12a
0055
(K12a
0055
)
A knot diagram
1
Linearized knot diagam
3 5 7 2 10 4 12 1 11 6 9 8
Solving Sequence
5,10
6
3,11
2 1 4 7 9 12 8
c
5
c
10
c
2
c
1
c
4
c
6
c
9
c
11
c
8
c
3
, c
7
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.73784 × 10
105
u
87
+ 2.33065 × 10
106
u
86
+ ··· + 1.32969 × 10
107
b + 6.87193 × 10
107
,
1.27360 × 10
106
u
87
+ 7.35251 × 10
105
u
86
+ ··· + 2.65937 × 10
107
a + 7.67895 × 10
107
,
u
88
+ 2u
87
+ ··· + 12u 8i
I
u
2
= hb + 1, 2u
7
u
6
3u
5
+ 3u
4
+ 4u
3
3u
2
+ a 2u + 4, u
8
u
7
u
6
+ 2u
5
+ u
4
2u
3
+ 2u 1i
I
v
1
= ha, v
2
+ b 3v + 1, v
3
+ 2v
2
3v + 1i
* 3 irreducible components of dim
C
= 0, with total 99 representations.
1
The image of knot diagram is generated by the software Draw programme developed by An-
drew Bartholomew(http://www.layer8.co.uk/maths/draw/index.htm#Running-draw), where we modi-
fied some parts for our purpose(https://github.com/CATsTAILs/LinksPainter).
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
1
I. I
u
1
= h−2.74 × 10
105
u
87
+ 2.33 × 10
106
u
86
+ · · · + 1.33 × 10
107
b + 6.87 ×
10
107
, 1.27 × 10
106
u
87
+ 7.35 × 10
105
u
86
+ · · · + 2.66 × 10
107
a + 7.68 ×
10
107
, u
88
+ 2u
87
+ · · · + 12u 8i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
6
=
1
u
2
a
3
=
0.0478909u
87
0.0276475u
86
+ ··· + 35.3569u 2.88750
0.0205902u
87
0.175279u
86
+ ··· + 0.764280u 5.16808
a
11
=
u
u
3
+ u
a
2
=
0.0684810u
87
0.202926u
86
+ ··· + 36.1212u 8.05559
0.0205902u
87
0.175279u
86
+ ··· + 0.764280u 5.16808
a
1
=
1.39916u
87
+ 3.39018u
86
+ ··· + 13.5712u + 13.1209
1.39649u
87
3.74999u
86
+ ··· 0.897228u 18.8300
a
4
=
0.408355u
87
+ 1.20087u
86
+ ··· + 32.6967u 0.441203
0.968270u
87
2.08814u
86
+ ··· 0.974469u 4.14421
a
7
=
0.00267385u
87
0.359809u
86
+ ··· + 12.6740u 5.70909
1.24468u
87
+ 3.55177u
86
+ ··· + 5.30050u + 15.9088
a
9
=
u
3
u
5
u
3
+ u
a
12
=
u
5
u
u
7
+ u
5
2u
3
+ u
a
8
=
0.290712u
87
1.73558u
86
+ ··· + 6.94662u 12.1213
1.45970u
87
+ 4.30683u
86
+ ··· + 8.54245u + 17.9540
(ii) Obstruction class = 1
(iii) Cusp Shapes = 6.18054u
87
+ 14.8609u
86
+ ··· + 127.311u + 12.9010
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
88
+ 38u
87
+ ··· + 101u + 1
c
2
, c
4
u
88
10u
87
+ ··· 7u + 1
c
3
, c
6
u
88
2u
87
+ ··· + 128u 256
c
5
, c
10
u
88
2u
87
+ ··· 12u 8
c
7
, c
8
, c
12
u
88
5u
87
+ ··· + 8u + 1
c
9
, c
11
u
88
+ 24u
87
+ ··· + 1872u + 64
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
88
+ 34y
87
+ ··· 4505y + 1
c
2
, c
4
y
88
38y
87
+ ··· 101y + 1
c
3
, c
6
y
88
+ 54y
87
+ ··· + 999424y + 65536
c
5
, c
10
y
88
24y
87
+ ··· 1872y + 64
c
7
, c
8
, c
12
y
88
71y
87
+ ··· + 62y + 1
c
9
, c
11
y
88
+ 76y
87
+ ··· 105728y + 4096
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.392572 + 0.920696I
a = 0.031296 0.890953I
b = 0.670708 + 0.469662I
1.30721 + 0.66243I 0
u = 0.392572 0.920696I
a = 0.031296 + 0.890953I
b = 0.670708 0.469662I
1.30721 0.66243I 0
u = 0.887881 + 0.457891I
a = 0.090976 + 0.352185I
b = 0.479587 + 0.533093I
1.43432 + 2.39937I 0
u = 0.887881 0.457891I
a = 0.090976 0.352185I
b = 0.479587 0.533093I
1.43432 2.39937I 0
u = 0.203330 + 1.003580I
a = 0.381810 + 0.869323I
b = 0.991760 0.565904I
2.39788 + 5.04856I 0
u = 0.203330 1.003580I
a = 0.381810 0.869323I
b = 0.991760 + 0.565904I
2.39788 5.04856I 0
u = 0.958732 + 0.139931I
a = 0.735606 + 0.670342I
b = 0.335372 0.551660I
5.40258 + 0.56073I 0
u = 0.958732 0.139931I
a = 0.735606 0.670342I
b = 0.335372 + 0.551660I
5.40258 0.56073I 0
u = 0.862313 + 0.579468I
a = 0.321746 + 0.371790I
b = 0.515120 + 0.203414I
1.47628 + 2.33295I 0
u = 0.862313 0.579468I
a = 0.321746 0.371790I
b = 0.515120 0.203414I
1.47628 2.33295I 0
5
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.947226 + 0.084231I
a = 1.94827 0.02918I
b = 0.941810 + 0.560456I
0.97747 2.78041I 12.00000 + 0.I
u = 0.947226 0.084231I
a = 1.94827 + 0.02918I
b = 0.941810 0.560456I
0.97747 + 2.78041I 12.00000 + 0.I
u = 1.000340 + 0.317524I
a = 1.70909 + 1.08359I
b = 1.024730 0.591282I
0.03297 + 7.08755I 0
u = 1.000340 0.317524I
a = 1.70909 1.08359I
b = 1.024730 + 0.591282I
0.03297 7.08755I 0
u = 1.044510 + 0.227043I
a = 0.930430 0.232517I
b = 1.224440 + 0.244106I
8.09834 2.07994I 0
u = 1.044510 0.227043I
a = 0.930430 + 0.232517I
b = 1.224440 0.244106I
8.09834 + 2.07994I 0
u = 0.870126 + 0.281441I
a = 0.615716 1.177220I
b = 0.759307 0.539626I
0.37405 + 1.65782I 12.00000 + 0.I
u = 0.870126 0.281441I
a = 0.615716 + 1.177220I
b = 0.759307 + 0.539626I
0.37405 1.65782I 12.00000 + 0.I
u = 1.058740 + 0.305027I
a = 0.70456 1.67547I
b = 1.073140 + 0.441465I
7.60787 + 4.58396I 0
u = 1.058740 0.305027I
a = 0.70456 + 1.67547I
b = 1.073140 0.441465I
7.60787 4.58396I 0
6
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.753149 + 0.812851I
a = 0.009896 1.120230I
b = 1.306960 + 0.017227I
1.25565 1.36378I 0
u = 0.753149 0.812851I
a = 0.009896 + 1.120230I
b = 1.306960 0.017227I
1.25565 + 1.36378I 0
u = 1.038570 + 0.425588I
a = 0.126062 + 0.339240I
b = 0.227675 0.708873I
3.58769 5.33790I 0
u = 1.038570 0.425588I
a = 0.126062 0.339240I
b = 0.227675 + 0.708873I
3.58769 + 5.33790I 0
u = 0.822672 + 0.764737I
a = 0.560044 1.062490I
b = 1.088910 + 0.759677I
4.24766 1.27868I 0
u = 0.822672 0.764737I
a = 0.560044 + 1.062490I
b = 1.088910 0.759677I
4.24766 + 1.27868I 0
u = 0.814865 + 0.778282I
a = 0.11774 + 2.41231I
b = 0.830940 0.592246I
0.329058 0.951263I 0
u = 0.814865 0.778282I
a = 0.11774 2.41231I
b = 0.830940 + 0.592246I
0.329058 + 0.951263I 0
u = 0.754800 + 0.876512I
a = 1.11868 1.17948I
b = 0.868291 + 0.595565I
0.20885 + 3.75440I 0
u = 0.754800 0.876512I
a = 1.11868 + 1.17948I
b = 0.868291 0.595565I
0.20885 3.75440I 0
7
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.794082 + 0.262125I
a = 1.46161 + 2.25876I
b = 0.977760 0.341426I
2.28886 2.45162I 16.2110 + 6.3903I
u = 0.794082 0.262125I
a = 1.46161 2.25876I
b = 0.977760 + 0.341426I
2.28886 + 2.45162I 16.2110 6.3903I
u = 0.852305 + 0.811962I
a = 1.07072 + 1.14717I
b = 0.811618 0.630399I
4.01818 + 0.54192I 0
u = 0.852305 0.811962I
a = 1.07072 1.14717I
b = 0.811618 + 0.630399I
4.01818 0.54192I 0
u = 0.886190 + 0.782136I
a = 0.057066 + 0.858549I
b = 1.336480 + 0.029864I
2.31687 2.94399I 0
u = 0.886190 0.782136I
a = 0.057066 0.858549I
b = 1.336480 0.029864I
2.31687 + 2.94399I 0
u = 0.790264 + 0.884911I
a = 0.576247 + 1.018820I
b = 1.111540 0.727657I
7.85733 + 5.61860I 0
u = 0.790264 0.884911I
a = 0.576247 1.018820I
b = 1.111540 + 0.727657I
7.85733 5.61860I 0
u = 0.881857 + 0.797266I
a = 0.10968 + 1.44896I
b = 0.605815 0.957019I
5.72724 + 4.97749I 0
u = 0.881857 0.797266I
a = 0.10968 1.44896I
b = 0.605815 + 0.957019I
5.72724 4.97749I 0
8
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.933371 + 0.742677I
a = 0.74662 + 2.29509I
b = 1.113350 0.705726I
3.90440 + 6.99279I 0
u = 0.933371 0.742677I
a = 0.74662 2.29509I
b = 1.113350 + 0.705726I
3.90440 6.99279I 0
u = 0.897183 + 0.796476I
a = 1.216610 0.564361I
b = 0.532139 + 0.928269I
5.68216 + 1.00101I 0
u = 0.897183 0.796476I
a = 1.216610 + 0.564361I
b = 0.532139 0.928269I
5.68216 1.00101I 0
u = 0.942078 + 0.752491I
a = 1.01680 1.12508I
b = 0.759566 + 0.665808I
0.06234 4.83478I 0
u = 0.942078 0.752491I
a = 1.01680 + 1.12508I
b = 0.759566 0.665808I
0.06234 + 4.83478I 0
u = 0.422280 + 0.670799I
a = 0.704032 0.641404I
b = 0.214950 + 0.166258I
1.40337 + 0.92720I 8.23175 0.58902I
u = 0.422280 0.670799I
a = 0.704032 + 0.641404I
b = 0.214950 0.166258I
1.40337 0.92720I 8.23175 + 0.58902I
u = 0.841271 + 0.874220I
a = 0.05629 1.46245I
b = 0.555731 + 0.949544I
9.56149 0.50937I 0
u = 0.841271 0.874220I
a = 0.05629 + 1.46245I
b = 0.555731 0.949544I
9.56149 + 0.50937I 0
9
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.925474 + 0.790304I
a = 0.08043 2.24661I
b = 0.884202 + 0.625072I
3.79156 + 5.46140I 0
u = 0.925474 0.790304I
a = 0.08043 + 2.24661I
b = 0.884202 0.625072I
3.79156 5.46140I 0
u = 1.220990 + 0.093727I
a = 0.893667 + 0.033167I
b = 0.943866 + 0.417931I
7.95540 1.57335I 0
u = 1.220990 0.093727I
a = 0.893667 0.033167I
b = 0.943866 0.417931I
7.95540 + 1.57335I 0
u = 0.794180 + 0.936665I
a = 0.00264 + 1.47095I
b = 0.507424 0.936810I
5.50773 3.95377I 0
u = 0.794180 0.936665I
a = 0.00264 1.47095I
b = 0.507424 + 0.936810I
5.50773 + 3.95377I 0
u = 0.088205 + 0.759173I
a = 1.39479 + 1.62378I
b = 1.025110 0.260624I
4.33853 0.93069I 17.4874 0.5005I
u = 0.088205 0.759173I
a = 1.39479 1.62378I
b = 1.025110 + 0.260624I
4.33853 + 0.93069I 17.4874 + 0.5005I
u = 0.758355 + 0.979789I
a = 0.587135 0.981162I
b = 1.128270 + 0.699547I
3.60923 9.94654I 0
u = 0.758355 0.979789I
a = 0.587135 + 0.981162I
b = 1.128270 0.699547I
3.60923 + 9.94654I 0
10
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.985719 + 0.755243I
a = 0.071592 0.666243I
b = 1.357700 0.065878I
1.95959 + 7.25560I 0
u = 0.985719 0.755243I
a = 0.071592 + 0.666243I
b = 1.357700 + 0.065878I
1.95959 7.25560I 0
u = 1.180680 + 0.413243I
a = 1.03880 1.13972I
b = 1.094140 + 0.563802I
5.89137 10.06180I 0
u = 1.180680 0.413243I
a = 1.03880 + 1.13972I
b = 1.094140 0.563802I
5.89137 + 10.06180I 0
u = 1.078160 + 0.638701I
a = 0.332709 0.353621I
b = 0.716392 0.192203I
3.33914 6.07366I 0
u = 1.078160 0.638701I
a = 0.332709 + 0.353621I
b = 0.716392 + 0.192203I
3.33914 + 6.07366I 0
u = 0.365420 + 0.646101I
a = 0.146644 + 1.102250I
b = 0.746131 0.685305I
3.13319 + 1.58793I 4.36565 2.62454I
u = 0.365420 0.646101I
a = 0.146644 1.102250I
b = 0.746131 + 0.685305I
3.13319 1.58793I 4.36565 + 2.62454I
u = 0.963850 + 0.822645I
a = 1.090440 + 0.696675I
b = 0.499212 0.961407I
9.17313 5.78375I 0
u = 0.963850 0.822645I
a = 1.090440 0.696675I
b = 0.499212 + 0.961407I
9.17313 + 5.78375I 0
11
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.710725 + 0.142036I
a = 2.49015 0.07252I
b = 1.090730 0.165721I
2.74417 + 0.55471I 16.6137 8.8786I
u = 0.710725 0.142036I
a = 2.49015 + 0.07252I
b = 1.090730 + 0.165721I
2.74417 0.55471I 16.6137 + 8.8786I
u = 1.008330 + 0.782072I
a = 0.05748 + 2.13739I
b = 0.926480 0.640157I
0.57700 9.90939I 0
u = 1.008330 0.782072I
a = 0.05748 2.13739I
b = 0.926480 + 0.640157I
0.57700 + 9.90939I 0
u = 0.998606 + 0.799996I
a = 0.54095 2.15791I
b = 1.142060 + 0.706012I
7.20070 11.86680I 0
u = 0.998606 0.799996I
a = 0.54095 + 2.15791I
b = 1.142060 0.706012I
7.20070 + 11.86680I 0
u = 1.021860 + 0.824555I
a = 0.979873 0.762766I
b = 0.466549 + 0.980590I
4.77490 + 10.43370I 0
u = 1.021860 0.824555I
a = 0.979873 + 0.762766I
b = 0.466549 0.980590I
4.77490 10.43370I 0
u = 0.199533 + 0.630090I
a = 0.349695 1.014370I
b = 0.931055 + 0.671220I
2.58372 3.65091I 4.88024 + 4.09202I
u = 0.199533 0.630090I
a = 0.349695 + 1.014370I
b = 0.931055 0.671220I
2.58372 + 3.65091I 4.88024 4.09202I
12
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.059800 + 0.822621I
a = 0.44539 + 2.02899I
b = 1.162810 0.698617I
2.6344 + 16.5403I 0
u = 1.059800 0.822621I
a = 0.44539 2.02899I
b = 1.162810 + 0.698617I
2.6344 16.5403I 0
u = 0.646965 + 0.080521I
a = 0.343025 1.213620I
b = 0.873530 + 0.830831I
0.75119 3.07502I 19.2370 + 4.9728I
u = 0.646965 0.080521I
a = 0.343025 + 1.213620I
b = 0.873530 0.830831I
0.75119 + 3.07502I 19.2370 4.9728I
u = 0.549522
a = 0.875721
b = 0.119846
0.718836 14.1050
u = 0.317305 + 0.268219I
a = 1.79149 0.55439I
b = 0.724370 + 0.147571I
0.979988 + 0.105759I 9.79769 + 1.06695I
u = 0.317305 0.268219I
a = 1.79149 + 0.55439I
b = 0.724370 0.147571I
0.979988 0.105759I 9.79769 1.06695I
u = 0.344030
a = 11.6544
b = 0.902968
2.97247 58.0340
13
II. I
u
2
= hb + 1, 2u
7
u
6
3u
5
+ 3u
4
+ 4u
3
3u
2
+ a 2u + 4, u
8
u
7
u
6
+ 2u
5
+ u
4
2u
3
+ 2u 1i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
6
=
1
u
2
a
3
=
2u
7
+ u
6
+ 3u
5
3u
4
4u
3
+ 3u
2
+ 2u 4
1
a
11
=
u
u
3
+ u
a
2
=
2u
7
+ u
6
+ 3u
5
3u
4
4u
3
+ 3u
2
+ 2u 5
1
a
1
=
1
0
a
4
=
2u
7
+ u
6
+ 3u
5
3u
4
4u
3
+ 3u
2
+ 2u 4
1
a
7
=
1
u
2
a
9
=
u
3
u
5
u
3
+ u
a
12
=
u
5
u
u
7
+ u
5
2u
3
+ u
a
8
=
u
5
+ u
u
5
u
3
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 2u
7
2u
6
+ 4u
4
+ 3u
3
u
2
13
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u 1)
8
c
3
, c
6
u
8
c
4
(u + 1)
8
c
5
u
8
u
7
u
6
+ 2u
5
+ u
4
2u
3
+ 2u 1
c
7
, c
8
u
8
+ u
7
3u
6
2u
5
+ 3u
4
+ 2u 1
c
9
u
8
3u
7
+ 7u
6
10u
5
+ 11u
4
10u
3
+ 6u
2
4u + 1
c
10
u
8
+ u
7
u
6
2u
5
+ u
4
+ 2u
3
2u 1
c
11
u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1
c
12
u
8
u
7
3u
6
+ 2u
5
+ 3u
4
2u 1
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y 1)
8
c
3
, c
6
y
8
c
5
, c
10
y
8
3y
7
+ 7y
6
10y
5
+ 11y
4
10y
3
+ 6y
2
4y + 1
c
7
, c
8
, c
12
y
8
7y
7
+ 19y
6
22y
5
+ 3y
4
+ 14y
3
6y
2
4y + 1
c
9
, c
11
y
8
+ 5y
7
+ 11y
6
+ 6y
5
17y
4
34y
3
22y
2
4y + 1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 0.570868 + 0.730671I
a = 0.281371 + 1.128550I
b = 1.00000
2.68559 + 1.13123I 17.2624 0.2227I
u = 0.570868 0.730671I
a = 0.281371 1.128550I
b = 1.00000
2.68559 1.13123I 17.2624 + 0.2227I
u = 0.855237 + 0.665892I
a = 0.208670 0.825203I
b = 1.00000
0.51448 + 2.57849I 14.1288 3.8797I
u = 0.855237 0.665892I
a = 0.208670 + 0.825203I
b = 1.00000
0.51448 2.57849I 14.1288 + 3.8797I
u = 1.09818
a = 0.829189
b = 1.00000
8.14766 19.7220
u = 1.031810 + 0.655470I
a = 0.284386 + 0.605794I
b = 1.00000
4.02461 6.44354I 19.1410 + 6.6674I
u = 1.031810 0.655470I
a = 0.284386 0.605794I
b = 1.00000
4.02461 + 6.44354I 19.1410 6.6674I
u = 0.603304
a = 2.74744
b = 1.00000
2.48997 12.2140
17
III. I
v
1
= ha, v
2
+ b 3v + 1, v
3
+ 2v
2
3v + 1i
(i) Arc colorings
a
5
=
1
0
a
10
=
v
0
a
6
=
1
0
a
3
=
0
v
2
+ 3v 1
a
11
=
v
0
a
2
=
v
2
+ 3v 1
v
2
+ 3v 1
a
1
=
v
2
+ 3v 1
v
2
2v + 3
a
4
=
2v
2
5v + 4
2v
2
5v + 3
a
7
=
v
2
3v + 1
v
2
+ 2v 3
a
9
=
v
0
a
12
=
v
0
a
8
=
v
2
2v + 1
v
2
+ 2v 3
(ii) Obstruction class = 1
(iii) Cusp Shapes = 2v
2
+ 5v 11
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
3
u
2
+ 2u 1
c
2
u
3
+ u
2
1
c
4
u
3
u
2
+ 1
c
5
, c
9
, c
10
c
11
u
3
c
6
u
3
+ u
2
+ 2u + 1
c
7
, c
8
(u 1)
3
c
12
(u + 1)
3
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
6
y
3
+ 3y
2
+ 2y 1
c
2
, c
4
y
3
y
2
+ 2y 1
c
5
, c
9
, c
10
c
11
y
3
c
7
, c
8
, c
12
(y 1)
3
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
1(vol +
1CS) Cusp shape
v = 0.539798 + 0.182582I
a = 0
b = 0.877439 + 0.744862I
1.37919 2.82812I 7.78492 + 1.30714I
v = 0.539798 0.182582I
a = 0
b = 0.877439 0.744862I
1.37919 + 2.82812I 7.78492 1.30714I
v = 3.07960
a = 0
b = 0.754878
2.75839 7.43020
21
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u 1)
8
)(u
3
u
2
+ 2u 1)(u
88
+ 38u
87
+ ··· + 101u + 1)
c
2
((u 1)
8
)(u
3
+ u
2
1)(u
88
10u
87
+ ··· 7u + 1)
c
3
u
8
(u
3
u
2
+ 2u 1)(u
88
2u
87
+ ··· + 128u 256)
c
4
((u + 1)
8
)(u
3
u
2
+ 1)(u
88
10u
87
+ ··· 7u + 1)
c
5
u
3
(u
8
u
7
+ ··· + 2u 1)(u
88
2u
87
+ ··· 12u 8)
c
6
u
8
(u
3
+ u
2
+ 2u + 1)(u
88
2u
87
+ ··· + 128u 256)
c
7
, c
8
((u 1)
3
)(u
8
+ u
7
+ ··· + 2u 1)(u
88
5u
87
+ ··· + 8u + 1)
c
9
u
3
(u
8
3u
7
+ 7u
6
10u
5
+ 11u
4
10u
3
+ 6u
2
4u + 1)
· (u
88
+ 24u
87
+ ··· + 1872u + 64)
c
10
u
3
(u
8
+ u
7
+ ··· 2u 1)(u
88
2u
87
+ ··· 12u 8)
c
11
u
3
(u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1)
· (u
88
+ 24u
87
+ ··· + 1872u + 64)
c
12
((u + 1)
3
)(u
8
u
7
+ ··· 2u 1)(u
88
5u
87
+ ··· + 8u + 1)
22
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y 1)
8
)(y
3
+ 3y
2
+ 2y 1)(y
88
+ 34y
87
+ ··· 4505y + 1)
c
2
, c
4
((y 1)
8
)(y
3
y
2
+ 2y 1)(y
88
38y
87
+ ··· 101y + 1)
c
3
, c
6
y
8
(y
3
+ 3y
2
+ 2y 1)(y
88
+ 54y
87
+ ··· + 999424y + 65536)
c
5
, c
10
y
3
(y
8
3y
7
+ 7y
6
10y
5
+ 11y
4
10y
3
+ 6y
2
4y + 1)
· (y
88
24y
87
+ ··· 1872y + 64)
c
7
, c
8
, c
12
(y 1)
3
(y
8
7y
7
+ 19y
6
22y
5
+ 3y
4
+ 14y
3
6y
2
4y + 1)
· (y
88
71y
87
+ ··· + 62y + 1)
c
9
, c
11
y
3
(y
8
+ 5y
7
+ 11y
6
+ 6y
5
17y
4
34y
3
22y
2
4y + 1)
· (y
88
+ 76y
87
+ ··· 105728y + 4096)
23