we sort 2D, 3D, 4D integer lattice points near the origin by distance from the origin, grouping together points at the same distance. in the lists at the end of this post, for each distance, we give only a reduced list of representative points whose coordinates are non-negative and non-descending, for brevity. (note: symmetrically expanding from a reduced list to a full list is nontrivial.)
we also provide some statistics about points all at the same distance:
all-even gives the number of points whose coordinates are all even. analogously all-odd. we could also count points with N odd coordinates and dimension-minus-N even coordinates, etc., but this revealed nothing interesting. 4D seems to be the first dimension in which, at a given distance, the parities of the coordinates do not always have the same signature. for example, this identity underlies the D4 lattice:
4 = 0^2 + 0^2 + 0^2 + 2^2 (all even) = 1^2 + 1^2 + 1^2 + 1^2 (all odd)
if the points split among parity classes in 4D, they split only between the all-even and all-odd classes, and never among the other possible classes (1-odd 3-even, etc.). the points seem to split if and only if (distance^2) mod 8 = 4 .
in 5D (not explored), we can have other splits:
4 = 0^2 + 0^2 + 0^2 + 0^2 + 2^2 (all even) = 0^2 + 1^2 + 1^2 + 1^2 + 1^2 (1 even, 4 odd)
distance^2 = 25 is the first instance of more than 1 point in the reduced list in 2D. it is the smallest Pythagorean triple.
25
= 0^2 + 5^2
= 3^2 + 4^2
325 is the first instance of more than 2 points in the reduced list in 2D:
325
= 1^2 + 18^2
= 6^2 + 17^2
= 10^2 + 15^2
3D:
9 = (0,0,3) = (1,2,2)
41 = (0,4,5) = (1,2,6) = (3,4,4).
at greater distances or dimensions, there are many points at a given distance. here are distances which have a record number of points, subsets of the full lists below. (the 3D and 4D records cover a greater range, to distance^2 = 399, than the full lists below, which go only to 99.)
2D records
distance-squared 0, record number of points 1, reduced list 1: (0,0)
distance-squared 1, record number of points 4, reduced list 1: (0,1)
distance-squared 5, record number of points 8, reduced list 1: (1,2)
distance-squared 25, record number of points 12, reduced list 2: (0,5); (3,4)
distance-squared 65, record number of points 16, reduced list 2: (1,8); (4,7)
distance-squared 325, record number of points 24, reduced list 3: (1,18); (6,17); (10,15)
3D records
distance-squared 0, record number of points 1, reduced list 1: (0,0,0)
distance-squared 1, record number of points 6, reduced list 1: (0,0,1)
distance-squared 2, record number of points 12, reduced list 1: (0,1,1)
distance-squared 5, record number of points 24, reduced list 1: (0,1,2)
distance-squared 9, record number of points 30, reduced list 2: (0,0,3); (1,2,2)
distance-squared 14, record number of points 48, reduced list 1: (1,2,3)
distance-squared 26, record number of points 72, reduced list 2: (0,1,5); (1,3,4)
distance-squared 41, record number of points 96, reduced list 3: (0,4,5); (1,2,6); (3,4,4)
distance-squared 74, record number of points 120, reduced list 3: (0,5,7); (1,3,8); (3,4,7)
distance-squared 89, record number of points 144, reduced list 4: (0,5,8); (2,2,9); (2,6,7); (3,4,8)
distance-squared 101, record number of points 168, reduced list 4: (0,1,10); (1,6,8); (2,4,9); (4,6,7)
distance-squared 146, record number of points 192, reduced list 5: (0,5,11); (1,1,12); (1,8,9); (3,4,11); (4,7,9)
distance-squared 194, record number of points 240, reduced list 6: (0,5,13); (1,7,12); (3,4,13); (3,8,11); (5,5,12); (7,8,9)
distance-squared 269, record number of points 264, reduced list 6: (0,10,13); (2,3,16); (2,11,12); (3,8,14); (5,10,12); (6,8,13)
distance-squared 314, record number of points 312, reduced list 7: (0,5,17); (1,12,13); (3,4,17); (3,7,16); (5,8,15); (7,11,12); (8,9,13)
distance-squared 341, record number of points 336, reduced list 7: (1,4,18); (1,12,14); (2,9,16); (4,6,17); (4,10,15); (6,7,16); (8,9,14)
4D records
distance-squared 0, record number of points 1, reduced list 1: (0,0,0,0)
distance-squared 1, record number of points 8, reduced list 1: (0,0,0,1)
distance-squared 2, record number of points 24, reduced list 1: (0,0,1,1)
distance-squared 3, record number of points 32, reduced list 1: (0,1,1,1)
distance-squared 5, record number of points 48, reduced list 1: (0,0,1,2)
distance-squared 6, record number of points 96, reduced list 1: (0,1,1,2)
distance-squared 9, record number of points 104, reduced list 2: (0,0,0,3); (0,1,2,2)
distance-squared 10, record number of points 144, reduced list 2: (0,0,1,3); (1,1,2,2)
distance-squared 14, record number of points 192, reduced list 1: (0,1,2,3)
distance-squared 18, record number of points 312, reduced list 3: (0,0,3,3); (0,1,1,4); (1,2,2,3)
distance-squared 26, record number of points 336, reduced list 3: (0,0,1,5); (0,1,3,4); (2,2,3,3)
distance-squared 30, record number of points 576, reduced list 2: (0,1,2,5); (1,2,3,4)
distance-squared 42, record number of points 768, reduced list 4: (0,1,4,5); (1,1,2,6); (1,3,4,4); (2,2,3,5)
distance-squared 54, record number of points 960, reduced list 5: (0,1,2,7); (0,2,5,5); (0,3,3,6); (1,1,4,6); (2,3,4,5)
distance-squared 66, record number of points 1152, reduced list 6: (0,1,1,8); (0,1,4,7); (0,4,5,5); (1,2,5,6); (2,2,3,7); (3,4,4,5)
distance-squared 78, record number of points 1344, reduced list 4: (0,2,5,7); (1,2,3,8); (1,4,5,6); (2,3,4,7)
distance-squared 90, record number of points 1872, reduced list 9: (0,0,3,9); (0,1,5,8); (0,4,5,7); (1,2,2,9); (1,2,6,7); (1,3,4,8); (2,5,5,6); (3,3,6,6); (3,4,4,7)
distance-squared 114, record number of points 1920, reduced list 8: (0,1,7,8); (0,4,7,7); (0,5,5,8); (1,2,3,10); (1,4,4,9); (2,2,5,9); (2,5,6,7); (3,4,5,8)
distance-squared 126, record number of points 2496, reduced list 8: (0,1,2,11); (0,1,5,10); (0,3,6,9); (1,3,4,10); (1,5,6,8); (2,3,7,8); (2,4,5,9); (4,5,6,7)
distance-squared 150, record number of points 2976, reduced list 11: (0,1,7,10); (0,2,5,11); (0,5,5,10); (1,1,2,12); (1,2,8,9); (1,6,7,8); (2,3,4,11); (2,4,7,9); (3,4,5,10); (4,6,7,7); (5,5,6,8)
distance-squared 186, record number of points 3072, reduced list 11: (0,1,4,13); (0,1,8,11); (0,4,7,11); (1,2,9,10); (1,4,5,12); (1,6,7,10); (2,2,3,13); (2,5,6,11); (3,7,8,8); (4,5,8,9); (5,5,6,10)
distance-squared 198, record number of points 3744, reduced list 14: (0,1,1,14); (0,2,5,13); (0,6,9,9); (0,7,7,10); (1,2,7,12); (1,4,9,10); (2,3,4,13); (2,3,8,11); (2,5,5,12); (2,7,8,9); (3,3,6,12); (3,5,8,10); (4,5,6,11); (6,7,7,8)
distance-squared 210, record number of points 4608, reduced list 16: (0,4,5,13); (0,5,8,11); (1,1,8,12); (1,2,3,14); (1,2,6,13); (1,3,10,10); (1,4,7,12); (1,8,8,9); (2,2,9,11); (2,5,9,10); (2,6,7,11); (3,4,4,13); (3,4,8,11); (4,5,5,12); (4,7,8,9); (5,6,7,10)
distance-squared 270, record number of points 5760, reduced list 17: (0,1,10,13); (0,3,6,15); (0,5,7,14); (0,7,10,11); (1,2,3,16); (1,2,11,12); (1,3,8,14); (1,5,10,12); (1,6,8,13); (2,4,5,15); (2,4,9,13); (2,8,9,11); (3,4,7,14); (3,6,9,12); (4,6,7,13); (5,8,9,10); (6,7,8,11)
distance-squared 330, record number of points 6912, reduced list 22: (0,4,5,17); (0,5,7,16); (1,1,2,18); (1,2,6,17); (1,2,10,15); (1,3,8,16); (1,4,12,13); (1,8,11,12); (2,3,11,14); (2,6,11,13); (2,7,9,14); (3,4,4,17); (3,4,7,16); (3,5,10,14); (3,10,10,11); (4,5,8,15); (4,7,11,12); (4,8,9,13); (5,6,10,13); (6,7,7,14); (7,9,10,10); (8,8,9,11)
distance-squared 378, record number of points 7680, reduced list 28: (0,1,4,19); (0,1,11,16); (0,3,12,15); (0,5,8,17); (1,2,7,18); (1,8,12,13); (1,9,10,14); (2,2,3,19); (2,2,9,17); (2,3,13,14); (2,5,5,18); (2,6,7,17); (2,6,13,13); (2,7,10,15); (3,3,6,18); (3,4,8,17); (3,7,8,16); (3,9,12,12); (3,10,10,13); (4,4,11,15); (4,5,9,16); (4,7,12,13); (5,6,11,14); (5,8,8,15); (6,6,9,15); (6,10,11,11); (7,8,11,12); (8,8,9,13)
distance-squared 390, record number of points 8064, reduced list 26: (0,1,10,17); (0,2,5,19); (0,5,13,14); (0,10,11,13); (1,1,8,18); (1,4,7,18); (1,6,8,17); (1,7,12,14); (1,8,10,15); (2,3,4,19); (2,3,11,16); (2,4,9,17); (2,7,9,16); (2,11,11,12); (3,4,13,14); (3,5,10,16); (3,8,11,14); (4,5,5,18); (4,6,7,17); (4,6,13,13); (4,7,10,15); (5,5,12,14); (5,10,11,12); (6,7,7,16); (6,8,11,13); (7,8,9,14)
in 4D, every non-negative integer is possible as a squared distance.
inspiration: random graphs in which each point is connected to a random subset of points not too far away from it.
digression: consider drawing (embedding) on a 2D plane such a graph from 3D or higher dimension. note that the graph is infinite. assume, for readability, nodes as drawn on the plane must all be separated by a minimum distance, but there is otherwise free placement. can the infinite graph be drawn bounding the length of edges? I suspect it cannot.
full lists:
2D
distance-squared 0, number of points 1, running total 1, all-even 1, all-odd 0, reduced list 1: (0,0)
distance-squared 1, number of points 4, running total 5, all-even 0, all-odd 0, reduced list 1: (0,1)
distance-squared 2, number of points 4, running total 9, all-even 0, all-odd 4, reduced list 1: (1,1)
distance-squared 4, number of points 4, running total 13, all-even 4, all-odd 0, reduced list 1: (0,2)
distance-squared 5, number of points 8, running total 21, all-even 0, all-odd 0, reduced list 1: (1,2)
distance-squared 8, number of points 4, running total 25, all-even 4, all-odd 0, reduced list 1: (2,2)
distance-squared 9, number of points 4, running total 29, all-even 0, all-odd 0, reduced list 1: (0,3)
distance-squared 10, number of points 8, running total 37, all-even 0, all-odd 8, reduced list 1: (1,3)
distance-squared 13, number of points 8, running total 45, all-even 0, all-odd 0, reduced list 1: (2,3)
distance-squared 16, number of points 4, running total 49, all-even 4, all-odd 0, reduced list 1: (0,4)
distance-squared 17, number of points 8, running total 57, all-even 0, all-odd 0, reduced list 1: (1,4)
distance-squared 18, number of points 4, running total 61, all-even 0, all-odd 4, reduced list 1: (3,3)
distance-squared 20, number of points 8, running total 69, all-even 8, all-odd 0, reduced list 1: (2,4)
distance-squared 25, number of points 12, running total 81, all-even 0, all-odd 0, reduced list 2: (0,5); (3,4)
distance-squared 26, number of points 8, running total 89, all-even 0, all-odd 8, reduced list 1: (1,5)
distance-squared 29, number of points 8, running total 97, all-even 0, all-odd 0, reduced list 1: (2,5)
distance-squared 32, number of points 4, running total 101, all-even 4, all-odd 0, reduced list 1: (4,4)
distance-squared 34, number of points 8, running total 109, all-even 0, all-odd 8, reduced list 1: (3,5)
distance-squared 36, number of points 4, running total 113, all-even 4, all-odd 0, reduced list 1: (0,6)
distance-squared 37, number of points 8, running total 121, all-even 0, all-odd 0, reduced list 1: (1,6)
distance-squared 40, number of points 8, running total 129, all-even 8, all-odd 0, reduced list 1: (2,6)
distance-squared 41, number of points 8, running total 137, all-even 0, all-odd 0, reduced list 1: (4,5)
distance-squared 45, number of points 8, running total 145, all-even 0, all-odd 0, reduced list 1: (3,6)
distance-squared 49, number of points 4, running total 149, all-even 0, all-odd 0, reduced list 1: (0,7)
distance-squared 50, number of points 12, running total 161, all-even 0, all-odd 12, reduced list 2: (1,7); (5,5)
distance-squared 52, number of points 8, running total 169, all-even 8, all-odd 0, reduced list 1: (4,6)
distance-squared 53, number of points 8, running total 177, all-even 0, all-odd 0, reduced list 1: (2,7)
distance-squared 58, number of points 8, running total 185, all-even 0, all-odd 8, reduced list 1: (3,7)
distance-squared 61, number of points 8, running total 193, all-even 0, all-odd 0, reduced list 1: (5,6)
distance-squared 64, number of points 4, running total 197, all-even 4, all-odd 0, reduced list 1: (0,8)
distance-squared 65, number of points 16, running total 213, all-even 0, all-odd 0, reduced list 2: (1,8); (4,7)
distance-squared 68, number of points 8, running total 221, all-even 8, all-odd 0, reduced list 1: (2,8)
distance-squared 72, number of points 4, running total 225, all-even 4, all-odd 0, reduced list 1: (6,6)
distance-squared 73, number of points 8, running total 233, all-even 0, all-odd 0, reduced list 1: (3,8)
distance-squared 74, number of points 8, running total 241, all-even 0, all-odd 8, reduced list 1: (5,7)
distance-squared 80, number of points 8, running total 249, all-even 8, all-odd 0, reduced list 1: (4,8)
distance-squared 81, number of points 4, running total 253, all-even 0, all-odd 0, reduced list 1: (0,9)
distance-squared 82, number of points 8, running total 261, all-even 0, all-odd 8, reduced list 1: (1,9)
distance-squared 85, number of points 16, running total 277, all-even 0, all-odd 0, reduced list 2: (2,9); (6,7)
distance-squared 89, number of points 8, running total 285, all-even 0, all-odd 0, reduced list 1: (5,8)
distance-squared 90, number of points 8, running total 293, all-even 0, all-odd 8, reduced list 1: (3,9)
distance-squared 97, number of points 8, running total 301, all-even 0, all-odd 0, reduced list 1: (4,9)
distance-squared 98, number of points 4, running total 305, all-even 0, all-odd 4, reduced list 1: (7,7)
distance-squared 100, number of points 12, running total 317, all-even 12, all-odd 0, reduced list 2: (0,10); (6,8)
distance-squared 101, number of points 8, running total 325, all-even 0, all-odd 0, reduced list 1: (1,10)
distance-squared 104, number of points 8, running total 333, all-even 8, all-odd 0, reduced list 1: (2,10)
distance-squared 106, number of points 8, running total 341, all-even 0, all-odd 8, reduced list 1: (5,9)
distance-squared 109, number of points 8, running total 349, all-even 0, all-odd 0, reduced list 1: (3,10)
distance-squared 113, number of points 8, running total 357, all-even 0, all-odd 0, reduced list 1: (7,8)
distance-squared 116, number of points 8, running total 365, all-even 8, all-odd 0, reduced list 1: (4,10)
distance-squared 117, number of points 8, running total 373, all-even 0, all-odd 0, reduced list 1: (6,9)
distance-squared 121, number of points 4, running total 377, all-even 0, all-odd 0, reduced list 1: (0,11)
distance-squared 122, number of points 8, running total 385, all-even 0, all-odd 8, reduced list 1: (1,11)
distance-squared 125, number of points 16, running total 401, all-even 0, all-odd 0, reduced list 2: (2,11); (5,10)
distance-squared 128, number of points 4, running total 405, all-even 4, all-odd 0, reduced list 1: (8,8)
distance-squared 130, number of points 16, running total 421, all-even 0, all-odd 16, reduced list 2: (3,11); (7,9)
distance-squared 136, number of points 8, running total 429, all-even 8, all-odd 0, reduced list 1: (6,10)
distance-squared 137, number of points 8, running total 437, all-even 0, all-odd 0, reduced list 1: (4,11)
distance-squared 144, number of points 4, running total 441, all-even 4, all-odd 0, reduced list 1: (0,12)
distance-squared 145, number of points 16, running total 457, all-even 0, all-odd 0, reduced list 2: (1,12); (8,9)
distance-squared 146, number of points 8, running total 465, all-even 0, all-odd 8, reduced list 1: (5,11)
distance-squared 148, number of points 8, running total 473, all-even 8, all-odd 0, reduced list 1: (2,12)
distance-squared 149, number of points 8, running total 481, all-even 0, all-odd 0, reduced list 1: (7,10)
distance-squared 153, number of points 8, running total 489, all-even 0, all-odd 0, reduced list 1: (3,12)
distance-squared 157, number of points 8, running total 497, all-even 0, all-odd 0, reduced list 1: (6,11)
distance-squared 160, number of points 8, running total 505, all-even 8, all-odd 0, reduced list 1: (4,12)
distance-squared 162, number of points 4, running total 509, all-even 0, all-odd 4, reduced list 1: (9,9)
distance-squared 164, number of points 8, running total 517, all-even 8, all-odd 0, reduced list 1: (8,10)
distance-squared 169, number of points 12, running total 529, all-even 0, all-odd 0, reduced list 2: (0,13); (5,12)
distance-squared 170, number of points 16, running total 545, all-even 0, all-odd 16, reduced list 2: (1,13); (7,11)
distance-squared 173, number of points 8, running total 553, all-even 0, all-odd 0, reduced list 1: (2,13)
distance-squared 178, number of points 8, running total 561, all-even 0, all-odd 8, reduced list 1: (3,13)
distance-squared 180, number of points 8, running total 569, all-even 8, all-odd 0, reduced list 1: (6,12)
distance-squared 181, number of points 8, running total 577, all-even 0, all-odd 0, reduced list 1: (9,10)
distance-squared 185, number of points 16, running total 593, all-even 0, all-odd 0, reduced list 2: (4,13); (8,11)
distance-squared 193, number of points 8, running total 601, all-even 0, all-odd 0, reduced list 1: (7,12)
distance-squared 194, number of points 8, running total 609, all-even 0, all-odd 8, reduced list 1: (5,13)
distance-squared 196, number of points 4, running total 613, all-even 4, all-odd 0, reduced list 1: (0,14)
distance-squared 197, number of points 8, running total 621, all-even 0, all-odd 0, reduced list 1: (1,14)
distance-squared 200, number of points 12, running total 633, all-even 12, all-odd 0, reduced list 2: (2,14); (10,10)
distance-squared 202, number of points 8, running total 641, all-even 0, all-odd 8, reduced list 1: (9,11)
distance-squared 205, number of points 16, running total 657, all-even 0, all-odd 0, reduced list 2: (3,14); (6,13)
distance-squared 208, number of points 8, running total 665, all-even 8, all-odd 0, reduced list 1: (8,12)
distance-squared 212, number of points 8, running total 673, all-even 8, all-odd 0, reduced list 1: (4,14)
distance-squared 218, number of points 8, running total 681, all-even 0, all-odd 8, reduced list 1: (7,13)
distance-squared 221, number of points 16, running total 697, all-even 0, all-odd 0, reduced list 2: (5,14); (10,11)
distance-squared 225, number of points 12, running total 709, all-even 0, all-odd 0, reduced list 2: (0,15); (9,12)
distance-squared 226, number of points 8, running total 717, all-even 0, all-odd 8, reduced list 1: (1,15)
distance-squared 229, number of points 8, running total 725, all-even 0, all-odd 0, reduced list 1: (2,15)
distance-squared 232, number of points 8, running total 733, all-even 8, all-odd 0, reduced list 1: (6,14)
distance-squared 233, number of points 8, running total 741, all-even 0, all-odd 0, reduced list 1: (8,13)
distance-squared 234, number of points 8, running total 749, all-even 0, all-odd 8, reduced list 1: (3,15)
distance-squared 241, number of points 8, running total 757, all-even 0, all-odd 0, reduced list 1: (4,15)
distance-squared 242, number of points 4, running total 761, all-even 0, all-odd 4, reduced list 1: (11,11)
distance-squared 244, number of points 8, running total 769, all-even 8, all-odd 0, reduced list 1: (10,12)
distance-squared 245, number of points 8, running total 777, all-even 0, all-odd 0, reduced list 1: (7,14)
distance-squared 250, number of points 16, running total 793, all-even 0, all-odd 16, reduced list 2: (5,15); (9,13)
distance-squared 256, number of points 4, running total 797, all-even 4, all-odd 0, reduced list 1: (0,16)
distance-squared 257, number of points 8, running total 805, all-even 0, all-odd 0, reduced list 1: (1,16)
distance-squared 260, number of points 16, running total 821, all-even 16, all-odd 0, reduced list 2: (2,16); (8,14)
distance-squared 261, number of points 8, running total 829, all-even 0, all-odd 0, reduced list 1: (6,15)
distance-squared 265, number of points 16, running total 845, all-even 0, all-odd 0, reduced list 2: (3,16); (11,12)
distance-squared 269, number of points 8, running total 853, all-even 0, all-odd 0, reduced list 1: (10,13)
distance-squared 272, number of points 8, running total 861, all-even 8, all-odd 0, reduced list 1: (4,16)
distance-squared 274, number of points 8, running total 869, all-even 0, all-odd 8, reduced list 1: (7,15)
distance-squared 277, number of points 8, running total 877, all-even 0, all-odd 0, reduced list 1: (9,14)
distance-squared 281, number of points 8, running total 885, all-even 0, all-odd 0, reduced list 1: (5,16)
distance-squared 288, number of points 4, running total 889, all-even 4, all-odd 0, reduced list 1: (12,12)
distance-squared 289, number of points 12, running total 901, all-even 0, all-odd 0, reduced list 2: (0,17); (8,15)
distance-squared 290, number of points 16, running total 917, all-even 0, all-odd 16, reduced list 2: (1,17); (11,13)
distance-squared 292, number of points 8, running total 925, all-even 8, all-odd 0, reduced list 1: (6,16)
distance-squared 293, number of points 8, running total 933, all-even 0, all-odd 0, reduced list 1: (2,17)
distance-squared 296, number of points 8, running total 941, all-even 8, all-odd 0, reduced list 1: (10,14)
distance-squared 298, number of points 8, running total 949, all-even 0, all-odd 8, reduced list 1: (3,17)
distance-squared 305, number of points 16, running total 965, all-even 0, all-odd 0, reduced list 2: (4,17); (7,16)
distance-squared 306, number of points 8, running total 973, all-even 0, all-odd 8, reduced list 1: (9,15)
distance-squared 313, number of points 8, running total 981, all-even 0, all-odd 0, reduced list 1: (12,13)
distance-squared 314, number of points 8, running total 989, all-even 0, all-odd 8, reduced list 1: (5,17)
distance-squared 317, number of points 8, running total 997, all-even 0, all-odd 0, reduced list 1: (11,14)
distance-squared 320, number of points 8, running total 1005, all-even 8, all-odd 0, reduced list 1: (8,16)
distance-squared 324, number of points 4, running total 1009, all-even 4, all-odd 0, reduced list 1: (0,18)
distance-squared 325, number of points 24, running total 1033, all-even 0, all-odd 0, reduced list 3: (1,18); (6,17); (10,15)
distance-squared 328, number of points 8, running total 1041, all-even 8, all-odd 0, reduced list 1: (2,18)
distance-squared 333, number of points 8, running total 1049, all-even 0, all-odd 0, reduced list 1: (3,18)
distance-squared 337, number of points 8, running total 1057, all-even 0, all-odd 0, reduced list 1: (9,16)
distance-squared 338, number of points 12, running total 1069, all-even 0, all-odd 12, reduced list 2: (7,17); (13,13)
distance-squared 340, number of points 16, running total 1085, all-even 16, all-odd 0, reduced list 2: (4,18); (12,14)
distance-squared 346, number of points 8, running total 1093, all-even 0, all-odd 8, reduced list 1: (11,15)
distance-squared 349, number of points 8, running total 1101, all-even 0, all-odd 0, reduced list 1: (5,18)
distance-squared 353, number of points 8, running total 1109, all-even 0, all-odd 0, reduced list 1: (8,17)
distance-squared 356, number of points 8, running total 1117, all-even 8, all-odd 0, reduced list 1: (10,16)
distance-squared 360, number of points 8, running total 1125, all-even 8, all-odd 0, reduced list 1: (6,18)
distance-squared 361, number of points 4, running total 1129, all-even 0, all-odd 0, reduced list 1: (0,19)
distance-squared 362, number of points 8, running total 1137, all-even 0, all-odd 8, reduced list 1: (1,19)
distance-squared 365, number of points 16, running total 1153, all-even 0, all-odd 0, reduced list 2: (2,19); (13,14)
distance-squared 369, number of points 8, running total 1161, all-even 0, all-odd 0, reduced list 1: (12,15)
distance-squared 370, number of points 16, running total 1177, all-even 0, all-odd 16, reduced list 2: (3,19); (9,17)
distance-squared 373, number of points 8, running total 1185, all-even 0, all-odd 0, reduced list 1: (7,18)
distance-squared 377, number of points 16, running total 1201, all-even 0, all-odd 0, reduced list 2: (4,19); (11,16)
distance-squared 386, number of points 8, running total 1209, all-even 0, all-odd 8, reduced list 1: (5,19)
distance-squared 388, number of points 8, running total 1217, all-even 8, all-odd 0, reduced list 1: (8,18)
distance-squared 389, number of points 8, running total 1225, all-even 0, all-odd 0, reduced list 1: (10,17)
distance-squared 392, number of points 4, running total 1229, all-even 4, all-odd 0, reduced list 1: (14,14)
distance-squared 394, number of points 8, running total 1237, all-even 0, all-odd 8, reduced list 1: (13,15)
distance-squared 397, number of points 8, running total 1245, all-even 0, all-odd 0, reduced list 1: (6,19)
3D
distance-squared 0, number of points 1, running total 1, all-even 1, all-odd 0, reduced list 1: (0,0,0)
distance-squared 1, number of points 6, running total 7, all-even 0, all-odd 0, reduced list 1: (0,0,1)
distance-squared 2, number of points 12, running total 19, all-even 0, all-odd 0, reduced list 1: (0,1,1)
distance-squared 3, number of points 8, running total 27, all-even 0, all-odd 8, reduced list 1: (1,1,1)
distance-squared 4, number of points 6, running total 33, all-even 6, all-odd 0, reduced list 1: (0,0,2)
distance-squared 5, number of points 24, running total 57, all-even 0, all-odd 0, reduced list 1: (0,1,2)
distance-squared 6, number of points 24, running total 81, all-even 0, all-odd 0, reduced list 1: (1,1,2)
distance-squared 8, number of points 12, running total 93, all-even 12, all-odd 0, reduced list 1: (0,2,2)
distance-squared 9, number of points 30, running total 123, all-even 0, all-odd 0, reduced list 2: (0,0,3); (1,2,2)
distance-squared 10, number of points 24, running total 147, all-even 0, all-odd 0, reduced list 1: (0,1,3)
distance-squared 11, number of points 24, running total 171, all-even 0, all-odd 24, reduced list 1: (1,1,3)
distance-squared 12, number of points 8, running total 179, all-even 8, all-odd 0, reduced list 1: (2,2,2)
distance-squared 13, number of points 24, running total 203, all-even 0, all-odd 0, reduced list 1: (0,2,3)
distance-squared 14, number of points 48, running total 251, all-even 0, all-odd 0, reduced list 1: (1,2,3)
distance-squared 16, number of points 6, running total 257, all-even 6, all-odd 0, reduced list 1: (0,0,4)
distance-squared 17, number of points 48, running total 305, all-even 0, all-odd 0, reduced list 2: (0,1,4); (2,2,3)
distance-squared 18, number of points 36, running total 341, all-even 0, all-odd 0, reduced list 2: (0,3,3); (1,1,4)
distance-squared 19, number of points 24, running total 365, all-even 0, all-odd 24, reduced list 1: (1,3,3)
distance-squared 20, number of points 24, running total 389, all-even 24, all-odd 0, reduced list 1: (0,2,4)
distance-squared 21, number of points 48, running total 437, all-even 0, all-odd 0, reduced list 1: (1,2,4)
distance-squared 22, number of points 24, running total 461, all-even 0, all-odd 0, reduced list 1: (2,3,3)
distance-squared 24, number of points 24, running total 485, all-even 24, all-odd 0, reduced list 1: (2,2,4)
distance-squared 25, number of points 30, running total 515, all-even 0, all-odd 0, reduced list 2: (0,0,5); (0,3,4)
distance-squared 26, number of points 72, running total 587, all-even 0, all-odd 0, reduced list 2: (0,1,5); (1,3,4)
distance-squared 27, number of points 32, running total 619, all-even 0, all-odd 32, reduced list 2: (1,1,5); (3,3,3)
distance-squared 29, number of points 72, running total 691, all-even 0, all-odd 0, reduced list 2: (0,2,5); (2,3,4)
distance-squared 30, number of points 48, running total 739, all-even 0, all-odd 0, reduced list 1: (1,2,5)
distance-squared 32, number of points 12, running total 751, all-even 12, all-odd 0, reduced list 1: (0,4,4)
distance-squared 33, number of points 48, running total 799, all-even 0, all-odd 0, reduced list 2: (1,4,4); (2,2,5)
distance-squared 34, number of points 48, running total 847, all-even 0, all-odd 0, reduced list 2: (0,3,5); (3,3,4)
distance-squared 35, number of points 48, running total 895, all-even 0, all-odd 48, reduced list 1: (1,3,5)
distance-squared 36, number of points 30, running total 925, all-even 30, all-odd 0, reduced list 2: (0,0,6); (2,4,4)
distance-squared 37, number of points 24, running total 949, all-even 0, all-odd 0, reduced list 1: (0,1,6)
distance-squared 38, number of points 72, running total 1021, all-even 0, all-odd 0, reduced list 2: (1,1,6); (2,3,5)
distance-squared 40, number of points 24, running total 1045, all-even 24, all-odd 0, reduced list 1: (0,2,6)
distance-squared 41, number of points 96, running total 1141, all-even 0, all-odd 0, reduced list 3: (0,4,5); (1,2,6); (3,4,4)
distance-squared 42, number of points 48, running total 1189, all-even 0, all-odd 0, reduced list 1: (1,4,5)
distance-squared 43, number of points 24, running total 1213, all-even 0, all-odd 24, reduced list 1: (3,3,5)
distance-squared 44, number of points 24, running total 1237, all-even 24, all-odd 0, reduced list 1: (2,2,6)
distance-squared 45, number of points 72, running total 1309, all-even 0, all-odd 0, reduced list 2: (0,3,6); (2,4,5)
distance-squared 46, number of points 48, running total 1357, all-even 0, all-odd 0, reduced list 1: (1,3,6)
distance-squared 48, number of points 8, running total 1365, all-even 8, all-odd 0, reduced list 1: (4,4,4)
distance-squared 49, number of points 54, running total 1419, all-even 0, all-odd 0, reduced list 2: (0,0,7); (2,3,6)
distance-squared 50, number of points 84, running total 1503, all-even 0, all-odd 0, reduced list 3: (0,1,7); (0,5,5); (3,4,5)
distance-squared 51, number of points 48, running total 1551, all-even 0, all-odd 48, reduced list 2: (1,1,7); (1,5,5)
distance-squared 52, number of points 24, running total 1575, all-even 24, all-odd 0, reduced list 1: (0,4,6)
distance-squared 53, number of points 72, running total 1647, all-even 0, all-odd 0, reduced list 2: (0,2,7); (1,4,6)
distance-squared 54, number of points 96, running total 1743, all-even 0, all-odd 0, reduced list 3: (1,2,7); (2,5,5); (3,3,6)
distance-squared 56, number of points 48, running total 1791, all-even 48, all-odd 0, reduced list 1: (2,4,6)
distance-squared 57, number of points 48, running total 1839, all-even 0, all-odd 0, reduced list 2: (2,2,7); (4,4,5)
distance-squared 58, number of points 24, running total 1863, all-even 0, all-odd 0, reduced list 1: (0,3,7)
distance-squared 59, number of points 72, running total 1935, all-even 0, all-odd 72, reduced list 2: (1,3,7); (3,5,5)
distance-squared 61, number of points 72, running total 2007, all-even 0, all-odd 0, reduced list 2: (0,5,6); (3,4,6)
distance-squared 62, number of points 96, running total 2103, all-even 0, all-odd 0, reduced list 2: (1,5,6); (2,3,7)
distance-squared 64, number of points 6, running total 2109, all-even 6, all-odd 0, reduced list 1: (0,0,8)
distance-squared 65, number of points 96, running total 2205, all-even 0, all-odd 0, reduced list 3: (0,1,8); (0,4,7); (2,5,6)
distance-squared 66, number of points 96, running total 2301, all-even 0, all-odd 0, reduced list 3: (1,1,8); (1,4,7); (4,5,5)
distance-squared 67, number of points 24, running total 2325, all-even 0, all-odd 24, reduced list 1: (3,3,7)
distance-squared 68, number of points 48, running total 2373, all-even 48, all-odd 0, reduced list 2: (0,2,8); (4,4,6)
distance-squared 69, number of points 96, running total 2469, all-even 0, all-odd 0, reduced list 2: (1,2,8); (2,4,7)
distance-squared 70, number of points 48, running total 2517, all-even 0, all-odd 0, reduced list 1: (3,5,6)
distance-squared 72, number of points 36, running total 2553, all-even 36, all-odd 0, reduced list 2: (0,6,6); (2,2,8)
distance-squared 73, number of points 48, running total 2601, all-even 0, all-odd 0, reduced list 2: (0,3,8); (1,6,6)
distance-squared 74, number of points 120, running total 2721, all-even 0, all-odd 0, reduced list 3: (0,5,7); (1,3,8); (3,4,7)
distance-squared 75, number of points 56, running total 2777, all-even 0, all-odd 56, reduced list 2: (1,5,7); (5,5,5)
distance-squared 76, number of points 24, running total 2801, all-even 24, all-odd 0, reduced list 1: (2,6,6)
distance-squared 77, number of points 96, running total 2897, all-even 0, all-odd 0, reduced list 2: (2,3,8); (4,5,6)
distance-squared 78, number of points 48, running total 2945, all-even 0, all-odd 0, reduced list 1: (2,5,7)
distance-squared 80, number of points 24, running total 2969, all-even 24, all-odd 0, reduced list 1: (0,4,8)
distance-squared 81, number of points 102, running total 3071, all-even 0, all-odd 0, reduced list 4: (0,0,9); (1,4,8); (3,6,6); (4,4,7)
distance-squared 82, number of points 48, running total 3119, all-even 0, all-odd 0, reduced list 2: (0,1,9); (3,3,8)
distance-squared 83, number of points 72, running total 3191, all-even 0, all-odd 72, reduced list 2: (1,1,9); (3,5,7)
distance-squared 84, number of points 48, running total 3239, all-even 48, all-odd 0, reduced list 1: (2,4,8)
distance-squared 85, number of points 48, running total 3287, all-even 0, all-odd 0, reduced list 2: (0,2,9); (0,6,7)
distance-squared 86, number of points 120, running total 3407, all-even 0, all-odd 0, reduced list 3: (1,2,9); (1,6,7); (5,5,6)
distance-squared 88, number of points 24, running total 3431, all-even 24, all-odd 0, reduced list 1: (4,6,6)
distance-squared 89, number of points 144, running total 3575, all-even 0, all-odd 0, reduced list 4: (0,5,8); (2,2,9); (2,6,7); (3,4,8)
distance-squared 90, number of points 120, running total 3695, all-even 0, all-odd 0, reduced list 3: (0,3,9); (1,5,8); (4,5,7)
distance-squared 91, number of points 48, running total 3743, all-even 0, all-odd 48, reduced list 1: (1,3,9)
distance-squared 93, number of points 48, running total 3791, all-even 0, all-odd 0, reduced list 1: (2,5,8)
distance-squared 94, number of points 96, running total 3887, all-even 0, all-odd 0, reduced list 2: (2,3,9); (3,6,7)
distance-squared 96, number of points 24, running total 3911, all-even 24, all-odd 0, reduced list 1: (4,4,8)
distance-squared 97, number of points 48, running total 3959, all-even 0, all-odd 0, reduced list 2: (0,4,9); (5,6,6)
distance-squared 98, number of points 108, running total 4067, all-even 0, all-odd 0, reduced list 3: (0,7,7); (1,4,9); (3,5,8)
distance-squared 99, number of points 72, running total 4139, all-even 0, all-odd 72, reduced list 3: (1,7,7); (3,3,9); (5,5,7)
4D
distance-squared 0, number of points 1, running total 1, all-even 1, all-odd 0, reduced list 1: (0,0,0,0)
distance-squared 1, number of points 8, running total 9, all-even 0, all-odd 0, reduced list 1: (0,0,0,1)
distance-squared 2, number of points 24, running total 33, all-even 0, all-odd 0, reduced list 1: (0,0,1,1)
distance-squared 3, number of points 32, running total 65, all-even 0, all-odd 0, reduced list 1: (0,1,1,1)
distance-squared 4, number of points 24, running total 89, all-even 8, all-odd 16, reduced list 2: (0,0,0,2); (1,1,1,1)
distance-squared 5, number of points 48, running total 137, all-even 0, all-odd 0, reduced list 1: (0,0,1,2)
distance-squared 6, number of points 96, running total 233, all-even 0, all-odd 0, reduced list 1: (0,1,1,2)
distance-squared 7, number of points 64, running total 297, all-even 0, all-odd 0, reduced list 1: (1,1,1,2)
distance-squared 8, number of points 24, running total 321, all-even 24, all-odd 0, reduced list 1: (0,0,2,2)
distance-squared 9, number of points 104, running total 425, all-even 0, all-odd 0, reduced list 2: (0,0,0,3); (0,1,2,2)
distance-squared 10, number of points 144, running total 569, all-even 0, all-odd 0, reduced list 2: (0,0,1,3); (1,1,2,2)
distance-squared 11, number of points 96, running total 665, all-even 0, all-odd 0, reduced list 1: (0,1,1,3)
distance-squared 12, number of points 96, running total 761, all-even 32, all-odd 64, reduced list 2: (0,2,2,2); (1,1,1,3)
distance-squared 13, number of points 112, running total 873, all-even 0, all-odd 0, reduced list 2: (0,0,2,3); (1,2,2,2)
distance-squared 14, number of points 192, running total 1065, all-even 0, all-odd 0, reduced list 1: (0,1,2,3)
distance-squared 15, number of points 192, running total 1257, all-even 0, all-odd 0, reduced list 1: (1,1,2,3)
distance-squared 16, number of points 24, running total 1281, all-even 24, all-odd 0, reduced list 2: (0,0,0,4); (2,2,2,2)
distance-squared 17, number of points 144, running total 1425, all-even 0, all-odd 0, reduced list 2: (0,0,1,4); (0,2,2,3)
distance-squared 18, number of points 312, running total 1737, all-even 0, all-odd 0, reduced list 3: (0,0,3,3); (0,1,1,4); (1,2,2,3)
distance-squared 19, number of points 160, running total 1897, all-even 0, all-odd 0, reduced list 2: (0,1,3,3); (1,1,1,4)
distance-squared 20, number of points 144, running total 2041, all-even 48, all-odd 96, reduced list 2: (0,0,2,4); (1,1,3,3)
distance-squared 21, number of points 256, running total 2297, all-even 0, all-odd 0, reduced list 2: (0,1,2,4); (2,2,2,3)
distance-squared 22, number of points 288, running total 2585, all-even 0, all-odd 0, reduced list 2: (0,2,3,3); (1,1,2,4)
distance-squared 23, number of points 192, running total 2777, all-even 0, all-odd 0, reduced list 1: (1,2,3,3)
distance-squared 24, number of points 96, running total 2873, all-even 96, all-odd 0, reduced list 1: (0,2,2,4)
distance-squared 25, number of points 248, running total 3121, all-even 0, all-odd 0, reduced list 3: (0,0,0,5); (0,0,3,4); (1,2,2,4)
distance-squared 26, number of points 336, running total 3457, all-even 0, all-odd 0, reduced list 3: (0,0,1,5); (0,1,3,4); (2,2,3,3)
distance-squared 27, number of points 320, running total 3777, all-even 0, all-odd 0, reduced list 3: (0,1,1,5); (0,3,3,3); (1,1,3,4)
distance-squared 28, number of points 192, running total 3969, all-even 64, all-odd 128, reduced list 3: (1,1,1,5); (1,3,3,3); (2,2,2,4)
distance-squared 29, number of points 240, running total 4209, all-even 0, all-odd 0, reduced list 2: (0,0,2,5); (0,2,3,4)
distance-squared 30, number of points 576, running total 4785, all-even 0, all-odd 0, reduced list 2: (0,1,2,5); (1,2,3,4)
distance-squared 31, number of points 256, running total 5041, all-even 0, all-odd 0, reduced list 2: (1,1,2,5); (2,3,3,3)
distance-squared 32, number of points 24, running total 5065, all-even 24, all-odd 0, reduced list 1: (0,0,4,4)
distance-squared 33, number of points 384, running total 5449, all-even 0, all-odd 0, reduced list 3: (0,1,4,4); (0,2,2,5); (2,2,3,4)
distance-squared 34, number of points 432, running total 5881, all-even 0, all-odd 0, reduced list 4: (0,0,3,5); (0,3,3,4); (1,1,4,4); (1,2,2,5)
distance-squared 35, number of points 384, running total 6265, all-even 0, all-odd 0, reduced list 2: (0,1,3,5); (1,3,3,4)
distance-squared 36, number of points 312, running total 6577, all-even 104, all-odd 208, reduced list 4: (0,0,0,6); (0,2,4,4); (1,1,3,5); (3,3,3,3)
distance-squared 37, number of points 304, running total 6881, all-even 0, all-odd 0, reduced list 3: (0,0,1,6); (1,2,4,4); (2,2,2,5)
distance-squared 38, number of points 480, running total 7361, all-even 0, all-odd 0, reduced list 3: (0,1,1,6); (0,2,3,5); (2,3,3,4)
distance-squared 39, number of points 448, running total 7809, all-even 0, all-odd 0, reduced list 2: (1,1,1,6); (1,2,3,5)
distance-squared 40, number of points 144, running total 7953, all-even 144, all-odd 0, reduced list 2: (0,0,2,6); (2,2,4,4)
distance-squared 41, number of points 336, running total 8289, all-even 0, all-odd 0, reduced list 3: (0,0,4,5); (0,1,2,6); (0,3,4,4)
distance-squared 42, number of points 768, running total 9057, all-even 0, all-odd 0, reduced list 4: (0,1,4,5); (1,1,2,6); (1,3,4,4); (2,2,3,5)
distance-squared 43, number of points 352, running total 9409, all-even 0, all-odd 0, reduced list 3: (0,3,3,5); (1,1,4,5); (3,3,3,4)
distance-squared 44, number of points 288, running total 9697, all-even 96, all-odd 192, reduced list 2: (0,2,2,6); (1,3,3,5)
distance-squared 45, number of points 624, running total 10321, all-even 0, all-odd 0, reduced list 4: (0,0,3,6); (0,2,4,5); (1,2,2,6); (2,3,4,4)
distance-squared 46, number of points 576, running total 10897, all-even 0, all-odd 0, reduced list 2: (0,1,3,6); (1,2,4,5)
distance-squared 47, number of points 384, running total 11281, all-even 0, all-odd 0, reduced list 2: (1,1,3,6); (2,3,3,5)
distance-squared 48, number of points 96, running total 11377, all-even 96, all-odd 0, reduced list 2: (0,4,4,4); (2,2,2,6)
distance-squared 49, number of points 456, running total 11833, all-even 0, all-odd 0, reduced list 4: (0,0,0,7); (0,2,3,6); (1,4,4,4); (2,2,4,5)
distance-squared 50, number of points 744, running total 12577, all-even 0, all-odd 0, reduced list 5: (0,0,1,7); (0,0,5,5); (0,3,4,5); (1,2,3,6); (3,3,4,4)
distance-squared 51, number of points 576, running total 13153, all-even 0, all-odd 0, reduced list 3: (0,1,1,7); (0,1,5,5); (1,3,4,5)
distance-squared 52, number of points 336, running total 13489, all-even 112, all-odd 224, reduced list 5: (0,0,4,6); (1,1,1,7); (1,1,5,5); (2,4,4,4); (3,3,3,5)
distance-squared 53, number of points 432, running total 13921, all-even 0, all-odd 0, reduced list 3: (0,0,2,7); (0,1,4,6); (2,2,3,6)
distance-squared 54, number of points 960, running total 14881, all-even 0, all-odd 0, reduced list 5: (0,1,2,7); (0,2,5,5); (0,3,3,6); (1,1,4,6); (2,3,4,5)
distance-squared 55, number of points 576, running total 15457, all-even 0, all-odd 0, reduced list 3: (1,1,2,7); (1,2,5,5); (1,3,3,6)
distance-squared 56, number of points 192, running total 15649, all-even 192, all-odd 0, reduced list 1: (0,2,4,6)
distance-squared 57, number of points 640, running total 16289, all-even 0, all-odd 0, reduced list 4: (0,2,2,7); (0,4,4,5); (1,2,4,6); (3,4,4,4)
distance-squared 58, number of points 720, running total 17009, all-even 0, all-odd 0, reduced list 5: (0,0,3,7); (1,2,2,7); (1,4,4,5); (2,2,5,5); (2,3,3,6)
distance-squared 59, number of points 480, running total 17489, all-even 0, all-odd 0, reduced list 3: (0,1,3,7); (0,3,5,5); (3,3,4,5)
distance-squared 60, number of points 576, running total 18065, all-even 192, all-odd 384, reduced list 3: (1,1,3,7); (1,3,5,5); (2,2,4,6)
distance-squared 61, number of points 496, running total 18561, all-even 0, all-odd 0, reduced list 4: (0,0,5,6); (0,3,4,6); (2,2,2,7); (2,4,4,5)
distance-squared 62, number of points 768, running total 19329, all-even 0, all-odd 0, reduced list 3: (0,1,5,6); (0,2,3,7); (1,3,4,6)
distance-squared 63, number of points 832, running total 20161, all-even 0, all-odd 0, reduced list 4: (1,1,5,6); (1,2,3,7); (2,3,5,5); (3,3,3,6)
distance-squared 64, number of points 24, running total 20185, all-even 24, all-odd 0, reduced list 2: (0,0,0,8); (4,4,4,4)
distance-squared 65, number of points 672, running total 20857, all-even 0, all-odd 0, reduced list 4: (0,0,1,8); (0,0,4,7); (0,2,5,6); (2,3,4,6)
distance-squared 66, number of points 1152, running total 22009, all-even 0, all-odd 0, reduced list 6: (0,1,1,8); (0,1,4,7); (0,4,5,5); (1,2,5,6); (2,2,3,7); (3,4,4,5)
distance-squared 67, number of points 544, running total 22553, all-even 0, all-odd 0, reduced list 4: (0,3,3,7); (1,1,1,8); (1,1,4,7); (1,4,5,5)
distance-squared 68, number of points 432, running total 22985, all-even 144, all-odd 288, reduced list 4: (0,0,2,8); (0,4,4,6); (1,3,3,7); (3,3,5,5)
distance-squared 69, number of points 768, running total 23753, all-even 0, all-odd 0, reduced list 4: (0,1,2,8); (0,2,4,7); (1,4,4,6); (2,2,5,6)
distance-squared 70, number of points 1152, running total 24905, all-even 0, all-odd 0, reduced list 5: (0,3,5,6); (1,1,2,8); (1,2,4,7); (2,4,5,5); (3,3,4,6)
distance-squared 71, number of points 576, running total 25481, all-even 0, all-odd 0, reduced list 2: (1,3,5,6); (2,3,3,7)
distance-squared 72, number of points 312, running total 25793, all-even 312, all-odd 0, reduced list 3: (0,0,6,6); (0,2,2,8); (2,4,4,6)
distance-squared 73, number of points 592, running total 26385, all-even 0, all-odd 0, reduced list 5: (0,0,3,8); (0,1,6,6); (1,2,2,8); (2,2,4,7); (4,4,4,5)
distance-squared 74, number of points 912, running total 27297, all-even 0, all-odd 0, reduced list 5: (0,0,5,7); (0,1,3,8); (0,3,4,7); (1,1,6,6); (2,3,5,6)
distance-squared 75, number of points 992, running total 28289, all-even 0, all-odd 0, reduced list 5: (0,1,5,7); (0,5,5,5); (1,1,3,8); (1,3,4,7); (3,4,5,5)
distance-squared 76, number of points 480, running total 28769, all-even 160, all-odd 320, reduced list 5: (0,2,6,6); (1,1,5,7); (1,5,5,5); (2,2,2,8); (3,3,3,7)
distance-squared 77, number of points 768, running total 29537, all-even 0, all-odd 0, reduced list 4: (0,2,3,8); (0,4,5,6); (1,2,6,6); (3,4,4,6)
distance-squared 78, number of points 1344, running total 30881, all-even 0, all-odd 0, reduced list 4: (0,2,5,7); (1,2,3,8); (1,4,5,6); (2,3,4,7)
distance-squared 79, number of points 640, running total 31521, all-even 0, all-odd 0, reduced list 3: (1,2,5,7); (2,5,5,5); (3,3,5,6)
distance-squared 80, number of points 144, running total 31665, all-even 144, all-odd 0, reduced list 2: (0,0,4,8); (2,2,6,6)
distance-squared 81, number of points 968, running total 32633, all-even 0, all-odd 0, reduced list 6: (0,0,0,9); (0,1,4,8); (0,3,6,6); (0,4,4,7); (2,2,3,8); (2,4,5,6)
distance-squared 82, number of points 1008, running total 33641, all-even 0, all-odd 0, reduced list 7: (0,0,1,9); (0,3,3,8); (1,1,4,8); (1,3,6,6); (1,4,4,7); (2,2,5,7); (4,4,5,5)
distance-squared 83, number of points 672, running total 34313, all-even 0, all-odd 0, reduced list 4: (0,1,1,9); (0,3,5,7); (1,3,3,8); (3,3,4,7)
distance-squared 84, number of points 768, running total 35081, all-even 256, all-odd 512, reduced list 5: (0,2,4,8); (1,1,1,9); (1,3,5,7); (3,5,5,5); (4,4,4,6)
distance-squared 85, number of points 864, running total 35945, all-even 0, all-odd 0, reduced list 5: (0,0,2,9); (0,0,6,7); (1,2,4,8); (2,3,6,6); (2,4,4,7)
distance-squared 86, number of points 1056, running total 37001, all-even 0, all-odd 0, reduced list 5: (0,1,2,9); (0,1,6,7); (0,5,5,6); (2,3,3,8); (3,4,5,6)
distance-squared 87, number of points 960, running total 37961, all-even 0, all-odd 0, reduced list 4: (1,1,2,9); (1,1,6,7); (1,5,5,6); (2,3,5,7)
distance-squared 88, number of points 288, running total 38249, all-even 288, all-odd 0, reduced list 2: (0,4,6,6); (2,2,4,8)
distance-squared 89, number of points 720, running total 38969, all-even 0, all-odd 0, reduced list 5: (0,0,5,8); (0,2,2,9); (0,2,6,7); (0,3,4,8); (1,4,6,6)
distance-squared 90, number of points 1872, running total 40841, all-even 0, all-odd 0, reduced list 9: (0,0,3,9); (0,1,5,8); (0,4,5,7); (1,2,2,9); (1,2,6,7); (1,3,4,8); (2,5,5,6); (3,3,6,6); (3,4,4,7)
distance-squared 91, number of points 896, running total 41737, all-even 0, all-odd 0, reduced list 5: (0,1,3,9); (1,1,5,8); (1,4,5,7); (3,3,3,8); (4,5,5,5)
distance-squared 92, number of points 576, running total 42313, all-even 192, all-odd 384, reduced list 3: (1,1,3,9); (2,4,6,6); (3,3,5,7)
distance-squared 93, number of points 1024, running total 43337, all-even 0, all-odd 0, reduced list 5: (0,2,5,8); (2,2,2,9); (2,2,6,7); (2,3,4,8); (4,4,5,6)
distance-squared 94, number of points 1152, running total 44489, all-even 0, all-odd 0, reduced list 4: (0,2,3,9); (0,3,6,7); (1,2,5,8); (2,4,5,7)
distance-squared 95, number of points 960, running total 45449, all-even 0, all-odd 0, reduced list 3: (1,2,3,9); (1,3,6,7); (3,5,5,6)
distance-squared 96, number of points 96, running total 45545, all-even 96, all-odd 0, reduced list 1: (0,4,4,8)
distance-squared 97, number of points 784, running total 46329, all-even 0, all-odd 0, reduced list 6: (0,0,4,9); (0,5,6,6); (1,4,4,8); (2,2,5,8); (3,4,6,6); (4,4,4,7)
distance-squared 98, number of points 1368, running total 47697, all-even 0, all-odd 0, reduced list 7: (0,0,7,7); (0,1,4,9); (0,3,5,8); (1,5,6,6); (2,2,3,9); (2,3,6,7); (3,3,4,8)
distance-squared 99, number of points 1248, running total 48945, all-even 0, all-odd 0, reduced list 6: (0,1,7,7); (0,3,3,9); (0,5,5,7); (1,1,4,9); (1,3,5,8); (3,4,5,7)
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