Generated 8/31/05 2-cocycle twisted invariants Z_5[t,t^(-1)]/( 5 element quandles [0 0 0 0 0] [ ] [1 1 1 1 1] [ ] [2 2 2 4 3] [ ] [3 3 4 3 2] [ ] [4 4 3 2 4] Knot, 1 [[11, 0]] Knot, 2 [[5, 0]] Knot, 3 [[5, 0]] Knot, 4 [[5, 0]] Knot, 5 [[5, 0], [1, (x[2] + 3 x[6] + 2 x[1]) t + x[2] + 4 x[1] + 2 x[6]], [1, (4 x[2] + 4 x[5] + x[1] + 3 x[6]) t + 4 x[2] + 4 x[5] + x[6] + 3 x[1]] , [1, (x[5] + 4 x[1] + 4 x[6] + 3 x[2]) t + x[2] + 4 x[1] + 4 x[6] + 3 x[5]] , [1, (x[5] + 2 x[1] + 4 x[6]) t + 2 x[6] + x[5] + 3 x[1]], [1, (4 x[2] + 2 x[5] + x[1]) t + 2 x[2] + 3 x[5] + x[1]], [1, (3 x[2] + x[6] + 2 x[5]) t + 2 x[2] + 4 x[5] + x[6]]] Knot, 6 [[5, 0]] Knot, 7 [[5, 0]] Knot, 8 [[5, 0]] Knot, 9 [[5, 0]] Knot, 10 [[5, 0]] Knot, 11 [[5, 0], [2, (2 x[5] + 2 x[1]) t + 3 x[6] + 3 x[2]], [2, (2 x[2] + 3 x[1] + 3 x[6]) t + 2 x[2] + 3 x[1] + 2 x[5]], [2, (3 x[2] + 3 x[5] + 2 x[6]) t + 3 x[5] + 2 x[6] + 2 x[1]]] Knot, 12 [[5, 0]] Knot, 13 [[5, 0]] Knot, 14 [[5, 0], [2, (x[2] + x[1] + x[6] + x[5]) t + 4 x[2] + x[5] + 4 x[6] + x[1]], [2, (4 x[2] + 4 x[1]) t + 3 x[5] + x[1] + 2 x[6] + 4 x[2]], [2, (4 x[5] + 4 x[6]) t + 2 x[2] + x[5] + 3 x[1] + 4 x[6]]] Knot, 15 [[5, 0]] Knot, 16 [[5, 0]] Knot, 17 [[5, 0]] Knot, 18 [[5, 0]] Knot, 19 [[11, 0]] Knot, 20 [[5, 0]] Knot, 21 [[5, 0]] Knot, 22 [[5, 0]] Knot, 23 [[5, 0]] Knot, 24 [[11, 0]] Knot, 25 [[5, 0], [2, (2 x[5] + 2 x[1]) t + 3 x[6] + 3 x[2]], [2, (3 x[2] + 3 x[5] + 2 x[6]) t + 2 x[6] + 3 x[5] + 2 x[1]], [2, (2 x[2] + 3 x[1] + 3 x[6]) t + 3 x[1] + 2 x[2] + 2 x[5]]] Knot, 26 [[5, 0]] Knot, 27 [[5, 0]] Knot, 28 [[5, 0]] Knot, 29 [[11, 0]] Knot, 30 [[5, 0]] Knot, 31 [[5, 0]] Knot, 32 [[5, 0], [4, (3 x[5] + x[1] + 2 x[6] + 4 x[2]) t + x[2] + x[1]], [4, (2 x[2] + x[5] + 3 x[1] + 4 x[6]) t + x[5] + x[6]], [4, (3 x[2] + 4 x[5] + x[6] + 2 x[1]) t + 4 x[5] + 4 x[6]], [4, (x[2] + 4 x[5] + 4 x[1] + x[6]) t + x[5] + x[6] + x[2] + x[1]], [ 4, (4 x[2] + x[5] + 4 x[6] + x[1]) t + 4 x[6] + 4 x[2] + 4 x[1] + 4 x[5]] , [4, (2 x[5] + 4 x[1] + 3 x[6] + x[2]) t + 4 x[1] + 4 x[2]]] Knot, 33 [[11, 0]] Knot, 34 [[11, 0]] Knot, 35 [[11, 0]] [0 0 1 1 1] [ ] [1 1 0 0 0] [ ] [2 2 2 4 3] [ ] [3 3 4 3 2] [ ] [4 4 3 2 4] Knot, 1 [[11, 0]] Knot, 2 [[5, 0]] Knot, 3 [[5, 0]] Knot, 4 [[5, 0]] Knot, 5 [[5, 0], [1, (x[2] + 4 x[3] + 4 x[6] + 3 x[7]) t + 4 x[3] + 4 x[6] + x[7] + 3 x[2]] , [1, (3 x[3] + x[7] + 2 x[6]) t + 2 x[3] + 4 x[6] + x[7]], [1, (4 x[3] + 2 x[6] + x[2]) t + 2 x[3] + x[2] + 3 x[6]], [1, (x[6] + 2 x[2] + 4 x[7]) t + 2 x[7] + 3 x[2] + x[6]], [1, (x[3] + 3 x[7] + 2 x[2]) t + x[3] + 4 x[2] + 2 x[7]], [1, (4 x[2] + x[6] + 4 x[7] + 3 x[3]) t + x[3] + 4 x[2] + 4 x[7] + 3 x[6]] ] Knot, 6 [[5, 0]] Knot, 7 [[5, 0]] Knot, 8 [[5, 0]] Knot, 9 [[5, 0]] Knot, 10 [[5, 0]] Knot, 11 [[5, 0], [2, (2 x[2] + 2 x[6]) t + 3 x[7] + 3 x[3]], [2, (3 x[3] + 3 x[6] + 2 x[7]) t + 3 x[6] + 2 x[7] + 2 x[2]], [2, (2 x[3] + 3 x[2] + 3 x[7]) t + 2 x[3] + 3 x[2] + 2 x[6]]] Knot, 12 [[5, 0]] Knot, 13 [[5, 0]] Knot, 14 [[5, 0], [2, (4 x[6] + 4 x[7]) t + 3 x[2] + 2 x[3] + x[6] + 4 x[7]], [2, (x[3] + x[2] + x[7] + x[6]) t + 4 x[3] + x[6] + 4 x[7] + x[2]], [2, (4 x[3] + 4 x[2]) t + x[2] + 3 x[6] + 2 x[7] + 4 x[3]]] Knot, 15 [[5, 0]] Knot, 16 [[5, 0]] Knot, 17 [[5, 0]] Knot, 18 [[5, 0]] Knot, 19 [[11, 0]] Knot, 20 [[5, 0]] Knot, 21 [[5, 0]] Knot, 22 [[5, 0]] Knot, 23 [[5, 0]] Knot, 24 [[11, 0]] Knot, 25 [[5, 0], [2, (2 x[3] + 3 x[2] + 3 x[7]) t + 3 x[2] + 2 x[3] + 2 x[6]], [2, (3 x[3] + 3 x[6] + 2 x[7]) t + 2 x[7] + 3 x[6] + 2 x[2]], [2, (2 x[6] + 2 x[2]) t + 3 x[7] + 3 x[3]]] Knot, 26 [[5, 0]] Knot, 27 [[5, 0]] Knot, 28 [[5, 0]] Knot, 29 [[11, 0]] Knot, 30 [[5, 0]] Knot, 31 [[5, 0]] Knot, 32 [[5, 0], [4, (x[3] + 4 x[6] + 4 x[2] + x[7]) t + x[6] + x[7] + x[3] + x[2]], [4, (3 x[3] + 4 x[6] + x[7] + 2 x[2]) t + 4 x[6] + 4 x[7]], [4, (4 x[3] + x[6] + 4 x[7] + x[2]) t + 4 x[7] + 4 x[3] + 4 x[2] + 4 x[6]] , [4, (x[2] + 3 x[6] + 2 x[7] + 4 x[3]) t + x[3] + x[2]], [4, (x[3] + 4 x[2] + 3 x[7] + 2 x[6]) t + 4 x[2] + 4 x[3]], [4, (3 x[2] + 2 x[3] + x[6] + 4 x[7]) t + x[6] + x[7]]] Knot, 33 [[11, 0]] Knot, 34 [[11, 0]] Knot, 35 [[11, 0]] [0 0 0 0 0] [ ] [1 1 1 2 2] [ ] [2 2 2 1 1] [ ] [3 4 4 3 3] [ ] [4 3 3 4 4] Knot, 1 [[5, 0]] Knot, 2 [[5, 0]] Knot, 3 [[5, 0]] Knot, 4 [[5, 0]] Knot, 5 [[5, 0]] Knot, 6 [[5, 0]] Knot, 7 [[5, 0]] Knot, 8 [[5, 0]] Knot, 9 [[5, 0]] Knot, 10 [[5, 0]] Knot, 11 [[5, 0]] Knot, 12 [[5, 0]] Knot, 13 [[5, 0]] Knot, 14 [[5, 0]] Knot, 15 [[5, 0]] Knot, 16 [[5, 0]] Knot, 17 [[5, 0]] Knot, 18 [[5, 0]] Knot, 19 [[5, 0]] Knot, 20 [[5, 0]] Knot, 21 [[5, 0]] Knot, 22 [[5, 0]] Knot, 23 [[5, 0]] Knot, 24 [[5, 0]] Knot, 25 [[5, 0]] Knot, 26 [[5, 0]] Knot, 27 [[5, 0]] Knot, 28 [[5, 0]] Knot, 29 [[5, 0]] Knot, 30 [[5, 0]] Knot, 31 [[5, 0]] Knot, 32 [[5, 0]] Knot, 33 [[5, 0]] Knot, 34 [[5, 0]] Knot, 35 [[5, 0]] [0 0 0 0 0] [ ] [1 1 4 2 3] [ ] [2 3 2 4 1] [ ] [3 4 1 3 2] [ ] [4 2 3 1 4] Knot, 1 [[17, 0]] Knot, 2 [[5, 0], [2, (3 x[1] + 2 x[4] + 2 x[2] + x[3] + x[7]) t + 4 x[3] + 4 x[7]], [2, (4 x[1] + 4 x[3] + 4 x[4] + x[5] + x[7]) t + 4 x[5] + x[1] + 4 x[3] + 4 x[4] + 4 x[7]], [2, (2 x[1] + 3 x[2] + 3 x[4] + 4 x[3] + 4 x[7]) t + x[3] + x[7]], [2, (x[2] + 4 x[4] + x[5] + 4 x[7]) t + x[7] + x[2] + x[4] + x[5]], [ 2, (4 x[2] + x[4] + 4 x[5] + x[7]) t + 4 x[7] + 4 x[2] + 4 x[4] + 4 x[5]] , [2, (x[1] + x[3] + x[4] + 4 x[5] + 4 x[7]) t + x[7] + x[3] + x[4] + x[5] + 4 x[1]]] Knot, 3 [[5, 0]] Knot, 4 [[5, 0]] Knot, 5 [[5, 0]] Knot, 6 [[5, 0]] Knot, 7 [[5, 0]] Knot, 8 [[5, 0]] Knot, 9 [[5, 0], [2, (2 x[1] + 3 x[2] + 4 x[3] + 3 x[4] + 4 x[7]) t + x[3] + x[7]], [2, (4 x[1] + 4 x[3] + 4 x[4] + x[5] + x[7]) t + 4 x[3] + 4 x[4] + 4 x[5] + 4 x[7] + x[1]], [2, (x[1] + x[3] + x[4] + 4 x[5] + 4 x[7]) t + 4 x[1] + x[3] + x[4] + x[5] + x[7]], [2, (3 x[1] + 2 x[2] + x[3] + 2 x[4] + x[7]) t + 4 x[3] + 4 x[7]], [2, (4 x[2] + x[4] + 4 x[5] + x[7]) t + 4 x[2] + 4 x[4] + 4 x[5] + 4 x[7]] , [2, (x[2] + 4 x[4] + x[5] + 4 x[7]) t + x[2] + x[4] + x[5] + x[7]]] Knot, 10 [[5, 0], [2, (2 x[1] + 3 x[2] + 4 x[3] + 3 x[4] + 4 x[7]) t + x[3] + x[7]], [2, (4 x[1] + 4 x[3] + 4 x[4] + x[5] + x[7]) t + 4 x[3] + 4 x[4] + 4 x[5] + 4 x[7] + x[1]], [2, (x[1] + x[3] + x[4] + 4 x[5] + 4 x[7]) t + 4 x[1] + x[3] + x[4] + x[5] + x[7]], [2, (3 x[1] + 2 x[2] + x[3] + 2 x[4] + x[7]) t + 4 x[3] + 4 x[7]], [2, (4 x[2] + x[4] + 4 x[5] + x[7]) t + 4 x[2] + 4 x[4] + 4 x[5] + 4 x[7]] , [2, (x[2] + 4 x[4] + x[5] + 4 x[7]) t + x[2] + x[4] + x[5] + x[7]]] Knot, 11 [[5, 0]] Knot, 12 [[5, 0]] Knot, 13 [[5, 0]] Knot, 14 [[5, 0]] Knot, 15 [[17, 0]] Knot, 16 [[5, 0]] Knot, 17 [[5, 0]] Knot, 18 [[5, 0], [2, (4 x[3] + 4 x[7]) t + 2 x[1] + 3 x[2] + 4 x[3] + 3 x[4] + 4 x[7]], [2, (x[3] + x[7]) t + x[3] + 2 x[4] + x[7] + 3 x[1] + 2 x[2]], [2, (x[2] + x[4] + x[5] + x[7]) t + 4 x[2] + x[4] + 4 x[5] + x[7]], [ 2, (4 x[1] + x[3] + x[4] + x[5] + x[7]) t + 4 x[1] + 4 x[3] + 4 x[4] + x[5] + x[7]], [2, (x[1] + 4 x[3] + 4 x[4] + 4 x[5] + 4 x[7]) t + x[1] + x[3] + 4 x[7] + x[4] + 4 x[5]], [2, (4 x[2] + 4 x[4] + 4 x[5] + 4 x[7]) t + x[2] + 4 x[4] + x[5] + 4 x[7]] ] Knot, 19 [[17, 0]] Knot, 20 [[5, 0]] Knot, 21 [[5, 0]] Knot, 22 [[5, 0]] Knot, 23 [[5, 0]] Knot, 24 [[17, 0]] Knot, 25 [[5, 0], [2, (2 x[1] + 3 x[5] + 3 x[7]) t + 2 x[4] + 2 x[3]], [2, (2 x[3] + 2 x[4] + 2 x[7] + 3 x[1] + 2 x[2]) t + 3 x[1] + 2 x[4] + 2 x[2]], [2, (3 x[4] + 3 x[7]) t + 2 x[5] + 2 x[2]], [2, (2 x[4] + 2 x[7]) t + 3 x[5] + 3 x[2]], [2, (3 x[1] + 2 x[5] + 2 x[7]) t + 3 x[4] + 3 x[3]], [2, (2 x[1] + 3 x[2] + 3 x[3] + 3 x[4] + 3 x[7]) t + 3 x[2] + 3 x[4] + 2 x[1]]] Knot, 26 [[5, 0]] Knot, 27 [[5, 0], [2, (x[2] + 4 x[4] + x[5] + 4 x[7]) t + x[5] + x[7] + x[2] + x[4]], [2, (2 x[1] + 3 x[2] + 4 x[3] + 3 x[4] + 4 x[7]) t + x[3] + x[7]], [2, (3 x[1] + 2 x[2] + x[3] + 2 x[4] + x[7]) t + 4 x[3] + 4 x[7]], [2, (x[1] + x[3] + x[4] + 4 x[5] + 4 x[7]) t + x[4] + x[5] + 4 x[1] + x[3] + x[7]], [2, (4 x[1] + 4 x[3] + 4 x[4] + x[5] + x[7]) t + 4 x[5] + 4 x[7] + 4 x[3] + 4 x[4] + x[1]], [2, (4 x[2] + x[4] + 4 x[5] + x[7]) t + 4 x[5] + 4 x[7] + 4 x[2] + 4 x[4]] ] Knot, 28 [[5, 0]] Knot, 29 [[17, 0]] Knot, 30 [[5, 0]] Knot, 31 [[5, 0]] Knot, 32 [[5, 0], [2, (4 x[1] + x[2] + x[4] + 3 x[3] + 3 x[7]) t + 2 x[3] + 2 x[7]], [8, (3 x[1] + 2 x[2] + x[3] + 2 x[4] + x[7]) t + 4 x[3] + 4 x[7]], [8, (4 x[1] + 4 x[3] + 4 x[4] + x[5] + x[7]) t + 4 x[3] + 4 x[5] + 4 x[7] + x[1] + 4 x[4]], [2, (2 x[2] + 3 x[4] + 2 x[5] + 3 x[7]) t + 2 x[7] + 2 x[2] + 2 x[4] + 2 x[5]], [2, (3 x[2] + 2 x[4] + 3 x[5] + 2 x[7]) t + 3 x[2] + 3 x[4] + 3 x[5] + 3 x[7]], [2, (2 x[1] + 2 x[3] + 2 x[4] + 3 x[5] + 3 x[7]) t + 2 x[3] + 2 x[5] + 2 x[7] + 3 x[1] + 2 x[4]], [2, (x[1] + 4 x[2] + 4 x[4] + 2 x[3] + 2 x[7]) t + 3 x[3] + 3 x[7]], [8, (3 x[2] + 4 x[3] + 3 x[4] + 2 x[1] + 4 x[7]) t + x[3] + x[7]], [8, (x[1] + x[4] + 4 x[5] + x[3] + 4 x[7]) t + x[7] + x[3] + x[4] + x[5] + 4 x[1]], [8, (x[2] + 4 x[4] + x[5] + 4 x[7]) t + x[7] + x[2] + x[4] + x[5]], [ 2, (3 x[1] + 3 x[3] + 3 x[4] + 2 x[5] + 2 x[7]) t + 2 x[1] + 3 x[4] + 3 x[3] + 3 x[7] + 3 x[5]], [8, (4 x[2] + x[4] + 4 x[5] + x[7]) t + 4 x[5] + 4 x[2] + 4 x[4] + 4 x[7]] ] Knot, 33 [[17, 0]] Knot, 34 [[17, 0]] Knot, 35 [[17, 0]] [0 0 1 1 1] [ ] [1 1 0 0 0] [ ] [3 4 2 4 3] [ ] [4 2 4 3 2] [ ] [2 3 3 2 4] Knot, 1 [[11, 0]] Knot, 2 [[5, 0]] Knot, 3 [[5, 0]] Knot, 4 [[5, 0]] Knot, 5 [[5, 0], [1, (x[2] + 3 x[6] + 2 x[1]) t + x[2] + 4 x[1] + 2 x[6]], [1, (4 x[2] + 2 x[5] + x[1]) t + 2 x[2] + x[1] + 3 x[5]], [1, (2 x[1] + x[5] + 4 x[6]) t + 2 x[6] + 3 x[1] + x[5]], [1, (3 x[2] + x[6] + 2 x[5]) t + 2 x[2] + 4 x[5] + x[6]], [1, (x[1] + 4 x[2] + 4 x[5] + 3 x[6]) t + 4 x[2] + 4 x[5] + x[6] + 3 x[1]] , [1, (4 x[1] + x[5] + 4 x[6] + 3 x[2]) t + 4 x[1] + x[2] + 4 x[6] + 3 x[5]] ] Knot, 6 [[5, 0]] Knot, 7 [[5, 0]] Knot, 8 [[5, 0]] Knot, 9 [[5, 0]] Knot, 10 [[5, 0]] Knot, 11 [[5, 0], [2, (2 x[1] + 2 x[5]) t + 3 x[6] + 3 x[2]], [2, (3 x[2] + 3 x[5] + 2 x[6]) t + 3 x[5] + 2 x[6] + 2 x[1]], [2, (3 x[1] + 2 x[2] + 3 x[6]) t + 3 x[1] + 2 x[2] + 2 x[5]]] Knot, 12 [[5, 0]] Knot, 13 [[5, 0]] Knot, 14 [[5, 0], [2, (x[1] + x[2] + x[6] + x[5]) t + 4 x[2] + x[5] + 4 x[6] + x[1]], [2, (4 x[2] + 4 x[1]) t + x[1] + 3 x[5] + 2 x[6] + 4 x[2]], [2, (4 x[5] + 4 x[6]) t + 3 x[1] + 2 x[2] + x[5] + 4 x[6]]] Knot, 15 [[5, 0]] Knot, 16 [[5, 0]] Knot, 17 [[5, 0]] Knot, 18 [[5, 0]] Knot, 19 [[11, 0]] Knot, 20 [[5, 0]] Knot, 21 [[5, 0]] Knot, 22 [[5, 0]] Knot, 23 [[5, 0]] Knot, 24 [[11, 0]] Knot, 25 [[5, 0], [2, (3 x[1] + 2 x[2] + 3 x[6]) t + 3 x[1] + 2 x[2] + 2 x[5]], [2, (3 x[2] + 3 x[5] + 2 x[6]) t + 2 x[6] + 2 x[1] + 3 x[5]], [2, (2 x[5] + 2 x[1]) t + 3 x[6] + 3 x[2]]] Knot, 26 [[5, 0]] Knot, 27 [[5, 0]] Knot, 28 [[5, 0]] Knot, 29 [[11, 0]] Knot, 30 [[5, 0]] Knot, 31 [[5, 0]] Knot, 32 [[5, 0], [4, (3 x[1] + 2 x[2] + x[5] + 4 x[6]) t + x[5] + x[6]], [4, (4 x[1] + x[2] + 3 x[6] + 2 x[5]) t + 4 x[1] + 4 x[2]], [4, (3 x[2] + 4 x[5] + x[6] + 2 x[1]) t + 4 x[5] + 4 x[6]], [4, (x[2] + 4 x[5] + 4 x[1] + x[6]) t + x[5] + x[6] + x[2] + x[1]], [ 4, (4 x[2] + x[5] + x[1] + 4 x[6]) t + 4 x[6] + 4 x[1] + 4 x[2] + 4 x[5]] , [4, (x[1] + 3 x[5] + 2 x[6] + 4 x[2]) t + x[2] + x[1]]] Knot, 33 [[11, 0]] Knot, 34 [[11, 0]] Knot, 35 [[11, 0]] [0 3 4 2 1] [ ] [2 1 3 4 0] [ ] [1 4 2 0 3] [ ] [4 0 1 3 2] [ ] [3 2 0 1 4] Knot, 1 [[5, 0]] Knot, 2 [[5, 0], [2, (4 x[1] + 2 x[3] + 2 x[5] + 4 x[4] + x[2] + 2 x[6]) t + 4 x[4] + 2 x[5] + 4 x[2] + 2 x[7] + 4 x[3] + 4 x[1]], [2, (x[1] + 4 x[4] + 4 x[5] + x[7]) t + x[1] + x[4] + x[7] + x[5]], [ 2, (4 x[4] + x[5] + 4 x[3] + 4 x[7] + x[2] + x[1]) t + x[5] + x[1] + x[4] + 4 x[3] + x[7] + 4 x[2]], [2, (4 x[1] + 2 x[4] + 4 x[6] + 2 x[7] + 2 x[3] + 4 x[2] + 2 x[5]) t + x[2] + 4 x[4] + x[3] + 4 x[1]], [2, (3 x[5] + 3 x[7] + 3 x[4] + x[2] + 3 x[3] + x[6] + x[1]) t + 4 x[2] + 4 x[3] + x[1] + x[4]], [2, (3 x[4] + 2 x[6] + 4 x[3] + 4 x[2] + 2 x[5]) t + 3 x[7] + x[2] + x[3] + 3 x[5]], [2, (4 x[1] + x[4] + x[5] + 4 x[7]) t + 4 x[1] + 4 x[4] + 4 x[5] + 4 x[7]] , [2, (x[4] + 3 x[5] + 3 x[6] + 3 x[3] + x[1] + 4 x[2]) t + 3 x[5] + x[1] + x[2] + x[3] + 3 x[7] + x[4]], [2, (4 x[1] + x[4] + 4 x[5] + x[3] + 4 x[2] + x[7]) t + 4 x[5] + 4 x[1] + x[2] + x[3] + 4 x[7] + 4 x[4]], [2, (2 x[4] + 3 x[5] + 3 x[6] + x[2] + x[3]) t + 4 x[2] + 2 x[5] + 2 x[7] + 4 x[3]]] Knot, 3 [[25, 0]] Knot, 4 [[5, 0]] Knot, 5 [[5, 0]] Knot, 6 [[5, 0]] Knot, 7 [[5, 0]] Knot, 8 [[5, 0]] Knot, 9 [[5, 0]] Knot, 10 [[5, 0]] Knot, 11 [[5, 0], [ 1, (3 x[5] + 2 x[6] + x[7] + x[3]) t + 3 x[1] + x[5] + 3 x[7] + 3 x[2] ], [1, (x[5] + x[6] + x[7] + 4 x[4] + 2 x[2] + 4 x[3] + 2 x[1]) t + x[3] + 2 x[5] + 2 x[6]], [1, (2 x[5] + 2 x[6] + 3 x[4] + 2 x[2] + 3 x[3] + 3 x[1]) t + x[6] + 2 x[3] + 2 x[4]], [1, (4 x[5] + 3 x[6] + x[7] + 2 x[4] + 4 x[2] + 3 x[3] + 2 x[1]) t + 4 x[5] + 2 x[4] + x[2] + 2 x[7] + x[3]], [1, (3 x[6] + 2 x[7] + x[4] + 4 x[1]) t + x[1] + x[4] + 3 x[6] + 3 x[2] + 2 x[3] + 2 x[7]], [1, (3 x[5] + x[7] + 4 x[2] + 4 x[3] + 3 x[1]) t + 2 x[5] + 3 x[6] + 4 x[2] + 3 x[3] + 4 x[7]], [1, (x[5] + 4 x[7] + 3 x[3] + 2 x[1]) t + 3 x[7] + x[3] + 3 x[5] + 4 x[6] + 3 x[2] + 3 x[4]], [1, (x[5] + 2 x[6] + 4 x[7] + 2 x[4] + 4 x[2] + 4 x[3] + 4 x[1]) t + x[3] + x[1] + 2 x[5] + 4 x[7] + x[2] + 4 x[4]], [1, (3 x[5] + 4 x[6] + 3 x[7] + 3 x[4] + 4 x[2] + 2 x[3]) t + x[2] + x[3] + 4 x[7] + 3 x[1] + x[5]], [1, (4 x[5] + 2 x[7] + 4 x[4] + 2 x[2] + x[1]) t + 3 x[6] + 3 x[4] + x[7] + 4 x[5] + x[1]], [1, (x[5] + 3 x[6] + 3 x[7] + x[4] + 4 x[3] + x[1]) t + 3 x[4] + 2 x[2] + x[5] + 3 x[7] + 2 x[3] + x[1] + 3 x[6]], [1, (2 x[5] + 2 x[6] + 2 x[4] + 4 x[1]) t + x[5] + x[6] + 4 x[3] + 3 x[4] + x[1] + x[7] + 2 x[2]], [1, (2 x[7] + 4 x[2] + 4 x[3] + 2 x[1]) t + 2 x[7] + 2 x[4] + 4 x[2] + x[3]], [1, (2 x[5] + 4 x[7] + 2 x[4] + 2 x[3]) t + 2 x[6] + 2 x[2] + 3 x[4] + x[5] + 4 x[7] + 3 x[3] + 3 x[1]], [1, (x[5] + 4 x[6] + x[7] + x[4] + 3 x[3] + 3 x[1]) t + 2 x[2] + 4 x[7] + x[5] + 3 x[4]], [1, (2 x[5] + 3 x[6] + 4 x[7] + x[4] + 2 x[2] + 2 x[3] + 4 x[1]) t + x[7] + x[1] + 3 x[3] + 4 x[4] + 3 x[5]], [1, (x[5] + 4 x[7] + 2 x[4] + 4 x[2] + 4 x[3]) t + 4 x[6] + 2 x[3] + 4 x[2] + x[5] + x[7] + 3 x[1] + x[4]], [ 1, (3 x[5] + 4 x[2] + x[3] + 3 x[1]) t + x[2] + 3 x[4] + x[3] + 3 x[5] ], [1, (x[5] + 3 x[7] + 4 x[4] + 4 x[2] + 4 x[3] + x[1]) t + 3 x[5] + 2 x[6] + 4 x[2] + 4 x[3] + x[7] + 4 x[4] + x[1]], [1, (x[6] + 3 x[4] + 2 x[3] + x[1]) t + 3 x[2] + 4 x[4] + 2 x[6] + 2 x[5] + x[1] + 3 x[3]]] Knot, 12 [[5, 0]] Knot, 13 [[5, 0]] Knot, 14 [[5, 0]] Knot, 15 [[5, 0]] Knot, 16 [[5, 0]] Knot, 17 [[5, 0]] Knot, 18 [[5, 0]] Knot, 19 [[5, 0]] Knot, 20 [[5, 0]] Knot, 21 [[5, 0]] Knot, 22 [[5, 0], [1, (x[5] + 4 x[6] + x[7] + 2 x[4] + 4 x[2] + 2 x[3] + 4 x[1]) t + 4 x[1] + 4 x[6] + 2 x[3] + x[2] + x[7] + 3 x[5]], [1, (3 x[5] + 3 x[6] + 4 x[2] + 3 x[3]) t + 4 x[5] + 2 x[1] + 4 x[4] + x[6] + 3 x[7] + x[2]], [1, (x[5] + x[6] + x[7] + 3 x[4] + 3 x[2] + x[1]) t + x[1] + 3 x[4] + 4 x[3] + 3 x[6] + x[2] + 3 x[7]], [1, (3 x[5] + 2 x[6] + x[7] + 2 x[4] + 3 x[2] + 3 x[3] + 4 x[1]) t + x[1] + 2 x[4] + 4 x[5] + 2 x[6] + 4 x[7]], [1, (2 x[6] + 3 x[7] + 4 x[4] + 3 x[2] + 4 x[3] + 4 x[1]) t + 4 x[1] + 4 x[3] + 2 x[5] + 3 x[6] + x[2] + x[4]], [1, (x[5] + 3 x[6] + 3 x[7] + x[4] + 3 x[2] + 2 x[3] + x[1]) t + 2 x[7] + 2 x[5] + 4 x[3] + x[1] + 3 x[4] + 3 x[6]], [1, (3 x[5] + 3 x[4] + 4 x[2] + x[3] + x[1]) t + 4 x[3] + 2 x[1] + 2 x[6] + 4 x[4] + x[2]], [1, (3 x[7] + 4 x[4] + x[2] + 4 x[3] + x[1]) t + 4 x[6] + 4 x[5] + 2 x[7] + 4 x[2] + 2 x[4] + x[1]], [1, (3 x[5] + 3 x[6] + x[4] + x[2] + x[3] + 4 x[1]) t + x[6] + x[1] + 3 x[3] + 3 x[5] + 4 x[2] + 3 x[4] + 2 x[7]], [1, (4 x[5] + 2 x[6] + 2 x[7] + 2 x[4] + 4 x[2] + 4 x[3] + 4 x[1]) t + 3 x[3] + x[4] + 3 x[5] + 3 x[6] + x[1] + x[7] + x[2]], [1, (3 x[5] + 4 x[6] + 3 x[7] + 4 x[4] + 3 x[2] + x[3] + x[1]) t + 3 x[3] + 2 x[1] + 3 x[5] + 2 x[4] + x[7] + 4 x[6]], [1, (4 x[5] + x[7] + 4 x[4] + 4 x[2] + 4 x[3] + x[1]) t + x[4] + 4 x[2] + x[3] + 3 x[7] + x[1] + 4 x[5]], [1, (4 x[5] + 2 x[7] + x[4] + 4 x[2] + 4 x[3] + 4 x[1]) t + 3 x[6] + 4 x[2] + x[4] + 3 x[5] + 3 x[3] + 3 x[7] + 4 x[1]], [1, (4 x[5] + x[7] + x[4] + 3 x[2] + 4 x[1]) t + x[7] + 4 x[4] + 2 x[5] + 2 x[3] + 4 x[1]], [1, (x[6] + 2 x[4] + x[2] + 3 x[3]) t + 2 x[1] + 3 x[7] + 3 x[6] + x[3] + 4 x[2] + 2 x[4]], [1, (2 x[7] + 3 x[4] + 4 x[2] + 4 x[3]) t + 2 x[5] + 2 x[1] + 4 x[2] + 4 x[3] + 2 x[6] + 2 x[7] + 3 x[4]], [1, (2 x[5] + 3 x[4] + 4 x[2] + 4 x[3] + x[1]) t + 2 x[5] + 2 x[1] + 4 x[2] + 2 x[3] + 2 x[4] + 4 x[6]], [1, (3 x[6] + 2 x[7] + x[4] + 3 x[2] + 3 x[3] + 4 x[1]) t + 3 x[6] + 4 x[3] + x[4] + x[5] + x[1] + x[7] + x[2]], [1, (x[5] + 2 x[6] + 4 x[7] + x[4] + x[2] + 2 x[3] + x[1]) t + 2 x[3] + 2 x[1] + 4 x[4] + 3 x[7] + 4 x[2] + 3 x[5] + 2 x[6]], [1, (3 x[5] + x[7] + 3 x[4] + 3 x[2] + x[3]) t + x[2] + 3 x[6] + 4 x[3] + 2 x[1] + 2 x[4]]] Knot, 23 [[5, 0], [2, (x[4] + x[5] + 4 x[7] + 4 x[1]) t + 4 x[4] + 4 x[5] + 4 x[7] + 4 x[1]] , [2, (3 x[4] + 2 x[5] + 2 x[6] + 4 x[3] + 4 x[2]) t + 3 x[5] + 3 x[7] + x[3] + x[2]], [2, (x[1] + 4 x[5] + x[7] + 4 x[4]) t + x[7] + x[4] + x[5] + x[1]], [ 2, (x[1] + x[4] + 3 x[5] + 3 x[6] + 3 x[3] + 4 x[2]) t + x[3] + 3 x[5] + 3 x[7] + x[4] + x[1] + x[2]], [2, (4 x[1] + x[2] + 2 x[3] + 2 x[5] + 2 x[6] + 4 x[4]) t + 4 x[1] + 4 x[3] + 2 x[5] + 2 x[7] + 4 x[2] + 4 x[4]], [2, (2 x[3] + 2 x[5] + 4 x[6] + 4 x[1] + 2 x[4] + 2 x[7] + 4 x[2]) t + 4 x[1] + x[3] + 4 x[4] + x[2]], [2, (x[1] + 4 x[4] + x[5] + 4 x[7] + 4 x[3] + x[2]) t + x[7] + x[5] + 4 x[3] + 4 x[2] + x[4] + x[1]], [2, (3 x[4] + 3 x[5] + 3 x[7] + x[1] + x[6] + 3 x[3] + x[2]) t + 4 x[3] + 4 x[2] + x[4] + x[1]], [2, (x[4] + x[3] + x[7] + 4 x[5] + 4 x[1] + 4 x[2]) t + x[2] + 4 x[1] + 4 x[4] + 4 x[7] + x[3] + 4 x[5]], [2, (2 x[4] + 3 x[5] + 3 x[6] + x[3] + x[2]) t + 4 x[3] + 2 x[5] + 2 x[7] + 4 x[2]]] Knot, 24 [[5, 0]] Knot, 25 [[5, 0]] Knot, 26 [[5, 0]] Knot, 27 [[5, 0]] Knot, 28 [[5, 0]] Knot, 29 [[5, 0]] Knot, 30 [[5, 0], [2, (x[1] + 3 x[4] + x[5] + x[6] + 4 x[3]) t + x[1] + x[4]], [2, (2 x[4] + 3 x[6] + 3 x[7] + 2 x[2]) t + 2 x[5] + 3 x[2] + 3 x[3] + 2 x[7]], [2, (4 x[5] + 3 x[6] + x[4] + 4 x[7] + 2 x[2] + x[1]) t + x[4] + 3 x[2] + 3 x[5] + 3 x[7] + x[1] + 3 x[3]], [2, (3 x[1] + 3 x[4] + 4 x[6] + x[7] + 2 x[3] + 3 x[5] + 4 x[2]) t + x[3] + 3 x[1] + 4 x[5] + 4 x[7] + x[2] + 3 x[4]], [2, (2 x[4] + x[5] + x[7] + 4 x[2] + 2 x[6] + 4 x[3] + x[1]) t + 4 x[7] + x[3] + x[1] + x[4] + 4 x[5] + x[2]], [2, (2 x[4] + 4 x[5] + 4 x[7] + 3 x[6] + 3 x[3] + 4 x[2]) t + 2 x[5] + 2 x[7] + x[2] + x[3]], [2, (x[4] + 3 x[6] + 2 x[3] + 3 x[7] + x[1]) t + x[4] + 3 x[5] + 3 x[7] + x[1]], [2, (3 x[1] + 3 x[3] + x[5] + x[7] + 2 x[6]) t + x[7] + 3 x[4] + 3 x[1] + x[5]], [2, (3 x[5] + x[3] + 4 x[2] + 2 x[7]) t + x[2] + x[3]], [2, (x[3] + x[4] + 3 x[5] + 4 x[6] + x[7]) t + x[5] + x[7]]] Knot, 31 [[5, 0]] Knot, 32 [[5, 0], [2, (3 x[1] + 4 x[3] + 4 x[5] + 3 x[4] + 2 x[2] + 4 x[6]) t + 3 x[4] + 4 x[5] + 3 x[2] + 4 x[7] + 3 x[3] + 3 x[1]], [2, (2 x[4] + x[5] + x[6] + x[3] + 2 x[1] + 3 x[2]) t + x[7] + 2 x[1] + 2 x[2] + 2 x[3] + 2 x[4] + x[5]], [2, (3 x[1] + 2 x[4] + 2 x[5] + 3 x[7]) t + 3 x[7] + 3 x[1] + 3 x[5] + 3 x[4]], [2, (3 x[4] + 3 x[5] + 2 x[7] + 2 x[1]) t + 2 x[4] + 2 x[1] + 2 x[5] + 2 x[7]], [2, (3 x[1] + 4 x[4] + 3 x[6] + 4 x[7] + 4 x[3] + 3 x[2] + 4 x[5]) t + 2 x[2] + 3 x[4] + 2 x[3] + 3 x[1]], [2, (3 x[4] + 2 x[5] + 3 x[3] + 3 x[7] + 2 x[2] + 2 x[1]) t + 2 x[7] + 2 x[4] + 3 x[3] + 2 x[5] + 3 x[2] + 2 x[1]], [2, (4 x[4] + x[5] + x[6] + 2 x[2] + 2 x[3]) t + 3 x[2] + 4 x[5] + 4 x[7] + 3 x[3]], [2, (x[4] + 4 x[6] + 3 x[3] + 3 x[2] + 4 x[5]) t + x[7] + 2 x[2] + 2 x[3] + x[5]], [2, (2 x[1] + x[4] + 2 x[6] + x[7] + x[3] + 2 x[2] + x[5]) t + 3 x[3] + 2 x[4] + 3 x[2] + 2 x[1]], [2, (3 x[1] + 2 x[4] + 3 x[5] + 2 x[3] + 3 x[2] + 2 x[7]) t + 3 x[5] + 3 x[1] + 2 x[2] + 2 x[3] + 3 x[7] + 3 x[4]]] Knot, 33 [[5, 0]] Knot, 34 [[5, 0]] Knot, 35 [[5, 0], [2, (2 x[5] + 3 x[7] + x[2] + 4 x[3]) t + 4 x[2] + 4 x[3]], [2, (4 x[4] + 2 x[7] + 4 x[1] + 2 x[6] + 3 x[3]) t + 4 x[4] + 2 x[5] + 4 x[1] + 2 x[7]], [2, (3 x[4] + x[5] + x[7] + 2 x[3] + 2 x[6] + x[2]) t + 3 x[7] + 4 x[3] + 4 x[2] + 3 x[5]], [2, (4 x[1] + 2 x[4] + 4 x[6] + x[3] + 4 x[5]) t + 4 x[1] + 4 x[4]], [ 2, (4 x[4] + x[5] + x[7] + 2 x[6] + 4 x[1] + 3 x[2]) t + 4 x[4] + 2 x[3] + 2 x[2] + 2 x[7] + 2 x[5] + 4 x[1]], [2, (4 x[5] + 4 x[7] + 3 x[6] + 2 x[3] + 2 x[1]) t + 2 x[1] + 4 x[5] + 2 x[4] + 4 x[7]], [2, (4 x[4] + 2 x[5] + 4 x[7] + x[6] + 4 x[3]) t + 4 x[5] + 4 x[7]], [ 2, (x[3] + 4 x[5] + 3 x[6] + 4 x[1] + 4 x[7] + 3 x[4] + x[2]) t + x[7] + 4 x[4] + 4 x[3] + x[5] + 4 x[1] + 4 x[2]], [2, (3 x[2] + 2 x[6] + 2 x[7] + 3 x[4]) t + 2 x[2] + 3 x[5] + 3 x[7] + 2 x[3]], [2, (3 x[3] + 2 x[5] + x[6] + 2 x[4] + 4 x[7] + x[2] + 2 x[1]) t + 4 x[2] + 2 x[1] + 4 x[3] + x[5] + 2 x[4] + x[7]]]