0.92

  0.92, -0.16, -0.32,  0.16
  0.32, -0.16,  0.68, -0.64
  0.16,  0.92, -0.16, -0.32
  0.16,  0.32,  0.64,  0.68

  0.92, -0.16,  0.32, -0.16
  0.32, -0.16, -0.68,  0.64
  0.16,  0.32, -0.64, -0.68
  0.16,  0.92,  0.16,  0.32

  0.92, -0.16,  0.16, -0.32
  0.32,  0.64, -0.64,  0.28
  0.16, -0.68, -0.32,  0.64
  0.16,  0.32,  0.68,  0.64

  0.88, -0.4,   0.2,  -0.16
  0.4,   0.88, -0.16, -0.2
  0.2,  -0.16, -0.88,  0.4
  0.16,  0.2,   0.4,   0.88

  0.88,  0.4,  -0.2,  -0.16
  0.4,  -0.88, -0.16,  0.2
  0.2,  -0.16,  0.88, -0.4
  0.16,  0.2,   0.4,   0.88

  0.88, -0.16, -0.4,   0.2
  0.4,   0.2,   0.4,  -0.8
  0.2,  -0.4,   0.8,   0.4
  0.16,  0.88,  0.2,   0.4

  0.68, -0.64,  0.32, -0.16
  0.64,  0.68, -0.16, -0.32
  0.32, -0.16, -0.68,  0.64
  0.16,  0.32,  0.64,  0.68

  0.68,  0.64, -0.32, -0.16
  0.64, -0.68, -0.16,  0.32
  0.32, -0.16,  0.68, -0.64
  0.16,  0.32,  0.64,  0.68

  0.68, -0.16, -0.64,  0.32
  0.64,  0.32,  0.28, -0.64
  0.32, -0.64,  0.64,  0.28
  0.16,  0.68,  0.32,  0.64

  0.9,  -0.3,   0.26, -0.18
  0.3,   0.9,  -0.18, -0.26
  0.26, -0.18, -0.9,   0.3
  0.18,  0.26,  0.3,   0.9

  0.9,   0.3,  -0.26, -0.18
  0.3,  -0.9,  -0.18,  0.26
  0.26, -0.18,  0.9,  -0.3
  0.18,  0.26,  0.3,   0.9

  0.78, -0.54, -0.26,  0.18
  0.54,  0.78, -0.18, -0.26
  0.26, -0.18,  0.78, -0.54
  0.18,  0.26,  0.54,  0.78

  0.78, -0.54,  0.26, -0.18
  0.54,  0.78, -0.18, -0.26
  0.26, -0.18, -0.78,  0.54
  0.18,  0.26,  0.54,  0.78

  0.78,  0.54, -0.26, -0.18
  0.54, -0.78, -0.18,  0.26
  0.26, -0.18,  0.78, -0.54
  0.18,  0.26,  0.54,  0.78

  0.62, -0.54,  0.54, -0.18
  0.54,  0.62, -0.18, -0.54
  0.54, -0.18, -0.62,  0.54
  0.18,  0.54,  0.54,  0.62

  0.62,  0.54, -0.54, -0.18
  0.54, -0.62, -0.18,  0.54
  0.54, -0.18,  0.62, -0.54
  0.18,  0.54,  0.54,  0.62

  0.8,  -0.4,  -0.4,   0.2
  0.4,   0.8,  -0.2,  -0.4
  0.4,  -0.2,   0.8,  -0.4
  0.2,   0.4,   0.4,   0.8

  0.8,  -0.4,   0.4,  -0.2
  0.4,   0.8,  -0.2,  -0.4
  0.4,  -0.2,  -0.8,   0.4
  0.2,   0.4,   0.4,   0.8

  0.8,   0.4,  -0.4,  -0.2
  0.4,  -0.8,  -0.2,   0.4
  0.4,  -0.2,   0.8,  -0.4
  0.2,   0.4,   0.4,   0.8

  0.86, -0.38,  0.26, -0.22
  0.38,  0.86, -0.22, -0.26
  0.26, -0.22, -0.86,  0.38
  0.22,  0.26,  0.38,  0.86

  0.86,  0.38, -0.26, -0.22
  0.38, -0.86, -0.22,  0.26
  0.26, -0.22,  0.86, -0.38
  0.22,  0.26,  0.38,  0.86

  0.82, -0.46,  0.26, -0.22
  0.46,  0.82, -0.22, -0.26
  0.26, -0.22, -0.82,  0.46
  0.22,  0.26,  0.46,  0.82

  0.82,  0.46, -0.26, -0.22
  0.46, -0.82, -0.22,  0.26
  0.26, -0.22,  0.82, -0.46
  0.22,  0.26,  0.46,  0.82

  0.74, -0.58,  0.26, -0.22
  0.58,  0.74, -0.22, -0.26
  0.26, -0.22, -0.74,  0.58
  0.22,  0.26,  0.58,  0.74

  0.74,  0.58, -0.26, -0.22
  0.58, -0.74, -0.22,  0.26
  0.26, -0.22,  0.74, -0.58
  0.22,  0.26,  0.58,  0.74

  0.7,  -0.5,   0.46, -0.22
  0.5,   0.7,  -0.22, -0.46
  0.46, -0.22, -0.7,   0.5
  0.22,  0.46,  0.5,   0.7

  0.7,   0.5,  -0.46, -0.22
  0.5,  -0.7,  -0.22,  0.46
  0.46, -0.22,  0.7,  -0.5
  0.22,  0.46,  0.5,   0.7

  0.72, -0.48,  0.44, -0.24
  0.48,  0.72, -0.24, -0.44
  0.44, -0.24, -0.72,  0.48
  0.24,  0.44,  0.48,  0.72

  0.72,  0.48, -0.44, -0.24
  0.48, -0.72, -0.24,  0.44
  0.44, -0.24,  0.72, -0.48
  0.24,  0.44,  0.48,  0.72

  0.82, -0.38,  0.34, -0.26
  0.38,  0.82, -0.26, -0.34
  0.34, -0.26, -0.82,  0.38
  0.26,  0.34,  0.38,  0.82

  0.82,  0.38, -0.34, -0.26
  0.38, -0.82, -0.26,  0.34
  0.34, -0.26,  0.82, -0.38
  0.26,  0.34,  0.38,  0.82

  0.62, -0.58,  0.46, -0.26
  0.58,  0.62, -0.26, -0.46
  0.46, -0.26, -0.62,  0.58
  0.26,  0.46,  0.58,  0.62

  0.62,  0.58, -0.46, -0.26
  0.58, -0.62, -0.26,  0.46
  0.46, -0.26,  0.62, -0.58
  0.26,  0.46,  0.58,  0.62

  0.64, -0.64,  0.32, -0.28
  0.64,  0.64, -0.28, -0.32
  0.32, -0.28, -0.64,  0.64
  0.28,  0.32,  0.64,  0.64

  0.64,  0.64, -0.32, -0.28
  0.64, -0.64, -0.28,  0.32
  0.32, -0.28,  0.64, -0.64
  0.28,  0.32,  0.64,  0.64

  0.78, -0.46,  0.3,  -0.3
  0.46,  0.78, -0.3,  -0.3
  0.3,  -0.3,  -0.78,  0.46
  0.3,   0.3,   0.46,  0.78

  0.78,  0.46, -0.3,  -0.3
  0.46, -0.78, -0.3,   0.3
  0.3,  -0.3,   0.78, -0.46
  0.3,   0.3,   0.46,  0.78

  0.66, -0.62,  0.3,  -0.3
  0.62,  0.66, -0.3,  -0.3
  0.3,  -0.3,  -0.66,  0.62
  0.3,   0.3,   0.62,  0.66

  0.66,  0.62, -0.3,  -0.3
  0.62, -0.66, -0.3,   0.3
  0.3,  -0.3,   0.66, -0.62
  0.3,   0.3,   0.62,  0.66

  0.76, -0.4,   0.4,  -0.32
  0.4,   0.76, -0.32, -0.4
  0.4,  -0.32, -0.76,  0.4
  0.32,  0.4,   0.4,   0.76

  0.76,  0.4,  -0.4,  -0.32
  0.4,  -0.76, -0.32,  0.4
  0.4,  -0.32,  0.76, -0.4
  0.32,  0.4,   0.4,   0.76

  0.56, -0.56,  0.52, -0.32
  0.56,  0.56, -0.32, -0.52
  0.52, -0.32, -0.56,  0.56
  0.32,  0.52,  0.56,  0.56

  0.56,  0.56, -0.52, -0.32
  0.56, -0.56, -0.32,  0.52
  0.52, -0.32,  0.56, -0.56
  0.32,  0.52,  0.56,  0.56

  0.62, -0.62, -0.34,  0.34
  0.62,  0.62, -0.34, -0.34
  0.34, -0.34,  0.62, -0.62
  0.34,  0.34,  0.62,  0.62

  0.62,  0.62, -0.34, -0.34
  0.62, -0.62, -0.34,  0.34
  0.34, -0.34,  0.62, -0.62
  0.34,  0.34,  0.62,  0.62

  0.62, -0.34, -0.5,   0.5
  0.62, -0.34,  0.5,  -0.5
  0.34,  0.62, -0.5,  -0.5
  0.34,  0.62,  0.5,   0.5

  0.7,  -0.5,   0.38, -0.34
  0.5,   0.7,  -0.34, -0.38
  0.38, -0.34, -0.7,   0.5
  0.34,  0.38,  0.5,   0.7

  0.7,   0.5,  -0.38, -0.34
  0.5,  -0.7,  -0.34,  0.38
  0.38, -0.34,  0.7,  -0.5
  0.34,  0.38,  0.5,   0.7

  0.58, -0.58,  0.46, -0.34
  0.58,  0.58, -0.34, -0.46
  0.46, -0.34, -0.58,  0.58
  0.34,  0.46,  0.58,  0.58

  0.58,  0.58, -0.46, -0.34
  0.58, -0.58, -0.34,  0.46
  0.46, -0.34,  0.58, -0.58
  0.34,  0.46,  0.58,  0.58

  0.62,  0.62, -0.34, -0.34
  0.5,  -0.5,  -0.5,   0.5
  0.5,  -0.5,   0.5,  -0.5
  0.34,  0.34,  0.62,  0.62

  0.62, -0.5,   0.5,  -0.34
  0.5,   0.62, -0.34, -0.5
  0.5,  -0.34, -0.62,  0.5
  0.34,  0.5,   0.5,   0.62

  0.62,  0.5,  -0.5,  -0.34
  0.5,  -0.62, -0.34,  0.5
  0.5,  -0.34,  0.62, -0.5
  0.34,  0.5,   0.5,   0.62

  0.64, -0.48, -0.48,  0.36
  0.48,  0.64, -0.36, -0.48
  0.48, -0.36,  0.64, -0.48
  0.36,  0.48,  0.48,  0.64

  0.64, -0.48,  0.48, -0.36
  0.48,  0.64, -0.36, -0.48
  0.48, -0.36, -0.64,  0.48
  0.36,  0.48,  0.48,  0.64

  0.64,  0.48, -0.48, -0.36
  0.48, -0.64, -0.36,  0.48
  0.48, -0.36,  0.64, -0.48
  0.36,  0.48,  0.48,  0.64

  0.64, -0.52,  0.4,  -0.4
  0.52,  0.64, -0.4,  -0.4
  0.4,  -0.4,  -0.64,  0.52
  0.4,   0.4,   0.52,  0.64

  0.64,  0.52, -0.4,  -0.4
  0.52, -0.64, -0.4,   0.4
  0.4,  -0.4,   0.64, -0.52
  0.4,   0.4,   0.52,  0.64

  0.66, -0.46,  0.42, -0.42
  0.46,  0.66, -0.42, -0.42
  0.42, -0.42, -0.66,  0.46
  0.42,  0.42,  0.46,  0.66

  0.66,  0.46, -0.42, -0.42
  0.46, -0.66, -0.42,  0.42
  0.42, -0.42,  0.66, -0.46
  0.42,  0.42,  0.46,  0.66

  0.5,  -0.5,  -0.5,   0.5
  0.5,  -0.5,   0.5,  -0.5
  0.5,   0.5,  -0.5,  -0.5
  0.5,   0.5,   0.5,   0.5

Orthogonal 5 × 5 matrices

We can create an orthogonal matrix by taking one or two $2 \times 2$ orthogonal matrices or a $3 \times 3$ orthogonal matrix and placing them on the diagonal:

 1, 0, 0, 0, 0
 0, 1, 0, 0, 0
 0, 0, 1, 0, 0
 0, 0, 0, 1, 0
 0, 0, 0, 0, 1

 1, 0, 0, 0,   0
 0, 1, 0, 0,   0
 0, 0, 1, 0,   0
 0, 0, 0, a11, a12
 0, 0, 0, a21, a22

 1, 0, 0,   0,   0
 0, 1, 0,   0,   0
 0, 0, a11, a12, a13
 0, 0, a21, a22, a23
 0, 0, a31, a32, a33

 1, 0,   0,   0,   0
 0, a11, a12, 0,   0
 0, a21, a22, 0,   0
 0, 0,   0,   b11, b12
 0, 0,   0,   b21, b22

 a11, a12, 0,   0,   0
 a21, a22, 0,   0,   0
 0,   0,   b11, b12, b13
 0,   0,   b21, b22, b23
 0,   0,   b31, b32, b33

Here are eleven other full matrices:

 0.8, -0.3,  0.3, -0.3,  0.3
 0.6,  0.4, -0.4,  0.4, -0.4
 0,   -0.7, -0.7,  0.1,  0.1
 0,   -0.5,  0.5,  0.5, -0.5
 0,    0.1,  0.1,  0.7,  0.7

 0.8, -0.3,  0.3, -0.3,  0.3
 0.6,  0.4, -0.4,  0.4, -0.4
 0,   -0.5,  0.5,  0.5, -0.5
 0,    0.7,  0.7, -0.1, -0.1
 0,    0.1,  0.1,  0.7,  0.7

 0.8, -0.3, -0.3,  0.3,  0.3
 0.6,  0.4,  0.4, -0.4, -0.4
 0,   -0.5,  0.5, -0.5,  0.5
 0,   -0.5,  0.5,  0.5, -0.5
 0,    0.5,  0.5,  0.5,  0.5

 0.9, -0.4,  0.1,  0.1, -0.1
 0.3,  0.8, -0.1,  0.1, -0.5
 0.3,  0.4,  0.1, -0.5,  0.7
 0.1,  0,   -0.9,  0.3,  0.3
 0,    0.2,  0.4,  0.8,  0.4

 0.7, -0.4,  0.3,  0.1, -0.5
 0.5,  0.4,  0.1, -0.7,  0.3
 0.5,  0,   -0.5,  0.5,  0.5
 0.1,  0.8, -0.1,  0.3, -0.5
 0,    0.2,  0.8,  0.4,  0.4

 0.8, -0.4, -0.2,  0,    0.4
 0.4,  0.4, -0.4,  0.4, -0.6
 0.4,  0,    0.8, -0.2, -0.4
 0.2,  0.8,  0,   -0.4,  0.4
 0,    0.2,  0.4,  0.8,  0.4

 0.8, -0.5, -0.1,  0.1,  0.3
 0.4,  0.5, -0.5,  0.3, -0.5
 0.4,  0.5,  0.3, -0.7,  0.1
 0.2,  0,    0.8,  0.4, -0.4
 0,    0.5,  0.1,  0.5,  0.7

 0.8, -0.5,  0.3,  0.1,  0.1
 0.4,  0.5, -0.1, -0.7,  0.3
 0.4,  0.5, -0.1,  0.3, -0.7
 0.2,  0,   -0.8,  0.4,  0.4
 0,    0.5,  0.5,  0.5,  0.5

 0.9, -0.1, -0.1,  0.1, -0.4
 0.4,  0.4,  0.4, -0.4,  0.6
 0.1, -0.9,  0.1, -0.1,  0.4
 0.1,  0.1, -0.9, -0.1,  0.4
 0.1,  0.1,  0.1,  0.9,  0.4

 0.7, -0.5, -0.3,  0.1,  0.4
 0.5, -0.1,  0.7, -0.3, -0.4
 0.4,  0.4, -0.4,  0.4, -0.6
 0.3,  0.7, -0.1, -0.5,  0.4
 0.1,  0.3,  0.5,  0.7,  0.4

 0.6, -0.4, -0.4, -0.4,  0.4
 0.4, -0.6,  0.4,  0.4, -0.4
 0.4,  0.4, -0.6,  0.4, -0.4
 0.4,  0.4,  0.4, -0.6, -0.4
 0.4,  0.4,  0.4,  0.4,  0.6