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[[648,326,6]] d =
n
648
k
326
d
6
kd²/n
18.1111
w
8
X/Z
1

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Distance

X/Z asymmetry 1 · d_X = 6, d_Z = 6 · w_X = 8, w_Z = 8 (max(d_X,d_Z)/min(d_X,d_Z); each side carries its own earned tier: = certified exact, ≤ witness upper bound)
d_X 6 · witness weight 6 (claimed exact)
witness operator (support, 6 qubits)
[0, 3, 8, 10, 27, 233]
d_Z 6 · witness weight 6 (claimed exact)
witness operator (support, 6 qubits)
[0, 1, 3, 4, 11, 67]
certificate exact, d = 6 · tropidist b03ec2d4077f (arXiv:2611.08247) exhaustive search · level solver: a solver verdict, no artifact a third party can check without re-running the encoding
X: no logical < 6 exists; Z: no logical < 6 exists

Diagnostics

computed by the verifier from the parity checks, the layout, and the stored witnesses; shown as evidence, not used for ranking
girth H_X 12 · H_Z 12 (shortest cycle of each side’s Tanner graph; longer is friendlier to belief propagation)
check weights H_X 8 · H_Z 8
qubit degrees H_X 2 · H_Z 2
trapping sets H_X (1,2)×648 (2,2)×4536 (3,2)×31752 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,2): 648 (2,2): 4536 (3,2): 31752 (3,4): 9072
trapping sets H_Z (1,2)×648 (2,2)×4536 (3,2)×31752 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,2): 648 (2,2): 4536 (3,2): 31752 (3,4): 9072

Construction & provenance

authors @TimoKellerMath
provenance submitted through the challenge
novelty new parameter set claimed by submitter
construction Surface code of the orientably-regular map C163.13 of type {8,8} (genus 163) in M. Conder's list of chiral maps of genus 2 to 301. Rotation group G = <r,s | r8, s8, (r*s)2, s-1*r-1*s2*r3*s2*r-1*s-1*r, s-1*r-1*s*r*s-1*r2*s-1*r*s-2*r> of order 1296. Darts = elements of G (right multiplication), faces = cosets g<r>, vertices = cosets g<s>, edges = cosets g<rs> = {g, grs}. Qubits on the 648 edges, X-checks on the 162 vertices (weight 8), Z-checks on the 162 faces (weight 8), incidences mod 2: H_X and H_Z are the boundary maps of the cellular chain complex over F_2, k = 2 - chi = 326, d_Z is the shortest homologically nontrivial cycle of the map and d_X that of the dual map. Found in a census of regular maps (normal subgroups of the triangle groups <r,s | r^p, s^q, (rs)2>, Magma's LowIndexNormalSubgroups). The qubit order is that of the dart permutations in the public package in the references (data/maps.json), whose src/rebuild.py rebuilds these matrices from them and from the presentation.
model Claude Claude Opus 5.5 (claimed, not verified)
builds on https://arxiv.org/abs/1506.04029, https://www.math.auckland.ac.nz/~conder/ChiralMaps301.txt, https://github.com/TimoKellerMath/quantum-error-correction/tree/2e97a5361e7b9327128baa242bdedd333f7d7e12/hyperbolic-map-codes
date 2026-11-10
notes Exact distance d_X = d_Z = 6: tropidist (arXiv:2611.08247) at the board's pinned commit b03ec2d4077f closes both sides (certs/648-326-6.json, level solver); independently two exact programs for check matrices with column weight 2 and an enumeration of all circuits of length <= 6 (24732 X-type and 24732 Z-type logical operators of weight 6, none lighter), see the research note. Novelty: no board entry with these n and k at commit 8042f9da; parameters not found in Breuckmann and Terhal (arXiv:1506.04029), Breuckmann et al. (arXiv:1703.00590), Breuckmann's thesis (arXiv:1802.01520), Mahmoud and Rayan (arXiv:2610.10948), Breuckmann and Burton (arXiv:2202.06647), Mahmoud, Ali and Rayan (arXiv:2504.07800), the catalogs of QEC-pages (Quantum_LDPC_Codes) and qecdb.org; Conder's lists contain the map, not the code. Equivalence with existing entries: checked, none has these n and k.
family topological (a tag, not a ranking)
locality unrestricted (computed from the layout)
weight class weight ≤ 8 (computed)

How this code was found

the research note submitted with this code · raw markdown · all notes

[[648,326,6]]: chiral {8,8} surface code, Conder's map C163.13

Direction & hypothesis

Cell: check weight 8, unrestricted locality (no layout submitted). Surface codes of regular maps of type {p,q} on closed hyperbolic surfaces (Breuckmann and Terhal, arXiv:1506.04029) have k = 2 - chi = (1 - 2/p - 2/q) n + 2, so {8,8} maps give k/n close to 1/2 at check weight 8, while the distance is the systole of the map (of the dual map for d_X) and grows only logarithmically in n. At board commit 8042f9da the entries of check weight at most 8 with d = 6 and the largest kd^2/n were the lifted-product codes [[780,318,6]] to [[1000,406,6]], kd^2/n about 14.6. Hypothesis: {8,8} maps whose systoles reach 6 dominate them, at kd^2/n about 18.

What was searched

A census of all regular maps of type {p,q}, 3 <= p,q <= 8, 1/p + 1/q < 1/2, with at most 2000 edges (chiral {8,8} maps up to 1000 edges): the normal subgroups of index 2E of the triangle groups <r,s | r^p, s^q, (rs)^2> in which r, s, rs keep their orders (Magma's LowIndexNormalSubgroups), the non-orientable maps from the extended triangle groups, and 2000 cyclic covers of the orientable maps with n <= 1000 (random voltage classes, seeds recorded). In total 2174 orientable and 340 non-orientable maps (up to duality and mirror image) and 2000 covers, 7063 codes with their X/Z duals, each with exact d_X and d_Z by the programs below. At board commit 8042f9da, 254 parameter points of the census were undominated; we submit nine of them, one per pull request, and left out the points we found in the literature: [[896,386,6]] ({7,7}) and [[960,194,8]] ({5,5}) are data points of Fig. 3.7 of Breuckmann's thesis (arXiv:1802.01520), [[588,254,6]] and [[273,119,5]] are in its Table 3.1. This code is the chiral {8,8} map C163.13 of M. Conder's list. It is the only {8,8} map of the census with 648 edges and d = 6. Sources checked without finding it: Breuckmann and Terhal (arXiv:1506.04029), Breuckmann et al. (arXiv:1703.00590), Breuckmann's thesis (arXiv:1802.01520), Mahmoud and Rayan (arXiv:2610.10948), Breuckmann and Burton (arXiv:2202.06647), Mahmoud, Ali and Rayan (arXiv:2504.07800), the catalogs of QEC-pages (Quantum_LDPC_Codes) and qecdb.org; Conder's lists contain the maps, not the codes.

Evidence trail

  • k = 326 = 648 - 161 - 161 (ranks over GF(2)) = 2 - chi; H_X H_Z^T = 0; every qubit lies in two X-checks and two Z-checks, so both sides are graph-like (computed).
  • Upper bound: an X-type and a Z-type logical operator of weight 6, in the entry.
  • Lower bound, exact, by four computations: (1) graphlike_A, shortest cycles with logical annotations in F_2^k; (2) graphlike_B, shortest paths in the double covers of the check graph given by the logical operators, written independently; their exactness is proved in github.com/TimoKellerMath/quantum-error-correction @ 2e97a5361e7b9327128baa242bdedd333f7d7e12, hyperbolic-map-codes/src/graphlike_A/NOTES.md and hyperbolic-map-codes/src/graphlike_B/NOTES.md, and they agree on all 7063 census codes; (3) an enumeration of all circuits of length at most 6 with a row-space test: the graph of the map and its dual have no circuit shorter than 6, and all 24732 circuits of length 6 are nontrivial, on both sides; (4) tropidist (Cheng, Guo and Pan, arXiv:2611.08247) at the board's pinned commit b03ec2d4077f, one thread, 600 s limit, on the board's css-sides problems: exact 6 and 6 in 1.1 s and 1.3 s, recorded in certs/648-326-6.json.
  • Final claim: d_X = d_Z = 6, exact (computer-assisted; the four computations agree). 24732 X-type and 24732 Z-type logical operators have weight 6.

Dead ends

  • Within the census no {8,8}, {6,6} or {7,7} map reaches d = 7; d >= 7 occurs only for {3,7}, {4,5}, {4,6} and {5,5} (n <= 2000).
  • Among the 1005 {8,8} maps of the census (up to mirror image), 19 have d = 6 (from n = 640 on) and none more; 937 have d = 2 or 4.

Tools

Claude Opus 5.5 (Claude Code). Magma V2.30 for the census (LowIndexNormalSubgroups, coset actions, the presentations and Conder's names); Python for the map codes; the C programs graphlike_A and graphlike_B and the Python circuit enumeration, all in the public package below; tropidist b03ec2d4077f. The largest Magma run of the census (orientable {6,6} maps, index at most 4000) took 33 CPU minutes; exact distances of all 7063 codes took 46 s with graphlike_A and 76 s with graphlike_B.

Reproduction

G = <r,s | r^8, s^8, (r*s)^2, s^-1*r^-1*s^2*r^3*s^2*r^-1*s^-1*r, s^-1*r^-1*s*r*s^-1*r^2*s^-1*r*s^-2*r> (order 1296); qubits = edges {g, grs}, X-checks = vertices g<s>, Z-checks = faces g<r>, incidences mod 2. In hyperbolic-map-codes/ of github.com/TimoKellerMath/quantum-error-correction @ 2e97a5361e7b: make check runs hyperbolic-map-codes/src/rebuild.py (standard library), which rebuilds these matrices from the stored darts and from the presentation, checks Conder's relators, k and the witnesses; make distances runs graphlike_A, graphlike_B and the circuit enumeration; make tropidist-inputs writes the tropidist problems.

Parity checks

X-checks 162 (max weight 8) · Z-checks 162 (max weight 8)
H_X (162 checks, sparse supports)
[0, 2, 3, 7, 10, 19, 27, 47] [0, 1, 5, 13, 15, 34, 39, 81] [2, 6, 8, 17, 22, 43, 55, 102] [1, 4, 12, 30, 32, 72, 77, 163] [7, 18, 20, 45, 50, 106, 117, 226] [8, 21, 23, 53, 58, 124, 133, 259] [3, 9, 25, 61, 63, 67, 139, 151] [4, 11, 29, 68, 70, 154, 159, 302] [13, 33, 35, 79, 84, 179, 188, 343] [5, 14, 37, 57, 88, 90, 131, 195] [6, 16, 29, 41, 69, 96, 98, 157] [19, 46, 48, 108, 112, 230, 238, 413] [20, 49, 51, 115, 120, 244, 252, 431] [22, 54, 56, 125, 129, 261, 267, 447] [23, 28, 57, 107, 135, 227, 276, 408] [9, 24, 60, 136, 138, 196, 282, 372] [10, 26, 65, 145, 147, 190, 241, 362] [11, 28, 67, 150, 152, 295, 299, 472] [30, 71, 73, 144, 161, 166, 217, 315] [12, 21, 31, 52, 75, 122, 170, 172] [34, 80, 82, 180, 184, 345, 352, 535] [35, 44, 83, 85, 103, 191, 220, 363] [14, 36, 87, 192, 194, 330, 370, 525] [15, 38, 92, 201, 203, 325, 355, 518] [16, 40, 95, 140, 206, 208, 284, 387] [17, 42, 100, 119, 162, 215, 251, 377] [18, 44, 95, 104, 172, 207, 222, 385] [47, 109, 110, 176, 232, 416, 418, 485] [48, 111, 113, 236, 240, 298, 425, 479] [50, 116, 118, 245, 249, 432, 436, 475] [51, 94, 119, 231, 254, 414, 441, 495] [55, 126, 127, 178, 262, 328, 448, 522] [56, 128, 130, 265, 270, 415, 436, 498] [58, 132, 134, 197, 274, 373, 425, 500] [24, 59, 77, 175, 278, 337, 417, 530] [61, 71, 87, 140, 160, 193, 314, 502] [25, 62, 83, 142, 186, 287, 289, 356] [26, 64, 144, 270, 290, 454, 469, 473] [27, 66, 121, 149, 233, 293, 466, 583] [68, 149, 153, 155, 200, 301, 305, 484] [72, 162, 164, 316, 320, 504, 510, 618] [73, 78, 165, 167, 176, 266, 326, 338] [31, 74, 169, 327, 329, 441, 494, 524] [32, 76, 174, 333, 335, 491, 512, 611] [33, 60, 78, 96, 137, 177, 209, 340] [81, 181, 182, 313, 347, 537, 538, 600] [82, 183, 185, 228, 267, 350, 354, 409] [84, 187, 189, 229, 252, 357, 360, 411] [59, 85, 190, 346, 365, 536, 547, 603] [36, 86, 159, 254, 312, 366, 442, 500] [88, 153, 169, 196, 300, 328, 483, 605] [37, 89, 165, 198, 322, 375, 377, 513] [38, 91, 120, 200, 253, 378, 439, 558] [39, 40, 93, 94, 205, 381, 382, 555] [41, 49, 97, 114, 211, 242, 392, 394] [42, 99, 188, 303, 358, 396, 486, 487] [43, 101, 217, 271, 398, 399, 566, 637] [45, 105, 224, 239, 309, 341, 424, 571] [46, 107, 220, 228, 394, 402, 410, 575] [110, 185, 204, 234, 353, 380, 420, 558] [112, 161, 237, 279, 351, 371, 461, 511] [113, 148, 219, 239, 292, 427, 469, 589] [117, 123, 164, 246, 247, 319, 321, 508] [92, 118, 136, 202, 248, 250, 279, 379] [52, 121, 209, 255, 389, 390, 435, 567] [53, 80, 123, 257, 269, 289, 338, 453] [54, 90, 115, 243, 255, 429, 437, 557] [102, 103, 218, 219, 317, 401, 505, 573] [127, 158, 263, 264, 310, 326, 449, 496] [129, 266, 268, 305, 428, 451, 489, 490] [130, 233, 269, 331, 400, 417, 525, 572] [105, 133, 193, 223, 272, 368, 456, 552] [134, 273, 275, 335, 395, 396, 489, 568] [135, 141, 212, 277, 285, 337, 411, 496] [139, 211, 235, 283, 322, 393, 458, 512] [62, 141, 225, 286, 405, 420, 467, 556] [63, 132, 265, 450, 455, 468, 504, 561] [64, 143, 234, 282, 369, 407, 419, 527] [145, 154, 250, 286, 303, 437, 578, 607] [65, 146, 206, 268, 291, 316, 383, 452] [66, 148, 202, 310, 354, 495, 543, 614] [150, 205, 210, 294, 296, 332, 391, 475] [116, 155, 160, 215, 236, 304, 306, 313] [69, 156, 308, 468, 492, 493, 547, 614] [70, 158, 272, 311, 498, 601, 609, 643] [163, 317, 318, 440, 482, 506, 579, 620] [166, 274, 323, 324, 344, 363, 514, 516] [86, 167, 325, 505, 519, 580, 619, 625] [74, 168, 299, 365, 447, 481, 520, 548] [170, 230, 294, 308, 330, 471, 588, 599] [75, 114, 171, 241, 304, 488, 526, 610] [76, 173, 191, 223, 332, 364, 457, 527] [79, 178, 237, 283, 341, 353, 383, 542] [182, 321, 336, 348, 457, 511, 529, 539] [184, 256, 301, 351, 367, 509, 550, 608] [174, 189, 192, 334, 359, 361, 367, 528] [142, 195, 273, 288, 349, 371, 488, 609] [89, 197, 342, 374, 445, 532, 539, 556] [91, 199, 214, 258, 348, 370, 449, 523] [201, 207, 295, 361, 374, 384, 473, 563] [93, 204, 246, 334, 479, 603, 623, 645] [157, 186, 309, 355, 388, 443, 474, 565] [97, 210, 320, 446, 467, 509, 521, 589] [98, 212, 345, 395, 478, 494, 569, 633] [99, 213, 281, 378, 387, 427, 481, 544] [100, 180, 214, 344, 389, 397, 534, 571] [101, 146, 173, 216, 240, 331, 426, 524] [104, 111, 221, 235, 352, 421, 541, 551] [106, 225, 340, 438, 506, 520, 626, 646] [108, 229, 257, 412, 419, 554, 585, 617] [109, 231, 408, 415, 529, 541, 579, 639] [238, 243, 263, 388, 422, 423, 462, 564] [156, 226, 227, 307, 406, 407, 519, 613] [247, 290, 312, 386, 433, 434, 499, 567] [249, 291, 356, 359, 435, 470, 586, 592] [253, 375, 440, 470, 549, 552, 569, 634] [122, 128, 198, 256, 376, 443, 507, 593] [124, 258, 297, 343, 477, 533, 612, 644] [125, 171, 224, 260, 404, 445, 503, 617] [126, 152, 298, 431, 480, 591, 593, 641] [216, 264, 318, 404, 430, 487, 499, 608] [131, 271, 385, 455, 554, 576, 590, 638] [181, 244, 259, 346, 430, 444, 594, 622] [199, 275, 372, 398, 402, 555, 574, 635] [137, 260, 276, 280, 333, 439, 463, 517] [203, 277, 323, 458, 459, 471, 508, 598] [232, 278, 373, 429, 460, 531, 550, 628] [138, 281, 423, 464, 516, 528, 587, 610] [151, 297, 465, 478, 557, 602, 625, 645] [143, 284, 459, 466, 477, 591, 597, 620] [287, 454, 460, 463, 537, 570, 596, 599] [147, 187, 296, 300, 350, 474, 476, 482] [292, 302, 444, 485, 546, 574, 598, 606] [168, 306, 418, 433, 491, 576, 584, 612] [311, 324, 327, 497, 515, 517, 521, 615] [175, 336, 358, 409, 497, 580, 592, 638] [177, 183, 339, 349, 510, 540, 622, 627] [179, 342, 502, 545, 564, 606, 613, 636] [208, 360, 379, 386, 513, 515, 559, 632] [364, 448, 450, 526, 546, 559, 562, 626] [222, 261, 347, 366, 446, 549, 595, 616] [194, 221, 369, 403, 451, 553, 565, 615] [285, 382, 401, 403, 461, 560, 561, 577] [213, 307, 390, 476, 538, 566, 601, 631] [392, 416, 483, 486, 560, 563, 604, 630] [218, 380, 400, 422, 472, 568, 600, 642] [384, 413, 414, 530, 533, 562, 582, 631] [288, 357, 426, 493, 501, 534, 616, 629] [242, 248, 397, 428, 570, 590, 623, 636] [245, 329, 339, 393, 412, 523, 531, 581] [405, 434, 456, 464, 480, 490, 492, 581] [251, 438, 518, 575, 624, 628, 640, 643] [280, 399, 442, 462, 535, 536, 597, 630] [262, 410, 432, 465, 532, 544, 553, 629] [362, 453, 545, 577, 595, 611, 641, 647] [376, 452, 514, 543, 585, 602, 604, 646] [293, 368, 548, 551, 596, 618, 619, 635] [314, 319, 501, 507, 573, 582, 607, 621] [315, 421, 503, 586, 605, 624, 642, 644] [381, 406, 522, 572, 578, 584, 627, 634] [391, 542, 583, 587, 594, 621, 633, 640] [424, 484, 540, 588, 632, 637, 639, 647]
H_Z (162 checks, sparse supports)
[0, 1, 2, 4, 8, 11, 23, 28] [2, 6, 7, 16, 20, 40, 51, 94] [0, 3, 9, 13, 24, 35, 59, 85] [1, 5, 14, 30, 36, 73, 86, 167] [7, 18, 19, 44, 48, 103, 113, 219] [8, 21, 22, 52, 56, 121, 130, 233] [3, 10, 26, 61, 64, 140, 143, 284] [4, 12, 31, 68, 74, 155, 168, 306] [13, 33, 34, 78, 82, 110, 176, 185] [5, 15, 38, 88, 91, 196, 199, 372] [6, 17, 42, 96, 99, 209, 213, 390] [19, 46, 47, 107, 110, 227, 234, 407] [20, 49, 50, 114, 118, 145, 241, 250] [22, 54, 55, 115, 127, 244, 264, 430] [23, 57, 58, 131, 134, 271, 275, 398] [9, 25, 62, 136, 141, 279, 285, 461] [10, 27, 66, 145, 148, 154, 292, 302] [11, 29, 69, 150, 156, 296, 307, 476] [30, 71, 72, 160, 164, 182, 313, 321] [12, 32, 76, 170, 173, 330, 331, 525] [34, 53, 80, 81, 124, 182, 258, 348] [35, 83, 84, 186, 189, 201, 355, 361] [14, 37, 89, 192, 197, 367, 373, 550] [15, 39, 93, 201, 204, 295, 380, 472] [16, 41, 97, 206, 210, 383, 391, 542] [17, 43, 72, 101, 162, 163, 216, 318] [18, 45, 75, 105, 172, 223, 364, 526] [27, 47, 109, 231, 233, 414, 417, 530] [48, 61, 71, 111, 112, 139, 161, 235] [50, 116, 117, 236, 247, 298, 434, 480] [51, 119, 120, 251, 253, 438, 440, 506] [21, 53, 123, 172, 247, 385, 433, 576] [55, 102, 126, 152, 219, 299, 427, 481] [56, 128, 129, 162, 198, 268, 316, 377] [58, 132, 133, 223, 265, 415, 457, 529] [28, 67, 135, 151, 277, 297, 459, 477] [24, 60, 137, 243, 278, 280, 429, 462] [25, 63, 132, 197, 287, 374, 454, 473] [26, 65, 146, 173, 270, 332, 436, 475] [68, 153, 154, 300, 303, 318, 482, 487] [29, 70, 98, 158, 310, 441, 494, 495] [73, 165, 166, 322, 324, 333, 512, 517] [31, 75, 125, 171, 261, 327, 446, 521] [32, 77, 175, 276, 333, 336, 408, 529] [33, 79, 96, 127, 157, 178, 263, 388] [39, 81, 94, 181, 254, 346, 442, 536] [82, 88, 153, 183, 184, 195, 301, 349] [84, 99, 187, 188, 228, 350, 410, 544] [85, 190, 191, 362, 364, 545, 546, 606] [36, 87, 104, 193, 222, 366, 368, 551] [37, 54, 90, 125, 253, 260, 375, 439] [38, 92, 120, 202, 252, 310, 411, 496] [40, 95, 207, 382, 384, 450, 561, 562] [41, 98, 141, 212, 286, 303, 392, 486] [42, 91, 100, 200, 214, 305, 396, 489] [43, 102, 218, 381, 398, 400, 555, 572] [44, 83, 104, 221, 289, 403, 453, 577] [45, 69, 106, 157, 225, 309, 405, 492] [46, 108, 211, 229, 277, 394, 411, 458] [112, 204, 237, 238, 334, 353, 423, 528] [113, 239, 240, 308, 424, 426, 493, 588] [49, 115, 243, 394, 423, 575, 587, 640] [93, 117, 205, 226, 246, 332, 407, 527] [118, 186, 248, 249, 309, 356, 397, 571] [52, 122, 256, 301, 389, 424, 484, 571] [129, 158, 266, 267, 311, 326, 409, 497] [130, 269, 270, 347, 453, 454, 537, 595] [57, 90, 107, 228, 409, 557, 580, 625] [70, 133, 159, 259, 272, 312, 430, 499] [80, 134, 142, 180, 273, 274, 289, 344] [135, 212, 276, 380, 395, 439, 558, 568] [59, 77, 163, 317, 365, 505, 548, 619] [136, 196, 250, 262, 328, 437, 465, 557] [60, 138, 225, 281, 340, 378, 420, 558] [79, 139, 151, 179, 283, 342, 465, 532] [140, 193, 206, 316, 456, 468, 492, 504] [62, 142, 229, 288, 357, 405, 412, 581] [63, 67, 152, 298, 468, 479, 547, 603] [64, 123, 144, 166, 257, 323, 419, 508] [65, 147, 187, 357, 452, 493, 543, 614] [66, 149, 200, 267, 354, 378, 447, 481] [150, 292, 294, 295, 469, 471, 473, 598] [155, 272, 304, 305, 456, 488, 490, 609] [122, 164, 170, 210, 294, 319, 320, 507] [167, 263, 325, 326, 422, 518, 624, 642] [74, 169, 177, 328, 340, 520, 522, 627] [76, 174, 191, 274, 334, 363, 425, 479] [78, 165, 177, 251, 339, 377, 531, 628] [184, 221, 336, 351, 352, 497, 511, 615] [185, 353, 354, 478, 542, 543, 602, 633] [175, 188, 258, 337, 343, 358, 449, 496] [189, 283, 291, 322, 359, 360, 383, 513] [86, 159, 302, 406, 418, 485, 519, 584] [108, 192, 207, 230, 330, 361, 385, 554] [87, 194, 342, 369, 457, 502, 527, 539] [131, 161, 195, 315, 371, 503, 554, 617] [89, 198, 344, 376, 514, 532, 534, 629] [92, 203, 248, 323, 514, 602, 623, 645] [95, 208, 222, 290, 386, 446, 469, 589] [137, 180, 209, 327, 345, 389, 494, 517] [97, 211, 245, 393, 432, 521, 553, 615] [100, 116, 215, 245, 329, 426, 524, 534] [101, 144, 217, 240, 290, 312, 425, 500] [103, 203, 220, 325, 402, 505, 574, 598] [105, 146, 216, 224, 291, 404, 470, 552] [106, 226, 317, 406, 506, 573, 578, 607] [109, 232, 352, 373, 442, 500, 535, 541] [176, 269, 335, 338, 400, 418, 491, 568] [234, 374, 419, 420, 556, 563, 585, 604] [111, 236, 306, 491, 541, 611, 639, 647] [218, 238, 285, 337, 401, 413, 422, 530] [114, 171, 242, 268, 428, 452, 585, 617] [249, 311, 386, 435, 436, 498, 515, 567] [119, 215, 231, 313, 415, 498, 538, 601] [208, 252, 281, 360, 387, 431, 464, 480] [254, 331, 366, 441, 524, 549, 572, 634] [121, 255, 437, 569, 578, 583, 633, 634] [124, 259, 293, 444, 466, 477, 574, 635] [126, 262, 296, 432, 443, 474, 475, 593] [148, 178, 202, 239, 341, 379, 448, 559] [169, 264, 329, 404, 449, 503, 523, 605] [128, 265, 450, 559, 593, 632, 641, 647] [232, 275, 396, 402, 416, 486, 575, 628] [199, 278, 370, 417, 460, 525, 596, 635] [279, 324, 371, 379, 488, 515, 516, 610] [138, 220, 282, 363, 369, 410, 516, 553] [235, 287, 356, 393, 421, 460, 531, 586] [213, 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Code ID 648-326-6 · download JSON · raw on GitHub