The Magic Encyclopedia ™


Pandiagonal Franklin Squares Order 8
(by Aale de Winkel)
NOTE: preliminary upload to be verified


<Arie Breedijk> allerted me to http://www.f1compiler.com/samples/samples.html where complete listings of the results of iterations for the {compact complete} as well as the {Franklin} order 8 magic squares can be found. Analysis of the {pandiagonal} shows the both the {pandiagonal compact complete} as well as the {pandiagonal Franklin} has a total 368640 (= 360 * 1024) squares, of which 23040 with 0 in the topleft corner.
The interchange of every other column / row (ie _x[0,1,2,3,4,7,6,5], _x[0,1,2,3,6,5,4,7], _x[0,3,2,1,4,5,6,7] and _x[2,1,0,3,4,5,6,7]; x=1,2) adding to it the monagonal permutation _x[1,0,3,2,5,4,7,6] a monsagonal permutation group of order 32 is formed which combine in a group of order 1024 {pandiagonal Franklin} invariant monagonal permutations could was found and thus 360 sets of these squares are formed. One further monagonal permutation _x[0,5,2,7,4,1,6,3] reduces the amount to a total of 90 squares
The listed binary components show the the square nicely constructs with the Dwane Campbel construction method
The spreadsheet PandiagonalSquaresOrder08.xlsx I developed in support of the below

Order08PandiagonalFranklin.html
panfranklin

00 15 49 62 16 31 33 46
51 60 02 13 35 44 18 29
14 01 63 48 30 17 47 32
61 50 12 03 45 34 28 19
04 11 53 58 20 27 37 42
55 56 06 09 39 40 22 25
10 05 59 52 26 21 43 36
57 54 08 07 41 38 24 23
fourbitperm

0 1 2 3 4 5
0 2 1 3 4 5
0 3 2 1 4 5
0 4 2 3 1 5
0 5 2 3 4 1
generators

[0,1,2,3,4,5,6,7]
[0,1,2,3,4,7,6,5]
[0,1,2,3,6,5,4,7]
[0,3,2,1,6,7,4,5]
[1,2,3,0,5,4,7,6]
[1,4,3,6,5,2,7,0]
[4,3,6,1,0,7,2,5]
{PanFranklin} invariant monagonal permutations
generatored by the above 'generators' (at least when applied in mentioned order)
[0,1,2,3,4,5,6,7]
[0,1,2,3,4,7,6,5]
[0,1,2,3,6,5,4,7]
[0,1,2,3,6,7,4,5]
[0,3,2,1,4,5,6,7]
[0,3,2,1,4,7,6,5]
[0,3,2,1,6,5,4,7]
[0,3,2,1,6,7,4,5]
[0,5,2,7,4,1,6,3]
[0,5,2,7,4,3,6,1]
[0,5,2,7,6,1,4,3]
[0,5,2,7,6,3,4,1]
[0,7,2,5,4,1,6,3]
[0,7,2,5,4,3,6,1]
[0,7,2,5,6,1,4,3]
[0,7,2,5,6,3,4,1]
[1,0,3,2,5,4,7,6]
[1,0,3,2,5,6,7,4]
[1,0,3,2,7,4,5,6]
[1,0,3,2,7,6,5,4]
[1,2,3,0,5,4,7,6]
[1,2,3,0,5,6,7,4]
[1,2,3,0,7,4,5,6]
[1,2,3,0,7,6,5,4]
[1,4,3,6,5,0,7,2]
[1,4,3,6,5,2,7,0]
[1,4,3,6,7,0,5,2]
[1,4,3,6,7,2,5,0]
[1,6,3,4,5,0,7,2]
[1,6,3,4,5,2,7,0]
[1,6,3,4,7,0,5,2]
[1,6,3,4,7,2,5,0]
[2,1,0,3,4,5,6,7]
[2,1,0,3,4,7,6,5]
[2,1,0,3,6,5,4,7]
[2,1,0,3,6,7,4,5]
[2,3,0,1,4,5,6,7]
[2,3,0,1,4,7,6,5]
[2,3,0,1,6,5,4,7]
[2,3,0,1,6,7,4,5]
[2,5,0,7,4,1,6,3]
[2,5,0,7,4,3,6,1]
[2,5,0,7,6,1,4,3]
[2,5,0,7,6,3,4,1]
[2,7,0,5,4,1,6,3]
[2,7,0,5,4,3,6,1]
[2,7,0,5,6,1,4,3]
[2,7,0,5,6,3,4,1]
[3,0,1,2,5,4,7,6]
[3,0,1,2,5,6,7,4]
[3,0,1,2,7,4,5,6]
[3,0,1,2,7,6,5,4]
[3,2,1,0,5,4,7,6]
[3,2,1,0,5,6,7,4]
[3,2,1,0,7,4,5,6]
[3,2,1,0,7,6,5,4]
[3,4,1,6,5,0,7,2]
[3,4,1,6,5,2,7,0]
[3,4,1,6,7,0,5,2]
[3,4,1,6,7,2,5,0]
[3,6,1,4,5,0,7,2]
[3,6,1,4,5,2,7,0]
[3,6,1,4,7,0,5,2]
[3,6,1,4,7,2,5,0]
[4,1,6,3,0,5,2,7]
[4,1,6,3,0,7,2,5]
[4,1,6,3,2,5,0,7]
[4,1,6,3,2,7,0,5]
[4,3,6,1,0,5,2,7]
[4,3,6,1,0,7,2,5]
[4,3,6,1,2,5,0,7]
[4,3,6,1,2,7,0,5]
[4,5,6,7,0,1,2,3]
[4,5,6,7,0,3,2,1]
[4,5,6,7,2,1,0,3]
[4,5,6,7,2,3,0,1]
[4,7,6,5,0,1,2,3]
[4,7,6,5,0,3,2,1]
[4,7,6,5,2,1,0,3]
[4,7,6,5,2,3,0,1]
[5,0,7,2,1,4,3,6]
[5,0,7,2,1,6,3,4]
[5,0,7,2,3,4,1,6]
[5,0,7,2,3,6,1,4]
[5,2,7,0,1,4,3,6]
[5,2,7,0,1,6,3,4]
[5,2,7,0,3,4,1,6]
[5,2,7,0,3,6,1,4]
[5,4,7,6,1,0,3,2]
[5,4,7,6,1,2,3,0]
[5,4,7,6,3,0,1,2]
[5,4,7,6,3,2,1,0]
[5,6,7,4,1,0,3,2]
[5,6,7,4,1,2,3,0]
[5,6,7,4,3,0,1,2]
[5,6,7,4,3,2,1,0]
[6,1,4,3,0,5,2,7]
[6,1,4,3,0,7,2,5]
[6,1,4,3,2,5,0,7]
[6,1,4,3,2,7,0,5]
[6,3,4,1,0,5,2,7]
[6,3,4,1,0,7,2,5]
[6,3,4,1,2,5,0,7]
[6,3,4,1,2,7,0,5]
[6,5,4,7,0,1,2,3]
[6,5,4,7,0,3,2,1]
[6,5,4,7,2,1,0,3]
[6,5,4,7,2,3,0,1]
[6,7,4,5,0,1,2,3]
[6,7,4,5,0,3,2,1]
[6,7,4,5,2,1,0,3]
[6,7,4,5,2,3,0,1]
[7,0,5,2,1,4,3,6]
[7,0,5,2,1,6,3,4]
[7,0,5,2,3,4,1,6]
[7,0,5,2,3,6,1,4]
[7,2,5,0,1,4,3,6]
[7,2,5,0,1,6,3,4]
[7,2,5,0,3,4,1,6]
[7,2,5,0,3,6,1,4]
[7,4,5,6,1,0,3,2]
[7,4,5,6,1,2,3,0]
[7,4,5,6,3,0,1,2]
[7,4,5,6,3,2,1,0]
[7,6,5,4,1,0,3,2]
[7,6,5,4,1,2,3,0]
[7,6,5,4,3,0,1,2]
[7,6,5,4,3,2,1,0]
Binary components
DC(33^55,3C^55,55^33,55^3C,55^66,66^55)
Octary components
33^55

0 0 1 1 0 0 1 1
1 1 0 0 1 1 0 0
0 0 1 1 0 0 1 1
1 1 0 0 1 1 0 0
0 0 1 1 0 0 1 1
1 1 0 0 1 1 0 0
0 0 1 1 0 0 1 1
1 1 0 0 1 1 0 0
3C^55

0 0 1 1 1 1 0 0
1 1 0 0 0 0 1 1
0 0 1 1 1 1 0 0
1 1 0 0 0 0 1 1
0 0 1 1 1 1 0 0
1 1 0 0 0 0 1 1
0 0 1 1 1 1 0 0
1 1 0 0 0 0 1 1
55^33

0 1 0 1 0 1 0 1
0 1 0 1 0 1 0 1
1 0 1 0 1 0 1 0
1 0 1 0 1 0 1 0
0 1 0 1 0 1 0 1
0 1 0 1 0 1 0 1
1 0 1 0 1 0 1 0
1 0 1 0 1 0 1 0
0 1 6 7 2 3 4 5
6 7 0 1 4 5 2 3
1 0 7 6 3 2 5 4
7 6 1 0 5 4 3 2
0 1 6 7 2 3 4 5
6 7 0 1 4 5 2 3
1 0 7 6 3 2 5 4
7 6 1 0 5 4 3 2
55^3C

0 1 0 1 0 1 0 1
0 1 0 1 0 1 0 1
1 0 1 0 1 0 1 0
1 0 1 0 1 0 1 0
1 0 1 0 1 0 1 0
1 0 1 0 1 0 1 0
0 1 0 1 0 1 0 1
0 1 0 1 0 1 0 1
55^66

0 1 0 1 0 1 0 1
1 0 1 0 1 0 1 0
1 0 1 0 1 0 1 0
0 1 0 1 0 1 0 1
0 1 0 1 0 1 0 1
1 0 1 0 1 0 1 0
1 0 1 0 1 0 1 0
0 1 0 1 0 1 0 1
66^55

0 1 1 0 0 1 1 0
1 0 0 1 1 0 0 1
0 1 1 0 0 1 1 0
1 0 0 1 1 0 0 1
0 1 1 0 0 1 1 0
1 0 0 1 1 0 0 1
0 1 1 0 0 1 1 0
1 0 0 1 1 0 0 1
0 7 1 6 0 7 1 6
3 4 2 5 3 4 2 5
6 1 7 0 6 1 7 0
5 2 4 3 5 2 4 3
4 3 5 2 4 3 5 2
7 0 6 1 7 0 6 1
2 5 3 4 2 5 3 4
1 6 0 7 1 6 0 7

hereunder a listing of the 90 lowest member of each set of squares
The list is compiled by using all 720 component permutations and combining the monagonal permutation (of type _x[0,perm(1..7)]) and test for the lowest obtainable. Permutations were combined as far as possible and the possible transposing (^[1,0]) positioned toward the end of the component permutation, but can be moved toward its front since the operations commute (ie #[perm(0..5)]^[perm(0,1)] = ^[perm(0,1)]#[perm(0..5)]) monagonal permution change of course direction (pe _1[perm(0..7)]^[perm(0,1)] = ^[perm(0,1)]_2[perm(0..7)]) rules obviously seen I reckon and used, further the monagonal permutations obviously can interchange an combine when equal into a diagonal permutation.

Order08PandiagonalFranklin.html
000 panfranklin

00 15 49 62 16 31 33 46
51 60 02 13 35 44 18 29
14 01 63 48 30 17 47 32
61 50 12 03 45 34 28 19
04 11 53 58 20 27 37 42
55 56 06 09 39 40 22 25
10 05 59 52 26 21 43 36
57 54 08 07 41 38 24 23
001 panfranklin
#[0,1,3,2,4,5]
_2[0,1,2,3,4,7,6,5]

00 15 49 62 16 31 33 46
51 60 02 13 35 44 18 29
14 01 63 48 30 17 47 32
61 50 12 03 45 34 28 19
08 07 57 54 24 23 41 38
53 58 04 11 37 42 20 27
06 09 55 56 22 25 39 40
59 52 10 05 43 36 26 21
002 panfranklin
#[0,1,2,4,3,5]

00 15 49 62 16 31 33 46
53 58 04 11 37 42 20 27
14 01 63 48 30 17 47 32
59 52 10 05 43 36 26 21
02 13 51 60 18 29 35 44
55 56 06 09 39 40 22 25
12 03 61 50 28 19 45 34
57 54 08 07 41 38 24 23
003 panfranklin
#[1,0,2,3,4,5]
_1[0,1,2,3,4,7,6,5]

00 15 49 62 32 30 17 47
51 60 02 13 19 45 34 28
14 01 63 48 46 16 31 33
61 50 12 03 29 35 44 18
04 11 53 58 36 26 21 43
55 56 06 09 23 41 38 24
10 05 59 52 42 20 27 37
57 54 08 07 25 39 40 22
004 panfranklin
#[1,0,3,2,4,5]
_3[0,1,2,3,4,7,6,5]

00 15 49 62 32 30 17 47
51 60 02 13 19 45 34 28
14 01 63 48 46 16 31 33
61 50 12 03 29 35 44 18
08 07 57 54 40 22 25 39
53 58 04 11 21 43 36 26
06 09 55 56 38 24 23 41
59 52 10 05 27 37 42 20
005 panfranklin
#[1,0,2,4,3,5]
_1[0,1,2,3,4,7,6,5]

00 15 49 62 32 30 17 47
53 58 04 11 21 43 36 26
14 01 63 48 46 16 31 33
59 52 10 05 27 37 42 20
02 13 51 60 34 28 19 45
55 56 06 09 23 41 38 24
12 03 61 50 44 18 29 35
57 54 08 07 25 39 40 22
006 panfranklin
#[0,1,2,3,5,4]

00 15 50 61 16 31 34 45
51 60 01 14 35 44 17 30
13 02 63 48 29 18 47 32
62 49 12 03 46 33 28 19
04 11 54 57 20 27 38 41
55 56 05 10 39 40 21 26
09 06 59 52 25 22 43 36
58 53 08 07 42 37 24 23
007 panfranklin
#[0,1,3,2,5,4]
_2[0,1,2,3,4,7,6,5]

00 15 50 61 16 31 34 45
51 60 01 14 35 44 17 30
13 02 63 48 29 18 47 32
62 49 12 03 46 33 28 19
08 07 58 53 24 23 42 37
54 57 04 11 38 41 20 27
05 10 55 56 21 26 39 40
59 52 09 06 43 36 25 22
008 panfranklin
#[0,1,2,5,3,4]

00 15 50 61 16 31 34 45
54 57 04 11 38 41 20 27
13 02 63 48 29 18 47 32
59 52 09 06 43 36 25 22
01 14 51 60 17 30 35 44
55 56 05 10 39 40 21 26
12 03 62 49 28 19 46 33
58 53 08 07 42 37 24 23
009 panfranklin
#[1,0,2,3,5,4]
_1[0,1,2,3,4,7,6,5]

00 15 50 61 32 29 18 47
51 60 01 14 19 46 33 28
13 02 63 48 45 16 31 34
62 49 12 03 30 35 44 17
04 11 54 57 36 25 22 43
55 56 05 10 23 42 37 24
09 06 59 52 41 20 27 38
58 53 08 07 26 39 40 21
010 panfranklin
#[1,0,3,2,5,4]
_3[0,1,2,3,4,7,6,5]

00 15 50 61 32 29 18 47
51 60 01 14 19 46 33 28
13 02 63 48 45 16 31 34
62 49 12 03 30 35 44 17
08 07 58 53 40 21 26 39
54 57 04 11 22 43 36 25
05 10 55 56 37 24 23 42
59 52 09 06 27 38 41 20
011 panfranklin
#[1,0,2,5,3,4]
_1[0,1,2,3,4,7,6,5]

00 15 50 61 32 29 18 47
54 57 04 11 22 43 36 25
13 02 63 48 45 16 31 34
59 52 09 06 27 38 41 20
01 14 51 60 33 28 19 46
55 56 05 10 23 42 37 24
12 03 62 49 44 17 30 35
58 53 08 07 26 39 40 21
012 panfranklin
#[0,1,2,4,5,3]

00 15 52 59 16 31 36 43
53 58 01 14 37 42 17 30
11 04 63 48 27 20 47 32
62 49 10 05 46 33 26 21
02 13 54 57 18 29 38 41
55 56 03 12 39 40 19 28
09 06 61 50 25 22 45 34
60 51 08 07 44 35 24 23
013 panfranklin
#[0,1,4,2,5,3]
_2[0,1,2,3,4,7,6,5]

00 15 52 59 16 31 36 43
53 58 01 14 37 42 17 30
11 04 63 48 27 20 47 32
62 49 10 05 46 33 26 21
08 07 60 51 24 23 44 35
54 57 02 13 38 41 18 29
03 12 55 56 19 28 39 40
61 50 09 06 45 34 25 22
014 panfranklin
#[0,1,2,5,4,3]

00 15 52 59 16 31 36 43
54 57 02 13 38 41 18 29
11 04 63 48 27 20 47 32
61 50 09 06 45 34 25 22
01 14 53 58 17 30 37 42
55 56 03 12 39 40 19 28
10 05 62 49 26 21 46 33
60 51 08 07 44 35 24 23
015 panfranklin
#[1,0,2,4,5,3]
_1[0,1,2,3,4,7,6,5]

00 15 52 59 32 27 20 47
53 58 01 14 21 46 33 26
11 04 63 48 43 16 31 36
62 49 10 05 30 37 42 17
02 13 54 57 34 25 22 45
55 56 03 12 23 44 35 24
09 06 61 50 41 18 29 38
60 51 08 07 28 39 40 19
016 panfranklin
#[1,0,4,2,5,3]
_3[0,1,2,3,4,7,6,5]

00 15 52 59 32 27 20 47
53 58 01 14 21 46 33 26
11 04 63 48 43 16 31 36
62 49 10 05 30 37 42 17
08 07 60 51 40 19 28 39
54 57 02 13 22 45 34 25
03 12 55 56 35 24 23 44
61 50 09 06 29 38 41 18
017 panfranklin
#[1,0,2,5,4,3]
_1[0,1,2,3,4,7,6,5]

00 15 52 59 32 27 20 47
54 57 02 13 22 45 34 25
11 04 63 48 43 16 31 36
61 50 09 06 29 38 41 18
01 14 53 58 33 26 21 46
55 56 03 12 23 44 35 24
10 05 62 49 42 17 30 37
60 51 08 07 28 39 40 19
018 panfranklin
#[0,1,3,4,5,2]

00 15 56 55 16 31 40 39
57 54 01 14 41 38 17 30
07 08 63 48 23 24 47 32
62 49 06 09 46 33 22 25
02 13 58 53 18 29 42 37
59 52 03 12 43 36 19 28
05 10 61 50 21 26 45 34
60 51 04 11 44 35 20 27
019 panfranklin
#[0,1,4,3,5,2]
_2[0,1,2,3,4,7,6,5]

00 15 56 55 16 31 40 39
57 54 01 14 41 38 17 30
07 08 63 48 23 24 47 32
62 49 06 09 46 33 22 25
04 11 60 51 20 27 44 35
58 53 02 13 42 37 18 29
03 12 59 52 19 28 43 36
61 50 05 10 45 34 21 26
020 panfranklin
#[0,1,3,5,4,2]

00 15 56 55 16 31 40 39
58 53 02 13 42 37 18 29
07 08 63 48 23 24 47 32
61 50 05 10 45 34 21 26
01 14 57 54 17 30 41 38
59 52 03 12 43 36 19 28
06 09 62 49 22 25 46 33
60 51 04 11 44 35 20 27
021 panfranklin
#[1,0,3,4,5,2]
_1[0,1,2,3,4,7,6,5]

00 15 56 55 32 23 24 47
57 54 01 14 25 46 33 22
07 08 63 48 39 16 31 40
62 49 06 09 30 41 38 17
02 13 58 53 34 21 26 45
59 52 03 12 27 44 35 20
05 10 61 50 37 18 29 42
60 51 04 11 28 43 36 19
022 panfranklin
#[1,0,4,3,5,2]
_3[0,1,2,3,4,7,6,5]

00 15 56 55 32 23 24 47
57 54 01 14 25 46 33 22
07 08 63 48 39 16 31 40
62 49 06 09 30 41 38 17
04 11 60 51 36 19 28 43
58 53 02 13 26 45 34 21
03 12 59 52 35 20 27 44
61 50 05 10 29 42 37 18
023 panfranklin
#[1,0,3,5,4,2]
_1[0,1,2,3,4,7,6,5]

00 15 56 55 32 23 24 47
58 53 02 13 26 45 34 21
07 08 63 48 39 16 31 40
61 50 05 10 29 42 37 18
01 14 57 54 33 22 25 46
59 52 03 12 27 44 35 20
06 09 62 49 38 17 30 41
60 51 04 11 28 43 36 19
024 panfranklin
#[0,2,1,3,4,5]

00 23 41 62 08 31 33 54
43 60 02 21 35 52 10 29
22 01 63 40 30 09 55 32
61 42 20 03 53 34 28 11
04 19 45 58 12 27 37 50
47 56 06 17 39 48 14 25
18 05 59 44 26 13 51 36
57 46 16 07 49 38 24 15
025 panfranklin
#[0,2,3,1,4,5]
_2[0,1,2,3,4,7,6,5]

00 23 41 62 08 31 33 54
43 60 02 21 35 52 10 29
22 01 63 40 30 09 55 32
61 42 20 03 53 34 28 11
16 07 57 46 24 15 49 38
45 58 04 19 37 50 12 27
06 17 47 56 14 25 39 48
59 44 18 05 51 36 26 13
026 panfranklin
#[0,2,1,4,3,5]

00 23 41 62 08 31 33 54
45 58 04 19 37 50 12 27
22 01 63 40 30 09 55 32
59 44 18 05 51 36 26 13
02 21 43 60 10 29 35 52
47 56 06 17 39 48 14 25
20 03 61 42 28 11 53 34
57 46 16 07 49 38 24 15
027 panfranklin
#[1,3,2,0,5,4]
^[1,0]
_1[0,1,2,3,4,7,6,5]

00 23 41 62 32 30 09 55
43 60 02 21 11 53 34 28
22 01 63 40 54 08 31 33
61 42 20 03 29 35 52 10
04 19 45 58 36 26 13 51
47 56 06 17 15 49 38 24
18 05 59 44 50 12 27 37
57 46 16 07 25 39 48 14
028 panfranklin
#[2,0,3,1,4,5]
_3[0,1,2,3,4,7,6,5]

00 23 41 62 32 30 09 55
43 60 02 21 11 53 34 28
22 01 63 40 54 08 31 33
61 42 20 03 29 35 52 10
16 07 57 46 48 14 25 39
45 58 04 19 13 51 36 26
06 17 47 56 38 24 15 49
59 44 18 05 27 37 50 12
029 panfranklin
#[1,4,2,0,5,3]
^[1,0]
_1[0,1,2,3,4,7,6,5]

00 23 41 62 32 30 09 55
45 58 04 19 13 51 36 26
22 01 63 40 54 08 31 33
59 44 18 05 27 37 50 12
02 21 43 60 34 28 11 53
47 56 06 17 15 49 38 24
20 03 61 42 52 10 29 35
57 46 16 07 25 39 48 14
030 panfranklin
#[0,2,1,3,5,4]

00 23 42 61 08 31 34 53
43 60 01 22 35 52 09 30
21 02 63 40 29 10 55 32
62 41 20 03 54 33 28 11
04 19 46 57 12 27 38 49
47 56 05 18 39 48 13 26
17 06 59 44 25 14 51 36
58 45 16 07 50 37 24 15
031 panfranklin
#[0,2,3,1,5,4]
_2[0,1,2,3,4,7,6,5]

00 23 42 61 08 31 34 53
43 60 01 22 35 52 09 30
21 02 63 40 29 10 55 32
62 41 20 03 54 33 28 11
16 07 58 45 24 15 50 37
46 57 04 19 38 49 12 27
05 18 47 56 13 26 39 48
59 44 17 06 51 36 25 14
032 panfranklin
#[0,2,1,5,3,4]

00 23 42 61 08 31 34 53
46 57 04 19 38 49 12 27
21 02 63 40 29 10 55 32
59 44 17 06 51 36 25 14
01 22 43 60 09 30 35 52
47 56 05 18 39 48 13 26
20 03 62 41 28 11 54 33
58 45 16 07 50 37 24 15
033 panfranklin
#[1,3,2,0,4,5]
^[1,0]
_1[0,1,2,3,4,7,6,5]

00 23 42 61 32 29 10 55
43 60 01 22 11 54 33 28
21 02 63 40 53 08 31 34
62 41 20 03 30 35 52 09
04 19 46 57 36 25 14 51
47 56 05 18 15 50 37 24
17 06 59 44 49 12 27 38
58 45 16 07 26 39 48 13
034 panfranklin
#[2,0,3,1,5,4]
_3[0,1,2,3,4,7,6,5]

00 23 42 61 32 29 10 55
43 60 01 22 11 54 33 28
21 02 63 40 53 08 31 34
62 41 20 03 30 35 52 09
16 07 58 45 48 13 26 39
46 57 04 19 14 51 36 25
05 18 47 56 37 24 15 50
59 44 17 06 27 38 49 12
035 panfranklin
#[1,5,2,0,4,3]
^[1,0]
_1[0,1,2,3,4,7,6,5]

00 23 42 61 32 29 10 55
46 57 04 19 14 51 36 25
21 02 63 40 53 08 31 34
59 44 17 06 27 38 49 12
01 22 43 60 33 28 11 54
47 56 05 18 15 50 37 24
20 03 62 41 52 09 30 35
58 45 16 07 26 39 48 13
036 panfranklin
#[0,2,1,4,5,3]

00 23 44 59 08 31 36 51
45 58 01 22 37 50 09 30
19 04 63 40 27 12 55 32
62 41 18 05 54 33 26 13
02 21 46 57 10 29 38 49
47 56 03 20 39 48 11 28
17 06 61 42 25 14 53 34
60 43 16 07 52 35 24 15
037 panfranklin
#[0,2,4,1,5,3]
_2[0,1,2,3,4,7,6,5]

00 23 44 59 08 31 36 51
45 58 01 22 37 50 09 30
19 04 63 40 27 12 55 32
62 41 18 05 54 33 26 13
16 07 60 43 24 15 52 35
46 57 02 21 38 49 10 29
03 20 47 56 11 28 39 48
61 42 17 06 53 34 25 14
038 panfranklin
#[0,2,1,5,4,3]

00 23 44 59 08 31 36 51
46 57 02 21 38 49 10 29
19 04 63 40 27 12 55 32
61 42 17 06 53 34 25 14
01 22 45 58 09 30 37 50
47 56 03 20 39 48 11 28
18 05 62 41 26 13 54 33
60 43 16 07 52 35 24 15
039 panfranklin
#[1,4,2,0,3,5]
^[1,0]
_1[0,1,2,3,4,7,6,5]

00 23 44 59 32 27 12 55
45 58 01 22 13 54 33 26
19 04 63 40 51 08 31 36
62 41 18 05 30 37 50 09
02 21 46 57 34 25 14 53
47 56 03 20 15 52 35 24
17 06 61 42 49 10 29 38
60 43 16 07 28 39 48 11
040 panfranklin
#[2,0,4,1,5,3]
_3[0,1,2,3,4,7,6,5]

00 23 44 59 32 27 12 55
45 58 01 22 13 54 33 26
19 04 63 40 51 08 31 36
62 41 18 05 30 37 50 09
16 07 60 43 48 11 28 39
46 57 02 21 14 53 34 25
03 20 47 56 35 24 15 52
61 42 17 06 29 38 49 10
041 panfranklin
#[1,5,2,0,3,4]
^[1,0]
_1[0,1,2,3,4,7,6,5]

00 23 44 59 32 27 12 55
46 57 02 21 14 53 34 25
19 04 63 40 51 08 31 36
61 42 17 06 29 38 49 10
01 22 45 58 33 26 13 54
47 56 03 20 15 52 35 24
18 05 62 41 50 09 30 37
60 43 16 07 28 39 48 11
042 panfranklin
#[0,2,3,4,5,1]

00 23 56 47 08 31 48 39
57 46 01 22 49 38 09 30
07 16 63 40 15 24 55 32
62 41 06 17 54 33 14 25
02 21 58 45 10 29 50 37
59 44 03 20 51 36 11 28
05 18 61 42 13 26 53 34
60 43 04 19 52 35 12 27
043 panfranklin
#[0,2,4,3,5,1]
_2[0,1,2,3,4,7,6,5]

00 23 56 47 08 31 48 39
57 46 01 22 49 38 09 30
07 16 63 40 15 24 55 32
62 41 06 17 54 33 14 25
04 19 60 43 12 27 52 35
58 45 02 21 50 37 10 29
03 20 59 44 11 28 51 36
61 42 05 18 53 34 13 26
044 panfranklin
#[0,2,3,5,4,1]

00 23 56 47 08 31 48 39
58 45 02 21 50 37 10 29
07 16 63 40 15 24 55 32
61 42 05 18 53 34 13 26
01 22 57 46 09 30 49 38
59 44 03 20 51 36 11 28
06 17 62 41 14 25 54 33
60 43 04 19 52 35 12 27
045 panfranklin
#[0,3,1,2,4,5]

00 27 37 62 04 31 33 58
39 60 02 25 35 56 06 29
26 01 63 36 30 05 59 32
61 38 24 03 57 34 28 07
08 19 45 54 12 23 41 50
47 52 10 17 43 48 14 21
18 09 55 44 22 13 51 40
53 46 16 11 49 42 20 15
046 panfranklin
#[0,3,2,1,4,5]
_2[0,1,2,3,4,7,6,5]

00 27 37 62 04 31 33 58
39 60 02 25 35 56 06 29
26 01 63 36 30 05 59 32
61 38 24 03 57 34 28 07
16 11 53 46 20 15 49 42
45 54 08 19 41 50 12 23
10 17 47 52 14 21 43 48
55 44 18 09 51 40 22 13
047 panfranklin
#[0,3,1,4,2,5]

00 27 37 62 04 31 33 58
45 54 08 19 41 50 12 23
26 01 63 36 30 05 59 32
55 44 18 09 51 40 22 13
02 25 39 60 06 29 35 56
47 52 10 17 43 48 14 21
24 03 61 38 28 07 57 34
53 46 16 11 49 42 20 15
048 panfranklin
#[1,2,3,0,5,4]
^[1,0]
_1[0,1,2,3,4,7,6,5]

00 27 37 62 32 30 05 59
39 60 02 25 07 57 34 28
26 01 63 36 58 04 31 33
61 38 24 03 29 35 56 06
08 19 45 54 40 22 13 51
47 52 10 17 15 49 42 20
18 09 55 44 50 12 23 41
53 46 16 11 21 43 48 14
049 panfranklin
#[2,1,3,0,5,4]
^[1,0]
_3[0,1,2,3,4,7,6,5]

00 27 37 62 32 30 05 59
39 60 02 25 07 57 34 28
26 01 63 36 58 04 31 33
61 38 24 03 29 35 56 06
16 11 53 46 48 14 21 43
45 54 08 19 13 51 40 22
10 17 47 52 42 20 15 49
55 44 18 09 23 41 50 12
050 panfranklin
#[1,4,3,0,5,2]
^[1,0]
_1[0,1,2,3,4,7,6,5]

00 27 37 62 32 30 05 59
45 54 08 19 13 51 40 22
26 01 63 36 58 04 31 33
55 44 18 09 23 41 50 12
02 25 39 60 34 28 07 57
47 52 10 17 15 49 42 20
24 03 61 38 56 06 29 35
53 46 16 11 21 43 48 14
051 panfranklin
#[0,3,1,2,5,4]

00 27 38 61 04 31 34 57
39 60 01 26 35 56 05 30
25 02 63 36 29 06 59 32
62 37 24 03 58 33 28 07
08 19 46 53 12 23 42 49
47 52 09 18 43 48 13 22
17 10 55 44 21 14 51 40
54 45 16 11 50 41 20 15
052 panfranklin
#[0,3,2,1,5,4]
_2[0,1,2,3,4,7,6,5]

00 27 38 61 04 31 34 57
39 60 01 26 35 56 05 30
25 02 63 36 29 06 59 32
62 37 24 03 58 33 28 07
16 11 54 45 20 15 50 41
46 53 08 19 42 49 12 23
09 18 47 52 13 22 43 48
55 44 17 10 51 40 21 14
053 panfranklin
#[0,3,1,5,2,4]

00 27 38 61 04 31 34 57
46 53 08 19 42 49 12 23
25 02 63 36 29 06 59 32
55 44 17 10 51 40 21 14
01 26 39 60 05 30 35 56
47 52 09 18 43 48 13 22
24 03 62 37 28 07 58 33
54 45 16 11 50 41 20 15
054 panfranklin
#[1,2,3,0,4,5]
^[1,0]
_1[0,1,2,3,4,7,6,5]

00 27 38 61 32 29 06 59
39 60 01 26 07 58 33 28
25 02 63 36 57 04 31 34
62 37 24 03 30 35 56 05
08 19 46 53 40 21 14 51
47 52 09 18 15 50 41 20
17 10 55 44 49 12 23 42
54 45 16 11 22 43 48 13
055 panfranklin
#[2,1,3,0,4,5]
^[1,0]
_3[0,1,2,3,4,7,6,5]

00 27 38 61 32 29 06 59
39 60 01 26 07 58 33 28
25 02 63 36 57 04 31 34
62 37 24 03 30 35 56 05
16 11 54 45 48 13 22 43
46 53 08 19 14 51 40 21
09 18 47 52 41 20 15 50
55 44 17 10 23 42 49 12
056 panfranklin
#[1,5,3,0,4,2]
^[1,0]
_1[0,1,2,3,4,7,6,5]

00 27 38 61 32 29 06 59
46 53 08 19 14 51 40 21
25 02 63 36 57 04 31 34
55 44 17 10 23 42 49 12
01 26 39 60 33 28 07 58
47 52 09 18 15 50 41 20
24 03 62 37 56 05 30 35
54 45 16 11 22 43 48 13
057 panfranklin
#[0,3,1,4,5,2]

00 27 44 55 04 31 40 51
45 54 01 26 41 50 05 30
19 08 63 36 23 12 59 32
62 37 18 09 58 33 22 13
02 25 46 53 06 29 42 49
47 52 03 24 43 48 07 28
17 10 61 38 21 14 57 34
60 39 16 11 56 35 20 15
058 panfranklin
#[0,3,4,1,5,2]
_2[0,1,2,3,4,7,6,5]

00 27 44 55 04 31 40 51
45 54 01 26 41 50 05 30
19 08 63 36 23 12 59 32
62 37 18 09 58 33 22 13
16 11 60 39 20 15 56 35
46 53 02 25 42 49 06 29
03 24 47 52 07 28 43 48
61 38 17 10 57 34 21 14
059 panfranklin
#[0,3,1,5,4,2]

00 27 44 55 04 31 40 51
46 53 02 25 42 49 06 29
19 08 63 36 23 12 59 32
61 38 17 10 57 34 21 14
01 26 45 54 05 30 41 50
47 52 03 24 43 48 07 28
18 09 62 37 22 13 58 33
60 39 16 11 56 35 20 15
060 panfranklin
#[0,3,2,4,5,1]

00 27 52 47 04 31 48 43
53 46 01 26 49 42 05 30
11 16 63 36 15 20 59 32
62 37 10 17 58 33 14 21
02 25 54 45 06 29 50 41
55 44 03 24 51 40 07 28
09 18 61 38 13 22 57 34
60 39 08 19 56 35 12 23
061 panfranklin
#[0,3,4,2,5,1]
_2[0,1,2,3,4,7,6,5]

00 27 52 47 04 31 48 43
53 46 01 26 49 42 05 30
11 16 63 36 15 20 59 32
62 37 10 17 58 33 14 21
08 19 60 39 12 23 56 35
54 45 02 25 50 41 06 29
03 24 55 44 07 28 51 40
61 38 09 18 57 34 13 22
062 panfranklin
#[0,3,2,5,4,1]

00 27 52 47 04 31 48 43
54 45 02 25 50 41 06 29
11 16 63 36 15 20 59 32
61 38 09 18 57 34 13 22
01 26 53 46 05 30 49 42
55 44 03 24 51 40 07 28
10 17 62 37 14 21 58 33
60 39 08 19 56 35 12 23
063 panfranklin
#[0,4,1,2,3,5]

00 29 35 62 02 31 33 60
39 58 04 25 37 56 06 27
28 01 63 34 30 03 61 32
59 38 24 05 57 36 26 07
08 21 43 54 10 23 41 52
47 50 12 17 45 48 14 19
20 09 55 42 22 11 53 40
51 46 16 13 49 44 18 15
064 panfranklin
#[0,4,2,1,3,5]
_2[0,1,2,3,4,7,6,5]

00 29 35 62 02 31 33 60
39 58 04 25 37 56 06 27
28 01 63 34 30 03 61 32
59 38 24 05 57 36 26 07
16 13 51 46 18 15 49 44
43 54 08 21 41 52 10 23
12 17 47 50 14 19 45 48
55 42 20 09 53 40 22 11
065 panfranklin
#[0,4,1,3,2,5]

00 29 35 62 02 31 33 60
43 54 08 21 41 52 10 23
28 01 63 34 30 03 61 32
55 42 20 09 53 40 22 11
04 25 39 58 06 27 37 56
47 50 12 17 45 48 14 19
24 05 59 38 26 07 57 36
51 46 16 13 49 44 18 15
066 panfranklin
#[1,2,4,0,5,3]
^[1,0]
_1[0,1,2,3,4,7,6,5]

00 29 35 62 32 30 03 61
39 58 04 25 07 57 36 26
28 01 63 34 60 02 31 33
59 38 24 05 27 37 56 06
08 21 43 54 40 22 11 53
47 50 12 17 15 49 44 18
20 09 55 42 52 10 23 41
51 46 16 13 19 45 48 14
067 panfranklin
#[2,1,4,0,5,3]
^[1,0]
_3[0,1,2,3,4,7,6,5]

00 29 35 62 32 30 03 61
39 58 04 25 07 57 36 26
28 01 63 34 60 02 31 33
59 38 24 05 27 37 56 06
16 13 51 46 48 14 19 45
43 54 08 21 11 53 40 22
12 17 47 50 44 18 15 49
55 42 20 09 23 41 52 10
068 panfranklin
#[1,3,4,0,5,2]
^[1,0]
_1[0,1,2,3,4,7,6,5]

00 29 35 62 32 30 03 61
43 54 08 21 11 53 40 22
28 01 63 34 60 02 31 33
55 42 20 09 23 41 52 10
04 25 39 58 36 26 07 57
47 50 12 17 15 49 44 18
24 05 59 38 56 06 27 37
51 46 16 13 19 45 48 14
069 panfranklin
#[0,4,1,2,5,3]

00 29 38 59 02 31 36 57
39 58 01 28 37 56 03 30
25 04 63 34 27 06 61 32
62 35 24 05 60 33 26 07
08 21 46 51 10 23 44 49
47 50 09 20 45 48 11 22
17 12 55 42 19 14 53 40
54 43 16 13 52 41 18 15
070 panfranklin
#[0,4,2,1,5,3]
_2[0,1,2,3,4,7,6,5]

00 29 38 59 02 31 36 57
39 58 01 28 37 56 03 30
25 04 63 34 27 06 61 32
62 35 24 05 60 33 26 07
16 13 54 43 18 15 52 41
46 51 08 21 44 49 10 23
09 20 47 50 11 22 45 48
55 42 17 12 53 40 19 14
071 panfranklin
#[0,4,1,5,2,3]

00 29 38 59 02 31 36 57
46 51 08 21 44 49 10 23
25 04 63 34 27 06 61 32
55 42 17 12 53 40 19 14
01 28 39 58 03 30 37 56
47 50 09 20 45 48 11 22
24 05 62 35 26 07 60 33
54 43 16 13 52 41 18 15
072 panfranklin
#[0,4,1,3,5,2]

00 29 42 55 02 31 40 53
43 54 01 28 41 52 03 30
21 08 63 34 23 10 61 32
62 35 20 09 60 33 22 11
04 25 46 51 06 27 44 49
47 50 05 24 45 48 07 26
17 12 59 38 19 14 57 36
58 39 16 13 56 37 18 15
073 panfranklin
#[0,4,3,1,5,2]
_2[0,1,2,3,4,7,6,5]

00 29 42 55 02 31 40 53
43 54 01 28 41 52 03 30
21 08 63 34 23 10 61 32
62 35 20 09 60 33 22 11
16 13 58 39 18 15 56 37
46 51 04 25 44 49 06 27
05 24 47 50 07 26 45 48
59 38 17 12 57 36 19 14
074 panfranklin
#[0,4,1,5,3,2]

00 29 42 55 02 31 40 53
46 51 04 25 44 49 06 27
21 08 63 34 23 10 61 32
59 38 17 12 57 36 19 14
01 28 43 54 03 30 41 52
47 50 05 24 45 48 07 26
20 09 62 35 22 11 60 33
58 39 16 13 56 37 18 15
075 panfranklin
#[0,4,2,3,5,1]

00 29 50 47 02 31 48 45
51 46 01 28 49 44 03 30
13 16 63 34 15 18 61 32
62 35 12 17 60 33 14 19
04 25 54 43 06 27 52 41
55 42 05 24 53 40 07 26
09 20 59 38 11 22 57 36
58 39 08 21 56 37 10 23
076 panfranklin
#[0,4,3,2,5,1]
_2[0,1,2,3,4,7,6,5]

00 29 50 47 02 31 48 45
51 46 01 28 49 44 03 30
13 16 63 34 15 18 61 32
62 35 12 17 60 33 14 19
08 21 58 39 10 23 56 37
54 43 04 25 52 41 06 27
05 24 55 42 07 26 53 40
59 38 09 20 57 36 11 22
077 panfranklin
#[0,4,2,5,3,1]

00 29 50 47 02 31 48 45
54 43 04 25 52 41 06 27
13 16 63 34 15 18 61 32
59 38 09 20 57 36 11 22
01 28 51 46 03 30 49 44
55 42 05 24 53 40 07 26
12 17 62 35 14 19 60 33
58 39 08 21 56 37 10 23
078 panfranklin
#[0,5,1,2,3,4]

00 30 35 61 01 31 34 60
39 57 04 26 38 56 05 27
28 02 63 33 29 03 62 32
59 37 24 06 58 36 25 07
08 22 43 53 09 23 42 52
47 49 12 18 46 48 13 19
20 10 55 41 21 11 54 40
51 45 16 14 50 44 17 15
079 panfranklin
#[0,5,2,1,3,4]
_2[0,1,2,3,4,7,6,5]

00 30 35 61 01 31 34 60
39 57 04 26 38 56 05 27
28 02 63 33 29 03 62 32
59 37 24 06 58 36 25 07
16 14 51 45 17 15 50 44
43 53 08 22 42 52 09 23
12 18 47 49 13 19 46 48
55 41 20 10 54 40 21 11
080 panfranklin
#[0,5,1,3,2,4]

00 30 35 61 01 31 34 60
43 53 08 22 42 52 09 23
28 02 63 33 29 03 62 32
55 41 20 10 54 40 21 11
04 26 39 57 05 27 38 56
47 49 12 18 46 48 13 19
24 06 59 37 25 07 58 36
51 45 16 14 50 44 17 15
081 panfranklin
#[0,5,1,2,4,3]

00 30 37 59 01 31 36 58
39 57 02 28 38 56 03 29
26 04 63 33 27 05 62 32
61 35 24 06 60 34 25 07
08 22 45 51 09 23 44 50
47 49 10 20 46 48 11 21
18 12 55 41 19 13 54 40
53 43 16 14 52 42 17 15
082 panfranklin
#[0,5,2,1,4,3]
_2[0,1,2,3,4,7,6,5]

00 30 37 59 01 31 36 58
39 57 02 28 38 56 03 29
26 04 63 33 27 05 62 32
61 35 24 06 60 34 25 07
16 14 53 43 17 15 52 42
45 51 08 22 44 50 09 23
10 20 47 49 11 21 46 48
55 41 18 12 54 40 19 13
083 panfranklin
#[0,5,1,4,2,3]

00 30 37 59 01 31 36 58
45 51 08 22 44 50 09 23
26 04 63 33 27 05 62 32
55 41 18 12 54 40 19 13
02 28 39 57 03 29 38 56
47 49 10 20 46 48 11 21
24 06 61 35 25 07 60 34
53 43 16 14 52 42 17 15
084 panfranklin
#[0,5,1,3,4,2]

00 30 41 55 01 31 40 54
43 53 02 28 42 52 03 29
22 08 63 33 23 09 62 32
61 35 20 10 60 34 21 11
04 26 45 51 05 27 44 50
47 49 06 24 46 48 07 25
18 12 59 37 19 13 58 36
57 39 16 14 56 38 17 15
085 panfranklin
#[0,5,3,1,4,2]
_2[0,1,2,3,4,7,6,5]

00 30 41 55 01 31 40 54
43 53 02 28 42 52 03 29
22 08 63 33 23 09 62 32
61 35 20 10 60 34 21 11
16 14 57 39 17 15 56 38
45 51 04 26 44 50 05 27
06 24 47 49 07 25 46 48
59 37 18 12 58 36 19 13
086 panfranklin
#[0,5,1,4,3,2]

00 30 41 55 01 31 40 54
45 51 04 26 44 50 05 27
22 08 63 33 23 09 62 32
59 37 18 12 58 36 19 13
02 28 43 53 03 29 42 52
47 49 06 24 46 48 07 25
20 10 61 35 21 11 60 34
57 39 16 14 56 38 17 15
087 panfranklin
#[0,5,2,3,4,1]

00 30 49 47 01 31 48 46
51 45 02 28 50 44 03 29
14 16 63 33 15 17 62 32
61 35 12 18 60 34 13 19
04 26 53 43 05 27 52 42
55 41 06 24 54 40 07 25
10 20 59 37 11 21 58 36
57 39 08 22 56 38 09 23
088 panfranklin
#[0,5,3,2,4,1]
_2[0,1,2,3,4,7,6,5]

00 30 49 47 01 31 48 46
51 45 02 28 50 44 03 29
14 16 63 33 15 17 62 32
61 35 12 18 60 34 13 19
08 22 57 39 09 23 56 38
53 43 04 26 52 42 05 27
06 24 55 41 07 25 54 40
59 37 10 20 58 36 11 21
089 panfranklin
#[0,5,2,4,3,1]

00 30 49 47 01 31 48 46
53 43 04 26 52 42 05 27
14 16 63 33 15 17 62 32
59 37 10 20 58 36 11 21
02 28 51 45 03 29 50 44
55 41 06 24 54 40 07 25
12 18 61 35 13 19 60 34
57 39 08 22 56 38 09 23