Invariant Table Check a Knot Higher Crossing Crossref Virtual Knots Please cite FlatKnotInfo

Flat knot 4.8

Min(phi) over symmetries of the knot is: [-2,0,1,1,0,2,2,0,1,0]
Flat knots (up to 7 crossings) with same phi are :['4.8', '7.44862']
Arrow polynomial of the knot is: -2K1*2 + K2 + 2
Flat knots (up to 7 crossings) with same arrow polynomial are :['4.6', '4.8', '6.780', '6.804', '6.914', '6.931', '6.946', '6.960', '6.1002', '6.1016', '6.1019', '6.1051', '6.1058', '6.1078', '6.1102', '6.1115', '6.1217', '6.1294', '6.1306', '6.1317', '6.1321', '6.1324', '6.1336', '6.1377', '6.1416', '6.1420', '6.1427', '6.1429', '6.1434', '6.1436', '6.1437', '6.1439', '6.1441', '6.1444', '6.1450', '6.1451', '6.1458', '6.1459', '6.1477', '6.1482', '6.1490', '6.1503', '6.1504', '6.1511', '6.1521', '6.1547', '6.1560', '6.1561', '6.1562', '6.1597', '6.1598', '6.1600', '6.1601', '6.1608', '6.1620', '6.1622', '6.1624', '6.1634', '6.1635', '6.1637', '6.1638', '6.1713', '6.1725', '6.1758', '6.1846', '6.1933', '6.1944', '6.1949', '6.1950', '6.1951']
Outer characteristic polynomial of the knot is: t^5+13t^3+6t
Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['4.8', '7.44862']
2-strand cable arrow polynomial of the knot is: -96K14 - 112K1*2K2*2 + 248K1*2K2 - 172K12 + 184K1K2K3 + 24K1K3K4 - 8K2*4 + 16K2*2K4 - 144K22 - 76K3*2 - 18K4**2 + 152
Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['4.8']
Virtual knots (up to 6 crossings) projecting to this knot are :'vk4.11', 'vk4.17', 'vk4.19', 'vk4.29', 'vk4.34', 'vk4.49', 'vk4.57', 'vk4.70', 'vk6.3531', 'vk6.3534', 'vk6.3539', 'vk6.3542', 'vk6.3679', 'vk6.3682', 'vk6.3687', 'vk6.3690', 'vk6.3711', 'vk6.3714', 'vk6.3719', 'vk6.3722', 'vk6.3775', 'vk6.3778', 'vk6.3783', 'vk6.3786', 'vk6.3871', 'vk6.3874', 'vk6.3879', 'vk6.3882', 'vk6.3903', 'vk6.3906', 'vk6.3911', 'vk6.3914', 'vk6.3967', 'vk6.3970', 'vk6.3975', 'vk6.3978', 'vk6.4899', 'vk6.4903', 'vk6.4919', 'vk6.4922', 'vk6.4927', 'vk6.4930', 'vk6.4967', 'vk6.4970', 'vk6.4975', 'vk6.4978', 'vk6.5011', 'vk6.5015', 'vk6.5247', 'vk6.5250', 'vk6.5255', 'vk6.5258', 'vk6.5735', 'vk6.5741', 'vk6.5743', 'vk6.5749', 'vk6.5768', 'vk6.5774', 'vk6.5776', 'vk6.5782', 'vk6.6047', 'vk6.6050', 'vk6.6053', 'vk6.6055', 'vk6.6058', 'vk6.6061', 'vk6.6079', 'vk6.6082', 'vk6.6087', 'vk6.6090', 'vk6.6111', 'vk6.6117', 'vk6.6119', 'vk6.6125', 'vk6.6143', 'vk6.6146', 'vk6.6151', 'vk6.6154', 'vk6.6175', 'vk6.6181', 'vk6.6183', 'vk6.6189', 'vk6.6207', 'vk6.6210', 'vk6.6213', 'vk6.6215', 'vk6.6218', 'vk6.6221', 'vk6.6287', 'vk6.6293', 'vk6.6295', 'vk6.6301', 'vk6.6447', 'vk6.6453', 'vk6.6455', 'vk6.6461', 'vk6.6503', 'vk6.6506', 'vk6.6511', 'vk6.6514', 'vk6.6566', 'vk6.6570', 'vk6.6600', 'vk6.6606', 'vk6.6608', 'vk6.6614', 'vk6.6648', 'vk6.6654', 'vk6.6656', 'vk6.6662', 'vk6.6678', 'vk6.6682', 'vk6.6728', 'vk6.6734', 'vk6.6736', 'vk6.6742', 'vk6.6868', 'vk6.6874', 'vk6.6876', 'vk6.6882', 'vk6.6915', 'vk6.6918', 'vk6.6923', 'vk6.6926', 'vk6.6947', 'vk6.6950', 'vk6.6955', 'vk6.6958', 'vk6.7075', 'vk6.7078', 'vk6.7083', 'vk6.7086', 'vk6.7107', 'vk6.7110', 'vk6.7115', 'vk6.7118', 'vk6.7167', 'vk6.7170', 'vk6.7175', 'vk6.7178', 'vk6.7251', 'vk6.7254', 'vk6.7259', 'vk6.7262', 'vk6.7283', 'vk6.7286', 'vk6.7291', 'vk6.7294', 'vk6.7343', 'vk6.7346', 'vk6.7351', 'vk6.7354', 'vk6.7802', 'vk6.7808', 'vk6.7810', 'vk6.7816', 'vk6.7835', 'vk6.7841', 'vk6.7843', 'vk6.7849', 'vk6.8086', 'vk6.8090', 'vk6.8122', 'vk6.8128', 'vk6.8130', 'vk6.8136', 'vk6.8170', 'vk6.8176', 'vk6.8178', 'vk6.8184', 'vk6.8198', 'vk6.8202', 'vk6.8250', 'vk6.8256', 'vk6.8258', 'vk6.8264', 'vk6.8410', 'vk6.8416', 'vk6.8418', 'vk6.8424', 'vk6.8462', 'vk6.8465', 'vk6.8468', 'vk6.8470', 'vk6.8473', 'vk6.8476', 'vk6.8497', 'vk6.8500', 'vk6.8505', 'vk6.8508', 'vk6.8526', 'vk6.8532', 'vk6.8534', 'vk6.8540', 'vk6.8561', 'vk6.8564', 'vk6.8569', 'vk6.8572', 'vk6.8590', 'vk6.8596', 'vk6.8598', 'vk6.8604', 'vk6.8621', 'vk6.8624', 'vk6.8627', 'vk6.8629', 'vk6.8632', 'vk6.8635', 'vk6.8701', 'vk6.8707', 'vk6.8709', 'vk6.8715', 'vk6.8831', 'vk6.8837', 'vk6.8839', 'vk6.8845', 'vk6.8884', 'vk6.8887', 'vk6.8892', 'vk6.8895', 'vk6.9465', 'vk6.9469', 'vk6.9486', 'vk6.9489', 'vk6.9494', 'vk6.9497', 'vk6.9534', 'vk6.9537', 'vk6.9542', 'vk6.9545', 'vk6.9577', 'vk6.9581', 'vk6.9800', 'vk6.9803', 'vk6.9808', 'vk6.9811', 'vk6.11040', 'vk6.11120', 'vk6.11381', 'vk6.11383', 'vk6.11396', 'vk6.11398', 'vk6.11658', 'vk6.11663', 'vk6.11676', 'vk6.11681', 'vk6.12011', 'vk6.12014', 'vk6.12029', 'vk6.12032', 'vk6.12562', 'vk6.12568', 'vk6.12579', 'vk6.12585', 'vk6.12675', 'vk6.12681', 'vk6.12690', 'vk6.12696', 'vk6.13004', 'vk6.13009', 'vk6.13018', 'vk6.13023', 'vk6.13270', 'vk6.13273', 'vk6.13290', 'vk6.13293', 'vk6.13302', 'vk6.13305', 'vk6.13322', 'vk6.13325', 'vk6.13430', 'vk6.13433', 'vk6.13450', 'vk6.13453', 'vk6.13462', 'vk6.13465', 'vk6.13482', 'vk6.13485', 'vk6.13526', 'vk6.13529', 'vk6.13546', 'vk6.13549', 'vk6.13620', 'vk6.13623', 'vk6.13640', 'vk6.13643', 'vk6.13652', 'vk6.13655', 'vk6.13672', 'vk6.13675', 'vk6.13716', 'vk6.13719', 'vk6.13736', 'vk6.13739', 'vk6.13911', 'vk6.14008', 'vk6.14180', 'vk6.14276', 'vk6.14279', 'vk6.14296', 'vk6.14299', 'vk6.14308', 'vk6.14311', 'vk6.14328', 'vk6.14331', 'vk6.14372', 'vk6.14375', 'vk6.14392', 'vk6.14395', 'vk6.14421', 'vk6.14436', 'vk6.14439', 'vk6.14456', 'vk6.14459', 'vk6.14757', 'vk6.14760', 'vk6.14767', 'vk6.14770', 'vk6.14788', 'vk6.14791', 'vk6.14808', 'vk6.14811', 'vk6.15360', 'vk6.15366', 'vk6.15369', 'vk6.15375', 'vk6.15487', 'vk6.15492', 'vk6.15506', 'vk6.15509', 'vk6.15526', 'vk6.15529', 'vk6.15538', 'vk6.15541', 'vk6.15558', 'vk6.15561', 'vk6.15602', 'vk6.15605', 'vk6.15622', 'vk6.15625', 'vk6.15652', 'vk6.15666', 'vk6.15669', 'vk6.15683', 'vk6.15915', 'vk6.15920', 'vk6.15921', 'vk6.15926', 'vk6.15945', 'vk6.15948', 'vk6.15965', 'vk6.15968', 'vk6.16108', 'vk6.16725', 'vk6.16873', 'vk6.16887', 'vk6.16888', 'vk6.17399', 'vk6.17404', 'vk6.17529', 'vk6.17586', 'vk6.18029', 'vk6.18030', 'vk6.18041', 'vk6.18042', 'vk6.18772', 'vk6.18776', 'vk6.18777', 'vk6.18781', 'vk6.18858', 'vk6.19078', 'vk6.19293', 'vk6.19297', 'vk6.19307', 'vk6.19446', 'vk6.19450', 'vk6.19451', 'vk6.19455', 'vk6.19587', 'vk6.19590', 'vk6.19600', 'vk6.19740', 'vk6.19743', 'vk6.19746', 'vk6.19749', 'vk6.19794', 'vk6.19797', 'vk6.19806', 'vk6.19809', 'vk6.19842', 'vk6.19845', 'vk6.19846', 'vk6.19849', 'vk6.20748', 'vk6.20754', 'vk6.20763', 'vk6.20769', 'vk6.20797', 'vk6.20802', 'vk6.20803', 'vk6.20808', 'vk6.20926', 'vk6.20933', 'vk6.21034', 'vk6.21036', 'vk6.21041', 'vk6.21043', 'vk6.21477', 'vk6.21488', 'vk6.21491', 'vk6.21494', 'vk6.21507', 'vk6.21527', 'vk6.21540', 'vk6.21543', 'vk6.21562', 'vk6.21573', 'vk6.21734', 'vk6.21737', 'vk6.21754', 'vk6.21757', 'vk6.21842', 'vk6.21845', 'vk6.21862', 'vk6.21865', 'vk6.22193', 'vk6.22197', 'vk6.22200', 'vk6.22204', 'vk6.22338', 'vk6.22343', 'vk6.22458', 'vk6.22460', 'vk6.22463', 'vk6.22465', 'vk6.22734', 'vk6.22835', 'vk6.22864', 'vk6.22870', 'vk6.22872', 'vk6.22878', 'vk6.22897', 'vk6.22903', 'vk6.22905', 'vk6.22911', 'vk6.23010', 'vk6.23063', 'vk6.23129', 'vk6.23136', 'vk6.23174', 'vk6.23180', 'vk6.23182', 'vk6.23188', 'vk6.23254', 'vk6.23269', 'vk6.23270', 'vk6.23284', 'vk6.23286', 'vk6.23312', 'vk6.23316', 'vk6.23318', 'vk6.23359', 'vk6.23373', 'vk6.23379', 'vk6.23420', 'vk6.23424', 'vk6.23426', 'vk6.23516', 'vk6.23518', 'vk6.23567', 'vk6.23577', 'vk6.23585', 'vk6.23587', 'vk6.23608', 'vk6.23611', 'vk6.23613', 'vk6.23655', 'vk6.23660', 'vk6.23675', 'vk6.23681', 'vk6.23683', 'vk6.23689', 'vk6.23724', 'vk6.23727', 'vk6.23729', 'vk6.23851', 'vk6.23853', 'vk6.23904', 'vk6.23914', 'vk6.24470', 'vk6.24471', 'vk6.24482', 'vk6.24483', 'vk6.24894', 'vk6.24897', 'vk6.24904', 'vk6.24907', 'vk6.25355', 'vk6.25360', 'vk6.25365', 'vk6.25370', 'vk6.25486', 'vk6.25703', 'vk6.25795', 'vk6.25801', 'vk6.25803', 'vk6.25809', 'vk6.25907', 'vk6.25913', 'vk6.25924', 'vk6.25930', 'vk6.26012', 'vk6.26061', 'vk6.26107', 'vk6.26230', 'vk6.26233', 'vk6.26242', 'vk6.26245', 'vk6.26284', 'vk6.26287', 'vk6.26288', 'vk6.26291', 'vk6.26396', 'vk6.26440', 'vk6.26482', 'vk6.26483', 'vk6.26497', 'vk6.26620', 'vk6.26627', 'vk6.26675', 'vk6.26676', 'vk6.26687', 'vk6.26688', 'vk6.26729', 'vk6.26730', 'vk6.26733', 'vk6.26734', 'vk6.27362', 'vk6.27365', 'vk6.27368', 'vk6.27379', 'vk6.27382', 'vk6.27385', 'vk6.27394', 'vk6.27397', 'vk6.27411', 'vk6.27418', 'vk6.27431', 'vk6.27435', 'vk6.27442', 'vk6.27456', 'vk6.27459', 'vk6.27466', 'vk6.27470', 'vk6.27483', 'vk6.27490', 'vk6.27493', 'vk6.27496', 'vk6.27507', 'vk6.27510', 'vk6.27513', 'vk6.27554', 'vk6.27563', 'vk6.27666', 'vk6.27672', 'vk6.27683', 'vk6.27689', 'vk6.27722', 'vk6.27725', 'vk6.27742', 'vk6.27745', 'vk6.27886', 'vk6.27889', 'vk6.27906', 'vk6.27909', 'vk6.28209', 'vk6.28215', 'vk6.28226', 'vk6.28232', 'vk6.28403', 'vk6.28412', 'vk6.28475', 'vk6.28481', 'vk6.28484', 'vk6.28490', 'vk6.29006', 'vk6.29011', 'vk6.29030', 'vk6.29040', 'vk6.29045', 'vk6.29062', 'vk6.29067', 'vk6.29078', 'vk6.29088', 'vk6.29093', 'vk6.29118', 'vk6.29125', 'vk6.29212', 'vk6.29218', 'vk6.29227', 'vk6.29233', 'vk6.29634', 'vk6.29640', 'vk6.29649', 'vk6.29655', 'vk6.29715', 'vk6.29717', 'vk6.29732', 'vk6.29734', 'vk6.29758', 'vk6.29759', 'vk6.29766', 'vk6.29767', 'vk6.29921', 'vk6.29970', 'vk6.30609', 'vk6.30706', 'vk6.30981', 'vk6.30987', 'vk6.30998', 'vk6.31004', 'vk6.31110', 'vk6.31116', 'vk6.31125', 'vk6.31131', 'vk6.31202', 'vk6.32165', 'vk6.32167', 'vk6.32182', 'vk6.32184', 'vk6.32370', 'vk6.32652', 'vk6.32655', 'vk6.32666', 'vk6.32669', 'vk6.32993', 'vk6.32998', 'vk6.33007', 'vk6.33012', 'vk6.33027', 'vk6.33030', 'vk6.33039', 'vk6.33042', 'vk6.33155', 'vk6.33158', 'vk6.33167', 'vk6.33170', 'vk6.33187', 'vk6.33190', 'vk6.33199', 'vk6.33202', 'vk6.33218', 'vk6.33221', 'vk6.33230', 'vk6.33233', 'vk6.33371', 'vk6.33377', 'vk6.33379', 'vk6.33391', 'vk6.33426', 'vk6.33438', 'vk6.33443', 'vk6.33455', 'vk6.33483', 'vk6.33495', 'vk6.33498', 'vk6.33510', 'vk6.33596', 'vk6.33607', 'vk6.33730', 'vk6.33807', 'vk6.34088', 'vk6.34091', 'vk6.34100', 'vk6.34112', 'vk6.34115', 'vk6.34450', 'vk6.34453', 'vk6.34523', 'vk6.34531', 'vk6.34533', 'vk6.34548', 'vk6.34560', 'vk6.34562', 'vk6.34574', 'vk6.34785', 'vk6.34796', 'vk6.34806', 'vk6.34818', 'vk6.34820', 'vk6.34832', 'vk6.34843', 'vk6.34849', 'vk6.34851', 'vk6.34857', 'vk6.34876', 'vk6.34882', 'vk6.34884', 'vk6.34890', 'vk6.35044', 'vk6.35128', 'vk6.35163', 'vk6.35169', 'vk6.35171', 'vk6.35177', 'vk6.35195', 'vk6.35198', 'vk6.35200', 'vk6.35206', 'vk6.35276', 'vk6.35282', 'vk6.35288', 'vk6.35290', 'vk6.35296', 'vk6.35302', 'vk6.35346', 'vk6.35352', 'vk6.35354', 'vk6.35360', 'vk6.35409', 'vk6.35415', 'vk6.35429', 'vk6.35435', 'vk6.35443', 'vk6.35454', 'vk6.35463', 'vk6.35493', 'vk6.35498', 'vk6.35504', 'vk6.35595', 'vk6.35607', 'vk6.35609', 'vk6.35621', 'vk6.35659', 'vk6.35665', 'vk6.35671', 'vk6.35673', 'vk6.35679', 'vk6.35685', 'vk6.35722', 'vk6.35725', 'vk6.35728', 'vk6.35730', 'vk6.35736', 'vk6.35742', 'vk6.35773', 'vk6.35776', 'vk6.35778', 'vk6.35784', 'vk6.35831', 'vk6.35837', 'vk6.35839', 'vk6.35845', 'vk6.35863', 'vk6.35869', 'vk6.35871', 'vk6.35877', 'vk6.35887', 'vk6.35893', 'vk6.35895', 'vk6.35907', 'vk6.35942', 'vk6.35945', 'vk6.35947', 'vk6.35953', 'vk6.36052', 'vk6.36057', 'vk6.36067', 'vk6.36094', 'vk6.36097', 'vk6.36100', 'vk6.36102', 'vk6.36108', 'vk6.36114', 'vk6.36141', 'vk6.36153', 'vk6.36155', 'vk6.36167', 'vk6.36172', 'vk6.36174', 'vk6.36181', 'vk6.36183', 'vk6.36185', 'vk6.36316', 'vk6.36391', 'vk6.36431', 'vk6.36437', 'vk6.36439', 'vk6.36451', 'vk6.36530', 'vk6.36542', 'vk6.36547', 'vk6.36559', 'vk6.36607', 'vk6.36619', 'vk6.36622', 'vk6.36634', 'vk6.37587', 'vk6.37747', 'vk6.37753', 'vk6.37755', 'vk6.37767', 'vk6.37807', 'vk6.37816', 'vk6.37828', 'vk6.37833', 'vk6.37845', 'vk6.37873', 'vk6.37885', 'vk6.37888', 'vk6.37900', 'vk6.37908', 'vk6.37911', 'vk6.37913', 'vk6.37919', 'vk6.37984', 'vk6.37990', 'vk6.38001', 'vk6.38007', 'vk6.38041', 'vk6.38047', 'vk6.38056', 'vk6.38062', 'vk6.38143', 'vk6.38797', 'vk6.38808', 'vk6.38829', 'vk6.38835', 'vk6.38846', 'vk6.38852', 'vk6.38877', 'vk6.38883', 'vk6.38894', 'vk6.38900', 'vk6.38909', 'vk6.38920', 'vk6.38957', 'vk6.38963', 'vk6.38969', 'vk6.38974', 'vk6.38980', 'vk6.38986', 'vk6.39053', 'vk6.39104', 'vk6.39110', 'vk6.39121', 'vk6.39127', 'vk6.39519', 'vk6.39531', 'vk6.39536', 'vk6.39548', 'vk6.39667', 'vk6.39673', 'vk6.39684', 'vk6.39690', 'vk6.39786', 'vk6.39788', 'vk6.39801', 'vk6.39803', 'vk6.39850', 'vk6.39852', 'vk6.39857', 'vk6.39859', 'vk6.39907', 'vk6.39919', 'vk6.39924', 'vk6.39936', 'vk6.39971', 'vk6.39983', 'vk6.39988', 'vk6.40000', 'vk6.40035', 'vk6.40047', 'vk6.40052', 'vk6.40064', 'vk6.40067', 'vk6.40073', 'vk6.40079', 'vk6.40084', 'vk6.40090', 'vk6.40096', 'vk6.40162', 'vk6.40174', 'vk6.40179', 'vk6.40191', 'vk6.40257', 'vk6.40263', 'vk6.40266', 'vk6.40272', 'vk6.40317', 'vk6.40323', 'vk6.40329', 'vk6.40334', 'vk6.40340', 'vk6.40346', 'vk6.40964', 'vk6.40967', 'vk6.40970', 'vk6.40979', 'vk6.40982', 'vk6.40985', 'vk6.40995', 'vk6.40998', 'vk6.41007', 'vk6.41010', 'vk6.41024', 'vk6.41030', 'vk6.41036', 'vk6.41042', 'vk6.41052', 'vk6.41055', 'vk6.41064', 'vk6.41067', 'vk6.41079', 'vk6.41085', 'vk6.41094', 'vk6.41100', 'vk6.41110', 'vk6.41113', 'vk6.41116', 'vk6.41125', 'vk6.41128', 'vk6.41131', 'vk6.41204', 'vk6.41210', 'vk6.41216', 'vk6.41219', 'vk6.41225', 'vk6.41231', 'vk6.41360', 'vk6.41366', 'vk6.41375', 'vk6.41381', 'vk6.41395', 'vk6.41398', 'vk6.41407', 'vk6.41410', 'vk6.41744', 'vk6.41756', 'vk6.41759', 'vk6.41771', 'vk6.41908', 'vk6.41914', 'vk6.41923', 'vk6.41929', 'vk6.42017', 'vk6.42044', 'vk6.42055', 'vk6.42088', 'vk6.42100', 'vk6.42103', 'vk6.42115', 'vk6.42120', 'vk6.42124', 'vk6.42131', 'vk6.42135', 'vk6.42140', 'vk6.42250', 'vk6.42261', 'vk6.42400', 'vk6.42412', 'vk6.42418', 'vk6.42430', 'vk6.42504', 'vk6.42616', 'vk6.42725', 'vk6.42775', 'vk6.42776', 'vk6.42783', 'vk6.42784', 'vk6.42795', 'vk6.42809', 'vk6.42877', 'vk6.42891', 'vk6.42899', 'vk6.42970', 'vk6.42984', 'vk6.42992', 'vk6.43018', 'vk6.43032', 'vk6.43050', 'vk6.43062', 'vk6.43068', 'vk6.43080', 'vk6.43082', 'vk6.43093', 'vk6.43183', 'vk6.43191', 'vk6.43200', 'vk6.43287', 'vk6.43295', 'vk6.43304', 'vk6.43329', 'vk6.43340', 'vk6.43356', 'vk6.43368', 'vk6.43374', 'vk6.43386', 'vk6.43387', 'vk6.43389', 'vk6.43396', 'vk6.43400', 'vk6.43403', 'vk6.43530', 'vk6.43536', 'vk6.43541', 'vk6.43553', 'vk6.43640', 'vk6.43652', 'vk6.43657', 'vk6.43669', 'vk6.43747', 'vk6.43759', 'vk6.43762', 'vk6.43774', 'vk6.43904', 'vk6.43905', 'vk6.43906', 'vk6.43907', 'vk6.44601', 'vk6.44619', 'vk6.44658', 'vk6.44704', 'vk6.44709', 'vk6.44712', 'vk6.44727', 'vk6.44730', 'vk6.44768', 'vk6.44900', 'vk6.44907', 'vk6.44951', 'vk6.44954', 'vk6.44971', 'vk6.44974', 'vk6.45015', 'vk6.45018', 'vk6.45027', 'vk6.45030', 'vk6.45551', 'vk6.45556', 'vk6.45568', 'vk6.45571', 'vk6.45580', 'vk6.45583', 'vk6.45616', 'vk6.45619', 'vk6.45628', 'vk6.45631', 'vk6.45663', 'vk6.45668', 'vk6.45744', 'vk6.45753', 'vk6.45809', 'vk6.45894', 'vk6.45897', 'vk6.45906', 'vk6.45909', 'vk6.46130', 'vk6.46142', 'vk6.46147', 'vk6.46159', 'vk6.46346', 'vk6.46352', 'vk6.46361', 'vk6.46367', 'vk6.46408', 'vk6.46412', 'vk6.46413', 'vk6.46417', 'vk6.46463', 'vk6.46471', 'vk6.46484', 'vk6.46511', 'vk6.46523', 'vk6.46528', 'vk6.46540', 'vk6.46567', 'vk6.46579', 'vk6.46584', 'vk6.46596', 'vk6.46598', 'vk6.46600', 'vk6.46611', 'vk6.46613', 'vk6.46620', 'vk6.46671', 'vk6.46683', 'vk6.46688', 'vk6.46700', 'vk6.46795', 'vk6.46804', 'vk6.46915', 'vk6.46918', 'vk6.46927', 'vk6.46930', 'vk6.47439', 'vk6.47446', 'vk6.47774', 'vk6.47786', 'vk6.47789', 'vk6.47801', 'vk6.47921', 'vk6.47927', 'vk6.47938', 'vk6.47944', 'vk6.48052', 'vk6.48303', 'vk6.48306', 'vk6.48327', 'vk6.48330', 'vk6.48387', 'vk6.48390', 'vk6.48411', 'vk6.48414', 'vk6.48847', 'vk6.48859', 'vk6.48863', 'vk6.48866', 'vk6.48887', 'vk6.48890', 'vk6.48911', 'vk6.48914', 'vk6.48935', 'vk6.48938', 'vk6.49119', 'vk6.49122', 'vk6.49143', 'vk6.49146', 'vk6.49381', 'vk6.49384', 'vk6.49387', 'vk6.49405', 'vk6.49408', 'vk6.49411', 'vk6.49413', 'vk6.49416', 'vk6.49437', 'vk6.49440', 'vk6.49445', 'vk6.49451', 'vk6.49469', 'vk6.49475', 'vk6.49477', 'vk6.49480', 'vk6.49501', 'vk6.49504', 'vk6.49509', 'vk6.49515', 'vk6.49533', 'vk6.49539', 'vk6.49589', 'vk6.49595', 'vk6.49613', 'vk6.49619', 'vk6.49636', 'vk6.49648', 'vk6.49666', 'vk6.49672', 'vk6.49690', 'vk6.49696', 'vk6.49714', 'vk6.49720', 'vk6.49738', 'vk6.49744', 'vk6.49748', 'vk6.49760', 'vk6.49794', 'vk6.49800', 'vk6.49818', 'vk6.49824', 'vk6.49928', 'vk6.49931', 'vk6.50029', 'vk6.50032', 'vk6.50053', 'vk6.50056', 'vk6.50089', 'vk6.50092', 'vk6.50105', 'vk6.50108', 'vk6.50113', 'vk6.50116', 'vk6.50137', 'vk6.50140', 'vk6.50488', 'vk6.50491', 'vk6.50505', 'vk6.50511', 'vk6.50671', 'vk6.50683', 'vk6.50703', 'vk6.50709', 'vk6.50727', 'vk6.50733', 'vk6.50755', 'vk6.50791', 'vk6.50797', 'vk6.50815', 'vk6.50821', 'vk6.50840', 'vk6.50843', 'vk6.50846', 'vk6.50864', 'vk6.50867', 'vk6.50870', 'vk6.50875', 'vk6.50878', 'vk6.50899', 'vk6.50902', 'vk6.50904', 'vk6.50910', 'vk6.50928', 'vk6.50934', 'vk6.50935', 'vk6.50938', 'vk6.50955', 'vk6.50958', 'vk6.51008', 'vk6.51014', 'vk6.51032', 'vk6.51038', 'vk6.51147', 'vk6.51159', 'vk6.51164', 'vk6.51167', 'vk6.51188', 'vk6.51191', 'vk6.51208', 'vk6.51211', 'vk6.51228', 'vk6.51231', 'vk6.51630', 'vk6.51836', 'vk6.52457', 'vk6.53347', 'vk6.53586', 'vk6.53589', 'vk6.53606', 'vk6.53609', 'vk6.53618', 'vk6.53621', 'vk6.53638', 'vk6.53641', 'vk6.53669', 'vk6.53672', 'vk6.53741', 'vk6.53752', 'vk6.54284', 'vk6.54298', 'vk6.54301', 'vk6.54318', 'vk6.54321', 'vk6.54513', 'vk6.54516', 'vk6.54548', 'vk6.54557', 'vk6.54568', 'vk6.54664', 'vk6.54675', 'vk6.54685', 'vk6.54697', 'vk6.54699', 'vk6.54711', 'vk6.54762', 'vk6.54944', 'vk6.55043', 'vk6.55045', 'vk6.55151', 'vk6.55153', 'vk6.55162', 'vk6.55223', 'vk6.55225', 'vk6.55234', 'vk6.55267', 'vk6.55269', 'vk6.55288', 'vk6.55290', 'vk6.55398', 'vk6.55400', 'vk6.55408', 'vk6.55475', 'vk6.55477', 'vk6.55485', 'vk6.55515', 'vk6.55517', 'vk6.55535', 'vk6.55547', 'vk6.55549', 'vk6.55561', 'vk6.55669', 'vk6.55675', 'vk6.55677', 'vk6.55689', 'vk6.55716', 'vk6.55728', 'vk6.55733', 'vk6.55745', 'vk6.55773', 'vk6.55785', 'vk6.55788', 'vk6.55800', 'vk6.57121', 'vk6.57130', 'vk6.57505', 'vk6.57517', 'vk6.57522', 'vk6.57534', 'vk6.57653', 'vk6.57660', 'vk6.57671', 'vk6.57683', 'vk6.57688', 'vk6.57700', 'vk6.57735', 'vk6.58138', 'vk6.58147', 'vk6.58156', 'vk6.58159', 'vk6.58176', 'vk6.58179', 'vk6.58202', 'vk6.58205', 'vk6.58222', 'vk6.58225', 'vk6.58242', 'vk6.58249', 'vk6.58313', 'vk6.58320', 'vk6.58391', 'vk6.58479', 'vk6.58482', 'vk6.58499', 'vk6.58502', 'vk6.58695', 'vk6.58707', 'vk6.58710', 'vk6.58722', 'vk6.58815', 'vk6.58819', 'vk6.58820', 'vk6.58824', 'vk6.58839', 'vk6.58869', 'vk6.58880', 'vk6.58901', 'vk6.58913', 'vk6.58916', 'vk6.58928', 'vk6.58938', 'vk6.59003', 'vk6.59013', 'vk6.59415', 'vk6.59421', 'vk6.59427', 'vk6.59433', 'vk6.59439', 'vk6.59445', 'vk6.59465', 'vk6.59469', 'vk6.59483', 'vk6.59513', 'vk6.59525', 'vk6.59531', 'vk6.59543', 'vk6.59566', 'vk6.59572', 'vk6.59590', 'vk6.59596', 'vk6.59621', 'vk6.59625', 'vk6.59635', 'vk6.59668', 'vk6.59674', 'vk6.59680', 'vk6.59686', 'vk6.59692', 'vk6.59698', 'vk6.59712', 'vk6.59715', 'vk6.59718', 'vk6.59722', 'vk6.59728', 'vk6.59734', 'vk6.59758', 'vk6.59761', 'vk6.59773', 'vk6.59779', 'vk6.59813', 'vk6.59819', 'vk6.59833', 'vk6.59837', 'vk6.59843', 'vk6.59861', 'vk6.59867', 'vk6.59872', 'vk6.59876', 'vk6.59885', 'vk6.59901', 'vk6.59904', 'vk6.59914', 'vk6.59959', 'vk6.59965', 'vk6.59970', 'vk6.59982', 'vk6.60015', 'vk6.60018', 'vk6.60021', 'vk6.60025', 'vk6.60031', 'vk6.60037', 'vk6.60220', 'vk6.60226', 'vk6.60231', 'vk6.60243', 'vk6.60292', 'vk6.60304', 'vk6.60309', 'vk6.60321', 'vk6.60375', 'vk6.60387', 'vk6.60390', 'vk6.60402', 'vk6.60741', 'vk6.60744', 'vk6.60747', 'vk6.60750', 'vk6.61532', 'vk6.61535', 'vk6.61538', 'vk6.61541', 'vk6.61544', 'vk6.61547', 'vk6.61554', 'vk6.61557', 'vk6.61571', 'vk6.61578', 'vk6.61585', 'vk6.61589', 'vk6.61596', 'vk6.61604', 'vk6.61607', 'vk6.61614', 'vk6.61618', 'vk6.61631', 'vk6.61639', 'vk6.61642', 'vk6.61645', 'vk6.61648', 'vk6.61651', 'vk6.61654', 'vk6.61719', 'vk6.61725', 'vk6.61731', 'vk6.61736', 'vk6.61742', 'vk6.61748', 'vk6.61849', 'vk6.61855', 'vk6.61866', 'vk6.61872', 'vk6.61905', 'vk6.61908', 'vk6.61925', 'vk6.61928', 'vk6.62201', 'vk6.62213', 'vk6.62218', 'vk6.62230', 'vk6.62303', 'vk6.62309', 'vk6.62312', 'vk6.62318', 'vk6.62720', 'vk6.62723', 'vk6.62752', 'vk6.62758', 'vk6.62763', 'vk6.62769', 'vk6.62792', 'vk6.62798', 'vk6.62806', 'vk6.62812', 'vk6.62821', 'vk6.62822', 'vk6.62861', 'vk6.62867', 'vk6.62873', 'vk6.62875', 'vk6.62881', 'vk6.62887', 'vk6.62915', 'vk6.62986', 'vk6.62992', 'vk6.63001', 'vk6.63007', 'vk6.63149', 'vk6.63161', 'vk6.63164', 'vk6.63176', 'vk6.63236', 'vk6.63242', 'vk6.63251', 'vk6.63257', 'vk6.64877', 'vk6.64880', 'vk6.64894', 'vk6.64912', 'vk6.64917', 'vk6.64934', 'vk6.64984', 'vk6.64989', 'vk6.65006', 'vk6.65066', 'vk6.65080', 'vk6.65098', 'vk6.65109', 'vk6.65126', 'vk6.65129', 'vk6.65142', 'vk6.65195', 'vk6.65198', 'vk6.65212', 'vk6.65258', 'vk6.65269', 'vk6.66088', 'vk6.66195', 'vk6.66241', 'vk6.66244', 'vk6.66657', 'vk6.66664', 'vk6.66683', 'vk6.66685', 'vk6.66690', 'vk6.66706', 'vk6.66711', 'vk6.66713', 'vk6.66722', 'vk6.66729', 'vk6.66752', 'vk6.66761', 'vk6.66848', 'vk6.66854', 'vk6.66865', 'vk6.66871', 'vk6.67095', 'vk6.67101', 'vk6.67104', 'vk6.67110', 'vk6.67480', 'vk6.67483', 'vk6.67486', 'vk6.67487', 'vk6.67490', 'vk6.67493', 'vk6.67503', 'vk6.67506', 'vk6.67507', 'vk6.67523', 'vk6.67528', 'vk6.67532', 'vk6.67545', 'vk6.67552', 'vk6.67555', 'vk6.67565', 'vk6.67569', 'vk6.67570', 'vk6.67584', 'vk6.67587', 'vk6.67590', 'vk6.67591', 'vk6.67594', 'vk6.67597', 'vk6.67636', 'vk6.67643', 'vk6.67718', 'vk6.67724', 'vk6.67733', 'vk6.67739', 'vk6.67753', 'vk6.67756', 'vk6.67765', 'vk6.67768', 'vk6.67959', 'vk6.67965', 'vk6.67966', 'vk6.67972', 'vk6.69305', 'vk6.69306', 'vk6.69318', 'vk6.69321', 'vk6.69323', 'vk6.69347', 'vk6.69349', 'vk6.69352', 'vk6.69371', 'vk6.69372', 'vk6.69506', 'vk6.69509', 'vk6.69518', 'vk6.69521', 'vk6.71346', 'vk6.71860', 'vk6.71874', 'vk6.72765', 'vk6.72768', 'vk6.72775', 'vk6.72784', 'vk6.72787', 'vk6.72792', 'vk6.72795', 'vk6.73081', 'vk6.73084', 'vk6.73089', 'vk6.73098', 'vk6.73101', 'vk6.73106', 'vk6.73109', 'vk6.73944', 'vk6.73946', 'vk6.73950', 'vk6.73952', 'vk6.74338', 'vk6.74344', 'vk6.74805', 'vk6.74815', 'vk6.74829', 'vk6.74833', 'vk6.74836', 'vk6.75254', 'vk6.75270', 'vk6.75611', 'vk6.75617', 'vk6.75620', 'vk6.75626', 'vk6.75643', 'vk6.75649', 'vk6.75652', 'vk6.75712', 'vk6.75717', 'vk6.75723', 'vk6.75754', 'vk6.75756', 'vk6.75761', 'vk6.75764', 'vk6.75773', 'vk6.75779', 'vk6.75782', 'vk6.75788', 'vk6.75805', 'vk6.75808', 'vk6.75814', 'vk6.75852', 'vk6.75855', 'vk6.75856', 'vk6.75921', 'vk6.76357', 'vk6.76360', 'vk6.76369', 'vk6.76372', 'vk6.76388', 'vk6.76391', 'vk6.76394', 'vk6.76550', 'vk6.76559', 'vk6.76991', 'vk6.77009', 'vk6.77915', 'vk6.77926', 'vk6.77931', 'vk6.77934', 'vk6.77990', 'vk6.77993', 'vk6.78452', 'vk6.78468', 'vk6.78592', 'vk6.78598', 'vk6.78601', 'vk6.78607', 'vk6.78656', 'vk6.78662', 'vk6.78667', 'vk6.78724', 'vk6.78726', 'vk6.78732', 'vk6.78763', 'vk6.78769', 'vk6.78772', 'vk6.78778', 'vk6.78795', 'vk6.78798', 'vk6.78799', 'vk6.78850', 'vk6.78853', 'vk6.78856', 'vk6.78928', 'vk6.79380', 'vk6.79695', 'vk6.79709', 'vk6.79719', 'vk6.79728', 'vk6.79731', 'vk6.80698', 'vk6.80701', 'vk6.80717', 'vk6.80720', 'vk6.80730', 'vk6.80740', 'vk6.80743', 'vk6.82477', 'vk6.82480', 'vk6.82867', 'vk6.82875', 'vk6.82987', 'vk6.82998', 'vk6.83113', 'vk6.83119', 'vk6.83122', 'vk6.83128', 'vk6.83149', 'vk6.83152', 'vk6.83188', 'vk6.83192', 'vk6.83215', 'vk6.83216', 'vk6.83221', 'vk6.83380', 'vk6.83388', 'vk6.83561', 'vk6.83567', 'vk6.83568', 'vk6.83574', 'vk6.83922', 'vk6.83925', 'vk6.84067', 'vk6.84079', 'vk6.84081', 'vk6.84093', 'vk6.84153', 'vk6.84160', 'vk6.84214', 'vk6.84216', 'vk6.84238', 'vk6.84240', 'vk6.84250', 'vk6.84407', 'vk6.84410', 'vk6.84415', 'vk6.84490', 'vk6.84495', 'vk6.84498', 'vk6.84680', 'vk6.84697', 'vk6.85001', 'vk6.85016', 'vk6.85457', 'vk6.85646', 'vk6.85649', 'vk6.85662', 'vk6.85665', 'vk6.85748', 'vk6.85889', 'vk6.85895', 'vk6.85898', 'vk6.85904', 'vk6.85953', 'vk6.85959', 'vk6.85962', 'vk6.85968', 'vk6.86006', 'vk6.86009', 'vk6.86014', 'vk6.86017', 'vk6.86184', 'vk6.86188', 'vk6.86346', 'vk6.86392', 'vk6.86404', 'vk6.86409', 'vk6.86421', 'vk6.86431', 'vk6.86453', 'vk6.86459', 'vk6.86460', 'vk6.86466', 'vk6.86536', 'vk6.86542', 'vk6.86545', 'vk6.86557', 'vk6.86920', 'vk6.87071', 'vk6.87085', 'vk6.87134', 'vk6.87293', 'vk6.87296', 'vk6.87556', 'vk6.87559', 'vk6.87568', 'vk6.87571', 'vk6.87691', 'vk6.87741', 'vk6.87747', 'vk6.87753', 'vk6.87790', 'vk6.87804', 'vk6.88044', 'vk6.88123', 'vk6.88134', 'vk6.88194', 'vk6.88206', 'vk6.88208', 'vk6.88220', 'vk6.88258', 'vk6.88270', 'vk6.88272', 'vk6.88284', 'vk6.88407', 'vk6.88409', 'vk6.88427', 'vk6.88656', 'vk6.88819', 'vk6.88823', 'vk6.89057', 'vk6.89060', 'vk6.89329', 'vk6.89335', 'vk6.89597', 'vk6.89603', 'vk6.89712', 'vk6.89716', 'vk6.89755', 'vk6.89760', 'vk6.90074']
The R3 orbit of minmal crossing diagrams contains:
The diagrammatic symmetry type of this knot is c.
The reverse -K is
The mirror image K* is
The reversed mirror image -K* is
The fillings (up to the first 10) associated to the algebraic genus:
Or click here to check the fillings

Min(phi) over symmetries of the knot is: [-2,0,1,1,0,2,2,0,1,0]

Flat knots (up to 7 crossings) with same phi are :['4.8', '7.44862']

Arrow polynomial of the knot is: -2*K1**2 + K2 + 2

Flat knots (up to 7 crossings) with same arrow polynomial are :['4.6', '4.8', '6.780', '6.804', '6.914', '6.931', '6.946', '6.960', '6.1002', '6.1016', '6.1019', '6.1051', '6.1058', '6.1078', '6.1102', '6.1115', '6.1217', '6.1294', '6.1306', '6.1317', '6.1321', '6.1324', '6.1336', '6.1377', '6.1416', '6.1420', '6.1427', '6.1429', '6.1434', '6.1436', '6.1437', '6.1439', '6.1441', '6.1444', '6.1450', '6.1451', '6.1458', '6.1459', '6.1477', '6.1482', '6.1490', '6.1503', '6.1504', '6.1511', '6.1521', '6.1547', '6.1560', '6.1561', '6.1562', '6.1597', '6.1598', '6.1600', '6.1601', '6.1608', '6.1620', '6.1622', '6.1624', '6.1634', '6.1635', '6.1637', '6.1638', '6.1713', '6.1725', '6.1758', '6.1846', '6.1933', '6.1944', '6.1949', '6.1950', '6.1951']

Outer characteristic polynomial of the knot is: t^5+13t^3+6t

Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['4.8', '7.44862']

2-strand cable arrow polynomial of the knot is: -96*K1**4 - 112*K1**2*K2**2 + 248*K1**2*K2 - 172*K1**2 + 184*K1*K2*K3 + 24*K1*K3*K4 - 8*K2**4 + 16*K2**2*K4 - 144*K2**2 - 76*K3**2 - 18*K4**2 + 152

Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['4.8']

Virtual knots (up to 6 crossings) projecting to this knot are :'vk4.11', 'vk4.17', 'vk4.19', 'vk4.29', 'vk4.34', 'vk4.49', 'vk4.57', 'vk4.70', 'vk6.3531', 'vk6.3534', 'vk6.3539', 'vk6.3542', 'vk6.3679', 'vk6.3682', 'vk6.3687', 'vk6.3690', 'vk6.3711', 'vk6.3714', 'vk6.3719', 'vk6.3722', 'vk6.3775', 'vk6.3778', 'vk6.3783', 'vk6.3786', 'vk6.3871', 'vk6.3874', 'vk6.3879', 'vk6.3882', 'vk6.3903', 'vk6.3906', 'vk6.3911', 'vk6.3914', 'vk6.3967', 'vk6.3970', 'vk6.3975', 'vk6.3978', 'vk6.4899', 'vk6.4903', 'vk6.4919', 'vk6.4922', 'vk6.4927', 'vk6.4930', 'vk6.4967', 'vk6.4970', 'vk6.4975', 'vk6.4978', 'vk6.5011', 'vk6.5015', 'vk6.5247', 'vk6.5250', 'vk6.5255', 'vk6.5258', 'vk6.5735', 'vk6.5741', 'vk6.5743', 'vk6.5749', 'vk6.5768', 'vk6.5774', 'vk6.5776', 'vk6.5782', 'vk6.6047', 'vk6.6050', 'vk6.6053', 'vk6.6055', 'vk6.6058', 'vk6.6061', 'vk6.6079', 'vk6.6082', 'vk6.6087', 'vk6.6090', 'vk6.6111', 'vk6.6117', 'vk6.6119', 'vk6.6125', 'vk6.6143', 'vk6.6146', 'vk6.6151', 'vk6.6154', 'vk6.6175', 'vk6.6181', 'vk6.6183', 'vk6.6189', 'vk6.6207', 'vk6.6210', 'vk6.6213', 'vk6.6215', 'vk6.6218', 'vk6.6221', 'vk6.6287', 'vk6.6293', 'vk6.6295', 'vk6.6301', 'vk6.6447', 'vk6.6453', 'vk6.6455', 'vk6.6461', 'vk6.6503', 'vk6.6506', 'vk6.6511', 'vk6.6514', 'vk6.6566', 'vk6.6570', 'vk6.6600', 'vk6.6606', 'vk6.6608', 'vk6.6614', 'vk6.6648', 'vk6.6654', 'vk6.6656', 'vk6.6662', 'vk6.6678', 'vk6.6682', 'vk6.6728', 'vk6.6734', 'vk6.6736', 'vk6.6742', 'vk6.6868', 'vk6.6874', 'vk6.6876', 'vk6.6882', 'vk6.6915', 'vk6.6918', 'vk6.6923', 'vk6.6926', 'vk6.6947', 'vk6.6950', 'vk6.6955', 'vk6.6958', 'vk6.7075', 'vk6.7078', 'vk6.7083', 'vk6.7086', 'vk6.7107', 'vk6.7110', 'vk6.7115', 'vk6.7118', 'vk6.7167', 'vk6.7170', 'vk6.7175', 'vk6.7178', 'vk6.7251', 'vk6.7254', 'vk6.7259', 'vk6.7262', 'vk6.7283', 'vk6.7286', 'vk6.7291', 'vk6.7294', 'vk6.7343', 'vk6.7346', 'vk6.7351', 'vk6.7354', 'vk6.7802', 'vk6.7808', 'vk6.7810', 'vk6.7816', 'vk6.7835', 'vk6.7841', 'vk6.7843', 'vk6.7849', 'vk6.8086', 'vk6.8090', 'vk6.8122', 'vk6.8128', 'vk6.8130', 'vk6.8136', 'vk6.8170', 'vk6.8176', 'vk6.8178', 'vk6.8184', 'vk6.8198', 'vk6.8202', 'vk6.8250', 'vk6.8256', 'vk6.8258', 'vk6.8264', 'vk6.8410', 'vk6.8416', 'vk6.8418', 'vk6.8424', 'vk6.8462', 'vk6.8465', 'vk6.8468', 'vk6.8470', 'vk6.8473', 'vk6.8476', 'vk6.8497', 'vk6.8500', 'vk6.8505', 'vk6.8508', 'vk6.8526', 'vk6.8532', 'vk6.8534', 'vk6.8540', 'vk6.8561', 'vk6.8564', 'vk6.8569', 'vk6.8572', 'vk6.8590', 'vk6.8596', 'vk6.8598', 'vk6.8604', 'vk6.8621', 'vk6.8624', 'vk6.8627', 'vk6.8629', 'vk6.8632', 'vk6.8635', 'vk6.8701', 'vk6.8707', 'vk6.8709', 'vk6.8715', 'vk6.8831', 'vk6.8837', 'vk6.8839', 'vk6.8845', 'vk6.8884', 'vk6.8887', 'vk6.8892', 'vk6.8895', 'vk6.9465', 'vk6.9469', 'vk6.9486', 'vk6.9489', 'vk6.9494', 'vk6.9497', 'vk6.9534', 'vk6.9537', 'vk6.9542', 'vk6.9545', 'vk6.9577', 'vk6.9581', 'vk6.9800', 'vk6.9803', 'vk6.9808', 'vk6.9811', 'vk6.11040', 'vk6.11120', 'vk6.11381', 'vk6.11383', 'vk6.11396', 'vk6.11398', 'vk6.11658', 'vk6.11663', 'vk6.11676', 'vk6.11681', 'vk6.12011', 'vk6.12014', 'vk6.12029', 'vk6.12032', 'vk6.12562', 'vk6.12568', 'vk6.12579', 'vk6.12585', 'vk6.12675', 'vk6.12681', 'vk6.12690', 'vk6.12696', 'vk6.13004', 'vk6.13009', 'vk6.13018', 'vk6.13023', 'vk6.13270', 'vk6.13273', 'vk6.13290', 'vk6.13293', 'vk6.13302', 'vk6.13305', 'vk6.13322', 'vk6.13325', 'vk6.13430', 'vk6.13433', 'vk6.13450', 'vk6.13453', 'vk6.13462', 'vk6.13465', 'vk6.13482', 'vk6.13485', 'vk6.13526', 'vk6.13529', 'vk6.13546', 'vk6.13549', 'vk6.13620', 'vk6.13623', 'vk6.13640', 'vk6.13643', 'vk6.13652', 'vk6.13655', 'vk6.13672', 'vk6.13675', 'vk6.13716', 'vk6.13719', 'vk6.13736', 'vk6.13739', 'vk6.13911', 'vk6.14008', 'vk6.14180', 'vk6.14276', 'vk6.14279', 'vk6.14296', 'vk6.14299', 'vk6.14308', 'vk6.14311', 'vk6.14328', 'vk6.14331', 'vk6.14372', 'vk6.14375', 'vk6.14392', 'vk6.14395', 'vk6.14421', 'vk6.14436', 'vk6.14439', 'vk6.14456', 'vk6.14459', 'vk6.14757', 'vk6.14760', 'vk6.14767', 'vk6.14770', 'vk6.14788', 'vk6.14791', 'vk6.14808', 'vk6.14811', 'vk6.15360', 'vk6.15366', 'vk6.15369', 'vk6.15375', 'vk6.15487', 'vk6.15492', 'vk6.15506', 'vk6.15509', 'vk6.15526', 'vk6.15529', 'vk6.15538', 'vk6.15541', 'vk6.15558', 'vk6.15561', 'vk6.15602', 'vk6.15605', 'vk6.15622', 'vk6.15625', 'vk6.15652', 'vk6.15666', 'vk6.15669', 'vk6.15683', 'vk6.15915', 'vk6.15920', 'vk6.15921', 'vk6.15926', 'vk6.15945', 'vk6.15948', 'vk6.15965', 'vk6.15968', 'vk6.16108', 'vk6.16725', 'vk6.16873', 'vk6.16887', 'vk6.16888', 'vk6.17399', 'vk6.17404', 'vk6.17529', 'vk6.17586', 'vk6.18029', 'vk6.18030', 'vk6.18041', 'vk6.18042', 'vk6.18772', 'vk6.18776', 'vk6.18777', 'vk6.18781', 'vk6.18858', 'vk6.19078', 'vk6.19293', 'vk6.19297', 'vk6.19307', 'vk6.19446', 'vk6.19450', 'vk6.19451', 'vk6.19455', 'vk6.19587', 'vk6.19590', 'vk6.19600', 'vk6.19740', 'vk6.19743', 'vk6.19746', 'vk6.19749', 'vk6.19794', 'vk6.19797', 'vk6.19806', 'vk6.19809', 'vk6.19842', 'vk6.19845', 'vk6.19846', 'vk6.19849', 'vk6.20748', 'vk6.20754', 'vk6.20763', 'vk6.20769', 'vk6.20797', 'vk6.20802', 'vk6.20803', 'vk6.20808', 'vk6.20926', 'vk6.20933', 'vk6.21034', 'vk6.21036', 'vk6.21041', 'vk6.21043', 'vk6.21477', 'vk6.21488', 'vk6.21491', 'vk6.21494', 'vk6.21507', 'vk6.21527', 'vk6.21540', 'vk6.21543', 'vk6.21562', 'vk6.21573', 'vk6.21734', 'vk6.21737', 'vk6.21754', 'vk6.21757', 'vk6.21842', 'vk6.21845', 'vk6.21862', 'vk6.21865', 'vk6.22193', 'vk6.22197', 'vk6.22200', 'vk6.22204', 'vk6.22338', 'vk6.22343', 'vk6.22458', 'vk6.22460', 'vk6.22463', 'vk6.22465', 'vk6.22734', 'vk6.22835', 'vk6.22864', 'vk6.22870', 'vk6.22872', 'vk6.22878', 'vk6.22897', 'vk6.22903', 'vk6.22905', 'vk6.22911', 'vk6.23010', 'vk6.23063', 'vk6.23129', 'vk6.23136', 'vk6.23174', 'vk6.23180', 'vk6.23182', 'vk6.23188', 'vk6.23254', 'vk6.23269', 'vk6.23270', 'vk6.23284', 'vk6.23286', 'vk6.23312', 'vk6.23316', 'vk6.23318', 'vk6.23359', 'vk6.23373', 'vk6.23379', 'vk6.23420', 'vk6.23424', 'vk6.23426', 'vk6.23516', 'vk6.23518', 'vk6.23567', 'vk6.23577', 'vk6.23585', 'vk6.23587', 'vk6.23608', 'vk6.23611', 'vk6.23613', 'vk6.23655', 'vk6.23660', 'vk6.23675', 'vk6.23681', 'vk6.23683', 'vk6.23689', 'vk6.23724', 'vk6.23727', 'vk6.23729', 'vk6.23851', 'vk6.23853', 'vk6.23904', 'vk6.23914', 'vk6.24470', 'vk6.24471', 'vk6.24482', 'vk6.24483', 'vk6.24894', 'vk6.24897', 'vk6.24904', 'vk6.24907', 'vk6.25355', 'vk6.25360', 'vk6.25365', 'vk6.25370', 'vk6.25486', 'vk6.25703', 'vk6.25795', 'vk6.25801', 'vk6.25803', 'vk6.25809', 'vk6.25907', 'vk6.25913', 'vk6.25924', 'vk6.25930', 'vk6.26012', 'vk6.26061', 'vk6.26107', 'vk6.26230', 'vk6.26233', 'vk6.26242', 'vk6.26245', 'vk6.26284', 'vk6.26287', 'vk6.26288', 'vk6.26291', 'vk6.26396', 'vk6.26440', 'vk6.26482', 'vk6.26483', 'vk6.26497', 'vk6.26620', 'vk6.26627', 'vk6.26675', 'vk6.26676', 'vk6.26687', 'vk6.26688', 'vk6.26729', 'vk6.26730', 'vk6.26733', 'vk6.26734', 'vk6.27362', 'vk6.27365', 'vk6.27368', 'vk6.27379', 'vk6.27382', 'vk6.27385', 'vk6.27394', 'vk6.27397', 'vk6.27411', 'vk6.27418', 'vk6.27431', 'vk6.27435', 'vk6.27442', 'vk6.27456', 'vk6.27459', 'vk6.27466', 'vk6.27470', 'vk6.27483', 'vk6.27490', 'vk6.27493', 'vk6.27496', 'vk6.27507', 'vk6.27510', 'vk6.27513', 'vk6.27554', 'vk6.27563', 'vk6.27666', 'vk6.27672', 'vk6.27683', 'vk6.27689', 'vk6.27722', 'vk6.27725', 'vk6.27742', 'vk6.27745', 'vk6.27886', 'vk6.27889', 'vk6.27906', 'vk6.27909', 'vk6.28209', 'vk6.28215', 'vk6.28226', 'vk6.28232', 'vk6.28403', 'vk6.28412', 'vk6.28475', 'vk6.28481', 'vk6.28484', 'vk6.28490', 'vk6.29006', 'vk6.29011', 'vk6.29030', 'vk6.29040', 'vk6.29045', 'vk6.29062', 'vk6.29067', 'vk6.29078', 'vk6.29088', 'vk6.29093', 'vk6.29118', 'vk6.29125', 'vk6.29212', 'vk6.29218', 'vk6.29227', 'vk6.29233', 'vk6.29634', 'vk6.29640', 'vk6.29649', 'vk6.29655', 'vk6.29715', 'vk6.29717', 'vk6.29732', 'vk6.29734', 'vk6.29758', 'vk6.29759', 'vk6.29766', 'vk6.29767', 'vk6.29921', 'vk6.29970', 'vk6.30609', 'vk6.30706', 'vk6.30981', 'vk6.30987', 'vk6.30998', 'vk6.31004', 'vk6.31110', 'vk6.31116', 'vk6.31125', 'vk6.31131', 'vk6.31202', 'vk6.32165', 'vk6.32167', 'vk6.32182', 'vk6.32184', 'vk6.32370', 'vk6.32652', 'vk6.32655', 'vk6.32666', 'vk6.32669', 'vk6.32993', 'vk6.32998', 'vk6.33007', 'vk6.33012', 'vk6.33027', 'vk6.33030', 'vk6.33039', 'vk6.33042', 'vk6.33155', 'vk6.33158', 'vk6.33167', 'vk6.33170', 'vk6.33187', 'vk6.33190', 'vk6.33199', 'vk6.33202', 'vk6.33218', 'vk6.33221', 'vk6.33230', 'vk6.33233', 'vk6.33371', 'vk6.33377', 'vk6.33379', 'vk6.33391', 'vk6.33426', 'vk6.33438', 'vk6.33443', 'vk6.33455', 'vk6.33483', 'vk6.33495', 'vk6.33498', 'vk6.33510', 'vk6.33596', 'vk6.33607', 'vk6.33730', 'vk6.33807', 'vk6.34088', 'vk6.34091', 'vk6.34100', 'vk6.34112', 'vk6.34115', 'vk6.34450', 'vk6.34453', 'vk6.34523', 'vk6.34531', 'vk6.34533', 'vk6.34548', 'vk6.34560', 'vk6.34562', 'vk6.34574', 'vk6.34785', 'vk6.34796', 'vk6.34806', 'vk6.34818', 'vk6.34820', 'vk6.34832', 'vk6.34843', 'vk6.34849', 'vk6.34851', 'vk6.34857', 'vk6.34876', 'vk6.34882', 'vk6.34884', 'vk6.34890', 'vk6.35044', 'vk6.35128', 'vk6.35163', 'vk6.35169', 'vk6.35171', 'vk6.35177', 'vk6.35195', 'vk6.35198', 'vk6.35200', 'vk6.35206', 'vk6.35276', 'vk6.35282', 'vk6.35288', 'vk6.35290', 'vk6.35296', 'vk6.35302', 'vk6.35346', 'vk6.35352', 'vk6.35354', 'vk6.35360', 'vk6.35409', 'vk6.35415', 'vk6.35429', 'vk6.35435', 'vk6.35443', 'vk6.35454', 'vk6.35463', 'vk6.35493', 'vk6.35498', 'vk6.35504', 'vk6.35595', 'vk6.35607', 'vk6.35609', 'vk6.35621', 'vk6.35659', 'vk6.35665', 'vk6.35671', 'vk6.35673', 'vk6.35679', 'vk6.35685', 'vk6.35722', 'vk6.35725', 'vk6.35728', 'vk6.35730', 'vk6.35736', 'vk6.35742', 'vk6.35773', 'vk6.35776', 'vk6.35778', 'vk6.35784', 'vk6.35831', 'vk6.35837', 'vk6.35839', 'vk6.35845', 'vk6.35863', 'vk6.35869', 'vk6.35871', 'vk6.35877', 'vk6.35887', 'vk6.35893', 'vk6.35895', 'vk6.35907', 'vk6.35942', 'vk6.35945', 'vk6.35947', 'vk6.35953', 'vk6.36052', 'vk6.36057', 'vk6.36067', 'vk6.36094', 'vk6.36097', 'vk6.36100', 'vk6.36102', 'vk6.36108', 'vk6.36114', 'vk6.36141', 'vk6.36153', 'vk6.36155', 'vk6.36167', 'vk6.36172', 'vk6.36174', 'vk6.36181', 'vk6.36183', 'vk6.36185', 'vk6.36316', 'vk6.36391', 'vk6.36431', 'vk6.36437', 'vk6.36439', 'vk6.36451', 'vk6.36530', 'vk6.36542', 'vk6.36547', 'vk6.36559', 'vk6.36607', 'vk6.36619', 'vk6.36622', 'vk6.36634', 'vk6.37587', 'vk6.37747', 'vk6.37753', 'vk6.37755', 'vk6.37767', 'vk6.37807', 'vk6.37816', 'vk6.37828', 'vk6.37833', 'vk6.37845', 'vk6.37873', 'vk6.37885', 'vk6.37888', 'vk6.37900', 'vk6.37908', 'vk6.37911', 'vk6.37913', 'vk6.37919', 'vk6.37984', 'vk6.37990', 'vk6.38001', 'vk6.38007', 'vk6.38041', 'vk6.38047', 'vk6.38056', 'vk6.38062', 'vk6.38143', 'vk6.38797', 'vk6.38808', 'vk6.38829', 'vk6.38835', 'vk6.38846', 'vk6.38852', 'vk6.38877', 'vk6.38883', 'vk6.38894', 'vk6.38900', 'vk6.38909', 'vk6.38920', 'vk6.38957', 'vk6.38963', 'vk6.38969', 'vk6.38974', 'vk6.38980', 'vk6.38986', 'vk6.39053', 'vk6.39104', 'vk6.39110', 'vk6.39121', 'vk6.39127', 'vk6.39519', 'vk6.39531', 'vk6.39536', 'vk6.39548', 'vk6.39667', 'vk6.39673', 'vk6.39684', 'vk6.39690', 'vk6.39786', 'vk6.39788', 'vk6.39801', 'vk6.39803', 'vk6.39850', 'vk6.39852', 'vk6.39857', 'vk6.39859', 'vk6.39907', 'vk6.39919', 'vk6.39924', 'vk6.39936', 'vk6.39971', 'vk6.39983', 'vk6.39988', 'vk6.40000', 'vk6.40035', 'vk6.40047', 'vk6.40052', 'vk6.40064', 'vk6.40067', 'vk6.40073', 'vk6.40079', 'vk6.40084', 'vk6.40090', 'vk6.40096', 'vk6.40162', 'vk6.40174', 'vk6.40179', 'vk6.40191', 'vk6.40257', 'vk6.40263', 'vk6.40266', 'vk6.40272', 'vk6.40317', 'vk6.40323', 'vk6.40329', 'vk6.40334', 'vk6.40340', 'vk6.40346', 'vk6.40964', 'vk6.40967', 'vk6.40970', 'vk6.40979', 'vk6.40982', 'vk6.40985', 'vk6.40995', 'vk6.40998', 'vk6.41007', 'vk6.41010', 'vk6.41024', 'vk6.41030', 'vk6.41036', 'vk6.41042', 'vk6.41052', 'vk6.41055', 'vk6.41064', 'vk6.41067', 'vk6.41079', 'vk6.41085', 'vk6.41094', 'vk6.41100', 'vk6.41110', 'vk6.41113', 'vk6.41116', 'vk6.41125', 'vk6.41128', 'vk6.41131', 'vk6.41204', 'vk6.41210', 'vk6.41216', 'vk6.41219', 'vk6.41225', 'vk6.41231', 'vk6.41360', 'vk6.41366', 'vk6.41375', 'vk6.41381', 'vk6.41395', 'vk6.41398', 'vk6.41407', 'vk6.41410', 'vk6.41744', 'vk6.41756', 'vk6.41759', 'vk6.41771', 'vk6.41908', 'vk6.41914', 'vk6.41923', 'vk6.41929', 'vk6.42017', 'vk6.42044', 'vk6.42055', 'vk6.42088', 'vk6.42100', 'vk6.42103', 'vk6.42115', 'vk6.42120', 'vk6.42124', 'vk6.42131', 'vk6.42135', 'vk6.42140', 'vk6.42250', 'vk6.42261', 'vk6.42400', 'vk6.42412', 'vk6.42418', 'vk6.42430', 'vk6.42504', 'vk6.42616', 'vk6.42725', 'vk6.42775', 'vk6.42776', 'vk6.42783', 'vk6.42784', 'vk6.42795', 'vk6.42809', 'vk6.42877', 'vk6.42891', 'vk6.42899', 'vk6.42970', 'vk6.42984', 'vk6.42992', 'vk6.43018', 'vk6.43032', 'vk6.43050', 'vk6.43062', 'vk6.43068', 'vk6.43080', 'vk6.43082', 'vk6.43093', 'vk6.43183', 'vk6.43191', 'vk6.43200', 'vk6.43287', 'vk6.43295', 'vk6.43304', 'vk6.43329', 'vk6.43340', 'vk6.43356', 'vk6.43368', 'vk6.43374', 'vk6.43386', 'vk6.43387', 'vk6.43389', 'vk6.43396', 'vk6.43400', 'vk6.43403', 'vk6.43530', 'vk6.43536', 'vk6.43541', 'vk6.43553', 'vk6.43640', 'vk6.43652', 'vk6.43657', 'vk6.43669', 'vk6.43747', 'vk6.43759', 'vk6.43762', 'vk6.43774', 'vk6.43904', 'vk6.43905', 'vk6.43906', 'vk6.43907', 'vk6.44601', 'vk6.44619', 'vk6.44658', 'vk6.44704', 'vk6.44709', 'vk6.44712', 'vk6.44727', 'vk6.44730', 'vk6.44768', 'vk6.44900', 'vk6.44907', 'vk6.44951', 'vk6.44954', 'vk6.44971', 'vk6.44974', 'vk6.45015', 'vk6.45018', 'vk6.45027', 'vk6.45030', 'vk6.45551', 'vk6.45556', 'vk6.45568', 'vk6.45571', 'vk6.45580', 'vk6.45583', 'vk6.45616', 'vk6.45619', 'vk6.45628', 'vk6.45631', 'vk6.45663', 'vk6.45668', 'vk6.45744', 'vk6.45753', 'vk6.45809', 'vk6.45894', 'vk6.45897', 'vk6.45906', 'vk6.45909', 'vk6.46130', 'vk6.46142', 'vk6.46147', 'vk6.46159', 'vk6.46346', 'vk6.46352', 'vk6.46361', 'vk6.46367', 'vk6.46408', 'vk6.46412', 'vk6.46413', 'vk6.46417', 'vk6.46463', 'vk6.46471', 'vk6.46484', 'vk6.46511', 'vk6.46523', 'vk6.46528', 'vk6.46540', 'vk6.46567', 'vk6.46579', 'vk6.46584', 'vk6.46596', 'vk6.46598', 'vk6.46600', 'vk6.46611', 'vk6.46613', 'vk6.46620', 'vk6.46671', 'vk6.46683', 'vk6.46688', 'vk6.46700', 'vk6.46795', 'vk6.46804', 'vk6.46915', 'vk6.46918', 'vk6.46927', 'vk6.46930', 'vk6.47439', 'vk6.47446', 'vk6.47774', 'vk6.47786', 'vk6.47789', 'vk6.47801', 'vk6.47921', 'vk6.47927', 'vk6.47938', 'vk6.47944', 'vk6.48052', 'vk6.48303', 'vk6.48306', 'vk6.48327', 'vk6.48330', 'vk6.48387', 'vk6.48390', 'vk6.48411', 'vk6.48414', 'vk6.48847', 'vk6.48859', 'vk6.48863', 'vk6.48866', 'vk6.48887', 'vk6.48890', 'vk6.48911', 'vk6.48914', 'vk6.48935', 'vk6.48938', 'vk6.49119', 'vk6.49122', 'vk6.49143', 'vk6.49146', 'vk6.49381', 'vk6.49384', 'vk6.49387', 'vk6.49405', 'vk6.49408', 'vk6.49411', 'vk6.49413', 'vk6.49416', 'vk6.49437', 'vk6.49440', 'vk6.49445', 'vk6.49451', 'vk6.49469', 'vk6.49475', 'vk6.49477', 'vk6.49480', 'vk6.49501', 'vk6.49504', 'vk6.49509', 'vk6.49515', 'vk6.49533', 'vk6.49539', 'vk6.49589', 'vk6.49595', 'vk6.49613', 'vk6.49619', 'vk6.49636', 'vk6.49648', 'vk6.49666', 'vk6.49672', 'vk6.49690', 'vk6.49696', 'vk6.49714', 'vk6.49720', 'vk6.49738', 'vk6.49744', 'vk6.49748', 'vk6.49760', 'vk6.49794', 'vk6.49800', 'vk6.49818', 'vk6.49824', 'vk6.49928', 'vk6.49931', 'vk6.50029', 'vk6.50032', 'vk6.50053', 'vk6.50056', 'vk6.50089', 'vk6.50092', 'vk6.50105', 'vk6.50108', 'vk6.50113', 'vk6.50116', 'vk6.50137', 'vk6.50140', 'vk6.50488', 'vk6.50491', 'vk6.50505', 'vk6.50511', 'vk6.50671', 'vk6.50683', 'vk6.50703', 'vk6.50709', 'vk6.50727', 'vk6.50733', 'vk6.50755', 'vk6.50791', 'vk6.50797', 'vk6.50815', 'vk6.50821', 'vk6.50840', 'vk6.50843', 'vk6.50846', 'vk6.50864', 'vk6.50867', 'vk6.50870', 'vk6.50875', 'vk6.50878', 'vk6.50899', 'vk6.50902', 'vk6.50904', 'vk6.50910', 'vk6.50928', 'vk6.50934', 'vk6.50935', 'vk6.50938', 'vk6.50955', 'vk6.50958', 'vk6.51008', 'vk6.51014', 'vk6.51032', 'vk6.51038', 'vk6.51147', 'vk6.51159', 'vk6.51164', 'vk6.51167', 'vk6.51188', 'vk6.51191', 'vk6.51208', 'vk6.51211', 'vk6.51228', 'vk6.51231', 'vk6.51630', 'vk6.51836', 'vk6.52457', 'vk6.53347', 'vk6.53586', 'vk6.53589', 'vk6.53606', 'vk6.53609', 'vk6.53618', 'vk6.53621', 'vk6.53638', 'vk6.53641', 'vk6.53669', 'vk6.53672', 'vk6.53741', 'vk6.53752', 'vk6.54284', 'vk6.54298', 'vk6.54301', 'vk6.54318', 'vk6.54321', 'vk6.54513', 'vk6.54516', 'vk6.54548', 'vk6.54557', 'vk6.54568', 'vk6.54664', 'vk6.54675', 'vk6.54685', 'vk6.54697', 'vk6.54699', 'vk6.54711', 'vk6.54762', 'vk6.54944', 'vk6.55043', 'vk6.55045', 'vk6.55151', 'vk6.55153', 'vk6.55162', 'vk6.55223', 'vk6.55225', 'vk6.55234', 'vk6.55267', 'vk6.55269', 'vk6.55288', 'vk6.55290', 'vk6.55398', 'vk6.55400', 'vk6.55408', 'vk6.55475', 'vk6.55477', 'vk6.55485', 'vk6.55515', 'vk6.55517', 'vk6.55535', 'vk6.55547', 'vk6.55549', 'vk6.55561', 'vk6.55669', 'vk6.55675', 'vk6.55677', 'vk6.55689', 'vk6.55716', 'vk6.55728', 'vk6.55733', 'vk6.55745', 'vk6.55773', 'vk6.55785', 'vk6.55788', 'vk6.55800', 'vk6.57121', 'vk6.57130', 'vk6.57505', 'vk6.57517', 'vk6.57522', 'vk6.57534', 'vk6.57653', 'vk6.57660', 'vk6.57671', 'vk6.57683', 'vk6.57688', 'vk6.57700', 'vk6.57735', 'vk6.58138', 'vk6.58147', 'vk6.58156', 'vk6.58159', 'vk6.58176', 'vk6.58179', 'vk6.58202', 'vk6.58205', 'vk6.58222', 'vk6.58225', 'vk6.58242', 'vk6.58249', 'vk6.58313', 'vk6.58320', 'vk6.58391', 'vk6.58479', 'vk6.58482', 'vk6.58499', 'vk6.58502', 'vk6.58695', 'vk6.58707', 'vk6.58710', 'vk6.58722', 'vk6.58815', 'vk6.58819', 'vk6.58820', 'vk6.58824', 'vk6.58839', 'vk6.58869', 'vk6.58880', 'vk6.58901', 'vk6.58913', 'vk6.58916', 'vk6.58928', 'vk6.58938', 'vk6.59003', 'vk6.59013', 'vk6.59415', 'vk6.59421', 'vk6.59427', 'vk6.59433', 'vk6.59439', 'vk6.59445', 'vk6.59465', 'vk6.59469', 'vk6.59483', 'vk6.59513', 'vk6.59525', 'vk6.59531', 'vk6.59543', 'vk6.59566', 'vk6.59572', 'vk6.59590', 'vk6.59596', 'vk6.59621', 'vk6.59625', 'vk6.59635', 'vk6.59668', 'vk6.59674', 'vk6.59680', 'vk6.59686', 'vk6.59692', 'vk6.59698', 'vk6.59712', 'vk6.59715', 'vk6.59718', 'vk6.59722', 'vk6.59728', 'vk6.59734', 'vk6.59758', 'vk6.59761', 'vk6.59773', 'vk6.59779', 'vk6.59813', 'vk6.59819', 'vk6.59833', 'vk6.59837', 'vk6.59843', 'vk6.59861', 'vk6.59867', 'vk6.59872', 'vk6.59876', 'vk6.59885', 'vk6.59901', 'vk6.59904', 'vk6.59914', 'vk6.59959', 'vk6.59965', 'vk6.59970', 'vk6.59982', 'vk6.60015', 'vk6.60018', 'vk6.60021', 'vk6.60025', 'vk6.60031', 'vk6.60037', 'vk6.60220', 'vk6.60226', 'vk6.60231', 'vk6.60243', 'vk6.60292', 'vk6.60304', 'vk6.60309', 'vk6.60321', 'vk6.60375', 'vk6.60387', 'vk6.60390', 'vk6.60402', 'vk6.60741', 'vk6.60744', 'vk6.60747', 'vk6.60750', 'vk6.61532', 'vk6.61535', 'vk6.61538', 'vk6.61541', 'vk6.61544', 'vk6.61547', 'vk6.61554', 'vk6.61557', 'vk6.61571', 'vk6.61578', 'vk6.61585', 'vk6.61589', 'vk6.61596', 'vk6.61604', 'vk6.61607', 'vk6.61614', 'vk6.61618', 'vk6.61631', 'vk6.61639', 'vk6.61642', 'vk6.61645', 'vk6.61648', 'vk6.61651', 'vk6.61654', 'vk6.61719', 'vk6.61725', 'vk6.61731', 'vk6.61736', 'vk6.61742', 'vk6.61748', 'vk6.61849', 'vk6.61855', 'vk6.61866', 'vk6.61872', 'vk6.61905', 'vk6.61908', 'vk6.61925', 'vk6.61928', 'vk6.62201', 'vk6.62213', 'vk6.62218', 'vk6.62230', 'vk6.62303', 'vk6.62309', 'vk6.62312', 'vk6.62318', 'vk6.62720', 'vk6.62723', 'vk6.62752', 'vk6.62758', 'vk6.62763', 'vk6.62769', 'vk6.62792', 'vk6.62798', 'vk6.62806', 'vk6.62812', 'vk6.62821', 'vk6.62822', 'vk6.62861', 'vk6.62867', 'vk6.62873', 'vk6.62875', 'vk6.62881', 'vk6.62887', 'vk6.62915', 'vk6.62986', 'vk6.62992', 'vk6.63001', 'vk6.63007', 'vk6.63149', 'vk6.63161', 'vk6.63164', 'vk6.63176', 'vk6.63236', 'vk6.63242', 'vk6.63251', 'vk6.63257', 'vk6.64877', 'vk6.64880', 'vk6.64894', 'vk6.64912', 'vk6.64917', 'vk6.64934', 'vk6.64984', 'vk6.64989', 'vk6.65006', 'vk6.65066', 'vk6.65080', 'vk6.65098', 'vk6.65109', 'vk6.65126', 'vk6.65129', 'vk6.65142', 'vk6.65195', 'vk6.65198', 'vk6.65212', 'vk6.65258', 'vk6.65269', 'vk6.66088', 'vk6.66195', 'vk6.66241', 'vk6.66244', 'vk6.66657', 'vk6.66664', 'vk6.66683', 'vk6.66685', 'vk6.66690', 'vk6.66706', 'vk6.66711', 'vk6.66713', 'vk6.66722', 'vk6.66729', 'vk6.66752', 'vk6.66761', 'vk6.66848', 'vk6.66854', 'vk6.66865', 'vk6.66871', 'vk6.67095', 'vk6.67101', 'vk6.67104', 'vk6.67110', 'vk6.67480', 'vk6.67483', 'vk6.67486', 'vk6.67487', 'vk6.67490', 'vk6.67493', 'vk6.67503', 'vk6.67506', 'vk6.67507', 'vk6.67523', 'vk6.67528', 'vk6.67532', 'vk6.67545', 'vk6.67552', 'vk6.67555', 'vk6.67565', 'vk6.67569', 'vk6.67570', 'vk6.67584', 'vk6.67587', 'vk6.67590', 'vk6.67591', 'vk6.67594', 'vk6.67597', 'vk6.67636', 'vk6.67643', 'vk6.67718', 'vk6.67724', 'vk6.67733', 'vk6.67739', 'vk6.67753', 'vk6.67756', 'vk6.67765', 'vk6.67768', 'vk6.67959', 'vk6.67965', 'vk6.67966', 'vk6.67972', 'vk6.69305', 'vk6.69306', 'vk6.69318', 'vk6.69321', 'vk6.69323', 'vk6.69347', 'vk6.69349', 'vk6.69352', 'vk6.69371', 'vk6.69372', 'vk6.69506', 'vk6.69509', 'vk6.69518', 'vk6.69521', 'vk6.71346', 'vk6.71860', 'vk6.71874', 'vk6.72765', 'vk6.72768', 'vk6.72775', 'vk6.72784', 'vk6.72787', 'vk6.72792', 'vk6.72795', 'vk6.73081', 'vk6.73084', 'vk6.73089', 'vk6.73098', 'vk6.73101', 'vk6.73106', 'vk6.73109', 'vk6.73944', 'vk6.73946', 'vk6.73950', 'vk6.73952', 'vk6.74338', 'vk6.74344', 'vk6.74805', 'vk6.74815', 'vk6.74829', 'vk6.74833', 'vk6.74836', 'vk6.75254', 'vk6.75270', 'vk6.75611', 'vk6.75617', 'vk6.75620', 'vk6.75626', 'vk6.75643', 'vk6.75649', 'vk6.75652', 'vk6.75712', 'vk6.75717', 'vk6.75723', 'vk6.75754', 'vk6.75756', 'vk6.75761', 'vk6.75764', 'vk6.75773', 'vk6.75779', 'vk6.75782', 'vk6.75788', 'vk6.75805', 'vk6.75808', 'vk6.75814', 'vk6.75852', 'vk6.75855', 'vk6.75856', 'vk6.75921', 'vk6.76357', 'vk6.76360', 'vk6.76369', 'vk6.76372', 'vk6.76388', 'vk6.76391', 'vk6.76394', 'vk6.76550', 'vk6.76559', 'vk6.76991', 'vk6.77009', 'vk6.77915', 'vk6.77926', 'vk6.77931', 'vk6.77934', 'vk6.77990', 'vk6.77993', 'vk6.78452', 'vk6.78468', 'vk6.78592', 'vk6.78598', 'vk6.78601', 'vk6.78607', 'vk6.78656', 'vk6.78662', 'vk6.78667', 'vk6.78724', 'vk6.78726', 'vk6.78732', 'vk6.78763', 'vk6.78769', 'vk6.78772', 'vk6.78778', 'vk6.78795', 'vk6.78798', 'vk6.78799', 'vk6.78850', 'vk6.78853', 'vk6.78856', 'vk6.78928', 'vk6.79380', 'vk6.79695', 'vk6.79709', 'vk6.79719', 'vk6.79728', 'vk6.79731', 'vk6.80698', 'vk6.80701', 'vk6.80717', 'vk6.80720', 'vk6.80730', 'vk6.80740', 'vk6.80743', 'vk6.82477', 'vk6.82480', 'vk6.82867', 'vk6.82875', 'vk6.82987', 'vk6.82998', 'vk6.83113', 'vk6.83119', 'vk6.83122', 'vk6.83128', 'vk6.83149', 'vk6.83152', 'vk6.83188', 'vk6.83192', 'vk6.83215', 'vk6.83216', 'vk6.83221', 'vk6.83380', 'vk6.83388', 'vk6.83561', 'vk6.83567', 'vk6.83568', 'vk6.83574', 'vk6.83922', 'vk6.83925', 'vk6.84067', 'vk6.84079', 'vk6.84081', 'vk6.84093', 'vk6.84153', 'vk6.84160', 'vk6.84214', 'vk6.84216', 'vk6.84238', 'vk6.84240', 'vk6.84250', 'vk6.84407', 'vk6.84410', 'vk6.84415', 'vk6.84490', 'vk6.84495', 'vk6.84498', 'vk6.84680', 'vk6.84697', 'vk6.85001', 'vk6.85016', 'vk6.85457', 'vk6.85646', 'vk6.85649', 'vk6.85662', 'vk6.85665', 'vk6.85748', 'vk6.85889', 'vk6.85895', 'vk6.85898', 'vk6.85904', 'vk6.85953', 'vk6.85959', 'vk6.85962', 'vk6.85968', 'vk6.86006', 'vk6.86009', 'vk6.86014', 'vk6.86017', 'vk6.86184', 'vk6.86188', 'vk6.86346', 'vk6.86392', 'vk6.86404', 'vk6.86409', 'vk6.86421', 'vk6.86431', 'vk6.86453', 'vk6.86459', 'vk6.86460', 'vk6.86466', 'vk6.86536', 'vk6.86542', 'vk6.86545', 'vk6.86557', 'vk6.86920', 'vk6.87071', 'vk6.87085', 'vk6.87134', 'vk6.87293', 'vk6.87296', 'vk6.87556', 'vk6.87559', 'vk6.87568', 'vk6.87571', 'vk6.87691', 'vk6.87741', 'vk6.87747', 'vk6.87753', 'vk6.87790', 'vk6.87804', 'vk6.88044', 'vk6.88123', 'vk6.88134', 'vk6.88194', 'vk6.88206', 'vk6.88208', 'vk6.88220', 'vk6.88258', 'vk6.88270', 'vk6.88272', 'vk6.88284', 'vk6.88407', 'vk6.88409', 'vk6.88427', 'vk6.88656', 'vk6.88819', 'vk6.88823', 'vk6.89057', 'vk6.89060', 'vk6.89329', 'vk6.89335', 'vk6.89597', 'vk6.89603', 'vk6.89712', 'vk6.89716', 'vk6.89755', 'vk6.89760', 'vk6.90074']

The R3 orbit of minmal crossing diagrams contains:

The diagrammatic symmetry type of this knot is c.

The reverse -K is

The mirror image K* is

The reversed mirror image -K* is

The fillings (up to the first 10) associated to the algebraic genus:

Or click here to check the fillings

invariant	value
Gauss code	O1O2O3U1U3O4U2U4
R3 orbit	{'O1O2O3U1U3O4U2U4'}
R3 orbit length	1
Gauss code of -K	O1O2O3U4U2O4U1U3
Gauss code of K*	O1O2U3O4O3U1U4U2
Gauss code of -K*	O1O2U1O3O4U3U2U4
Diagrammatic symmetry type	c
Flat genus of the diagram	2
If K is checkerboard colorable	False
If K is almost classical	False
Based matrix from Gauss code	[[ 0 -2 0 1 1],[ 2 0 2 1 1],[ 0 -2 0 0 1],[-1 -1 0 0 0],[-1 -1 -1 0 0]]
Primitive based matrix	[[ 0 1 1 0 -2],[-1 0 0 0 -1],[-1 0 0 -1 -1],[ 0 0 1 0 -2],[ 2 1 1 2 0]]
If based matrix primitive	True
Phi of primitive based matrix	[-1,-1,0,2,0,0,1,1,1,2]
Phi over symmetry	[-2,0,1,1,0,2,2,0,1,0]
Phi of -K	[-2,0,1,1,0,2,2,0,1,0]
Phi of K*	[-1,-1,0,2,0,0,2,1,2,0]
Phi of -K*	[-2,0,1,1,2,1,1,0,1,0]
Symmetry type of based matrix	c
u-polynomial	t^2-2t
Normalized Jones-Krushkal polynomial	5z+11
Enhanced Jones-Krushkal polynomial	5w^2z+11w
Inner characteristic polynomial	t^4+7t^2+1
Outer characteristic polynomial	t^5+13t^3+6t
Flat arrow polynomial	-2K1*2 + K2 + 2
2-strand cable arrow polynomial	-96K14 - 112K1*2K2*2 + 248K1*2K2 - 172K12 + 184K1K2K3 + 24K1K3K4 - 8K2*4 + 16K2*2K4 - 144K22 - 76K3*2 - 18K4**2 + 152
Genus of based matrix	1
Fillings of based matrix	[[{1, 4}, {2, 3}], [{2, 4}, {1, 3}], [{3, 4}, {1, 2}], [{4}, {2, 3}, {1}]]
If K is slice	False

Contact