Graph forms
for C4 [ 512, 166 ] = UG(ATD[512,338])
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On this page are computer-accessible forms for the graph C4[ 512, 166 ] =
UG(ATD[512,338]).
(I) Following is a form readable by MAGMA:
g:=Graph<512|{ {40, 41}, {510, 511}, {418, 419}, {172, 173}, {154, 155}, {68,
69}, {56, 57}, {192, 193}, {278, 279}, {284, 285}, {296, 297}, {298, 299}, {361,
363}, {472, 474}, {384, 386}, {1, 2}, {485, 486}, {461, 462}, {184, 187}, {132,
135}, {13, 14}, {205, 206}, {241, 242}, {1, 5}, {411, 415}, {378, 382}, {3, 7},
{2, 6}, {24, 29}, {131, 134}, {10, 12}, {498, 500}, {491, 493}, {458, 460},
{362, 364}, {123, 125}, {194, 196}, {32, 39}, {347, 348}, {139, 140}, {96, 103},
{219, 220}, {235, 236}, {264, 271}, {288, 295}, {502, 510}, {66, 75}, {70, 79},
{263, 270}, {68, 78}, {485, 495}, {368, 378}, {23, 28}, {470, 477}, {437, 446},
{85, 94}, {65, 74}, {53, 62}, {273, 282}, {274, 281}, {4, 8}, {38, 42}, {133,
136}, {146, 159}, {7, 9}, {374, 376}, {323, 333}, {86, 88}, {263, 265}, {67,
76}, {386, 402}, {487, 503}, {480, 496}, {419, 435}, {488, 505}, {2, 16}, {459,
473}, {449, 467}, {333, 351}, {331, 345}, {7, 21}, {6, 20}, {3, 17}, {196, 214},
{11, 24}, {489, 506}, {358, 373}, {352, 371}, {324, 343}, {138, 153}, {203,
216}, {10, 30}, {458, 478}, {421, 433}, {334, 346}, {130, 150}, {97, 117}, {76,
88}, {64, 84}, {15, 27}, {14, 26}, {13, 25}, {192, 212}, {288, 308}, {291, 311},
{456, 477}, {4, 18}, {5, 19}, {297, 319}, {71, 80}, {484, 499}, {197, 210},
{206, 214}, {294, 318}, {293, 316}, {198, 220}, {424, 434}, {225, 251}, {226,
248}, {267, 272}, {481, 506}, {171, 183}, {492, 496}, {321, 349}, {10, 23},
{457, 468}, {8, 22}, {452, 474}, {165, 187}, {200, 215}, {463, 464}, {364, 371},
{355, 380}, {292, 315}, {299, 308}, {134, 166}, {475, 507}, {468, 500}, {142,
174}, {130, 163}, {329, 363}, {479, 509}, {398, 428}, {140, 175}, {388, 423},
{16, 53}, {26, 63}, {24, 61}, {18, 55}, {8, 46}, {9, 47}, {17, 54}, {414, 441},
{146, 181}, {25, 62}, {207, 231}, {476, 500}, {412, 436}, {275, 314}, {351,
374}, {6, 44}, {479, 501}, {466, 504}, {143, 165}, {84, 126}, {7, 45}, {19, 56},
{405, 446}, {347, 368}, {23, 60}, {328, 356}, {20, 57}, {465, 508}, {145, 188},
{22, 59}, {5, 43}, {387, 429}, {21, 58}, {159, 176}, {211, 252}, {153, 169},
{467, 483}, {415, 431}, {158, 174}, {157, 173}, {156, 172}, {154, 170}, {200,
248}, {286, 302}, {451, 498}, {270, 316}, {478, 492}, {456, 506}, {455, 501},
{339, 353}, {137, 186}, {276, 295}, {144, 164}, {151, 163}, {149, 161}, {346,
367}, {460, 505}, {457, 510}, {475, 483}, {31, 38}, {470, 495}, {136, 177},
{259, 314}, {10, 48}, {413, 423}, {11, 49}, {15, 52}, {473, 482}, {409, 418},
{75, 112}, {92, 96}, {402, 430}, {192, 252}, {257, 317}, {260, 312}, {14, 51},
{471, 490}, {349, 352}, {277, 296}, {12, 50}, {152, 166}, {27, 37}, {196, 250},
{134, 185}, {274, 301}, {283, 292}, {34, 98}, {435, 499}, {389, 453}, {317,
381}, {179, 243}, {178, 242}, {191, 254}, {432, 497}, {391, 454}, {43, 105},
{275, 337}, {438, 501}, {291, 359}, {403, 470}, {425, 492}, {408, 477}, {38,
97}, {181, 253}, {44, 101}, {54, 127}, {163, 233}, {437, 511}, {417, 491}, {397,
454}, {443, 496}, {440, 499}, {445, 497}, {31, 81}, {430, 480}, {406, 472},
{384, 462}, {164, 234}, {48, 127}, {439, 504}, {184, 247}, {285, 338}, {41,
121}, {445, 493}, {385, 465}, {164, 244}, {42, 122}, {45, 124}, {446, 495}, {47,
126}, {282, 331}, {32, 114}, {37, 119}, {36, 118}, {33, 115}, {46, 125}, {433,
482}, {276, 327}, {51, 102}, {34, 116}, {35, 117}, {274, 324}, {44, 123}, {432,
487}, {21, 77}, {436, 492}, {35, 123}, {287, 326}, {27, 65}, {27, 64}, {281,
325}, {282, 326}, {31, 66}, {431, 498}, {168, 246}, {270, 336}, {39, 120}, {40,
72}, {41, 73}, {278, 374}, {422, 455}, {32, 67}, {392, 491}, {36, 71}, {61, 89},
{394, 494}, {33, 68}, {403, 502}, {35, 70}, {283, 382}, {286, 379}, {281, 383},
{34, 69}, {428, 453}, {298, 320}, {440, 466}, {426, 448}, {157, 246}, {425,
450}, {388, 495}, {319, 340}, {303, 324}, {150, 250}, {447, 467}, {303, 322},
{30, 112}, {31, 113}, {305, 350}, {427, 452}, {385, 494}, {393, 505}, {183,
198}, {28, 110}, {176, 194}, {32, 82}, {29, 111}, {262, 372}, {16, 99}, {443,
456}, {435, 448}, {422, 469}, {182, 197}, {24, 107}, {20, 103}, {141, 249},
{414, 490}, {17, 100}, {442, 463}, {38, 83}, {25, 108}, {19, 102}, {18, 101},
{444, 459}, {26, 109}, {304, 327}, {390, 510}, {429, 469}, {404, 494}, {177,
202}, {446, 453}, {406, 493}, {290, 345}, {187, 199}, {21, 104}, {23, 106},
{387, 509}, {22, 105}, {392, 503}, {128, 255}, {25, 153}, {320, 448}, {127,
254}, {381, 508}, {377, 507}, {273, 405}, {326, 450}, {93, 216}, {287, 409},
{304, 438}, {272, 407}, {345, 478}, {339, 468}, {301, 421}, {313, 433}, {40,
161}, {325, 460}, {316, 437}, {45, 167}, {327, 461}, {94, 210}, {354, 494},
{340, 472}, {109, 225}, {256, 396}, {114, 255}, {277, 408}, {108, 226}, {380,
498}, {115, 253}, {257, 399}, {90, 213}, {113, 254}, {106, 250}, {107, 251},
{309, 421}, {34, 179}, {363, 506}, {109, 252}, {104, 249}, {90, 200}, {341,
455}, {340, 454}, {319, 429}, {111, 253}, {280, 395}, {315, 424}, {52, 160},
{343, 451}, {60, 168}, {96, 245}, {318, 427}, {98, 247}, {87, 193}, {310, 416},
{97, 246}, {381, 490}, {258, 405}, {118, 238}, {284, 389}, {360, 497}, {65,
219}, {376, 482}, {318, 420}, {101, 255}, {69, 223}, {68, 222}, {37, 190}, {96,
252}, {357, 505}, {356, 504}, {66, 220}, {102, 248}, {89, 199}, {67, 221}, {291,
444}, {5, 165}, {326, 486}, {325, 485}, {324, 484}, {323, 483}, {322, 482},
{265, 425}, {305, 401}, {81, 240}, {356, 453}, {320, 481}, {113, 208}, {300,
398}, {91, 248}, {93, 249}, {317, 408}, {70, 224}, {79, 232}, {308, 412}, {72,
225}, {78, 231}, {76, 229}, {74, 227}, {273, 440}, {275, 442}, {90, 240}, {361,
451}, {121, 211}, {91, 241}, {73, 226}, {95, 244}, {77, 230}, {77, 224}, {92,
242}, {360, 454}, {93, 243}, {304, 414}, {75, 228}, {278, 441}, {306, 386}, {49,
128}, {379, 458}, {355, 466}, {266, 443}, {269, 444}, {301, 412}, {54, 132},
{347, 489}, {55, 133}, {264, 442}, {303, 413}, {50, 129}, {378, 457}, {63, 140},
{59, 136}, {60, 137}, {354, 471}, {338, 487}, {72, 253}, {62, 139}, {18, 164},
{103, 209}, {89, 239}, {53, 131}, {52, 130}, {47, 152}, {61, 138}, {81, 233},
{86, 238}, {85, 237}, {84, 236}, {83, 235}, {82, 234}, {99, 218}, {362, 464},
{105, 210}, {289, 410}, {58, 135}, {312, 389}, {307, 398}, {293, 411}, {57,
134}, {383, 448}, {343, 488}, {95, 159}, {90, 155}, {375, 438}, {92, 157}, {84,
151}, {368, 435}, {336, 403}, {93, 158}, {366, 426}, {83, 150}, {351, 410}, {91,
156}, {262, 449}, {104, 160}, {272, 472}, {377, 434}, {65, 141}, {338, 414},
{67, 143}, {66, 142}, {85, 152}, {358, 427}, {103, 170}, {87, 154}, {348, 402},
{86, 153}, {357, 426}, {100, 180}, {367, 447}, {71, 149}, {263, 468}, {309,
486}, {331, 415}, {69, 144}, {372, 417}, {344, 397}, {71, 146}, {261, 467}, {70,
145}, {350, 390}, {369, 424}, {268, 470}, {359, 445}, {269, 471}, {42, 241},
{87, 140}, {72, 147}, {316, 480}, {73, 148}, {370, 431}, {367, 434}, {264, 469},
{359, 441}, {334, 401}, {335, 400}, {94, 190}, {112, 145}, {366, 399}, {349,
444}, {43, 201}, {51, 209}, {50, 208}, {47, 205}, {46, 204}, {372, 407}, {55,
211}, {315, 479}, {61, 217}, {60, 216}, {63, 218}, {41, 207}, {312, 478}, {45,
203}, {44, 202}, {53, 210}, {383, 408}, {76, 171}, {110, 132}, {365, 391}, {310,
476}, {30, 245}, {382, 405}, {328, 419}, {56, 212}, {352, 396}, {333, 417},
{332, 416}, {119, 155}, {59, 215}, {58, 214}, {57, 213}, {92, 177}, {365, 384},
{342, 443}, {125, 147}, {345, 439}, {337, 447}, {307, 477}, {331, 420}, {336,
416}, {28, 237}, {321, 432}, {83, 162}, {64, 178}, {336, 418}, {297, 475}, {78,
189}, {342, 421}, {115, 128}, {260, 503}, {64, 180}, {370, 390}, {352, 404},
{332, 440}, {349, 424}, {354, 407}, {298, 476}, {333, 442}, {350, 425}, {339,
420}, {35, 218}, {80, 169}, {288, 473}, {85, 175}, {289, 474}, {348, 423}, {330,
433}, {124, 129}, {330, 439}, {329, 436}, {48, 206}, {344, 422}, {49, 207},
{258, 508}, {241, 497}, {99, 354}, {133, 391}, {203, 456}, {74, 334}, {109,
360}, {161, 420}, {111, 362}, {80, 342}, {100, 355}, {110, 361}, {206, 457},
{46, 295}, {188, 438}, {108, 359}, {104, 356}, {48, 317}, {107, 358}, {202,
455}, {106, 357}, {221, 461}, {222, 462}, {223, 463}, {244, 484}, {217, 459},
{89, 330}, {219, 460}, {116, 365}, {119, 366}, {50, 296}, {113, 363}, {208,
458}, {40, 308}, {82, 332}, {114, 364}, {220, 450}, {245, 469}, {121, 344}, {73,
365}, {79, 360}, {228, 451}, {52, 285}, {171, 386}, {169, 384}, {94, 375}, {16,
314}, {174, 388}, {91, 369}, {43, 256}, {170, 385}, {239, 452}, {237, 449}, {8,
294}, {173, 387}, {160, 399}, {167, 392}, {199, 488}, {4, 310}, {181, 391},
{180, 390}, {101, 337}, {188, 392}, {17, 292}, {229, 464}, {191, 393}, {178,
389}, {13, 309}, {58, 258}, {51, 267}, {176, 393}, {232, 465}, {235, 466}, {172,
406}, {2, 313}, {175, 404}, {14, 306}, {112, 305}, {208, 401}, {234, 427}, {116,
310}, {222, 413}, {233, 426}, {118, 306}, {161, 484}, {211, 406}, {231, 416},
{195, 395}, {122, 307}, {232, 417}, {111, 293}, {192, 394}, {56, 371}, {29,
339}, {121, 311}, {247, 423}, {221, 396}, {179, 481}, {217, 395}, {223, 397},
{9, 346}, {122, 302}, {204, 410}, {147, 452}, {79, 279}, {12, 341}, {106, 307},
{87, 269}, {246, 428}, {171, 502}, {187, 486}, {205, 400}, {209, 396}, {107,
309}, {124, 290}, {120, 294}, {148, 459}, {168, 503}, {6, 358}, {240, 400},
{243, 402}, {251, 410}, {237, 399}, {242, 401}, {190, 471}, {249, 403}, {102,
269}, {105, 261}, {178, 479}, {216, 437}, {22, 376}, {209, 447}, {224, 398},
{201, 422}, {204, 445}, {255, 397}, {199, 436}, {108, 280}, {117, 257}, {116,
256}, {239, 411}, {119, 258}, {127, 266}, {125, 264}, {26, 364}, {225, 407},
{226, 404}, {126, 265}, {219, 428}, {240, 394}, {110, 277}, {124, 263}, {120,
259}, {129, 509}, {197, 441}, {229, 409}, {123, 262}, {122, 260}, {130, 508},
{227, 355}, {156, 285}, {158, 287}, {33, 419}, {169, 299}, {148, 279}, {157,
286}, {152, 283}, {144, 276}, {145, 277}, {15, 394}, {147, 278}, {137, 268},
{126, 507}, {212, 337}, {235, 366}, {42, 429}, {155, 284}, {136, 271}, {196,
332}, {135, 270}, {141, 260}, {81, 475}, {194, 328}, {128, 267}, {167, 300},
{129, 268}, {151, 282}, {149, 280}, {231, 362}, {236, 353}, {176, 318}, {150,
281}, {215, 344}, {39, 439}, {186, 298}, {197, 341}, {198, 342}, {98, 499},
{185, 296}, {182, 292}, {183, 293}, {190, 300}, {191, 301}, {200, 346}, {37,
432}, {202, 351}, {13, 411}, {181, 291}, {180, 290}, {189, 299}, {214, 320},
{215, 321}, {1, 409}, {177, 297}, {117, 493}, {4, 413}, {218, 323}, {138, 272},
{141, 273}, {143, 275}, {142, 274}, {184, 295}, {228, 379}, {254, 353}, {184,
280}, {250, 347}, {205, 361}, {78, 489}, {77, 487}, {82, 511}, {49, 415}, {1,
430}, {115, 476}, {156, 300}, {186, 266}, {146, 289}, {188, 271}, {224, 341},
{75, 509}, {142, 312}, {86, 480}, {195, 373}, {243, 325}, {80, 488}, {201, 369},
{230, 350}, {88, 481}, {182, 271}, {245, 335}, {172, 279}, {204, 375}, {236,
343}, {15, 434}, {159, 288}, {185, 262}, {137, 329}, {193, 257}, {3, 449}, {39,
485}, {191, 380}, {131, 327}, {195, 261}, {232, 302}, {74, 387}, {174, 357},
{28, 465}, {54, 507}, {36, 489}, {247, 313}, {189, 370}, {36, 500}, {213, 261},
{158, 330}, {239, 314}, {168, 383}, {162, 379}, {167, 382}, {238, 311}, {120,
418}, {160, 378}, {20, 463}, {166, 381}, {162, 377}, {88, 388}, {114, 430},
{189, 353}, {19, 462}, {201, 276}, {33, 511}, {151, 328}, {163, 380}, {97, 385},
{148, 375}, {154, 377}, {198, 290}, {221, 313}, {63, 474}, {166, 323}, {144,
374}, {186, 348}, {12, 491}, {165, 322}, {62, 473}, {55, 464}, {99, 395}, {3,
490}, {222, 311}, {118, 412}, {227, 265}, {230, 268}, {98, 393}, {212, 319},
{217, 306}, {131, 367}, {173, 321}, {149, 376}, {162, 335}, {194, 303}, {207,
289}, {213, 315}, {228, 266}, {229, 267}, {238, 256}, {193, 302}, {95, 431},
{179, 322}, {195, 304}, {100, 400}, {133, 369}, {132, 368}, {135, 370}, {234,
287}, {59, 461}, {185, 335}, {233, 286}, {244, 259}, {182, 334}, {251, 259},
{138, 371}, {223, 294}, {143, 373}, {203, 305}, {11, 496}, {9, 501}, {11, 502},
{175, 338}, {30, 483}, {230, 283}, {139, 373}, {183, 329}, {170, 340}, {139,
372}, {227, 284}, {29, 512}, {95, 512}, {450, 512}, {504, 512} }>;
(II) A more general form is to represent the graph as the orbit of {40, 41}
under the group generated by the following permutations:
a: (2, 409)(3, 382)(4, 13)(5, 430)(6, 287)(7, 283)(8, 411)(9, 230)(10, 284)(11,
276)(12, 227)(14, 413)(15, 408)(16, 418)(17, 167)(18, 309)(19, 402)(20, 158)(21,
152)(22, 293)(23, 155)(24, 144)(25, 310)(26, 303)(27, 277)(28, 119)(29, 374)(30,
389)(31, 157)(32, 143)(33, 395)(34, 138)(35, 151)(36, 291)(37, 110)(38, 286)(39,
275)(41, 308)(42, 379)(43, 480)(44, 326)(45, 292)(46, 415)(47, 77)(48, 285)(49,
295)(50, 74)(51, 423)(52, 317)(53, 336)(54, 300)(55, 421)(56, 243)(57, 93)(58,
85)(59, 183)(60, 90)(61, 69)(62, 416)(63, 194)(64, 145)(65, 296)(66, 92)(68,
217)(70, 84)(71, 181)(72, 161)(73, 299)(75, 242)(76, 221)(78, 459)(79, 236)(80,
391)(81, 246)(82, 373)(83, 302)(86, 256)(87, 250)(88, 396)(89, 223)(91, 266)(94,
135)(95, 410)(96, 142)(97, 233)(98, 272)(99, 419)(100, 392)(101, 486)(102,
348)(103, 174)(104, 166)(105, 316)(106, 154)(107, 164)(108, 476)(109, 324)(111,
376)(112, 178)(113, 173)(114, 165)(115, 280)(116, 153)(117, 163)(118, 311)(120,
314)(121, 412)(122, 162)(123, 282)(124, 182)(125, 331)(126, 224)(127, 156)(128,
184)(129, 334)(130, 257)(131, 403)(132, 190)(133, 342)(134, 249)(136, 198)(137,
200)(139, 332)(140, 196)(141, 185)(147, 420)(148, 189)(149, 253)(150, 193)(159,
289)(160, 381)(168, 240)(169, 365)(170, 357)(171, 461)(172, 254)(175, 214)(176,
474)(177, 220)(179, 371)(180, 188)(186, 248)(187, 255)(191, 406)(192, 281)(195,
511)(197, 263)(199, 397)(201, 496)(202, 450)(203, 315)(204, 431)(205, 487)(206,
338)(207, 288)(208, 387)(209, 388)(210, 270)(211, 301)(212, 325)(213, 216)(215,
329)(218, 328)(219, 297)(222, 306)(225, 484)(226, 298)(228, 241)(229, 313)(231,
473)(232, 235)(234, 358)(237, 258)(239, 294)(244, 251)(245, 312)(247, 267)(252,
274)(260, 335)(261, 437)(262, 273)(264, 345)(265, 341)(268, 346)(269, 347)(271,
290)(278, 339)(279, 353)(304, 510)(305, 479)(307, 377)(318, 452)(319, 460)(320,
404)(321, 363)(322, 364)(323, 356)(327, 502)(330, 463)(333, 504)(337, 485)(340,
505)(343, 360)(344, 436)(349, 506)(350, 501)(351, 512)(352, 481)(354, 435)(355,
491)(359, 500)(361, 432)(362, 482)(366, 465)(367, 470)(368, 471)(369, 443)(370,
375)(372, 440)(378, 490)(380, 493)(383, 394)(385, 426)(386, 462)(390, 438)(393,
472)(398, 507)(399, 508)(400, 503)(401, 509)(405, 449)(407, 499)(414, 457)(417,
466)(422, 492)(424, 456)(425, 455)(428, 475)(429, 458)(433, 464)(434, 477)(439,
442)(441, 468)(444, 489)(445, 498)(446, 467)(447, 495)(448, 494)(451, 497)(453,
483)(454, 488)(469, 478) (III) Last is Groups&Graphs. Copy everything between (not including)
the lines of asterisks into a plain text file and save it as "graph.txt". Then
launch G&G (Groups&Graphs) and select Read Text from the File menu.
**************
&Graph **************
b: (2, 5)(3, 9)(4, 13)(6, 19)(8, 25)(10, 27)(11, 33)(12, 37)(14, 18)(15, 30)(16,
43)(17, 47)(20, 56)(21, 45)(22, 62)(23, 65)(24, 68)(26, 55)(28, 74)(29, 78)(31,
83)(32, 76)(34, 89)(35, 91)(36, 95)(39, 88)(41, 72)(42, 97)(44, 102)(46,
108)(48, 64)(49, 115)(50, 119)(51, 101)(52, 112)(53, 105)(54, 126)(58, 124)(59,
139)(60, 141)(61, 69)(63, 133)(66, 150)(70, 156)(71, 159)(73, 147)(75, 130)(77,
167)(79, 172)(80, 176)(81, 162)(82, 171)(84, 127)(85, 182)(86, 120)(87, 177)(90,
185)(92, 193)(94, 197)(96, 192)(98, 199)(99, 201)(100, 205)(103, 212)(104,
203)(106, 219)(107, 222)(109, 211)(110, 227)(111, 231)(113, 235)(114, 229)(116,
239)(117, 241)(118, 244)(121, 225)(122, 246)(123, 248)(125, 226)(129, 258)(131,
261)(132, 265)(134, 213)(135, 263)(136, 140)(137, 273)(138, 223)(142, 281)(143,
221)(144, 217)(145, 285)(148, 278)(149, 288)(151, 266)(152, 292)(153, 294)(154,
297)(155, 296)(157, 302)(158, 243)(160, 305)(161, 308)(163, 228)(164, 306)(165,
313)(166, 315)(168, 260)(169, 318)(170, 319)(173, 232)(174, 325)(175, 271)(178,
317)(179, 330)(180, 206)(181, 289)(183, 332)(186, 282)(187, 247)(188, 338)(189,
339)(190, 341)(191, 343)(194, 342)(195, 327)(196, 198)(200, 262)(202, 269)(204,
359)(207, 253)(208, 366)(209, 337)(214, 290)(215, 372)(216, 249)(218, 369)(220,
250)(224, 300)(230, 382)(233, 379)(234, 386)(236, 254)(237, 334)(238, 259)(240,
335)(242, 257)(245, 394)(251, 311)(255, 267)(256, 314)(264, 404)(268, 405)(272,
397)(275, 396)(276, 395)(277, 284)(280, 295)(287, 402)(291, 410)(293, 416)(298,
331)(299, 420)(301, 324)(303, 421)(307, 428)(309, 413)(310, 411)(312, 383)(316,
336)(320, 345)(321, 417)(322, 433)(323, 424)(326, 348)(328, 443)(329, 440)(333,
349)(344, 407)(346, 449)(347, 450)(350, 378)(351, 444)(352, 442)(354, 422)(355,
361)(356, 456)(357, 460)(358, 462)(360, 406)(363, 466)(364, 464)(365, 452)(367,
467)(368, 425)(370, 468)(371, 463)(373, 461)(374, 459)(375, 441)(376, 473)(377,
475)(380, 451)(381, 479)(384, 427)(385, 429)(387, 465)(388, 485)(389, 408)(390,
457)(391, 474)(392, 487)(393, 488)(399, 401)(403, 437)(409, 430)(412, 484)(414,
438)(415, 476)(418, 480)(419, 496)(423, 486)(426, 458)(431, 500)(432, 491)(434,
483)(435, 492)(436, 499)(439, 481)(446, 470)(448, 478)(453, 477)(454, 472)(455,
471)(469, 494)(489, 512)(490, 501)(493, 497)(502, 511)(504, 506)(508, 509)
c: (1, 2, 6, 20, 57, 134, 185, 335, 400, 205, 361, 451, 498, 500, 36, 71, 146,
181, 291, 359, 445, 497, 432, 487, 503, 260, 141, 249, 93, 158, 287, 409)(3, 10,
31, 84, 135, 186, 301, 420, 231, 384, 473, 147, 211, 248, 94, 70, 157, 284, 382,
477, 460, 504, 511, 88, 187, 259, 255, 396, 195, 333, 319, 434)(4, 14, 22, 63,
136, 87, 182, 257, 401, 366, 350, 448, 492, 499, 11, 34, 61, 144, 272, 201, 354,
455, 385, 479, 508, 129, 150, 290, 196, 183, 303, 411)(5, 16, 44, 103, 213, 166,
296, 162, 100, 206, 363, 343, 431, 476, 118, 149, 289, 391, 444, 441, 493, 241,
37, 77, 168, 312, 273, 403, 243, 330, 234, 229)(7, 23, 66, 151, 270, 348, 421,
318, 362, 462, 62, 125, 252, 200, 85, 145, 286, 227, 378, 456, 505, 512, 33, 86,
184, 251, 397, 352, 304, 417, 429, 15)(8, 26, 59, 140, 271, 193, 334, 399, 305,
426, 425, 435, 496, 98, 24, 69, 138, 276, 407, 422, 494, 501, 465, 509, 130,
124, 250, 198, 194, 293, 413, 13)(9, 28, 75, 163, 263, 347, 342, 176, 111, 222,
25, 46, 109, 215, 175, 188, 302, 74, 160, 203, 357, 450, 419, 480, 247, 107,
223, 371, 327, 372, 469, 394)(12, 38, 64, 58, 137, 274, 331, 416, 386, 482, 452,
55, 102, 210, 35, 92, 155, 283, 408, 458, 466, 510, 481, 199, 244, 128, 256,
395, 351, 340, 424, 490)(17, 48, 113, 236, 370, 298, 412, 161, 207, 365, 459,
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320, 436, 484, 49, 116, 217, 374, 472, 369, 471, 341, 97, 178, 258, 268, 281,
345, 332, 171, 322, 239)(19, 53, 123, 96, 90, 152, 277, 379, 355, 457, 506, 488,
95, 115, 238, 280, 410, 454, 349, 414, 491, 42, 27, 21, 60, 142, 282, 336, 402,
433, 427, 464)(29, 68, 153, 295, 225, 344, 404, 438, 232, 387, 52, 45, 106, 220,
328, 316, 423, 309, 294, 364, 461, 139, 264, 192, 346, 237, 112, 233, 265, 368,
443, 393)(30, 81, 126, 132, 266, 191, 339, 78, 169, 288, 72, 121, 226, 375, 79,
173, 285, 167, 307, 219, 356, 437, 388, 486, 120, 114, 221, 373, 442, 212, 367,
449)(32, 67, 143, 275, 337, 447, 467, 483, 475, 507, 54, 127, 254, 353, 189,
299, 308, 40, 41, 73, 148, 279, 172, 156, 300, 398, 428, 453, 446, 495, 485,
39)(43, 99, 202, 170, 315, 381, 50, 83, 180, 214, 329, 324, 415, 310, 306, 376,
474, 133, 269, 197, 117, 242, 119, 230, 383, 478, 440, 502, 179, 89, 164,
267)(47, 110, 228, 380, 468, 489, 80, 159, 253, 311, 108, 204, 360, 321, 338,
392, 122, 65, 104, 216, 174, 326, 418, 430, 313, 358, 463, 56, 131, 262, 245,
240)
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0