12n
0848
(K12n
0848
)
A knot diagram
1
Linearized knot diagam
4 9 10 1 11 3 4 5 7 5 6 9
Solving Sequence
5,10
11
1,6
4 3 7 8 9 2 12
c
10
c
5
c
4
c
3
c
6
c
7
c
9
c
2
c
12
c
1
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h1490992711u
33
+ 21038016102u
32
+ ··· + 104665856b + 191326556928,
746029u
33
− 897227141u
32
+ ··· + 313997568a − 74904566272, u
34
+ 16u
33
+ ··· + 512u + 256i
I
u
2
= h9001u
25
− 3749u
24
+ ··· + 24457b + 25814, −17555u
25
− 14121u
24
+ ··· + 73371a + 84484,
u
26
− 14u
24
+ ··· + u + 3i
I
u
3
= h−6a
3
bu − 4a
3
b + 4a
2
bu + 2a
2
b − bau − a
2
u + b
2
− ba − 2bu − a
2
+ 2au + u − 1,
a
4
− a
3
u + a
3
− a
2
u + 2a
2
+ 2au − 3a − 3u + 5, u
2
− u − 1i
I
u
4
= h−6a
3
bu − 4a
3
b + 8a
2
bu + 4a
2
b − 3bau − a
2
u + b
2
− 3ba + 2bu − a
2
+ 2au + u − 1,
a
4
− 2a
3
u + 2a
3
− 2a
2
u + 4a
2
− 2au + 3a − 3u + 5, u
2
− u − 1i
I
u
5
= hb − u, a, u
2
+ u − 1i
* 5 irreducible components of dim
C
= 0, with total 94 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
=
h1.49×10
9
u
33
+2.10×10
10
u
32
+· · · +1.05×10
8
b+1.91×10
11
, 7.46×10
5
u
33
−
8.97 × 10
8
u
32
+ · · · + 3.14 × 10
8
a − 7.49 × 10
10
, u
34
+ 16u
33
+ · · · + 512u + 256i
(i) Arc colorings
a
5
=
0
u
a
10
=
1
0
a
11
=
1
u
2
a
1
=
−0.00237591u
33
+ 2.85743u
32
+ ··· + 210.618u + 238.551
−14.2453u
33
− 201.002u
32
+ ··· − 2806.15u − 1827.97
a
6
=
−u
−u
3
+ u
a
4
=
−9.99391u
33
− 154.470u
32
+ ··· − 2993.11u − 2567.55
46.6896u
33
+ 675.692u
32
+ ··· + 10474.3u + 7478.64
a
3
=
36.6957u
33
+ 521.222u
32
+ ··· + 7481.16u + 4911.09
46.6896u
33
+ 675.692u
32
+ ··· + 10474.3u + 7478.64
a
7
=
30.0648u
33
+ 443.715u
32
+ ··· + 7461.44u + 6086.67
8.51516u
33
+ 125.472u
32
+ ··· + 2106.90u + 1857.91
a
8
=
13.1190u
33
+ 186.388u
32
+ ··· + 2673.13u + 1806.42
−28.4932u
33
− 403.883u
32
+ ··· − 5742.22u − 3935.80
a
9
=
−13.1190u
33
− 186.388u
32
+ ··· − 2673.13u − 1806.42
−12.1032u
33
− 178.316u
32
+ ··· − 2939.47u − 2084.28
a
2
=
0.811803u
33
+ 19.0064u
32
+ ··· + 712.808u + 606.416
−28.5552u
33
− 410.268u
32
+ ··· − 6140.23u − 4213.59
a
12
=
−u
2
+ 1
−u
4
+ 2u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes =
470816681
3270808
u
33
+
27543600709
13083232
u
32
+ ··· +
13947213170
408851
u +
10499734540
408851
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
34
− 9u
33
+ ··· − 135u + 45
c
2
, c
7
u
34
+ 15u
32
+ ··· + 3u + 31
c
3
, c
6
u
34
+ u
33
+ ··· − 2u + 1
c
5
, c
10
, c
11
u
34
− 16u
33
+ ··· − 512u + 256
c
8
, c
12
u
34
+ 2u
33
+ ··· + 2u + 1
c
9
u
34
+ 14u
33
+ ··· + 540u + 45
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
34
+ 9y
33
+ ··· + 7425y + 2025
c
2
, c
7
y
34
+ 30y
33
+ ··· + 16297y + 961
c
3
, c
6
y
34
− 25y
33
+ ··· − 22y + 1
c
5
, c
10
, c
11
y
34
− 28y
33
+ ··· − 65536y + 65536
c
8
, c
12
y
34
− 48y
33
+ ··· − 10y + 1
c
9
y
34
− 6y
33
+ ··· + 31050y + 2025
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.795593 + 0.740595I
a = −0.290888 + 0.609919I
b = 0.853986 + 1.101180I
3.51064 + 1.64445I 7.07709 − 8.00929I
u = −0.795593 − 0.740595I
a = −0.290888 − 0.609919I
b = 0.853986 − 1.101180I
3.51064 − 1.64445I 7.07709 + 8.00929I
u = 1.092680 + 0.387055I
a = −0.383036 − 0.709367I
b = 1.43819 − 0.26328I
−0.064466 − 0.761171I 0
u = 1.092680 − 0.387055I
a = −0.383036 + 0.709367I
b = 1.43819 + 0.26328I
−0.064466 + 0.761171I 0
u = 0.697499 + 0.930339I
a = 0.027330 + 1.123010I
b = −0.506447 − 0.080887I
−6.81076 − 4.03336I 0
u = 0.697499 − 0.930339I
a = 0.027330 − 1.123010I
b = −0.506447 + 0.080887I
−6.81076 + 4.03336I 0
u = −0.939424 + 0.738369I
a = 0.552486 − 0.224603I
b = −1.85831 − 0.64729I
3.08759 + 3.98437I 0
u = −0.939424 − 0.738369I
a = 0.552486 + 0.224603I
b = −1.85831 + 0.64729I
3.08759 − 3.98437I 0
u = 0.144340 + 0.791374I
a = 1.60313 − 0.01473I
b = −1.48435 + 0.51718I
2.79908 − 3.47479I −8.15502 + 3.50613I
u = 0.144340 − 0.791374I
a = 1.60313 + 0.01473I
b = −1.48435 − 0.51718I
2.79908 + 3.47479I −8.15502 − 3.50613I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.560287 + 1.062520I
a = −0.967599 + 0.348568I
b = 1.58175 − 0.28106I
−6.28578 − 2.44883I 0
u = 0.560287 − 1.062520I
a = −0.967599 − 0.348568I
b = 1.58175 + 0.28106I
−6.28578 + 2.44883I 0
u = 0.715757 + 1.021220I
a = −1.114730 + 0.080818I
b = 1.84474 − 0.41176I
−5.93132 − 10.98960I 0
u = 0.715757 − 1.021220I
a = −1.114730 − 0.080818I
b = 1.84474 + 0.41176I
−5.93132 + 10.98960I 0
u = 0.664796 + 1.099000I
a = 0.343002 + 0.963985I
b = −0.939763 + 0.206515I
−5.69125 + 4.02411I 0
u = 0.664796 − 1.099000I
a = 0.343002 − 0.963985I
b = −0.939763 − 0.206515I
−5.69125 − 4.02411I 0
u = −1.291770 + 0.282900I
a = −0.690521 + 0.673761I
b = 1.16812 + 1.17671I
−3.78332 + 5.21759I 0
u = −1.291770 − 0.282900I
a = −0.690521 − 0.673761I
b = 1.16812 − 1.17671I
−3.78332 − 5.21759I 0
u = −1.370090 + 0.033595I
a = −0.889375 + 0.029970I
b = 0.244301 + 0.277763I
−6.81111 + 0.91596I 0
u = −1.370090 − 0.033595I
a = −0.889375 − 0.029970I
b = 0.244301 − 0.277763I
−6.81111 − 0.91596I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.351170 + 0.333518I
a = −0.648443 + 0.927412I
b = 1.31097 + 1.11405I
−1.91040 + 7.52741I 0
u = −1.351170 − 0.333518I
a = −0.648443 − 0.927412I
b = 1.31097 − 1.11405I
−1.91040 − 7.52741I 0
u = 0.057196 + 0.549178I
a = 1.41929 − 0.58161I
b = −0.916802 + 0.411033I
0.35102 − 2.00388I −3.74140 + 5.07186I
u = 0.057196 − 0.549178I
a = 1.41929 + 0.58161I
b = −0.916802 − 0.411033I
0.35102 + 2.00388I −3.74140 − 5.07186I
u = 0.467415 + 0.199735I
a = 0.822304 − 0.650309I
b = 0.404343 + 0.377457I
−1.146940 − 0.238863I −10.78369 + 2.61801I
u = 0.467415 − 0.199735I
a = 0.822304 + 0.650309I
b = 0.404343 − 0.377457I
−1.146940 + 0.238863I −10.78369 − 2.61801I
u = −1.63628 + 0.32409I
a = 0.537236 + 0.644759I
b = −0.368302 − 0.377949I
−14.4434 + 8.7543I 0
u = −1.63628 − 0.32409I
a = 0.537236 − 0.644759I
b = −0.368302 + 0.377949I
−14.4434 − 8.7543I 0
u = −1.66486 + 0.33880I
a = 0.668565 − 0.515867I
b = −2.25117 − 1.06102I
−13.7374 + 16.0989I 0
u = −1.66486 − 0.33880I
a = 0.668565 + 0.515867I
b = −2.25117 + 1.06102I
−13.7374 − 16.0989I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.66017 + 0.38893I
a = 0.630339 − 0.408666I
b = −2.15582 − 1.03899I
−13.5280 + 7.9597I 0
u = −1.66017 − 0.38893I
a = 0.630339 + 0.408666I
b = −2.15582 + 1.03899I
−13.5280 − 7.9597I 0
u = −1.69061 + 0.34903I
a = 0.380909 + 0.625669I
b = −0.365451 + 0.042202I
−13.49590 + 1.47115I 0
u = −1.69061 − 0.34903I
a = 0.380909 − 0.625669I
b = −0.365451 − 0.042202I
−13.49590 − 1.47115I 0
8
II. I
u
2
= h9001u
25
− 3749u
24
+ · · · + 24457b + 25814, −17555u
25
−
14121u
24
+ · · · + 73371a + 84484, u
26
− 14u
24
+ · · · + u + 3i
(i) Arc colorings
a
5
=
0
u
a
10
=
1
0
a
11
=
1
u
2
a
1
=
0.239263u
25
+ 0.192460u
24
+ ··· + 0.129438u − 1.15146
−0.368034u
25
+ 0.153289u
24
+ ··· − 3.69919u − 1.05549
a
6
=
−u
−u
3
+ u
a
4
=
0.133486u
25
+ 0.561148u
24
+ ··· − 2.94220u + 2.26110
−0.941285u
25
+ 0.413051u
24
+ ··· + 4.01889u − 0.499203
a
3
=
−0.807799u
25
+ 0.974200u
24
+ ··· + 1.07669u + 1.76190
−0.941285u
25
+ 0.413051u
24
+ ··· + 4.01889u − 0.499203
a
7
=
−1.37857u
25
+ 1.35262u
24
+ ··· + 4.31739u − 4.85565
−0.395183u
25
− 0.0794864u
24
+ ··· + 0.306006u + 0.0778509
a
8
=
0.386869u
25
+ 0.659811u
24
+ ··· − 5.29940u − 0.572161
−0.474670u
25
− 1.13448u
24
+ ··· − 0.220959u + 0.263401
a
9
=
0.386869u
25
+ 0.659811u
24
+ ··· − 5.29940u − 0.572161
−0.319091u
25
− 0.428589u
24
+ ··· − 2.04138u − 1.71603
a
2
=
−0.217225u
25
+ 1.32330u
24
+ ··· − 5.90926u + 3.22244
−1.02441u
25
+ 1.62354u
24
+ ··· − 1.93961u − 5.52018
a
12
=
−u
2
+ 1
−u
4
+ 2u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes =
49040
24457
u
25
+
47416
24457
u
24
+ ··· +
432909
24457
u −
279738
24457
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
26
− 10u
25
+ ··· − 7u + 1
c
2
, c
7
u
26
+ u
25
+ ··· + u + 1
c
3
, c
6
u
26
+ 3u
24
+ ··· + 2u + 1
c
4
u
26
+ 10u
25
+ ··· + 7u + 1
c
5
u
26
− 14u
24
+ ··· − u + 3
c
8
, c
12
u
26
− u
25
+ ··· − 2u + 1
c
9
u
26
− 15u
25
+ ··· − 3u
2
+ 1
c
10
, c
11
u
26
− 14u
24
+ ··· + u + 3
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
26
+ 8y
25
+ ··· + 25y + 1
c
2
, c
7
y
26
+ 9y
25
+ ··· + y + 1
c
3
, c
6
y
26
+ 6y
25
+ ··· − 2y + 1
c
5
, c
10
, c
11
y
26
− 28y
25
+ ··· − 139y + 9
c
8
, c
12
y
26
− y
25
+ ··· + 10y + 1
c
9
y
26
− 7y
25
+ ··· − 6y + 1
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.893260 + 0.637608I
a = 0.560326 + 0.364777I
b = −2.06321 + 0.72664I
3.35683 − 4.09621I 9.04442 + 9.36453I
u = 0.893260 − 0.637608I
a = 0.560326 − 0.364777I
b = −2.06321 − 0.72664I
3.35683 + 4.09621I 9.04442 − 9.36453I
u = 0.880673 + 0.813599I
a = −0.199661 − 0.634313I
b = 0.933273 − 0.889664I
3.23266 − 1.47692I −14.8020 − 4.6669I
u = 0.880673 − 0.813599I
a = −0.199661 + 0.634313I
b = 0.933273 + 0.889664I
3.23266 + 1.47692I −14.8020 + 4.6669I
u = −1.185480 + 0.207955I
a = −0.955887 + 0.901453I
b = 0.811448 + 0.957313I
−4.63801 + 5.99993I −14.9211 − 9.9188I
u = −1.185480 − 0.207955I
a = −0.955887 − 0.901453I
b = 0.811448 − 0.957313I
−4.63801 − 5.99993I −14.9211 + 9.9188I
u = 1.202230 + 0.117764I
a = −0.637447 − 0.487886I
b = 2.06384 − 0.07791I
−0.49786 − 5.55128I −9.12515 + 7.27164I
u = 1.202230 − 0.117764I
a = −0.637447 + 0.487886I
b = 2.06384 + 0.07791I
−0.49786 + 5.55128I −9.12515 − 7.27164I
u = 1.243290 + 0.193806I
a = −0.489545 − 0.716730I
b = 1.52007 + 0.02768I
0.692396 + 0.908891I −7.23329 − 0.60855I
u = 1.243290 − 0.193806I
a = −0.489545 + 0.716730I
b = 1.52007 − 0.02768I
0.692396 − 0.908891I −7.23329 + 0.60855I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.658052 + 0.322237I
a = −0.42930 − 1.84882I
b = 0.1212750 − 0.0229366I
−2.72945 − 3.92062I −4.89712 + 0.84761I
u = −0.658052 − 0.322237I
a = −0.42930 + 1.84882I
b = 0.1212750 + 0.0229366I
−2.72945 + 3.92062I −4.89712 − 0.84761I
u = 0.253711 + 0.648614I
a = 1.54093 + 0.37558I
b = −1.54024 + 0.65815I
3.74733 − 3.59988I 2.14910 + 5.61503I
u = 0.253711 − 0.648614I
a = 1.54093 − 0.37558I
b = −1.54024 − 0.65815I
3.74733 + 3.59988I 2.14910 − 5.61503I
u = −1.323060 + 0.064355I
a = −0.913064 − 0.390548I
b = 0.186999 − 0.379225I
−6.94880 − 1.74984I −16.2080 + 5.2909I
u = −1.323060 − 0.064355I
a = −0.913064 + 0.390548I
b = 0.186999 + 0.379225I
−6.94880 + 1.74984I −16.2080 − 5.2909I
u = 0.523416 + 0.235808I
a = −0.028987 + 1.090670I
b = −1.72849 + 0.71878I
1.85328 + 4.23193I 1.90603 − 3.22437I
u = 0.523416 − 0.235808I
a = −0.028987 − 1.090670I
b = −1.72849 − 0.71878I
1.85328 − 4.23193I 1.90603 + 3.22437I
u = −1.39226 + 0.31614I
a = −0.575637 + 0.854749I
b = 1.37916 + 1.22716I
−1.47076 + 7.28765I −1.27616 − 2.61256I
u = −1.39226 − 0.31614I
a = −0.575637 − 0.854749I
b = 1.37916 − 1.22716I
−1.47076 − 7.28765I −1.27616 + 2.61256I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.424309 + 0.245639I
a = −2.57995 + 0.40653I
b = 0.973329 − 0.091897I
−3.57929 + 2.94101I −6.02456 − 4.67234I
u = −0.424309 − 0.245639I
a = −2.57995 − 0.40653I
b = 0.973329 + 0.091897I
−3.57929 − 2.94101I −6.02456 + 4.67234I
u = 1.62079 + 0.00745I
a = 0.614461 + 0.601198I
b = −1.63692 + 0.02907I
−11.33640 − 3.61266I −11.52145 + 2.34970I
u = 1.62079 − 0.00745I
a = 0.614461 − 0.601198I
b = −1.63692 − 0.02907I
−11.33640 + 3.61266I −11.52145 − 2.34970I
u = −1.63421 + 0.00977I
a = −0.072905 − 0.173246I
b = 1.47945 − 0.36272I
−6.35593 + 3.58442I −8.09065 − 3.04488I
u = −1.63421 − 0.00977I
a = −0.072905 + 0.173246I
b = 1.47945 + 0.36272I
−6.35593 − 3.58442I −8.09065 + 3.04488I
14
III.
I
u
3
= h−6a
3
bu + 4a
2
bu + · · · − a
2
− 1, −a
3
u − a
2
u + · · · − 3a + 5, u
2
− u − 1i
(i) Arc colorings
a
5
=
0
u
a
10
=
1
0
a
11
=
1
u + 1
a
1
=
a
b
a
6
=
−u
−u − 1
a
4
=
a
2
u
bau + u
a
3
=
bau + a
2
u + u
bau + u
a
7
=
a
3
bu + a
3
b + a
2
u + a
2
− 2au − 1
−2a
3
u − a
3
+ a
2
u + a
2
− au − 1
a
8
=
−a
2
bu − 2a
3
u − a
3
+ a
2
u + a
2
− 2au
2a
2
bu + 3a
3
u + a
2
b + 2a
3
− a
2
u + 2au + 2a
a
9
=
a
2
bu + 2a
3
u + a
3
− a
2
u − a
2
+ 2au
2a
3
u + a
3
− 2a
2
u − 2a
2
+ 2au
a
2
=
a
3
u + a
3
+ a
a
2
bu + a
2
b + au + b + a
a
12
=
−u
−u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −8a
3
u − 4a
3
+ 12a
2
u + 12a
2
− 8au − 10
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
(u
4
+ u
3
+ u
2
− u + 1)
4
c
2
, c
7
u
16
+ 2u
15
+ ··· + 138u + 379
c
3
, c
6
u
16
+ u
15
+ ··· + 56u + 59
c
5
, c
10
, c
11
(u
2
+ u − 1)
8
c
8
, c
12
u
16
− u
15
+ ··· + 284u + 59
c
9
(u
4
− u
3
+ u
2
+ u + 1)
4
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
9
(y
4
+ y
3
+ 5y
2
+ y + 1)
4
c
2
, c
7
y
16
+ 16y
15
+ ··· + 431966y + 143641
c
3
, c
6
y
16
+ 7y
15
+ ··· − 9862y + 3481
c
5
, c
10
, c
11
(y
2
− 3y + 1)
8
c
8
, c
12
y
16
− y
15
+ ··· − 39710y + 3481
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.618034
a = 0.701224 + 0.850806I
b = 0.921506 + 0.765153I
1.25412 − 4.68603I −8.70941 + 10.27938I
u = −0.618034
a = 0.701224 + 0.850806I
b = −2.34307 + 0.30970I
1.25412 − 4.68603I −8.70941 + 10.27938I
u = −0.618034
a = 0.701224 − 0.850806I
b = 0.921506 − 0.765153I
1.25412 + 4.68603I −8.70941 − 10.27938I
u = −0.618034
a = 0.701224 − 0.850806I
b = −2.34307 − 0.30970I
1.25412 + 4.68603I −8.70941 − 10.27938I
u = −0.618034
a = −1.51024 + 1.83240I
b = 0.658617 + 0.576443I
−3.22804 + 4.68603I −11.2906 − 10.2794I
u = −0.618034
a = −1.51024 + 1.83240I
b = 0.453931 − 0.626400I
−3.22804 + 4.68603I −11.2906 − 10.2794I
u = −0.618034
a = −1.51024 − 1.83240I
b = 0.658617 − 0.576443I
−3.22804 − 4.68603I −11.2906 + 10.2794I
u = −0.618034
a = −1.51024 − 1.83240I
b = 0.453931 + 0.626400I
−3.22804 − 4.68603I −11.2906 + 10.2794I
u = 1.61803
a = 0.576861 + 0.699914I
b = −1.43394 + 0.81776I
−11.12370 − 4.68603I −11.2906 + 10.2794I
u = 1.61803
a = 0.576861 + 0.699914I
b = −1.47875 − 0.94855I
−11.12370 − 4.68603I −11.2906 + 10.2794I
18
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.61803
a = 0.576861 − 0.699914I
b = −1.43394 − 0.81776I
−11.12370 + 4.68603I −11.2906 − 10.2794I
u = 1.61803
a = 0.576861 − 0.699914I
b = −1.47875 + 0.94855I
−11.12370 + 4.68603I −11.2906 − 10.2794I
u = 1.61803
a = −0.267844 + 0.324979I
b = 0.169969 + 0.304317I
−6.64156 + 4.68603I −8.70941 − 10.27938I
u = 1.61803
a = −0.267844 + 0.324979I
b = 3.55174 + 2.50968I
−6.64156 + 4.68603I −8.70941 − 10.27938I
u = 1.61803
a = −0.267844 − 0.324979I
b = 0.169969 − 0.304317I
−6.64156 − 4.68603I −8.70941 + 10.27938I
u = 1.61803
a = −0.267844 − 0.324979I
b = 3.55174 − 2.50968I
−6.64156 − 4.68603I −8.70941 + 10.27938I
19
IV.
I
u
4
= h−6a
3
bu + 8a
2
bu + · · · − a
2
− 1, −2a
3
u − 2a
2
u + · · · + 3a + 5, u
2
− u − 1i
(i) Arc colorings
a
5
=
0
u
a
10
=
1
0
a
11
=
1
u + 1
a
1
=
a
b
a
6
=
−u
−u − 1
a
4
=
a
2
u
bau + u
a
3
=
bau + a
2
u + u
bau + u
a
7
=
a
3
bu + a
3
b + 4a
3
u + 2a
3
− a
2
u − a
2
+ 2au − 1
au − 1
a
8
=
−a
3
bu − a
3
b + 2a
2
bu − 2a
3
u − a
3
+ a
2
u − ba + bu + a
2
+ au − b
3a
3
bu − 4a
2
bu + ··· − a − 1
a
9
=
a
3
bu + a
3
b − 2a
2
bu + 2a
3
u + a
3
− a
2
u + ba − bu − a
2
− au + b
a
2
u + a
2
− 2au + 1
a
2
=
a
3
u + a
3
+ a
a
2
bu + a
2
b + au + b + a
a
12
=
−u
−u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 16a
3
u + 8a
3
− 12a
2
u − 12a
2
+ 4au − 10
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
(u
4
+ 2u
3
+ 2u
2
+ u + 1)
4
c
2
, c
7
u
16
− u
15
+ ··· + 140u + 31
c
3
, c
6
u
16
− 2u
14
+ ··· − 50u + 19
c
5
, c
10
, c
11
(u
2
+ u − 1)
8
c
8
, c
12
u
16
− 10u
14
+ ··· − 348u + 181
c
9
(u
4
− 2u
3
+ 2u
2
− u + 1)
4
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
9
(y
4
+ 2y
2
+ 3y + 1)
4
c
2
, c
7
y
16
+ 7y
15
+ ··· − 4534y + 961
c
3
, c
6
y
16
− 4y
15
+ ··· − 2006y + 361
c
5
, c
10
, c
11
(y
2
− 3y + 1)
8
c
8
, c
12
y
16
− 20y
15
+ ··· − 157666y + 32761
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.618034
a = 0.114389 + 1.227680I
b = −1.240620 − 0.088689I
2.40496 + 2.59539I −2.46048 − 0.91892I
u = −0.618034
a = 0.114389 + 1.227680I
b = 1.04645 + 1.23483I
2.40496 + 2.59539I −2.46048 − 0.91892I
u = −0.618034
a = 0.114389 − 1.227680I
b = −1.240620 + 0.088689I
2.40496 − 2.59539I −2.46048 + 0.91892I
u = −0.618034
a = 0.114389 − 1.227680I
b = 1.04645 − 1.23483I
2.40496 − 2.59539I −2.46048 + 0.91892I
u = −0.618034
a = −1.73242 + 1.22768I
b = 1.46250 + 0.00227I
−4.37888 + 2.59539I −17.5395 − 0.9189I
u = −0.618034
a = −1.73242 + 1.22768I
b = −0.0322538 + 0.0734044I
−4.37888 + 2.59539I −17.5395 − 0.9189I
u = −0.618034
a = −1.73242 − 1.22768I
b = 1.46250 − 0.00227I
−4.37888 − 2.59539I −17.5395 + 0.9189I
u = −0.618034
a = −1.73242 − 1.22768I
b = −0.0322538 − 0.0734044I
−4.37888 − 2.59539I −17.5395 + 0.9189I
u = 1.61803
a = 0.661727 + 0.468930I
b = −0.723384 − 0.015686I
−12.27460 − 2.59539I −17.5395 + 0.9189I
u = 1.61803
a = 0.661727 + 0.468930I
b = −3.02105 + 0.21381I
−12.27460 − 2.59539I −17.5395 + 0.9189I
23
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.61803
a = 0.661727 − 0.468930I
b = −0.723384 + 0.015686I
−12.27460 + 2.59539I −17.5395 − 0.9189I
u = 1.61803
a = 0.661727 − 0.468930I
b = −3.02105 − 0.21381I
−12.27460 + 2.59539I −17.5395 − 0.9189I
u = 1.61803
a = −0.043693 + 0.468930I
b = 0.491811 − 0.313559I
−5.49072 − 2.59539I −2.46048 + 0.91892I
u = 1.61803
a = −0.043693 + 0.468930I
b = 0.01655 + 3.31420I
−5.49072 − 2.59539I −2.46048 + 0.91892I
u = 1.61803
a = −0.043693 − 0.468930I
b = 0.491811 + 0.313559I
−5.49072 + 2.59539I −2.46048 − 0.91892I
u = 1.61803
a = −0.043693 − 0.468930I
b = 0.01655 − 3.31420I
−5.49072 + 2.59539I −2.46048 − 0.91892I
24
V. I
u
5
= hb − u, a, u
2
+ u − 1i
(i) Arc colorings
a
5
=
0
u
a
10
=
1
0
a
11
=
1
−u + 1
a
1
=
0
u
a
6
=
−u
−u + 1
a
4
=
0
u
a
3
=
u
u
a
7
=
−1
0
a
8
=
−1
−u + 1
a
9
=
1
0
a
2
=
0
u
a
12
=
u
u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −10
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
9
u
2
c
2
, c
3
, c
5
c
6
, c
7
, c
8
c
10
, c
11
, c
12
u
2
− u − 1
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
9
y
2
c
2
, c
3
, c
5
c
6
, c
7
, c
8
c
10
, c
11
, c
12
y
2
− 3y + 1
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.618034
a = 0
b = 0.618034
−0.986960 −10.0000
u = −1.61803
a = 0
b = −1.61803
−8.88264 −10.0000
28
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
2
(u
4
+ u
3
+ u
2
− u + 1)
4
(u
4
+ 2u
3
+ 2u
2
+ u + 1)
4
· (u
26
− 10u
25
+ ··· − 7u + 1)(u
34
− 9u
33
+ ··· − 135u + 45)
c
2
, c
7
(u
2
− u − 1)(u
16
− u
15
+ ··· + 140u + 31)(u
16
+ 2u
15
+ ··· + 138u + 379)
· (u
26
+ u
25
+ ··· + u + 1)(u
34
+ 15u
32
+ ··· + 3u + 31)
c
3
, c
6
(u
2
− u − 1)(u
16
− 2u
14
+ ··· − 50u + 19)(u
16
+ u
15
+ ··· + 56u + 59)
· (u
26
+ 3u
24
+ ··· + 2u + 1)(u
34
+ u
33
+ ··· − 2u + 1)
c
4
u
2
(u
4
+ u
3
+ u
2
− u + 1)
4
(u
4
+ 2u
3
+ 2u
2
+ u + 1)
4
· (u
26
+ 10u
25
+ ··· + 7u + 1)(u
34
− 9u
33
+ ··· − 135u + 45)
c
5
(u
2
− u − 1)(u
2
+ u − 1)
16
(u
26
− 14u
24
+ ··· − u + 3)
· (u
34
− 16u
33
+ ··· − 512u + 256)
c
8
, c
12
(u
2
− u − 1)(u
16
− 10u
14
+ ··· − 348u + 181)
· (u
16
− u
15
+ ··· + 284u + 59)(u
26
− u
25
+ ··· − 2u + 1)
· (u
34
+ 2u
33
+ ··· + 2u + 1)
c
9
u
2
(u
4
− 2u
3
+ 2u
2
− u + 1)
4
(u
4
− u
3
+ u
2
+ u + 1)
4
· (u
26
− 15u
25
+ ··· − 3u
2
+ 1)(u
34
+ 14u
33
+ ··· + 540u + 45)
c
10
, c
11
(u
2
− u − 1)(u
2
+ u − 1)
16
(u
26
− 14u
24
+ ··· + u + 3)
· (u
34
− 16u
33
+ ··· − 512u + 256)
29
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
2
(y
4
+ 2y
2
+ 3y + 1)
4
(y
4
+ y
3
+ 5y
2
+ y + 1)
4
· (y
26
+ 8y
25
+ ··· + 25y + 1)(y
34
+ 9y
33
+ ··· + 7425y + 2025)
c
2
, c
7
(y
2
− 3y + 1)(y
16
+ 7y
15
+ ··· − 4534y + 961)
· (y
16
+ 16y
15
+ ··· + 431966y + 143641)(y
26
+ 9y
25
+ ··· + y + 1)
· (y
34
+ 30y
33
+ ··· + 16297y + 961)
c
3
, c
6
(y
2
− 3y + 1)(y
16
− 4y
15
+ ··· − 2006y + 361)
· (y
16
+ 7y
15
+ ··· − 9862y + 3481)(y
26
+ 6y
25
+ ··· − 2y + 1)
· (y
34
− 25y
33
+ ··· − 22y + 1)
c
5
, c
10
, c
11
((y
2
− 3y + 1)
17
)(y
26
− 28y
25
+ ··· − 139y + 9)
· (y
34
− 28y
33
+ ··· − 65536y + 65536)
c
8
, c
12
(y
2
− 3y + 1)(y
16
− 20y
15
+ ··· − 157666y + 32761)
· (y
16
− y
15
+ ··· − 39710y + 3481)(y
26
− y
25
+ ··· + 10y + 1)
· (y
34
− 48y
33
+ ··· − 10y + 1)
c
9
y
2
(y
4
+ 2y
2
+ 3y + 1)
4
(y
4
+ y
3
+ 5y
2
+ y + 1)
4
· (y
26
− 7y
25
+ ··· − 6y + 1)(y
34
− 6y
33
+ ··· + 31050y + 2025)
30
