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