A list of septuples that are very likely to lead to irrationality proofs in \ the Generalized Beukers Zeta(3) integral By Shalosh B. Ekhad For the following septuples [a1,a2,b1,b2,c1,c2,e] it is very likely that the\ re exists an Apery-style irrationality proof for the Beukers-like integral 1 1 1 / / / a1 a2 b1 b2 c1 c2 | | | x (1 - x) y (1 - y) z (1 - z) | | | ----------------------------------------- dx dy dz | | | (e + 1) / / / (x y z - z + 1) 0 0 0 divided by 1 1 1 / / / a1 a2 b1 b2 c1 c2 | | | x (1 - x) y (1 - y) z (1 - z) | | | ----------------------------------------- dx dy dz | | | e / / / (x y z - z + 1) 0 0 0 --------------------------------------------------- Parameters with denominator , 2 [[0, 0, 1/2, 0, 0, 0, 1/2], 0.2746476372] [[1/2, 0, 0, 0, 0, 0, 1/2], 0.2746476372] [[1/2, 1/2, 1/2, 0, 0, 1/2, 0], 0.2755371602] [[1/2, 1/2, 0, 0, 0, 1/2, 1/2], 0.2758944688] [[0, 0, 1/2, 1/2, 1/2, 0, 0], 0.2760558110] [[0, 0, 0, 1/2, 1/2, 0, 1/2], 0.2745952063] [[0, 1/2, 1/2, 1/2, 1/2, 1/2, 0], 0.2755987021] [[1/2, 1/2, 0, 1/2, 1/2, 1/2, 0], 0.2755987021] --------------------------------------------------- Parameters with denominator , 3 [[0, 0, 2/3, 0, 0, 0, 1/3], 0.2202402127] [[0, 0, 1/3, 0, 0, 0, 2/3], 0.2176526144] [[1/3, 0, 2/3, 0, 0, 0, 1/3], 0.2178232576] [[1/3, 0, 0, 0, 0, 0, 2/3], 0.2176526144] [[1/3, 0, 2/3, 0, 0, 0, 2/3], 0.2202095465] [[1/3, 1/3, 0, 0, 0, 1/3, 1/3], 0.2178364318] [[1/3, 1/3, 0, 0, 0, 1/3, 2/3], 0.2202227657] [[1/3, 1/3, 1/3, 0, 0, 1/3, 2/3], 0.2177628007] [[1/3, 2/3, 2/3, 0, 0, 2/3, 0], 0.2202452177] [[1/3, 2/3, 0, 0, 0, 2/3, 1/3], 0.2214609477] [[1/3, 2/3, 2/3, 0, 0, 2/3, 1/3], 0.08283944841] [[2/3, 0, 0, 0, 0, 0, 1/3], 0.2202402127] [[2/3, 0, 1/3, 0, 0, 0, 1/3], 0.2178232576] [[2/3, 0, 1/3, 0, 0, 0, 2/3], 0.2202095465] [[2/3, 1/3, 1/3, 0, 0, 1/3, 0], 0.2190548635] [[2/3, 1/3, 0, 0, 0, 1/3, 2/3], 0.2181365246] [[2/3, 1/3, 1/3, 0, 0, 1/3, 2/3], 0.08381172199] [[2/3, 2/3, 0, 0, 0, 2/3, 1/3], 0.2186399002] [[2/3, 2/3, 2/3, 0, 0, 2/3, 1/3], 0.2199933277] [[2/3, 2/3, 0, 0, 0, 2/3, 2/3], 0.2205661532] [[0, 0, 1/3, 1/3, 1/3, 0, 0], 0.2180074324] [[0, 0, 0, 1/3, 1/3, 0, 2/3], 0.2176657961] [[0, 0, 1/3, 1/3, 1/3, 0, 2/3], 0.08337890162] [[0, 1/3, 2/3, 1/3, 1/3, 1/3, 0], 0.2190917066] [[0, 1/3, 1/3, 1/3, 1/3, 1/3, 2/3], 0.2178593323] [[0, 1/3, 2/3, 1/3, 1/3, 1/3, 2/3], 0.08379577641] [[0, 2/3, 1/3, 1/3, 1/3, 2/3, 0], 0.08284986387] [[0, 2/3, 2/3, 1/3, 1/3, 2/3, 0], 0.2202876375] [[0, 2/3, 2/3, 1/3, 1/3, 2/3, 1/3], 0.08284986387] [[1/3, 1/3, 2/3, 1/3, 1/3, 1/3, 0], 0.08286027970] [[1/3, 1/3, 0, 1/3, 1/3, 1/3, 2/3], 0.2178593323] [[2/3, 0, 0, 1/3, 1/3, 0, 1/3], 0.2178030843] [[2/3, 0, 0, 1/3, 1/3, 0, 2/3], 0.2202227837] [[2/3, 0, 1/3, 1/3, 1/3, 0, 2/3], 0.2178461575] [[2/3, 1/3, 0, 1/3, 1/3, 1/3, 0], 0.2190917066] [[2/3, 1/3, 1/3, 1/3, 1/3, 1/3, 0], 0.08286027970] [[2/3, 1/3, 0, 1/3, 1/3, 1/3, 2/3], 0.08379577641] [[2/3, 2/3, 1/3, 1/3, 1/3, 2/3, 0], 0.2191471976] [[2/3, 2/3, 2/3, 1/3, 1/3, 2/3, 0], 0.08332280174] [[2/3, 2/3, 1/3, 1/3, 1/3, 2/3, 2/3], 0.08286795488] [[0, 0, 2/3, 2/3, 2/3, 0, 0], 0.2207735234] [[0, 0, 0, 2/3, 2/3, 0, 1/3], 0.2202067503] [[0, 0, 2/3, 2/3, 2/3, 0, 1/3], 0.08401979954] [[0, 1/3, 1/3, 2/3, 2/3, 1/3, 0], 0.2191207557] [[0, 1/3, 2/3, 2/3, 2/3, 1/3, 0], 0.08367468663] [[0, 1/3, 1/3, 2/3, 2/3, 1/3, 2/3], 0.08378536373] [[0, 2/3, 1/3, 2/3, 2/3, 2/3, 0], 0.2203215197] [[0, 2/3, 1/3, 2/3, 2/3, 2/3, 1/3], 0.08285753907] [[0, 2/3, 2/3, 2/3, 2/3, 2/3, 1/3], 0.2201334307] [[1/3, 0, 0, 2/3, 2/3, 0, 1/3], 0.2177899110] [[1/3, 0, 2/3, 2/3, 2/3, 0, 1/3], 0.2214496881] [[1/3, 0, 0, 2/3, 2/3, 0, 2/3], 0.2201154437] [[1/3, 1/3, 1/3, 2/3, 2/3, 1/3, 0], 0.08286795488] [[1/3, 1/3, 2/3, 2/3, 2/3, 1/3, 0], 0.2203347479] [[1/3, 1/3, 2/3, 2/3, 2/3, 1/3, 1/3], 0.08286795488] [[1/3, 2/3, 0, 2/3, 2/3, 2/3, 0], 0.2203215197] [[1/3, 2/3, 2/3, 2/3, 2/3, 2/3, 0], 0.08344168893] [[1/3, 2/3, 0, 2/3, 2/3, 2/3, 1/3], 0.08285753907] [[2/3, 2/3, 1/3, 2/3, 2/3, 2/3, 0], 0.08344168893] [[2/3, 2/3, 0, 2/3, 2/3, 2/3, 1/3], 0.2201334307] --------------------------------------------------- Parameters with denominator , 4 [[1/4, 0, 1/2, 0, 0, 0, 3/4], 0.2751917195] [[1/4, 1/4, 3/4, 0, 0, 1/4, 1/2], 0.2752628630] [[1/4, 1/4, 0, 0, 0, 1/4, 3/4], 0.2752005093] [[1/4, 1/2, 0, 0, 0, 1/2, 1/4], 0.2753761812] [[1/4, 1/2, 1/2, 0, 0, 1/2, 3/4], 0.2752697022] [[1/2, 0, 3/4, 0, 0, 0, 1/4], 0.2753605397] [[1/2, 0, 1/4, 0, 0, 0, 3/4], 0.2751917195] [[3/4, 0, 1/2, 0, 0, 0, 1/4], 0.2753605397] [[3/4, 1/2, 1/2, 0, 0, 1/2, 1/4], 0.2753682241] [[3/4, 1/2, 0, 0, 0, 1/2, 3/4], 0.2739234871] [[3/4, 3/4, 0, 0, 0, 3/4, 1/4], 0.2735258952] [[3/4, 3/4, 1/4, 0, 0, 3/4, 1/2], 0.2755986944] [[0, 1/2, 3/4, 1/4, 1/4, 1/2, 0], 0.2758014855] [[0, 1/2, 1/2, 1/4, 1/4, 1/2, 3/4], 0.2752575044] [[1/2, 0, 3/4, 1/4, 1/4, 0, 1/2], 0.2753434085] [[1/2, 0, 0, 1/4, 1/4, 0, 3/4], 0.2751200773] [[3/4, 3/4, 1/2, 1/4, 1/4, 3/4, 0], 0.2751905277] [[3/4, 3/4, 0, 1/4, 1/4, 3/4, 1/2], 0.2756881781] [[0, 1/2, 3/4, 1/2, 1/2, 1/2, 1/4], 0.2756101762] [[0, 1/2, 1/4, 1/2, 1/2, 1/2, 3/4], 0.2754357376] [[1/4, 0, 1/2, 1/2, 1/2, 0, 1/4], 0.2753681632] [[1/4, 0, 0, 1/2, 1/2, 0, 3/4], 0.2752073702] [[1/4, 1/4, 3/4, 1/2, 1/2, 1/4, 0], 0.2758411395] [[1/4, 1/4, 1/2, 1/2, 1/2, 1/4, 3/4], 0.2754445395] [[1/4, 1/2, 0, 1/2, 1/2, 1/2, 3/4], 0.2754357376] [[3/4, 0, 0, 1/2, 1/2, 0, 1/4], 0.2753395396] [[3/4, 0, 1/2, 1/2, 1/2, 0, 3/4], 0.2754200948] [[3/4, 1/2, 0, 1/2, 1/2, 1/2, 1/4], 0.2756101762] [[3/4, 3/4, 1/4, 1/2, 1/2, 3/4, 0], 0.2752213404] [[3/4, 3/4, 1/2, 1/2, 1/2, 3/4, 1/4], 0.2753254695] [[0, 1/2, 1/4, 3/4, 3/4, 1/2, 0], 0.2758534494] [[0, 1/2, 1/2, 3/4, 3/4, 1/2, 1/4], 0.2753894533] [[1/4, 1/4, 1/2, 3/4, 3/4, 1/4, 0], 0.2758622614] [[1/4, 1/4, 0, 3/4, 3/4, 1/4, 1/2], 0.2753155692] [[1/2, 0, 0, 3/4, 3/4, 0, 1/4], 0.2753326994] [[1/2, 0, 1/4, 3/4, 3/4, 0, 1/2], 0.2753067688] --------------------------------------------------- Parameters with denominator , 5 [[1/5, 0, 2/5, 0, 0, 0, 3/5], 0.02531043907] [[1/5, 1/5, 0, 0, 0, 1/5, 3/5], 0.02531427647] [[1/5, 3/5, 0, 0, 0, 3/5, 2/5], 0.02514725669] [[1/5, 3/5, 2/5, 0, 0, 3/5, 4/5], 0.02517401188] [[2/5, 0, 4/5, 0, 0, 0, 1/5], 0.02514776002] [[2/5, 0, 1/5, 0, 0, 0, 3/5], 0.02531043907] [[2/5, 2/5, 0, 0, 0, 2/5, 1/5], 0.02516036656] [[2/5, 2/5, 3/5, 0, 0, 2/5, 4/5], 0.02517710551] [[3/5, 0, 4/5, 0, 0, 0, 2/5], 0.02513774372] [[3/5, 3/5, 2/5, 0, 0, 3/5, 1/5], 0.02461491772] [[4/5, 0, 2/5, 0, 0, 0, 1/5], 0.02514776002] [[4/5, 0, 3/5, 0, 0, 0, 2/5], 0.02513774372] [[4/5, 2/5, 3/5, 0, 0, 2/5, 1/5], 0.02461233504] [[2/5, 0, 4/5, 1/5, 1/5, 0, 2/5], 0.02519300714] [[2/5, 0, 0, 1/5, 1/5, 0, 3/5], 0.02536941965] [[3/5, 0, 4/5, 1/5, 1/5, 0, 3/5], 0.02521031360] [[3/5, 4/5, 0, 1/5, 1/5, 4/5, 2/5], 0.02449569874] [[1/5, 0, 3/5, 2/5, 2/5, 0, 1/5], 0.02515552543] [[1/5, 0, 0, 2/5, 2/5, 0, 3/5], 0.02527103618] [[3/5, 3/5, 0, 2/5, 2/5, 3/5, 1/5], 0.02470984217] [[4/5, 0, 0, 2/5, 2/5, 0, 1/5], 0.02513892520] [[1/5, 0, 2/5, 3/5, 3/5, 0, 1/5], 0.02515243192] [[2/5, 2/5, 0, 3/5, 3/5, 2/5, 4/5], 0.02520127989] [[4/5, 0, 0, 3/5, 3/5, 0, 2/5], 0.02516191625] [[4/5, 0, 2/5, 3/5, 3/5, 0, 4/5], 0.02518867220] [[4/5, 2/5, 0, 3/5, 3/5, 2/5, 1/5], 0.02470416822] [[1/5, 1/5, 0, 4/5, 4/5, 1/5, 2/5], 0.02512340500] [[2/5, 0, 0, 4/5, 4/5, 0, 1/5], 0.02513324649] [[2/5, 1/5, 0, 4/5, 4/5, 1/5, 3/5], 0.02517990419] [[3/5, 0, 1/5, 4/5, 4/5, 0, 3/5], 0.02517297610] --------------------------------------------------- Parameters with denominator , 6 [[1/6, 1/6, 1/2, 0, 0, 1/6, 2/3], 0.2519305764] [[1/6, 1/6, 2/3, 0, 0, 1/6, 5/6], 0.2513712018] [[1/6, 1/2, 5/6, 0, 0, 1/2, 1/3], 0.2555744248] [[1/6, 1/2, 1/3, 0, 0, 1/2, 5/6], 0.2548671493] [[1/6, 5/6, 1/3, 0, 0, 5/6, 1/2], 0.2555093274] [[1/6, 5/6, 1/2, 0, 0, 5/6, 2/3], 0.2554185530] [[1/3, 1/3, 5/6, 0, 0, 1/3, 1/6], 0.2555456385] [[1/3, 1/3, 1/2, 0, 0, 1/3, 5/6], 0.2548705738] [[1/3, 2/3, 1/6, 0, 0, 2/3, 1/2], 0.2510186623] [[1/3, 2/3, 1/2, 0, 0, 2/3, 5/6], 0.2511694813] [[1/2, 1/2, 1/3, 0, 0, 1/2, 1/6], 0.2553634259] [[1/2, 1/2, 1/6, 0, 0, 1/2, 1/3], 0.2508793395] [[1/2, 1/2, 5/6, 0, 0, 1/2, 2/3], 0.2554303398] [[1/2, 1/2, 2/3, 0, 0, 1/2, 5/6], 0.2511723739] [[2/3, 1/3, 1/2, 0, 0, 1/3, 1/6], 0.2553605110] [[2/3, 1/3, 5/6, 0, 0, 1/3, 1/2], 0.2555182005] [[2/3, 2/3, 1/2, 0, 0, 2/3, 1/6], 0.2509792783] [[2/3, 2/3, 1/6, 0, 0, 2/3, 5/6], 0.2509182403] [[5/6, 1/6, 1/2, 0, 0, 1/6, 1/3], 0.2508676495] [[5/6, 1/6, 2/3, 0, 0, 1/6, 1/2], 0.2510098616] [[5/6, 1/2, 2/3, 0, 0, 1/2, 1/6], 0.2509767640] [[5/6, 1/2, 1/6, 0, 0, 1/2, 2/3], 0.2507938336] [[5/6, 5/6, 1/3, 0, 0, 5/6, 1/6], 0.2539219084] [[5/6, 5/6, 1/2, 0, 0, 5/6, 1/3], 0.2537622104] [[0, 0, 1/2, 1/6, 1/6, 0, 1/3], 0.2520395979] [[0, 0, 2/3, 1/6, 1/6, 0, 1/2], 0.2513463739] [[0, 1/3, 2/3, 1/6, 1/6, 1/3, 1/2], 0.3200722654] [[0, 1/3, 5/6, 1/6, 1/6, 1/3, 2/3], 0.3187331767] [[0, 2/3, 5/6, 1/6, 1/6, 2/3, 1/3], 0.3194191270] [[0, 2/3, 1/3, 1/6, 1/6, 2/3, 5/6], 0.3199790653] [[1/3, 0, 1/2, 1/6, 1/6, 0, 2/3], 0.2519983991] [[1/3, 0, 2/3, 1/6, 1/6, 0, 5/6], 0.2513051383] [[1/3, 1/3, 5/6, 1/6, 1/6, 1/3, 0], 0.3194621348] [[1/3, 1/3, 2/3, 1/6, 1/6, 1/3, 5/6], 0.3199944800] [[1/3, 2/3, 1/2, 1/6, 1/6, 2/3, 0], 0.2525361125] [[1/3, 2/3, 0, 1/6, 1/6, 2/3, 1/2], 0.2510997232] [[1/2, 1/2, 2/3, 1/6, 1/6, 1/2, 0], 0.2525390157] [[1/2, 1/2, 0, 1/6, 1/6, 1/2, 1/3], 0.2511143159] [[1/2, 5/6, 2/3, 1/6, 1/6, 5/6, 0], 0.3196500549] [[1/2, 5/6, 1/3, 1/6, 1/6, 5/6, 2/3], 0.3196808154] [[2/3, 2/3, 5/6, 1/6, 1/6, 2/3, 0], 0.3196528639] [[2/3, 2/3, 1/2, 1/6, 1/6, 2/3, 1/3], 0.2525505309] [[2/3, 2/3, 1/3, 1/6, 1/6, 2/3, 1/2], 0.3192848228] [[2/3, 2/3, 0, 1/6, 1/6, 2/3, 5/6], 0.2508564450] [[5/6, 1/2, 2/3, 1/6, 1/6, 1/2, 1/3], 0.2525480053] [[5/6, 1/2, 0, 1/6, 1/6, 1/2, 2/3], 0.2508656213] [[5/6, 5/6, 1/3, 1/6, 1/6, 5/6, 0], 0.3177195515] [[5/6, 5/6, 2/3, 1/6, 1/6, 5/6, 1/3], 0.3192635954] [[0, 0, 1/2, 1/3, 1/3, 0, 1/6], 0.2549278183] [[0, 0, 5/6, 1/3, 1/3, 0, 1/2], 0.2538361160] [[0, 2/3, 5/6, 1/3, 1/3, 2/3, 1/2], 0.3195029802] [[0, 2/3, 1/6, 1/3, 1/3, 2/3, 5/6], 0.3199744852] [[1/6, 1/6, 2/3, 1/3, 1/3, 1/6, 1/2], 0.3199944800] [[1/6, 1/6, 5/6, 1/3, 1/3, 1/6, 2/3], 0.3188777089] [[1/6, 1/2, 5/6, 1/3, 1/3, 1/2, 2/3], 0.2554433464] [[1/6, 1/2, 0, 1/3, 1/3, 1/2, 5/6], 0.2548458697] [[1/6, 5/6, 1/2, 1/3, 1/3, 5/6, 0], 0.2554392947] [[1/6, 5/6, 0, 1/3, 1/3, 5/6, 1/2], 0.2555232105] [[1/2, 1/6, 5/6, 1/3, 1/3, 1/6, 0], 0.3194728712] [[1/2, 1/6, 2/3, 1/3, 1/3, 1/6, 5/6], 0.3199861012] [[1/2, 1/2, 5/6, 1/3, 1/3, 1/2, 0], 0.2554511116] [[1/2, 1/2, 0, 1/3, 1/3, 1/2, 1/6], 0.2555574651] [[1/2, 5/6, 2/3, 1/3, 1/3, 5/6, 1/6], 0.3192762057] [[1/2, 5/6, 1/6, 1/3, 1/3, 5/6, 2/3], 0.3196846029] [[2/3, 0, 5/6, 1/3, 1/3, 0, 1/6], 0.2557564978] [[2/3, 0, 1/2, 1/3, 1/3, 0, 5/6], 0.2548353983] [[2/3, 2/3, 5/6, 1/3, 1/3, 2/3, 1/6], 0.3192790173] [[2/3, 2/3, 1/6, 1/3, 1/3, 2/3, 1/2], 0.3192886082] [[5/6, 5/6, 1/6, 1/3, 1/3, 5/6, 0], 0.3177340650] [[5/6, 5/6, 0, 1/3, 1/3, 5/6, 1/6], 0.2541466379] [[5/6, 5/6, 2/3, 1/3, 1/3, 5/6, 1/2], 0.3192044345] [[5/6, 5/6, 1/2, 1/3, 1/3, 5/6, 2/3], 0.2556373727] [[0, 0, 1/3, 1/2, 1/2, 0, 1/6], 0.2549243934] [[0, 0, 1/6, 1/2, 1/2, 0, 1/3], 0.2520228840] [[0, 0, 5/6, 1/2, 1/2, 0, 2/3], 0.2539962912] [[0, 0, 2/3, 1/2, 1/2, 0, 5/6], 0.2497734400] [[1/6, 1/6, 2/3, 1/2, 1/2, 1/6, 1/3], 0.2509036702] [[1/6, 1/6, 0, 1/2, 1/2, 1/6, 2/3], 0.2519574390] [[1/6, 5/6, 1/3, 1/2, 1/2, 5/6, 0], 0.2554012751] [[1/6, 5/6, 0, 1/2, 1/2, 5/6, 2/3], 0.2555066036] [[1/3, 0, 2/3, 1/2, 1/2, 0, 1/6], 0.2511156423] [[1/3, 0, 1/6, 1/2, 1/2, 0, 2/3], 0.2519533437] [[1/3, 1/3, 5/6, 1/2, 1/2, 1/3, 2/3], 0.2554496826] [[1/3, 1/3, 0, 1/2, 1/2, 1/3, 5/6], 0.2548199869] [[1/3, 2/3, 1/6, 1/2, 1/2, 2/3, 0], 0.2525568410] [[1/3, 2/3, 0, 1/2, 1/2, 2/3, 5/6], 0.2510551190] [[2/3, 0, 5/6, 1/2, 1/2, 0, 1/3], 0.2557462240] [[2/3, 0, 1/3, 1/2, 1/2, 0, 5/6], 0.2548060916] [[2/3, 1/3, 5/6, 1/2, 1/2, 1/3, 0], 0.2554101601] [[2/3, 1/3, 0, 1/2, 1/2, 1/3, 1/6], 0.2555511279] [[2/3, 2/3, 0, 1/2, 1/2, 2/3, 1/6], 0.2510060721] [[2/3, 2/3, 1/6, 1/2, 1/2, 2/3, 1/3], 0.2525622700] [[5/6, 1/6, 2/3, 1/2, 1/2, 1/6, 0], 0.2525480053] [[5/6, 1/6, 0, 1/2, 1/2, 1/6, 1/3], 0.2510859244] [[5/6, 5/6, 0, 1/2, 1/2, 5/6, 1/3], 0.2539443145] [[5/6, 5/6, 1/3, 1/2, 1/2, 5/6, 2/3], 0.2556402932] [[0, 0, 1/6, 2/3, 2/3, 0, 1/2], 0.2513073489] [[0, 0, 1/2, 2/3, 2/3, 0, 5/6], 0.2499296020] [[0, 1/3, 5/6, 2/3, 2/3, 1/3, 1/6], 0.3176959776] [[0, 1/3, 1/6, 2/3, 2/3, 1/3, 1/2], 0.3200606478] [[1/6, 1/6, 5/6, 2/3, 2/3, 1/6, 0], 0.3180715394] [[1/6, 1/6, 1/2, 2/3, 2/3, 1/6, 1/3], 0.2508238336] [[1/6, 1/6, 1/3, 2/3, 2/3, 1/6, 1/2], 0.3200652283] [[1/6, 1/6, 0, 2/3, 2/3, 1/6, 5/6], 0.2513952056] [[1/3, 0, 1/2, 2/3, 2/3, 0, 1/6], 0.2511127502] [[1/3, 0, 1/6, 2/3, 2/3, 0, 5/6], 0.2513911055] [[1/3, 1/3, 5/6, 2/3, 2/3, 1/3, 1/2], 0.3195296677] [[1/3, 1/3, 1/6, 2/3, 2/3, 1/3, 5/6], 0.3199508812] [[1/2, 1/6, 5/6, 2/3, 2/3, 1/6, 1/3], 0.3194565472] [[1/2, 1/6, 1/3, 2/3, 2/3, 1/6, 5/6], 0.3199470826] [[1/2, 1/2, 1/6, 2/3, 2/3, 1/2, 0], 0.2525622700] [[1/2, 1/2, 0, 2/3, 2/3, 1/2, 5/6], 0.2512144940] [[1/2, 5/6, 1/6, 2/3, 2/3, 5/6, 0], 0.3197163799] [[1/2, 5/6, 1/3, 2/3, 2/3, 5/6, 1/6], 0.3192104778] [[5/6, 1/6, 1/2, 2/3, 2/3, 1/6, 0], 0.2525505309] [[5/6, 1/6, 0, 2/3, 2/3, 1/6, 1/2], 0.2510519707] [[5/6, 1/2, 0, 2/3, 2/3, 1/2, 1/6], 0.2510006677] [[5/6, 1/2, 1/6, 2/3, 2/3, 1/2, 1/3], 0.2525568410] [[5/6, 5/6, 1/6, 2/3, 2/3, 5/6, 1/3], 0.3192034351] [[5/6, 5/6, 1/3, 2/3, 2/3, 5/6, 1/2], 0.3192157743] [[0, 0, 1/3, 5/6, 5/6, 0, 1/2], 0.2538041121] [[0, 0, 1/2, 5/6, 5/6, 0, 2/3], 0.2539677403] [[0, 1/3, 2/3, 5/6, 5/6, 1/3, 1/6], 0.3177842797] [[0, 1/3, 1/6, 5/6, 5/6, 1/3, 2/3], 0.3186381854] [[0, 2/3, 1/6, 5/6, 5/6, 2/3, 1/3], 0.3194421631] [[0, 2/3, 1/3, 5/6, 5/6, 2/3, 1/2], 0.3195114953] [[1/6, 1/6, 2/3, 5/6, 5/6, 1/6, 0], 0.3182457744] [[1/6, 1/6, 1/3, 5/6, 5/6, 1/6, 2/3], 0.3186427513] [[1/6, 1/2, 0, 5/6, 5/6, 1/2, 1/3], 0.2555270142] [[1/6, 1/2, 1/3, 5/6, 5/6, 1/2, 2/3], 0.2552166996] [[1/3, 1/3, 1/6, 5/6, 5/6, 1/3, 0], 0.3194851722] [[1/3, 1/3, 0, 5/6, 5/6, 1/3, 1/6], 0.2555436214] [[1/3, 1/3, 2/3, 5/6, 5/6, 1/3, 1/2], 0.3195268608] [[1/3, 1/3, 1/2, 5/6, 5/6, 1/3, 2/3], 0.2552201192] [[1/2, 1/6, 1/3, 5/6, 5/6, 1/6, 0], 0.3194813859] [[1/2, 1/6, 2/3, 5/6, 5/6, 1/6, 1/3], 0.3194537406] [[1/2, 1/2, 1/3, 5/6, 5/6, 1/2, 0], 0.2554717071] [[1/2, 1/2, 0, 5/6, 5/6, 1/2, 2/3], 0.2554897718] [[2/3, 0, 1/3, 5/6, 5/6, 0, 1/6], 0.2555297381] [[2/3, 0, 1/2, 5/6, 5/6, 0, 1/3], 0.2555165524] [[2/3, 1/3, 1/2, 5/6, 5/6, 1/3, 0], 0.2554687845] [[2/3, 1/3, 0, 5/6, 5/6, 1/3, 1/2], 0.2555000416] [[2/3, 2/3, 1/6, 5/6, 5/6, 2/3, 0], 0.3197119560] [[2/3, 2/3, 1/3, 5/6, 5/6, 2/3, 1/6], 0.3193017945] --------------------------------------------------- Parameters with denominator , 7 [[0, 2/7, 4/7, 1/7, 1/7, 2/7, 3/7], 0.02360137620] [[0, 2/7, 3/7, 1/7, 1/7, 2/7, 5/7], 0.01840021198] [[0, 2/7, 6/7, 1/7, 1/7, 2/7, 5/7], 0.02322015119] [[0, 2/7, 4/7, 1/7, 1/7, 2/7, 6/7], 0.01865796937] [[0, 3/7, 5/7, 1/7, 1/7, 3/7, 4/7], 0.01638494556] [[0, 4/7, 5/7, 1/7, 1/7, 4/7, 2/7], 0.01648998219] [[0, 4/7, 6/7, 1/7, 1/7, 4/7, 2/7], 0.02272454177] [[0, 4/7, 2/7, 1/7, 1/7, 4/7, 5/7], 0.02355420221] [[0, 4/7, 2/7, 1/7, 1/7, 4/7, 6/7], 0.01614980118] [[0, 5/7, 6/7, 1/7, 1/7, 5/7, 2/7], 0.01642393973] [[0, 5/7, 3/7, 1/7, 1/7, 5/7, 6/7], 0.01641972947] [[2/7, 2/7, 5/7, 1/7, 1/7, 2/7, 0], 0.01668543218] [[2/7, 2/7, 6/7, 1/7, 1/7, 2/7, 0], 0.02285868288] [[2/7, 2/7, 4/7, 1/7, 1/7, 2/7, 5/7], 0.02356132537] [[2/7, 2/7, 4/7, 1/7, 1/7, 2/7, 6/7], 0.01615680408] [[2/7, 3/7, 6/7, 1/7, 1/7, 3/7, 0], 0.01639624905] [[2/7, 3/7, 5/7, 1/7, 1/7, 3/7, 6/7], 0.01642957980] [[3/7, 5/7, 2/7, 1/7, 1/7, 5/7, 4/7], 0.01638783767] [[3/7, 5/7, 4/7, 1/7, 1/7, 5/7, 6/7], 0.01638783767] [[3/7, 6/7, 4/7, 1/7, 1/7, 6/7, 0], 0.02251973388] [[3/7, 6/7, 2/7, 1/7, 1/7, 6/7, 5/7], 0.02293037200] [[4/7, 4/7, 2/7, 1/7, 1/7, 4/7, 3/7], 0.01644006403] [[4/7, 4/7, 2/7, 1/7, 1/7, 4/7, 5/7], 0.01853705674] [[4/7, 4/7, 3/7, 1/7, 1/7, 4/7, 6/7], 0.01878067064] [[4/7, 4/7, 5/7, 1/7, 1/7, 4/7, 6/7], 0.01638915729] [[4/7, 6/7, 5/7, 1/7, 1/7, 6/7, 0], 0.01630407277] [[5/7, 3/7, 2/7, 1/7, 1/7, 3/7, 4/7], 0.01849798133] [[5/7, 3/7, 4/7, 1/7, 1/7, 3/7, 6/7], 0.01877934201] [[5/7, 4/7, 3/7, 1/7, 1/7, 4/7, 0], 0.01861350900] [[5/7, 4/7, 6/7, 1/7, 1/7, 4/7, 0], 0.02252226628] [[5/7, 4/7, 2/7, 1/7, 1/7, 4/7, 3/7], 0.02294535838] [[5/7, 4/7, 2/7, 1/7, 1/7, 4/7, 6/7], 0.01745105086] [[5/7, 5/7, 6/7, 1/7, 1/7, 5/7, 0], 0.01630525023] [[5/7, 6/7, 2/7, 1/7, 1/7, 6/7, 0], 0.02224777595] [[5/7, 6/7, 4/7, 1/7, 1/7, 6/7, 2/7], 0.02256825431] [[6/7, 2/7, 4/7, 1/7, 1/7, 2/7, 3/7], 0.01643474753] [[6/7, 2/7, 3/7, 1/7, 1/7, 2/7, 4/7], 0.01849396042] [[6/7, 2/7, 5/7, 1/7, 1/7, 2/7, 4/7], 0.01638384146] [[6/7, 2/7, 4/7, 1/7, 1/7, 2/7, 5/7], 0.01853170753] [[6/7, 3/7, 4/7, 1/7, 1/7, 3/7, 0], 0.01861099961] [[6/7, 3/7, 2/7, 1/7, 1/7, 3/7, 5/7], 0.01741399818] [[6/7, 5/7, 2/7, 1/7, 1/7, 5/7, 0], 0.01476694376] [[6/7, 5/7, 4/7, 1/7, 1/7, 5/7, 2/7], 0.01567297828] [[6/7, 6/7, 3/7, 1/7, 1/7, 6/7, 0], 0.01608880914] [[6/7, 6/7, 5/7, 1/7, 1/7, 6/7, 2/7], 0.01654050202] [[0, 1/7, 4/7, 2/7, 2/7, 1/7, 3/7], 0.01592357109] [[0, 1/7, 3/7, 2/7, 2/7, 1/7, 4/7], 0.01836258801] [[0, 1/7, 5/7, 2/7, 2/7, 1/7, 4/7], 0.01568491892] [[0, 1/7, 4/7, 2/7, 2/7, 1/7, 5/7], 0.01850498103] [[0, 3/7, 5/7, 2/7, 2/7, 3/7, 4/7], 0.01695896865] [[0, 3/7, 6/7, 2/7, 2/7, 3/7, 5/7], 0.01682034203] [[0, 4/7, 5/7, 2/7, 2/7, 4/7, 3/7], 0.01654769116] [[0, 4/7, 6/7, 2/7, 2/7, 4/7, 3/7], 0.02273241202] [[0, 4/7, 1/7, 2/7, 2/7, 4/7, 5/7], 0.02360388067] [[0, 4/7, 1/7, 2/7, 2/7, 4/7, 6/7], 0.01601377308] [[0, 6/7, 3/7, 2/7, 2/7, 6/7, 1/7], 0.01724059196] [[0, 6/7, 5/7, 2/7, 2/7, 6/7, 3/7], 0.01746234637] [[1/7, 1/7, 4/7, 2/7, 2/7, 1/7, 3/7], 0.02349291399] [[1/7, 1/7, 3/7, 2/7, 2/7, 1/7, 5/7], 0.01839772335] [[1/7, 1/7, 6/7, 2/7, 2/7, 1/7, 5/7], 0.02319373338] [[1/7, 1/7, 4/7, 2/7, 2/7, 1/7, 6/7], 0.01860448214] [[1/7, 5/7, 3/7, 2/7, 2/7, 5/7, 0], 0.01731209000] [[1/7, 5/7, 6/7, 2/7, 2/7, 5/7, 3/7], 0.01747018180] [[3/7, 1/7, 5/7, 2/7, 2/7, 1/7, 0], 0.01650204947] [[3/7, 1/7, 6/7, 2/7, 2/7, 1/7, 0], 0.02281314202] [[3/7, 1/7, 4/7, 2/7, 2/7, 1/7, 5/7], 0.02360924376] [[3/7, 1/7, 4/7, 2/7, 2/7, 1/7, 6/7], 0.01601904375] [[3/7, 3/7, 5/7, 2/7, 2/7, 3/7, 0], 0.01731818731] [[3/7, 3/7, 6/7, 2/7, 2/7, 3/7, 1/7], 0.01725452037] [[3/7, 5/7, 4/7, 2/7, 2/7, 5/7, 0], 0.01600805726] [[3/7, 5/7, 1/7, 2/7, 2/7, 5/7, 4/7], 0.01638956928] [[3/7, 6/7, 4/7, 2/7, 2/7, 6/7, 1/7], 0.02284706114] [[3/7, 6/7, 1/7, 2/7, 2/7, 6/7, 5/7], 0.02276838096] [[4/7, 4/7, 3/7, 2/7, 2/7, 4/7, 0], 0.01831055700] [[4/7, 4/7, 5/7, 2/7, 2/7, 4/7, 0], 0.01600937531] [[4/7, 4/7, 1/7, 2/7, 2/7, 4/7, 3/7], 0.01649270770] [[4/7, 4/7, 1/7, 2/7, 2/7, 4/7, 5/7], 0.01853500015] [[4/7, 6/7, 5/7, 2/7, 2/7, 6/7, 0], 0.01692426383] [[4/7, 6/7, 3/7, 2/7, 2/7, 6/7, 5/7], 0.01708523079] [[5/7, 3/7, 4/7, 2/7, 2/7, 3/7, 0], 0.01830923356] [[5/7, 3/7, 1/7, 2/7, 2/7, 3/7, 4/7], 0.01849592489] [[5/7, 4/7, 3/7, 2/7, 2/7, 4/7, 1/7], 0.01838730621] [[5/7, 4/7, 6/7, 2/7, 2/7, 4/7, 1/7], 0.02284959768] [[5/7, 4/7, 1/7, 2/7, 2/7, 4/7, 3/7], 0.02278336274] [[5/7, 4/7, 1/7, 2/7, 2/7, 4/7, 6/7], 0.01739556431] [[5/7, 5/7, 6/7, 2/7, 2/7, 5/7, 0], 0.01692544669] [[5/7, 5/7, 3/7, 2/7, 2/7, 5/7, 4/7], 0.01734881864] [[5/7, 6/7, 1/7, 2/7, 2/7, 6/7, 0], 0.02232404221] [[5/7, 6/7, 4/7, 2/7, 2/7, 6/7, 3/7], 0.02295924740] [[6/7, 3/7, 4/7, 2/7, 2/7, 3/7, 1/7], 0.01838480176] [[6/7, 3/7, 1/7, 2/7, 2/7, 3/7, 5/7], 0.01735851567] [[6/7, 5/7, 1/7, 2/7, 2/7, 5/7, 0], 0.01458597804] [[6/7, 5/7, 4/7, 2/7, 2/7, 5/7, 3/7], 0.01608494136] [[0, 1/7, 2/7, 3/7, 3/7, 1/7, 4/7], 0.01827540694] [[0, 1/7, 4/7, 3/7, 3/7, 1/7, 6/7], 0.01811143338] [[0, 2/7, 4/7, 3/7, 3/7, 2/7, 1/7], 0.01864317089] [[0, 2/7, 1/7, 3/7, 3/7, 2/7, 5/7], 0.01826772998] [[0, 5/7, 6/7, 3/7, 3/7, 5/7, 4/7], 0.01632041798] [[0, 5/7, 1/7, 3/7, 3/7, 5/7, 6/7], 0.01657774613] [[0, 6/7, 2/7, 3/7, 3/7, 6/7, 1/7], 0.01736578978] [[0, 6/7, 5/7, 3/7, 3/7, 6/7, 4/7], 0.01746062049] [[1/7, 1/7, 4/7, 3/7, 3/7, 1/7, 0], 0.01875641187] [[1/7, 1/7, 2/7, 3/7, 3/7, 1/7, 5/7], 0.01826977931] [[1/7, 2/7, 5/7, 3/7, 3/7, 2/7, 4/7], 0.01709006145] [[1/7, 2/7, 6/7, 3/7, 3/7, 2/7, 5/7], 0.01700263325] [[1/7, 5/7, 2/7, 3/7, 3/7, 5/7, 0], 0.01743730557] [[1/7, 5/7, 6/7, 3/7, 3/7, 5/7, 4/7], 0.01746845575] [[2/7, 1/7, 5/7, 3/7, 3/7, 1/7, 4/7], 0.01631109171] [[4/7, 1/7, 6/7, 3/7, 3/7, 1/7, 0], 0.01656042973] [[4/7, 1/7, 5/7, 3/7, 3/7, 1/7, 6/7], 0.01658435949] [[4/7, 2/7, 5/7, 3/7, 3/7, 2/7, 0], 0.01744189292] [[4/7, 2/7, 6/7, 3/7, 3/7, 2/7, 1/7], 0.01737821050] [[4/7, 4/7, 2/7, 3/7, 3/7, 4/7, 0], 0.01836667819] [[4/7, 4/7, 1/7, 3/7, 3/7, 4/7, 6/7], 0.01869109790] [[4/7, 6/7, 5/7, 3/7, 3/7, 6/7, 1/7], 0.01704150834] [[4/7, 6/7, 5/7, 3/7, 3/7, 6/7, 2/7], 0.01703481744] [[4/7, 6/7, 2/7, 3/7, 3/7, 6/7, 5/7], 0.01708674090] [[5/7, 4/7, 1/7, 3/7, 3/7, 4/7, 0], 0.01863572472] [[5/7, 4/7, 2/7, 3/7, 3/7, 4/7, 1/7], 0.01831040258] [[5/7, 5/7, 6/7, 3/7, 3/7, 5/7, 1/7], 0.01704269147] [[5/7, 5/7, 6/7, 3/7, 3/7, 5/7, 2/7], 0.01703599410] [[5/7, 5/7, 2/7, 3/7, 3/7, 5/7, 4/7], 0.01729902319] [[6/7, 2/7, 4/7, 3/7, 3/7, 2/7, 0], 0.01836134695] [[6/7, 2/7, 1/7, 3/7, 3/7, 2/7, 4/7], 0.01840443808] [[6/7, 6/7, 1/7, 3/7, 3/7, 6/7, 0], 0.01615421774] [[6/7, 6/7, 5/7, 3/7, 3/7, 6/7, 4/7], 0.01721693918] [[0, 1/7, 2/7, 4/7, 4/7, 1/7, 3/7], 0.01599718373] [[0, 1/7, 2/7, 4/7, 4/7, 1/7, 5/7], 0.01848780899] [[0, 1/7, 3/7, 4/7, 4/7, 1/7, 6/7], 0.01818143379] [[0, 1/7, 5/7, 4/7, 4/7, 1/7, 6/7], 0.01533870581] [[0, 2/7, 3/7, 4/7, 4/7, 2/7, 1/7], 0.01854847349] [[0, 2/7, 6/7, 4/7, 4/7, 2/7, 1/7], 0.02229611391] [[0, 2/7, 1/7, 4/7, 4/7, 2/7, 3/7], 0.02364777403] [[0, 2/7, 1/7, 4/7, 4/7, 2/7, 6/7], 0.01852694616] [[1/7, 1/7, 3/7, 4/7, 4/7, 1/7, 0], 0.01876417319] [[1/7, 1/7, 6/7, 4/7, 4/7, 1/7, 0], 0.02250925404] [[1/7, 1/7, 2/7, 4/7, 4/7, 1/7, 3/7], 0.02364985236] [[1/7, 1/7, 2/7, 4/7, 4/7, 1/7, 6/7], 0.01852899345] [[2/7, 2/7, 5/7, 4/7, 4/7, 2/7, 3/7], 0.01674848322] [[2/7, 2/7, 6/7, 4/7, 4/7, 2/7, 3/7], 0.02274718625] [[2/7, 2/7, 1/7, 4/7, 4/7, 2/7, 5/7], 0.02347340853] [[2/7, 2/7, 1/7, 4/7, 4/7, 2/7, 6/7], 0.01602609697] [[3/7, 1/7, 5/7, 4/7, 4/7, 1/7, 2/7], 0.01650736668] [[3/7, 1/7, 6/7, 4/7, 4/7, 1/7, 2/7], 0.02264214708] [[3/7, 1/7, 2/7, 4/7, 4/7, 1/7, 5/7], 0.02347164824] [[3/7, 1/7, 2/7, 4/7, 4/7, 1/7, 6/7], 0.01602436645] [[3/7, 5/7, 2/7, 4/7, 4/7, 5/7, 0], 0.01612117596] [[3/7, 5/7, 1/7, 4/7, 4/7, 5/7, 6/7], 0.01638256317] [[3/7, 6/7, 1/7, 4/7, 4/7, 6/7, 0], 0.02275199473] [[3/7, 6/7, 2/7, 4/7, 4/7, 6/7, 1/7], 0.02285868155] [[5/7, 3/7, 2/7, 4/7, 4/7, 3/7, 0], 0.01818487514] [[5/7, 3/7, 1/7, 4/7, 4/7, 3/7, 6/7], 0.01864105324] [[5/7, 6/7, 1/7, 4/7, 4/7, 6/7, 2/7], 0.02258378548] [[5/7, 6/7, 2/7, 4/7, 4/7, 6/7, 3/7], 0.02291520634] [[6/7, 2/7, 3/7, 4/7, 4/7, 2/7, 0], 0.01818086876] [[6/7, 2/7, 5/7, 4/7, 4/7, 2/7, 0], 0.01611718375] [[6/7, 2/7, 1/7, 4/7, 4/7, 2/7, 3/7], 0.01648038318] [[6/7, 2/7, 1/7, 4/7, 4/7, 2/7, 5/7], 0.01851240057] [[6/7, 3/7, 1/7, 4/7, 4/7, 3/7, 0], 0.01864096289] [[6/7, 3/7, 2/7, 4/7, 4/7, 3/7, 1/7], 0.01821354779] [[6/7, 5/7, 1/7, 4/7, 4/7, 5/7, 2/7], 0.01568505542] [[6/7, 5/7, 2/7, 4/7, 4/7, 5/7, 3/7], 0.01627844884] [[0, 1/7, 2/7, 5/7, 5/7, 1/7, 4/7], 0.01566887562] [[0, 1/7, 4/7, 5/7, 5/7, 1/7, 6/7], 0.01524923206] [[0, 3/7, 6/7, 5/7, 5/7, 3/7, 1/7], 0.01573241285] [[0, 3/7, 1/7, 5/7, 5/7, 3/7, 4/7], 0.01637833493] [[0, 3/7, 2/7, 5/7, 5/7, 3/7, 4/7], 0.01697789304] [[0, 4/7, 1/7, 5/7, 5/7, 4/7, 2/7], 0.01638256317] [[0, 4/7, 2/7, 5/7, 5/7, 4/7, 3/7], 0.01662188795] [[0, 6/7, 2/7, 5/7, 5/7, 6/7, 3/7], 0.01737056468] [[0, 6/7, 3/7, 5/7, 5/7, 6/7, 4/7], 0.01733275151] [[1/7, 2/7, 6/7, 5/7, 5/7, 2/7, 0], 0.01587599415] [[1/7, 2/7, 3/7, 5/7, 5/7, 2/7, 4/7], 0.01698168622] [[2/7, 1/7, 3/7, 5/7, 5/7, 1/7, 4/7], 0.01638211983] [[2/7, 2/7, 1/7, 5/7, 5/7, 2/7, 0], 0.01657797184] [[2/7, 2/7, 4/7, 5/7, 5/7, 2/7, 3/7], 0.01662889736] [[2/7, 3/7, 6/7, 5/7, 5/7, 3/7, 4/7], 0.01633497824] [[2/7, 3/7, 1/7, 5/7, 5/7, 3/7, 6/7], 0.01644905888] [[3/7, 1/7, 2/7, 5/7, 5/7, 1/7, 0], 0.01657623959] [[3/7, 1/7, 4/7, 5/7, 5/7, 1/7, 2/7], 0.01638783767] [[3/7, 3/7, 2/7, 5/7, 5/7, 3/7, 0], 0.01739686350] [[3/7, 3/7, 6/7, 5/7, 5/7, 3/7, 4/7], 0.01734668244] [[4/7, 1/7, 6/7, 5/7, 5/7, 1/7, 2/7], 0.01655177439] [[4/7, 1/7, 3/7, 5/7, 5/7, 1/7, 6/7], 0.01644581974] [[4/7, 2/7, 3/7, 5/7, 5/7, 2/7, 0], 0.01739535233] [[4/7, 2/7, 6/7, 5/7, 5/7, 2/7, 3/7], 0.01738298551] [[4/7, 4/7, 2/7, 5/7, 5/7, 4/7, 0], 0.01612473182] [[4/7, 4/7, 1/7, 5/7, 5/7, 4/7, 6/7], 0.01637480733] [[4/7, 6/7, 1/7, 5/7, 5/7, 6/7, 0], 0.01641132531] [[4/7, 6/7, 2/7, 5/7, 5/7, 6/7, 0], 0.01687557345] [[4/7, 6/7, 3/7, 5/7, 5/7, 6/7, 1/7], 0.01693313290] [[4/7, 6/7, 3/7, 5/7, 5/7, 6/7, 2/7], 0.01709430206] [[6/7, 2/7, 4/7, 5/7, 5/7, 2/7, 0], 0.01611942125] [[6/7, 2/7, 1/7, 5/7, 5/7, 2/7, 4/7], 0.01636949151] [[6/7, 6/7, 1/7, 5/7, 5/7, 6/7, 2/7], 0.01666176812] [[6/7, 6/7, 3/7, 5/7, 5/7, 6/7, 4/7], 0.01722167452] [[0, 2/7, 4/7, 6/7, 6/7, 2/7, 1/7], 0.02221656512] [[0, 2/7, 1/7, 6/7, 6/7, 2/7, 5/7], 0.02324369285] [[0, 3/7, 5/7, 6/7, 6/7, 3/7, 1/7], 0.01588292229] [[0, 3/7, 2/7, 6/7, 6/7, 3/7, 5/7], 0.01698494462] [[0, 4/7, 1/7, 6/7, 6/7, 4/7, 2/7], 0.02268590134] [[0, 4/7, 2/7, 6/7, 6/7, 4/7, 3/7], 0.02273754421] [[0, 5/7, 1/7, 6/7, 6/7, 5/7, 2/7], 0.01636787775] [[1/7, 1/7, 4/7, 6/7, 6/7, 1/7, 0], 0.02251152660] [[1/7, 1/7, 2/7, 6/7, 6/7, 1/7, 5/7], 0.02324576954] [[1/7, 2/7, 5/7, 6/7, 6/7, 2/7, 0], 0.01594556365] [[1/7, 2/7, 3/7, 6/7, 6/7, 2/7, 5/7], 0.01698873976] [[1/7, 5/7, 2/7, 6/7, 6/7, 5/7, 3/7], 0.01730233118] [[1/7, 5/7, 3/7, 6/7, 6/7, 5/7, 4/7], 0.01729453283] [[2/7, 2/7, 1/7, 6/7, 6/7, 2/7, 0], 0.02282003231] [[2/7, 2/7, 4/7, 6/7, 6/7, 2/7, 3/7], 0.02274465259] [[2/7, 3/7, 1/7, 6/7, 6/7, 3/7, 0], 0.01639109197] [[3/7, 1/7, 2/7, 6/7, 6/7, 1/7, 0], 0.02281827501] [[3/7, 1/7, 4/7, 6/7, 6/7, 1/7, 2/7], 0.02269125214] [[3/7, 3/7, 2/7, 6/7, 6/7, 3/7, 1/7], 0.01720582903] [[3/7, 3/7, 5/7, 6/7, 6/7, 3/7, 4/7], 0.01730062978] [[4/7, 1/7, 3/7, 6/7, 6/7, 1/7, 0], 0.01638786111] [[4/7, 1/7, 5/7, 6/7, 6/7, 1/7, 2/7], 0.01637447183] [[4/7, 2/7, 3/7, 6/7, 6/7, 2/7, 1/7], 0.01720431843] [[4/7, 2/7, 5/7, 6/7, 6/7, 2/7, 3/7], 0.01730691746] [[5/7, 4/7, 1/7, 6/7, 6/7, 4/7, 0], 0.02267494818] [[5/7, 4/7, 2/7, 6/7, 6/7, 4/7, 1/7], 0.02286349345] [[5/7, 5/7, 1/7, 6/7, 6/7, 5/7, 0], 0.01641356528] [[5/7, 5/7, 2/7, 6/7, 6/7, 5/7, 0], 0.01694639272] [[5/7, 5/7, 3/7, 6/7, 6/7, 5/7, 1/7], 0.01705510796] [[5/7, 5/7, 3/7, 6/7, 6/7, 5/7, 2/7], 0.01709654048] This took, 2217.038, seconds.