12a
0786
(K12a
0786
)
A knot diagram
1
Linearized knot diagam
3 8 11 10 12 9 2 7 5 1 6 4
Solving Sequence
2,7
8
3,11
4 9 1 6 12 5 10
c
7
c
2
c
3
c
8
c
1
c
6
c
11
c
5
c
10
c
4
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h7.76879 × 10
80
u
103
+ 8.52236 × 10
80
u
102
+ ··· + 3.56472 × 10
80
b − 4.99373 × 10
81
,
− 6.43118 × 10
80
u
103
− 4.09372 × 10
81
u
102
+ ··· + 2.49530 × 10
81
a + 1.23254 × 10
82
, u
104
+ u
103
+ ··· − 7u + 7i
I
u
2
= h−2u
19
+ 5u
17
+ ··· + b − 1, 2u
19
− u
18
+ ··· + a − 1, u
20
− 3u
18
+ ··· + u + 1i
* 2 irreducible components of dim
C
= 0, with total 124 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
= h7.77 × 10
80
u
103
+ 8.52 × 10
80
u
102
+ · · · + 3.56 × 10
80
b − 4.99 ×
10
81
, −6.43 × 10
80
u
103
− 4.09 × 10
81
u
102
+ · · · + 2.50 × 10
81
a + 1.23 ×
10
82
, u
104
+ u
103
+ · · · − 7u + 7i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
3
=
−u
−u
3
+ u
a
11
=
0.257732u
103
+ 1.64057u
102
+ ··· − 20.8766u − 4.93944
−2.17936u
103
− 2.39075u
102
+ ··· + 25.2220u + 14.0088
a
4
=
4.54650u
103
+ 4.71983u
102
+ ··· − 21.6024u − 22.5070
0.732669u
103
+ 0.154268u
102
+ ··· + 7.64667u + 3.76015
a
9
=
−u
2
+ 1
u
2
a
1
=
u
3
u
5
− u
3
+ u
a
6
=
u
4
− u
2
+ 1
−u
4
a
12
=
−1.07483u
103
+ 0.848416u
102
+ ··· − 4.82910u − 1.91321
−2.87953u
103
− 3.09296u
102
+ ··· + 28.4903u + 13.0462
a
5
=
1.07670u
103
+ 1.40144u
102
+ ··· + 0.0336515u − 10.1638
−0.478154u
103
− 0.659756u
102
+ ··· + 20.1108u + 3.76858
a
10
=
−0.224309u
103
+ 2.43305u
102
+ ··· − 12.2602u − 13.0672
−1.89620u
103
− 2.01139u
102
+ ··· + 26.0423u + 7.99311
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4.36792u
103
+ 16.1678u
102
+ ··· − 14.8053u − 125.030
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
, c
8
u
104
+ 25u
103
+ ··· + 749u + 49
c
2
, c
7
u
104
+ u
103
+ ··· − 7u + 7
c
3
u
104
− 10u
102
+ ··· + 34258u + 3709
c
4
, c
9
u
104
− 2u
103
+ ··· − 728u + 121
c
5
, c
11
u
104
− u
103
+ ··· − u + 7
c
10
u
104
+ 11u
103
+ ··· + 131198u + 14113
c
12
u
104
+ 7u
103
+ ··· − u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
, c
8
y
104
+ 115y
103
+ ··· + 32487y + 2401
c
2
, c
7
y
104
− 25y
103
+ ··· − 749y + 49
c
3
y
104
− 20y
103
+ ··· − 305407844y + 13756681
c
4
, c
9
y
104
+ 76y
103
+ ··· + 509890y + 14641
c
5
, c
11
y
104
+ 57y
103
+ ··· + 1693y + 49
c
10
y
104
− 43y
103
+ ··· − 10011615824y + 199176769
c
12
y
104
− 5y
103
+ ··· + 89y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.766662 + 0.632934I
a = 0.157630 + 0.376131I
b = 0.354923 + 0.313305I
2.70022 − 2.40792I 0
u = 0.766662 − 0.632934I
a = 0.157630 − 0.376131I
b = 0.354923 − 0.313305I
2.70022 + 2.40792I 0
u = 0.990161 + 0.226156I
a = 0.345510 + 0.630720I
b = 0.456131 − 0.442211I
−0.06685 − 3.01354I 0
u = 0.990161 − 0.226156I
a = 0.345510 − 0.630720I
b = 0.456131 + 0.442211I
−0.06685 + 3.01354I 0
u = −0.898218 + 0.484385I
a = −0.375200 + 1.107920I
b = 0.789176 − 1.165220I
3.58702 + 6.98929I 0
u = −0.898218 − 0.484385I
a = −0.375200 − 1.107920I
b = 0.789176 + 1.165220I
3.58702 − 6.98929I 0
u = 0.906841 + 0.328078I
a = 1.43990 + 0.82818I
b = −0.805047 − 0.092018I
−1.74282 − 5.46943I 0
u = 0.906841 − 0.328078I
a = 1.43990 − 0.82818I
b = −0.805047 + 0.092018I
−1.74282 + 5.46943I 0
u = 0.731510 + 0.614247I
a = −0.229128 + 0.377392I
b = 0.452360 + 0.444639I
2.77148 − 2.27111I 0
u = 0.731510 − 0.614247I
a = −0.229128 − 0.377392I
b = 0.452360 − 0.444639I
2.77148 + 2.27111I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.946665 + 0.445873I
a = 1.110950 − 0.256330I
b = −0.172865 + 0.593087I
−3.47387 + 7.06916I 0
u = −0.946665 − 0.445873I
a = 1.110950 + 0.256330I
b = −0.172865 − 0.593087I
−3.47387 − 7.06916I 0
u = 0.429102 + 0.835909I
a = 0.621121 − 0.556923I
b = −0.449537 + 0.417666I
3.48038 − 4.88988I 0
u = 0.429102 − 0.835909I
a = 0.621121 + 0.556923I
b = −0.449537 − 0.417666I
3.48038 + 4.88988I 0
u = 0.933574 + 0.046772I
a = 0.268196 − 0.407068I
b = −0.577101 − 1.046790I
−5.72348 + 1.88899I 0
u = 0.933574 − 0.046772I
a = 0.268196 + 0.407068I
b = −0.577101 + 1.046790I
−5.72348 − 1.88899I 0
u = 0.855864 + 0.353216I
a = 0.512007 + 0.795136I
b = −0.105151 − 0.893329I
−0.24953 − 3.56298I 0
u = 0.855864 − 0.353216I
a = 0.512007 − 0.795136I
b = −0.105151 + 0.893329I
−0.24953 + 3.56298I 0
u = −0.901014 + 0.209728I
a = −0.667920 − 0.366820I
b = −0.404203 + 1.238470I
−2.37554 − 0.53656I 0
u = −0.901014 − 0.209728I
a = −0.667920 + 0.366820I
b = −0.404203 − 1.238470I
−2.37554 + 0.53656I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.872757 + 0.636215I
a = −0.921173 − 0.839949I
b = 0.145920 + 0.925194I
−2.23261 + 2.46085I 0
u = −0.872757 − 0.636215I
a = −0.921173 + 0.839949I
b = 0.145920 − 0.925194I
−2.23261 − 2.46085I 0
u = −1.081480 + 0.026581I
a = −0.133652 − 0.172093I
b = 0.616078 − 0.692280I
−2.16276 − 6.51848I 0
u = −1.081480 − 0.026581I
a = −0.133652 + 0.172093I
b = 0.616078 + 0.692280I
−2.16276 + 6.51848I 0
u = −0.795173 + 0.379218I
a = −1.78364 − 0.31075I
b = 0.736381 + 0.569274I
−2.74142 + 1.90360I 0
u = −0.795173 − 0.379218I
a = −1.78364 + 0.31075I
b = 0.736381 − 0.569274I
−2.74142 − 1.90360I 0
u = −0.780756 + 0.394948I
a = 1.63110 − 0.64652I
b = 0.735324 − 0.701901I
1.33892 + 4.93257I 0
u = −0.780756 − 0.394948I
a = 1.63110 + 0.64652I
b = 0.735324 + 0.701901I
1.33892 − 4.93257I 0
u = −1.064430 + 0.374375I
a = −0.296034 + 0.425423I
b = −0.436153 − 0.006085I
0.83535 + 3.47388I 0
u = −1.064430 − 0.374375I
a = −0.296034 − 0.425423I
b = −0.436153 + 0.006085I
0.83535 − 3.47388I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.032620 + 0.455050I
a = −0.868126 − 0.506848I
b = 0.136396 + 0.458095I
0.43075 − 13.03650I 0
u = 1.032620 − 0.455050I
a = −0.868126 + 0.506848I
b = 0.136396 − 0.458095I
0.43075 + 13.03650I 0
u = 0.300979 + 0.788432I
a = 0.941826 + 0.087842I
b = −0.158311 − 0.511357I
2.84217 + 8.57300I 0
u = 0.300979 − 0.788432I
a = 0.941826 − 0.087842I
b = −0.158311 + 0.511357I
2.84217 − 8.57300I 0
u = 0.895050 + 0.778119I
a = −0.0114617 + 0.1300560I
b = 0.458745 + 0.554629I
3.11399 − 2.93489I 0
u = 0.895050 − 0.778119I
a = −0.0114617 − 0.1300560I
b = 0.458745 − 0.554629I
3.11399 + 2.93489I 0
u = −0.468867 + 0.652301I
a = 1.67663 − 0.15872I
b = −0.769802 − 0.269370I
4.96708 − 2.78599I 5.45184 + 0.I
u = −0.468867 − 0.652301I
a = 1.67663 + 0.15872I
b = −0.769802 + 0.269370I
4.96708 + 2.78599I 5.45184 + 0.I
u = −0.837269 + 0.858305I
a = 1.71955 − 1.12101I
b = −2.47926 − 0.90809I
6.98765 − 0.83385I 0
u = −0.837269 − 0.858305I
a = 1.71955 + 1.12101I
b = −2.47926 + 0.90809I
6.98765 + 0.83385I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.857688 + 0.848054I
a = 1.34507 − 1.62875I
b = −3.28470 − 0.20003I
5.55138 − 2.69728I 0
u = −0.857688 − 0.848054I
a = 1.34507 + 1.62875I
b = −3.28470 + 0.20003I
5.55138 + 2.69728I 0
u = 0.727404 + 0.308828I
a = 1.55109 − 0.19015I
b = −0.07706 + 1.94742I
−3.22727 − 1.25096I −2.00000 + 7.02823I
u = 0.727404 − 0.308828I
a = 1.55109 + 0.19015I
b = −0.07706 − 1.94742I
−3.22727 + 1.25096I −2.00000 − 7.02823I
u = 1.078300 + 0.561549I
a = 0.288763 − 0.501283I
b = 0.140095 + 0.441770I
1.39183 − 0.25582I 0
u = 1.078300 − 0.561549I
a = 0.288763 + 0.501283I
b = 0.140095 − 0.441770I
1.39183 + 0.25582I 0
u = −0.757240 + 0.174967I
a = 0.039857 − 0.279716I
b = −0.536813 + 0.538199I
−1.263330 + 0.418486I −7.09557 − 0.72347I
u = −0.757240 − 0.174967I
a = 0.039857 + 0.279716I
b = −0.536813 − 0.538199I
−1.263330 − 0.418486I −7.09557 + 0.72347I
u = −0.890714 + 0.843520I
a = 1.90421 − 1.78407I
b = −3.15861 − 0.74730I
6.78735 − 0.08301I 0
u = −0.890714 − 0.843520I
a = 1.90421 + 1.78407I
b = −3.15861 + 0.74730I
6.78735 + 0.08301I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.890419 + 0.847639I
a = −0.66583 − 1.29156I
b = 2.37783 + 0.54118I
4.51852 − 1.93015I 0
u = 0.890419 − 0.847639I
a = −0.66583 + 1.29156I
b = 2.37783 − 0.54118I
4.51852 + 1.93015I 0
u = 0.818432 + 0.920455I
a = −1.46291 − 0.80542I
b = 2.13933 − 0.57457I
9.65675 + 2.00371I 0
u = 0.818432 − 0.920455I
a = −1.46291 + 0.80542I
b = 2.13933 + 0.57457I
9.65675 − 2.00371I 0
u = 0.717756 + 0.257429I
a = −2.47456 − 0.58230I
b = −0.198074 + 0.179300I
0.59876 + 1.75726I −4.14188 + 1.37130I
u = 0.717756 − 0.257429I
a = −2.47456 + 0.58230I
b = −0.198074 − 0.179300I
0.59876 − 1.75726I −4.14188 − 1.37130I
u = −0.908019 + 0.843254I
a = 0.037172 + 0.239025I
b = −0.474318 + 0.556665I
3.46367 + 3.13699I 0
u = −0.908019 − 0.843254I
a = 0.037172 − 0.239025I
b = −0.474318 − 0.556665I
3.46367 − 3.13699I 0
u = −0.922624 + 0.832948I
a = −1.81548 + 1.58635I
b = 3.50548 + 0.24041I
6.68785 + 6.32651I 0
u = −0.922624 − 0.832948I
a = −1.81548 − 1.58635I
b = 3.50548 − 0.24041I
6.68785 − 6.32651I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.860422 + 0.899570I
a = 1.18975 + 2.21934I
b = −3.18431 − 0.74729I
5.25028 + 4.20090I 0
u = 0.860422 − 0.899570I
a = 1.18975 − 2.21934I
b = −3.18431 + 0.74729I
5.25028 − 4.20090I 0
u = −0.835559 + 0.923554I
a = −1.35608 + 1.79331I
b = 2.93378 − 0.19568I
9.6493 − 11.0115I 0
u = −0.835559 − 0.923554I
a = −1.35608 − 1.79331I
b = 2.93378 + 0.19568I
9.6493 + 11.0115I 0
u = 0.897180 + 0.864300I
a = 2.40675 + 0.58401I
b = −3.07009 + 1.40635I
8.90543 + 0.76441I 0
u = 0.897180 − 0.864300I
a = 2.40675 − 0.58401I
b = −3.07009 − 1.40635I
8.90543 − 0.76441I 0
u = 0.923845 + 0.837317I
a = 1.51875 + 0.63637I
b = −1.92655 + 1.55181I
4.41536 − 4.33842I 0
u = 0.923845 − 0.837317I
a = 1.51875 − 0.63637I
b = −1.92655 − 1.55181I
4.41536 + 4.33842I 0
u = −0.945789 + 0.818483I
a = −1.75271 + 1.29108I
b = 3.18525 + 1.25735I
5.27707 + 8.90594I 0
u = −0.945789 − 0.818483I
a = −1.75271 − 1.29108I
b = 3.18525 − 1.25735I
5.27707 − 8.90594I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.873603 + 0.897281I
a = −1.36566 − 1.37873I
b = 2.39646 − 0.67516I
12.37940 + 3.59050I 0
u = 0.873603 − 0.897281I
a = −1.36566 + 1.37873I
b = 2.39646 + 0.67516I
12.37940 − 3.59050I 0
u = −0.187535 + 0.719880I
a = 0.232590 + 0.647272I
b = −0.128930 + 0.419958I
3.68141 + 0.48804I 5.79013 − 0.50832I
u = −0.187535 − 0.719880I
a = 0.232590 − 0.647272I
b = −0.128930 − 0.419958I
3.68141 − 0.48804I 5.79013 + 0.50832I
u = −0.963501 + 0.810928I
a = −1.26184 + 1.52225I
b = 2.89267 + 0.00173I
6.59081 + 7.04791I 0
u = −0.963501 − 0.810928I
a = −1.26184 − 1.52225I
b = 2.89267 − 0.00173I
6.59081 − 7.04791I 0
u = −0.617883 + 0.408127I
a = −0.400975 − 0.043091I
b = −0.09166 − 1.74158I
1.87920 − 1.73073I 4.58908 − 1.47296I
u = −0.617883 − 0.408127I
a = −0.400975 + 0.043091I
b = −0.09166 + 1.74158I
1.87920 + 1.73073I 4.58908 + 1.47296I
u = 0.928998 + 0.851199I
a = −0.92786 − 2.44910I
b = 2.89100 + 0.71756I
8.80452 − 7.12890I 0
u = 0.928998 − 0.851199I
a = −0.92786 + 2.44910I
b = 2.89100 − 0.71756I
8.80452 + 7.12890I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.365151 + 0.631995I
a = −1.066770 + 0.402812I
b = −0.148212 − 0.556282I
−1.64752 − 3.05905I −1.73633 + 4.13553I
u = −0.365151 − 0.631995I
a = −1.066770 − 0.402812I
b = −0.148212 + 0.556282I
−1.64752 + 3.05905I −1.73633 − 4.13553I
u = 0.963585 + 0.856077I
a = 1.38676 + 1.16739I
b = −3.01233 + 0.20429I
12.0914 − 10.0706I 0
u = 0.963585 − 0.856077I
a = 1.38676 − 1.16739I
b = −3.01233 − 0.20429I
12.0914 + 10.0706I 0
u = −0.904384 + 0.920281I
a = −0.558498 + 0.960408I
b = 1.318600 − 0.099299I
12.29660 + 3.00090I 0
u = −0.904384 − 0.920281I
a = −0.558498 − 0.960408I
b = 1.318600 + 0.099299I
12.29660 − 3.00090I 0
u = 0.972962 + 0.849039I
a = −2.36110 − 0.95510I
b = 3.18761 − 1.65953I
4.89111 − 10.66500I 0
u = 0.972962 − 0.849039I
a = −2.36110 + 0.95510I
b = 3.18761 + 1.65953I
4.89111 + 10.66500I 0
u = −0.938245 + 0.909899I
a = 0.884162 + 1.060980I
b = 0.12123 − 1.71305I
12.18760 + 3.35080I 0
u = −0.938245 − 0.909899I
a = 0.884162 − 1.060980I
b = 0.12123 + 1.71305I
12.18760 − 3.35080I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.958471 + 0.889493I
a = 1.098670 − 0.306796I
b = −1.52693 − 0.70793I
12.11800 + 3.65766I 0
u = −0.958471 − 0.889493I
a = 1.098670 + 0.306796I
b = −1.52693 + 0.70793I
12.11800 − 3.65766I 0
u = 1.007110 + 0.835986I
a = 1.03463 + 1.30135I
b = −2.29795 + 0.08686I
9.05723 − 8.48405I 0
u = 1.007110 − 0.835986I
a = 1.03463 − 1.30135I
b = −2.29795 − 0.08686I
9.05723 + 8.48405I 0
u = −0.999143 + 0.845974I
a = 1.94604 − 1.15637I
b = −3.14503 − 1.10552I
9.1250 + 17.5346I 0
u = −0.999143 − 0.845974I
a = 1.94604 + 1.15637I
b = −3.14503 + 1.10552I
9.1250 − 17.5346I 0
u = 0.651033 + 0.030608I
a = −0.59854 + 1.49435I
b = 1.12942 − 0.94839I
0.72830 − 3.26919I −3.48089 + 6.93706I
u = 0.651033 − 0.030608I
a = −0.59854 − 1.49435I
b = 1.12942 + 0.94839I
0.72830 + 3.26919I −3.48089 − 6.93706I
u = −0.383604 + 0.502974I
a = −0.47635 − 1.37590I
b = 0.178945 + 0.823418I
−1.63832 + 1.39384I −2.50160 − 4.01659I
u = −0.383604 − 0.502974I
a = −0.47635 + 1.37590I
b = 0.178945 − 0.823418I
−1.63832 − 1.39384I −2.50160 + 4.01659I
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.320616 + 0.461824I
a = −1.40865 + 0.41281I
b = 0.312590 + 0.113240I
1.35107 + 0.45706I 6.25564 − 0.31459I
u = 0.320616 − 0.461824I
a = −1.40865 − 0.41281I
b = 0.312590 − 0.113240I
1.35107 − 0.45706I 6.25564 + 0.31459I
u = 0.108145 + 0.451884I
a = −1.54856 − 1.08085I
b = 0.527286 + 0.804510I
0.38768 + 2.59628I 0.25241 − 3.90373I
u = 0.108145 − 0.451884I
a = −1.54856 + 1.08085I
b = 0.527286 − 0.804510I
0.38768 − 2.59628I 0.25241 + 3.90373I
15
II.
I
u
2
= h−2u
19
+5u
17
+· · ·+b−1, 2u
19
−u
18
+· · ·+a−1, u
20
−3u
18
+· · ·+u+1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
3
=
−u
−u
3
+ u
a
11
=
−2u
19
+ u
18
+ ··· + 5u
2
+ 1
2u
19
− 5u
17
+ ··· − 2u + 1
a
4
=
u
19
− 2u
17
+ ··· + 2u − 2
−u
19
+ u
18
+ ··· − 2u − 3
a
9
=
−u
2
+ 1
u
2
a
1
=
u
3
u
5
− u
3
+ u
a
6
=
u
4
− u
2
+ 1
−u
4
a
12
=
−u
19
+ u
18
+ ··· − u + 1
u
19
− 2u
17
+ ··· − u + 1
a
5
=
3u
19
+ u
18
+ ··· − 4u + 1
u
18
− 3u
16
+ ··· − 2u − 3
a
10
=
−2u
19
+ u
18
+ ··· + u + 1
u
19
− 2u
17
+ ··· − u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 9u
19
− u
18
− 27u
17
+ 3u
16
+ 86u
15
− 10u
14
− 164u
13
+ 28u
12
+
261u
11
− 47u
10
− 316u
9
+ 74u
8
+ 292u
7
− 76u
6
− 201u
5
+ 56u
4
+ 88u
3
− 31u
2
− 24u + 2
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
20
− 6u
19
+ ··· − 11u + 1
c
2
u
20
− 3u
18
+ ··· − u + 1
c
3
u
20
− u
19
+ ··· + 2u + 1
c
4
u
20
− u
19
+ ··· + 10u
2
+ 1
c
5
u
20
+ 10u
18
+ ··· + u + 1
c
7
u
20
− 3u
18
+ ··· + u + 1
c
8
u
20
+ 6u
19
+ ··· + 11u + 1
c
9
u
20
+ u
19
+ ··· + 10u
2
+ 1
c
10
u
20
− 6u
18
+ ··· + 8u + 1
c
11
u
20
+ 10u
18
+ ··· − u + 1
c
12
u
20
− 2u
19
+ ··· + u + 1
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
, c
8
y
20
+ 22y
19
+ ··· + 5y + 1
c
2
, c
7
y
20
− 6y
19
+ ··· − 11y + 1
c
3
y
20
− y
19
+ ··· + 2y + 1
c
4
, c
9
y
20
+ 19y
19
+ ··· + 20y + 1
c
5
, c
11
y
20
+ 20y
19
+ ··· + 19y + 1
c
10
y
20
− 12y
19
+ ··· − 10y + 1
c
12
y
20
+ 2y
19
+ ··· − y + 1
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.930125 + 0.251909I
a = −0.555551 + 1.090100I
b = −0.237834 − 0.115011I
−0.42842 + 4.43650I −4.15561 − 8.27213I
u = −0.930125 − 0.251909I
a = −0.555551 − 1.090100I
b = −0.237834 + 0.115011I
−0.42842 − 4.43650I −4.15561 + 8.27213I
u = −0.843361 + 0.606962I
a = −1.19766 − 0.86307I
b = 0.198932 + 1.255640I
−1.51818 + 2.38684I 3.66992 − 3.46346I
u = −0.843361 − 0.606962I
a = −1.19766 + 0.86307I
b = 0.198932 − 1.255640I
−1.51818 − 2.38684I 3.66992 + 3.46346I
u = 0.993297 + 0.523875I
a = 0.265213 − 0.240081I
b = 0.380693 − 0.228858I
1.17594 − 0.95837I −1.61521 + 3.89652I
u = 0.993297 − 0.523875I
a = 0.265213 + 0.240081I
b = 0.380693 + 0.228858I
1.17594 + 0.95837I −1.61521 − 3.89652I
u = 0.595627 + 0.611850I
a = −0.310105 − 0.045545I
b = −0.844286 − 0.027975I
2.48431 − 3.51175I 1.91261 + 6.52734I
u = 0.595627 − 0.611850I
a = −0.310105 + 0.045545I
b = −0.844286 + 0.027975I
2.48431 + 3.51175I 1.91261 − 6.52734I
u = 0.850202 + 0.853643I
a = −2.03545 − 1.33030I
b = 3.20640 − 0.94291I
6.68936 + 1.94064I 3.10110 − 3.51621I
u = 0.850202 − 0.853643I
a = −2.03545 + 1.33030I
b = 3.20640 + 0.94291I
6.68936 − 1.94064I 3.10110 + 3.51621I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.897079 + 0.812456I
a = −0.274825 − 0.094266I
b = −0.559706 + 1.176180I
2.08436 + 3.04014I −6.90827 − 2.70849I
u = −0.897079 − 0.812456I
a = −0.274825 + 0.094266I
b = −0.559706 − 1.176180I
2.08436 − 3.04014I −6.90827 + 2.70849I
u = 0.740567 + 0.185874I
a = 1.67918 − 0.06454I
b = −0.36120 + 1.64428I
−3.64557 − 0.76917I −11.12228 − 2.09345I
u = 0.740567 − 0.185874I
a = 1.67918 + 0.06454I
b = −0.36120 − 1.64428I
−3.64557 + 0.76917I −11.12228 + 2.09345I
u = 0.954211 + 0.815743I
a = 1.46027 + 1.84888I
b = −3.33935 + 0.17377I
6.36262 − 8.15795I 2.38095 + 8.44173I
u = 0.954211 − 0.815743I
a = 1.46027 − 1.84888I
b = −3.33935 − 0.17377I
6.36262 + 8.15795I 2.38095 − 8.44173I
u = −0.941711 + 0.919429I
a = −0.825370 − 0.992714I
b = −0.14284 + 1.66170I
11.93900 + 3.38003I −15.3248 − 4.1187I
u = −0.941711 − 0.919429I
a = −0.825370 + 0.992714I
b = −0.14284 − 1.66170I
11.93900 − 3.38003I −15.3248 + 4.1187I
u = −0.521628 + 0.220168I
a = 2.29430 − 0.58796I
b = −0.300816 + 1.237010I
1.17551 − 2.39551I 1.56153 + 4.24080I
u = −0.521628 − 0.220168I
a = 2.29430 + 0.58796I
b = −0.300816 − 1.237010I
1.17551 + 2.39551I 1.56153 − 4.24080I
20
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
(u
20
− 6u
19
+ ··· − 11u + 1)(u
104
+ 25u
103
+ ··· + 749u + 49)
c
2
(u
20
− 3u
18
+ ··· − u + 1)(u
104
+ u
103
+ ··· − 7u + 7)
c
3
(u
20
− u
19
+ ··· + 2u + 1)(u
104
− 10u
102
+ ··· + 34258u + 3709)
c
4
(u
20
− u
19
+ ··· + 10u
2
+ 1)(u
104
− 2u
103
+ ··· − 728u + 121)
c
5
(u
20
+ 10u
18
+ ··· + u + 1)(u
104
− u
103
+ ··· − u + 7)
c
7
(u
20
− 3u
18
+ ··· + u + 1)(u
104
+ u
103
+ ··· − 7u + 7)
c
8
(u
20
+ 6u
19
+ ··· + 11u + 1)(u
104
+ 25u
103
+ ··· + 749u + 49)
c
9
(u
20
+ u
19
+ ··· + 10u
2
+ 1)(u
104
− 2u
103
+ ··· − 728u + 121)
c
10
(u
20
− 6u
18
+ ··· + 8u + 1)(u
104
+ 11u
103
+ ··· + 131198u + 14113)
c
11
(u
20
+ 10u
18
+ ··· − u + 1)(u
104
− u
103
+ ··· − u + 7)
c
12
(u
20
− 2u
19
+ ··· + u + 1)(u
104
+ 7u
103
+ ··· − u + 1)
21
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
, c
8
(y
20
+ 22y
19
+ ··· + 5y + 1)(y
104
+ 115y
103
+ ··· + 32487y + 2401)
c
2
, c
7
(y
20
− 6y
19
+ ··· − 11y + 1)(y
104
− 25y
103
+ ··· − 749y + 49)
c
3
(y
20
− y
19
+ ··· + 2y + 1)
· (y
104
− 20y
103
+ ··· − 305407844y + 13756681)
c
4
, c
9
(y
20
+ 19y
19
+ ··· + 20y + 1)(y
104
+ 76y
103
+ ··· + 509890y + 14641)
c
5
, c
11
(y
20
+ 20y
19
+ ··· + 19y + 1)(y
104
+ 57y
103
+ ··· + 1693y + 49)
c
10
(y
20
− 12y
19
+ ··· − 10y + 1)
· (y
104
− 43y
103
+ ··· − 10011615824y + 199176769)
c
12
(y
20
+ 2y
19
+ ··· − y + 1)(y
104
− 5y
103
+ ··· + 89y + 1)
22
