12a
1228
(K12a
1228
)
A knot diagram
1
Linearized knot diagam
5 6 8 12 10 11 4 3 1 2 7 9
Solving Sequence
4,7 8,11
12 5 3 9 1 6 2 10
c
7
c
11
c
4
c
3
c
8
c
12
c
6
c
2
c
10
c
1
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−6.01811 × 10
386
u
129
− 3.95810 × 10
385
u
128
+ ··· + 1.46054 × 10
387
b − 5.70213 × 10
386
,
1.81978 × 10
387
u
129
+ 1.68335 × 10
386
u
128
+ ··· + 1.46054 × 10
387
a − 7.47460 × 10
388
,
u
130
+ 65u
128
+ ··· + 25u + 1i
I
u
2
= h2337u
31
− 6u
30
+ ··· + 631b + 5039, 1267570u
31
+ 992573u
30
+ ··· + 239149a + 339493,
u
32
+ u
31
+ ··· + 4u − 1i
* 2 irreducible components of dim
C
= 0, with total 162 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−6.02 × 10
386
u
129
− 3.96 × 10
385
u
128
+ · · · + 1.46 × 10
387
b − 5.70 ×
10
386
, 1.82 × 10
387
u
129
+ 1.68 × 10
386
u
128
+ · · · + 1.46 × 10
387
a − 7.47 ×
10
388
, u
130
+ 65u
128
+ · · · + 25u + 1i
(i) Arc colorings
a
4
=
0
u
a
7
=
1
0
a
8
=
1
−u
2
a
11
=
−1.24596u
129
− 0.115255u
128
+ ··· + 72.2066u + 51.1769
0.412047u
129
+ 0.0271002u
128
+ ··· − 33.1795u + 0.390412
a
12
=
−1.65801u
129
− 0.142356u
128
+ ··· + 105.386u + 50.7865
0.412047u
129
+ 0.0271002u
128
+ ··· − 33.1795u + 0.390412
a
5
=
2.49008u
129
+ 1.08728u
128
+ ··· − 622.790u + 26.2361
0.690479u
129
+ 0.332737u
128
+ ··· − 117.082u − 2.07945
a
3
=
−u
u
3
+ u
a
9
=
u
2
+ 1
−u
4
− 2u
2
a
1
=
−1.17148u
129
− 0.0845750u
128
+ ··· + 93.0440u + 51.8431
0.316454u
129
+ 0.174664u
128
+ ··· − 29.3185u + 0.537108
a
6
=
1.66777u
129
+ 0.545132u
128
+ ··· + 118.027u − 65.5786
−0.411679u
129
− 0.145347u
128
+ ··· + 52.8301u − 0.482638
a
2
=
7.00138u
129
+ 0.814010u
128
+ ··· − 2243.97u + 34.5505
−0.0796178u
129
+ 0.188534u
128
+ ··· − 79.5670u + 1.05186
a
10
=
4.05410u
129
+ 0.547154u
128
+ ··· − 65.5783u − 74.4592
−0.0343714u
129
+ 0.0978812u
128
+ ··· + 30.9080u − 1.20261
(ii) Obstruction class = −1
(iii) Cusp Shapes = 2.01406u
129
+ 0.00528034u
128
+ ··· − 230.499u − 15.4118
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
130
+ u
129
+ ··· + 4u + 1
c
2
u
130
+ 3u
129
+ ··· + 11268u + 1367
c
3
, c
7
, c
8
u
130
+ 65u
128
+ ··· − 25u + 1
c
4
u
130
− 20u
128
+ ··· + 4232509101u + 1162172247
c
5
u
130
+ 3u
129
+ ··· − 4845u − 2433
c
6
, c
11
u
130
− u
129
+ ··· + 20276u − 12013
c
9
, c
12
u
130
− u
129
+ ··· + 72388u − 2507
c
10
u
130
+ 7u
129
+ ··· − 3637u − 1103
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
130
+ 21y
129
+ ··· − 332y + 1
c
2
y
130
+ 27y
129
+ ··· + 8414388y + 1868689
c
3
, c
7
, c
8
y
130
+ 130y
129
+ ··· − 2035y + 1
c
4
y
130
− 40y
129
+ ··· − 4.82 × 10
19
y + 1.35 × 10
18
c
5
y
130
− 27y
129
+ ··· − 381850059y + 5919489
c
6
, c
11
y
130
− 109y
129
+ ··· + 3652617438y + 144312169
c
9
, c
12
y
130
− 89y
129
+ ··· − 1089734184y + 6285049
c
10
y
130
− 25y
129
+ ··· − 58049277y + 1216609
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.878351 + 0.479501I
a = 0.267905 − 0.715082I
b = 1.265230 − 0.145494I
−4.46528 + 3.18471I 0
u = −0.878351 − 0.479501I
a = 0.267905 + 0.715082I
b = 1.265230 + 0.145494I
−4.46528 − 3.18471I 0
u = −0.904178 + 0.479209I
a = 0.677224 − 0.825676I
b = 1.42958 + 0.41209I
−0.7984 − 14.1663I 0
u = −0.904178 − 0.479209I
a = 0.677224 + 0.825676I
b = 1.42958 − 0.41209I
−0.7984 + 14.1663I 0
u = −0.597787 + 0.841552I
a = −0.603320 + 0.306989I
b = −0.114008 − 0.193764I
2.91845 − 3.75419I 0
u = −0.597787 − 0.841552I
a = −0.603320 − 0.306989I
b = −0.114008 + 0.193764I
2.91845 + 3.75419I 0
u = −0.724677 + 0.634607I
a = −0.768164 + 0.720424I
b = −1.37841 − 0.37858I
−5.07932 − 8.49653I 0
u = −0.724677 − 0.634607I
a = −0.768164 − 0.720424I
b = −1.37841 + 0.37858I
−5.07932 + 8.49653I 0
u = −0.982121 + 0.472548I
a = −0.484899 + 0.576892I
b = −1.183440 − 0.246868I
1.58463 − 5.74871I 0
u = −0.982121 − 0.472548I
a = −0.484899 − 0.576892I
b = −1.183440 + 0.246868I
1.58463 + 5.74871I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.615550 + 0.655227I
a = 1.23994 + 1.59607I
b = 1.248160 − 0.021656I
−1.13752 + 4.31310I 0
u = 0.615550 − 0.655227I
a = 1.23994 − 1.59607I
b = 1.248160 + 0.021656I
−1.13752 − 4.31310I 0
u = 0.385384 + 0.792448I
a = −1.231870 + 0.402891I
b = 0.105055 + 0.547279I
3.03102 − 5.24392I 0
u = 0.385384 − 0.792448I
a = −1.231870 − 0.402891I
b = 0.105055 − 0.547279I
3.03102 + 5.24392I 0
u = −0.818503 + 0.290253I
a = 0.142451 + 0.334207I
b = −0.086924 − 0.484757I
4.56441 − 1.19346I 0
u = −0.818503 − 0.290253I
a = 0.142451 − 0.334207I
b = −0.086924 + 0.484757I
4.56441 + 1.19346I 0
u = −0.820647 + 0.789678I
a = −0.634880 + 0.632957I
b = −1.350430 + 0.261267I
−1.65517 + 8.35247I 0
u = −0.820647 − 0.789678I
a = −0.634880 − 0.632957I
b = −1.350430 − 0.261267I
−1.65517 − 8.35247I 0
u = 0.386861 + 1.075540I
a = 1.351750 − 0.141898I
b = 0.493213 − 0.154400I
2.20870 + 1.30818I 0
u = 0.386861 − 1.075540I
a = 1.351750 + 0.141898I
b = 0.493213 + 0.154400I
2.20870 − 1.30818I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.712561 + 0.448408I
a = −0.63173 − 1.27602I
b = −1.338250 + 0.447663I
−2.99150 + 6.35567I 0
u = 0.712561 − 0.448408I
a = −0.63173 + 1.27602I
b = −1.338250 − 0.447663I
−2.99150 − 6.35567I 0
u = 0.829587
a = 0.323136
b = −1.48778
−4.55769 0
u = 0.646603 + 0.513783I
a = 0.371738 + 0.586985I
b = 1.289990 + 0.231810I
−3.27855 − 1.86425I 0
u = 0.646603 − 0.513783I
a = 0.371738 − 0.586985I
b = 1.289990 − 0.231810I
−3.27855 + 1.86425I 0
u = 1.033090 + 0.570815I
a = 0.853456 + 0.628055I
b = 1.306130 − 0.156354I
0.26850 + 3.54378I 0
u = 1.033090 − 0.570815I
a = 0.853456 − 0.628055I
b = 1.306130 + 0.156354I
0.26850 − 3.54378I 0
u = −0.782500 + 0.949740I
a = 0.676862 − 0.554508I
b = 1.124950 − 0.039839I
0.214016 − 0.410424I 0
u = −0.782500 − 0.949740I
a = 0.676862 + 0.554508I
b = 1.124950 + 0.039839I
0.214016 + 0.410424I 0
u = −0.765551
a = 0.996922
b = −1.07406
2.38604 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.293830 + 1.202900I
a = 0.267092 − 0.713391I
b = 1.032950 + 0.235404I
−1.28452 − 3.87204I 0
u = −0.293830 − 1.202900I
a = 0.267092 + 0.713391I
b = 1.032950 − 0.235404I
−1.28452 + 3.87204I 0
u = 0.755209
a = −0.818690
b = −1.40811
0.825266 0
u = −0.172994 + 1.236950I
a = 1.010490 + 0.983822I
b = −0.553804 + 0.385324I
−0.29613 − 4.62984I 0
u = −0.172994 − 1.236950I
a = 1.010490 − 0.983822I
b = −0.553804 − 0.385324I
−0.29613 + 4.62984I 0
u = 0.680901 + 0.316640I
a = 0.043183 − 0.636995I
b = −0.240222 + 0.999581I
4.48026 + 9.15437I 0
u = 0.680901 − 0.316640I
a = 0.043183 + 0.636995I
b = −0.240222 − 0.999581I
4.48026 − 9.15437I 0
u = 0.907749 + 0.880383I
a = −0.931871 − 0.374887I
b = −1.262540 − 0.007209I
−0.55631 + 3.09812I 0
u = 0.907749 − 0.880383I
a = −0.931871 + 0.374887I
b = −1.262540 + 0.007209I
−0.55631 − 3.09812I 0
u = 0.549788 + 0.436843I
a = 0.481999 + 1.016070I
b = 1.44060 − 0.34552I
−5.20986 + 2.23420I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.549788 − 0.436843I
a = 0.481999 − 1.016070I
b = 1.44060 + 0.34552I
−5.20986 − 2.23420I 0
u = −0.198012 + 0.660781I
a = 0.941167 − 0.516068I
b = 0.605312 + 0.327412I
−0.45180 − 1.44547I 0
u = −0.198012 − 0.660781I
a = 0.941167 + 0.516068I
b = 0.605312 − 0.327412I
−0.45180 + 1.44547I 0
u = 0.640848 + 0.248842I
a = −0.624993 + 0.530930I
b = −0.207654 − 0.661667I
4.55789 + 2.41284I 0
u = 0.640848 − 0.248842I
a = −0.624993 − 0.530930I
b = −0.207654 + 0.661667I
4.55789 − 2.41284I 0
u = −0.003165 + 1.314500I
a = 2.51529 + 0.49435I
b = 1.53646 + 0.66593I
−1.70839 + 2.06002I 0
u = −0.003165 − 1.314500I
a = 2.51529 − 0.49435I
b = 1.53646 − 0.66593I
−1.70839 − 2.06002I 0
u = 0.481434 + 0.475913I
a = −0.34312 − 1.73148I
b = −1.283160 − 0.031411I
−5.34195 + 1.26907I 0
u = 0.481434 − 0.475913I
a = −0.34312 + 1.73148I
b = −1.283160 + 0.031411I
−5.34195 − 1.26907I 0
u = 0.047332 + 1.339880I
a = 0.891276 − 0.261218I
b = 0.746224 + 0.725294I
−1.387670 + 0.222118I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.047332 − 1.339880I
a = 0.891276 + 0.261218I
b = 0.746224 − 0.725294I
−1.387670 − 0.222118I 0
u = 0.068839 + 1.349240I
a = −0.373812 + 0.116030I
b = −0.942190 − 0.670685I
−2.67934 − 5.08676I 0
u = 0.068839 − 1.349240I
a = −0.373812 − 0.116030I
b = −0.942190 + 0.670685I
−2.67934 + 5.08676I 0
u = 0.043777 + 1.357340I
a = 2.39054 − 0.17868I
b = 1.100650 + 0.282181I
−1.37511 + 1.88610I 0
u = 0.043777 − 1.357340I
a = 2.39054 + 0.17868I
b = 1.100650 − 0.282181I
−1.37511 − 1.88610I 0
u = −0.183770 + 1.357780I
a = −0.793688 + 0.411879I
b = −0.576633 − 0.928190I
−1.52719 − 0.68054I 0
u = −0.183770 − 1.357780I
a = −0.793688 − 0.411879I
b = −0.576633 + 0.928190I
−1.52719 + 0.68054I 0
u = −0.186654 + 1.357790I
a = −0.458767 − 0.472489I
b = −0.012757 − 0.569359I
−4.00591 − 3.47140I 0
u = −0.186654 − 1.357790I
a = −0.458767 + 0.472489I
b = −0.012757 + 0.569359I
−4.00591 + 3.47140I 0
u = −0.065013 + 1.377570I
a = 0.91114 − 1.09535I
b = 0.96985 − 1.44530I
−2.74451 − 4.13753I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.065013 − 1.377570I
a = 0.91114 + 1.09535I
b = 0.96985 + 1.44530I
−2.74451 + 4.13753I 0
u = 0.290700 + 0.537887I
a = −2.30465 − 0.48448I
b = −1.054250 + 0.323843I
−1.56827 + 4.27892I −1.40759 − 8.91376I
u = 0.290700 − 0.537887I
a = −2.30465 + 0.48448I
b = −1.054250 − 0.323843I
−1.56827 − 4.27892I −1.40759 + 8.91376I
u = 0.035608 + 1.395810I
a = −3.38425 + 0.34756I
b = −1.224580 + 0.160316I
−2.71386 + 6.58703I 0
u = 0.035608 − 1.395810I
a = −3.38425 − 0.34756I
b = −1.224580 − 0.160316I
−2.71386 − 6.58703I 0
u = −0.009747 + 1.410940I
a = −2.17215 − 0.53564I
b = −1.53403 + 0.30115I
−6.45759 − 0.12198I 0
u = −0.009747 − 1.410940I
a = −2.17215 + 0.53564I
b = −1.53403 − 0.30115I
−6.45759 + 0.12198I 0
u = −0.14870 + 1.41051I
a = −0.596599 − 0.610104I
b = −0.095364 − 1.151950I
−4.52718 − 3.68202I 0
u = −0.14870 − 1.41051I
a = −0.596599 + 0.610104I
b = −0.095364 + 1.151950I
−4.52718 + 3.68202I 0
u = −0.28006 + 1.39162I
a = 0.494115 − 0.027065I
b = 0.417573 + 0.706412I
−0.73826 − 5.10736I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.28006 − 1.39162I
a = 0.494115 + 0.027065I
b = 0.417573 − 0.706412I
−0.73826 + 5.10736I 0
u = 0.08530 + 1.41776I
a = −0.797089 + 0.934847I
b = −0.63152 + 1.53765I
−5.42127 + 5.20183I 0
u = 0.08530 − 1.41776I
a = −0.797089 − 0.934847I
b = −0.63152 − 1.53765I
−5.42127 − 5.20183I 0
u = −0.461485 + 0.342497I
a = 0.697444 − 0.802577I
b = −0.077226 + 0.844098I
1.04116 − 1.46431I −0.71657 + 3.65612I
u = −0.461485 − 0.342497I
a = 0.697444 + 0.802577I
b = −0.077226 − 0.844098I
1.04116 + 1.46431I −0.71657 − 3.65612I
u = −0.561393 + 0.101743I
a = −1.26827 − 1.50964I
b = 0.567221 + 0.706722I
3.11725 + 1.98534I 6.85144 − 2.18321I
u = −0.561393 − 0.101743I
a = −1.26827 + 1.50964I
b = 0.567221 − 0.706722I
3.11725 − 1.98534I 6.85144 + 2.18321I
u = 0.20547 + 1.42554I
a = −0.002859 + 0.302596I
b = 0.053895 + 1.035460I
−0.86547 + 5.40565I 0
u = 0.20547 − 1.42554I
a = −0.002859 − 0.302596I
b = 0.053895 − 1.035460I
−0.86547 − 5.40565I 0
u = 0.36834 + 1.39918I
a = 1.45946 + 1.01129I
b = 1.55482 − 0.14774I
−9.13006 + 4.36537I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.36834 − 1.39918I
a = 1.45946 − 1.01129I
b = 1.55482 + 0.14774I
−9.13006 − 4.36537I 0
u = 0.233772 + 0.496655I
a = 1.36274 − 1.04709I
b = 0.176878 − 0.210114I
−0.96711 − 1.54704I −2.41396 − 0.36879I
u = 0.233772 − 0.496655I
a = 1.36274 + 1.04709I
b = 0.176878 + 0.210114I
−0.96711 + 1.54704I −2.41396 + 0.36879I
u = 0.23607 + 1.43584I
a = 0.800263 − 0.436336I
b = 0.414096 − 1.262410I
−1.16551 + 12.45170I 0
u = 0.23607 − 1.43584I
a = 0.800263 + 0.436336I
b = 0.414096 + 1.262410I
−1.16551 − 12.45170I 0
u = −0.500081 + 0.212374I
a = 0.595144 − 0.272323I
b = −0.180192 + 0.565372I
0.956398 − 0.962055I 6.03045 + 1.88099I
u = −0.500081 − 0.212374I
a = 0.595144 + 0.272323I
b = −0.180192 − 0.565372I
0.956398 + 0.962055I 6.03045 − 1.88099I
u = 0.005862 + 0.543268I
a = 0.969732 − 0.107902I
b = 1.180790 + 0.603741I
−1.68067 − 2.91742I −11.07453 + 3.11081I
u = 0.005862 − 0.543268I
a = 0.969732 + 0.107902I
b = 1.180790 − 0.603741I
−1.68067 + 2.91742I −11.07453 − 3.11081I
u = 0.04669 + 1.46872I
a = −0.317423 + 0.358759I
b = −0.073696 − 0.495255I
−7.31537 − 0.73791I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.04669 − 1.46872I
a = −0.317423 − 0.358759I
b = −0.073696 + 0.495255I
−7.31537 + 0.73791I 0
u = 0.18521 + 1.47509I
a = −2.18595 − 0.51282I
b = −1.71102 + 0.47552I
−11.43610 + 4.90281I 0
u = 0.18521 − 1.47509I
a = −2.18595 + 0.51282I
b = −1.71102 − 0.47552I
−11.43610 − 4.90281I 0
u = 0.14443 + 1.50571I
a = 1.86482 + 0.97913I
b = 1.352160 − 0.221798I
−11.90240 + 3.47629I 0
u = 0.14443 − 1.50571I
a = 1.86482 − 0.97913I
b = 1.352160 + 0.221798I
−11.90240 − 3.47629I 0
u = 0.26191 + 1.49075I
a = 1.95805 + 0.81840I
b = 1.45285 − 0.56782I
−9.27069 + 9.92657I 0
u = 0.26191 − 1.49075I
a = 1.95805 − 0.81840I
b = 1.45285 + 0.56782I
−9.27069 − 9.92657I 0
u = −0.09744 + 1.51353I
a = 0.125674 − 0.460826I
b = −0.219409 + 0.279876I
−4.89332 − 5.59507I 0
u = −0.09744 − 1.51353I
a = 0.125674 + 0.460826I
b = −0.219409 − 0.279876I
−4.89332 + 5.59507I 0
u = 0.22905 + 1.51053I
a = −1.78934 − 0.67579I
b = −1.46516 − 0.01842I
−9.84771 + 1.38248I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.22905 − 1.51053I
a = −1.78934 + 0.67579I
b = −1.46516 + 0.01842I
−9.84771 − 1.38248I 0
u = −0.06162 + 1.53827I
a = −1.97016 − 0.19495I
b = −1.58796 − 0.68750I
−8.73447 − 3.47295I 0
u = −0.06162 − 1.53827I
a = −1.97016 + 0.19495I
b = −1.58796 + 0.68750I
−8.73447 + 3.47295I 0
u = 0.371720 + 0.235007I
a = −0.310980 + 0.290500I
b = 0.227435 − 1.022650I
−0.10767 + 3.70505I 2.74727 − 13.27960I
u = 0.371720 − 0.235007I
a = −0.310980 − 0.290500I
b = 0.227435 + 1.022650I
−0.10767 − 3.70505I 2.74727 + 13.27960I
u = 0.23568 + 1.54603I
a = −1.85989 − 1.16308I
b = −1.266550 + 0.197806I
−8.29668 + 7.58722I 0
u = 0.23568 − 1.54603I
a = −1.85989 + 1.16308I
b = −1.266550 − 0.197806I
−8.29668 − 7.58722I 0
u = −0.32817 + 1.53205I
a = −1.94604 + 0.74188I
b = −1.54921 − 0.49226I
−7.3079 − 18.6467I 0
u = −0.32817 − 1.53205I
a = −1.94604 − 0.74188I
b = −1.54921 + 0.49226I
−7.3079 + 18.6467I 0
u = −0.23255 + 1.55567I
a = 2.00664 − 0.44118I
b = 1.59935 + 0.48550I
−12.2657 − 11.9906I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.23255 − 1.55567I
a = 2.00664 + 0.44118I
b = 1.59935 − 0.48550I
−12.2657 + 11.9906I 0
u = 0.18039 + 1.56433I
a = 2.18609 + 0.36844I
b = 1.41126 − 0.22394I
−8.98805 + 6.28691I 0
u = 0.18039 − 1.56433I
a = 2.18609 − 0.36844I
b = 1.41126 + 0.22394I
−8.98805 − 6.28691I 0
u = −0.34223 + 1.54613I
a = 1.60199 − 0.60685I
b = 1.328650 + 0.427406I
−4.98303 − 10.52040I 0
u = −0.34223 − 1.54613I
a = 1.60199 + 0.60685I
b = 1.328650 − 0.427406I
−4.98303 + 10.52040I 0
u = −0.12880 + 1.58791I
a = −1.69628 + 0.20298I
b = −1.289580 − 0.451232I
−8.49217 − 2.94716I 0
u = −0.12880 − 1.58791I
a = −1.69628 − 0.20298I
b = −1.289580 + 0.451232I
−8.49217 + 2.94716I 0
u = −0.30686 + 1.57844I
a = −1.43518 + 0.75757I
b = −1.301000 − 0.119352I
−11.24220 − 1.26863I 0
u = −0.30686 − 1.57844I
a = −1.43518 − 0.75757I
b = −1.301000 + 0.119352I
−11.24220 + 1.26863I 0
u = 0.35907 + 1.57898I
a = −1.88641 − 0.71128I
b = −1.45217 + 0.25923I
−6.70202 + 8.60411I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.35907 − 1.57898I
a = −1.88641 + 0.71128I
b = −1.45217 − 0.25923I
−6.70202 − 8.60411I 0
u = −0.12106 + 1.62349I
a = 1.82984 − 0.51769I
b = 1.377390 − 0.001363I
−10.26370 + 5.02475I 0
u = −0.12106 − 1.62349I
a = 1.82984 + 0.51769I
b = 1.377390 + 0.001363I
−10.26370 − 5.02475I 0
u = −0.292599 + 0.100882I
a = −0.19699 − 1.47954I
b = −1.08004 + 0.94210I
2.00640 − 2.90128I 19.4629 + 9.4955I
u = −0.292599 − 0.100882I
a = −0.19699 + 1.47954I
b = −1.08004 − 0.94210I
2.00640 + 2.90128I 19.4629 − 9.4955I
u = 0.270851 + 0.030304I
a = −3.06598 + 3.02737I
b = −0.701050 − 0.221904I
2.94768 − 0.93202I 4.67553 + 3.22730I
u = 0.270851 − 0.030304I
a = −3.06598 − 3.02737I
b = −0.701050 + 0.221904I
2.94768 + 0.93202I 4.67553 − 3.22730I
u = 0.139901 + 0.034692I
a = 0.35663 − 13.34670I
b = 0.980046 + 0.343604I
1.99500 − 6.03837I 8.72732 + 7.41792I
u = 0.139901 − 0.034692I
a = 0.35663 + 13.34670I
b = 0.980046 − 0.343604I
1.99500 + 6.03837I 8.72732 − 7.41792I
u = −0.0228074
a = 45.9496
b = 1.44123
−1.54394 −6.88820
17
II. I
u
2
= h2337u
31
− 6u
30
+ · · · + 631b + 5039, 1.27 × 10
6
u
31
+ 9.93 ×
10
5
u
30
+ · · · + 2.39 × 10
5
a + 3.39 × 10
5
, u
32
+ u
31
+ · · · + 4u − 1i
(i) Arc colorings
a
4
=
0
u
a
7
=
1
0
a
8
=
1
−u
2
a
11
=
−5.30034u
31
− 4.15044u
30
+ ··· + 20.6869u − 1.41959
−3.70365u
31
+ 0.00950872u
30
+ ··· + 28.4089u − 7.98574
a
12
=
−1.59669u
31
− 4.15995u
30
+ ··· − 7.72202u + 6.56615
−3.70365u
31
+ 0.00950872u
30
+ ··· + 28.4089u − 7.98574
a
5
=
−5.44632u
31
− 6.09473u
30
+ ··· − 8.20803u − 1.85582
2.09877u
31
+ 0.892732u
30
+ ··· + 3.79909u + 0.639890
a
3
=
−u
u
3
+ u
a
9
=
u
2
+ 1
−u
4
− 2u
2
a
1
=
−3.47161u
31
− 6.20553u
30
+ ··· + 3.17546u + 2.12442
−2.14039u
31
+ 2.45216u
30
+ ··· + 33.4560u − 9.38905
a
6
=
1.63989u
31
+ 3.73866u
30
+ ··· − 10.8946u + 7.35865
u
31
+ u
30
+ ··· − 11u + 1
a
2
=
4.93064u
31
+ 11.0192u
30
+ ··· + 12.5588u − 7.51211
−3.27823u
31
− 2.88564u
30
+ ··· + 21.6195u − 4.00787
a
10
=
0.505568u
31
+ 7.56423u
30
+ ··· − 1.35553u + 4.89516
−3.09481u
31
− 8.08433u
30
+ ··· − 13.4995u + 2.92760
(ii) Obstruction class = 1
(iii) Cusp Shapes =
739750
239149
u
31
+
7850251
239149
u
30
+ ··· +
31823625
239149
u −
11103106
239149
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
32
+ 10u
30
+ ··· − u − 1
c
2
u
32
− 4u
31
+ ··· + u − 1
c
3
u
32
− u
31
+ ··· − 4u − 1
c
4
u
32
+ u
31
+ ··· − 8u − 1
c
5
u
32
− 4u
30
+ ··· − 4u
2
+ 1
c
6
u
32
− 13u
30
+ ··· + 3u + 1
c
7
, c
8
u
32
+ u
31
+ ··· + 4u − 1
c
9
u
32
− 13u
30
+ ··· + 29u + 1
c
10
u
32
− u
30
+ ··· − 3u
2
+ 1
c
11
u
32
− 13u
30
+ ··· − 3u + 1
c
12
u
32
− 13u
30
+ ··· − 29u + 1
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
32
+ 20y
31
+ ··· + 11y + 1
c
2
y
32
+ 18y
31
+ ··· − y + 1
c
3
, c
7
, c
8
y
32
+ 33y
31
+ ··· + 28y + 1
c
4
y
32
+ 11y
31
+ ··· + 34y + 1
c
5
y
32
− 8y
31
+ ··· − 8y + 1
c
6
, c
11
y
32
− 26y
31
+ ··· − 39y + 1
c
9
, c
12
y
32
− 26y
31
+ ··· − 853y + 1
c
10
y
32
− 2y
31
+ ··· − 6y + 1
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.487953 + 0.806481I
a = −0.125588 − 0.135831I
b = −0.738483 − 0.210641I
2.16674 + 3.11635I 2.52582 − 3.28583I
u = 0.487953 − 0.806481I
a = −0.125588 + 0.135831I
b = −0.738483 + 0.210641I
2.16674 − 3.11635I 2.52582 + 3.28583I
u = 0.413152 + 0.973822I
a = 1.38308 + 0.48888I
b = 0.734899 + 0.159771I
1.87700 + 0.53920I 3.40143 + 2.52576I
u = 0.413152 − 0.973822I
a = 1.38308 − 0.48888I
b = 0.734899 − 0.159771I
1.87700 − 0.53920I 3.40143 − 2.52576I
u = −0.751467 + 0.794913I
a = 0.754134 − 0.301288I
b = 1.248340 + 0.108268I
−0.18285 − 1.72470I 1.25158 + 1.80974I
u = −0.751467 − 0.794913I
a = 0.754134 + 0.301288I
b = 1.248340 − 0.108268I
−0.18285 + 1.72470I 1.25158 − 1.80974I
u = −0.933653 + 0.714953I
a = −0.985948 + 0.784089I
b = −1.249270 − 0.091457I
−0.03671 − 4.33244I 3.73411 + 9.59889I
u = −0.933653 − 0.714953I
a = −0.985948 − 0.784089I
b = −1.249270 + 0.091457I
−0.03671 + 4.33244I 3.73411 − 9.59889I
u = 0.059501 + 1.201540I
a = −1.025630 + 0.092892I
b = 0.883133 − 0.328106I
−0.76484 + 6.41596I 1.55951 − 7.59182I
u = 0.059501 − 1.201540I
a = −1.025630 − 0.092892I
b = 0.883133 + 0.328106I
−0.76484 − 6.41596I 1.55951 + 7.59182I
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.103639 + 1.290290I
a = −0.402195 + 0.549295I
b = −0.584388 + 0.607280I
−4.42591 + 4.06684I −5.84079 − 5.51367I
u = 0.103639 − 1.290290I
a = −0.402195 − 0.549295I
b = −0.584388 − 0.607280I
−4.42591 − 4.06684I −5.84079 + 5.51367I
u = 0.207615 + 1.285740I
a = 0.712522 − 0.721672I
b = −0.275818 + 0.122841I
0.17205 + 3.02622I 4.32560 − 2.19241I
u = 0.207615 − 1.285740I
a = 0.712522 + 0.721672I
b = −0.275818 − 0.122841I
0.17205 − 3.02622I 4.32560 + 2.19241I
u = 0.002920 + 1.326090I
a = 2.33068 − 0.44533I
b = 1.31110 − 0.90212I
−2.00157 − 2.48669I −3.99457 + 8.83308I
u = 0.002920 − 1.326090I
a = 2.33068 + 0.44533I
b = 1.31110 + 0.90212I
−2.00157 + 2.48669I −3.99457 − 8.83308I
u = 0.047122 + 0.659210I
a = −3.57985 − 0.58464I
b = −0.998636 − 0.273022I
1.28173 − 5.91897I −2.36688 + 5.32829I
u = 0.047122 − 0.659210I
a = −3.57985 + 0.58464I
b = −0.998636 + 0.273022I
1.28173 + 5.91897I −2.36688 − 5.32829I
u = 0.653768
a = −1.32573
b = 0.317079
4.04613 10.7920
u = −0.596192
a = −0.908572
b = 1.40186
−5.46167 −8.19610
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.12781 + 1.41707I
a = −0.113512 + 0.672939I
b = 0.235524 + 1.022770I
−4.00918 + 4.33888I 0. − 7.82866I
u = 0.12781 − 1.41707I
a = −0.113512 − 0.672939I
b = 0.235524 − 1.022770I
−4.00918 − 4.33888I 0. + 7.82866I
u = −0.23390 + 1.46212I
a = −1.72159 + 0.82623I
b = −1.46036 − 0.21565I
−10.55490 − 3.10377I 0
u = −0.23390 − 1.46212I
a = −1.72159 − 0.82623I
b = −1.46036 + 0.21565I
−10.55490 + 3.10377I 0
u = −0.07356 + 1.55907I
a = −1.86796 − 0.07839I
b = −1.44603 − 0.61412I
−8.49476 − 3.48331I 0
u = −0.07356 − 1.55907I
a = −1.86796 + 0.07839I
b = −1.44603 + 0.61412I
−8.49476 + 3.48331I 0
u = 0.115165 + 0.399617I
a = 2.03473 + 0.33450I
b = 0.963064 + 0.544751I
−1.23939 − 3.12612I 3.40722 + 7.64554I
u = 0.115165 − 0.399617I
a = 2.03473 − 0.33450I
b = 0.963064 − 0.544751I
−1.23939 + 3.12612I 3.40722 − 7.64554I
u = −0.27035 + 1.57486I
a = 1.98133 − 0.79427I
b = 1.353040 + 0.294691I
−7.64206 − 8.57742I 0
u = −0.27035 − 1.57486I
a = 1.98133 + 0.79427I
b = 1.353040 − 0.294691I
−7.64206 + 8.57742I 0
23
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.169265 + 0.273346I
a = 1.74293 + 0.28410I
b = −0.835581 − 0.750642I
1.66368 + 2.81317I −3.44179 − 3.42840I
u = 0.169265 − 0.273346I
a = 1.74293 − 0.28410I
b = −0.835581 + 0.750642I
1.66368 − 2.81317I −3.44179 + 3.42840I
24
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
32
+ 10u
30
+ ··· − u − 1)(u
130
+ u
129
+ ··· + 4u + 1)
c
2
(u
32
− 4u
31
+ ··· + u − 1)(u
130
+ 3u
129
+ ··· + 11268u + 1367)
c
3
(u
32
− u
31
+ ··· − 4u − 1)(u
130
+ 65u
128
+ ··· − 25u + 1)
c
4
(u
32
+ u
31
+ ··· − 8u − 1)
· (u
130
− 20u
128
+ ··· + 4232509101u + 1162172247)
c
5
(u
32
− 4u
30
+ ··· − 4u
2
+ 1)(u
130
+ 3u
129
+ ··· − 4845u − 2433)
c
6
(u
32
− 13u
30
+ ··· + 3u + 1)(u
130
− u
129
+ ··· + 20276u − 12013)
c
7
, c
8
(u
32
+ u
31
+ ··· + 4u − 1)(u
130
+ 65u
128
+ ··· − 25u + 1)
c
9
(u
32
− 13u
30
+ ··· + 29u + 1)(u
130
− u
129
+ ··· + 72388u − 2507)
c
10
(u
32
− u
30
+ ··· − 3u
2
+ 1)(u
130
+ 7u
129
+ ··· − 3637u − 1103)
c
11
(u
32
− 13u
30
+ ··· − 3u + 1)(u
130
− u
129
+ ··· + 20276u − 12013)
c
12
(u
32
− 13u
30
+ ··· − 29u + 1)(u
130
− u
129
+ ··· + 72388u − 2507)
25
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
32
+ 20y
31
+ ··· + 11y + 1)(y
130
+ 21y
129
+ ··· − 332y + 1)
c
2
(y
32
+ 18y
31
+ ··· − y + 1)
· (y
130
+ 27y
129
+ ··· + 8414388y + 1868689)
c
3
, c
7
, c
8
(y
32
+ 33y
31
+ ··· + 28y + 1)(y
130
+ 130y
129
+ ··· − 2035y + 1)
c
4
(y
32
+ 11y
31
+ ··· + 34y + 1)
· (y
130
− 40y
129
+ ··· − 4.82 × 10
19
y + 1.35 × 10
18
)
c
5
(y
32
− 8y
31
+ ··· − 8y + 1)
· (y
130
− 27y
129
+ ··· − 381850059y + 5919489)
c
6
, c
11
(y
32
− 26y
31
+ ··· − 39y + 1)
· (y
130
− 109y
129
+ ··· + 3652617438y + 144312169)
c
9
, c
12
(y
32
− 26y
31
+ ··· − 853y + 1)
· (y
130
− 89y
129
+ ··· − 1089734184y + 6285049)
c
10
(y
32
− 2y
31
+ ··· − 6y + 1)
· (y
130
− 25y
129
+ ··· − 58049277y + 1216609)
26
