Heisenberg group over Z2, zero-point distances histograms

Histograms.txt

Order = 1
       # 0 1  2
    hist 1 3  4
       Δ 1 1 -2
    2C₂ᵏ 2 4  2
   NoZ Δ 1 2  0
 NoZHist 1 2  2 2 1
Order = 2
       # 0 1  2  3  4
    hist 1 5 12 12  2
       Δ 1 3  0 -4  0
    2C₄ᵏ 2 8 12  8  2
   NoZ Δ 1 4  4 -4 -5
 NoZHist 1 4  8 12  7
Order = 3
       # 0  1  2  3   4  5 6
    hist 1  7 24 44  38 12 2
       Δ 1  5  6 -4  -8  0 0
    2C₆ᵏ 2 12 30 40  30 12 2
   NoZ Δ 1  6 12  2 -13 -8 0
 NoZHist 1  6 18 38  43 20 2
Order = 4
       # 0  1  2   3   4   5   6  7 8
    hist 1  9 40 104 156 128  56 16 2
       Δ 1  7 16   8 -16 -16   0  0 0
    2C₈ᵏ 2 16 56 112 140 112  56 16 2
   NoZ Δ 1  8 24  24  -9 -32 -16  0 0
 NoZHist 1  8 32  88 149 144  72 16 2
Order = 5
       # 0  1  2   3   4   5   6   7  8  9 10
    hist 1 11 60 200 420 552 452 240 90 20  2
       Δ 1  9 30  40   0 -48 -32   0  0  0  0
   2C₁₀ᵏ 2 20 90 240 420 504 420 240 90 20  2
   NoZ Δ 1 10 40  70  39 -48 -80 -32  0  0  0
 NoZHist 1 10 50 170 381 552 500 272 90 20  2
Order = 6
       # 0  1   2   3   4    5    6    7    8   9  10 11 12
    hist 1 13  84 340 910 1632 1976 1648  990 440 132 24  2
       Δ 1 11  48 100  80  -48 -128  -64    0   0   0  0  0
   2C₁₂ᵏ 2 24 132 440 990 1584 1848 1584  990 440 132 24  2
   NoZ Δ 1 12  60 148 179   32 -176 -192  -64   0   0  0  0
 NoZHist 1 12  72 292 811 1552 2024 1776 1054 440 132 24  2
Order = 7
       # 0  1   2   3    4    5    6    7    8    9   10  11  12 13 14
    hist 1 15 112 532 1722 3892 6230 7184 6134 4004 2002 728 182 28  2
       Δ 1 13  70 196  280  112 -224 -320 -128    0    0   0   0  0  0
   2C₁₄ᵏ 2 28 182 728 2002 4004 6006 6864 6006 4004 2002 728 182 28  2
   NoZ Δ 1 14  84 266  475  392 -112 -544 -448 -128    0   0   0  0  0
 NoZHist 1 14  98 462 1527 3612 6118 7408 6454 4132 2002 728 182 28  2
Order = 8
       # 0  1   2    3    4    5     6     7     8     9    10   11   12   13  14 15 16
    hist 1 17 144  784 2968 8064 16016 23648 26508 23136 16016 8736 3640 1120 240 32  2
       Δ 1 15  96  336  672  672     0  -768  -768  -256     0    0    0    0   0  0  0
   2C₁₆ᵏ 2 32 240 1120 3640 8736 16016 22880 25740 22880 16016 8736 3640 1120 240 32  2
   NoZ Δ 1 16 112  432 1007 1344   672  -768 -1536 -1024  -256    0    0    0   0  0  0
 NoZHist 1 16 128  688 2633 7392 15344 23648 27276 23904 16272 8736 3640 1120 240 32  2
Order = 9
       # 0  1   2    3    4     5     6     7     8      9    10    11    12    13   14   15  16 17 18
    hist 1 19 180 1104 4776 15120 35784 64416 89820  99032 88028 63648 37128 17136 6120 1632 306 36  2
       Δ 1 17 126  528 1344  2016  1344  -768 -2304  -1792  -512     0     0     0    0    0   0  0  0
   2C₁₈ᵏ 2 36 306 1632 6120 17136 37128 63648 87516  97240 87516 63648 37128 17136 6120 1632 306 36  2
   NoZ Δ 1 18 144  654 1871  3360  3360   576 -3072  -4096 -2304  -512     0     0    0    0   0  0  0
 NoZHist 1 18 162  978 4249 13776 33768 63072 90588 101336 89820 64160 37128 17136 6120 1632 306 36  2
Order = 10
       # 0  1   2    3    4     5     6      7      8      9     10     11     12     13    14    15   16   17  18 19 20
    hist 1 21 220 1500 7290 26304 72144 153120 255780 342320 373608 336944 251940 155040 77520 31008 9690 2280 380 40  2
       Δ 1 19 160  780 2400  4704  5376   1920  -3840  -6400  -4096  -1024      0      0     0     0    0    0   0  0  0
   2C₂₀ᵏ 2 40 380 2280 9690 31008 77520 155040 251940 335920 369512 335920 251940 155040 77520 31008 9690 2280 380 40  2
   NoZ Δ 1 20 180  940 3179  7104 10080   7296  -1920 -10240 -10496  -5120  -1024      0     0     0    0    0   0  0  0
 NoZHist 1 20 200 1340 6511 23904 67440 147744 253860 346160 380008 341040 252964 155040 77520 31008 9690 2280 380 40  2