12a
0353
(K12a
0353
)
A knot diagram
1
Linearized knot diagam
3 6 9 8 2 5 11 1 12 7 10 4
Solving Sequence
7,10
11
4,8
5 12 1 6 9 3 2
c
10
c
7
c
4
c
11
c
12
c
6
c
9
c
3
c
2
c
1
, c
5
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h2u
12
+ 3u
11
− 2u
10
− 7u
9
+ 3u
8
+ 11u
7
− 13u
5
− 3u
4
+ 6u
3
+ 3u
2
+ b + 3,
u
12
+ u
11
− u
10
− 3u
9
+ u
8
+ 4u
7
+ u
6
− 5u
5
− 2u
4
+ 2u
3
+ 2u
2
+ a + 1,
u
13
+ 2u
12
− 4u
10
− u
9
+ 6u
8
+ 4u
7
− 6u
6
− 6u
5
+ 2u
4
+ 4u
3
+ u
2
+ u + 1i
I
u
2
= h−1.50748 × 10
77
u
85
− 3.49171 × 10
77
u
84
+ ··· + 4.87932 × 10
75
b + 2.17543 × 10
77
,
− 5.24953 × 10
76
u
85
− 1.15851 × 10
77
u
84
+ ··· + 2.43966 × 10
75
a + 6.61885 × 10
76
, u
86
+ 3u
85
+ ··· − 9u − 1i
I
u
3
= h−2u
2
+ b, 2u
2
+ a − u − 1, u
3
− u
2
+ 1i
I
u
4
= hb
3
− b
2
+ 2b − 1, a, u + 1i
* 4 irreducible components of dim
C
= 0, with total 105 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
= h2u
12
+ 3u
11
+ · · · + b + 3, u
12
+ u
11
+ · · · + a + 1, u
13
+ 2u
12
+ · · · + u + 1i
(i) Arc colorings
a
7
=
0
u
a
10
=
1
0
a
11
=
1
u
2
a
4
=
−u
12
− u
11
+ u
10
+ 3u
9
− u
8
− 4u
7
− u
6
+ 5u
5
+ 2u
4
− 2u
3
− 2u
2
− 1
−2u
12
− 3u
11
+ 2u
10
+ 7u
9
− 3u
8
− 11u
7
+ 13u
5
+ 3u
4
− 6u
3
− 3u
2
− 3
a
8
=
−u
−u
3
+ u
a
5
=
−u
−2u
12
− 3u
11
+ ··· + u − 3
a
12
=
−u
2
+ 1
u
2
a
1
=
−u
6
+ u
4
− 2u
2
+ 1
−u
12
− u
11
+ u
10
+ 3u
9
− 2u
8
− 4u
7
+ u
6
+ 5u
5
− 2u
3
− u − 1
a
6
=
u
3
u
12
+ u
11
− u
10
− 3u
9
+ u
8
+ 4u
7
+ u
6
− 4u
5
− 2u
4
+ u
3
+ 2u
2
+ 1
a
9
=
u
4
− u
2
+ 1
−u
4
a
3
=
u
4
− u
2
+ 1
−3u
12
− 4u
11
+ ··· − 4u
2
− 4
a
2
=
−u
2
+ 1
−2u
12
− 3u
11
+ ··· − 3u
2
− 3
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 32u
12
+36u
11
−28u
10
−96u
9
+52u
8
+136u
7
+8u
6
−180u
5
−24u
4
+76u
3
+48u
2
−12u+38
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
, c
9
c
11
u
13
+ 4u
12
+ ··· − u + 1
c
2
, c
5
, c
7
c
10
u
13
+ 2u
12
− 4u
10
− u
9
+ 6u
8
+ 4u
7
− 6u
6
− 6u
5
+ 2u
4
+ 4u
3
+ u
2
+ u + 1
c
3
u
13
− 19u
12
+ ··· + 208u − 32
c
4
u
13
− 19u
12
+ ··· + 1920u − 256
c
8
, c
12
u
13
− 2u
10
+ 7u
9
+ 8u
7
− 10u
6
+ 8u
5
− 10u
4
+ 14u
3
− 7u
2
+ 5u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
, c
9
c
11
y
13
+ 12y
12
+ ··· + 7y −1
c
2
, c
5
, c
7
c
10
y
13
− 4y
12
+ ··· − y −1
c
3
y
13
− 39y
12
+ ··· − 17664y −1024
c
4
y
13
− 33y
12
+ ··· + 49152y −65536
c
8
, c
12
y
13
+ 14y
11
+ ··· + 11y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.904846 + 0.518485I
a = −0.096373 − 0.132562I
b = −0.852642 − 0.464727I
−1.81047 + 4.05578I −10.11630 − 6.00928I
u = −0.904846 − 0.518485I
a = −0.096373 + 0.132562I
b = −0.852642 + 0.464727I
−1.81047 − 4.05578I −10.11630 + 6.00928I
u = 1.036990 + 0.250355I
a = −0.283354 + 0.764990I
b = 0.595552 + 0.354344I
−4.27978 − 7.04225I −12.2400 + 9.0192I
u = 1.036990 − 0.250355I
a = −0.283354 − 0.764990I
b = 0.595552 − 0.354344I
−4.27978 + 7.04225I −12.2400 − 9.0192I
u = 0.893443 + 0.777704I
a = 2.38786 + 1.96721I
b = −2.39968 − 0.31504I
6.69849 − 5.87553I −15.0059 + 0.9974I
u = 0.893443 − 0.777704I
a = 2.38786 − 1.96721I
b = −2.39968 + 0.31504I
6.69849 + 5.87553I −15.0059 − 0.9974I
u = −0.772869 + 0.915587I
a = −1.36740 − 1.45596I
b = 0.25765 + 2.33554I
11.49150 − 5.30654I 0.126296 + 1.125513I
u = −0.772869 − 0.915587I
a = −1.36740 + 1.45596I
b = 0.25765 − 2.33554I
11.49150 + 5.30654I 0.126296 − 1.125513I
u = −0.782810
a = −1.86558
b = −3.59947
−2.34512 76.3620
u = −1.031240 + 0.801398I
a = 1.18484 + 1.74923I
b = 0.77868 − 2.51426I
9.8415 + 18.0172I −2.44507 − 10.27984I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.031240 − 0.801398I
a = 1.18484 − 1.74923I
b = 0.77868 + 2.51426I
9.8415 − 18.0172I −2.44507 + 10.27984I
u = 0.169926 + 0.521088I
a = 0.107226 − 0.405489I
b = −0.579822 − 0.331833I
1.43793 + 1.09121I 2.49987 − 1.33623I
u = 0.169926 − 0.521088I
a = 0.107226 + 0.405489I
b = −0.579822 + 0.331833I
1.43793 − 1.09121I 2.49987 + 1.33623I
6
II.
I
u
2
= h−1.51×10
77
u
85
−3.49×10
77
u
84
+· · ·+4.88×10
75
b+2.18×10
77
, −5.25 ×
10
76
u
85
−1.16×10
77
u
84
+· · ·+2.44×10
75
a+6.62×10
76
, u
86
+3u
85
+· · ·−9u−1i
(i) Arc colorings
a
7
=
0
u
a
10
=
1
0
a
11
=
1
u
2
a
4
=
21.5175u
85
+ 47.4865u
84
+ ··· − 223.630u − 27.1302
30.8953u
85
+ 71.5614u
84
+ ··· − 332.611u − 44.5847
a
8
=
−u
−u
3
+ u
a
5
=
0.251807u
85
− 1.22232u
84
+ ··· − 2.59267u + 1.81135
42.1634u
85
+ 96.0188u
84
+ ··· − 439.121u − 58.4380
a
12
=
−u
2
+ 1
u
2
a
1
=
−1.20192u
85
− 4.20915u
84
+ ··· + 41.1638u + 11.5038
4.01802u
85
+ 8.63943u
84
+ ··· − 34.0326u − 2.81610
a
6
=
−5.13993u
85
− 10.2842u
84
+ ··· + 45.1346u + 7.41626
−16.5884u
85
− 40.3873u
84
+ ··· + 197.046u + 27.1217
a
9
=
u
4
− u
2
+ 1
−u
4
a
3
=
−0.405126u
85
− 2.91912u
84
+ ··· + 7.79562u + 4.06769
37.1638u
85
+ 86.1844u
84
+ ··· − 402.124u − 53.8512
a
2
=
2.39134u
85
+ 2.75645u
84
+ ··· + 9.79591u + 6.65558
15.1058u
85
+ 36.6780u
84
+ ··· − 177.568u − 23.1796
(ii) Obstruction class = −1
(iii) Cusp Shapes = −58.8881u
85
− 125.536u
84
+ ··· + 540.615u + 58.9944
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
, c
9
c
11
u
86
+ 25u
85
+ ··· + 77u + 1
c
2
, c
5
, c
7
c
10
u
86
+ 3u
85
+ ··· − 9u − 1
c
3
(u
43
+ 8u
42
+ ··· + 168u + 17)
2
c
4
(u
43
+ 7u
42
+ ··· + 736u − 47)
2
c
8
, c
12
u
86
+ 10u
85
+ ··· − 12u − 8
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
, c
9
c
11
y
86
+ 75y
85
+ ··· − 1501y + 1
c
2
, c
5
, c
7
c
10
y
86
− 25y
85
+ ··· − 77y + 1
c
3
(y
43
− 48y
42
+ ··· + 9150y −289)
2
c
4
(y
43
− 9y
42
+ ··· + 645754y −2209)
2
c
8
, c
12
y
86
− 24y
85
+ ··· − 1872y + 64
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.917621 + 0.295314I
a = −0.040621 − 1.079690I
b = −0.333482 − 0.208136I
−0.79965 − 4.04123I 0
u = 0.917621 − 0.295314I
a = −0.040621 + 1.079690I
b = −0.333482 + 0.208136I
−0.79965 + 4.04123I 0
u = 0.717623 + 0.768123I
a = −0.054307 + 1.203790I
b = −0.77615 − 1.18911I
3.47079 + 0.34806I 0
u = 0.717623 − 0.768123I
a = −0.054307 − 1.203790I
b = −0.77615 + 1.18911I
3.47079 − 0.34806I 0
u = 0.876794 + 0.142275I
a = −0.48167 + 1.45763I
b = 0.571323 − 0.108452I
−3.83371 − 0.47604I −14.5101 + 6.2522I
u = 0.876794 − 0.142275I
a = −0.48167 − 1.45763I
b = 0.571323 + 0.108452I
−3.83371 + 0.47604I −14.5101 − 6.2522I
u = −1.060200 + 0.334825I
a = −0.274900 + 0.163237I
b = −0.332050 − 0.365366I
−3.83371 − 0.47604I 0
u = −1.060200 − 0.334825I
a = −0.274900 − 0.163237I
b = −0.332050 + 0.365366I
−3.83371 + 0.47604I 0
u = 0.048645 + 0.881375I
a = 0.613415 + 0.147896I
b = 0.246733 + 0.301746I
5.86063 + 7.97916I 0. − 7.01416I
u = 0.048645 − 0.881375I
a = 0.613415 − 0.147896I
b = 0.246733 − 0.301746I
5.86063 − 7.97916I 0. + 7.01416I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.821986 + 0.314452I
a = −1.25468 − 0.84044I
b = 1.235000 + 0.353410I
2.64548 − 6.03975I −6.00000 + 8.80568I
u = 0.821986 − 0.314452I
a = −1.25468 + 0.84044I
b = 1.235000 − 0.353410I
2.64548 + 6.03975I −6.00000 − 8.80568I
u = 0.094579 + 0.867631I
a = −0.556786 − 0.095510I
b = −0.266643 − 0.351424I
6.29916 + 1.89386I 0
u = 0.094579 − 0.867631I
a = −0.556786 + 0.095510I
b = −0.266643 + 0.351424I
6.29916 − 1.89386I 0
u = −1.12880
a = 0.312114
b = 0.0354189
−2.43233 0
u = 0.866972 + 0.726106I
a = −2.76658 − 0.35303I
b = 1.62157 − 1.38197I
1.75351 − 2.44365I 0
u = 0.866972 − 0.726106I
a = −2.76658 + 0.35303I
b = 1.62157 + 1.38197I
1.75351 + 2.44365I 0
u = −0.762384 + 0.840513I
a = 1.51688 + 1.40891I
b = −0.17717 − 2.46303I
2.89716 − 6.12343I 0
u = −0.762384 − 0.840513I
a = 1.51688 − 1.40891I
b = −0.17717 + 2.46303I
2.89716 + 6.12343I 0
u = 0.880885 + 0.729604I
a = 1.16854 + 2.90880I
b = −2.36887 − 1.57171I
1.71280 − 3.10788I 0
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.880885 − 0.729604I
a = 1.16854 − 2.90880I
b = −2.36887 + 1.57171I
1.71280 + 3.10788I 0
u = 0.750808 + 0.405787I
a = 1.063390 + 0.813737I
b = −1.177760 − 0.479406I
3.47079 − 0.34806I 0. + 2.44010I
u = 0.750808 − 0.405787I
a = 1.063390 − 0.813737I
b = −1.177760 + 0.479406I
3.47079 + 0.34806I 0. − 2.44010I
u = −0.846576 + 0.783100I
a = 1.76856 + 1.13808I
b = −0.49787 − 2.92558I
1.70345 + 1.79198I 0
u = −0.846576 − 0.783100I
a = 1.76856 − 1.13808I
b = −0.49787 + 2.92558I
1.70345 − 1.79198I 0
u = 1.105160 + 0.366027I
a = 0.072699 − 0.394651I
b = −0.515812 − 0.642478I
2.89716 − 6.12343I 0
u = 1.105160 − 0.366027I
a = 0.072699 + 0.394651I
b = −0.515812 + 0.642478I
2.89716 + 6.12343I 0
u = −0.818643 + 0.838124I
a = −1.49455 − 1.26439I
b = 0.34626 + 2.52990I
6.29916 − 1.89386I 0
u = −0.818643 − 0.838124I
a = −1.49455 + 1.26439I
b = 0.34626 − 2.52990I
6.29916 + 1.89386I 0
u = −0.686110 + 0.456826I
a = 0.541999 + 0.343912I
b = 0.844191 + 0.091293I
−1.05881 −7.04899 + 0.I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.686110 − 0.456826I
a = 0.541999 − 0.343912I
b = 0.844191 − 0.091293I
−1.05881 −7.04899 + 0.I
u = 0.879564 + 0.782202I
a = −2.48262 − 1.84244I
b = 2.33766 + 0.15453I
6.74222 0
u = 0.879564 − 0.782202I
a = −2.48262 + 1.84244I
b = 2.33766 − 0.15453I
6.74222 0
u = 1.128620 + 0.339818I
a = −0.179591 + 0.381211I
b = 0.592065 + 0.635114I
2.19501 − 12.13950I 0
u = 1.128620 − 0.339818I
a = −0.179591 − 0.381211I
b = 0.592065 − 0.635114I
2.19501 + 12.13950I 0
u = 0.846457 + 0.825135I
a = 0.65254 − 1.45537I
b = 0.50726 + 1.67242I
4.38253 − 2.76075I 0
u = 0.846457 − 0.825135I
a = 0.65254 + 1.45537I
b = 0.50726 − 1.67242I
4.38253 + 2.76075I 0
u = −0.802208 + 0.140973I
a = 0.557150 − 0.373276I
b = 0.628483 − 0.240632I
−1.40474 + 0.34878I −7.38819 − 0.48879I
u = −0.802208 − 0.140973I
a = 0.557150 + 0.373276I
b = 0.628483 + 0.240632I
−1.40474 − 0.34878I −7.38819 + 0.48879I
u = −0.852796 + 0.826238I
a = 0.72480 + 1.58821I
b = 1.37042 − 1.46910I
9.40416 − 3.01245I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.852796 − 0.826238I
a = 0.72480 − 1.58821I
b = 1.37042 + 1.46910I
9.40416 + 3.01245I 0
u = −0.756346 + 0.920914I
a = 1.37912 + 1.48912I
b = −0.23915 − 2.32246I
10.7083 − 11.6657I 0
u = −0.756346 − 0.920914I
a = 1.37912 − 1.48912I
b = −0.23915 + 2.32246I
10.7083 + 11.6657I 0
u = −0.921144 + 0.766234I
a = 1.08970 + 1.99177I
b = 1.49532 − 2.56248I
1.47289 + 4.05110I 0
u = −0.921144 − 0.766234I
a = 1.08970 − 1.99177I
b = 1.49532 + 2.56248I
1.47289 − 4.05110I 0
u = −0.786752 + 0.107835I
a = −1.44543 − 0.59084I
b = −2.95462 + 1.12027I
1.71280 + 3.10788I 15.5620 + 5.8107I
u = −0.786752 − 0.107835I
a = −1.44543 + 0.59084I
b = −2.95462 − 1.12027I
1.71280 − 3.10788I 15.5620 − 5.8107I
u = −0.878782 + 0.827666I
a = −0.82029 − 1.67464I
b = −1.33935 + 1.71105I
10.31220 + 3.55575I 0
u = −0.878782 − 0.827666I
a = −0.82029 + 1.67464I
b = −1.33935 − 1.71105I
10.31220 − 3.55575I 0
u = 0.730111 + 0.963083I
a = −0.536660 + 1.024380I
b = −0.317022 − 1.266980I
10.20200 + 2.57833I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.730111 − 0.963083I
a = −0.536660 − 1.024380I
b = −0.317022 + 1.266980I
10.20200 − 2.57833I 0
u = 0.928153 + 0.792251I
a = 1.14740 − 1.16199I
b = 0.09332 + 1.78424I
4.12750 − 3.28305I 0
u = 0.928153 − 0.792251I
a = 1.14740 + 1.16199I
b = 0.09332 − 1.78424I
4.12750 + 3.28305I 0
u = −0.914373 + 0.816465I
a = −1.28901 − 0.79743I
b = 0.80994 + 2.29058I
10.20200 + 2.57833I 0
u = −0.914373 − 0.816465I
a = −1.28901 + 0.79743I
b = 0.80994 − 2.29058I
10.20200 − 2.57833I 0
u = 0.759578 + 0.962546I
a = 0.559992 − 1.061620I
b = 0.311745 + 1.317460I
10.31220 − 3.55575I 0
u = 0.759578 − 0.962546I
a = 0.559992 + 1.061620I
b = 0.311745 − 1.317460I
10.31220 + 3.55575I 0
u = −0.932557 + 0.800894I
a = 1.199860 + 0.650051I
b = −0.91908 − 2.15138I
9.15662 + 9.09299I 0
u = −0.932557 − 0.800894I
a = 1.199860 − 0.650051I
b = −0.91908 + 2.15138I
9.15662 − 9.09299I 0
u = 0.995053 + 0.728678I
a = −1.055620 + 0.564454I
b = 0.05946 − 1.44187I
2.64548 − 6.03975I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.995053 − 0.728678I
a = −1.055620 − 0.564454I
b = 0.05946 + 1.44187I
2.64548 + 6.03975I 0
u = −0.753137 + 0.142943I
a = 1.48723 + 0.69495I
b = 2.46674 − 1.23724I
1.75351 − 2.44365I 7.89478 + 9.66086I
u = −0.753137 − 0.142943I
a = 1.48723 − 0.69495I
b = 2.46674 + 1.23724I
1.75351 + 2.44365I 7.89478 − 9.66086I
u = −1.225610 + 0.208224I
a = 0.391824 − 0.174448I
b = −0.013628 + 0.275145I
1.70345 + 1.79198I 0
u = −1.225610 − 0.208224I
a = 0.391824 + 0.174448I
b = −0.013628 − 0.275145I
1.70345 − 1.79198I 0
u = −0.960073 + 0.791715I
a = −1.11430 − 1.81231I
b = −1.11043 + 2.41682I
5.86063 + 7.97916I 0
u = −0.960073 − 0.791715I
a = −1.11430 + 1.81231I
b = −1.11043 − 2.41682I
5.86063 − 7.97916I 0
u = −1.221170 + 0.248957I
a = −0.377952 + 0.202515I
b = −0.011493 − 0.335636I
1.47289 − 4.05110I 0
u = −1.221170 − 0.248957I
a = −0.377952 − 0.202515I
b = −0.011493 + 0.335636I
1.47289 + 4.05110I 0
u = −0.991388 + 0.769708I
a = 1.18009 + 1.79469I
b = 0.97907 − 2.57885I
2.19501 + 12.13950I 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.991388 − 0.769708I
a = 1.18009 − 1.79469I
b = 0.97907 + 2.57885I
2.19501 − 12.13950I 0
u = −1.021020 + 0.807696I
a = −1.17604 − 1.74715I
b = −0.80186 + 2.47329I
10.7083 + 11.6657I 0
u = −1.021020 − 0.807696I
a = −1.17604 + 1.74715I
b = −0.80186 − 2.47329I
10.7083 − 11.6657I 0
u = −0.069448 + 0.675458I
a = 0.492940 + 0.490759I
b = 0.446685 + 0.191115I
−0.79965 + 4.04123I −5.17521 − 7.54146I
u = −0.069448 − 0.675458I
a = 0.492940 − 0.490759I
b = 0.446685 − 0.191115I
−0.79965 − 4.04123I −5.17521 + 7.54146I
u = 1.048440 + 0.831393I
a = 0.737106 − 0.872873I
b = 0.16449 + 1.52379I
9.40416 − 3.01245I 0
u = 1.048440 − 0.831393I
a = 0.737106 + 0.872873I
b = 0.16449 − 1.52379I
9.40416 + 3.01245I 0
u = 1.063500 + 0.815094I
a = −0.716411 + 0.821122I
b = −0.16567 − 1.50016I
9.15662 − 9.09299I 0
u = 1.063500 − 0.815094I
a = −0.716411 − 0.821122I
b = −0.16567 + 1.50016I
9.15662 + 9.09299I 0
u = 0.651510
a = −1.91887
b = 1.19129
−2.43233 10.8950
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.425242 + 0.386203I
a = −1.28226 − 2.39252I
b = 0.230663 + 0.508900I
4.38253 − 2.76075I −0.23115 + 5.66298I
u = 0.425242 − 0.386203I
a = −1.28226 + 2.39252I
b = 0.230663 − 0.508900I
4.38253 + 2.76075I −0.23115 − 5.66298I
u = 0.291531 + 0.377070I
a = 1.62731 + 2.63950I
b = −0.180225 − 0.647686I
4.12750 + 3.28305I −0.737032 − 0.421466I
u = 0.291531 − 0.377070I
a = 1.62731 − 2.63950I
b = −0.180225 + 0.647686I
4.12750 − 3.28305I −0.737032 + 0.421466I
u = −0.177953 + 0.028058I
a = 3.73111 − 0.78030I
b = 0.526611 − 0.507482I
−1.40474 + 0.34878I −7.38819 − 0.48879I
u = −0.177953 − 0.028058I
a = 3.73111 + 0.78030I
b = 0.526611 + 0.507482I
−1.40474 − 0.34878I −7.38819 + 0.48879I
18
III. I
u
3
= h−2u
2
+ b, 2u
2
+ a − u − 1, u
3
− u
2
+ 1i
(i) Arc colorings
a
7
=
0
u
a
10
=
1
0
a
11
=
1
u
2
a
4
=
−2u
2
+ u + 1
2u
2
a
8
=
−u
−u
2
+ u + 1
a
5
=
−u
2
+ u
u
2
− u
a
12
=
−u
2
+ 1
u
2
a
1
=
u
2
− u
−u
2
a
6
=
−u
2
+ u
u
2
a
9
=
−u
−u
2
+ u + 1
a
3
=
−u
2
+ u
u
2
− u
a
2
=
0
−u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −2u
2
+ 7u − 10
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
12
(u − 1)
3
c
3
, c
4
, c
11
u
3
+ u
2
+ 2u + 1
c
5
, c
6
(u + 1)
3
c
7
u
3
+ u
2
− 1
c
8
u
3
c
9
u
3
− u
2
+ 2u − 1
c
10
u
3
− u
2
+ 1
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
12
(y −1)
3
c
3
, c
4
, c
9
c
11
y
3
+ 3y
2
+ 2y −1
c
7
, c
10
y
3
− y
2
+ 2y −1
c
8
y
3
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.877439 + 0.744862I
a = 1.44728 − 1.86942I
b = 0.43016 + 2.61428I
1.37919 − 2.82812I −4.28809 + 2.59975I
u = 0.877439 − 0.744862I
a = 1.44728 + 1.86942I
b = 0.43016 − 2.61428I
1.37919 + 2.82812I −4.28809 − 2.59975I
u = −0.754878
a = −0.894558
b = 1.13968
−2.75839 −16.4240
22
IV. I
u
4
= hb
3
− b
2
+ 2b − 1, a, u + 1i
(i) Arc colorings
a
7
=
0
−1
a
10
=
1
0
a
11
=
1
1
a
4
=
0
b
a
8
=
1
0
a
5
=
−b
b
a
12
=
0
1
a
1
=
0
1
a
6
=
−b
2
b
2
− 1
a
9
=
1
−1
a
3
=
−b
2b
a
2
=
−b
2
2b
2
+ 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −7b
2
+ 5b − 17
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
3
− u
2
+ 2u − 1
c
2
u
3
+ u
2
− 1
c
3
, c
4
, c
6
u
3
+ u
2
+ 2u + 1
c
5
u
3
− u
2
+ 1
c
7
, c
8
, c
9
(u − 1)
3
c
10
, c
11
(u + 1)
3
c
12
u
3
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
6
y
3
+ 3y
2
+ 2y −1
c
2
, c
5
y
3
− y
2
+ 2y −1
c
7
, c
8
, c
9
c
10
, c
11
(y −1)
3
c
12
y
3
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 0
b = 0.215080 + 1.307140I
1.37919 − 2.82812I −4.28809 + 2.59975I
u = −1.00000
a = 0
b = 0.215080 − 1.307140I
1.37919 + 2.82812I −4.28809 − 2.59975I
u = −1.00000
a = 0
b = 0.569840
−2.75839 −16.4240
26
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
9
((u − 1)
3
)(u
3
− u
2
+ 2u − 1)(u
13
+ 4u
12
+ ··· − u + 1)
· (u
86
+ 25u
85
+ ··· + 77u + 1)
c
2
, c
7
(u − 1)
3
(u
3
+ u
2
− 1)
· (u
13
+ 2u
12
− 4u
10
− u
9
+ 6u
8
+ 4u
7
− 6u
6
− 6u
5
+ 2u
4
+ 4u
3
+ u
2
+ u + 1)
· (u
86
+ 3u
85
+ ··· − 9u − 1)
c
3
((u
3
+ u
2
+ 2u + 1)
2
)(u
13
− 19u
12
+ ··· + 208u − 32)
· (u
43
+ 8u
42
+ ··· + 168u + 17)
2
c
4
((u
3
+ u
2
+ 2u + 1)
2
)(u
13
− 19u
12
+ ··· + 1920u − 256)
· (u
43
+ 7u
42
+ ··· + 736u − 47)
2
c
5
, c
10
(u + 1)
3
(u
3
− u
2
+ 1)
· (u
13
+ 2u
12
− 4u
10
− u
9
+ 6u
8
+ 4u
7
− 6u
6
− 6u
5
+ 2u
4
+ 4u
3
+ u
2
+ u + 1)
· (u
86
+ 3u
85
+ ··· − 9u − 1)
c
6
, c
11
((u + 1)
3
)(u
3
+ u
2
+ 2u + 1)(u
13
+ 4u
12
+ ··· − u + 1)
· (u
86
+ 25u
85
+ ··· + 77u + 1)
c
8
, c
12
u
3
(u − 1)
3
· (u
13
− 2u
10
+ 7u
9
+ 8u
7
− 10u
6
+ 8u
5
− 10u
4
+ 14u
3
− 7u
2
+ 5u − 1)
· (u
86
+ 10u
85
+ ··· − 12u − 8)
27
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
, c
9
c
11
((y −1)
3
)(y
3
+ 3y
2
+ 2y −1)(y
13
+ 12y
12
+ ··· + 7y −1)
· (y
86
+ 75y
85
+ ··· − 1501y + 1)
c
2
, c
5
, c
7
c
10
((y −1)
3
)(y
3
− y
2
+ 2y −1)(y
13
− 4y
12
+ ··· − y −1)
· (y
86
− 25y
85
+ ··· − 77y + 1)
c
3
((y
3
+ 3y
2
+ 2y −1)
2
)(y
13
− 39y
12
+ ··· − 17664y −1024)
· (y
43
− 48y
42
+ ··· + 9150y −289)
2
c
4
((y
3
+ 3y
2
+ 2y −1)
2
)(y
13
− 33y
12
+ ··· + 49152y −65536)
· (y
43
− 9y
42
+ ··· + 645754y −2209)
2
c
8
, c
12
y
3
(y −1)
3
(y
13
+ 14y
11
+ ··· + 11y −1)
· (y
86
− 24y
85
+ ··· − 1872y + 64)
28
