Catalog of CHM
Appendix A: CHM Characteristics
created: 2019-07-08
updated: 2023-02-27 by W. Bruzda
This is an informal appendix to the Catalog of Complex Hadamard Matrices containing additional information about defect and Haagerup invariants for a particular CHM. Another characterization of CHM with respect to their internal symmetry is summarized in Appendix C containig a collection of symmetric (Hermitian) CHM.
For every isolated matrix H we provide its defect; d(H), and cardinality of Haagerup invariants; #Λ(H). Other matrix fingerprints defined by F. Szöllősi are yet to be calculated. In case of families, (almost) every known matrix H = H(p) was probed by drawing its internal parameters p = (p1, ..., pk) at random, where every pj was of the form pj = nj / dj for some non-negative integers nj < dj; of course these parameters are not unique and for a given (d, #Λ) one can easily find different p's which recover such a pair. For every matrix the lists of pairs (d, #Λ) are apparently more than incomplete, although, in many cases one can guess what value of defect, or (rather) #Λ, is probably missing. Anyway, it proved to be quite helpful during the searching and identifying new CHM, as one can quickly compare whether a new matrix might be the one from the set presented below. For instance, if one can find an 11-dim. matrix H with d(H) > 0, it is very likely, it is something new! ;)
Generic values of families are marked with pj = rj ∈ [0, 1) and a star *. If you can, please help us to fill the gaps, either by providing a particular vector of parameters, or by a formal algebraic explanation which can replace some or all of these lame tables. The most wanted solution is to provide fully theoretical prediction and explanation of all numbers described below or to prove impossibility of such a thing...
table of contents
- Isolated Matrices or "Non-Families" (including unknown cases)
- Butson-Type Families grouped by a type
- 2.1. Fourier CHM
- 2.2. Other BH-type Matrices
- Non-BH-Type Matrices
- Defect of BH-Type Matrices
1. Isolated Matrices or "Non-Families"
In this section we list CHM H which are explicitly isolated (vanishing defect), or those for which d(H) > 0 but they are either implicitly isolated or it remains an open task whether they really admit free parameters.
This table does not (yet) include isolated matrices LN and VN – see J. Math. Phys. 64, 052201 (2023) (arXiv:2204.11727). Also, defects of BH matrices from Butson Home (without #Λ's) have been calculated separately.
| H | defect(H) | #Λ(H) | comment |
|---|---|---|---|
| F2 | 0 | 2 | BH(2, 2) |
| F3 | 0 | 3 | BH(3, 3) |
| F5 | 0 | 5 | BH(5, 5) |
| S6 | 0 | 3 | BH(6, 3) |
| C7A | 0 | 5 | all known CHM of order 7 can be rediscovered by the Sinkhorn algorithm; all of them can be symmetrized |
| C7B | 0 | 5 | |
| F7 | 0 | 7 | BH(7, 7) |
| C7C | 0 | 43 | |
| C7D | 0 | 43 | |
| Q7 | 0 | 97 | |
| A8 | 0 | 10 | |
| S9 | 0 | 6 | BH(9, 6) |
| N9 | 0 | 18 | |
| Y9,0,76 | 0 | 76 | not included in the Catalog; see here how to decode the symbols in YN,d,L |
| Y9,0,89 | 0 | 89 | not included in the Catalog |
| Y9,0,105 | 0 | 105 | a.k.a. Y9 |
| Y9,0,201 | 0 | 201 | not included in the Catalog |
| Y9,0,625 | 0 | 625 | not included in the Catalog |
| B9 | 2 | 10 | isolated BH(9, 10) |
| S10 | 0 | 5 | BH(10, 5) |
| Y9,0,6 | 0 | 6 | not included in the Catalog |
| N10A | 0 | 9 | |
| N10C | 0 | 10 | |
| Y10,0,99 | 0 | 99 | not included in the Catalog |
| Y10,0,143 | 0 | 143 | not included in the Catalog |
| Y10,d,... | 0 | ... | there are many other 10-dim. matrices found by the Sinkhorn algorithm with different #Λ's |
| C11A | 0 | 5 | all known CHM of order 7 can be rediscovered by the Sinkhorn algorithm; all of them can be symmetrized |
| C11B | 0 | 5 | |
| N11A | 0 | 10 | |
| N11B | 0 | 10 | |
| F11 | 0 | 11 | BH(11, 11) |
| Q11A | 0 | 63 | |
| Q11B | 0 | 63 | |
| Y11,0,... | 0 | ... | there are many other 11-dim. matrices found by the Sinkhorn algorithm with different #Λ's |
| M13A | 0 | 6 | BH(13, 6) |
| C13A | 0 | 9 | |
| C13B | 0 | 9 | |
| F13 | 0 | 13 | BH(13, 13) |
| S14 | 0 | 7 | BH(14, 7) |
| C14 | 0 | 9 | not included in the Catalog |
| L14Σ | 0 | ... | |
| A15A | 0 | 5 | |
| A15B | 0 | 5 | |
| A15G | 0 | 38 | |
| A15H | 0 | 38 | |
| A15E | 10 | 9 | |
| A15F | 10 | 9 | |
| A15C | 16 | 10 | |
| A15D | 16 | 10 |
2. Butson-Type Families (grouped roughly by type)
2.1. Fourier Matrices
Fourier matrices are special cases of Butson-type matrices; ∀ N : FN ∈ BH(N, N). For prime dimension they are isolated – cf. Section: Isolated Matrices.... All Fouriers listed below have composite dimension and all of them stem from the symmetric origin; [FN]jk = exp{2 π i (j - 1) (k - 1) / N}. In each case, every parameter is normalized to the unit interval; pj ∈ [0, 1).
F4(p1)↑
show data
p1 d #Λ ----------------- 0 1 4 1/3 1 6 r1 1 6* ----------------- 1/4 3 2 -----------------
F6(p1, p2)↑
show data
p1 p2 d #Λ -------------------------- 0 0 4 6 1/2 3/4 4 12 7/9 13/18 4 16 3/11 1/3 4 18 5/8 3/4 4 22 13/15 11/15 4 28 9/11 11/12 4 34 13/20 3/5 4 40 r1 r1 4 40* --------------------------
F8(p1, p2, p3, p4, p5)↑
show data
p1 p2 p3 p4 p5 d #Λ -------------------------------------------------- 1/2 0 0 0 0 5 8 2/5 0 1/8 0 2/5 5 12 0 0 1/8 0 1/16 5 16 5/6 2/3 0 2/3 0 5 18 5/6 1/2 0 1/2 0 5 20 2/3 5/6 1/2 1/12 1/4 5 22 8/13 3/8 3/8 0 3/4 5 24 4/5 1/8 1/2 1/5 1/2 5 26 2/7 0 5/6 1/2 2/3 5 28 1/2 3/8 1/8 2/5 1/10 5 30 1/2 1/2 4/5 2/5 0 5 32 2/5 4/5 1/5 5/8 0 5 34 0 0 3/16 0 2/3 5 36 0 4/5 5/16 7/16 15/16 5 38 1/2 0 2/3 11/13 1/2 5 40 5/11 5/8 1/8 7/12 0 5 42 2/3 0 2/5 2/11 2/3 5 44 2/5 1/7 0 1/7 1/2 5 46 1/6 0 0 4/5 1/2 5 48 2/15 2/5 3/5 1/3 1/4 5 50 9/10 0 5/8 12/13 6/13 5 52 1/4 1/8 3/7 1/14 5/14 5 54 2/5 0 7/12 2/5 1/8 5 56 1/3 2/15 1/6 9/16 0 5 58 1/8 3/16 1/6 1/2 2/15 5 60 3/5 1/6 0 3/5 3/7 5 62 2/7 1/2 6/7 2/9 1/7 5 64 2/5 2/5 1/3 1/11 1/15 5 66 2/5 1/2 3/5 1/3 1/2 5 68 0 7/16 1/12 7/11 2/3 5 70 0 0 9/14 3/16 3/5 5 72 4/5 10/13 3/16 2/5 1/2 5 74 9/13 2/15 3/5 7/8 0 5 76 3/4 2/11 4/9 1/3 2/3 5 78 8/11 0 5/11 4/5 4/7 5 80 3/4 1/6 3/7 4/9 1/11 5 82 r1 r2 r3 r4 r5 5 82* -------------------------------------------------- 1/8 1/2 3/4 2/3 3/4 6 24 -------------------------------------------------- 0 1/8 0 1/8 1/2 7 8 7/10 0 1/8 0 1/8 7 12 0 3/4 1/3 2/3 1/3 7 14 1/2 0 0 5/16 3/4 7 16 1/3 3/4 0 1/3 0 7 18 0 0 0 3/4 1/3 7 20 11/12 2/3 1/4 1/4 0 7 22 3/10 0 3/4 3/4 1/2 7 24 1/14 14/15 7/15 3/4 1/8 7 26 5/8 3/4 8/15 0 1/7 7 28 9/11 3/4 0 1/8 2/5 7 30 1/4 0 0 3/7 5/14 7 32 8/11 1/6 0 3/4 1/2 7 34 3/4 1/2 8/9 1/4 11/16 7 36 11/13 3/4 1/4 8/11 0 7 38 0 2/7 2/5 0 3/4 7 40 1/7 1/15 0 1/4 5/14 7 42 5/8 1/4 1/3 13/14 1/5 7 44 2/3 12/13 6/7 3/4 1/2 7 46 -------------------------------------------------- 3/8 0 5/8 0 3/4 8 8 0 3/4 0 1/8 5/16 8 16 3/8 2/3 1/4 3/4 1/2 8 18 0 3/4 0 11/15 1/2 8 20 0 0 5/12 5/6 3/4 8 24 0 4/5 1/2 2/5 1/4 8 32 5/12 3/4 7/12 0 11/14 8 36 -------------------------------------------------- 1/4 1/4 0 1/2 1/4 9 8 0 1/6 3/4 2/3 3/4 9 14 0 0 0 1/16 5/16 9 16 1/4 3/5 1/2 2/5 0 9 18 0 0 6/11 1/4 1/4 9 20 5/16 3/4 1/2 3/4 4/7 9 22 1/3 0 1/3 7/12 0 9 24 6/13 1/4 5/13 3/4 0 9 26 -------------------------------------------------- 0 0 3/4 1/4 3/8 10 8 3/8 2/5 5/8 1/2 1/8 10 12 8/11 1/4 5/8 3/4 0 10 14 -------------------------------------------------- 7/8 3/4 2/3 3/4 7/12 11 6 1/2 3/4 0 1/2 1/2 11 8 0 1/4 3/5 1/4 1/4 11 14 -------------------------------------------------- 3/4 1/4 0 1/4 0 13 6 --------------------------------------------------
F9(p1, p2, p3, p4)↑
show data
p1 p2 p3 p4 d #Λ
------------------------------------------
0 0 0 0 4 9
1/6 2/3 2/3 1/9 4 15
1/2 2/3 8/9 1/2 4 18
4/23 5/7 7/9 2/9 4 21
8/9 1/4 1/4 0 4 24
2/3 0 7/8 7/9 4 27
3/4 1/4 7/9 2/3 4 30
2/3 1/2 5/7 0 4 33
1/3 8/21 8/9 1/6 4 36
12/17 6/19 7/9 2/3 4 39
1/2 0 1/16 13/18 4 42
1/4 5/6 4/5 1/2 4 45
3/22 5/9 7/22 1/2 4 48
2/3 2/5 3/4 3/8 4 51
2/11 11/18 7/10 2/3 4 54
0 1/5 4/7 5/23 4 57
r1 r2 r3 r4 4 57*
------------------------------------------
5/9 0 0 7/9 6 9
0 1/2 1/3 0 6 15
1/18 0 0 4/9 6 18
0 1/7 6/7 2/3 6 21
0 1/6 0 3/4 6 27
1/3 0 4/5 9/10 6 33
6 36 observed but not recorded
4/5 1/6 1/2 1/5 6 39
1/2 0 2/5 14/15 6 45
0 1/2 1/4 13/24 6 51
5/7 5/7 4/7 5/6 6 57
------------------------------------------
5/9 1/3 7/9 1/3 8 9
2/9 4/9 1/2 0 8 15
0 1/18 4/9 1/3 8 18
------------------------------------------
0 0 1/3 0 10 9
0 1/2 5/6 0 10 15
5/8 0 2/3 3/8 10 21
------------------------------------------
0 1/9 2/9 0 12 9
------------------------------------------
F10(p1, p2, p3, p4)↑
show data
p1 p2 p3 p4 d #Λ ------------------------------------------ 0 0 0 0 8 10 3/4 3/5 11/20 1/2 8 20 4/5 1/2 1/16 3/10 8 30 1/2 1/4 2/5 7/8 8 40 2/7 1/7 0 0 8 50 4/11 0 0 3/4 8 60 1/11 15/17 0 1/2 8 70 3/4 3/5 3/14 2/7 8 80 4/9 2/9 1/3 2/3 8 86 2/3 13/19 0 1/3 8 90 1/4 3/4 1/3 5/8 8 100 4/17 1/2 1/7 5/14 8 110 1/3 1/4 7/8 2/3 8 116 3/4 9/13 0 5/14 8 120 5/8 1/6 3/7 3/5 8 130 5/12 2/3 8/9 3/4 8 136 1/7 11/15 4/7 3/7 8 146 1/4 3/7 1/14 7/18 8 156 5/9 1/6 5/6 1/8 8 166 6/11 1/4 11/15 5/8 8 176 5/7 17/19 18/19 8/11 8 186 4/7 6/7 4/17 1/4 8 196 5/18 15/19 5/13 4/9 8 206 r1 r2 r3 r4 8 206* ------------------------------------------
F12A(p1, ..., p9)↑
show data
p1 p2 p3 p4 p5 p6 p7 p8 p9 d #Λ ----------------------------------------------------------------------------------- 1/2 1/2 0 2/3 0 1/3 2/3 0 0 17 12 0 1/3 1/3 1/5 0 3/4 3/4 0 1/4 17 32 0 0 0 1/2 5/6 0 0 7/13 1/4 17 36 1/2 0 0 0 1/2 3/5 1/2 0 2/5 17 40 2/3 3/5 0 1/4 2/5 0 1/2 0 1/2 17 44 0 0 4/5 2/3 1/5 1/4 0 0 0 17 48 0 3/4 2/5 1/2 0 2/3 2/5 2/5 0 17 52 3/4 1/2 1/2 2/5 3/5 0 3/5 3/5 0 17 56 0 3/4 3/4 5/9 2/3 6/11 2/3 3/4 1/3 17 76 3/20 1/3 19/20 1/5 4/5 5/12 1/10 1/4 3/4 17 60 0 5/8 11/12 0 0 1/2 5/22 1/12 1/3 17 64 1/6 3/5 0 7/20 0 1/4 1/2 5/8 1/12 17 68 0 1/4 0 11/12 0 7/16 0 3/7 0 17 72 1/2 0 0 1/3 7/12 2/3 1/3 19/22 7/9 17 80 2/3 0 1/23 1/6 1/4 11/20 1/2 7/15 0 17 84 2/3 0 3/5 15/23 1/4 0 0 0 2/5 17 88 0 4/15 2/9 1/6 1/4 11/18 0 2/9 3/4 17 96 1/6 0 1/4 8/9 1/4 20/21 0 2/3 2/7 17 100 1/2 7/8 1/2 2/3 15/23 1/3 1/2 5/7 0 17 108 0 9/11 5/12 2/3 7/8 9/19 2/3 0 0 17 112 0 0 1/6 0 2/3 3/5 10/11 1/2 11/17 17 116 1/2 0 1/6 8/15 2/3 7/22 1/2 3/16 1/2 17 120 2/5 0 4/17 0 1/4 2/5 1/5 0 0 17 124 1/6 3/4 3/5 7/10 2/11 3/20 2/5 2/3 0 17 128 7/9 1/8 0 0 1/2 1/8 3/8 1/2 3/7 17 132 0 7/10 5/8 1/2 2/3 5/8 8/11 1/3 0 17 136 1/6 1/3 3/5 10/23 3/7 0 3/4 1/2 1/3 17 140 1/3 5/9 4/11 1/3 7/9 4/13 1/2 1/2 0 17 144 2/3 0 8/11 5/16 0 8/11 1/2 2/3 4/9 17 148 16/19 2/3 1/4 5/6 1/2 1/7 1/12 1/3 6/11 17 152 10/11 1/15 0 1/2 4/7 3/5 1/2 0 1/2 17 156 1/16 1/4 10/13 1/3 7/11 1/3 2/3 7/11 1/2 17 160 1/2 5/9 5/9 1/9 10/17 1/2 9/19 0 1/3 17 164 4/11 1/2 3/5 0 7/12 1/24 4/9 3/8 3/4 17 166 6/7 10/11 9/10 2/3 0 11/15 1/6 0 11/21 17 168 11/19 1/3 5/6 0 10/13 1/3 13/18 0 3/10 17 172 5/14 1/2 3/5 1/2 6/19 1/3 1/12 1/20 1/5 17 174 4/5 2/3 2/5 2/3 2/19 0 2/5 2/5 6/11 17 176 1/2 1/10 5/9 9/20 3/4 1/2 16/21 2/3 0 17 180 1/2 16/21 16/19 0 5/9 1/2 4/13 1/3 0 17 184 3/4 0 5/24 6/13 11/14 19/20 7/12 0 2/7 17 186 0 2/17 3/4 3/4 2/9 2/3 3/16 5/8 1/2 17 188 3/10 1/8 5/6 6/17 0 9/10 1/3 5/8 0 17 190 1/6 2/13 4/13 0 0 3/4 4/11 7/9 1/2 17 192 4/7 1/3 3/20 1/2 1/17 11/15 1/5 2/3 2/5 17 194 1/2 14/15 5/7 1/3 16/21 2/3 4/11 0 1/14 17 196 3/4 5/11 3/8 0 8/13 1/3 5/9 0 7/20 17 198 1/3 3/19 6/7 1/3 1/2 13/18 1/6 1/4 6/11 17 200 1/5 9/16 0 2/3 5/6 4/7 3/5 3/5 0 17 204 7/9 1/6 19/23 0 1/4 1/10 17/20 7/10 5/8 17 206 0 3/22 4/5 2/3 4/9 5/18 4/15 1/2 0 17 208 4/11 1/6 1/5 1/11 3/4 0 4/7 0 7/16 17 210 4/11 0 1/2 13/23 6/7 1/6 0 3/7 2/3 17 212 0 17/18 8/9 6/19 2/11 5/11 2/3 2/3 0 17 214 1/4 1/3 9/11 1/7 1/3 0 8/13 17/19 0 17 216 2/17 3/14 5/24 1/3 11/16 0 5/24 7/16 2/3 17 218 1/17 1/16 0 1/4 0 9/17 13/15 1/2 1/6 17 220 3/4 11/14 0 11/12 1/2 15/17 0 10/11 2/5 17 224 3/23 1/3 1/5 4/5 2/3 2/3 1/6 4/15 4/13 17 226 6/7 5/9 1/3 1/6 0 20/23 13/16 1/6 2/3 17 228 0 5/9 19/20 8/11 1/2 1/8 2/3 9/16 1/2 17 230 0 5/14 9/10 1/8 2/5 3/4 0 1/7 16/21 17 232 8/23 5/12 0 0 5/7 1/5 1/4 1/4 9/14 17 236 3/5 2/21 2/3 8/15 4/7 1/9 3/5 1/2 1/2 17 238 21/23 0 1/5 7/24 0 7/10 0 5/6 9/23 17 240 5/8 1/3 15/19 0 3/7 4/5 1/2 0 11/13 17 244 9/16 2/7 4/7 1/5 3/8 0 4/21 2/3 1/4 17 246 1/6 5/17 6/7 1/21 6/7 0 5/13 2/3 2/5 17 248 2/5 0 1/10 14/19 10/21 2/3 3/8 0 3/7 17 250 5/6 5/11 0 13/18 10/11 1/3 9/14 9/19 2/3 17 252 0 0 3/5 14/17 7/11 5/19 3/8 0 1/2 17 256 5/9 0 7/10 5/6 4/15 2/3 5/8 5/7 1/7 17 258 3/5 1/3 3/8 5/14 9/14 0 2/7 3/5 0 17 260 3/7 5/13 3/4 5/9 4/7 0 4/11 1/3 11/20 17 262 10/21 1/5 0 0 13/23 2/3 10/19 7/20 1/7 17 264 2/3 3/4 2/3 7/8 1/5 3/11 1/19 9/19 1/3 17 268 1/22 5/11 10/11 0 4/7 5/8 7/8 0 1/21 17 270 1/4 3/13 0 15/16 7/8 0 13/14 9/10 0 17 272 1/6 17/19 6/11 3/4 1/2 1/7 1/6 3/20 5/8 17 276 2/13 4/5 1/4 2/3 6/11 0 17/22 3/5 3/13 17 278 5/7 20/21 1/8 16/23 9/11 1/2 1/2 3/22 0 17 280 0 23/24 15/16 7/9 1/2 11/24 6/17 17/20 8/9 17 282 21/23 1/20 0 3/4 3/4 1/2 10/11 5/7 2/13 17 284 3/4 6/11 9/11 1/2 5/9 0 19/20 5/7 3/7 17 286 9/20 7/11 2/11 3/11 3/19 0 0 1/5 0 17 288 4/9 2/3 3/5 12/13 3/17 2/13 1/4 23/24 17/18 17 290 0 5/23 1/3 2/15 1/10 1/3 1/5 9/13 10/17 17 292 7/8 3/11 3/5 5/18 1/5 2/3 1/24 1/23 3/4 17 294 9/11 0 0 15/23 5/8 1/2 0 6/7 2/7 17 296 1/3 1/5 2/3 2/3 9/20 1/10 1/21 12/17 2/19 17 298 1/20 7/15 7/20 1/4 0 6/11 0 1/17 19/23 17 300 21/22 5/7 2/3 1/15 0 7/20 3/8 9/22 0 17 302 1/5 1/13 0 4/7 2/3 1/2 8/13 1/13 2/7 17 304 2/5 1/3 1/11 3/16 0 8/9 6/7 1/3 1/2 17 308 13/21 3/10 5/6 9/10 1/2 3/19 7/15 1/14 1/2 17 310 13/22 2/21 1/3 10/11 3/11 11/19 5/11 1/4 10/11 17 312 11/23 0 5/12 10/21 4/13 6/7 7/11 3/17 0 17 314 2/21 13/14 1/6 10/11 0 1/19 0 20/21 2/15 17 316 1/15 1/5 7/8 4/19 16/17 1/3 1/12 7/15 1/13 17 318 1/11 1/24 7/20 2/17 0 2/23 7/8 1/2 0 17 320 1/8 23/24 4/9 8/9 0 1/10 5/7 1/5 1/3 17 322 0 8/9 2/9 1/19 13/24 1/5 2/13 5/9 0 17 324 5/7 1/3 8/13 2/11 6/11 1/10 1/11 0 2/21 17 326 1/8 8/17 1/6 0 3/4 5/11 8/11 5/7 2/5 17 328 1/5 2/3 2/11 0 3/17 16/17 7/8 21/23 3/16 17 330 11/14 0 3/14 11/13 8/13 1/20 1/3 1/2 4/9 17 332 1/3 1/18 16/19 5/11 1/2 9/14 6/13 3/8 2/3 17 334 1/3 4/9 6/11 1/5 1/7 0 1/6 15/16 3/5 17 336 5/7 11/17 3/11 1/3 1/5 7/8 8/21 10/11 3/10 17 338 7/16 2/7 8/19 1/3 0 7/13 3/7 1/6 7/22 17 340 13/15 9/17 1/12 11/17 3/13 6/11 4/5 0 0 17 342 1/8 1/12 1/21 8/15 0 3/17 14/17 3/5 2/3 17 344 5/18 5/19 3/7 1/6 17/22 0 15/22 12/13 11/17 17 346 9/11 5/12 14/23 5/24 14/15 8/17 0 1/3 5/11 17 348 3/7 2/7 1/10 3/11 9/13 7/16 5/7 0 9/14 17 350 1/9 21/23 0 4/5 2/3 3/8 6/11 6/11 5/9 17 352 6/13 1/2 7/8 0 3/5 11/14 4/5 3/7 3/14 17 354 16/17 3/4 7/13 12/13 2/7 0 21/23 3/11 1/2 17 356 1/16 10/11 14/23 11/13 2/3 1/10 2/3 2/5 0 17 358 1/6 1/11 1/8 3/5 3/10 1/18 0 15/17 11/12 17 360 1/5 5/21 0 11/17 6/7 5/14 1/7 13/14 3/8 17 362 2/7 8/9 11/13 7/16 0 19/21 0 1/2 4/5 17 364 7/24 3/5 5/11 1/2 3/22 9/23 4/21 3/8 2/17 17 366 1/4 4/23 1/3 19/24 6/7 1/13 1/2 4/11 7/9 17 368 21/22 5/9 10/13 3/4 6/11 11/18 13/18 1/11 5/23 17 370 9/13 3/5 0 2/17 2/13 1/3 1/8 16/17 1/3 17 372 15/17 3/11 9/10 9/14 8/11 3/8 0 5/11 0 17 376 0 1/5 3/4 5/11 15/19 5/21 1/8 10/23 8/15 17 378 13/18 1/2 5/6 6/11 9/11 7/19 7/13 11/23 2/3 17 380 15/23 1/15 4/5 1/8 0 9/10 0 2/9 5/7 17 382 5/23 12/13 1/15 1/4 2/3 4/13 6/17 3/10 1/3 17 384 3/10 1/2 5/7 3/13 2/5 11/19 2/13 3/5 3/16 17 386 19/21 7/8 10/13 6/17 7/8 1/10 3/16 1/6 1/7 17 388 3/20 5/8 2/7 3/5 0 1/9 5/6 4/7 19/22 17 390 15/23 16/19 8/9 3/23 6/13 2/3 1/5 5/9 1/3 17 392 11/14 2/5 19/23 4/23 7/19 9/20 0 0 12/13 17 396 3/19 3/5 1/7 11/14 1/2 2/5 1/10 3/7 4/5 17 398 1/8 11/19 1/9 0 6/11 3/10 3/5 14/17 0 17 400 5/6 5/8 14/17 8/21 2/3 11/13 5/17 6/7 1/22 17 402 1/2 6/19 0 15/19 19/21 4/9 10/11 7/24 5/16 17 404 8/23 11/18 9/10 1/7 4/7 1/13 3/10 0 7/22 17 406 4/19 2/9 3/10 7/13 5/7 3/4 1/22 1/3 11/24 17 408 4/7 4/5 9/19 17/19 11/14 1/3 2/11 5/11 0 17 410 7/8 3/16 1/5 5/12 0 7/11 4/9 3/5 18/19 17 412 1/4 15/23 1/15 3/4 7/10 23/24 9/13 6/7 3/7 17 416 12/13 5/9 3/10 3/14 15/17 1/3 1/3 6/7 10/11 17 414 1/2 13/21 13/24 9/10 12/13 4/5 3/4 7/13 3/19 17 418 0 6/7 6/11 5/19 5/12 4/5 8/13 1/14 2/5 17 420 1/4 6/7 5/18 9/10 1/18 15/17 7/23 4/7 11/13 17 422 9/11 8/19 3/7 7/8 0 10/11 4/5 16/19 3/4 17 426 2/3 4/5 11/19 19/21 6/7 5/8 2/9 1/11 3/4 17 428 1/10 9/11 6/23 2/5 1/9 8/17 2/21 1/9 1/2 17 430 0 3/5 9/13 14/23 8/13 7/16 13/14 5/17 1/4 17 432 4/5 3/7 1/2 9/19 7/8 6/17 4/7 7/10 8/17 17 434 22/23 7/8 1/3 1/5 3/22 5/17 3/22 11/13 4/13 17 444 15/22 11/16 2/7 8/17 11/18 6/7 19/23 13/16 1/5 17 448 3/11 1/16 20/23 5/8 1/3 2/9 4/11 11/14 10/11 17 450 22/23 16/19 4/11 11/12 1/23 7/9 23/24 1/20 2/7 17 454 5/16 6/19 9/11 3/5 14/17 14/19 5/24 1/5 5/6 17 458 1/3 1/17 10/11 1/11 15/17 9/14 1/21 1/13 13/17 17 460 5/9 2/7 1/17 8/11 18/19 3/5 3/7 1/4 9/11 17 466 3/5 12/19 7/10 1/11 11/14 6/19 3/8 5/7 1/7 17 468 8/9 3/17 2/13 5/14 3/19 3/8 5/11 5/9 13/23 17 472 r1 r2 r3 r4 r5 r6 r7 r8 r9 17 472* ----------------------------------------------------------------------------------- 0 0 1/3 1/2 0 0 2/3 2/3 1/3 18 12 0 0 0 5/6 0 0 1/6 5/6 2/5 18 36 2/3 3/5 1/2 3/5 0 0 0 3/5 0 18 48 ----------------------------------------------------------------------------------- 0 0 0 3/4 1/2 1/6 0 1/2 0 19 12 0 0 1/4 0 4/5 1/2 0 1/2 1/2 19 36 1/2 0 0 0 1/2 1/5 2/3 3/4 4/5 19 40 0 1/3 3/4 2/5 3/5 1/2 0 1/2 1/2 19 48 0 0 1/5 1/2 1/2 0 1/5 1/4 4/5 19 60 ----------------------------------------------------------------------------------- 2/3 1/3 5/6 5/6 2/3 1/2 1/2 0 0 20 12 ----------------------------------------------------------------------------------- 0 0 0 0 1/2 3/4 1/4 2/3 0 21 12 0 1/2 1/2 0 0 1/2 3/4 4/5 1/4 21 28 0 4/5 0 1/5 3/4 0 1/2 1/2 0 21 48 ----------------------------------------------------------------------------------- 0 1/2 0 1/2 1/2 0 0 1/2 3/4 23 12 -----------------------------------------------------------------------------------
F12B(p1, ..., p9)↑
show data
p1 p2 p3 p4 p5 p6 p7 p8 p9 d #Λ ----------------------------------------------------------------------------------- 2/3 0 0 5/7 0 0 1/12 0 1/2 13 36 1/2 1/4 1/5 2/5 1/6 5/6 0 1/6 1/4 13 60 5/12 2/3 2/3 6/19 1/4 1/2 0 1/4 18/25 13 72 0 1/17 2/3 1/2 1/3 1/3 0 3/4 2/5 13 84 17/20 1/4 17/20 1/2 1/4 0 0 2/27 1/2 13 96 5/12 11/14 5/7 2/7 5/6 0 2/3 5/7 9/23 13 108 0 1/8 1/2 0 0 1/2 0 22/23 5/23 13 144 1/7 1/6 1/3 13/15 3/4 1/4 2/3 12/13 6/7 13 172 0 8/9 6/7 0 7/8 1/12 0 0 8/23 13 184 5/7 5/6 0 19/30 1/5 1/2 1/2 26/29 2/5 13 220 3/4 1/5 12/23 2/3 11/14 6/19 0 14/17 0 13 222 1/2 1/3 1/5 2/13 3/10 1/9 10/11 2/3 0 13 244 1/22 15/29 8/13 1/4 0 2/3 1/3 15/28 7/9 13 280 0 1/2 1/2 1/6 8/19 7/24 1/5 2/5 1/10 13 288 0 25/26 7/8 7/22 9/17 1/2 1/2 2/9 4/9 13 296 11/25 0 1/6 1/2 1/3 1/5 5/13 4/27 5/6 13 300 5/8 5/9 5/12 14/23 2/17 12/13 3/7 1/4 0 13 330 6/11 1/9 1/2 0 7/11 19/24 1/2 3/5 2/3 13 372 0 9/17 5/12 5/9 13/24 3/17 14/19 1/3 15/19 13 380 5/7 0 3/10 15/19 5/11 6/7 0 11/14 5/7 13 382 2/25 1/4 7/23 4/7 3/5 0 9/20 1/12 7/23 13 384 3/5 2/5 2/3 3/5 7/9 2/13 22/27 1/3 2/9 13 388 1/2 5/7 1/15 1/2 9/11 0 4/11 14/17 1/4 13 400 21/22 20/21 10/13 1/2 5/8 5/6 5/13 15/16 3/8 13 402 1/9 5/8 9/23 19/26 5/7 0 17/28 5/18 0 13 406 1/2 11/27 2/7 2/7 1/2 2/9 0 12/25 7/17 13 408 6/7 4/5 2/11 1/15 1/10 0 3/23 10/19 3/10 13 410 4/7 22/27 1/2 1/10 1/7 0 11/14 1/3 21/26 13 412 6/7 9/10 3/17 2/5 5/8 2/5 2/3 9/25 10/13 13 414 17/23 1/2 11/14 3/19 1/8 0 2/9 4/13 5/18 13 418 13/29 8/9 11/19 6/29 4/15 0 4/15 1/21 5/9 13 420 1/3 7/8 15/22 11/16 1/2 7/30 1/2 4/5 8/19 13 424 9/17 0 3/10 5/6 4/9 13/19 1/25 11/12 3/16 13 426 4/15 4/17 2/5 1/2 3/19 1/7 1/6 10/11 4/7 13 430 1/2 0 3/11 2/7 1/16 4/19 6/19 3/8 0 13 436 7/30 11/15 11/14 1/12 2/9 11/12 12/29 13/14 1/2 13 432 5/14 5/23 0 9/25 1/5 8/11 0 19/20 5/23 13 440 1/21 0 2/5 3/4 6/7 2/19 1/7 1/2 6/11 13 444 11/13 4/11 2/3 3/10 3/14 0 11/13 3/13 4/5 13 446 9/23 0 4/15 3/11 1/5 17/25 11/18 1/3 0 13 448 8/11 1/17 8/11 17/23 1/4 3/26 7/16 3/13 2/3 13 450 1/3 15/28 3/8 1/27 2/15 1/26 1/5 5/7 3/4 13 452 14/25 13/18 1/11 4/5 23/27 2/5 11/15 8/9 2/5 13 454 5/13 0 3/26 21/23 1/10 15/17 23/30 1/4 18/25 13 456 4/7 11/19 0 17/19 4/29 5/12 12/17 1/3 3/8 13 460 3/8 14/29 5/14 1/7 1/22 16/17 1/2 1/9 0 13 462 11/13 1/13 11/12 11/27 13/24 3/5 5/13 0 4/29 13 464 10/23 0 19/22 3/5 7/8 1/16 9/20 1/17 0 13 466 0 1/4 5/7 8/15 7/24 20/29 7/11 17/18 3/8 13 468 7/9 3/17 7/12 2/13 8/23 1/30 13/29 25/29 4/7 13 470 17/18 11/14 5/6 10/13 1/6 1/5 11/16 3/5 1/2 13 472 13/14 17/29 5/6 7/8 3/14 2/7 0 2/15 1/17 13 474 2/7 7/10 14/17 1/12 19/21 2/3 5/7 15/23 13/16 13 476 1/5 3/14 8/17 1/3 10/21 4/11 1/3 7/23 21/23 13 478 2/11 17/28 11/25 0 1/2 6/7 4/11 7/30 5/6 13 480 1/5 9/25 5/9 1/2 2/5 10/11 9/19 3/4 1/4 13 484 14/23 8/11 9/10 0 5/12 4/7 21/23 3/5 14/19 13 486 2/25 19/29 1/5 13/28 9/10 1/5 1/2 0 13/17 13 488 2/5 7/9 12/19 3/4 5/21 9/20 0 1/8 5/9 13 492 15/28 5/12 7/13 1/11 1/8 7/13 13/30 3/20 0 13 496 3/5 6/13 7/22 1/2 3/14 3/14 9/13 20/21 0 13 498 2/3 2/5 1/19 13/28 0 11/13 12/13 7/12 4/7 13 504 1/28 19/24 1/14 13/30 2/3 1/3 4/5 16/19 9/14 13 508 1/2 3/14 9/25 9/16 1/18 3/22 1/9 17/22 1/4 13 514 10/11 13/15 9/19 1/2 2/3 23/25 13/27 5/13 0 13 516 10/11 7/8 0 4/9 23/27 0 9/16 2/11 4/7 13 520 16/17 17/18 1/15 13/14 7/13 1/3 1/15 22/23 3/10 13 524 3/7 7/27 6/7 3/10 4/11 0 1/16 4/5 3/4 13 528 8/25 3/10 13/23 21/25 4/15 3/16 0 21/22 3/7 13 542 2/7 4/7 7/10 5/18 0 10/11 1/29 5/28 0 13 544 6/23 15/16 6/19 6/11 1/5 3/5 0 10/29 6/17 13 546 2/7 2/19 7/13 4/5 5/28 7/10 14/15 9/10 1/2 13 550 3/7 3/20 3/8 2/5 5/22 4/7 2/19 4/5 0 13 556 18/25 1/7 2/15 12/13 9/10 17/30 7/25 0 16/25 13 562 22/27 3/7 4/5 4/15 24/25 10/11 22/25 1/11 3/5 13 564 5/29 1/3 1/11 1/5 0 3/8 8/27 11/14 1/20 13 568 0 16/21 3/7 6/19 4/5 1/5 4/9 2/7 2/5 13 570 21/29 5/7 2/5 4/25 3/5 9/10 4/9 9/16 0 13 574 1/4 14/19 9/10 8/13 26/29 1/10 1/7 1/7 16/23 13 580 12/19 3/7 5/27 5/9 11/19 1/10 3/14 8/9 0 13 586 10/13 0 1/9 4/5 0 16/25 13/23 1/17 3/7 13 592 8/17 15/16 6/17 11/16 0 13/21 3/5 1/16 6/19 13 594 15/26 14/17 5/17 15/16 7/10 7/11 7/8 4/13 1/2 13 598 7/9 2/5 1/28 1/14 1/3 4/5 3/5 15/17 11/29 13 602 4/7 3/20 1/7 5/7 7/10 5/9 16/27 8/17 8/13 13 612 4/5 4/19 0 12/13 8/13 1/19 2/7 5/7 5/7 13 618 1/6 21/25 5/14 26/29 1/5 2/11 4/5 13/14 2/5 13 622 4/29 16/23 1/15 22/27 1/5 1/4 2/7 7/13 1/7 13 646 17/19 1/4 2/17 13/16 4/7 16/27 4/25 6/13 15/26 13 658 1/19 9/10 8/19 2/11 2/15 5/7 4/9 1/17 16/29 13 664 0 19/28 0 0 1/2 5/9 1/2 3/8 7/8 13 168 2/3 1/2 4/9 5/9 4/11 0 7/24 0 2/5 13 348 5/11 5/8 0 3/5 18/19 3/4 1/4 1/30 7/22 13 332 3/7 1/6 1/3 1/9 19/21 17/18 1/2 3/8 13/15 13 336 17/28 0 7/12 1/5 12/17 0 5/13 1/2 1/4 13 252 1/6 7/16 1/6 2/7 9/10 5/11 2/3 13/20 4/5 13 396 3/11 17/19 1/27 14/19 4/7 0 0 18/19 4/21 13 342 3/4 0 1/2 9/10 0 1/9 2/7 1/3 4/9 13 204 23/30 5/8 3/11 2/3 0 2/5 14/25 1/3 1/2 13 312 19/29 5/6 7/16 1/3 3/7 8/15 14/19 5/8 0 13 366 0 2/3 1/3 7/10 5/9 7/20 1/4 0 1/29 13 240 25/28 21/25 5/6 1/2 11/23 23/25 3/4 0 2/5 13 376 2/15 5/6 1/2 1/6 3/4 3/20 1/2 2/11 5/23 13 228 15/19 0 21/26 6/11 11/29 10/13 2/7 1/4 0 13 390 14/17 3/5 0 7/9 0 22/29 1/3 4/9 1/5 13 364 1/10 3/7 19/29 1/2 11/13 2/3 6/7 13/14 9/10 13 394 23/24 2/9 11/18 0 25/26 1/2 2/19 5/9 0 13 282 18/23 13/17 1/2 11/21 4/15 1/3 0 4/5 7/13 13 340 2/7 1/2 11/30 11/18 19/24 0 1/9 1/2 0 13 268 1/4 7/30 13/30 2/11 3/4 9/28 0 1/2 7/9 13 360 1/10 3/10 17/22 5/8 5/7 1/2 1/6 3/4 1/13 13 286 1/2 2/3 0 0 14/27 6/7 0 0 1/10 13 180 1/2 5/9 2/3 1/6 11/18 9/14 0 1/22 1/30 13 324 7/23 14/27 0 19/21 8/11 2/3 3/4 3/4 19/26 13 352 1/18 0 0 1/3 5/22 0 5/12 6/19 21/22 13 276 4/11 0 0 2/11 24/29 0 0 7/9 1/2 13 192 15/19 1/5 1/25 1/3 3/5 19/29 0 9/11 2/3 13 378 1/2 17/26 2/3 1/3 0 2/3 1/3 4/5 3/7 13 156 1/6 3/5 3/17 0 2/23 2/3 9/17 1/8 14/15 13 328 22/23 1/5 3/10 8/27 0 0 0 6/7 25/26 13 308 2/3 0 7/15 0 1/2 1/4 12/19 3/5 0 13 132 5/24 1/2 11/17 1/15 18/19 1/3 5/6 13/24 3/13 13 214 0 9/29 3/7 3/14 0 1/3 0 8/9 19/21 13 256 6/13 11/25 23/27 3/8 20/21 9/10 1/7 1/7 12/19 13 640 8/29 19/23 3/8 0 5/6 5/6 1/2 1/2 2/3 13 120 1/4 12/29 3/8 2/5 7/9 13/14 20/23 3/19 1/6 13 522 6/29 6/11 2/7 23/29 17/21 13/15 3/5 0 10/19 13 634 3/14 9/16 4/5 7/30 2/7 1/2 0 4/13 13/14 13 306 5/6 15/28 0 7/15 20/27 2/3 1/3 0 16/21 13 196 3/4 1/2 0 3/5 10/27 4/19 0 1/2 4/9 13 264 7/23 3/7 2/5 26/27 0 17/25 1/2 5/7 2/11 13 540 7/15 0 4/5 13/14 4/5 7/10 0 3/5 28/29 13 258 3/19 2/7 21/26 0 22/27 2/7 2/3 27/28 0 13 294 5/6 1/4 1/2 3/4 8/11 7/17 22/25 9/14 7/12 13 216 1/2 0 14/25 4/11 3/16 5/14 1/10 1/9 3/4 13 532 3/5 8/9 1/9 3/26 15/23 7/10 1/7 5/14 7/16 13 636 1/2 1/11 4/19 17/26 7/12 2/5 1/2 0 10/11 13 316 13/14 3/4 3/5 7/10 7/15 2/7 0 0 9/10 13 292 3/28 1/3 3/13 7/13 4/9 2/3 3/10 4/13 1/2 13 334 13/15 17/22 14/25 0 1/9 0 1/3 11/18 8/29 13 238 7/10 7/10 5/8 11/15 3/5 3/5 1/14 1/2 9/14 13 358 11/13 7/9 14/15 1/4 24/25 6/17 9/10 1/5 1/5 13 534 4/7 1/2 4/5 9/11 7/12 1/6 21/22 10/11 0 13 202 1/16 13/14 0 5/14 5/16 1/2 4/9 19/29 5/23 13 500 0 9/11 12/13 1/10 0 0 2/3 2/3 7/12 13 136 5/9 1/19 10/11 2/9 1/3 1/2 7/9 3/11 1/4 13 304 7/26 3/4 13/24 6/11 1/5 3/8 23/27 2/3 7/10 13 506 19/23 18/19 9/14 22/25 0 17/25 9/13 9/19 2/7 13 654 2/23 3/5 0 6/13 19/22 12/23 6/7 12/17 7/8 13 650 17/21 18/19 12/23 2/3 1/5 4/15 1/2 3/10 1/2 13 270 3/11 11/24 5/7 1/9 0 14/27 9/10 0 22/29 13 606 7/12 2/7 3/10 8/15 2/5 2/7 1/21 2/5 1/2 13 234 9/11 13/14 3/5 1/5 3/8 1/3 0 11/14 9/29 13 338 10/11 23/30 14/15 4/13 1/3 13/14 4/19 11/14 13/22 13 582 13/14 19/20 14/23 1/2 19/25 1/28 2/3 2/21 5/17 13 346 7/15 9/16 1/11 1/5 7/8 2/5 3/29 1/13 4/7 13 632 6/7 3/17 0 15/23 23/25 4/17 1/5 6/17 1/13 13 662 0 19/29 5/7 22/23 22/23 0 4/13 7/19 3/25 13 512 2/19 2/25 11/13 9/10 2/3 3/28 4/7 1/3 2/11 13 610 8/13 0 1/15 13/17 4/7 3/14 6/7 1/14 11/17 13 538 5/28 9/25 7/25 1/2 0 1/3 0 2/3 7/9 13 232 6/7 1/5 1/2 6/7 3/13 3/4 0 0 11/16 13 208 14/29 4/5 5/6 3/8 3/10 16/29 16/19 1/30 14/27 13 530 3/8 19/30 11/19 3/4 3/5 13/14 4/19 3/7 16/27 13 590 19/22 7/8 11/12 1/2 9/11 0 0 1/4 7/27 13 142 14/19 9/14 0 2/5 11/17 6/7 17/28 1/19 21/22 13 630 5/7 1/7 5/6 11/18 19/28 1/5 3/5 10/23 12/23 13 624 10/11 10/13 6/25 4/7 14/17 17/27 3/5 4/13 9/10 13 652 17/21 22/25 21/25 2/3 1/17 9/16 4/5 6/7 1/2 13 510 1/7 3/16 3/7 20/21 8/11 0 0 14/29 3/5 13 314 22/25 3/8 12/13 1/5 3/4 5/8 0 4/17 4/5 13 370 14/25 1/7 3/5 4/5 2/11 5/8 19/30 16/27 5/7 13 604 3/11 1/12 6/23 9/13 2/3 1/2 11/21 8/9 3/10 13 344 5/13 14/17 1/2 5/18 3/10 6/7 19/26 5/18 9/11 13 614 7/16 5/16 2/3 3/14 3/10 2/7 12/23 2/27 7/25 13 616 r1 r2 r3 r4 r5 r6 r7 r8 r9 13 664* ----------------------------------------------------------------------------------- 11/12 3/4 3/14 1/3 0 23/24 2/7 1/2 1/3 15 72 1/12 1/12 3/4 1/5 3/4 3/4 2/3 7/23 1/4 15 84 23/25 0 3/4 0 3/7 2/3 0 6/19 1/2 15 90 0 11/12 13/28 0 1/6 10/13 5/13 1/3 3/4 15 120 1/2 1/2 1/4 18/23 3/13 0 1/3 2/3 5/8 15 124 5/13 1/4 1/3 12/25 0 0 0 0 2/11 15 132 2/7 1/3 11/12 1/28 9/11 7/9 1/6 1/5 2/3 15 138 0 0 5/13 3/4 22/25 3/23 0 3/4 3/4 15 144 6/13 3/4 0 5/6 0 1/3 12/13 5/6 1/17 15 156 1/2 2/3 3/4 1/2 3/8 1/14 0 1/2 23/30 15 168 2/9 0 3/4 6/11 4/7 1/2 0 4/9 1/25 15 178 1/2 0 5/7 1/4 0 0 11/13 0 18/19 15 180 3/7 4/5 1/4 12/17 5/13 1/2 0 1/18 0 15 190 5/6 1/4 7/8 7/12 1/3 8/17 3/19 23/26 1/2 15 192 9/11 0 1/4 1/2 7/12 7/9 11/14 7/20 25/29 15 198 1/4 0 3/22 22/29 1/4 11/12 7/30 0 1/21 15 216 1/19 1/2 4/7 0 3/4 1/2 16/17 14/19 7/11 15 222 11/12 2/11 10/13 2/3 8/15 0 11/19 7/12 2/15 15 238 2/3 9/28 1/8 5/12 0 8/11 4/5 1/2 2/3 15 240 11/28 0 1/8 10/19 3/4 2/3 17/21 7/8 6/11 15 244 1/4 1/2 2/29 0 9/10 0 4/5 11/14 13/17 15 246 1/4 1/2 1/13 11/15 1/4 4/19 1/3 1/2 2/17 15 252 25/26 3/4 4/5 4/15 0 1/2 3/4 13/17 23/24 15 256 17/21 2/3 2/19 1/3 11/12 25/26 1/2 6/23 13/18 15 258 1/18 2/3 1/4 1/21 1/2 0 2/7 1/20 4/17 15 264 1/2 9/10 1/4 3/17 5/12 0 14/23 12/13 2/3 15 268 1/4 1/9 0 1/2 16/17 14/25 7/9 4/9 7/22 15 276 2/27 17/20 3/5 15/16 3/5 4/5 2/27 1/6 0 15 280 1/4 9/13 5/29 0 8/11 4/7 0 14/19 3/22 15 286 2/3 7/13 3/4 1/3 1/11 3/5 7/10 3/5 2/13 15 316 2/19 5/6 2/13 3/4 7/12 6/7 5/8 0 7/16 15 324 2/3 5/27 3/4 16/17 7/9 1/4 0 6/7 3/5 15 328 3/22 1/2 3/4 0 3/8 14/17 6/23 11/19 27/29 15 330 4/13 7/19 3/4 6/13 12/13 1/3 7/8 5/14 1/2 15 334 1/2 7/11 13/25 3/4 6/7 17/29 6/17 0 0 15 336 0 23/25 3/4 3/5 4/7 0 9/13 0 6/11 15 344 0 1/2 20/21 1/8 1/4 2/5 3/4 3/11 12/17 15 348 13/30 9/13 3/4 1/2 4/23 10/11 2/5 1/3 17/18 15 352 3/4 5/7 3/16 0 1/15 4/9 17/29 0 5/9 15 364 6/11 1/14 3/4 5/29 4/21 5/6 6/7 17/21 9/10 15 368 7/9 11/29 3/4 0 8/15 19/24 2/7 1/5 11/23 15 370 3/16 5/8 1/4 0 4/25 8/15 2/13 0 3/29 15 388 13/16 0 3/4 16/23 3/22 2/7 5/9 9/28 11/16 15 394 11/14 0 3/4 16/17 1/6 7/29 15/23 15/16 19/30 15 400 3/13 0 3/4 21/23 15/19 4/5 6/7 5/22 17/23 15 406 0 1/2 2/29 3/4 9/25 13/15 5/17 13/22 8/9 15 408 4/5 1/4 9/10 7/22 0 11/18 2/5 15/29 13/14 15 410 7/9 7/8 1/4 7/20 1/22 10/19 3/5 8/15 1/5 15 438 7/10 15/19 3/4 1/4 22/27 2/9 1/5 10/21 3/26 15 458 5/8 2/5 1/4 3/17 19/27 7/11 6/17 24/25 3/7 15 468 ----------------------------------------------------------------------------------- 0 0 0 0 0 0 0 0 0 17 12 ----------------------------------------------------------------------------------- 1/3 0 1/4 2/3 16/19 1/6 2/15 11/30 2/3 19 108 ----------------------------------------------------------------------------------- 0 0 0 0 0 2/3 2/3 2/3 3/5 17 36 UNSORTED 0 1/3 1/2 0 0 1/3 1/2 5/6 1/6 13 12 1/3 0 1/2 1/2 1/5 1/2 1/2 0 1/2 13 36 1/5 1/2 1/5 0 0 2/3 0 0 2/3 13 48 1/5 0 0 0 1/4 1/2 2/3 1/4 1/2 15 36 1/5 3/4 0 1/3 2/5 0 1/5 0 0 13 60 1/4 0 1/2 0 1/2 0 1/4 0 1/6 15 12 3/4 0 0 1/3 0 0 1/2 1/2 0 17 12 3/5 1/4 0 0 1/2 2/5 1/2 1/2 2/3 15 60 1/2 1/2 3/4 3/4 5/6 0 2/3 0 1/2 21 12 0 1/5 3/4 3/4 0 0 0 2/3 0 21 36 0 1/2 1/2 0 1/2 3/5 1/3 4/5 1/2 17 60 0 2/3 0 1/4 3/4 1/2 2/3 1/3 0 19 12 1/5 1/4 1/3 0 0 2/3 4/5 1/4 0 15 48 1/4 0 3/4 0 2/5 1/3 0 3/5 0 21 30 4/5 1/2 0 1/6 3/4 1/5 1/2 0 0 19 60 3/4 0 3/4 0 1/4 0 3/4 4/5 0 27 36 1/4 1/2 2/5 0 1/3 5/6 2/3 3/4 1/2 19 36 1/2 1/2 0 3/4 0 1/2 1/2 0 0 23 12 1/4 0 3/5 0 3/4 5/6 3/5 3/4 2/3 21 42 0 1/5 1/4 3/4 3/4 1/2 4/5 3/4 0 21 60 0 0 0 0 3/4 0 0 4/5 2/5 23 60 4/5 1/3 1/5 0 4/5 3/5 1/2 3/4 0 13 54 0 1/6 1/5 2/3 4/5 2/3 0 0 1/2 17 48 1/4 2/3 4/5 2/3 1/5 0 2/5 1/5 0 13 42 1/3 1/3 3/5 1/5 1/4 1/3 0 0 5/6 13 52 1/4 1/4 1/4 0 1/2 1/6 0 0 0 27 12 1/2 1/3 3/4 3/5 3/4 0 2/3 0 1/2 19 28 0 0 1/4 2/5 1/4 0 0 1/2 0 21 28 3/5 0 1/4 1/3 4/5 0 1/2 3/5 0 15 42 1/3 1/2 3/4 4/5 1/5 1/6 0 2/3 0 19 48 3/4 3/5 1/4 0 3/4 1/2 1/3 4/5 1/5 21 54 0 2/3 3/4 2/5 1/4 2/3 0 1/6 2/3 15 28 2/5 0 1/4 4/5 1/4 0 1/3 0 1/4 21 48 3/4 3/4 3/4 4/5 1/5 1/2 0 0 0 23 48 1/4 1/2 3/5 0 3/5 0 0 2/5 1/5 15 54 1/2 3/4 3/5 1/4 1/2 1/5 1/5 2/3 3/4 21 52 ----------------------------------------------------------------------------------
F12C(p1, ..., p9)↑
show data
p1 p2 p3 p4 p5 p6 p7 p8 p9 d #Λ ----------------------------------------------------------------------------------- 0 0 0 0 0 1/6 1/6 1/2 1/3 13 12 0 1/2 0 0 1/2 1/2 2/3 0 19/23 13 36 1/5 0 0 0 1/3 1/2 1/3 4/5 2/3 13 40 3/4 1/5 3/5 2/5 0 1/3 1/4 1/5 3/5 13 42 0 1/3 0 1/4 2/5 0 1/3 0 3/5 13 44 0 1/2 0 4/5 1/5 1/3 0 0 0 13 48 1/4 5/6 1/2 0 0 0 4/5 3/5 4/5 13 52 1/2 1/6 5/6 2/5 3/4 2/3 4/5 1/4 2/3 13 56 3/5 2/3 4/5 0 5/6 2/3 1/2 0 1/2 13 60 7/8 1/8 0 3/8 1/4 1/6 9/10 0 0 13 72 1/12 0 11/29 1/2 1/4 2/3 0 11/19 0 13 76 1/4 0 1/2 0 7/11 1/3 2/7 0 0 13 84 7/10 4/5 3/11 3/4 1/2 1/3 11/15 1/2 1/12 13 90 1/3 2/9 3/5 3/4 0 1/3 0 7/12 4/9 13 96 1/2 1/5 1/2 8/15 10/17 0 0 1/3 4/5 13 108 0 0 4/5 1/10 11/21 2/3 2/3 1/2 3/4 13 116 1/3 1/2 8/9 11/12 1/2 0 19/22 0 10/23 13 120 0 10/27 0 0 1/3 0 22/23 5/17 3/4 13 124 1/2 7/12 5/6 0 7/24 1/6 2/3 1/10 12/17 13 128 0 0 5/9 11/12 1/3 4/29 1/2 0 3/8 13 132 1/2 19/26 7/24 1/2 1/4 1/2 23/25 7/8 2/3 13 136 9/22 3/4 2/3 0 9/11 1/3 5/19 3/4 1/2 13 140 4/21 11/14 9/28 0 0 6/7 0 9/14 5/8 13 144 1/4 0 1/2 13/22 1/2 1/2 6/11 4/7 2/3 13 148 5/12 0 1/21 2/15 7/9 1/2 3/4 4/9 19/28 13 150 0 0 1/4 1/3 0 15/29 1/18 2/11 1/3 13 156 1/10 0 1/6 0 0 1/4 23/26 11/14 1/2 13 160 6/7 5/6 0 1/28 1/10 1/2 1/2 1/2 17/21 13 164 9/16 5/6 1/3 4/5 1/2 11/20 2/3 1/15 2/3 13 168 2/3 8/9 1/2 1/2 0 3/28 19/21 7/13 3/4 13 176 1/3 11/15 5/14 0 0 1/2 4/7 9/14 0 13 180 19/29 0 0 0 5/19 16/19 1/3 3/4 11/12 13 184 13/16 0 6/7 9/17 1/2 1/3 7/20 1/2 2/7 13 186 9/11 1/2 9/11 9/10 5/6 2/3 1/2 23/25 13/15 13 188 5/8 1/3 4/21 6/7 3/8 0 5/6 1/5 19/23 13 190 1/3 5/7 7/17 1/12 5/7 5/13 0 5/7 3/4 13 192 2/5 2/3 7/30 8/11 1/3 2/3 5/11 1/15 5/7 13 194 7/18 5/12 0 7/12 4/5 0 10/13 2/15 1/2 13 196 7/9 1/3 13/25 11/15 0 2/5 13/20 0 3/20 13 198 3/4 1/6 1/2 5/9 1/3 0 19/24 3/10 5/27 13 200 2/3 14/15 0 1/3 1/14 9/20 0 5/9 1/2 13 204 0 0 9/26 4/5 1/2 2/3 4/5 6/7 13/15 13 208 7/9 1/3 11/29 10/13 0 0 1/9 1/24 16/29 13 210 7/8 0 2/3 2/11 4/5 2/3 0 16/19 1/2 13 212 6/7 23/29 0 1/2 19/21 4/7 1/3 5/7 0 13 216 11/20 1/6 1/4 4/9 0 1/3 2/7 7/24 7/11 13 218 1/4 3/10 3/7 1/4 2/3 2/3 11/15 9/10 6/11 13 220 19/27 1/3 5/18 21/22 0 2/7 1/4 0 5/11 13 222 1/5 1/3 0 0 0 4/23 4/11 2/21 1/4 13 224 1/4 0 3/7 3/25 1/2 2/19 0 1/2 1/24 13 228 11/14 12/23 3/4 5/16 1/3 0 11/21 6/17 6/7 13 230 7/15 4/5 4/5 5/6 1/12 4/5 3/5 12/19 15/29 13 232 5/21 1/3 2/5 10/19 1/2 3/17 15/17 1/2 3/4 13 234 9/16 1/2 1/2 0 0 15/16 4/7 10/17 20/21 13 236 11/28 3/8 0 0 13/23 5/7 0 5/12 1/21 13 240 20/27 1/2 0 1/4 5/9 0 0 1/5 1/8 13 244 7/16 5/6 6/7 3/14 0 14/27 7/12 0 1/5 13 246 2/3 0 13/22 1/16 17/22 2/3 9/11 7/8 9/16 13 248 2/5 0 4/5 8/13 0 1/7 5/7 1/3 1/3 13 252 7/9 1/8 1/3 0 0 0 0 5/14 11/17 13 256 3/23 0 1/21 13/20 1/3 11/17 5/12 1/29 1/4 13 258 0 5/8 13/14 5/9 3/26 3/8 1/2 0 5/8 13 260 6/7 0 7/12 1/4 1/2 2/9 3/5 5/11 10/17 13 262 0 25/29 2/3 3/5 0 1/4 1/2 3/26 11/14 13 264 0 5/7 3/5 5/6 19/25 5/16 5/6 1/2 11/12 13 268 3/5 1/2 3/5 4/15 15/19 1/5 5/13 14/19 3/8 13 270 9/17 0 11/12 0 0 3/8 3/4 5/7 8/29 13 272 19/25 5/8 9/26 1/4 1/2 1/9 0 0 7/8 13 276 22/29 3/5 3/4 5/13 3/8 0 1/4 13/23 3/4 13 278 0 2/5 0 14/27 3/5 4/21 19/20 3/5 4/5 13 280 16/17 1/2 4/5 2/9 17/19 1/3 11/24 0 4/25 13 282 0 8/9 5/6 0 9/10 5/26 10/13 0 10/29 13 284 7/20 2/3 7/13 7/8 1/10 0 17/29 9/10 2/9 13 286 1/3 1/5 0 9/16 0 13/14 9/20 7/23 3/4 13 288 8/15 3/4 17/28 2/3 0 10/27 0 3/8 1/6 13 292 7/9 9/11 5/11 1/7 0 0 1/5 0 7/11 13 294 2/3 8/17 1/6 3/7 19/30 3/5 1/2 7/12 8/13 13 296 1/26 1/6 7/9 7/11 9/25 0 5/8 1/30 3/4 13 298 7/8 4/5 7/23 0 0 2/15 17/30 4/5 3/11 13 300 9/10 2/3 7/8 1/3 5/21 2/3 3/11 11/27 5/6 13 304 1/16 9/17 4/5 7/15 3/5 5/6 15/16 1/2 12/23 13 306 22/25 2/3 1/2 1/9 13/20 1/5 5/12 1/2 16/25 13 308 1/3 4/29 2/3 2/11 0 9/29 4/29 1/4 3/10 13 312 2/3 5/6 3/4 2/7 3/4 5/27 2/5 5/7 2/15 13 316 3/4 8/21 4/5 6/13 2/7 4/7 5/22 0 11/12 13 318 2/3 8/15 1/6 9/11 5/7 11/14 0 1/2 26/27 13 320 0 1/2 5/23 2/5 0 5/9 9/17 1/6 15/17 13 324 1/5 1/2 3/11 2/5 1/8 1/5 9/11 0 11/24 13 326 5/21 2/5 0 0 17/27 1/6 7/18 11/16 1/4 13 328 5/18 2/3 1/5 2/5 1/2 9/13 13/16 0 20/29 13 330 2/3 2/3 1/18 29/30 1/2 17/18 13/15 8/17 5/7 13 332 1/5 1/3 3/8 6/19 1/14 0 4/5 11/15 11/13 13 334 0 1/3 5/17 7/8 5/6 2/5 19/30 4/7 1/2 13 336 1/4 3/13 2/5 0 10/13 1/17 1/2 17/18 1/3 13 340 2/7 2/9 11/14 1/8 1/2 3/5 3/5 1/3 18/29 13 342 5/28 16/21 12/25 1/10 1/3 0 0 7/8 8/11 13 344 2/11 1/18 3/4 9/29 5/9 2/3 20/23 15/16 1/4 13 346 1/6 6/13 4/11 1/2 2/3 2/21 10/13 4/11 21/23 13 348 7/12 16/19 9/19 1/10 5/24 0 26/29 0 9/20 13 350 4/9 7/27 0 0 13/18 0 19/29 17/22 11/15 13 352 4/5 5/11 17/20 3/14 13/29 1/3 1/5 1/3 17/23 13 354 1/9 1/2 9/11 1/2 8/13 5/6 18/29 1/14 4/13 13 356 2/15 2/11 1/5 7/16 1/2 1/3 1/5 4/7 2/5 13 358 2/3 1/2 5/11 2/7 0 5/26 11/20 1/15 0 13 360 1/12 8/27 2/11 12/13 2/3 0 3/22 3/5 27/28 13 362 17/28 11/27 14/15 1/4 11/16 0 1/4 9/16 1/16 13 364 1/4 5/26 8/17 4/9 1/3 17/26 6/11 0 13/14 13 366 3/8 11/14 6/7 1/2 1/4 11/30 11/12 0 13/19 13 368 5/12 7/15 1/2 0 8/23 2/27 8/9 22/23 1/2 13 372 0 25/27 1/14 0 6/7 2/7 1/17 2/5 0 13 376 17/18 0 17/23 21/29 13/19 13/19 3/4 6/11 17/24 13 378 5/9 1/7 0 15/28 1/3 1/3 2/17 4/29 0 13 380 5/9 4/5 3/8 1/2 2/5 1/4 3/20 23/24 1/7 13 384 1/4 16/17 7/8 7/12 8/19 7/24 13/23 5/9 8/17 13 386 3/4 7/9 1/6 22/29 13/25 1/27 4/17 1/3 0 13 388 13/28 3/14 1/5 1/4 7/19 4/5 3/28 0 3/8 13 390 1/25 3/5 1/3 1/16 9/14 3/4 3/4 15/16 1/4 13 392 4/11 0 3/11 3/11 1/14 11/14 5/22 1/5 22/29 13 394 5/24 4/17 9/19 0 1/13 0 3/13 1/24 1/2 13 396 3/5 3/4 4/7 5/8 4/5 7/8 0 7/24 14/27 13 398 0 17/29 3/5 0 14/19 0 5/8 4/5 6/7 13 400 17/29 3/8 5/7 15/26 0 0 5/22 1/29 16/29 13 402 8/15 5/13 0 3/7 1/6 2/3 7/30 7/13 1/16 13 404 7/11 0 1/27 9/23 1/2 6/7 1/6 1/10 2/5 13 408 6/7 7/9 7/22 11/24 1/9 0 13/27 1/8 0 13 412 4/5 3/13 6/11 5/14 1/7 13/15 11/15 0 25/28 13 414 4/15 1/2 7/19 7/22 3/4 10/13 1/2 7/19 1/5 13 416 9/20 23/27 0 5/22 1/6 12/13 17/22 0 22/25 13 420 5/22 9/23 1/11 4/11 5/6 0 2/5 13/15 4/7 13 422 5/9 5/7 0 0 1/2 9/29 14/25 1/8 2/17 13 424 5/9 0 7/29 4/5 2/3 22/27 9/26 5/7 1/5 13 426 2/7 13/22 5/6 8/19 6/11 1/3 1/8 1/22 5/7 13 428 8/17 7/13 14/17 9/10 11/14 0 2/3 18/19 0 13 432 2/17 1/2 0 4/5 5/19 11/21 2/5 1/5 0 13 436 3/28 9/23 2/5 0 1/13 13/19 1/4 1/4 5/7 13 438 1/3 3/16 6/11 1/6 6/19 17/25 9/11 8/9 3/4 13 440 0 5/14 3/5 7/18 3/5 1/15 5/11 3/4 1/5 13 442 3/13 4/15 1/2 5/7 1/2 3/5 12/13 4/11 13/28 13 444 2/3 5/9 7/12 1/3 13/27 1/19 15/19 1/7 13/23 13 448 5/14 15/16 1/13 1/5 0 8/27 8/13 0 7/10 13 450 0 0 1/5 7/26 6/7 1/9 2/5 3/8 0 13 452 5/28 1/2 17/22 17/18 3/8 16/21 2/7 12/13 1/4 13 454 20/21 1/5 3/8 1/2 0 13/17 12/29 3/13 1/4 13 456 18/19 9/14 4/5 7/23 14/15 1/2 25/28 5/7 8/15 13 458 4/5 7/27 1/2 4/5 4/13 1/11 22/29 18/29 1/6 13 460 19/20 3/28 1/13 13/14 0 7/11 7/18 1/3 3/20 13 462 0 2/7 2/5 1/8 1/4 8/29 1/15 0 7/17 13 464 4/5 19/20 14/23 0 2/5 9/25 4/15 19/23 1/2 13 466 25/27 1/3 4/5 2/13 0 8/25 9/14 17/20 2/3 13 468 17/19 0 11/13 1/20 3/5 6/7 9/10 3/10 24/29 13 470 1/2 2/7 0 3/5 7/9 11/21 4/15 11/16 15/19 13 472 3/11 4/5 10/27 5/7 1/3 3/7 10/19 0 1/8 13 474 5/29 11/21 2/15 0 4/7 4/5 17/21 13/16 9/14 13 476 16/23 1/3 5/8 3/4 17/18 2/19 22/25 12/29 1/23 13 478 15/28 17/22 24/29 3/10 7/19 3/4 0 1/24 0 13 480 11/13 23/24 2/15 5/7 17/29 0 14/15 7/15 0 13 484 13/22 1/3 6/11 12/13 6/25 7/8 1/4 20/29 13/15 13 486 11/12 2/7 22/27 0 2/3 2/5 7/10 6/11 5/23 13 488 19/28 5/9 5/13 26/27 3/7 1/2 11/14 5/29 5/22 13 490 23/27 1/28 1/7 19/28 4/27 0 8/9 3/5 3/5 13 492 1/12 13/27 7/15 17/27 1/2 8/9 13/17 2/7 2/17 13 494 4/11 1/3 3/26 2/7 19/30 27/29 8/15 3/4 13/20 13 496 3/7 8/11 16/17 5/11 0 1/16 5/8 9/20 3/7 13 498 3/4 15/17 9/28 1/6 4/17 2/5 7/9 17/18 3/5 13 500 4/5 9/13 19/25 7/12 13/20 5/7 3/13 10/21 11/15 13 502 1/4 2/13 0 8/15 16/25 9/26 17/18 18/23 0 13 504 7/12 20/23 4/7 5/17 5/6 8/15 5/22 2/7 9/25 13 506 4/5 0 5/7 4/7 5/29 7/10 0 3/29 22/23 13 508 5/9 26/27 4/9 8/9 7/11 7/10 7/17 2/11 3/13 13 510 2/9 4/5 1/2 6/7 2/3 4/13 7/15 19/22 1/3 13 512 1/10 2/19 0 1/27 7/24 3/5 3/4 1/21 7/16 13 514 11/26 7/12 16/27 7/16 7/10 11/30 3/8 7/15 7/20 13 516 5/28 3/10 9/20 2/19 7/8 2/19 3/10 1/4 6/7 13 518 14/25 3/8 1/17 0 14/19 18/29 4/5 1/2 14/19 13 520 11/18 8/11 0 2/5 17/18 17/26 1/6 5/14 1/15 13 522 23/25 3/4 13/20 1/3 6/7 4/11 2/7 15/16 3/4 13 524 1/7 1/14 8/25 4/5 6/7 1/7 1/2 1/10 25/29 13 526 4/7 1/30 4/13 0 0 4/21 6/13 3/5 3/13 13 528 5/14 3/8 1/5 4/7 0 1/7 4/11 5/11 7/10 13 530 7/9 11/25 6/7 2/13 0 19/23 0 4/21 12/25 13 532 11/13 11/30 0 2/15 11/15 7/24 1/25 4/21 3/10 13 534 2/7 0 16/21 5/27 17/27 1/4 3/5 2/27 9/17 13 536 23/27 3/5 19/29 2/9 1/7 1/3 1/13 11/24 13/18 13 538 13/14 7/13 11/15 1/5 14/29 13/18 1/5 3/4 2/3 13 540 4/5 3/10 2/3 10/11 23/26 1/5 10/19 8/29 1/10 13 542 8/15 21/25 1/3 7/9 3/11 19/28 2/3 6/23 1/5 13 544 5/7 1/5 1/15 4/5 1/18 0 1/6 6/13 5/26 13 546 1/14 6/13 1/6 14/23 4/9 7/11 2/27 0 0 13 548 11/18 16/27 8/9 5/24 23/24 4/11 1/18 3/7 11/20 13 550 16/19 1/3 17/21 19/23 5/19 4/9 11/28 7/12 3/10 13 552 2/9 5/8 2/3 4/23 3/16 3/19 1/2 13/19 9/16 13 554 20/21 1/5 12/13 1/11 3/16 0 0 7/30 14/25 13 556 3/8 13/16 6/19 20/29 1/5 1/3 9/19 3/11 11/13 13 558 1/5 11/16 5/27 2/7 21/22 11/12 11/15 0 2/7 13 560 6/29 1/2 8/9 7/25 27/29 4/7 11/18 15/22 17/28 13 562 26/27 0 3/10 1/22 7/22 1/4 4/19 13/23 3/5 13 564 11/24 1/6 3/14 2/9 10/27 10/23 7/16 9/26 13/29 13 566 8/13 1/7 9/10 2/19 1/3 7/11 14/15 2/5 2/13 13 568 9/10 2/3 11/14 11/18 2/23 1/11 21/22 3/22 19/23 13 570 3/5 3/22 2/7 14/19 2/3 3/7 0 7/15 17/29 13 572 1/9 6/11 0 16/21 10/21 1/25 1/4 3/5 9/11 13 574 3/17 7/8 3/5 3/11 2/19 2/15 0 0 3/7 13 576 7/29 23/28 3/7 1/3 7/29 8/25 1/2 2/25 11/20 13 578 8/9 26/27 3/4 1/28 3/5 5/23 4/27 7/10 0 13 580 1/20 13/23 13/27 13/21 22/29 9/10 4/7 1/3 1/5 13 582 1/2 15/22 9/29 7/27 5/21 2/5 3/8 5/11 0 13 584 4/5 2/9 1/6 2/7 3/10 4/11 4/23 5/23 1/2 13 586 4/23 12/13 5/7 1/6 5/6 14/15 8/9 3/11 9/13 13 588 1/9 3/7 1/2 18/23 4/5 5/14 9/10 1/14 22/25 13 590 1/11 1/10 13/14 5/12 1/4 5/8 20/23 15/23 8/29 13 592 2/7 2/23 4/15 13/27 1/3 6/7 7/15 8/9 10/13 13 594 1/23 17/18 7/9 3/20 1/5 8/25 5/26 22/23 1/3 13 598 3/10 11/18 1/7 10/11 1/29 1/10 0 15/16 17/30 13 602 1/3 11/12 14/29 22/27 22/23 11/16 2/7 3/7 7/10 13 604 9/26 6/7 1/29 4/19 5/14 12/13 3/14 13/16 0 13 606 7/10 8/11 4/5 3/7 5/8 12/13 4/5 4/9 4/15 13 608 14/17 2/15 1/4 14/15 4/11 11/17 13/21 15/16 9/11 13 610 14/23 11/19 6/25 1/2 1/16 3/4 23/30 3/8 13/15 13 614 18/25 3/11 2/5 12/13 4/5 11/28 24/25 6/13 2/5 13 616 0 5/11 1/22 17/21 2/15 7/11 4/13 17/22 8/27 13 618 26/29 4/5 3/19 3/8 17/26 1/26 7/10 6/13 1/8 13 620 0 1/9 1/15 10/17 2/5 8/15 22/23 7/8 22/27 13 622 3/11 3/10 0 5/14 15/28 3/8 6/7 3/5 2/17 13 626 7/9 1/8 2/7 4/11 3/10 1/7 7/18 7/11 2/7 13 628 13/23 7/9 9/11 3/8 1/16 5/9 25/26 3/4 11/15 13 630 3/8 6/17 5/26 0 2/5 4/9 2/13 17/21 2/5 13 634 17/26 16/23 1/9 1/2 5/18 9/25 9/20 6/29 10/11 13 638 0 8/13 6/13 4/7 5/8 1/20 8/9 6/7 17/18 13 642 4/29 17/23 1/15 2/7 4/5 11/17 2/19 5/8 2/7 13 644 8/9 11/15 10/13 1/3 24/29 7/29 10/23 2/9 3/14 13 646 1/27 4/11 14/25 11/15 1/15 5/17 1/28 15/28 9/17 13 650 17/26 2/5 5/7 3/5 4/7 7/27 5/14 3/8 18/23 13 652 1/8 9/17 3/23 0 4/5 12/19 4/17 15/19 1/16 13 654 2/19 15/28 25/26 13/14 11/14 5/24 6/7 7/25 18/23 13 656 17/24 9/19 1/7 7/16 11/13 13/22 19/26 7/18 1/2 13 658 3/5 4/11 6/11 25/28 11/19 23/28 2/3 9/13 1/7 13 660 13/20 3/7 13/16 7/22 23/30 3/19 0 1/18 7/11 13 662 12/23 4/9 13/22 8/9 14/15 24/25 5/6 7/15 12/29 13 664 5/16 15/17 12/13 12/19 3/4 9/13 3/20 1/24 1/11 13 666 5/6 4/11 18/25 19/24 11/18 4/13 8/29 2/15 23/26 13 670 1/14 4/19 2/13 23/29 11/21 4/9 13/20 17/21 4/29 13 672 2/13 3/23 7/19 5/11 7/24 4/17 1/2 5/13 6/7 13 674 18/29 1/11 16/25 13/25 4/7 15/19 1/8 2/21 6/7 13 676 11/18 11/23 1/2 6/13 7/10 9/29 13/24 5/13 3/5 13 678 8/25 4/5 1/2 5/13 5/19 10/17 7/16 1/21 2/5 13 682 1/22 13/17 7/25 5/28 2/5 8/19 19/24 5/14 15/17 13 684 17/19 13/20 14/17 11/17 15/17 11/14 1/2 9/11 4/19 13 686 5/27 5/9 17/20 2/5 13/14 9/19 20/21 12/17 6/25 13 688 r1 r2 r3 r4 r5 r6 r7 r8 r9 13 688* ----------------------------------------------------------------------------------- 0 1/2 2/3 0 1/2 1/2 1/3 0 1/2 14 12 0 0 0 2/5 0 1/4 0 0 3/5 14 36 0 1/2 0 1/5 1/2 1/2 1/5 0 0 14 48 0 1/2 1/2 3/5 1/2 0 1/2 1/5 0 14 60 ----------------------------------------------------------------------------------- 1/6 2/3 0 1/6 1/3 0 3/4 0 1/4 15 12 0 2/3 0 1/2 2/5 2/3 1/4 0 0 15 36 1/4 0 3/5 5/6 0 2/5 2/3 0 3/4 15 48 0 0 0 0 1/3 1/6 3/4 4/5 2/5 15 52 0 0 0 0 1/3 3/5 3/5 3/4 0 15 60 1/4 1/2 1/7 4/7 2/3 0 2/7 1/2 1/18 15 114 17/18 1/2 19/24 8/15 3/4 1/4 0 11/14 0 15 216 1/14 1/2 3/5 0 13/27 0 1/26 3/4 17/18 15 300 0 2/7 2/5 9/19 17/20 1/7 3/20 2/5 3/5 15 384 ----------------------------------------------------------------------------------- 0 1/2 1/4 2/3 0 0 1/3 0 0 16 12 ----------------------------------------------------------------------------------- 0 0 0 0 0 0 0 0 0 17 12 3/5 0 2/5 2/5 1/3 0 3/5 0 3/4 17 30 1/2 1/2 1/3 0 0 0 3/4 4/5 1/4 17 32 7/15 0 4/5 0 1/2 0 4/5 0 0 17 36 4/5 0 5/6 2/3 0 0 1/4 1/5 0 17 40 0 0 2/3 0 4/5 0 0 0 1/5 17 44 0 0 0 3/5 2/5 0 5/6 3/4 0 17 48 0 2/3 0 0 4/5 1/3 3/5 4/5 4/5 17 52 1/2 1/5 0 2/3 1/4 0 2/5 1/4 0 17 56 3/4 4/5 1/2 1/2 1/4 1/5 0 0 0 17 60 0 1/3 1/12 5/12 5/6 2/3 3/11 5/6 7/15 17 72 0 0 1/3 0 26/27 0 4/5 0 5/8 17 104 3/4 0 1/5 23/24 2/3 0 1/2 1/6 5/13 17 108 15/17 0 0 1/3 1/2 0 7/9 5/6 17/27 17 120 1/2 0 1/3 0 3/7 0 1/15 2/17 7/12 17 116 7/12 0 6/13 1/6 5/11 0 0 0 9/26 17 132 7/15 0 1/2 3/10 20/29 0 0 7/25 1/2 17 140 15/23 0 12/29 5/9 0 0 1/3 1/2 2/9 17 156 5/7 0 0 10/19 1/3 0 15/28 0 9/16 17 168 9/11 0 1/2 1/6 6/7 0 7/10 0 13/20 17 180 1/24 0 7/20 0 7/12 0 3/4 19/28 23/28 17 184 10/13 0 0 0 5/17 0 3/8 5/9 7/8 17 188 5/6 0 8/9 0 5/6 0 1/7 1/15 27/28 17 192 17/24 0 3/10 1/4 4/9 0 3/4 18/29 4/5 17 194 27/29 0 5/12 1/2 0 0 4/19 19/20 17/30 17 204 15/17 0 4/5 7/23 1/2 0 7/12 5/19 6/13 17 210 12/13 0 3/4 1/11 0 0 18/23 4/7 1/2 17 212 1/18 0 0 9/20 8/9 0 4/17 1/3 5/26 17 224 0 0 0 1/7 2/25 0 25/28 13/22 5/17 17 236 5/6 0 0 17/20 7/23 0 2/7 9/16 1/8 17 244 10/17 0 4/7 3/7 13/14 0 0 21/25 19/21 17 248 7/10 0 4/7 3/5 0 0 13/21 6/7 3/19 17 250 3/7 0 14/15 2/11 2/3 0 16/29 1/8 11/15 17 258 7/9 0 7/10 0 1/13 0 7/11 0 19/22 17 264 14/23 0 5/11 9/11 0 0 1/11 3/14 0 17 276 3/23 0 2/5 23/26 2/19 0 7/9 2/3 2/27 17 282 3/29 0 0 9/10 4/15 0 8/9 22/23 1/3 17 284 1/9 0 2/11 1/29 4/5 0 9/23 3/4 0 17 292 4/5 2/3 1/4 3/14 3/11 1/3 3/5 3/8 6/7 17 298 2/7 0 0 3/8 28/29 0 0 2/5 9/17 17 312 1/15 0 0 23/25 6/7 0 25/27 11/16 0 17 316 1/19 0 9/23 1/2 5/8 0 3/5 9/11 3/16 17 348 7/16 1/3 0 10/21 8/9 2/3 20/29 7/8 6/25 17 352 4/5 0 4/11 3/19 1/8 0 20/23 4/27 0 17 356 2/5 0 13/27 1/21 11/26 0 25/26 6/7 13/29 17 362 ----------------------------------------------------------------------------------- 0 0 1/3 1/3 1/2 0 1/2 0 1/3 18 12 3/4 2/3 0 3/4 0 1/3 1/2 4/5 0 18 36 ----------------------------------------------------------------------------------- 0 0 1/6 0 0 0 3/4 1/2 1/2 19 12 0 0 0 4/5 1/2 0 3/4 0 1/2 19 36 0 1/8 0 1/2 2/3 7/8 3/4 10/21 0 19 60 ----------------------------------------------------------------------------------- 2/3 2/3 1/3 2/3 2/3 1/3 2/3 0 5/6 20 12 ----------------------------------------------------------------------------------- 0 3/4 3/4 1/4 1/2 1/3 1/2 1/2 0 21 12 0 0 1/2 0 0 1/2 1/4 1/5 3/4 21 28 0 0 0 0 0 0 3/4 3/4 1/5 21 36 1/2 1/3 1/2 1/2 3/4 2/5 1/4 2/5 0 21 48 ----------------------------------------------------------------------------------- 0 0 1/2 0 1/2 0 0 0 3/4 23 12 -----------------------------------------------------------------------------------
F12D(p1, ..., p9)↑
show data
p1 p2 p3 p4 p5 p6 p7 p8 p9 d #Λ ----------------------------------------------------------------------------------- 1/6 0 0 0 0 0 0 0 0 13 12 1/6 1/6 1/4 1/8 1/6 0 0 0 0 13 24 0 0 0 0 0 1/6 1/2 5/9 1/3 13 36 1/5 2/3 2/3 0 2/3 2/3 1/2 1/3 1/5 13 48 1/3 0 1/6 1/2 1/4 1/4 1/5 3/5 3/5 13 52 1/4 17/24 1/4 1/3 0 3/5 5/12 0 1/3 13 60 4/11 1/6 0 5/9 0 1/3 2/3 0 0 13 72 3/7 0 7/20 0 1/6 3/5 7/12 13/23 3/4 13 78 1/2 5/12 1/10 2/3 1/2 5/6 14/25 1/2 3/5 13 84 23/30 7/8 3/5 0 2/3 5/8 1/4 0 4/5 13 90 0 1/2 0 17/18 19/21 0 0 0 8/9 13 96 1/3 7/8 2/3 9/28 0 0 4/5 0 2/3 13 108 0 1/2 0 3/4 3/5 11/21 0 9/14 1/7 13 112 0 0 10/23 9/11 1/3 0 20/23 1/2 1/4 13 120 19/23 3/8 1/6 1/2 0 2/3 0 3/10 1/6 13 132 1/4 1/3 3/14 1/6 0 25/29 6/7 5/6 27/29 13 138 9/22 3/11 1/6 0 1/2 0 2/3 0 8/25 13 144 1/4 8/11 0 0 0 4/15 8/15 4/5 0 13 148 1/12 1/2 5/23 13/14 0 1/2 16/25 1/3 8/15 13 150 0 7/12 0 5/6 1/2 2/13 1/10 0 11/25 13 156 3/11 1/3 6/11 4/7 0 2/3 1/3 5/21 5/6 13 160 1/3 2/3 16/21 1/2 3/26 5/6 17/28 19/28 2/7 13 168 11/18 1/2 4/21 1/6 3/4 17/24 7/10 3/8 0 13 172 4/5 16/25 7/12 0 0 0 3/4 9/14 5/7 13 174 6/29 1/6 1/3 1/2 0 0 4/5 7/20 11/29 13 176 1/15 0 0 2/5 1/4 1/4 2/3 10/11 16/23 13 180 9/13 0 4/5 1/3 1/6 17/26 1/9 5/9 3/4 13 182 5/6 2/3 0 0 3/8 7/20 6/13 3/4 26/27 13 184 17/28 1/3 8/9 1/6 5/7 0 1/4 11/13 5/8 13 186 0 2/3 12/13 1/13 12/29 1/2 3/4 0 23/29 13 192 1/19 0 25/27 2/3 6/11 16/23 3/4 1/3 15/19 13 194 0 17/18 1/6 0 7/12 3/4 11/23 5/11 3/5 13 196 0 0 0 5/6 0 7/9 6/7 19/27 1/8 13 200 19/26 1/3 1/2 1/3 3/11 3/4 1/6 4/5 3/5 13 204 21/23 0 24/29 1/2 11/12 1/2 0 1/13 9/10 13 208 1/5 0 0 5/14 2/3 2/3 1/8 9/22 3/4 13 212 1/2 9/22 0 17/21 13/15 26/29 1/2 1/2 2/3 13 216 12/13 0 0 3/8 0 11/27 23/24 18/29 5/6 13 220 1/30 5/7 19/24 10/23 5/6 0 3/13 0 1/8 13 222 19/25 0 0 5/6 1/6 17/29 11/16 27/29 0 13 224 3/7 1/2 0 3/11 2/3 4/13 0 1/2 17/19 13 228 3/8 14/17 11/26 0 2/3 0 1/4 13/23 4/15 13 230 5/24 1/2 1/3 11/12 7/8 21/26 8/13 0 7/30 13 232 4/9 1/3 10/13 1/24 2/5 1/3 11/12 1/3 1/5 13 234 2/3 4/11 0 1/11 1/6 0 4/11 2/13 14/15 13 236 0 1/8 6/13 6/7 2/19 2/3 6/13 0 2/3 13 240 0 7/25 7/9 1/2 11/12 0 1/7 5/8 5/12 13 244 3/4 0 9/11 7/8 2/3 3/14 8/19 0 1/20 13 246 5/6 7/29 7/12 13/18 1/4 5/12 0 25/28 2/7 13 248 9/17 1/2 17/30 1/3 3/7 7/10 1/4 5/9 12/23 13 250 13/30 21/26 1/3 1/4 0 7/10 3/5 16/21 1/30 13 252 4/21 1/2 11/21 21/26 1/6 2/17 5/12 7/11 11/14 13 254 1/8 3/4 1/5 3/4 13/19 1/5 5/8 9/11 4/5 13 256 20/21 2/3 5/14 5/9 3/22 1/2 4/23 0 13/21 13 258 1/14 0 1/2 7/13 0 8/11 8/11 17/30 1/3 13 260 14/15 0 10/29 1/2 3/7 4/7 3/14 1/2 14/27 13 262 1/2 0 2/3 2/11 5/7 23/29 1/12 14/15 0 13 264 9/14 1/2 6/13 0 6/19 4/13 1/2 0 1/14 13 268 11/19 2/7 3/4 1/18 2/3 13/18 11/19 1/2 8/13 13 270 11/29 5/14 5/14 1/6 4/7 1/3 1/6 18/25 1/4 13 272 3/7 0 13/19 1/9 1/12 1/2 4/7 0 6/7 13 276 2/7 0 3/7 0 7/27 2/19 11/19 1/2 0 13 280 6/7 12/25 1/9 1/3 0 16/29 3/5 0 14/15 13 282 16/23 0 5/22 1/3 1/2 1/5 2/3 18/23 1/9 13 284 4/7 1/6 7/12 8/11 2/15 1/3 5/8 14/19 7/12 13 286 7/16 3/4 5/24 1/12 1/2 1/2 18/23 19/26 1/5 13 288 11/23 1/2 11/16 2/3 1/2 9/10 7/11 12/25 8/13 13 290 7/25 1/2 1/3 2/7 2/9 1/4 13/21 5/22 2/9 13 292 18/25 4/9 4/5 0 9/11 1/2 7/15 10/21 3/4 13 294 3/10 3/5 1/13 0 2/3 4/7 3/8 11/20 4/15 13 300 1/5 0 1/23 11/28 1/2 1/6 5/8 5/7 11/16 13 302 13/18 1/6 11/19 5/16 11/18 9/25 0 1/4 0 13 304 1/4 4/5 11/24 13/21 0 3/14 1/5 1/2 7/25 13 306 3/8 0 0 7/30 7/17 11/14 5/12 0 1/18 13 308 1/3 11/25 0 1/3 15/17 8/15 1/3 1/13 5/13 13 312 2/9 0 8/11 1/3 5/23 8/25 0 7/10 7/10 13 316 1/7 3/14 1/2 11/14 1/12 3/5 7/9 1/10 1/3 13 318 18/25 0 3/20 4/13 7/16 7/11 3/4 1/2 1/6 13 320 3/4 3/5 13/15 11/14 1/3 2/5 4/7 7/8 1/8 13 322 0 1/5 3/5 0 4/11 19/30 4/11 2/7 2/5 13 324 26/27 20/21 14/15 1/2 0 9/26 1/4 7/18 8/15 13 326 9/14 1/3 13/18 2/7 8/11 3/8 0 0 1/4 13 328 2/5 23/27 1/10 2/3 0 13/17 14/15 3/7 13/21 13 330 0 4/7 24/25 4/7 5/23 1/4 17/21 0 7/23 13 332 17/20 1/7 19/27 2/5 1/2 7/17 5/12 4/17 1/4 13 338 3/13 3/13 7/9 17/23 0 4/19 1/2 4/19 0 13 340 9/16 13/20 19/30 0 9/13 0 5/7 1/2 8/11 13 342 1/4 3/5 1/5 1/9 0 1/2 1/2 5/23 14/27 13 344 1/9 2/3 0 0 15/17 1/19 23/26 11/24 3/17 13 348 9/13 2/3 15/23 0 8/9 11/15 19/25 28/29 2/9 13 350 1/2 14/17 1/3 1/10 5/7 1/2 10/27 29/30 4/5 13 352 17/23 2/3 5/14 1/6 4/7 17/18 1/5 1/10 5/23 13 354 1/22 3/4 1/2 9/13 2/3 1/2 22/27 6/7 4/19 13 356 3/4 0 9/10 15/17 9/10 0 13/16 2/11 11/13 13 358 11/19 23/26 0 1/21 9/19 6/11 0 2/3 1/2 13 360 4/5 5/11 5/9 3/4 20/23 3/4 0 0 9/10 13 364 17/30 7/18 1/4 3/25 1/16 0 4/9 0 5/14 13 366 1/7 5/7 19/28 3/7 2/5 1/4 1/16 3/7 1/6 13 368 2/3 1/9 7/9 13/15 1/2 1/2 16/25 17/30 11/14 13 372 3/4 4/7 7/13 13/22 1/7 0 13/18 13/29 5/9 13 374 9/10 1/5 3/7 0 3/4 1/13 1/4 3/17 1/11 13 376 2/7 5/6 3/10 1/5 5/8 9/10 3/4 24/25 8/19 13 378 1/13 0 13/16 10/19 2/3 29/30 2/3 18/19 17/30 13 380 3/4 1/5 5/13 2/5 29/30 13/17 5/12 3/23 3/28 13 382 1/6 1/3 11/13 5/21 0 15/16 3/25 1/7 3/7 13 384 8/9 1/2 1/12 1/7 4/7 11/21 16/19 10/23 2/29 13 386 1/2 2/3 1/16 7/15 17/22 6/7 8/15 2/9 0 13 388 26/27 3/5 1/12 4/17 3/13 1/3 20/29 5/6 11/25 13 390 2/13 7/26 1/2 7/8 2/3 4/5 1/8 10/29 1/24 13 392 7/8 0 8/17 1/23 8/11 22/23 6/19 1/2 14/15 13 394 1/4 1/2 13/21 5/7 16/25 2/9 1/8 13/27 5/7 13 396 1/11 1/2 11/13 18/19 11/18 3/5 3/4 8/17 1/3 13 400 1/3 19/24 2/5 2/5 7/11 8/15 4/7 2/3 3/4 13 404 10/13 1/2 8/29 9/14 19/24 1/5 3/4 1/9 7/30 13 406 9/20 8/13 0 12/29 2/3 3/26 3/4 6/7 6/29 13 408 2/3 3/14 5/6 11/30 12/17 0 11/29 4/5 19/27 13 412 5/17 2/5 1/5 2/25 2/3 27/29 3/5 0 20/27 13 414 6/25 14/23 0 0 13/15 2/3 10/23 20/27 17/30 13 416 17/19 1/9 2/9 0 7/8 3/14 2/7 7/9 8/15 13 418 1/7 11/27 4/5 11/18 15/16 5/6 5/6 1/2 2/9 13 420 13/16 0 8/27 9/23 7/13 3/25 12/13 1/2 1/13 13 422 1/2 1/2 12/17 6/7 1/2 1/20 4/17 4/7 7/9 13 424 19/20 10/11 8/23 1/6 0 12/17 11/24 1/9 10/17 13 426 5/7 11/27 5/13 0 0 1/15 0 11/23 13/16 13 428 11/24 5/18 2/5 1/2 0 6/7 5/13 4/5 21/22 13 430 1/3 7/23 3/5 19/23 1/2 8/9 7/9 7/9 9/29 13 432 7/15 0 3/7 7/26 3/17 2/3 13/25 15/19 22/23 13 434 9/11 2/3 1/13 2/19 0 13/27 9/14 19/23 16/21 13 438 7/19 3/5 2/21 3/5 9/13 5/28 0 19/26 5/16 13 440 5/27 3/5 3/4 3/5 7/19 13/25 3/7 2/7 4/9 13 442 0 1/17 1/2 1/5 3/5 16/27 11/13 14/29 0 13 444 1/4 8/15 1/14 13/15 6/19 21/22 0 7/11 1/9 13 448 2/5 10/11 13/24 1/18 12/13 1/2 1/9 0 4/5 13 450 2/15 17/19 2/3 2/11 1/3 9/11 15/29 9/28 0 13 452 26/27 4/7 2/11 11/19 1/2 17/24 4/13 0 1/2 13 456 7/8 2/9 21/25 9/10 5/8 1/15 1/13 1/2 5/7 13 458 1/2 0 1/27 2/7 2/29 3/7 2/15 11/30 2/21 13 460 23/26 1/5 17/20 4/7 1/3 28/29 1/21 0 3/13 13 462 1/5 20/27 13/29 22/25 1/4 11/27 3/5 2/3 4/5 13 464 4/11 15/23 1/2 6/17 0 9/20 6/7 0 5/11 13 468 23/30 1/2 17/30 4/7 7/15 20/21 1/7 17/22 9/11 13 470 1/8 1/23 3/5 1/6 16/19 2/9 1/2 9/29 17/24 13 472 3/4 5/17 8/29 8/9 2/15 10/23 9/14 0 6/13 13 474 8/29 0 0 5/23 1/17 14/15 7/8 3/20 4/29 13 476 1/23 1/4 1/2 1/25 6/17 7/25 1/16 0 5/24 13 480 4/5 9/20 7/12 4/11 1/22 1/3 18/29 6/23 7/8 13 482 1/2 12/23 0 11/14 7/20 17/22 13/19 2/9 5/12 13 484 7/10 0 27/28 11/16 1/20 7/17 2/5 18/25 7/13 13 486 19/25 21/25 1/6 7/10 2/3 7/9 4/5 17/28 6/25 13 488 7/20 16/27 12/17 3/5 1/3 6/25 13/25 7/15 10/27 13 490 11/13 0 0 4/27 7/24 5/7 7/29 11/21 9/13 13 492 1/2 1/21 3/7 7/19 7/10 1/10 9/14 23/30 5/9 13 494 0 3/5 26/29 1/3 8/15 1/13 23/25 7/24 9/25 13 496 0 7/25 24/29 1/4 16/23 0 4/15 5/22 12/13 13 500 2/3 1/2 9/13 4/11 9/16 21/22 24/25 7/25 7/22 13 504 3/4 3/5 6/13 11/28 2/17 15/19 3/7 27/29 1/4 13 506 13/17 3/5 3/8 1/3 16/29 11/23 0 1/9 16/19 13 508 10/29 0 14/17 4/19 12/17 3/10 6/13 9/11 19/25 13 510 0 2/11 4/5 7/9 18/29 1/2 5/9 7/30 11/13 13 512 1/5 7/18 1/14 23/24 3/29 3/4 3/20 4/15 2/3 13 514 7/10 11/21 1/2 10/23 21/22 9/16 19/22 2/3 2/3 13 516 4/27 9/14 1/14 1/18 7/9 5/26 7/11 1/3 17/26 13 518 12/23 13/25 4/19 2/3 1/7 9/25 0 4/5 10/27 13 520 3/23 2/3 13/28 19/25 18/19 2/9 4/11 22/23 19/21 13 522 0 4/27 1/6 26/29 19/20 7/24 17/18 1/5 13/14 13 524 1/15 3/20 3/5 7/12 10/13 3/4 13/19 5/16 18/25 13 528 5/6 22/27 19/29 5/16 18/29 3/4 8/23 11/17 3/4 13 532 23/30 2/17 19/23 15/23 0 14/27 22/23 1/5 2/5 13 534 9/13 22/27 7/18 5/9 2/5 0 0 1/7 5/13 13 536 1/5 3/5 0 2/15 5/24 19/28 3/8 8/21 7/13 13 538 4/15 13/21 7/8 7/9 0 23/26 5/8 4/5 1/7 13 540 13/21 1/8 1/3 4/13 8/11 7/8 13/17 14/15 1/3 13 542 0 13/19 5/11 2/9 0 1/15 4/5 17/18 9/11 13 544 1/24 15/17 22/25 4/9 5/14 7/8 4/7 0 5/11 13 546 5/6 8/11 8/15 20/29 0 16/23 8/11 5/7 6/17 13 548 4/9 2/19 5/6 5/21 1/4 5/14 25/26 1/14 11/27 13 550 0 1/13 0 5/8 17/26 4/9 21/22 12/23 11/25 13 552 6/13 19/30 11/13 1/7 1/11 7/15 7/9 0 8/27 13 554 4/29 3/5 13/17 2/5 1/7 2/7 3/10 0 4/23 13 558 1/20 6/17 0 3/7 4/5 1/8 11/17 3/11 1/11 13 560 2/23 13/14 5/23 10/27 5/8 1/2 0 25/28 4/17 13 564 11/15 3/10 3/4 13/19 14/25 2/19 5/28 5/14 0 13 568 12/17 22/29 2/7 13/27 7/16 2/7 15/16 11/12 1/10 13 570 2/3 9/25 3/17 18/25 17/29 1/9 3/8 2/5 0 13 572 13/15 8/9 0 7/9 5/17 17/19 20/27 13/22 0 13 574 1/15 1/16 2/13 1/4 0 9/25 27/29 14/15 3/14 13 576 9/23 6/7 3/4 17/18 7/8 5/18 17/19 7/29 2/15 13 578 3/13 5/18 3/14 1/4 28/29 7/8 17/19 18/19 0 13 580 2/9 1/9 4/27 16/29 2/15 0 13/21 2/17 19/29 13 582 1/3 3/20 5/7 4/27 1/2 4/7 2/13 1/5 11/23 13 584 4/7 15/19 2/5 1/8 9/10 7/8 0 11/26 16/25 13 586 4/5 3/23 10/17 9/23 2/3 11/15 0 5/9 5/23 13 588 12/13 11/21 0 5/26 3/4 5/21 13/25 16/29 8/13 13 590 3/4 5/8 0 20/29 17/18 10/29 14/19 4/25 14/25 13 592 21/23 3/16 4/15 7/24 6/17 1/2 7/9 1/7 1/13 13 594 11/30 2/29 3/10 8/17 1/14 6/7 1/2 2/19 3/7 13 598 0 12/29 11/15 11/14 4/9 11/28 8/29 1/8 5/12 13 600 9/23 4/17 7/11 3/5 3/5 23/24 1/27 7/12 5/8 13 602 5/21 6/17 0 3/11 11/24 5/26 3/5 1/13 7/12 13 604 5/8 8/9 5/6 12/19 6/7 13/15 10/11 8/9 1/11 13 606 3/4 22/29 7/30 8/9 20/21 1/23 5/7 2/5 5/19 13 610 23/25 3/26 8/11 25/28 1/9 5/11 0 3/5 5/18 13 614 9/19 4/7 26/27 13/14 1/4 3/7 7/9 11/15 3/29 13 618 1/5 3/5 5/21 26/27 5/7 3/11 5/6 3/10 6/7 13 620 2/3 1/7 4/7 2/9 17/19 5/9 8/23 7/25 13/16 13 626 3/5 2/5 2/11 4/21 6/17 5/12 8/11 5/8 5/14 13 630 8/9 3/8 1/5 5/7 18/29 13/16 13/21 7/8 4/11 13 632 4/5 4/19 1/5 17/20 18/19 1/25 1/13 18/23 1/2 13 634 1/8 1/8 6/7 15/29 3/14 15/26 1/5 11/21 5/11 13 638 8/13 4/13 11/26 6/11 8/19 7/26 6/7 3/5 22/27 13 640 1/22 1/5 1/18 3/29 1/5 7/17 7/16 13/28 3/5 13 644 6/13 5/8 4/11 17/18 11/26 3/14 0 13/20 23/26 13 646 0 7/29 16/29 7/10 9/17 1/19 15/17 2/25 7/15 13 650 0 6/13 21/25 3/10 1/15 27/28 13/14 6/7 8/9 13 654 17/20 11/26 22/25 8/9 11/13 19/24 11/16 5/18 5/7 13 656 1/8 4/7 13/17 14/23 6/7 4/5 0 2/29 3/5 13 658 10/17 3/8 5/9 5/26 10/27 7/20 27/29 13/14 0 13 670 15/17 2/7 5/9 17/20 3/8 4/5 27/28 19/25 9/11 13 672 13/19 11/15 19/27 2/15 2/11 23/29 4/11 13/19 16/23 13 674 4/5 1/5 7/11 5/13 5/11 3/20 8/23 3/11 13/27 13 676 3/7 8/23 5/14 1/11 3/22 7/12 1/8 27/29 2/5 13 678 2/9 5/8 1/7 12/13 16/21 3/10 3/13 1/4 4/19 13 682 1/11 6/11 17/30 9/26 1/14 4/9 1/3 26/29 20/23 13 684 23/29 21/23 1/13 3/17 25/29 23/25 2/13 8/15 2/9 13 688 r1 r2 r3 r4 r5 r6 r7 r8 r9 13 688* ----------------------------------------------------------------------------------- 1/6 0 0 3/4 2/3 2/3 0 0 1/6 14 12 0 2/3 4/5 1/2 0 4/5 2/3 0 1/2 14 36 0 0 1/3 4/5 1/2 3/5 0 0 4/5 14 60 ----------------------------------------------------------------------------------- 1/4 0 0 0 0 0 0 0 0 15 12 0 0 1/2 3/4 0 0 0 2/5 1/2 15 36 0 0 4/5 0 0 0 0 3/4 1/5 15 48 0 0 0 0 1/3 1/5 3/4 3/5 3/4 15 52 2/5 0 1/5 0 2/5 5/6 1/4 0 0 15 60 2/11 0 6/7 1/2 7/12 8/11 1/4 3/4 7/9 15 192 1/2 19/25 2/7 1/4 1/2 5/7 1/2 26/27 1/6 15 228 0 12/25 7/9 2/5 0 7/18 16/29 9/28 1/4 15 432 ----------------------------------------------------------------------------------- 0 1/2 2/3 1/3 2/3 1/2 0 0 1/4 16 12 0 1/4 1/5 1/6 0 4/5 0 0 2/3 16 60 ----------------------------------------------------------------------------------- 0 0 0 0 0 0 0 0 0 17 12 3/4 0 4/5 1/4 0 0 0 1/2 0 17 36 0 0 0 1/5 3/4 1/4 1/2 1/5 0 17 48 1/3 1/2 0 3/5 0 1/3 1/4 1/5 1/4 17 56 0 1/4 0 1/5 0 0 3/5 1/3 1/3 17 60 0 2/5 0 0 11/20 11/20 11/12 24/29 13/19 17 172 0 2/17 0 3/11 0 0 8/17 2/19 7/10 17 276 ----------------------------------------------------------------------------------- 0 1/3 0 0 0 0 1/3 3/4 0 18 12 ----------------------------------------------------------------------------------- 0 0 1/2 1/3 0 0 2/3 1/4 1/3 19 12 0 0 2/5 3/4 1/2 0 1/4 0 1/4 19 36 0 3/4 2/5 0 0 3/5 0 0 0 19 60 ----------------------------------------------------------------------------------- 0 0 0 1/3 1/4 0 1/4 3/4 0 21 12 1/4 1/3 4/5 0 0 0 3/4 0 1/4 21 18 0 0 1/2 1/2 1/2 0 3/4 3/4 2/5 21 36 0 1/2 4/5 0 3/5 1/2 3/4 3/4 1/3 21 60 ----------------------------------------------------------------------------------- 0 1/2 0 0 0 0 0 1/4 1/2 23 12 -----------------------------------------------------------------------------------
F14(p1, ..., p6)↑
show data
p1 p2 p3 p4 p5 p6 d #Λ ----------------------------------------------------------- 0 0 0 0 0 0 12 14 0 0 0 0 0 1/4 12 28 0 0 0 0 0 1/3 12 42 0 1/2 1/5 0 2/5 1/2 12 70 7/9 1/2 1/28 1/2 3/4 1/4 12 84 0 1/2 19/21 1/2 4/7 4/9 12 98 2/3 0 5/7 2/25 0 1/3 12 126 12/13 0 6/13 5/21 17/21 0 12 154 13/14 0 1/4 4/19 1/2 2/15 12 168 0 0 2/17 11/14 5/9 5/24 12 182 7/20 1/10 0 0 18/25 1/4 12 196 12/23 3/14 6/13 3/8 1/8 0 12 252 2/3 1/2 7/11 3/11 2/3 1/5 12 266 1/4 15/16 29/30 0 0 23/29 12 280 6/13 1/7 0 5/6 22/29 5/13 12 294 4/5 1/4 1/6 2/5 2/5 1/3 12 308 2/3 5/21 10/13 3/4 11/15 2/5 12 364 8/9 2/9 5/6 1/6 9/10 17/28 12 386 1/2 19/20 2/13 1/8 1/3 1/6 12 378 1/5 2/5 7/16 9/16 9/13 1/10 12 400 6/17 4/5 11/21 4/7 1/29 1/12 12 406 3/14 23/25 3/4 6/25 7/15 13/25 12 420 4/5 14/23 1/17 14/15 0 20/23 12 434 1/28 4/5 8/11 20/23 1/3 1/5 12 526 7/13 3/4 13/22 11/15 2/3 10/27 12 582 1/15 2/23 10/13 1/11 7/11 2/21 12 596 r1 r2 r3 r4 r5 r6 12 596* -----------------------------------------------------------
F15(p1, ..., p8)↑
show data
p1 p2 p3 p4 p5 p6 p7 p8 d #Λ --------------------------------------------------------------------------- 0 0 0 0 0 0 0 0 16 15 0 1/2 1/2 1/2 1/3 0 3/5 7/10 16 30 2/3 1/3 2/5 2/3 2/15 2/17 3/5 2/3 16 45 1/2 0 13/20 1/5 1/10 5/6 1/2 1/2 16 60 1/2 1/5 3/10 2/5 9/14 7/10 1/2 14/15 16 90 0 0 0 1/3 1/3 0 8/11 7/8 16 105 2/5 1/3 3/4 13/15 1/8 7/8 1/2 0 16 120 1/10 13/15 0 2/7 5/6 3/4 0 8/15 16 150 2/3 11/17 1/3 5/17 1/15 11/20 0 2/5 16 165 1/2 9/14 0 1/2 0 4/9 0 0 16 180 6/17 1/16 0 0 1/9 2/3 1/3 0 16 195 0 10/11 0 12/17 1/3 13/15 7/10 1/2 16 210 0 3/11 1/20 0 2/3 0 1/9 1/12 16 225 14/19 5/14 1/2 3/5 6/7 1/2 0 0 16 240 0 5/7 0 1/8 5/8 1/4 0 0 16 255 0 0 0 15/16 9/10 1/5 8/9 3/4 16 270 0 3/4 9/16 1/8 0 4/5 4/5 12/13 16 285 14/17 4/5 4/13 5/18 2/3 0 1/2 0 16 300 8/9 14/15 11/17 0 14/15 9/11 7/8 0 16 315 1/2 3/5 1/7 5/7 7/19 2/3 1/3 5/6 16 330 3/11 1/3 11/16 4/5 3/4 3/4 0 5/11 16 345 0 0 2/9 0 7/9 3/8 3/4 5/7 16 375 1/2 2/3 12/13 1/16 2/3 13/15 6/7 5/8 16 360 12/17 1/3 0 5/6 0 3/20 4/7 1/8 16 390 5/13 17/19 3/4 1/3 0 2/3 1/9 3/4 16 405 4/5 1/2 6/7 1/8 1/5 5/13 0 12/19 16 420 7/11 0 7/18 4/17 1/8 4/5 3/4 0 16 435 2/3 0 0 13/17 11/16 1/6 9/19 1/18 16 450 0 4/19 4/5 0 2/9 8/13 5/8 3/4 16 465 9/16 3/4 1/2 3/17 1/3 5/6 5/18 0 16 480 9/11 0 8/9 2/13 10/19 0 7/9 3/7 16 495 0 1/5 6/13 10/13 5/7 15/17 1/6 4/13 16 510 0 3/7 0 1/9 5/8 3/8 1/4 8/11 16 525 1/2 16/17 7/8 1/14 3/4 5/7 1/3 0 16 540 13/20 5/7 8/11 11/17 0 0 3/4 6/7 16 555 5/9 3/4 1/2 5/11 10/11 7/16 1/6 0 16 570 5/7 1/3 0 3/4 1/4 17/19 7/9 9/16 16 585 5/7 2/11 0 0 5/19 5/17 4/17 1/6 16 600 4/7 2/3 3/13 9/19 1/4 7/19 0 5/14 16 615 17/20 8/13 5/7 4/9 0 5/17 1/6 1/10 16 630 16/19 0 3/4 15/19 3/4 6/7 3/7 3/16 16 645 7/16 4/5 9/14 1/2 3/19 7/9 1/17 8/9 16 660 1/11 11/17 2/7 5/7 13/17 4/9 0 1/7 16 675 1/4 7/8 4/13 3/4 1/7 5/8 3/8 3/14 16 682 3/11 1/6 1/17 11/17 13/16 7/8 0 7/16 16 690 6/7 1/3 4/7 10/11 3/7 5/9 9/20 7/11 16 705 1/13 0 11/12 1/2 1/9 5/8 3/17 4/17 16 720 3/19 1/20 11/19 11/17 3/5 7/8 3/13 7/17 16 735 1/8 10/17 5/12 10/13 4/7 5/6 8/13 1/8 16 742 5/9 11/19 1/2 2/11 3/11 1/4 2/7 2/5 16 750 11/14 5/19 17/18 0 13/17 4/13 1/4 7/11 16 765 5/18 5/8 4/9 3/7 5/14 17/18 8/19 1/14 16 772 4/9 3/8 7/13 3/19 4/19 3/16 8/11 1/9 16 787 11/14 3/10 2/7 5/9 8/17 11/17 3/7 15/16 16 802 4/7 7/8 3/20 1/10 6/11 1/9 11/14 12/19 16 832 r1 r2 r3 r4 r5 r6 r7 r8 16 907* ---------------------------------------------------------------------------
F16(p1, ..., p17)↑
show data
p1 p2 p3 p4 p5 p6 p7 p8 p9 p10 p11 p12 p13 p14 p15 p16 p17 d7 #Λ
---------------------------------------------------------------------------------------------------------------------------------------------------
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 17 16
0 1/3 5/6 0 1/2 0 0 1/2 0 2/3 0 1/2 0 0 1/3 0 1/2 17 44
0 0 0 0 0 1/3 0 1/2 1/3 0 1/3 1/2 1/4 0 1/2 0 3/4 17 48
1/2 0 2/5 1/2 0 1/2 3/5 0 0 2/5 1/2 0 2/5 1/2 0 1/2 1/2 17 72
1/2 1/3 1/2 4/5 0 1/3 0 0 0 1/2 1/2 1/2 0 0 1/2 5/6 0 17 96
7/8 2/5 0 1/3 1/15 7/8 0 0 8/11 3/8 1/2 0 2/5 0 0 1/3 1/2 17 368
2/9 0 1/3 5/8 1/3 2/5 1/4 1/2 1/2 2/3 0 0 3/10 13/16 0 0 2/3 17 396
0 5/8 1/3 0 0 0 3/16 1/3 9/10 1/4 6/7 15/16 0 1/2 7/9 0 1/3 17 428
1/8 1/2 0 1/5 1/2 4/5 1/5 0 0 6/11 13/20 2/19 1/10 0 0 7/19 3/10 17 496
1/2 0 2/3 1/3 1/2 2/3 7/18 1/2 1/10 11/12 3/4 3/5 3/14 9/10 1/2 4/9 2/3 17 524
5/7 0 5/9 0 1/2 1/6 1/2 2/3 0 3/5 2/3 1/6 9/10 11/12 0 3/4 0 17 552
2/3 1/5 1/2 1/5 15/19 1/2 0 1/2 0 3/8 5/6 6/19 1/2 0 0 14/17 5/6 17 556
1/2 2/3 0 0 7/8 9/10 0 3/8 12/17 1/2 3/10 0 0 11/17 0 9/11 1/2 17 560
7/9 1/2 0 0 5/18 1/3 3/5 6/13 1/8 0 0 1/8 10/19 0 5/6 1/3 12/17 17 588
1/5 0 0 0 5/7 0 1/3 0 4/7 0 1/2 1/2 15/16 0 3/5 1/7 8/17 17 604
1/14 1/5 7/10 5/8 3/5 11/14 0 1/2 0 3/7 0 0 1/14 5/8 0 2/5 6/13 17 612
0 9/10 0 1/2 1/8 1/5 0 10/11 2/5 3/14 0 5/12 0 3/5 13/19 5/11 1/2 17 616
0 5/6 7/17 0 9/13 0 0 0 3/5 5/8 3/4 1/18 15/16 5/17 0 3/8 3/4 17 624
13/16 1/2 7/8 0 1/4 0 0 15/17 2/7 1/3 3/14 0 4/19 1/6 4/11 11/16 0 17 632
13/18 0 3/7 2/19 0 3/10 1/2 7/19 0 0 0 1/8 0 0 1/8 18/19 1/2 17 636
0 1/2 1/3 5/9 1/3 1/2 0 4/19 1/2 15/19 2/3 1/3 0 1/3 5/8 3/11 11/13 17 656
3/8 0 0 1/8 7/18 7/16 8/11 0 6/13 0 14/19 7/8 5/8 2/3 2/7 0 7/16 17 660
1/3 0 1/17 7/8 0 0 5/9 1/11 0 17/18 1/12 6/7 1/4 1/6 5/9 7/18 0 17 668
0 2/5 0 1/3 6/17 3/7 11/20 10/19 2/3 2/3 1/2 0 0 0 0 0 2/5 17 676
1/2 1/2 1/2 10/17 5/8 4/5 3/19 0 1/2 1/2 3/4 5/16 8/9 1/6 6/17 0 3/10 17 684
3/5 1/2 9/14 1/2 8/9 3/5 0 2/17 0 7/13 1/2 13/15 6/17 0 1/2 0 0 17 704
1/6 0 1/2 1/3 1/3 0 5/6 5/7 2/7 2/9 3/5 2/5 6/7 1/2 0 1/3 7/12 17 708
1/2 8/9 5/12 1/20 7/12 13/16 1/2 12/17 0 1/2 1/10 2/5 0 1/2 0 10/17 2/5 17 716
0 3/4 9/16 7/8 4/7 9/10 0 1/2 0 4/9 0 15/17 1/8 1/7 0 1/3 6/17 17 720
1/19 16/17 3/13 0 5/8 1/19 1/4 1/3 1/2 5/8 13/17 18/19 5/16 1/2 3/5 0 3/5 17 740
1/10 2/3 0 0 0 3/4 11/20 1/5 11/13 1/6 2/3 1/2 4/5 0 8/11 2/7 1/2 17 748
11/16 9/13 1/2 19/20 1/2 2/7 2/7 7/8 8/19 9/13 1/3 0 5/6 1/3 2/5 0 0 17 756
0 2/7 1/5 10/11 8/9 1/11 7/9 0 5/12 8/9 3/4 1/4 2/17 0 0 5/16 3/4 17 760
7/16 1/4 3/5 1/15 5/13 3/5 0 1/5 0 0 0 4/11 0 0 3/5 3/7 1/5 17 764
0 2/5 2/5 1/2 8/11 3/4 3/4 1/4 9/19 2/3 2/3 8/19 9/19 8/11 7/8 4/11 1/6 17 772
1/4 1/3 2/3 6/11 1/10 2/3 1/2 2/3 6/7 1/9 1/5 13/20 1/2 3/10 3/5 5/9 1/5 17 776
0 1/2 2/19 3/7 9/13 7/15 2/17 8/17 1/3 7/8 1/2 7/12 9/16 1/6 0 2/3 0 17 792
1/3 0 1/15 0 5/7 4/9 2/3 1/12 1/2 3/5 0 1/2 2/9 4/7 5/7 4/5 3/8 17 796
2/5 14/19 1/8 13/14 1/3 3/16 0 5/8 0 0 1/10 2/5 4/9 15/16 1/2 2/5 17/19 17 804
1/2 15/17 4/5 7/10 1/5 0 1/3 1/18 11/19 1/2 0 2/3 3/10 1/9 1/3 1/2 1/2 17 812
1/9 2/3 0 3/5 2/3 1/6 0 4/5 1/2 4/7 12/13 7/11 0 0 7/18 7/10 4/7 17 816
3/5 11/13 5/12 1/2 3/7 0 0 0 5/14 2/9 7/9 1/3 1/3 0 1/10 1/6 7/15 17 820
0 3/7 4/13 0 1/2 2/5 0 6/19 1/19 1/3 0 1/6 4/7 0 4/7 0 3/7 17 824
1/6 0 0 2/3 1/3 7/10 5/8 3/7 3/11 3/17 4/5 4/5 3/7 0 1/14 3/7 3/5 17 828
1/2 0 0 9/10 1/2 5/7 6/17 0 0 1/5 0 1/2 3/13 1/2 1/3 9/19 5/12 17 832
3/8 5/14 9/20 1/2 1/16 2/3 7/8 2/5 7/20 11/19 1/11 1/4 1/4 11/20 0 13/17 1/2 17 836
10/11 5/14 2/5 0 9/14 2/5 4/9 2/5 1/2 7/8 7/8 9/14 3/5 0 1/11 1/3 2/3 17 840
5/8 13/19 1/2 9/11 1/2 0 2/3 3/8 16/17 2/5 6/17 1/4 3/5 1/3 0 1/20 3/5 17 842
13/16 6/19 12/13 2/3 1/3 0 11/15 10/19 4/15 0 15/16 0 2/11 0 17/20 0 0 17 852
1/3 0 2/9 9/19 3/5 1/2 3/4 0 2/3 1/16 5/17 1/13 3/8 7/16 1/14 1/2 13/15 17 856
8/15 1/3 3/7 5/8 4/5 0 7/19 2/5 1/8 0 7/16 4/7 1/10 1/10 1/11 6/7 0 17 860
14/17 12/19 0 1/5 5/6 2/7 3/10 1/6 8/17 0 3/4 9/20 1/2 14/17 1/3 0 2/3 17 862
5/6 2/3 0 3/10 5/8 13/14 13/20 3/5 1/13 17/18 0 1/2 1/10 0 5/6 11/19 13/15 17 864
1/2 1/8 4/9 2/3 17/19 1/3 0 9/13 2/3 2/3 0 3/5 13/14 1/3 1/3 6/7 0 17 868
3/7 0 0 1/2 6/7 2/11 1/2 7/11 3/10 1/16 0 5/12 15/19 5/6 3/7 10/13 3/5 17 884
14/15 2/19 4/5 2/3 0 0 7/10 1/5 4/5 0 13/20 1/7 11/17 1/8 0 4/13 2/3 17 890
1/18 1/13 1/2 2/7 1/2 0 0 1/2 1/10 11/20 1/4 8/9 6/19 0 13/16 2/17 15/17 17 908
2/5 4/7 1/3 1/6 9/11 1/2 0 2/3 11/20 1/13 11/16 2/3 5/6 5/17 8/9 0 0 17 910
0 2/3 1/10 13/20 1/2 1/5 0 1/14 1/13 1/3 4/5 13/19 1/2 3/5 5/7 4/13 2/5 17 912
3/14 5/8 0 1/3 3/4 0 1/2 7/12 2/11 1/4 7/17 2/5 5/9 1/2 7/13 7/17 3/20 17 916
9/10 0 16/19 0 15/17 1/2 0 9/17 0 7/8 9/11 2/3 1/8 13/20 2/3 2/5 12/13 17 928
11/12 2/17 0 4/17 0 6/17 9/10 2/5 3/7 6/11 8/9 7/16 1/3 1/3 0 0 1/3 17 934
3/5 1/3 1/6 0 6/13 1/3 3/5 11/19 2/3 19/20 0 2/7 0 3/10 0 1/3 7/18 17 944
0 5/6 11/12 0 2/5 5/7 10/11 5/8 2/15 0 0 5/19 0 5/17 1/2 3/10 17/18 17 952
2/5 0 0 11/19 3/4 1/9 19/20 11/20 1/3 0 13/14 3/17 13/19 2/3 5/8 1/3 0 17 954
0 3/5 18/19 2/3 5/19 0 7/12 5/9 0 1/3 2/9 14/15 1/4 3/7 1/3 3/4 16/17 17 960
11/15 0 1/20 3/5 4/7 1/11 0 4/9 0 11/18 1/2 5/8 5/9 8/9 19/20 3/13 0 17 964
6/19 9/10 5/13 4/9 1/4 1/2 0 1/10 1/3 2/3 1/3 2/3 0 3/5 8/17 3/5 7/17 17 968
5/9 3/7 3/5 8/17 2/3 6/7 3/4 7/18 2/3 0 1/3 0 4/11 1/2 7/16 4/7 1/2 17 972
1/2 2/3 5/7 0 1/2 3/4 3/5 8/17 6/7 1/3 2/5 13/19 1/2 7/9 7/9 0 3/4 17 976
9/13 7/17 9/10 1/2 1/2 1/4 3/5 4/19 1/2 3/11 4/5 8/9 0 0 1/3 3/4 2/9 17 980
3/8 2/3 6/17 2/5 3/8 7/17 14/17 1/2 3/5 2/5 7/12 3/4 9/10 1/2 4/7 9/11 6/11 17 984
13/16 7/16 1/2 2/11 5/11 1/3 1/17 1/8 1/3 0 7/20 2/7 4/17 9/20 0 1/10 1/5 17 988
1/2 0 10/13 5/7 8/9 9/19 0 4/13 7/18 0 0 2/5 1/2 1/14 1/2 7/20 3/5 17 992
0 0 10/13 0 2/5 4/9 5/12 11/14 2/17 2/3 10/19 13/18 2/9 2/7 0 11/16 7/11 17 996
1/3 3/8 1/2 7/9 9/11 2/11 3/5 3/7 1/6 1/10 1/4 0 5/6 5/9 5/7 2/11 7/18 17 998
2/11 6/11 1/2 1/5 0 1/2 2/5 3/5 8/13 1/3 5/7 6/17 5/7 0 6/11 3/8 0 17 1000
2/3 3/13 0 9/13 0 4/9 2/13 1/3 1/3 14/15 7/15 0 5/9 1/9 5/18 1/9 2/15 17 1002
15/19 1/2 5/7 1/2 1/4 6/11 1/5 0 14/15 5/9 2/19 14/15 13/20 1/2 1/4 1/3 11/15 17 1004
16/17 0 4/7 1/3 1/9 6/7 3/10 10/19 0 1/2 8/11 3/8 1/2 0 1/4 10/11 1/2 17 1008
0 8/9 5/7 1/7 1/3 2/5 7/18 8/19 1/2 3/7 6/11 0 0 5/7 7/18 8/19 7/9 17 1012
3/5 6/7 8/9 2/9 3/4 1/3 0 2/15 0 13/15 0 2/3 0 7/19 8/13 4/5 1/3 17 1016
1/20 0 2/11 0 3/7 7/16 9/19 4/11 2/3 0 1/2 4/17 7/16 3/8 1/12 2/5 4/13 17 1020
1/3 11/20 4/5 12/17 10/13 2/3 11/14 0 1/3 0 15/17 5/6 11/19 1/2 0 9/16 8/19 17 1028
1/6 0 0 8/19 7/11 1/7 19/20 4/9 1/8 0 2/19 7/9 1/8 1/9 4/13 1/3 0 17 1032
0 0 1/7 1/5 10/11 8/11 0 11/12 5/12 1/2 0 0 10/17 5/17 0 3/17 2/7 17 1036
10/13 4/9 9/11 1/3 4/13 9/16 2/3 1/3 1/2 2/7 17/19 11/14 3/4 5/9 5/8 7/8 1/4 17 1048
0 0 13/20 7/12 1/10 3/10 5/14 1/4 9/14 8/13 5/6 5/7 4/13 2/5 11/18 14/15 1/4 17 1050
1/2 11/13 1/4 1/3 7/13 1/2 10/17 10/17 7/10 1/10 6/17 1/2 0 5/8 2/7 9/17 0 17 1054
1/3 9/13 3/5 14/15 2/5 11/20 2/3 4/11 1/16 0 0 2/7 1/7 3/19 4/5 13/18 9/17 17 1058
1/5 3/7 0 2/7 5/9 1/2 11/16 2/5 1/19 6/13 2/9 0 1/11 0 5/8 1/2 1/4 17 1060
3/5 4/7 1/2 0 11/14 1/3 2/3 4/15 7/10 3/4 1/2 7/12 1/7 14/17 1/15 1/17 2/3 17 1064
13/15 0 14/15 0 11/16 17/19 12/13 5/9 1/3 9/19 1/4 7/9 2/3 3/10 1/2 1/3 14/17 17 1072
3/11 3/5 3/10 6/17 2/7 0 1/11 0 3/8 1/11 1/2 9/10 1/4 8/13 4/15 1/3 0 17 1080
0 10/13 1/5 2/3 1/9 9/17 4/7 0 1/3 0 11/19 1/3 3/8 1/2 3/14 3/13 1/5 17 1084
0 5/14 11/12 0 11/18 15/17 2/5 2/15 5/6 2/5 3/5 1/5 6/7 10/17 2/3 1/3 0 17 1088
17 1100 not recorded
8/15 5/13 2/3 1/12 5/6 3/5 2/3 1/9 1/6 2/3 0 2/7 2/7 3/5 10/13 1/2 2/13 17 1104
0 1/2 8/15 1/11 0 3/5 2/9 5/6 2/3 5/18 10/17 3/10 0 2/3 2/7 0 2/11 17 1108
4/7 4/9 2/9 4/5 3/5 1/12 4/5 1/2 1/2 0 12/19 4/13 1/2 3/5 1/3 0 11/13 17 1116
0 2/5 4/5 4/15 3/19 6/19 12/19 1/3 9/16 6/17 0 1/9 1/7 2/5 3/20 0 8/15 17 1118
0 12/17 4/17 0 1/3 4/5 11/13 10/13 2/17 2/17 1/6 10/19 1/6 1/2 4/15 3/20 4/7 17 1120
13/17 6/7 7/11 5/13 0 1/5 0 2/9 0 0 0 5/9 0 9/11 5/7 2/9 3/7 17 1132
8/9 6/11 8/13 11/20 0 1/7 3/8 4/7 0 8/13 0 0 17/20 1/6 13/15 11/19 0 17 1136
1/14 2/5 0 2/7 1/5 2/3 6/13 5/6 13/14 5/19 13/16 11/12 12/13 0 1/2 1/7 3/5 17 1140
1/6 0 1/2 4/11 16/17 9/13 6/17 3/4 6/17 1/5 0 7/18 1/3 11/17 14/15 9/14 3/5 17 1144
1/5 2/5 7/19 11/17 2/3 1/9 3/13 3/4 0 4/5 14/15 8/15 2/5 1/7 2/9 2/3 7/8 17 1148
1/6 2/15 1/2 3/5 1/7 12/13 17/20 0 0 0 7/9 2/3 5/17 5/7 5/6 4/5 12/19 17 1152
15/17 7/10 14/15 16/17 2/3 1/6 3/5 6/7 13/17 15/19 11/18 1/5 4/9 0 9/14 1/6 0 17 1156
10/11 2/9 11/14 10/13 5/14 5/6 0 7/9 5/18 0 9/13 7/9 0 4/9 3/5 13/16 5/17 17 1166
3/7 0 5/7 2/3 18/19 9/19 0 1/8 2/11 3/7 5/9 1/17 1/6 1/2 14/19 8/19 9/13 17 1168
1/5 0 3/19 1/17 7/15 9/10 0 5/7 7/10 4/9 0 1/6 3/20 10/11 0 7/9 1/6 17 1174
3/4 15/17 1/8 3/5 2/3 4/5 3/11 3/7 11/13 4/5 7/15 11/19 1/7 1/3 5/11 2/5 9/11 17 1178
17 1180 not recorded
1/2 3/13 0 3/11 4/7 0 1/3 11/14 6/7 1/3 7/15 1/2 13/20 7/13 7/9 3/20 4/15 17 1194
17 1196 not recorded
1/3 5/7 1/10 6/7 17/18 11/15 13/18 7/19 7/12 1/9 0 3/8 13/16 4/7 2/3 1/2 4/11 17 1200
0 6/17 4/5 4/9 6/11 6/7 3/19 11/13 2/5 1/2 12/17 5/7 1/4 3/10 4/5 15/19 4/9 17 1202
4/17 2/13 1/4 6/11 9/10 2/5 1/7 2/17 0 5/19 2/9 0 1/2 4/5 5/8 6/7 8/11 17 1204
8/9 5/16 5/12 11/13 8/13 0 2/7 1/5 8/9 4/11 1/10 1/2 1/3 2/7 2/5 2/5 2/13 17 1208
1/6 8/11 8/19 3/5 1/2 5/7 1/8 1/2 10/17 3/13 3/10 1/17 10/19 14/17 0 6/7 0 17 1212
2/15 9/17 12/13 11/17 0 11/20 9/20 5/9 8/9 3/19 0 8/9 2/7 0 5/7 0 1/5 17 1216
17 1220 not recorded
17 1236 not recorded
8/9 6/19 2/9 17/18 8/11 1/18 7/15 3/4 3/7 19/20 6/7 1/3 3/5 3/11 0 9/10 4/5 17 1238
17 1244 not recorded
17 1248 not recorded
0 6/7 13/17 3/5 1/7 2/19 15/17 6/11 9/20 5/6 1/2 2/5 0 9/11 0 1/6 1/11 17 1252
17 1256 not recorded
3/4 1/2 11/13 2/5 9/20 1/3 3/11 8/9 6/11 6/7 2/9 13/14 0 15/19 3/7 3/5 2/3 17 1258
3/11 8/19 1/2 3/10 8/13 1/4 11/12 2/7 0 6/7 7/13 1/3 1/2 12/17 0 2/13 3/14 17 1260
17 1274 not recorded
1/3 3/10 10/13 0 7/20 1/3 8/17 1/4 2/7 2/3 5/11 7/13 2/7 11/17 4/13 3/5 9/10 17 1280
17 1290 not recorded
1/11 1/13 5/6 8/9 8/15 13/18 0 0 5/14 13/17 11/19 4/13 10/11 1/15 2/7 1/5 0 17 1302
r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12 r13 r14 r15 r16 r17 17 1330*
---------------------------------------------------------------------------------------------------------------------------------------------------
0 3/4 3/4 0 1/2 2/3 1/3 5/6 1/4 0 0 1/3 1/3 0 0 1/2 0 19 48
0 2/5 0 2/5 2/5 3/4 0 1/5 1/2 1/2 0 3/4 0 3/4 0 0 1/2 19 76
1/2 1/2 1/2 0 0 0 1/2 0 0 1/2 0 1/2 0 1/4 0 3/5 1/3 19 88
3/5 1/2 1/4 0 1/4 1/2 0 4/5 0 6/7 19/20 1/2 3/8 0 1/16 0 1/13 19 296
7/16 0 1/2 0 3/4 1/2 1/5 0 3/7 1/2 2/3 1/4 4/19 0 0 0 13/20 19 336
1/2 0 1/3 1/9 0 3/4 3/16 9/16 7/18 0 2/3 7/15 5/6 5/6 2/3 1/4 7/11 19 412
1/3 7/12 0 1/4 1/3 2/5 4/7 2/3 1/2 5/6 9/10 1/2 0 0 0 0 2/9 19 416
4/5 9/17 1/4 0 9/10 0 1/16 0 7/19 3/4 3/8 1/2 1/2 0 4/5 2/3 1/4 19 436
2/3 0 1/2 4/9 8/11 0 3/10 3/4 7/18 1/6 4/9 1/5 3/4 0 0 0 1/5 19 472
1/2 0 0 1/3 2/3 7/9 0 3/4 1/4 2/5 1/6 6/17 0 9/16 5/8 2/5 0 19 476
2/3 17/18 0 1/2 0 0 0 1/2 0 3/8 0 4/19 4/5 7/18 13/15 2/7 1/4 19 524
0 1/4 2/3 1/5 1/5 0 19/20 1/2 1/2 0 6/13 2/3 4/5 1/10 13/18 8/15 0 19 532
0 1/2 1/2 1/4 1/8 9/11 10/17 6/17 0 13/20 0 1/2 0 0 8/9 1/2 1/3 19 544
4/7 3/5 0 1/4 2/3 0 0 5/17 0 1/20 2/3 2/3 3/4 2/3 0 1/2 0 19 580
0 1/14 0 1/2 14/15 1/4 0 1/3 1/4 2/5 1/2 5/6 6/7 1/5 15/16 5/9 1/2 19 612
0 1/3 0 1/14 4/5 1/7 1/2 4/7 3/4 0 1/2 2/5 2/11 1/2 7/8 5/9 0 19 628
3/4 5/8 0 4/17 13/17 1/7 1/13 12/13 0 1/7 7/16 3/20 1/2 0 1/2 1/3 0 19 648
3/7 8/13 3/4 1/4 3/8 16/17 13/17 0 0 7/12 1/2 0 0 3/16 7/10 2/3 2/3 19 656
0 1/2 14/17 5/8 1/6 0 11/14 18/19 8/9 5/6 0 9/10 0 1/4 1/3 2/3 5/6 19 664
13/15 7/9 5/6 0 1/6 13/18 3/16 1/17 7/12 1/3 3/4 1/2 4/5 3/4 2/7 0 3/4 19 676
1/3 3/10 3/11 0 0 0 0 1/10 7/20 0 16/17 0 13/19 3/4 1/19 2/5 2/3 19 680
3/4 4/15 11/19 1/3 4/7 1/16 15/16 4/7 0 0 1/7 3/4 1/3 1/3 0 2/5 2/15 19 684
3/5 2/5 1/2 11/15 13/16 0 1/19 5/8 9/11 1/6 5/12 0 1/18 7/12 1/5 4/9 1/6 19 692
0 1/3 11/12 1/3 1/7 0 0 5/8 4/17 2/3 1/4 1/5 9/16 9/11 1/4 1/2 8/9 19 700
2/3 1/4 5/9 0 0 7/8 2/17 3/16 2/9 4/9 9/10 0 1/2 2/7 2/7 3/4 0 19 704
17/19 0 0 1/2 1/4 1/5 3/10 8/19 1/20 3/7 0 1/3 13/16 5/6 0 1/9 3/4 19 708
2/13 1/2 0 0 0 4/5 0 6/11 9/14 0 3/4 0 1/14 5/6 15/17 1/13 0 19 732
9/20 0 2/9 3/4 0 7/8 1/2 1/2 2/3 0 9/11 0 7/15 2/13 11/13 9/20 8/11 19 740
0 7/17 1/2 3/5 4/5 0 3/4 1/16 9/10 1/11 8/11 0 2/3 1/8 17/18 1/2 3/13 19 742
7/10 3/7 7/10 0 2/7 1/3 4/5 4/5 1/3 1/2 0 5/13 3/4 0 9/13 0 9/13 19 752
1/4 4/19 4/11 7/9 1/2 2/15 7/8 0 1/9 1/2 6/19 1/5 7/16 13/18 2/13 1/3 7/8 19 756
4/5 8/9 1/4 5/11 0 3/4 0 1/18 7/12 1/4 8/15 1/4 10/13 6/11 1/10 8/15 9/11 19 766
7/10 8/15 1/2 13/15 12/13 0 3/19 0 1/13 1/2 1/3 4/5 1/6 13/18 1/2 3/4 11/16 19 768
16/19 14/17 1/2 1/8 12/17 1/4 1/4 0 11/12 7/8 6/19 1/2 1/2 2/3 1/7 12/13 1/3 19 772
15/16 5/8 0 4/9 3/4 3/5 6/17 1/11 13/17 8/9 7/9 4/15 7/10 1/4 1/8 0 2/3 19 784
7/18 1/3 0 1/4 1/5 7/17 1/2 7/9 1/13 1/12 2/3 1/5 0 3/5 13/16 1/4 7/12 19 788
16/17 4/5 2/3 17/18 8/17 4/5 0 3/4 2/5 1/17 7/8 0 1/3 3/5 0 0 3/11 19 792
0 1/6 1/4 1/4 1/5 6/19 5/9 5/8 17/19 0 5/13 0 11/13 1/5 0 2/5 1/6 19 796
4/13 5/7 2/3 0 3/4 1/2 0 4/7 1/2 0 2/9 13/17 5/14 1/4 3/7 4/5 1/2 19 804
4/9 1/3 5/19 3/4 0 3/4 11/20 1/6 3/20 7/19 0 1/2 1/3 5/18 1/5 9/14 3/5 19 814
1/3 1/16 9/14 9/10 2/3 1/3 11/18 1/7 1/2 2/19 0 0 0 1/4 9/10 11/20 2/7 19 820
2/5 3/7 1/2 0 0 1/4 5/9 0 3/4 3/17 0 7/13 1/3 1/2 14/17 1/9 2/3 19 824
7/8 3/8 3/5 1/15 1/16 0 5/9 4/15 7/8 2/3 7/13 0 3/13 12/19 5/8 7/11 2/3 19 828
4/11 7/17 4/15 3/5 5/7 17/18 2/7 0 2/5 2/9 9/16 0 5/14 0 1/2 0 5/16 19 832
0 1/2 1/18 6/7 1/2 1/6 4/7 11/16 7/11 1/2 10/13 4/5 1/16 11/13 1/4 1/7 3/14 19 844
1/14 1/2 2/3 3/10 13/18 3/7 4/19 7/11 1/6 1/5 1/10 1/10 1/3 3/4 1/2 3/4 3/7 19 854
9/13 1/2 1/4 2/3 1/4 9/19 2/17 2/15 1/10 1/11 1/4 5/6 18/19 1/2 1/2 4/9 1/2 19 864
4/5 4/5 2/3 1/4 1/4 4/7 1/17 16/19 4/7 6/11 1/3 0 6/7 4/11 1/10 0 1/6 19 870
1/3 1/3 6/7 1/4 4/15 10/11 6/11 1/14 16/19 3/8 1/7 1/2 3/4 0 9/10 19/20 6/19 19 872
1/2 0 3/13 8/13 7/9 11/12 1/2 1/5 8/13 4/5 7/12 3/7 5/7 18/19 0 3/10 1/3 19 880
13/14 9/11 13/14 1/4 1/15 0 1/14 3/4 2/3 1/4 10/19 5/9 0 2/13 17/20 2/11 0 19 884
0 3/8 7/13 1/6 6/19 1/6 1/8 11/17 4/15 1/15 10/11 1/15 1/16 4/7 3/4 1/2 8/9 19 890
19 896 not recorded
1/3 0 0 8/15 1/5 1/4 5/9 6/7 7/11 13/17 3/11 18/19 5/6 2/3 1/3 5/11 1/5 19 904
6/7 10/19 13/18 3/4 1/2 2/3 2/3 1/4 13/19 3/4 17/18 2/3 10/17 1/3 13/15 3/7 2/3 19 912
4/5 1/2 8/19 1/4 0 1/11 5/8 11/12 10/11 9/10 4/5 1/2 2/13 14/19 1/9 0 11/13 19 916
6/13 3/4 1/3 2/3 3/7 0 11/13 7/9 2/11 4/7 0 5/8 5/6 1/20 11/19 2/3 2/7 19 924
16/19 10/13 5/8 3/5 3/7 8/15 19/20 1/9 3/8 1/14 3/13 1/7 0 1/4 4/5 0 13/20 19 932
1/4 5/14 3/20 10/17 5/9 1/2 1/15 5/6 2/19 9/14 1/2 3/14 12/13 0 1/2 4/5 1/5 19 940
7/9 1/11 11/13 3/7 9/13 15/16 2/3 0 3/17 7/16 1/4 13/17 15/16 1/19 4/9 2/5 0 19 946
13/15 1/5 0 5/9 15/16 8/17 1/6 7/11 13/18 3/7 5/11 8/11 0 3/4 2/3 1/2 0 19 948
1/2 0 1/2 1/3 1/2 7/9 4/7 1/4 1/2 1/2 2/7 7/20 10/13 4/5 0 2/19 11/18 19 952
3/5 1/4 2/5 7/11 7/8 5/12 0 4/19 4/9 1/6 7/13 1/13 3/4 3/4 5/14 0 16/17 19 956
19 966 not recorded
5/14 3/8 1/4 1/3 9/19 5/9 1/3 1/4 4/19 0 7/17 3/16 2/7 1/6 9/11 1/3 2/5 19 978
3/17 12/19 12/13 1/4 4/9 0 7/8 2/9 5/11 0 1/2 5/6 2/15 1/2 14/19 4/11 3/7 19 988
6/19 6/7 0 11/18 0 1/20 7/11 4/7 1/4 2/3 0 2/3 1/2 0 1/4 3/10 11/20 19 992
2/3 1/2 1/2 0 4/5 10/17 2/5 2/9 2/13 0 1/2 12/13 7/12 4/5 2/7 0 8/9 19 1000
0 0 2/3 2/5 14/19 5/7 6/13 0 1/5 0 9/19 1/4 3/19 1/3 10/17 1/5 1/2 19 1024
19 1026 not recorded
7/11 7/18 0 10/19 9/17 9/14 0 2/11 3/5 5/17 1/3 8/9 9/13 1/4 4/7 3/4 9/19 19 1028
19 1030 not recorded
1/3 3/4 1/11 1/6 1/6 9/19 7/10 6/7 4/15 19/20 3/7 0 3/5 5/7 7/11 0 1/5 19 1034
11/16 11/19 5/17 3/11 1/2 7/18 15/19 2/5 0 1/2 9/13 14/15 1/2 0 1/5 3/4 0 19 1052
5/7 3/10 0 0 2/5 1/3 2/3 7/9 1/4 3/5 2/7 0 3/7 13/15 17/19 0 1/2 19 1068
19 1072 not recorded
1/14 4/17 3/20 3/5 2/19 11/13 0 4/15 1/4 3/4 12/19 1/2 0 4/5 4/5 11/19 0 19 1078
7/10 1/3 4/15 3/5 1/2 3/16 0 9/17 3/4 7/19 10/13 2/15 5/6 5/7 2/7 0 5/12 19 1080
0 1/5 1/3 7/8 17/18 4/7 2/3 6/17 3/4 2/5 5/13 4/9 1/2 1/10 1/19 1/7 8/9 19 1114
1/4 2/17 1/3 1/10 12/13 3/4 7/13 0 9/11 1/4 1/10 11/19 5/17 6/7 4/9 0 5/16 19 1156
3/7 1/5 2/7 9/13 8/9 1/4 0 3/4 1/5 1/2 2/3 1/3 2/19 3/7 9/11 7/15 1/2 19 1158
18/19 2/3 0 12/19 1/2 3/7 1/3 1/2 2/5 3/5 13/19 11/12 4/7 5/13 7/19 1/17 9/14 19 1178
9/17 5/11 3/10 13/19 0 8/9 3/11 0 1/4 3/8 11/13 1/2 2/5 3/14 4/5 1/3 1/5 19 1192
---------------------------------------------------------------------------------------------------------------------------------------------------
1/2 0 0 0 0 0 0 5/6 0 2/3 0 0 1/3 0 1/2 0 3/4 20 44
3/4 0 1/3 0 1/3 1/3 1/2 1/3 1/2 1/2 1/2 0 0 1/2 1/4 0 1/4 20 48
0 0 1/4 1/2 0 0 0 0 0 1/2 0 0 3/5 0 0 5/6 0 20 88
5/6 0 0 1/2 0 0 0 0 1/5 0 0 1/2 0 1/4 0 0 0 20 96
3/13 1/2 2/5 3/4 0 1/2 12/17 2/3 0 0 4/5 7/8 1/4 2/5 1/4 0 1/2 20 472
2/13 2/3 0 0 0 11/12 0 2/5 0 0 12/19 0 0 2/3 4/7 2/11 0 20 624
1/3 1/4 5/6 0 2/7 0 13/15 6/13 0 3/4 18/19 7/12 1/2 1/2 1/6 3/5 15/17 20 660
2/3 2/3 2/3 19/20 1/3 0 1/3 5/14 3/7 2/13 3/4 5/6 0 0 2/3 5/9 11/18 20 704
---------------------------------------------------------------------------------------------------------------------------------------------------
1/2 0 1/4 0 0 0 1/4 0 2/3 1/2 0 0 2/3 1/3 1/2 0 1/2 21 48
2/3 7/16 7/12 1/8 0 1/7 0 3/4 3/4 1/2 0 7/8 17/18 5/7 1/2 15/16 0 21 396
0 1/2 1/16 1/2 4/7 3/4 7/12 15/16 3/4 1/9 1/2 13/20 2/5 2/5 1/5 0 3/8 21 460
0 4/15 1/2 1/3 3/4 1/9 5/9 7/10 3/4 0 5/8 0 1/12 3/5 7/20 13/19 1/4 21 532
1/2 4/7 17/19 15/19 13/16 1/4 0 3/4 0 8/9 0 4/5 15/17 5/6 1/3 0 1/4 21 536
0 9/10 1/2 3/16 5/7 1/6 3/4 12/19 1/2 8/11 2/5 0 2/3 1/2 1/4 11/17 2/3 21 544
1/2 11/13 0 0 2/19 5/8 7/8 11/13 2/7 8/13 3/4 3/17 0 9/11 5/7 5/8 0 21 576
3/4 7/8 3/4 0 1/3 3/5 0 5/7 5/12 14/17 13/17 0 3/7 1/12 0 15/17 3/5 21 608
3/4 1/9 15/16 0 8/19 2/3 1/9 0 9/19 2/7 3/11 5/6 1/2 3/4 1/2 0 1/5 21 616
1/4 1/4 7/12 15/19 2/5 1/2 1/3 2/5 17/19 3/4 10/11 2/3 11/12 7/16 3/4 1/7 8/19 21 632
1/4 0 0 0 0 3/13 11/14 4/5 0 1/3 3/17 2/3 1/2 0 10/17 5/12 3/14 21 636
3/4 3/5 1/2 1/2 0 2/7 16/19 1/5 1/10 1/2 1/4 0 1/4 1/2 2/13 7/13 2/3 21 640
1/4 6/7 3/5 0 0 5/8 4/5 8/13 11/19 9/11 3/4 3/7 5/17 4/5 3/14 8/17 0 21 664
2/3 7/9 5/12 0 2/15 0 4/11 1/4 2/3 3/4 0 1/7 0 5/6 3/14 0 4/9 21 672
1/11 3/4 0 1/4 4/19 0 12/19 3/17 2/3 14/15 12/17 1/6 10/17 0 7/10 8/17 0 21 700
1/2 3/14 8/9 3/4 3/7 1/2 2/5 4/5 3/13 13/19 0 1/4 8/9 1/4 7/13 17/18 1/2 21 708
6/7 1/4 11/13 0 3/4 0 1/7 1/5 10/19 0 1/2 1/2 2/3 2/17 0 3/8 4/7 21 732
2/5 18/19 0 3/4 1/3 11/16 3/4 4/5 13/18 8/17 2/5 11/19 9/19 1/2 7/9 1/2 4/7 21 736
1/3 2/5 0 2/5 13/14 17/18 0 0 2/3 1/4 0 13/16 10/11 1/7 0 3/4 3/13 21 756
1/5 1/10 1/10 5/9 2/3 5/6 2/17 0 3/4 3/4 6/7 0 1/2 0 4/5 0 10/19 21 768
17/18 3/14 3/4 5/17 9/19 9/10 0 12/19 1/3 5/7 6/17 4/17 0 3/4 1/2 6/7 4/5 21 802
0 11/13 10/11 9/10 1/2 11/18 4/5 7/9 3/4 0 1/3 7/12 1/3 9/11 3/4 1/16 8/13 21 828
1/4 7/16 2/3 11/12 0 5/7 4/5 3/4 3/17 0 3/5 2/15 7/10 1/9 14/19 14/19 2/17 21 864
---------------------------------------------------------------------------------------------------------------------------------------------------
3/4 1/2 0 1/2 0 5/6 1/2 3/4 2/3 0 1/3 0 0 0 1/6 1/3 1/2 22 48
0 0 5/6 2/3 1/2 0 1/3 0 2/3 7/19 0 1/4 1/10 5/19 3/7 0 1/4 22 392
0 0 1/4 3/4 7/10 0 0 4/9 0 8/11 1/6 5/8 5/13 13/14 4/13 4/5 0 22 524
---------------------------------------------------------------------------------------------------------------------------------------------------
0 0 0 1/2 0 1/2 0 0 0 0 2/3 1/4 1/2 1/2 0 0 1/2 23 44
0 1/3 1/2 0 0 3/4 3/4 2/3 0 1/3 1/4 1/2 2/3 1/3 1/6 0 0 23 48
0 0 0 0 0 0 4/5 0 0 0 0 0 0 1/2 3/5 3/4 3/5 23 72
0 1/2 1/2 1/2 0 1/2 2/3 1/5 0 0 0 0 0 0 1/2 1/5 3/4 23 80
1/2 2/3 0 1/2 3/4 3/5 0 0 0 0 1/2 1/2 1/4 0 1/2 0 0 23 96
0 3/8 7/9 1/2 1/2 0 17/19 1/4 0 1/2 13/17 9/14 1/2 1/4 10/17 3/4 1/6 23 392
7/11 1/4 2/5 4/7 5/14 0 0 3/4 5/19 0 7/20 1/2 3/4 0 2/5 5/8 1/2 23 460
7/10 2/3 2/3 2/9 0 1/13 0 5/6 3/4 0 1/2 18/19 1/2 3/4 5/14 1/6 1/4 23 486
0 11/12 1/4 4/11 3/4 1/2 0 1/5 4/7 1/2 3/11 0 5/14 1/4 1/5 2/15 16/17 23 510
23 696 not recorded
1/6 3/4 14/17 6/7 15/19 0 1/2 8/13 1/4 0 4/5 0 2/7 0 3/4 0 3/5 23 728
---------------------------------------------------------------------------------------------------------------------------------------------------
0 1/3 1/2 3/4 1/2 1/2 1/4 1/3 1/4 0 0 1/3 0 1/2 0 1/2 1/2 24 44
4/5 1/19 5/12 3/4 6/19 1/15 0 7/8 7/9 1/8 9/10 10/19 13/20 0 1/2 5/8 11/13 24 636
---------------------------------------------------------------------------------------------------------------------------------------------------
0 0 5/6 0 1/4 1/4 1/6 2/3 3/4 0 0 1/2 0 1/2 2/3 2/3 0 25 44
0 1/3 1/3 0 0 2/3 0 3/4 0 5/6 0 0 1/4 1/4 0 0 0 25 48
0 1/2 0 0 0 0 0 0 0 0 1/4 1/5 1/2 1/5 0 0 0 25 60
0 0 1/2 1/4 1/4 0 1/2 1/6 0 0 0 0 1/5 1/2 0 1/2 0 25 96
---------------------------------------------------------------------------------------------------------------------------------------------------
0 5/6 0 0 2/3 0 1/2 0 0 0 1/2 0 0 0 0 1/4 1/4 26 44
---------------------------------------------------------------------------------------------------------------------------------------------------
1/2 1/2 0 0 3/4 3/4 2/3 0 1/6 2/3 0 3/4 0 0 0 2/3 1/2 27 44
---------------------------------------------------------------------------------------------------------------------------------------------------
1/2 0 0 0 2/5 0 1/5 1/2 3/4 0 1/4 0 0 3/5 4/5 1/2 1/2 29 72
0 0 0 0 0 3/4 0 2/3 0 3/5 1/2 0 1/4 1/2 3/4 0 1/2 29 96
---------------------------------------------------------------------------------------------------------------------------------------------------
3/4 0 0 1/4 0 0 1/2 0 0 1/2 1/4 0 2/5 0 1/4 0 1/2 30 44
3/4 0 0 0 1/3 0 1/4 0 1/2 0 3/4 3/4 1/2 1/2 0 1/6 0 30 48
---------------------------------------------------------------------------------------------------------------------------------------------------
0 1/2 1/4 0 3/4 3/4 1/2 0 0 1/4 1/4 0 0 2/3 0 0 3/5 31 88
---------------------------------------------------------------------------------------------------------------------------------------------------
0 1/4 0 1/2 3/4 3/4 0 0 0 3/4 1/3 1/2 1/4 0 0 1/2 0 32 48
---------------------------------------------------------------------------------------------------------------------------------------------------
1/2 0 1/2 1/2 1/4 0 0 0 1/4 0 1/4 0 0 2/3 0 1/2 1/2 34 44
---------------------------------------------------------------------------------------------------------------------------------------------------
0 0 1/4 1/4 0 1/2 0 0 0 0 0 0 0 3/4 0 1/6 1/2 36 44
---------------------------------------------------------------------------------------------------------------------------------------------------
2.2. Other BH-Type Matrices
Most (or even all) families, especially those usually named by D... or S... are stemming from Butson type matrices. Actually, vast majority of Catalog records are related to or they stem from a BH; as of January 2023 there are (at least) 57 of them:
F2,
F3,
H4,
F4,
F5,
F6,
S6,
D6,
F6,
P7,
F7,
H8,
S8,
F2 ⊗ F4,
F8,
B8A,
B8B,
F3 ⊗ F3,
S9,
F9,
B9,
D10,
X10,
S10,
F10,
F11,
H12,
X12,
D6 ⊗ F2,
D12,
F2 ⊗ F2 ⊗ F2,
S6 ⊗ F2,
F12,
S12,
M13A,
M13B,
M13C,
F13,
P13,
D14,
L14A...,
P7 ⊗ F2,
S14,
L14,
F14,
FP14...,
F15,
H16A,
H16B,
H16C,
H16D,
H16E,
F4 ⊗ F4,
S8 ⊗ F2,
F8 ⊗ F2,
S16,
F16.
For more, check Butson Home (maintained by P. Lampio) which provides the catalog of all BH matrices in dimensions: 2 – 21. Almost all of these matrices can be extended to multi-parametric (affine) families. Further detailed classification of all of them is currently questionable, and anyway, it requires a lot of time and resources. Some preliminary attempt is presented here, where we print the defects of all Butsons from Butson Home, focusing the attention on the isolated cases.
Below we present some particular BH examples from the Catalog.
S8(p1, p2, p3, p4)↑
show data
p1 p2 p3 p4 d #Λ ------------------------------------------ 0 0 0 0 5 4 1/4 1/4 1/4 1/3 5 6 0 0 0 3/8 5 8 1/4 1/4 1/4 1/5 5 10 0 6/7 0 0 5 12 1/2 2/5 0 2/5 5 16 1/4 1/4 4/7 2/3 5 18 1/2 1/4 0 1/7 5 20 1/6 1/3 2/5 0 5 22 0 5/8 3/4 2/3 5 24 19/20 3/8 1/10 1/5 5 26 4/7 4/5 0 0 5 28 1/4 2/3 2/3 2/5 5 30 2/3 0 2/5 1/3 5 32 17/19 13/24 2/3 1/2 5 34 6/7 0 0 2/3 5 36 1/3 1/7 5/7 0 5 38 0 1/4 1/6 1/7 5 40 1/4 1/8 2/3 1/5 5 42 1/5 4/5 4/7 4/5 5 44 1/7 1/3 2/3 3/7 5 46 2/3 0 2/3 2/5 5 48 8/11 5/13 1/22 13/22 5 50 4/5 0 3/8 1/3 5 52 5/6 2/5 5/6 2/7 5 54 0 6/7 2/3 5/7 5 56 4/21 5/6 6/7 1/14 5 58 1/2 1/8 1/3 2/7 5 60 5/8 1/7 1/3 5/7 5 62 2/3 2/5 4/7 1/5 5 64 6/7 2/5 1/8 1/7 5 66 r1 r2 r2 r3 5 66* ------------------------------------------ 1/4 5/6 0 5/6 7 12 0 1/4 11/16 11/16 7 16 1/4 1/2 1/7 1/7 7 20 ------------------------------------------ 3/4 0 0 0 9 4 1/4 0 3/8 0 9 8 2/5 3/4 2/5 0 9 10 1/2 0 2/3 3/4 9 12 1/2 19/20 3/4 1/5 9 16 1/8 2/3 3/4 3/8 9 18 ------------------------------------------ 1/4 1/4 1/2 1/4 11 4 ------------------------------------------ 0 0 3/4 1/4 15 4 3/7 3/4 1/4 1/2 15 6 ------------------------------------------ 1/4 1/4 1/4 1 21 2 ------------------------------------------
P8(p1, p2, p3)↑
show data
p1 p2 p3 d #Λ ---------------------------------- 3/5 2/5 4/5 9 10 1/3 1/6 3/4 9 12 1/3 4/9 8/9 9 14 7/20 7/10 1/10 9 16 1/3 2/3 1/5 9 18 1/4 8/9 4/9 9 20 6/7 3/7 1/3 9 22 1/3 2/5 3/4 9 24 1/3 4/7 4/9 9 26 r1 r2 r3 9 26* ---------------------------------- 5/6 0 1/6 11 6 1/4 0 1/8 11 8 7/9 7/9 8/9 11 10 2/3 3/4 0 11 12 2/9 2/3 1/2 11 14 ---------------------------------- 1/2 3/4 3/4 13 4 3/8 3/8 0 13 6 ---------------------------------- 3/4 0 0 15 4 0 1/6 0 15 6 ---------------------------------- 0 0 0 21 2 ----------------------------------
D8(p1, p2, p3, p4)↑
show data
p1 p2 p3 p4 d #Λ ------------------------------------------ 0 3/4 3/4 3/4 5 4 1/3 0 1/3 2/3 5 6 0 3/4 1/8 3/4 5 8 1/12 7/12 7/12 0 5 10 0 1/4 5/18 3/4 5 12 1/14 2/7 11/14 6/7 5 14 0 3/4 11/18 1/9 5 16 2/3 0 2/11 1/3 5 18 7/10 3/20 1/4 0 5 20 0 4/9 5/9 21/22 5 22 5/23 1/4 0 5/8 5 24 13/23 0 8/23 21/23 5 26 5/19 1/2 1/3 3/4 5 28 1/5 1/3 3/5 7/15 5 30 1/6 5/9 0 5/12 5 32 3/20 4/5 0 4/7 5 34 1/2 7/20 2/5 5/19 5 36 0 6/7 3/5 1/3 5 38 3/8 1/8 2/5 3/7 5 40 3/8 7/10 4/5 2/15 5 42 7/11 2/5 3/4 1/5 5 44 5/9 1/6 12/13 2/9 5 46 1/6 3/11 3/4 7/8 5 48 6/7 10/21 8/9 7/9 5 50 1/4 3/5 1/6 19/21 5 52 4/15 1/7 5/12 13/20 5 54 5/21 7/12 2/3 9/14 5 56 9/11 4/19 3/10 3/5 5 58 1/6 4/9 1/12 12/23 5 60 5/7 10/17 1/7 1/3 5 62 2/3 4/5 5/21 1/20 5 64 1/5 8/11 13/22 1/9 5 66 r1 r2 r3 r4 5 66* ------------------------------------------ 1/3 1/4 3/4 5/6 7 12 5/8 1/8 1/3 1/3 7 20 3/7 1/3 4/7 2/3 7 22 9/14 5/8 6/7 3/8 7 24 5/7 3/5 1/10 5/7 7 26 ------------------------------------------ 3/4 3/4 0 0 9 4 2/3 0 0 1/6 9 6 3/4 5/8 0 0 9 8 1/2 0 3/7 3/7 9 10 0 5/17 0 3/4 9 12 2/7 0 1/2 9/14 9 14 1/2 4/5 0 9/20 9 16 0 2/13 4/17 0 9 18 ------------------------------------------ 0 0 1/4 0 15 4 0 9/10 0 0 15 6 ------------------------------------------ 0 0 0 0 21 2 ------------------------------------------
D8B(p1, p2, p3, p4, p5)↑
show data
p1 p2 p3 p4 p5 d #Λ ------------------------------------------------ 1/3 0 2/3 0 1/3 5 6 3/5 4/5 7/10 3/5 0 5 10 5/12 1/3 1/3 1/3 1/6 5 12 1/7 5/7 2/7 1/14 2/7 5 14 15/16 3/8 3/4 1/2 7/8 5 16 1/3 1/2 2/7 0 2/3 5 18 6/11 1/8 3/8 6/11 0 5 20 2/3 7/10 1/5 0 1/3 5 22 11/12 3/4 2/3 3/4 3/8 5 24 8/9 1/3 1/5 1/2 1/3 5 26 6/7 0 1/6 1/4 1/4 5 28 4/5 0 3/5 1/6 1/3 5 30 4/7 0 1/4 0 9/16 5 32 9/14 6/13 1/3 1/2 1/7 5 34 1/5 3/4 1/3 1/3 0 5 36 8/9 1/3 8/19 0 1/9 5 38 2/9 7/9 12/19 1/4 5/18 5 40 2/5 5/9 2/7 0 7/9 5 42 11/14 1/2 14/15 1/7 1/4 5 44 1/5 3/5 5/8 1/7 0 5 46 0 6/19 7/8 3/4 10/11 5 48 3/13 1/12 15/17 2/3 0 5 50 3/7 0 1/6 3/4 16/19 5 52 0 3/19 2/3 1/9 11/16 5 54 7/13 7/12 1/3 5/7 3/4 5 56 7/10 5/11 7/9 5/11 4/5 5 58 9/17 1/6 3/4 2/3 13/18 5 60 13/19 8/15 2/3 2/3 12/19 5 62 4/5 2/11 1/4 17/20 5/9 5 64 14/17 1/18 7/13 1/3 2/3 5 66 2/3 11/12 13/19 18/19 16/19 5 68 2/5 8/9 1/8 3/5 10/19 5 70 7/12 6/7 13/17 7/13 1/3 5 72 1/7 2/15 1/10 7/19 1/8 5 74 r1 r2 r3 r4 r5 5 74* ------------------------------------------------ 1/2 1/10 2/5 1/5 0 6 10 1/3 1/12 1/3 1/2 3/4 6 12 0 6/7 5/7 0 3/7 6 14 0 3/8 13/16 1/16 1/2 6 16 1/6 8/15 1/3 0 0 6 18 3/20 1/2 1/5 1/5 0 6 20 5/14 5/11 6/7 0 8/11 6 22 1/4 5/8 3/4 1/2 5/7 6 24 3/14 1/2 8/19 6/7 0 6 26 1/2 3/4 1/6 0 11/16 6 28 0 4/7 7/19 0 11/15 6 30 0 17/18 3/7 2/7 2/9 6 38 2/7 5/14 1/4 5/7 3/8 6 44 3/4 3/20 2/5 1/16 1/5 6 48 ------------------------------------------------ 1/4 0 0 0 3/4 7 4 2/3 1/3 2/3 0 0 7 6 1/8 0 1/4 0 0 7 8 1/2 2/5 1/5 4/5 1/2 7 10 0 0 8/17 3/4 3/4 7 12 11/18 0 1/2 9/10 2/5 7 14 17/18 3/4 1/2 1/2 5/9 7 16 0 1/2 2/3 1/6 1/13 7 18 3/5 0 0 2/5 1/4 7 20 1/9 0 1/2 13/18 2/5 7 22 0 0 3/4 5/8 5/11 7 24 3/7 4/7 1/2 0 4/9 7 26 0 0 6/7 1/4 6/11 7 28 2/3 1/9 0 0 2/13 7 30 7/12 6/7 1/2 3/4 11/12 7 32 0 2/3 1/6 4/17 1/17 7 34 3/4 3/4 12/17 1/7 6/7 7 36 1/3 2/3 0 6/11 4/5 7 38 3/8 7/8 10/11 8/9 5/8 7 40 4/5 17/18 0 3/5 2/17 7 42 11/12 1/4 0 4/7 3/5 7 44 5/13 1/6 0 4/15 2/7 7 46 ------------------------------------------------ 3/4 0 0 1/8 1/4 8 8 0 2/3 1/2 2/3 1/4 8 12 0 7/8 0 1/4 11/16 8 16 1/2 1/10 0 7/10 3/4 8 20 3/8 1/8 0 1/6 1/3 8 24 2/3 2/3 1/3 3/4 16/19 8 32 2/3 11/12 1/2 1/10 1/5 8 36 ------------------------------------------------ 3/4 0 3/4 1/2 1/2 9 4 0 5/6 1/3 2/3 1/2 9 6 1/2 1/8 1/8 0 1/2 9 8 1/2 4/5 4/5 7/10 3/10 9 10 0 19/20 1/4 0 1/2 9 12 0 2/7 13/14 0 0 9 14 3/4 1/4 0 11/14 5/7 9 16 0 8/13 7/15 0 0 9 18 3/5 9/10 0 19/20 0 9 20 5/14 6/7 1/2 5/9 4/9 9 22 3/4 3/4 2/3 0 1/7 9 24 6/7 6/7 4/7 0 4/5 9 26 ------------------------------------------------ 0 1/2 1/3 1/3 1/2 10 6 1/4 0 1/2 3/4 3/8 10 8 3/11 6/11 0 0 0 10 10 1/4 2/5 1/2 1/2 0 10 12 0 0 1/5 0 11/14 10 14 ------------------------------------------------ 0 0 3/4 1/4 1/2 11 4 3/10 0 1/2 0 1/2 11 6 1/4 1/4 0 1/8 0 11 8 0 1/2 0 4/5 13/20 11 10 1/3 1/3 7/12 0 1/3 11 12 1/10 3/5 1/2 2/17 1/2 11 14 ------------------------------------------------ 3/4 1/4 0 0 1/4 13 4 5/6 1/3 0 1/3 1/2 13 6 ------------------------------------------------ 0 0 0 0 1/4 15 4 0 0 0 1/2 9/19 15 6 ------------------------------------------------ 0 0 0 0 0 21 2 ------------------------------------------------
D8C(p1, p2, p3, p4, p5, p6)↑
show data
p1 p2 p3 p4 p5 p6 d #Λ ----------------------------------------------------------- 0 1/4 0 1/2 1/4 0 5 4 1/2 2/3 0 0 1/2 0 5 6 3/4 0 0 1/2 8/15 0 5 12 2/9 0 1/3 1/2 1/2 1/2 5 14 15/16 1/4 3/4 0 0 5/8 5 16 1/3 1/2 0 0 11/16 2/3 5 18 0 2/15 0 1/2 1/2 1/2 5 10 3/10 1/4 0 11/20 0 1/5 5 20 16/17 1/5 4/5 0 0 0 5 22 1/3 5/12 0 5/8 7/8 0 5 24 5/6 2/5 9/10 1/2 1/10 1/2 5 26 0 3/4 0 0 6/13 7/9 5 28 0 7/10 1/5 0 1/2 5/8 5 30 1/2 0 0 2/3 1/12 4/5 5 32 1/10 9/11 0 1/2 1/5 0 5 34 0 4/5 1/4 2/3 1/2 3/10 5 36 11/12 1/4 0 3/5 1/8 0 5 38 8/17 2/5 1/10 11/12 2/3 1/6 5 40 7/15 8/17 1/3 2/19 3/8 3/8 5 42 1/4 0 19/20 2/5 0 15/16 5 44 0 4/9 5/6 9/17 0 5/9 5 46 1/10 1/3 3/4 2/3 14/15 0 5 48 11/19 0 2/15 2/5 2/3 14/15 5 50 1/3 1/3 2/3 1/4 9/14 11/16 5 52 1/2 1/7 2/3 2/15 3/10 1/2 5 54 1/5 4/9 9/10 19/20 2/7 5/6 5 56 0 8/11 1/2 1/3 1/6 12/13 5 58 1/3 9/16 2/3 2/19 1/4 0 5 60 12/13 0 1/6 1/4 3/8 12/13 5 62 7/12 3/5 3/7 1/14 1/2 1/4 5 64 4/15 5/11 2/3 10/19 0 2/7 5 66 r1 r2 r3 r4 r5 r6 5 66* ----------------------------------------------------------- 1/2 3/4 3/10 0 0 1/5 7 16 1/11 0 1/4 1/2 1/4 1/2 7 20 1/16 9/14 1/2 0 0 2/7 7 26 ----------------------------------------------------------- 1/3 0 2/3 0 2/3 1/2 9 6 0 0 1/5 1/10 0 1/2 9 10 5/8 1/8 1/2 0 5/19 0 9 12 4/5 4/5 1/2 1/2 0 13/20 9 16 13/20 13/20 1/3 5/14 0 1/2 9 18 ----------------------------------------------------------- 1/2 0 0 0 4/11 0 15 6 ----------------------------------------------------------- 0 0 0 0 0 0 21 2 -----------------------------------------------------------
BH(10, 6)(p1)↑
show data
p1 d #Λ ------------------ 0 4 6 1/4 4 12 5/9 4 18 3/8 4 24 r1 4 26* ------------------ 1/3 12 6 ------------------
D10(p1, p2, p3)↑
show data
p1 p2 p3 d #Λ ---------------------------------- 0 1/8 1/4 9 8 1/4 0 8/9 9 12 1/5 4/5 0 9 20 3/5 1/2 7/8 9 24 7/9 1/9 0 9 28 0 1/3 9/10 9 32 5/6 2/3 1/10 9 36 1/10 4/9 4/9 9 48 1/7 8/9 2/9 9 52 7/8 1/10 5/9 9 56 1/3 4/9 2/7 9 60 r1 r2 r3 9 60* ---------------------------------- 3/4 0 0 10 4 0 5/8 0 10 8 1/2 0 2/9 10 12 2/5 0 2/5 10 20 ---------------------------------- 1/6 0 1/3 12 12 ---------------------------------- 0 0 0 16 4 ----------------------------------
Y10,2,76(p1, p2)↑
show data
p1 p2 d #Λ -------------------------- 1/3 5/6 2 12 0 7/10 2 36 1/5 1/5 2 40 3/8 9/10 2 64 3/7 2/7 2 72 2/5 3/7 2 76 r1 r1 2 76* -------------------------- 0 0 3 12 5/8 3/8 3 24 3/5 2/5 3 48 -------------------------- 1/4 1/4 4 12 --------------------------
S12(p1, p2, p3, p4, p5)↑
show data
p1 p2 p3 p4 p5 d #Λ ------------------------------------------------- 7/18 3/4 0 4/9 1/3 11 36 3/5 1/9 2/11 11/12 1/6 11 54 11/16 11/24 0 0 1/3 11 60 7/8 5/18 0 1/2 4/9 11 72 1/9 1/3 1/2 0 9/23 11 84 3/7 0 5/6 7/12 7/18 11 96 4/9 5/6 11/12 5/8 2/7 11 102 1/3 1/4 0 2/3 6/11 11 108 0 1/18 7/17 11/24 5/6 11 114 11/24 13/24 1/3 7/16 2/3 11 120 1/11 5/9 5/12 10/13 5/6 11 126 1/3 1/9 0 8/17 11/24 11 132 3/4 7/23 13/19 6/19 2/3 11 138 0 1/6 0 4/7 7/13 11 144 17/22 1/6 7/10 1/5 11/18 11 150 1/8 0 1/3 5/11 3/4 11 156 13/14 7/12 11/19 1/18 1/3 11 162 0 2/5 0 17/24 1/3 11 168 3/4 3/4 8/17 10/21 1/3 11 174 5/12 4/5 2/3 9/11 1/3 11 180 7/8 5/18 9/10 3/8 16/17 11 186 0 5/11 1/2 4/23 7/9 11 192 0 4/5 11/13 17/20 1/15 11 198 7/12 2/5 5/18 1/6 3/23 11 204 8/15 3/4 12/19 19/20 13/15 11 210 0 1/7 5/9 0 11/17 11 216 17/20 2/5 8/17 2/5 2/3 11 222 1/7 0 1/8 11/16 1/8 11 228 4/21 6/11 5/9 9/10 1/3 11 234 1/6 4/5 0 13/14 3/5 11 240 18/19 11/14 2/5 3/5 4/7 11 246 0 3/5 11/15 5/7 1/4 11 252 1/4 1/3 16/21 1/5 6/7 11 258 2/7 5/6 0 14/15 4/7 11 264 1/6 4/5 2/5 4/5 3/11 11 270 3/8 10/17 0 4/13 4/9 11 276 13/20 0 20/21 19/20 3/5 11 282 1/5 19/23 1/3 4/11 1/22 11 288 0 5/8 14/17 7/8 1/7 11 294 6/17 0 1/17 1/3 7/10 11 300 2/3 1/7 7/22 3/5 1/7 11 306 10/11 2/3 3/14 5/9 16/21 11 312 1/16 1/5 6/7 2/21 4/7 11 318 4/13 0 2/9 16/17 3/20 11 324 11/21 1/2 1/14 7/23 2/17 11 330 10/11 0 1/11 3/5 3/5 11 336 1/2 1/5 2/7 7/8 19/21 11 342 5/18 13/20 8/19 9/11 9/10 11 348 0 6/23 2/17 2/21 5/7 11 354 r1 r2 r3 r4 r5 11 354* ------------------------------------------------- 0 0 0 0 8/9 13 36 2/3 0 2/3 7/12 1/8 13 72 0 1/3 5/6 2/5 3/4 13 84 0 0 0 8/9 3/10 13 96 0 0 17/20 4/5 1/3 13 102 2/3 0 0 3/11 3/11 13 108 0 0 6/7 5/8 11/18 13 114 2/5 4/5 7/20 0 3/4 13 120 2/3 2/3 17/20 13/16 2/5 13 126 1/2 0 0 19/20 1/10 13 132 1/3 1/2 1/2 7/16 1/11 13 144 0 2/3 6/17 8/17 1/4 13 156 1/2 0 3/7 7/18 11/14 13 168 1/2 7/12 11/13 6/17 2/3 13 174 0 0 5/11 1/13 1/13 13 180 1/3 1/2 3/20 5/19 3/8 13 186 3/4 11/12 0 6/11 1/15 13 192 7/12 1/6 18/19 0 15/22 13 204 5/8 1/4 0 6/17 11/15 13 216 9/13 5/13 9/22 0 15/19 13 228 5/6 3/4 13/19 9/20 1/8 13 246 11/12 3/4 4/7 8/17 2/5 13 270 ------------------------------------------------- 5/9 10/21 1/2 0 0 15 36 1/18 4/5 2/5 1/12 0 15 54 3/8 0 1/2 1/3 1/2 15 60 1/2 1/2 4/15 2/5 0 15 66 3/19 1/9 7/24 0 1/2 15 72 3/4 6/11 1/9 17/18 0 15 78 1/2 2/3 1/10 1/6 0 15 84 1/4 0 5/12 10/11 0 15 90 0 7/23 0 8/9 1/2 15 96 5/6 1/2 3/4 10/11 5/11 15 102 3/4 8/13 2/9 1/6 0 15 108 5/12 1/9 17/22 3/5 1/2 15 114 1/8 5/7 3/4 7/12 15/17 15 126 2/5 1/2 13/20 0 1/2 15 132 2/15 9/20 6/7 4/21 0 15 138 7/10 1/4 2/3 2/5 0 15 144 0 1/4 3/5 7/8 1/2 15 150 1/7 11/12 2/7 0 0 15 156 2/21 1/21 1/4 1/8 4/5 15 162 1/7 9/11 3/4 0 1/8 15 168 7/8 0 7/8 10/13 1/2 15 174 8/23 1/3 5/9 1/8 0 15 180 2/11 2/3 1/4 17/18 8/15 15 192 11/14 1/4 3/4 3/5 5/18 15 204 1/11 1/11 5/11 6/19 0 15 210 1/9 16/21 3/4 5/21 11/17 15 216 1/7 5/7 1/4 2/9 15/22 15 222 0 1/16 17/20 2/5 0 15 228 1/8 3/7 12/13 1/4 18/23 15 234 ------------------------------------------------- 1/3 1/3 1/4 1/12 5/12 17 36 1/3 1/2 1/20 7/12 0 17 54 0 0 1/4 7/9 7/8 17 72 1/3 1/2 0 14/19 1/2 17 84 2/3 0 2/23 17/18 0 17 96 5/8 1/4 8/9 15/16 1/2 17 102 3/4 11/12 1/4 5/6 7/17 17 108 0 0 2/15 3/4 3/8 17 114 3/4 1/2 3/8 7/10 0 17 150 1/2 1/12 3/4 10/11 5/23 17 162 5/12 13/24 3/10 1/21 0 17 174 ------------------------------------------------- 13/18 5/12 5/9 3/4 0 21 30 0 7/12 3/4 1/3 0 21 36 3/13 1/2 3/4 1/4 1/3 21 42 2/3 5/9 1/21 3/4 0 21 54 3/5 3/20 3/4 0 0 21 60 4/5 1/2 3/4 1/20 0 21 78 0 1/10 1/4 1/3 1/2 21 84 3/7 4/7 11/14 1/4 0 21 90 3/10 1/2 3/4 8/9 0 21 96 0 1/15 1/4 9/10 0 21 114 1/7 1/6 1/4 1/4 4/13 21 126 ------------------------------------------------- 7/15 6/7 1/4 3/4 0 27 42 -------------------------------------------------
H12(p1, ..., p7)↑
show data
p1 p2 p3 p4 p5 p6 p7 d #Λ q
---------------------------------------------------------------------------
1/3 0 1/3 3/4 1/3 1/3 1/4 8 12 12
1/5 2/3 1/3 1/6 3/10 1/3 0 8 22 30
7/8 1/4 1/2 4/5 3/4 3/8 3/8 8 24 40
3/5 1/2 2/3 2/3 1/3 4/5 4/5 8 30 30
2/3 1/3 1/3 0 1/4 2/3 5/9 8 32 36
0 1/3 5/6 13/14 1/6 5/7 2/3 8 34 42
13/16 1/3 1/2 1/3 11/12 2/3 1/4 8 36 48
1/6 1/5 2/3 1/6 1/7 1/6 2/3 8 42 210
0 1/3 9/10 7/9 2/3 1/3 4/9 8 46 90
0 3/4 11/13 9/10 3/4 3/5 7/10 8 48 260
1/6 7/15 1/2 1/7 6/7 2/3 2/3 8 50 210
7/8 2/5 3/5 5/8 1/2 1/3 2/3 8 52 120
6/7 9/10 3/14 0 4/5 6/7 1/5 8 54 70
1/16 4/5 1/3 3/4 1/5 3/4 0 8 56 240
5/6 0 4/5 5/6 1/6 1/8 3/5 8 58 120
11/12 5/8 3/4 8/9 0 2/3 1/9 8 60 72
1/14 2/5 3/5 3/10 1/3 1/5 2/5 8 62 210
1/3 5/13 1/6 2/3 1/7 0 3/4 8 64 1092
2/3 5/7 2/7 6/7 5/14 1/2 11/15 8 66 210
5/6 3/4 5/6 9/11 1/4 0 1/9 8 68 396
4/15 5/6 2/3 1/5 3/5 2/3 5/9 8 70 90
2/3 1/3 7/15 2/11 11/12 0 1/4 8 72 660
1/13 2/5 2/5 11/14 2/3 2/7 0 8 74 2730
0 3/4 1/3 11/12 1/5 8/11 4/5 8 76 660
5/6 0 7/11 9/16 15/16 4/7 2/3 8 78 3696
3/4 7/13 2/15 3/7 13/15 4/15 1/2 8 80 5460
5/14 1/5 4/5 1/2 5/7 1/7 1/3 8 82 210
3/4 4/9 11/15 0 5/6 3/4 3/5 8 84 180
2/5 2/5 1/3 1/11 4/9 0 1/3 8 86 990
1/8 1/4 6/7 4/5 7/9 0 1/4 8 88 2520
3/5 0 2/3 11/15 10/11 7/8 1/3 8 90 1320
0 13/15 3/5 4/5 3/16 13/15 3/4 8 92 240
0 3/7 4/7 2/3 4/5 1/5 8/13 8 94 2730
1/3 9/14 7/10 1/6 11/12 8/9 0 8 96 1260
2/5 11/14 2/7 1/16 1/2 3/11 1/7 8 98 6160
3/4 2/3 3/7 2/3 11/13 2/5 1/3 8 100 5460
9/14 5/14 2/15 0 3/8 1/6 13/16 8 102 1680
1/13 1/13 13/14 6/11 3/4 1/2 9/16 8 104 -
2/3 3/7 5/16 5/7 0 2/3 11/15 8 106 1680
5/7 6/7 7/12 2/3 1/2 1/11 1/4 8 108 924
3/16 0 7/10 1/3 2/3 9/11 4/7 8 110 -
4/5 3/7 5/8 0 3/4 7/15 1/6 8 112 840
0 11/16 4/9 2/3 5/6 6/11 1/10 8 114 7920
3/4 7/8 3/7 7/10 5/9 8/9 0 8 116 2520
3/5 6/13 13/16 1/3 5/13 5/13 1/3 8 118 3120
8/15 2/7 1/5 0 2/3 8/13 3/4 8 120 5460
11/16 2/5 3/5 3/8 5/7 2/5 2/11 8 122 6160
1/3 1/4 5/16 9/11 1/10 5/7 1/2 8 124 -
1/14 1/3 2/13 11/13 1/15 2/13 9/11 8 126 -
13/16 0 1/6 6/13 1/4 2/9 2/11 8 128 -
7/11 6/13 2/7 2/3 5/8 2/3 5/7 8 130 -
2/3 6/7 13/16 1/4 2/13 0 8/13 8 132 4368
0 1/3 1/7 8/15 2/9 7/11 2/7 8 134 6930
7/12 1/3 0 1/7 2/5 3/14 6/11 8 136 4620
8/15 13/15 3/7 1/2 7/16 1/15 5/9 8 138 5040
3/4 1/3 4/11 13/14 1/3 5/7 4/13 8 140 -
6/11 4/7 1/2 3/5 5/14 11/15 2/13 8 142 -
11/12 8/11 1/10 1/7 0 2/13 3/4 8 144 -
2/3 7/16 2/7 7/16 1/15 2/13 3/8 8 146 -
2/5 6/13 5/11 1/14 2/3 0 3/4 8 148 -
3/7 2/15 4/5 3/5 5/11 7/13 4/5 8 150 -
2/3 5/9 11/12 1/4 4/5 10/13 2/5 8 152 2340
1/3 4/5 3/16 3/5 4/7 2/3 12/13 8 154 -
7/11 11/16 8/9 11/16 2/5 1/3 1/4 8 156 7920
1/9 1/3 3/10 5/16 2/3 5/7 4/13 8 158 -
3/10 4/11 6/11 1/5 13/15 9/13 3/4 8 160 8580
2/7 5/11 9/11 2/3 1/3 2/13 2/9 8 162 -
1/13 5/12 1/7 2/5 10/13 3/5 1/4 8 164 5460
6/11 1/11 3/7 3/4 2/11 7/16 2/5 8 168 6160
4/7 6/11 4/7 6/13 2/3 5/8 7/11 8 170 -
4/7 4/5 7/8 7/13 10/13 3/5 3/4 8 172 3640
2/5 1/15 9/16 1/8 6/7 1/6 4/5 8 174 1680
4/5 1/4 8/11 12/13 3/5 10/13 7/15 8 176 8580
4/9 11/12 1/7 3/8 4/7 5/7 2/5 8 178 2520
1/8 3/7 9/14 7/9 1/3 3/4 6/11 8 180 5544
5/16 4/7 2/7 2/11 6/7 2/3 7/10 8 182 -
7/12 1/14 15/16 4/5 3/4 8/13 2/9 8 184 -
13/15 4/7 4/9 1/16 5/8 7/10 5/6 8 186 5040
8/13 4/7 7/8 11/13 1/5 1/3 3/5 8 190 -
6/7 5/8 7/11 9/10 5/6 10/11 1/12 8 194 9240
9/10 4/5 4/13 5/16 6/7 1/13 11/12 8 198 -
2/3 3/7 3/16 2/7 10/11 4/13 5/8 8 202 -
1/15 4/9 2/3 4/7 10/11 13/16 3/4 8 204 -
4/7 7/9 1/5 1/11 1/13 3/8 1/3 8 206 -
r1 r2 r3 r4 r5 r6 r7 8 206* -
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2/3 1/3 2/3 2/3 0 2/3 0 9 6 6
1/3 2/3 3/4 2/3 2/3 0 0 9 12 12
0 1/6 2/3 1/16 2/3 1/3 0 9 18 48
1/4 1/3 1/3 7/12 0 7/8 5/6 9 24 24
3/7 1/3 1/3 3/7 1/3 1/2 1/3 9 26 42
1/4 2/3 1/3 0 13/15 3/4 0 9 28 60
5/6 2/5 8/15 4/5 1/10 0 0 9 30 30
5/6 1/6 1/3 1/7 1/2 11/12 0 9 32 84
3/11 1/3 7/11 0 1/3 1/3 1/2 9 34 66
3/4 1/5 1/4 7/12 2/3 3/4 0 9 36 60
5/8 1/6 2/3 4/5 0 2/3 0 9 38 120
5/8 4/5 1/10 0 3/8 3/4 0 9 40 40
3/5 11/13 0 3/5 2/5 5/6 1/2 9 42 390
3/5 1/3 1/3 7/10 3/4 0 0 9 44 60
1/3 5/9 1/6 0 8/9 1/5 2/3 9 46 90
1/4 0 1/4 5/9 7/8 3/13 0 9 48 936
2/3 1/3 3/7 7/15 4/5 0 0 9 50 210
5/6 5/7 3/4 2/5 0 5/6 0 9 52 420
1/5 2/3 15/16 0 7/15 4/5 0 9 54 240
3/4 0 1/10 7/12 5/8 5/6 0 9 56 120
2/3 0 1/5 3/10 2/5 1/7 0 9 58 210
1/2 5/12 3/4 4/7 12/13 3/4 1/4 9 60 1092
0 2/3 5/8 3/16 5/11 2/3 0 9 62 528
3/8 4/5 2/3 3/4 13/15 1/2 0 9 64 120
6/7 1/2 7/8 2/9 2/3 2/3 0 9 66 504
3/8 5/8 2/15 0 6/11 3/13 0 9 68 -
9/11 1/5 2/9 0 1/5 5/7 0 9 70 6930
5/8 2/3 1/16 1/4 1/2 1/11 1/2 9 72 528
1/2 4/5 3/13 1/3 1/14 5/6 2/3 9 74 2730
2/5 1/4 4/7 2/3 0 4/5 0 9 76 420
0 3/4 1/3 3/7 5/7 4/11 1/2 9 80 924
8/11 9/16 1/11 2/11 3/8 0 0 9 82 176
1/9 2/11 0 3/10 1/14 3/4 1/2 9 84 -
1/6 1/16 4/7 1/10 11/15 0 0 9 86 1680
0 2/3 3/5 4/5 1/13 3/4 3/4 9 88 780
1/8 13/15 3/5 5/12 0 1/5 1/2 9 90 120
3/4 1/2 7/8 1/7 4/7 7/9 2/9 9 92 504
8/13 0 9/14 3/5 2/3 4/5 0 9 94 2730
7/16 12/13 0 1/14 1/6 5/12 0 9 96 4368
1/10 5/7 1/7 1/2 3/11 1/3 0 9 98 2310
0 2/5 2/3 3/4 9/11 1/7 6/7 9 100 4620
14/15 1/5 6/7 0 2/9 8/11 0 9 102 6930
3/7 10/13 3/5 1/9 1/16 4/7 0 9 106 -
3/8 1/9 0 3/13 2/5 2/3 1/3 9 114 4680
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2/3 0 1/4 3/4 0 3/4 2/3 10 12 12
2/9 1/4 1/2 1/4 0 3/4 3/8 10 24 72
1/4 2/3 0 1/2 1/4 1/3 1/7 10 32 84
2/11 0 2/3 2/3 0 1/3 1/4 10 36 132
1/2 11/16 2/3 0 3/4 15/16 7/12 10 40 48
2/3 0 4/13 1/6 0 1/3 5/14 10 42 546
2/7 0 1/8 0 3/8 3/4 7/16 10 44 112
3/8 0 8/13 3/8 5/8 0 7/9 10 48 936
0 1/10 5/7 2/3 0 2/3 2/7 10 50 210
1/4 4/9 0 0 2/3 2/3 10/11 10 52 396
1/12 8/9 0 0 5/14 6/7 7/12 10 54 252
3/8 0 2/3 0 7/12 2/3 1/11 10 56 264
2/5 7/11 0 2/11 1/2 2/11 11/16 10 58 880
3/5 7/8 0 3/14 3/5 0 3/4 10 60 280
2/3 0 1/3 1/9 1/2 4/5 7/11 10 62 990
2/7 3/4 0 5/14 0 1/16 5/8 10 64 112
5/7 1/2 3/5 2/15 13/15 0 5/12 10 66 420
11/12 0 11/16 1/2 2/3 3/4 1/9 10 68 144
5/6 2/7 0 5/7 0 7/8 1/5 10 70 840
1/13 5/13 0 8/15 1/4 0 8/13 10 72 780
1/3 0 1/3 8/11 0 1/5 5/13 10 74 4290
0 4/7 4/5 3/4 0 8/9 3/5 10 76 1260
2/9 0 3/13 0 1/10 1/6 2/9 10 78 1170
5/16 3/8 1/2 1/5 10/13 0 3/4 10 80 1040
1/13 11/13 0 4/5 1/2 3/8 2/5 10 82 520
3/11 7/9 0 0 3/4 4/5 1/14 10 84 -
13/14 0 10/13 1/2 4/13 1/8 3/7 10 86 728
0 3/4 3/7 1/11 0 2/3 5/13 10 88 -
4/5 1/2 3/8 3/16 6/7 0 3/5 10 90 560
6/11 0 1/3 13/15 3/5 1/2 3/4 10 92 660
9/10 0 8/9 2/9 0 3/13 4/11 10 94 -
0 2/3 1/9 0 7/12 7/10 2/7 10 96 1260
0 1/5 1/11 9/11 0 7/8 2/3 10 98 1320
3/8 0 6/13 3/5 8/13 0 1/3 10 102 1560
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1/3 2/3 1/3 2/3 1/3 0 0 11 6 6
1/2 2/3 3/4 1/3 0 3/4 3/4 11 12 12
4/5 3/5 0 3/4 3/5 0 3/5 11 20 20
1/2 7/8 11/12 0 2/3 1/3 1/3 11 24 24
2/3 0 4/5 0 14/15 2/3 7/10 11 30 30
2/3 0 2/3 2/7 1/7 0 1/3 11 34 42
1/2 2/9 5/6 2/3 2/3 0 1/7 11 38 126
1/8 3/7 1/2 0 3/8 9/16 5/8 11 40 112
0 2/5 1/3 2/3 1/2 1/8 5/6 11 42 120
0 7/8 5/8 0 2/9 2/3 5/6 11 48 72
6/7 3/5 0 2/3 0 3/5 3/5 11 50 210
1/2 1/5 5/8 3/4 0 2/3 1/3 11 52 120
1/5 0 1/3 8/15 9/16 1/2 5/6 11 54 240
7/12 1/2 4/5 1/2 3/4 6/13 3/4 11 56 780
1/4 1/13 0 3/11 4/5 1/2 1/4 11 60 2860
0 2/3 1/7 2/3 7/12 0 6/11 11 64 924
9/10 7/11 1/2 15/16 0 9/10 3/4 11 68 880
2/3 0 6/7 1/8 1/2 7/11 5/6 11 70 1848
0 13/16 1/16 1/3 4/5 1/2 1/3 11 72 240
0 5/11 2/3 1/5 4/5 0 7/8 11 78 1320
0 15/16 1/7 5/6 11/12 1/2 3/8 11 80 336
1/2 5/9 8/9 1/5 6/11 0 1/3 11 82 990
1/2 7/9 6/7 3/7 1/4 0 13/15 11 84 1260
0 3/4 5/6 9/11 12/13 1/2 4/5 11 88 8580
0 3/5 1/3 2/15 7/8 0 9/16 11 90 240
0 2/15 1/9 5/8 7/9 0 10/11 11 98 3960
0 13/16 7/12 2/5 4/7 0 3/4 11 100 1680
1/2 10/11 4/5 1/3 1/8 0 8/9 11 102 3960
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2/3 0 1/3 1/4 2/3 0 1/3 12 12 12
5/6 1/6 0 1/8 1/8 0 2/3 12 20 24
1/5 1/4 1/2 0 1/4 3/13 1/4 12 28 260
4/7 14/15 0 0 4/7 5/7 13/14 12 38 210
5/7 1/2 2/3 10/13 0 1/3 2/3 12 42 546
2/7 2/5 0 8/9 1/2 3/5 2/5 12 46 630
0 5/9 3/5 1/5 1/4 0 3/4 12 48 180
0 1/6 4/7 8/11 3/4 1/2 1/6 12 60 924
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3/4 1/4 1/4 1/3 0 2/3 1/4 13 12 12
0 3/5 3/5 7/12 2/3 1/2 3/5 13 36 60
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1/4 3/4 2/3 3/4 1/2 0 1/3 14 12 12
0 1/3 1/3 2/3 8/9 1/2 5/6 14 18 18
1/4 3/5 1/4 0 1/10 1/2 4/5 14 20 20
1/3 2/3 11/15 2/5 1/2 0 5/6 14 22 30
0 1/3 0 11/12 2/3 1/3 5/8 14 24 24
2/3 2/5 1/4 0 1/3 0 2/3 14 28 60
0 0 3/14 2/3 5/6 2/3 13/14 14 30 42
5/12 3/4 10/11 1/4 1/2 1/2 1/3 14 32 132
1/3 4/9 3/4 1/2 2/3 0 11/12 14 36 36
0 0 1/3 1/3 10/13 5/6 7/11 14 38 858
15/16 1/16 5/6 1/3 1/2 0 6/7 14 42 336
5/11 11/16 3/8 3/4 0 0 1/16 14 44 176
0 9/11 0 11/16 9/16 9/11 1/8 14 48 176
1/5 1/8 1/3 5/6 1/2 0 5/12 14 52 120
0 1/2 1/4 4/15 1/7 6/7 13/15 14 56 420
1/2 4/7 0 2/3 8/15 1/6 5/12 14 58 420
0 1/4 0 1/3 2/3 1/7 8/13 14 60 1092
3/7 1/13 3/7 0 1/3 0 6/7 14 62 546
0 0 7/16 7/16 10/11 2/5 1/4 14 64 880
2/3 8/15 11/16 1/2 2/3 0 3/11 14 66 2640
11/13 2/5 8/15 0 3/5 0 6/11 14 70 4290
0 0 1/8 1/3 2/5 1/4 1/5 14 72 120
2/15 3/11 1/7 2/3 1/2 0 7/10 14 74 2310
0 10/11 1/2 1/5 5/7 3/4 3/5 14 76 1540
7/11 1/4 2/3 0 2/5 0 3/8 14 80 1320
0 0 2/5 2/3 9/14 3/11 3/5 14 82 2310
5/6 3/4 2/7 0 3/5 0 12/13 14 84 5460
13/14 1/7 2/5 0 4/5 0 11/15 14 86 210
0 0 8/13 2/5 4/11 1/5 3/4 14 88 2860
2/7 3/5 1/13 1/2 3/10 0 2/3 14 90 2730
0 1/2 1/7 7/16 7/8 4/11 3/5 14 94 6160
8/9 4/5 1/3 0 3/7 0 1/4 14 96 1260
4/7 7/15 7/12 11/13 0 1/2 1/7 14 98 5460
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1/3 2/3 0 0 1/3 1/3 0 15 6 6
2/3 2/3 0 3/4 0 1/3 0 15 12 12
2/3 0 2/3 0 5/9 1/9 0 15 18 18
0 1/5 1/2 1/5 1/3 3/10 1/5 15 22 30
1/4 7/8 0 1/2 3/8 1/13 0 15 24 104
1/11 1/4 1/2 3/4 1/2 6/7 1/2 15 28 308
2/5 3/5 0 4/5 0 8/11 1/2 15 30 110
0 1/2 1/10 1/6 5/6 1/4 2/3 15 32 60
3/7 1/14 1/2 13/15 1/2 2/7 1/2 15 34 210
2/3 2/9 0 5/12 0 1/9 1/2 15 36 36
5/8 2/3 0 3/13 0 1/3 0 15 38 312
9/16 13/16 0 1/4 0 10/13 0 15 40 208
3/5 7/8 0 4/7 0 2/5 1/2 15 42 280
3/4 4/5 4/5 0 0 3/5 7/13 15 44 260
1/10 5/9 1/11 1/2 1/11 0 2/5 15 46 990
5/8 3/4 7/8 0 1/2 2/3 1/7 15 48 168
3/7 0 0 5/6 14/15 5/6 3/5 15 50 210
3/4 1/2 1/9 0 4/11 7/16 0 15 52 1584
7/12 11/12 3/16 0 0 1/6 3/7 15 56 336
5/11 3/5 0 0 4/5 13/15 1/2 15 58 330
4/9 7/16 3/4 0 0 7/16 1/6 15 60 144
9/13 5/14 1/2 0 5/7 3/5 1/2 15 62 910
13/15 1/2 7/13 1/2 1/5 1/11 1/2 15 66 4290
5/6 1/7 13/16 0 0 5/14 3/4 15 68 336
1/7 1/2 1/2 5/12 6/7 5/11 1/8 15 70 1848
7/9 0 0 4/7 1/4 7/8 3/14 15 72 504
2/11 1/3 1/8 1/2 4/5 0 1/3 15 74 1320
4/11 1/2 1/2 5/6 1/4 2/11 4/15 15 76 660
2/3 10/11 1/9 0 1/2 5/7 1/11 15 78 1386
5/7 0 1/2 1/4 3/11 1/5 2/3 15 80 4620
2/5 0 0 4/5 4/7 1/7 7/13 15 82 910
1/4 1/2 0 8/11 11/16 9/11 2/7 15 84 1232
1/13 2/7 2/3 1/2 0 6/7 2/13 15 90 546
11/14 1/2 0 1/5 7/8 4/13 1/9 15 94 -
---------------------------------------------------------------------------
2/3 1/3 1/3 1/3 0 0 0 16 6 6
1/2 1/4 1/2 1/3 2/3 1/3 1/2 16 12 12
2/7 3/4 1/4 1/2 0 1/4 0 16 12 28
0 1/6 2/3 2/3 0 3/8 0 16 18 24
3/4 3/4 2/5 0 1/5 1/2 1/2 16 20 20
1/2 0 10/11 1/3 1/3 3/4 0 16 28 132
2/3 1/2 1/2 1/3 2/5 1/5 0 16 30 30
2/7 1/4 7/9 2/9 0 0 0 16 32 252
5/12 4/15 3/4 0 1/2 3/5 1/2 16 36 60
1/8 1/2 2/3 1/3 3/14 0 0 16 38 168
3/16 0 0 3/8 1/4 14/15 1/2 16 40 240
4/7 9/11 1/3 1/14 0 0 0 16 42 462
0 1/3 5/9 11/13 0 1/9 0 16 46 234
0 3/5 1/11 1/2 1/8 1/4 0 16 48 440
9/14 14/15 3/5 0 1/2 1/3 0 16 50 210
1/7 7/16 3/4 1/3 0 0 0 16 52 336
2/3 0 1/2 3/4 4/13 10/13 1/4 16 56 156
0 7/10 1/2 2/3 5/16 3/5 0 16 58 240
0 1/2 1/12 7/16 1/6 6/11 0 16 60 528
6/7 7/11 0 13/14 5/8 0 0 16 62 616
1/2 4/11 0 5/14 4/5 2/3 0 16 66 2310
4/9 0 1/2 9/13 3/13 1/10 2/5 16 70 1170
---------------------------------------------------------------------------
1/2 1/4 1/4 1/4 3/4 0 1/2 17 4 4
0 1/3 2/3 1/3 2/3 0 0 17 6 6
0 2/3 0 2/3 2/3 1/4 1/2 17 12 12
0 3/4 0 9/14 3/4 6/7 3/4 17 16 28
0 4/15 2/15 1/6 5/6 0 0 17 30 30
0 2/7 3/4 3/5 2/5 0 0 17 32 140
0 1/8 3/8 5/9 13/16 0 0 17 36 144
0 2/7 2/5 2/3 5/6 0 0 17 38 210
0 9/13 1/8 3/4 9/14 1/2 0 17 48 728
0 3/8 5/11 2/3 4/9 0 0 17 66 792
---------------------------------------------------------------------------
1/2 0 1/3 0 2/3 2/3 2/3 18 6 6
0 1/3 0 1/3 1/3 1/2 1/4 18 12 12
2/3 3/4 0 0 1/8 0 2/3 18 24 24
0 0 2/5 2/3 2/3 1/2 3/10 18 26 30
1/4 7/9 0 1/3 0 0 1/3 18 28 36
1/4 0 2/3 6/7 1/2 0 1/3 18 32 84
2/5 9/10 1/2 0 8/13 1/2 9/13 18 34 130
1/5 5/11 0 0 3/10 1/2 1/4 18 36 220
0 2/3 0 5/6 0 8/9 4/11 18 38 198
0 0 1/4 0 11/15 4/5 4/5 18 40 60
6/7 0 0 6/7 1/5 0 3/11 18 42 770
0 0 3/13 1/2 4/5 1/4 2/5 18 44 260
0 3/4 7/15 0 14/15 0 1/7 18 48 420
0 9/10 0 1/8 4/15 0 4/5 18 50 120
0 0 4/11 0 1/5 1/4 1/3 18 52 660
0 2/5 4/5 0 5/14 0 2/13 18 54 910
0 12/13 2/13 0 0 7/11 1/4 18 56 572
0 6/7 1/3 0 1/2 4/7 5/8 18 58 168
3/5 0 0 7/9 7/15 0 3/4 18 60 180
1/3 0 0 7/9 13/14 1/2 3/5 18 62 630
---------------------------------------------------------------------------
0 1/3 1/3 1/2 1/2 1/3 2/3 19 6 6
1/2 2/3 2/3 3/4 1/2 0 1/4 19 12 12
0 2/3 1/2 0 1/11 1/6 2/3 19 18 66
3/4 1/2 1/2 1/12 0 1/12 3/8 19 24 24
2/3 0 0 3/16 3/4 1/2 1/3 19 28 48
1/2 2/5 1/5 5/9 0 0 2/5 19 30 90
0 3/11 1/4 1/12 0 0 1/4 19 32 132
2/3 1/3 0 0 0 13/15 1/8 19 34 120
2/5 0 2/3 0 1/2 3/8 1/3 19 38 120
8/9 1/2 7/10 1/2 0 5/6 5/9 19 42 90
5/7 7/8 0 0 0 5/12 5/8 19 44 168
1/3 0 0 1/14 0 3/7 7/8 19 46 168
1/8 9/11 0 0 0 12/13 3/4 19 48 1144
3/4 0 15/16 1/2 1/2 1/5 2/7 19 52 560
11/15 0 1/2 0 6/13 10/13 1/10 19 54 390
1/6 1/2 5/16 0 0 2/13 1/4 19 56 624
10/11 0 0 0 2/9 1/7 2/3 19 58 1386
---------------------------------------------------------------------------
0 1/3 2/3 1/2 1/3 1/2 2/3 20 6 6
1/4 1/2 1/4 1/2 0 1/3 2/3 20 12 12
7/8 0 0 1/4 0 2/3 3/4 20 20 24
3/4 0 5/8 0 0 3/4 2/13 20 24 104
3/4 0 0 0 12/13 3/4 1/5 20 28 260
1/3 0 4/5 1/2 0 1/12 1/6 20 36 60
---------------------------------------------------------------------------
1/4 3/4 0 3/4 0 1/2 1/4 21 4 4
2/3 1/2 1/3 1/2 0 1/3 1/3 21 6 6
1/3 2/3 0 0 0 3/4 2/3 21 12 12
8/13 0 1/2 0 2/5 9/10 3/5 21 22 130
---------------------------------------------------------------------------
2/3 0 1/2 0 1/3 2/3 1/3 22 6 6
3/4 1/2 0 0 1/3 3/4 1/4 22 12 12
---------------------------------------------------------------------------
0 0 0 3/4 1/4 3/4 1/3 23 12 12
0 0 1/2 3/4 5/6 1/4 2/5 23 24 60
0 1/2 1/2 5/6 1/6 5/11 3/4 23 28 132
0 0 0 1/3 10/13 1/6 3/11 23 34 858
0 0 0 9/14 1/3 4/13 1/3 23 38 546
3/8 3/10 1/4 0 0 0 2/7 23 40 280
0 0 0 6/7 2/5 3/4 1/3 23 44 420
1/2 0 1/2 6/7 4/5 2/5 3/8 23 46 280
1/2 0 1/2 3/5 1/9 2/15 4/5 23 50 90
0 0 0 2/3 3/11 2/7 4/7 23 54 462
---------------------------------------------------------------------------
3/4 2/5 5/16 0 1/2 0 1/4 24 28 80
---------------------------------------------------------------------------
3/4 0 0 3/4 0 3/4 0 25 4 4
2/3 0 0 0 1/3 1/3 0 25 6 6
1/2 1/4 1/2 1/3 1/4 0 0 25 12 12
1/3 1/2 0 1/3 0 3/4 0 25 12 12
0 4/7 0 4/7 5/14 1/2 0 25 14 14
0 1/2 11/15 1/3 2/3 0 0 25 18 30
1/8 0 10/13 1/2 0 1/8 0 25 20 104
1/3 0 2/5 0 0 3/5 0 25 22 30
1/5 3/4 1/2 1/2 1/8 1/2 1/2 25 24 40
4/11 0 0 0 1/4 2/3 1/2 25 28 132
3/5 0 4/5 1/2 0 3/8 1/2 25 30 40
0 0 1/7 5/12 2/3 0 0 25 32 84
13/16 1/8 0 0 8/11 0 0 25 34 176
0 1/5 0 0 3/16 9/14 1/2 25 38 560
---------------------------------------------------------------------------
0 1/2 0 1/3 1/3 2/3 1/3 26 6 6
2/3 1/3 1/4 0 0 0 3/4 26 12 12
---------------------------------------------------------------------------
0 1/3 0 0 2/3 1/2 2/3 27 6 6
0 0 0 3/4 1/4 0 5/8 27 8 8
1/2 2/3 0 1/3 0 0 3/4 27 12 12
2/3 1/2 5/6 0 0 0 3/4 27 12 12
0 7/16 1/2 3/4 0 0 3/8 27 16 16
1/6 0 0 0 11/16 1/2 1/6 27 18 48
0 3/4 1/3 0 1/2 0 7/8 27 20 24
0 3/4 7/9 0 0 0 1/6 27 24 36
0 13/14 0 0 1/2 1/3 1/14 27 26 42
0 3/5 0 1/2 0 1/4 7/15 27 28 60
7/11 0 1/8 0 0 0 4/7 27 30 616
1/2 0 15/16 0 1/9 0 3/4 27 32 144
1/2 1/2 5/8 1/2 1/6 1/2 7/10 27 34 120
---------------------------------------------------------------------------
0 1/3 2/3 0 0 0 1/3 28 6 6
0 3/4 0 0 0 1/3 1/4 28 12 12
0 2/5 0 1/2 1/2 3/4 1/4 28 12 20
11/16 0 1/2 0 0 14/15 11/16 28 26 240
3/4 0 0 0 0 1/5 5/6 28 28 60
2/7 1/2 0 0 1/2 1/13 1/12 28 30 1092
---------------------------------------------------------------------------
0 1/4 0 1/4 0 0 1/4 29 4 4
1/2 1/3 0 0 0 2/3 1/3 29 6 6
3/4 1/2 1/2 0 0 1/4 1/3 29 12 12
4/7 0 0 1/2 0 1/10 2/5 29 14 70
---------------------------------------------------------------------------
1/3 2/3 2/3 1/2 0 0 2/3 30 6 6
---------------------------------------------------------------------------
1/4 0 0 1/2 0 1/4 1/4 31 4 4
1/3 0 0 0 0 1/3 2/3 31 6 6
---------------------------------------------------------------------------
0 1/4 0 1/2 0 3/4 1/2 35 4 4
1/2 0 1/3 0 2/3 0 0 35 6 6
0 1/4 2/3 1/2 0 0 0 35 12 12
0 0 1/4 0 0 7/10 0 35 12 20
0 0 0 1/15 1/3 0 0 35 18 30
0 3/14 0 0 0 9/14 0 35 14 14
---------------------------------------------------------------------------
0 2/3 0 0 1/2 0 1/3 36 6 6
0 0 1/2 0 1/3 1/2 3/4 36 12 12
0 0 0 5/6 0 0 5/8 36 14 24
---------------------------------------------------------------------------
0 1/3 1/2 1/2 0 0 1/3 37 6 6
1/2 0 1/4 1/2 0 0 3/4 37 4 4
---------------------------------------------------------------------------
38 not recorded
---------------------------------------------------------------------------
41 not recorded
---------------------------------------------------------------------------
42 not recorded
---------------------------------------------------------------------------
0 0 1/2 1/4 0 0 0 45 4 4
0 0 2/3 0 0 0 0 45 6 6
---------------------------------------------------------------------------
49 not recorded
---------------------------------------------------------------------------
54 not recorded
---------------------------------------------------------------------------
0 0 0 0 0 0 0 55 2 2
---------------------------------------------------------------------------
M13B(p1)↑
show data
p1 d #Λ q -------------------------- 0 1 6 6 3/4 1 12 12 9/11 1 18 66 r1 1 18* - -------------------------- 1/3 4 6 6 --------------------------
M13C(p1, p2)↑
show data
p1 p2 d #Λ q ----------------------------------- 0 0 2 6 6 3/4 1/2 2 12 12 7/8 0 2 18 24 5/12 1/8 2 24 24 3/5 4/5 2 30 30 4/17 3/4 2 36 204 4/13 7/11 2 42 858 r1 r2 2 42* - ----------------------------------- 1/4 1/12 3 12 12 ----------------------------------- 1/6 2/3 4 6 6 ----------------------------------- 0 1/3 6 6 6 -----------------------------------
D14(p1, p2, p3, p4, p5)↑
show data
p1 p2 p3 p4 p5 d #Λ q ----------------------------------------------------------- 1/6 1/2 2/3 1/4 1/2 14 12 12 1/4 1/10 0 0 3/5 14 16 20 3/4 1/2 0 1/5 2/5 14 20 20 7/8 1/4 13/20 5/8 0 14 24 40 1/3 0 10/19 0 1/4 14 32 228 2/5 3/4 0 0 1/9 14 36 180 1/4 1/4 5/6 3/10 4/5 14 40 60 1/8 1/2 1/2 1/6 3/16 14 44 48 1/2 9/10 1/5 15/16 0 14 48 80 0 9/20 9/10 3/19 0 14 52 380 0 0 9/14 5/18 4/7 14 56 252 3/4 2/7 0 6/7 5/6 14 60 84 1/6 11/13 1/4 7/17 1/2 14 64 2652 3/5 2/7 7/18 1/4 2/7 14 68 1260 4/5 7/9 2/3 1/6 1/4 14 72 180 7/11 1/4 5/12 0 8/13 14 76 1716 7/8 7/20 9/10 15/16 4/5 14 80 80 0 2/3 3/5 4/9 1/3 14 84 180 7/10 7/8 1/2 7/15 1/3 14 88 120 13/16 7/18 0 11/15 4/15 14 92 720 0 3/10 1/5 1/7 1/16 14 96 560 1/8 0 1/18 13/18 8/11 14 104 792 1/2 4/5 1/11 5/6 2/9 14 112 1980 1/16 18/19 8/15 15/17 3/4 14 116 - 8/9 3/7 7/13 6/7 4/7 14 128 3276 2/9 2/17 4/9 9/10 9/14 14 160 - 1/15 8/17 1/18 13/19 4/5 14 172 - 5/14 2/9 7/8 2/5 15/16 14 152 5040 3/11 12/17 6/11 8/9 7/9 14 144 6732 9/10 11/13 2/9 0 1/20 14 100 2340 7/8 1/6 0 3/14 4/5 14 108 840 3/7 0 7/9 4/15 5/16 14 124 5040 8/11 14/15 2/9 1/9 7/18 14 132 1980 5/12 9/14 3/14 1/3 7/10 14 148 420 7/8 7/17 1/19 13/14 3/5 14 168 - 7/16 7/17 9/20 5/6 4/15 14 156 4080 2/3 1/16 3/4 11/19 5/9 14 120 2736 3/11 11/15 1/8 3/14 8/11 14 136 9240 11/18 3/8 8/13 3/13 5/16 14 140 1872 11/18 17/20 2/5 3/11 1/14 14 164 - r1 r2 r3 r4 r5 14 172* - ----------------------------------------------------------- 1/2 3/4 1/2 1/3 5/8 15 24 24 1/2 5/13 1/2 1/18 3/4 15 32 468 4/9 17/18 3/4 1/15 0 15 36 180 0 11/19 1/2 12/19 4/19 15 40 76 1/5 0 11/18 0 4/5 15 48 180 1/2 1/6 0 7/8 6/7 15 52 168 0 11/17 1/2 14/17 4/9 15 56 612 0 4/7 0 5/9 6/7 15 60 252 1/3 1/3 7/8 13/14 0 15 64 168 5/9 5/6 1/3 1/2 3/5 15 72 180 5/6 6/7 13/16 1/2 2/3 15 76 336 13/16 2/5 6/7 0 11/16 15 88 560 ----------------------------------------------------------- 0 3/4 7/8 1/4 1/4 16 8 8 1/4 1/2 0 3/4 2/9 16 12 36 1/10 0 0 3/5 9/10 16 20 20 0 13/14 5/18 1/2 3/7 16 32 252 0 1/7 1/7 0 5/9 16 36 252 1/19 5/6 1/3 0 1/19 16 40 228 1/2 1/5 5/16 7/8 1/5 16 52 80 2/15 5/9 0 5/9 2/7 16 64 1260 11/18 4/5 2/3 11/18 1/2 16 72 180 ----------------------------------------------------------- 0 5/8 1/4 1/2 0 18 8 8 1/2 5/6 1/2 0 1/6 18 12 12 0 0 0 3/7 1/14 18 20 28 3/8 0 2/5 0 1/2 18 24 40 11/15 1/2 0 4/5 1/2 18 32 60 ----------------------------------------------------------- 1/4 0 0 0 10/19 19 12 76 0 1/2 0 2/5 2/5 19 16 20 9/10 0 0 1/2 4/5 19 20 20 1/5 0 0 0 1/8 19 24 40 5/14 0 0 0 2/7 19 28 28 1/3 0 0 0 4/11 19 32 132 ----------------------------------------------------------- 1/3 0 0 0 5/6 20 12 12 4/5 1/2 1/2 0 1/5 20 20 20 ----------------------------------------------------------- 1/4 0 1/2 0 0 26 4 4 0 0 0 0 9/10 26 12 20 ----------------------------------------------------------- 0 0 0 0 0 36 4 4 -----------------------------------------------------------
S16(p1, ..., p11)↑
show data
p1 p2 p3 p4 p5 p6 p7 p8 p9 p10 p11 d #Λ q ----------------------------------------------------------------------------------------------------------- 1/3 0 0 3/8 6/13 9/17 5/19 1/13 1/2 0 1/2 12 192 - 8/13 0 0 1/2 0 1/5 3/8 1/11 0 1/7 5/8 12 204 - 9/16 3/4 15/16 7/8 0 1/17 1/12 1/4 2/9 1/12 0 12 228 2448 1/8 1/2 7/12 1/2 5/6 8/11 1/7 0 0 2/7 3/8 12 236 1848 14/15 2/3 1/12 4/7 0 2/19 1/2 1/4 1/6 5/8 0 12 244 - 5/8 4/5 3/4 0 0 3/8 2/3 17/18 14/19 4/5 0 12 256 6840 8/9 8/9 2/3 4/9 1/2 3/19 2/9 2/11 0 1/2 0 12 272 - 4/5 7/18 0 2/9 6/11 13/16 1/8 3/4 0 1/2 1/2 12 276 7920 7/9 3/19 0 2/3 2/13 1/8 13/17 2/9 3/8 5/12 0 12 328 - 1/6 2/5 3/5 5/16 9/11 2/3 7/12 6/7 1/8 0 5/8 12 344 - 1/8 3/5 0 1/10 2/3 3/7 2/3 5/7 2/5 1/2 7/10 12 348 840 5/7 1/5 0 9/17 1/9 11/13 0 0 13/17 0 0 12 376 - 2/11 1/14 5/9 1/3 0 5/8 7/10 7/9 3/10 0 1/2 12 380 - 1/16 2/13 9/11 9/20 0 1/4 8/9 1/4 1/2 7/20 13/18 12 384 - 0 2/3 13/17 2/3 2/5 3/17 1/4 3/8 6/11 3/8 5/13 12 392 - 7/15 3/4 2/5 4/13 1/3 9/10 1/17 1/5 0 1/20 3/8 12 396 - 2/17 7/20 1/2 7/12 1/5 9/10 11/15 2/7 14/15 7/15 5/6 12 400 - 1/3 2/11 4/13 5/6 1/3 4/11 1/17 1/3 2/3 1/6 3/13 12 408 - 1/3 1/13 1/5 2/7 6/7 7/8 1/2 1/2 1/6 10/11 3/4 12 412 - 8/9 1/2 2/7 4/7 1/4 4/15 1/6 0 17/20 3/5 13/20 12 416 2520 7/17 0 2/13 4/13 0 5/17 1/2 11/12 1/8 1/7 3/4 12 420 - 3/5 4/5 0 10/13 1/6 3/5 5/6 1/2 8/19 2/15 3/4 12 424 - 0 4/5 5/6 4/7 1/2 1/3 1/2 1/13 5/8 5/16 8/19 12 432 - 1/20 2/5 9/20 9/11 3/10 1/5 5/8 9/14 4/7 7/17 0 12 438 - 2/11 4/13 11/20 4/7 0 2/3 0 4/7 2/5 15/17 1/2 12 440 - 2/3 10/13 0 2/3 3/4 6/7 2/17 1/4 7/16 0 14/15 12 448 - 5/18 2/5 9/17 1/6 17/19 1/6 6/17 2/3 5/16 2/3 5/6 12 452 - 0 7/8 0 11/17 7/9 4/5 1/9 3/5 18/19 1/10 0 12 464 - 11/20 9/13 2/5 1/3 5/9 1/7 7/9 1/2 1/11 0 0 12 468 - 7/10 1/2 4/5 6/7 0 5/14 8/13 1/14 8/9 1/11 0 12 480 - 8/9 1/3 3/16 5/6 1/10 1/20 4/7 5/6 7/9 0 1/2 12 492 5040 5/6 16/19 7/11 2/19 5/11 8/13 0 1/9 1/2 3/5 0 12 500 - 11/17 12/19 3/5 2/15 7/18 3/4 5/9 1/10 1/5 1/3 0 12 504 - 1/5 1/2 4/5 12/19 11/14 5/18 1/8 1/4 1/3 1/3 1/13 12 512 - 2/11 14/19 1/2 2/3 6/13 11/15 11/14 0 1/5 0 5/8 12 528 - 4/5 8/19 5/7 6/17 7/10 4/9 6/11 0 0 1/2 1/16 12 536 - 0 4/11 9/14 3/7 2/3 3/4 2/17 2/3 9/10 0 7/9 12 540 - 9/11 9/20 0 3/5 1/3 7/12 15/19 1/2 1/20 10/17 6/11 12 544 - 0 0 0 6/17 9/20 1/9 7/11 1/6 1/2 6/13 11/20 12 552 - 1/3 1/13 2/3 2/15 1/4 14/17 8/9 3/8 11/17 9/13 0 12 556 - 0 5/13 5/8 1/8 13/17 8/9 3/7 7/11 7/9 5/12 4/11 12 560 - 2/3 1/10 1/4 1/18 1/4 8/9 1/10 5/14 1/2 1/17 2/7 12 576 - 0 3/5 2/19 7/9 1/2 4/15 1/5 16/17 2/3 16/19 3/20 12 586 - 15/17 1/3 2/3 1/11 10/11 1/6 11/12 7/8 8/9 2/7 9/11 12 608 - 16/17 0 13/14 1/10 1/19 14/19 11/13 8/11 4/11 1/2 0 12 620 - 2/3 8/9 15/17 7/8 2/7 13/16 4/5 6/17 5/11 3/8 4/5 12 650 - 0 1/5 1/4 4/5 5/7 7/20 15/19 1/3 1/3 5/17 1/17 12 652 - 0 2/3 2/9 3/10 3/5 2/3 1/8 16/19 5/19 13/16 5/18 12 676 - 7/9 1/6 1/3 8/15 10/13 9/10 11/14 4/11 0 7/10 6/7 12 704 - 0 2/3 13/20 1/13 17/18 8/19 4/7 1/5 8/9 15/17 9/13 12 786 - r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 12 794* - ----------------------------------------------------------------------------------------------------------- 0 0 0 5/9 1/2 3/4 1/2 1/4 1/5 1/5 3/4 13 64 360 1/2 5/8 6/19 1/5 1/2 0 0 3/4 7/19 0 1/19 13 144 760 2/7 9/20 0 0 1/5 0 5/9 0 11/16 0 1/20 13 220 5040 1/7 6/7 1/4 1/2 6/7 0 7/10 0 13/14 3/5 3/10 13 236 280 5/7 2/5 0 0 2/3 0 0 1/2 5/9 11/20 4/5 13 272 2520 1/5 0 5/11 0 9/14 4/5 6/7 1/3 3/5 0 4/5 13 276 9240 1/10 0 1/18 17/18 11/15 0 1/2 2/7 5/7 0 13/14 13 292 2520 5/18 1/4 7/10 1/3 0 0 4/5 11/12 1/2 0 5/7 13 296 2520 2/5 1/14 5/7 2/3 18/19 0 0 0 1/3 0 3/5 13 316 - 11/13 0 4/5 4/13 11/16 0 5/8 1/2 1/3 1/8 1/10 13 320 3120 1/17 5/19 0 0 3/4 0 2/5 7/19 1/3 2/3 5/6 13 328 - 5/8 1/3 0 7/17 5/17 5/6 17/20 3/4 3/7 1/2 1/3 13 336 - 0 1/17 7/12 0 5/11 1/2 11/20 2/3 0 2/3 15/17 13 360 - 1/2 1/18 0 2/3 2/3 1/14 4/15 3/17 1/2 1/2 5/8 13 372 - 1/11 0 7/15 3/8 0 0 5/7 8/9 2/3 0 1/5 13 392 - 10/13 3/8 8/11 0 12/19 1/2 5/13 0 1/3 5/8 11/14 13 396 - 1/3 6/7 0 2/3 0 0 17/20 9/11 1/18 15/16 1/4 13 420 - 0 5/8 1/4 3/5 1/14 0 4/5 10/13 3/5 9/19 6/7 13 424 - 0 9/16 0 0 1/3 0 6/17 1/6 4/5 13/19 3/13 13 428 - 4/11 8/9 5/9 7/12 1/10 0 9/16 0 0 3/8 10/19 13 432 - 0 11/13 3/13 1/9 7/15 0 8/13 1/2 1/12 1/3 11/16 13 442 9360 4/5 0 7/17 0 9/14 0 7/13 2/3 2/5 4/5 5/17 13 508 - 4/17 6/7 1/2 8/17 2/15 3/10 9/20 5/6 1/3 2/19 4/5 13 536 - ----------------------------------------------------------------------------------------------------------- 1/6 0 19/20 0 5/6 12/17 1/2 2/5 3/4 2/5 3/20 14 200 2040 0 1/3 2/19 2/3 9/14 1/5 5/8 3/4 1/4 5/13 5/12 14 352 - 1/4 5/17 3/13 10/19 0 7/8 11/12 1/14 1/2 5/6 7/11 14 408 - 3/4 13/20 2/5 1/8 0 15/16 2/5 8/9 11/19 2/7 1/14 14 412 - 0 1/2 7/9 4/5 3/8 5/14 2/3 11/13 3/4 0 4/19 14 420 - 2/5 5/13 0 1/7 2/9 1/6 4/5 1/3 3/4 0 5/9 14 476 - ----------------------------------------------------------------------------------------------------------- 2/3 0 7/15 1/3 5/6 0 12/17 4/9 3/4 0 1/4 15 240 6120 1/3 2/5 1/8 11/13 1/3 0 0 4/7 3/4 3/8 10/17 15 312 - 1/2 11/13 2/3 2/5 7/15 1/8 12/19 5/14 1/2 2/5 0 15 340 - ----------------------------------------------------------------------------------------------------------- 0 1/5 1/3 5/6 1/16 0 0 0 1/6 7/11 1/2 16 212 2640 3/4 17/18 1/3 3/4 9/13 3/4 2/5 1/2 8/11 9/20 1/2 16 280 - 7/12 0 1/2 3/14 0 6/11 3/7 2/5 1/2 1/4 1/3 16 304 9240 2/3 7/9 0 0 7/9 0 6/17 0 1/10 4/7 0 16 340 - 1/2 1/2 5/6 17/20 7/12 0 2/7 2/15 2/5 10/11 0 16 348 9240 6/7 4/5 9/19 5/16 0 4/5 13/16 2/3 7/10 3/4 5/9 16 370 - 1/6 0 1/9 5/13 2/5 1/9 5/7 0 13/19 3/4 9/17 16 394 - 0 1/3 4/7 8/19 1/10 0 1/8 4/7 1/5 8/15 0 16 396 - 9/17 0 13/15 3/4 3/4 7/15 6/11 17/19 4/5 3/16 0 16 400 - 1/16 4/5 7/15 1/4 5/6 4/19 7/19 3/16 2/9 0 3/4 16 408 - 2/3 3/20 5/6 0 4/5 0 2/17 2/7 3/8 16/19 0 16 412 - 13/15 1/3 0 4/7 6/7 0 7/15 2/11 0 5/13 0 16 460 - ----------------------------------------------------------------------------------------------------------- 2/3 1/17 1/6 0 1/2 0 3/8 1/4 12/13 1/2 1/2 17 112 5304 ----------------------------------------------------------------------------------------------------------- 11/18 1/3 1/12 13/18 0 0 0 1/4 8/11 0 0 18 68 792 0 2/15 1/8 3/4 6/11 1/2 9/16 5/7 1/3 12/13 1/8 18 250 - 14/17 0 1/2 3/7 0 10/17 4/13 1/9 3/4 0 1/5 18 316 - ----------------------------------------------------------------------------------------------------------- 3/4 5/9 0 0 3/19 0 3/17 0 3/4 1/2 11/19 19 152 - 8/17 9/17 0 2/3 0 1/3 2/3 0 1/2 4/13 0 19 172 5304 0 1/3 0 7/12 0 5/9 0 1/2 8/11 2/5 1/2 19 208 3960 5/6 15/16 3/16 1/4 3/5 1/2 2/3 9/10 3/5 7/8 11/14 19 232 1680 ----------------------------------------------------------------------------------------------------------- 13/19 1/2 1/8 2/15 5/8 0 7/13 4/5 5/6 1/4 0 20 218 - ----------------------------------------------------------------------------------------------------------- 1/2 6/7 0 1/4 3/8 1/11 11/17 1/2 1/4 3/10 8/13 23 228 - 2/3 3/10 2/7 0 0 1/2 8/13 0 4/7 1/3 1/2 23 252 - ----------------------------------------------------------------------------------------------------------- 0 0 1/2 0 2/9 1/2 1/2 17/19 10/19 3/4 0 24 108 1368 ----------------------------------------------------------------------------------------------------------- 1/16 1/3 0 3/4 1/7 1/5 3/4 0 4/5 1/5 13/20 27 174 1680 7/8 3/4 9/10 4/5 1/2 1/2 5/11 0 0 2/7 2/5 27 180 3080 7/11 11/20 11/17 3/4 1/6 5/6 3/4 0 2/7 7/9 0 27 198 - ----------------------------------------------------------------------------------------------------------- 1/7 3/10 13/20 0 1/2 0 3/4 0 3/7 1/3 5/13 32 220 - ----------------------------------------------------------------------------------------------------------- 0 4/7 3/11 3/17 0 3/4 3/4 0 3/4 3/13 3/13 39 192 - -----------------------------------------------------------------------------------------------------------
3. Non-BH-Type Matrices
under construction...
B6(p1)↑
show data
p1 d #Λ ------------------ 1/2 4 4 BH(6, 4) 2*a 4 16 a = acos((sqrt(3)-1)/2)/2/pi a 4 28 1/3 4 34 r1 4 34* ------------------
K9(ζ)↑
Most data concerning this matrix found by B. Karlsson must be confirmed... Meanwhile, admire the picture of the set D ⊂ C, containing the allowed scope for the parameter ζ with particulary important regions and points.
show data
ζ d #Λ | BH class
------------------------------------|----------
1 + 1j*sqrt(12) 2 6 | BH(9, 6)
0 2 9 |
5/2 + 1j*sqrt(15/4) 2 18 |
1j 2 32 |
2 + 1j*sqrt(7) 2 36 |
2j 2 37 |
r + i*r in D 2 37* |
0.5 + 1j*sqrt(55/4) 2 41 |
2*exp(2j*pi*rand) - 3 2 74 |
2 + 2j 2 89 |
1 + 1j 2 87 |
------------------------------------|----------
4 -- |
------------------------------------|----------
1 + 2j 10 12 |
1 + 2*exp(2j*pi*rand) 10 15 |
------------------------------------|----------
2 + 1j*sqrt(3) 12 6 | BH(9, 6)
------------------------------------|----------
3 16 3 | BH(9, 3)
------------------------------------|----------
N10B(p1, p2, p3)↑
show data
p1 p2 p3 d #L ---------------------------------- 0 0 0 7 4 1/2 0 7/8 7 8 0 2/3 1/2 7 12 0 9/16 1/8 7 16 0 7/10 3/5 7 20 7/8 2/17 1/2 7 24 1/3 1/5 0 7 28 0 1/14 1/3 7 32 2/3 2/9 5/9 7 36 6/7 2/7 5/8 7 40 1/8 7/18 15/16 7 44 1/10 1/3 2/5 7 48 3/5 1/6 1/5 7 52 7/8 6/7 11/18 7 56 19/23 11/17 4/9 7 60 r1 r2 r3 7 60* ---------------------------------- 1/8 0 5/8 8 8 0 1/4 2/3 8 12 11/16 5/8 7/16 8 16 4/7 4/7 3/4 8 20 3/5 7/8 3/4 8 24 9/10 13/17 1/4 8 28 4/15 2/5 7/12 8 36 ---------------------------------- 0 5/8 1/4 10 8 0 2/3 1/4 10 12 0 1/5 11/20 10 16 ---------------------------------- 0 0 1/4 11 4 ----------------------------------
P13A(p1, p2, p3, p4)↑
show data
p1 p2 p3 p4 d #Λ ------------------------------------------- 1/3 1/2 0 0 4 30 1/2 0 1/4 0 4 60 0 2/25 0 0 4 70 0 5/14 4/21 0 4 90 0 1/10 2/5 2/3 4 110 14/15 0 13/15 9/10 4 112 1/28 5/6 7/20 0 4 140 13/14 6/7 2/3 0 4 146 5/13 0 7/17 1/2 4 150 1/21 2/3 1/4 0 4 156 0 1/2 1/5 3/8 4 160 3/10 1/10 1/4 4/5 4 162 1/10 25/28 5/16 0 4 170 0 1/2 1/2 7/13 4 172 1/6 8/13 7/8 1/2 4 186 5/8 9/10 4/17 0 4 190 1/5 0 5/22 14/15 4 196 0 0 1/3 3/7 4 198 3/4 1/2 4/5 7/15 4 200 5/12 3/4 5/6 2/3 4 202 21/23 1/2 0 13/20 4 210 0 12/29 11/15 3/5 4 212 5/8 3/14 3/4 1/2 4 216 1/27 8/15 0 19/20 4 220 9/10 2/3 2/3 2/11 4 230 0 13/15 11/13 4/5 4 232 20/23 4/23 17/23 0 4 246 6/11 1/3 8/15 2/3 4 250 20/29 1/5 13/30 1/12 4 252 13/29 1/4 7/19 0 4 256 4/7 22/25 15/22 0 4 266 4/9 0 1/6 9/10 4 272 11/12 0 0 21/29 4 276 1/3 3/4 7/8 2/5 4 282 1/2 1/13 0 1/8 4 286 4/5 0 3/4 9/14 4 288 9/11 7/15 2/3 2/3 4 290 3/8 1/2 1/3 9/16 4 292 11/19 0 0 8/11 4 296 0 25/27 4/5 13/16 4 298 3/5 1/7 5/12 1/3 4 300 3/10 12/13 3/4 1/8 4 302 2/9 1/3 0 7/13 4 306 4/5 13/17 25/29 3/5 4 312 7/8 2/3 17/20 3/20 4 316 0 14/29 8/17 19/30 4 320 0 1/3 3/11 1/8 4 326 1/3 1/4 0 5/13 4 328 1/12 0 1/4 5/14 4 330 1/2 25/27 1/3 4/17 4 338 11/12 1/7 1/2 17/30 4 346 2/3 8/21 1/3 2/7 4 358 3/4 0 1/6 16/19 4 368 5/16 5/6 3/4 3/16 4 376 8/9 17/24 0 1/9 4 378 4/9 7/16 11/15 7/9 4 382 0 11/30 5/21 3/8 4 386 1/4 4/7 1/2 2/7 4 388 13/22 0 5/7 5/6 4 396 4/9 1/15 1/2 6/7 4 398 2/3 18/19 2/3 22/25 4 400 5/11 4/15 5/12 11/12 4 402 1/18 7/8 2/3 2/5 4 404 5/8 0 5/12 3/14 4 406 2/3 19/21 15/19 1/3 4 416 1/2 2/13 7/9 7/15 4 420 21/25 5/12 8/13 1/10 4 424 11/12 1/11 0 3/7 4 426 4/21 4/29 2/3 2/3 4 432 7/25 9/11 3/4 2/5 4 434 20/27 1/3 1/12 6/29 4 436 2/11 0 7/9 4/9 4 438 2/7 2/7 6/11 4/7 4 442 9/13 23/28 19/21 4/5 4 444 15/22 9/17 13/30 1/7 4 446 0 7/24 1/4 17/23 4 452 9/20 7/16 1/4 6/11 4 454 4/5 9/25 13/25 6/13 4 462 2/3 17/26 11/13 15/29 4 466 9/20 7/11 24/25 17/24 4 470 4/5 8/17 3/4 4/13 4 472 1/5 3/29 6/7 17/26 4 482 1/8 1/4 5/7 1/12 4 490 5/9 1/4 6/7 1/8 4 506 5/8 10/19 3/4 5/12 4 510 1/24 1/7 2/3 1/14 4 516 7/8 5/12 21/26 3/8 4 526 7/12 13/16 2/23 1/3 4 530 9/28 3/4 2/3 9/13 4 540 2/3 3/14 5/27 1/28 4 546 4/19 1/4 4/23 1/6 4 550 9/19 5/18 11/21 1/6 4 560 19/27 5/9 5/14 1/9 4 562 22/23 4/9 15/19 13/30 4 564 2/3 19/29 8/25 10/11 4 566 6/11 5/12 8/11 1/11 4 568 5/13 5/12 8/13 10/11 4 570 7/8 1/8 9/17 15/19 4 580 2/25 11/25 5/11 2/7 4 590 5/7 10/11 1/4 13/14 4 596 3/4 8/9 6/11 3/14 4 600 14/27 5/16 22/25 11/27 4 606 7/9 10/29 13/21 8/19 4 610 r1 r2 r3 r4 4 610* ------------------------------------------- 0 3/4 0 1/4 6 60 2/3 0 19/21 3/4 6 90 0 5/12 10/19 1/4 6 180 26/27 1/5 5/13 1/4 6 210 1/12 1/14 3/13 3/4 6 356 6/17 14/25 16/23 1/4 6 386 -------------------------------------------
G10(p1)↑
show data
p1 d #Λ ------------------ 0 8 4 1/8 8 8 1/3 8 12 r1 8 12* ------------------
4. Defect of BH Matrices from Butson Home
In order to save space, integer matrices in a LOG-form are encoded in plain-text files (the core together with surrounding 2N-1 zeros in the first row and the first column), where overdecadic numbers are replaced by single ASCII characters. Decoding procedure is straightforward, but in some cases the total number of arrays makes it impossible to process them in a single run. All procedures are designed for *NIX system. When working in m$ OS, currently (2022-07-26) it is not easy to combine w7, MinGW, and Octave-5.1.0.0 (CLI) into a "one-script-to-run-and-forget" environment:
C:\MinGW\msys\1.0\bin> .\bash.exe
bash.exe"-3.1$ ./BHr.out SPLIT_FILE_ax # fatality...
Possible Linux issue:
QStandardPaths: XDG_RUNTIME_DIR not set, defaulting to '/DIRECTORY' → $ export XDG_RUNTIME_DIR=DIRECTORY $ export RUNLEVEL=3 $ source .bashrc
Actually, the main purpose was to calculate the linear entropy of all Butsons (for a project concerning k-unitary CHM... – under construction). Later, slightly modified scripts were reused to calculate the defects.
Download appropriate zip from Butson Home and follow the steps:
1. Linear Entropy (or Entangling Power)
Only squared-dimension matries are of interest. All Butsons are normalized to be unitary: B → B/√{N} for N=9 or N=16.
There is one problematic (squared-dim.) file: BH-16-4.txt (1'786'763 entries) and q = 4. Before calculating SL the file must be split:
- split file:
$ split BH-16-4.txt -l 100000 SPLIT_FILE && shred -zuv BH-16-4.txt - this produces several files, each with 100000 lines:
SPLIT_FILEaa
SPLIT_FILEab
...
SPLIT_FILEar ./get_SL.sh SPLIT_FILEax SL_BH_NN_qq_ax.txt
scriptget_SL.shuses another one:b2m.shwhich extracts n-th line from a raw BH-file:$ ./b2m.sh BH-16-14.txt 4 123- check:
$ wc -l SL_BH_NN_qq_ax.txt
should yield 100000 (lines)
or RT inspection:
$ tail -F FILE
alternative and much faster method:
- prepare M-file (using chunks of ≈10000 lines) with a simple C-script:
> cc BHrc.c -lm -o BHrc.ELF > BHrc.ELF SPLIT_FILEax 4 CHUNK_SIZE # watch 4 = q = BUTSON parameter!
BHrc.ELF creates (a large) OCTAVE_OUTPUT.m file, which can be handled very quickly on Intel(R) Core(TM) i7-4770 CPU @ 3.40GHz with 16+GB of RAM;
>> clear all; B=OCTAVE_INPUT; B_SIZE=size(B,2); # this might take a while...
>> diary on; diary SL_BH_NN_qq_ax.txt; for k=2:B_SIZE; disp(sprintf("%g\t%g", SL(R(B{k})), SL(T(B{k})))); end; diary off
>> exit- clean SL_BH_NN_qq_ax.txt file (remove the first and the last line), remove
diary(if exists), and remove OCTAVE_OUTPUT.m (to save space it is good todos2unixall files)
When all SPLIT_FILEax are done, merge all SL_BH_NN_qq_ax.txt into a single file: SL_BH_NN_qq.txt to be supplied for gnuplot.
Dimension N=9 is much simpler, it is enough to apply BHrc.c and get_SL.sh scripts for several files.
2. Defect of BH
This time, there are two problematic files: BH-16-4.txt (1'786'763 entries) and BH-12-12.txt (4'497'733 entries). Moreover, the calculation of defect takes much longer than calculation of "linear entropy".
The procedure is similar, for small files do:
- download BH-NN-qq.txt
$ ./BHrc BB-NN-qq.txt q BH_CARDINAILTY$ octave get_defect.m > BB-NN-qq.txt$ ./count_isolated.sh defect_BH_NN_qq.txt # this number goes to the table
while, for big files, apply the two-step mechanism:
- splitting...
$ octave... # ---> get_defect.m- cleaning...
Cardinality check:
$ wc -l defect_BH* # should return: 6815584 (this excludes N=2, 3, 5 and 11)
Finally, perform some random tests (independently calculated values of defect must match!)
$ ./check_defect.sh BH-14-4.txt 4 123 defect_BH_14_4.txt # manual check$ ./test_defect.sh BH-12-12.txt defect_12_12.txt 12 100000 # run overnight...
3. Defect of BH – results
Entries in the table below correspond to the content of Lampio-Szöllősi table from Butson Home. Among the total number of 6'815'601 matrices, at least 9'026 of them are explicitly isolated. There are possibly more isolated matrices, but currently there is no way to check it (quickly), hence we restrict the attention only to those with vanishing defect.
Zipped packages with results: defect_BH.zip and SL_BH_16_4.txt.zip.
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