12a
1177
(K12a
1177
)
A knot diagram
1
Linearized knot diagam
4 10 8 9 11 12 3 1 2 5 7 6
Solving Sequence
2,9
10
3,5
11 6 4 1 8 7 12
c
9
c
2
c
10
c
5
c
4
c
1
c
8
c
7
c
12
c
3
, c
6
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−4.26355 × 10
21
u
36
− 4.65847 × 10
21
u
35
+ ··· + 8.18871 × 10
21
b − 1.58097 × 10
21
,
6.44134 × 10
21
u
36
+ 4.23042 × 10
21
u
35
+ ··· + 8.18871 × 10
21
a + 1.81600 × 10
21
, u
37
+ u
36
+ ··· + 2u
2
+ 1i
I
u
2
= h−1.64908 × 10
149
u
59
+ 3.34873 × 10
149
u
58
+ ··· + 7.81855 × 10
149
b − 4.35814 × 10
151
,
− 6.45563 × 10
151
u
59
+ 1.26626 × 10
152
u
58
+ ··· + 2.11883 × 10
152
a − 1.81648 × 10
154
,
u
60
− u
59
+ ··· − 152u + 271i
I
u
3
= h−u
20
+ u
19
+ ··· + b − 1, −u
19
+ u
18
+ ··· + a − 1, u
21
− u
20
+ ··· + u − 1i
I
u
4
= h932291063u
17
+ 893351307u
16
+ ··· + 714572543b + 14866160218,
18572309288u
17
+ 15580732761u
16
+ ··· + 7860297973a + 300923661828,
u
18
− 6u
16
+ ··· + 26u − 11i
* 4 irreducible components of dim
C
= 0, with total 136 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−4.26×10
21
u
36
−4.66×10
21
u
35
+· · ·+8.19×10
21
b−1.58×10
21
, 6.44×
10
21
u
36
+4.23×10
21
u
35
+· · ·+8.19×10
21
a+1.82×10
21
, u
37
+u
36
+· · ·+2u
2
+1i
(i) Arc colorings
a
2
=
0
u
a
9
=
1
0
a
10
=
1
u
2
a
3
=
−u
−u
3
+ u
a
5
=
−0.786612u
36
− 0.516616u
35
+ ··· + 0.307274u − 0.221769
0.520662u
36
+ 0.568889u
35
+ ··· − 0.0878633u + 0.193067
a
11
=
0.169413u
36
− 0.278568u
35
+ ··· + 0.100583u + 1.08723
−0.193067u
36
+ 0.327595u
35
+ ··· − 0.742279u − 1.08786
a
6
=
−0.771491u
36
+ 0.281145u
35
+ ··· + 0.204847u − 1.00896
−0.582458u
36
− 0.514755u
35
+ ··· + 0.796684u + 0.548671
a
4
=
−1.30727u
36
− 1.08551u
35
+ ··· + 0.395137u − 0.414836
0.520662u
36
+ 0.568889u
35
+ ··· − 0.0878633u + 0.193067
a
1
=
−0.607890u
36
− 0.486704u
35
+ ··· + 0.388479u − 0.0924838
0.520662u
36
+ 0.568889u
35
+ ··· − 0.0878633u + 0.193067
a
8
=
−0.414836u
36
+ 0.892438u
35
+ ··· − 0.327443u − 1.39514
0.193067u
36
− 0.327595u
35
+ ··· + 0.742279u + 1.08786
a
7
=
−0.414836u
36
+ 0.892438u
35
+ ··· − 0.327443u − 1.39514
0.193067u
36
− 0.327595u
35
+ ··· + 0.742279u + 1.08786
a
12
=
0.456823u
36
+ 0.679879u
35
+ ··· − 0.501075u − 1.20565
−0.449008u
36
− 0.538538u
35
+ ··· − 1.03063u + 0.204677
(ii) Obstruction class = −1
(iii) Cusp Shapes =
14266512891898453968337
8188710458299948771387
u
36
+
42200187178412249372194
8188710458299948771387
u
35
+ ··· +
4891160629825285242867
8188710458299948771387
u −
36295754117365129264878
8188710458299948771387
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
37
− 30u
36
+ ··· + 159744u − 8192
c
2
, c
3
, c
7
c
9
u
37
− u
36
+ ··· − 2u
2
− 1
c
4
, c
8
u
37
− 6u
35
+ ··· − u + 1
c
5
, c
10
u
37
− 7u
36
+ ··· − 3368u + 464
c
6
, c
11
, c
12
u
37
+ 7u
36
+ ··· + 24u + 8
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
37
− 6y
36
+ ··· − 16777216y −67108864
c
2
, c
3
, c
7
c
9
y
37
− 23y
36
+ ··· − 4y −1
c
4
, c
8
y
37
− 12y
36
+ ··· + 25y −1
c
5
, c
10
y
37
− 21y
36
+ ··· − 1481536y −215296
c
6
, c
11
, c
12
y
37
+ 31y
36
+ ··· + 96y −64
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.786239 + 0.506891I
a = −0.05205 − 1.43237I
b = 0.564891 − 0.231667I
−0.47617 − 1.67526I 3.31637 + 3.88563I
u = 0.786239 − 0.506891I
a = −0.05205 + 1.43237I
b = 0.564891 + 0.231667I
−0.47617 + 1.67526I 3.31637 − 3.88563I
u = −0.938042 + 0.514832I
a = −0.11839 − 1.74298I
b = −0.527751 − 0.388617I
1.95031 + 5.87839I 4.68305 − 8.83918I
u = −0.938042 − 0.514832I
a = −0.11839 + 1.74298I
b = −0.527751 + 0.388617I
1.95031 − 5.87839I 4.68305 + 8.83918I
u = −0.871027 + 0.217583I
a = 1.13089 − 2.14076I
b = −0.275665 − 0.186662I
−7.65556 + 1.16201I 9.69224 − 3.73584I
u = −0.871027 − 0.217583I
a = 1.13089 + 2.14076I
b = −0.275665 + 0.186662I
−7.65556 − 1.16201I 9.69224 + 3.73584I
u = −0.197332 + 0.860026I
a = −0.493764 − 0.476709I
b = −1.077980 + 0.353331I
2.88989 + 2.19276I 5.78492 − 1.61701I
u = −0.197332 − 0.860026I
a = −0.493764 + 0.476709I
b = −1.077980 − 0.353331I
2.88989 − 2.19276I 5.78492 + 1.61701I
u = 0.867464 + 0.083394I
a = 0.529466 + 0.182358I
b = −1.342910 + 0.189263I
0.61724 − 4.98585I −5.04944 + 5.32957I
u = 0.867464 − 0.083394I
a = 0.529466 − 0.182358I
b = −1.342910 − 0.189263I
0.61724 + 4.98585I −5.04944 − 5.32957I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.014480 + 0.500016I
a = 0.20956 − 1.88598I
b = 0.486016 − 0.467133I
−3.05947 − 10.02590I −0.75769 + 10.58122I
u = 1.014480 − 0.500016I
a = 0.20956 + 1.88598I
b = 0.486016 + 0.467133I
−3.05947 + 10.02590I −0.75769 − 10.58122I
u = 0.112842 + 0.850155I
a = 0.486442 − 0.375861I
b = 1.104810 + 0.459227I
6.59902 + 2.08871I 9.63522 − 2.30278I
u = 0.112842 − 0.850155I
a = 0.486442 + 0.375861I
b = 1.104810 − 0.459227I
6.59902 − 2.08871I 9.63522 + 2.30278I
u = −0.854222
a = −0.533319
b = 1.36822
4.57429 −2.43030
u = −0.040212 + 0.829668I
a = −0.467034 − 0.291029I
b = −1.123270 + 0.557085I
2.48071 − 6.37865I 5.52659 + 5.53285I
u = −0.040212 − 0.829668I
a = −0.467034 + 0.291029I
b = −1.123270 − 0.557085I
2.48071 + 6.37865I 5.52659 − 5.53285I
u = 1.188220 + 0.324567I
a = 0.393074 + 1.111990I
b = −0.985784 + 0.826481I
−4.69685 − 4.30202I −1.33639 + 3.29100I
u = 1.188220 − 0.324567I
a = 0.393074 − 1.111990I
b = −0.985784 − 0.826481I
−4.69685 + 4.30202I −1.33639 − 3.29100I
u = −1.230060 + 0.209006I
a = −0.642023 + 1.250600I
b = 0.802751 + 0.762812I
−10.76160 + 1.15123I −6.36296 − 3.58931I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.230060 − 0.209006I
a = −0.642023 − 1.250600I
b = 0.802751 − 0.762812I
−10.76160 − 1.15123I −6.36296 + 3.58931I
u = 0.631734 + 0.394223I
a = −0.346242 − 1.053410I
b = 0.495352 − 0.068506I
−0.69024 − 1.62727I 2.64679 + 4.87601I
u = 0.631734 − 0.394223I
a = −0.346242 + 1.053410I
b = 0.495352 + 0.068506I
−0.69024 + 1.62727I 2.64679 − 4.87601I
u = −1.252060 + 0.433441I
a = −0.181287 + 1.213950I
b = 1.04062 + 0.98120I
−5.43992 + 8.56805I −2.09898 − 8.35054I
u = −1.252060 − 0.433441I
a = −0.181287 − 1.213950I
b = 1.04062 − 0.98120I
−5.43992 − 8.56805I −2.09898 + 8.35054I
u = −1.30438 + 0.61058I
a = 0.097835 + 1.270040I
b = 1.16668 + 1.13599I
−3.73598 + 9.12102I 0. − 4.65522I
u = −1.30438 − 0.61058I
a = 0.097835 − 1.270040I
b = 1.16668 − 1.13599I
−3.73598 − 9.12102I 0. + 4.65522I
u = 1.38464 + 0.43559I
a = 0.14229 + 1.42555I
b = −0.95760 + 1.11622I
−12.1564 − 10.3966I −6.47193 + 7.01607I
u = 1.38464 − 0.43559I
a = 0.14229 − 1.42555I
b = −0.95760 − 1.11622I
−12.1564 + 10.3966I −6.47193 − 7.01607I
u = −0.221706 + 0.476004I
a = −0.033162 − 0.434804I
b = −0.513564 + 0.368891I
0.879441 − 0.628295I 7.91035 + 3.37637I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.221706 − 0.476004I
a = −0.033162 + 0.434804I
b = −0.513564 − 0.368891I
0.879441 + 0.628295I 7.91035 − 3.37637I
u = 0.038612 + 0.501156I
a = 0.096662 − 0.249135I
b = 0.472964 + 0.818630I
−3.56193 + 2.44936I 0.40204 − 2.98462I
u = 0.038612 − 0.501156I
a = 0.096662 + 0.249135I
b = 0.472964 − 0.818630I
−3.56193 − 2.44936I 0.40204 + 2.98462I
u = 1.36064 + 0.64031I
a = −0.146569 + 1.344680I
b = −1.16515 + 1.19888I
−0.89573 − 13.68010I 0
u = 1.36064 − 0.64031I
a = −0.146569 − 1.344680I
b = −1.16515 − 1.19888I
−0.89573 + 13.68010I 0
u = −1.40294 + 0.64611I
a = 0.160954 + 1.401230I
b = 1.15149 + 1.23900I
−5.6972 + 18.0402I 0
u = −1.40294 − 0.64611I
a = 0.160954 − 1.401230I
b = 1.15149 − 1.23900I
−5.6972 − 18.0402I 0
8
II. I
u
2
= h−1.65 × 10
149
u
59
+ 3.35 × 10
149
u
58
+ · · · + 7.82 × 10
149
b − 4.36 ×
10
151
, −6.46 × 10
151
u
59
+ 1.27 × 10
152
u
58
+ · · · + 2.12 × 10
152
a − 1.82 ×
10
154
, u
60
− u
59
+ · · · − 152u + 271i
(i) Arc colorings
a
2
=
0
u
a
9
=
1
0
a
10
=
1
u
2
a
3
=
−u
−u
3
+ u
a
5
=
0.304679u
59
− 0.597623u
58
+ ··· − 120.013u + 85.7306
0.210919u
59
− 0.428306u
58
+ ··· − 86.8024u + 55.7410
a
11
=
0.212530u
59
− 0.398757u
58
+ ··· − 104.727u + 66.5187
0.0861476u
59
− 0.151846u
58
+ ··· − 50.7134u + 30.3048
a
6
=
−0.147270u
59
+ 0.330434u
58
+ ··· + 62.1929u − 34.5388
0.0408018u
59
− 0.0659039u
58
+ ··· − 29.5324u + 14.4631
a
4
=
0.0937608u
59
− 0.169317u
58
+ ··· − 33.2105u + 29.9895
0.210919u
59
− 0.428306u
58
+ ··· − 86.8024u + 55.7410
a
1
=
−0.147726u
59
+ 0.290344u
58
+ ··· + 55.4703u − 45.1729
−0.0744110u
59
+ 0.136591u
58
+ ··· + 37.9043u − 21.2506
a
8
=
−0.0422375u
59
+ 0.0735826u
58
+ ··· + 19.0597u − 15.5910
−0.0920046u
59
+ 0.187343u
58
+ ··· + 39.5968u − 24.1190
a
7
=
−0.159880u
59
+ 0.312300u
58
+ ··· + 65.4094u − 45.4178
−0.103369u
59
+ 0.209046u
58
+ ··· + 43.5317u − 27.1035
a
12
=
−0.0182647u
59
+ 0.0433689u
58
+ ··· − 2.37838u + 1.23113
−0.0692578u
59
+ 0.143295u
58
+ ··· + 23.4970u − 14.3756
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.227141u
59
− 0.403413u
58
+ ··· − 118.008u + 71.1453
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
3
+ u
2
− 1)
20
c
2
, c
3
, c
7
c
9
u
60
+ u
59
+ ··· + 152u + 271
c
4
, c
8
u
60
+ 3u
59
+ ··· − 36u + 19
c
5
, c
10
(u
10
− 2u
9
− u
8
+ 5u
7
− 3u
6
− 4u
5
+ 12u
4
− 13u
3
+ 5u
2
− u + 2)
6
c
6
, c
11
, c
12
(u
10
− u
9
+ 5u
8
− 5u
7
+ 9u
6
− 9u
5
+ 6u
4
− 6u
3
+ u
2
+ 1)
6
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
3
− y
2
+ 2y −1)
20
c
2
, c
3
, c
7
c
9
y
60
− 45y
59
+ ··· + 1471732y + 73441
c
4
, c
8
y
60
+ 15y
59
+ ··· + 18996y + 361
c
5
, c
10
(y
10
− 6y
9
+ ··· + 19y + 4)
6
c
6
, c
11
, c
12
(y
10
+ 9y
9
+ 33y
8
+ 59y
7
+ 41y
6
− 21y
5
− 44y
4
− 6y
3
+ 13y
2
+ 2y + 1)
6
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.949017 + 0.391733I
a = −0.483459 − 1.011210I
b = 0.583332 − 0.666684I
−1.46262 − 1.59643I 0. − 2.46963I
u = 0.949017 − 0.391733I
a = −0.483459 + 1.011210I
b = 0.583332 + 0.666684I
−1.46262 + 1.59643I 0. + 2.46963I
u = 1.020530 + 0.161032I
a = −0.45536 − 1.74866I
b = −1.17709 − 1.63477I
−1.17160 − 4.14585I −2.03817 + 3.97600I
u = 1.020530 − 0.161032I
a = −0.45536 + 1.74866I
b = −1.17709 + 1.63477I
−1.17160 + 4.14585I −2.03817 − 3.97600I
u = −0.956646 + 0.064272I
a = 0.52931 + 2.36356I
b = −0.33169 + 1.52710I
−4.32428 + 0.65027I −3.68528 + 0.18430I
u = −0.956646 − 0.064272I
a = 0.52931 − 2.36356I
b = −0.33169 − 1.52710I
−4.32428 − 0.65027I −3.68528 − 0.18430I
u = −1.027300 + 0.318565I
a = 0.85428 + 1.15311I
b = 0.280199 + 0.250015I
2.96598 + 1.31773I 0
u = −1.027300 − 0.318565I
a = 0.85428 − 1.15311I
b = 0.280199 − 0.250015I
2.96598 − 1.31773I 0
u = −1.057720 + 0.214913I
a = 0.61197 − 1.80291I
b = 1.29735 − 1.66365I
−5.66711 + 8.28632I −6.84391 − 6.14881I
u = −1.057720 − 0.214913I
a = 0.61197 + 1.80291I
b = 1.29735 + 1.66365I
−5.66711 − 8.28632I −6.84391 + 6.14881I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.591936 + 0.655690I
a = 0.204582 + 0.281777I
b = −1.086930 + 0.109518I
2.96598 − 1.31773I 4.49110 + 0.99655I
u = −0.591936 − 0.655690I
a = 0.204582 − 0.281777I
b = −1.086930 − 0.109518I
2.96598 + 1.31773I 4.49110 − 0.99655I
u = −1.065430 + 0.366634I
a = 0.09675 − 1.46464I
b = −0.854715 − 1.092930I
−1.46262 + 4.05981I 0. − 8.42852I
u = −1.065430 − 0.366634I
a = 0.09675 + 1.46464I
b = −0.854715 + 1.092930I
−1.46262 − 4.05981I 0. + 8.42852I
u = 0.095981 + 0.859804I
a = −0.469554 + 0.223461I
b = 0.498617 − 0.688972I
−1.46262 − 4.05981I 0.41153 + 8.42852I
u = 0.095981 − 0.859804I
a = −0.469554 − 0.223461I
b = 0.498617 + 0.688972I
−1.46262 + 4.05981I 0.41153 − 8.42852I
u = 0.496944 + 0.690303I
a = −0.211127 + 0.592953I
b = 1.102290 + 0.267379I
−1.52952 + 5.45819I −0.31464 − 3.16937I
u = 0.496944 − 0.690303I
a = −0.211127 − 0.592953I
b = 1.102290 − 0.267379I
−1.52952 − 5.45819I −0.31464 + 3.16937I
u = 1.136570 + 0.255121I
a = −0.86601 + 1.15426I
b = −0.271085 + 0.365359I
−1.52952 − 5.45819I 0
u = 1.136570 − 0.255121I
a = −0.86601 − 1.15426I
b = −0.271085 − 0.365359I
−1.52952 + 5.45819I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.129850 + 0.298665I
a = 0.695035 − 1.125510I
b = −0.193732 − 0.701189I
−6.84786 + 0.51807I 0
u = −1.129850 − 0.298665I
a = 0.695035 + 1.125510I
b = −0.193732 + 0.701189I
−6.84786 − 0.51807I 0
u = −0.306666 + 1.169970I
a = 0.137559 − 0.288978I
b = −0.642106 − 0.834586I
−6.84786 + 5.13818I 0
u = −0.306666 − 1.169970I
a = 0.137559 + 0.288978I
b = −0.642106 + 0.834586I
−6.84786 − 5.13818I 0
u = 1.189300 + 0.239410I
a = 0.04818 − 1.88316I
b = 0.87839 − 1.42398I
−6.84786 − 5.13818I 0
u = 1.189300 − 0.239410I
a = 0.04818 + 1.88316I
b = 0.87839 + 1.42398I
−6.84786 + 5.13818I 0
u = −1.253810 + 0.064221I
a = 0.443202 + 0.969300I
b = 1.04370 + 1.00006I
−5.60020 − 1.23169I 0
u = −1.253810 − 0.064221I
a = 0.443202 − 0.969300I
b = 1.04370 − 1.00006I
−5.60020 + 1.23169I 0
u = 0.848510 + 0.976049I
a = −0.407894 − 0.894438I
b = 0.471875 − 1.028600I
−4.32428 + 0.65027I 0
u = 0.848510 − 0.976049I
a = −0.407894 + 0.894438I
b = 0.471875 + 1.028600I
−4.32428 − 0.65027I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.303470 + 0.112078I
a = −0.94280 − 1.13531I
b = −1.51768 − 1.08588I
−10.98540 − 2.31006I 0
u = 1.303470 − 0.112078I
a = −0.94280 + 1.13531I
b = −1.51768 + 1.08588I
−10.98540 + 2.31006I 0
u = −0.655621 + 0.216382I
a = 0.90509 + 2.79934I
b = 0.036354 + 1.376510I
−4.32428 − 6.30651I −3.68528 + 5.77459I
u = −0.655621 − 0.216382I
a = 0.90509 − 2.79934I
b = 0.036354 − 1.376510I
−4.32428 + 6.30651I −3.68528 − 5.77459I
u = 1.091390 + 0.734445I
a = −0.531703 − 1.115870I
b = 0.337789 − 1.018500I
−4.32428 − 6.30651I 0
u = 1.091390 − 0.734445I
a = −0.531703 + 1.115870I
b = 0.337789 + 1.018500I
−4.32428 + 6.30651I 0
u = 0.148294 + 1.315270I
a = −0.313494 + 0.114021I
b = −0.798431 − 0.607771I
2.96598 + 6.97397I 0
u = 0.148294 − 1.315270I
a = −0.313494 − 0.114021I
b = −0.798431 + 0.607771I
2.96598 − 6.97397I 0
u = 1.277550 + 0.477103I
a = 0.50774 − 1.54041I
b = 1.30157 − 1.25383I
2.96598 − 6.97397I 0
u = 1.277550 − 0.477103I
a = 0.50774 + 1.54041I
b = 1.30157 + 1.25383I
2.96598 + 6.97397I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.090952 + 1.384330I
a = 0.333310 + 0.011702I
b = 0.827600 − 0.654612I
−1.52952 − 11.11440I 0
u = −0.090952 − 1.384330I
a = 0.333310 − 0.011702I
b = 0.827600 + 0.654612I
−1.52952 + 11.11440I 0
u = −1.317010 + 0.448694I
a = −0.53512 − 1.64564I
b = −1.30472 − 1.34226I
−1.52952 + 11.11440I 0
u = −1.317010 − 0.448694I
a = −0.53512 + 1.64564I
b = −1.30472 + 1.34226I
−1.52952 − 11.11440I 0
u = 1.39543 + 0.38171I
a = 0.037365 + 0.681468I
b = −0.465941 + 0.819143I
−5.60020 − 1.23169I 0
u = 1.39543 − 0.38171I
a = 0.037365 − 0.681468I
b = −0.465941 − 0.819143I
−5.60020 + 1.23169I 0
u = −1.49038 + 0.04106I
a = 1.352130 − 0.312952I
b = 1.85824 − 0.29901I
−8.46186 − 3.47839I 0
u = −1.49038 − 0.04106I
a = 1.352130 + 0.312952I
b = 1.85824 + 0.29901I
−8.46186 + 3.47839I 0
u = −1.27671 + 0.82477I
a = −0.285197 + 0.803525I
b = 0.131972 + 1.073020I
−1.17160 + 4.14585I 0
u = −1.27671 − 0.82477I
a = −0.285197 − 0.803525I
b = 0.131972 − 1.073020I
−1.17160 − 4.14585I 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.35652 + 0.87787I
a = 0.313842 + 0.787115I
b = −0.078377 + 1.040940I
−5.66711 − 8.28632I 0
u = 1.35652 − 0.87787I
a = 0.313842 − 0.787115I
b = −0.078377 − 1.040940I
−5.66711 + 8.28632I 0
u = −0.004417 + 0.300026I
a = 2.08759 + 3.65698I
b = −0.437568 + 0.769612I
−6.84786 + 0.51807I −5.35393 + 0.54188I
u = −0.004417 − 0.300026I
a = 2.08759 − 3.65698I
b = −0.437568 − 0.769612I
−6.84786 − 0.51807I −5.35393 − 0.54188I
u = −1.63680 + 0.55171I
a = −0.256327 + 0.568035I
b = 0.157812 + 0.707626I
−10.98540 + 2.31006I 0
u = −1.63680 − 0.55171I
a = −0.256327 − 0.568035I
b = 0.157812 − 0.707626I
−10.98540 − 2.31006I 0
u = 0.127336 + 0.235183I
a = 0.82768 + 3.66897I
b = −0.059409 − 0.542206I
−1.46262 + 1.59643I 0.41153 + 2.46963I
u = 0.127336 − 0.235183I
a = 0.82768 − 3.66897I
b = −0.059409 + 0.542206I
−1.46262 − 1.59643I 0.41153 − 2.46963I
u = 1.92440 + 0.15962I
a = 0.301949 + 0.152335I
b = −0.087637 + 0.184649I
−8.46186 + 3.47839I 0
u = 1.92440 − 0.15962I
a = 0.301949 − 0.152335I
b = −0.087637 − 0.184649I
−8.46186 − 3.47839I 0
17
III.
I
u
3
= h−u
20
+ u
19
+ · · · + b − 1, −u
19
+ u
18
+ · · · + a − 1, u
21
− u
20
+ · · · + u − 1i
(i) Arc colorings
a
2
=
0
u
a
9
=
1
0
a
10
=
1
u
2
a
3
=
−u
−u
3
+ u
a
5
=
u
19
− u
18
+ ··· − 3u + 1
u
20
− u
19
+ ··· + 8u + 1
a
11
=
−5u
20
+ 5u
19
+ ··· − 6u + 3
−u
20
+ 11u
18
+ ··· − u − 8
a
6
=
2u
20
− 10u
19
+ ··· + 33u − 10
−6u
20
+ 5u
19
+ ··· − 16u − 7
a
4
=
−u
20
+ 2u
19
+ ··· + 43u
3
− 11u
u
20
− u
19
+ ··· + 8u + 1
a
1
=
u
20
− 6u
19
+ ··· + 17u − 5
−u
20
+ u
19
+ ··· − 8u − 1
a
8
=
−u
19
+ 2u
18
+ ··· + 43u
2
− 10
u
20
− 11u
18
+ ··· + u + 8
a
7
=
−u
19
+ 2u
18
+ ··· + 42u
2
− 10
u
20
− 11u
18
+ ··· + u + 8
a
12
=
−36u
20
+ 17u
19
+ ··· − 41u − 61
13u
20
− 5u
19
+ ··· + 14u + 20
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −40u
20
+34u
19
+381u
18
−319u
17
−1499u
16
+1270u
15
+3294u
14
−2889u
13
−4717u
12
+
4263u
11
+4746u
10
−4354u
9
−3290u
8
+3085u
7
+1604u
6
−1431u
5
−500u
4
+414u
3
+95u
2
−57u
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
21
− 9u
20
+ ··· + 6u
2
− 1
c
2
, c
7
u
21
+ u
20
+ ··· + u + 1
c
3
, c
9
u
21
− u
20
+ ··· + u − 1
c
4
, c
8
u
21
+ u
19
+ ··· + 2u
2
+ 1
c
5
u
21
− 6u
19
+ ··· + 2u − 1
c
6
u
21
+ 10u
19
+ ··· + 3u
2
− 1
c
10
u
21
− 6u
19
+ ··· + 2u + 1
c
11
, c
12
u
21
+ 10u
19
+ ··· − 3u
2
+ 1
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
21
− 5y
20
+ ··· + 12y −1
c
2
, c
3
, c
7
c
9
y
21
− 21y
20
+ ··· + 19y −1
c
4
, c
8
y
21
+ 2y
20
+ ··· − 4y −1
c
5
, c
10
y
21
− 12y
20
+ ··· + 2y −1
c
6
, c
11
, c
12
y
21
+ 20y
20
+ ··· + 6y −1
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.856036 + 0.576602I
a = 0.81416 − 1.46919I
b = 0.052448 − 1.117880I
0.54548 + 4.58464I 3.48780 − 6.53727I
u = −0.856036 − 0.576602I
a = 0.81416 + 1.46919I
b = 0.052448 + 1.117880I
0.54548 − 4.58464I 3.48780 + 6.53727I
u = 0.751882 + 0.581250I
a = −0.80538 − 1.39418I
b = 0.080602 − 1.224810I
−2.76943 − 0.75968I 0.74636 + 3.01079I
u = 0.751882 − 0.581250I
a = −0.80538 + 1.39418I
b = 0.080602 + 1.224810I
−2.76943 + 0.75968I 0.74636 − 3.01079I
u = −0.891534 + 0.236502I
a = 1.43236 − 2.01578I
b = −0.156384 − 0.514490I
−7.97861 + 1.20750I −15.3765 − 6.3394I
u = −0.891534 − 0.236502I
a = 1.43236 + 2.01578I
b = −0.156384 + 0.514490I
−7.97861 − 1.20750I −15.3765 + 6.3394I
u = 0.939172 + 0.585801I
a = −0.79058 − 1.50161I
b = −0.172630 − 1.063930I
−3.98074 − 8.53235I −1.71885 + 7.62072I
u = 0.939172 − 0.585801I
a = −0.79058 + 1.50161I
b = −0.172630 + 1.063930I
−3.98074 + 8.53235I −1.71885 − 7.62072I
u = 0.749002 + 0.339937I
a = −1.17638 − 1.34538I
b = 0.358070 − 0.842385I
−2.05316 − 2.41016I −6.17082 + 3.86618I
u = 0.749002 − 0.339937I
a = −1.17638 + 1.34538I
b = 0.358070 + 0.842385I
−2.05316 + 2.41016I −6.17082 − 3.86618I
21
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.602435 + 0.391145I
a = 0.94702 − 1.09177I
b = −0.565251 − 1.149290I
−4.68125 + 3.54794I −4.14026 − 4.31569I
u = −0.602435 − 0.391145I
a = 0.94702 + 1.09177I
b = −0.565251 + 1.149290I
−4.68125 − 3.54794I −4.14026 + 4.31569I
u = 0.570751 + 0.057815I
a = −1.39693 − 0.22361I
b = 1.163530 − 0.233492I
1.24666 − 4.78275I 6.90631 + 2.29841I
u = 0.570751 − 0.057815I
a = −1.39693 + 0.22361I
b = 1.163530 + 0.233492I
1.24666 + 4.78275I 6.90631 − 2.29841I
u = −0.570103
a = 1.41472
b = −1.18397
5.19724 11.3100
u = −1.45983 + 0.15027I
a = 0.274885 − 0.483709I
b = 0.782001 − 0.220049I
−9.98663 + 1.50889I −5.72964 + 1.39769I
u = −1.45983 − 0.15027I
a = 0.274885 + 0.483709I
b = 0.782001 + 0.220049I
−9.98663 − 1.50889I −5.72964 − 1.39769I
u = 1.46834
a = −0.198185
b = −0.787304
−5.75131 −8.43610
u = −1.68158
a = 0.761529
b = 1.08690
−3.69725 8.76420
u = 1.69070 + 0.06877I
a = −0.788190 − 0.144884I
b = −1.100200 − 0.092788I
−7.69508 + 3.60581I 2.67681 − 4.75349I
22
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.69070 − 0.06877I
a = −0.788190 + 0.144884I
b = −1.100200 + 0.092788I
−7.69508 − 3.60581I 2.67681 + 4.75349I
23
IV. I
u
4
=
h9.32×10
8
u
17
+8.93×10
8
u
16
+· · · +7.15×10
8
b+1.49×10
10
, 1.86×10
10
u
17
+
1.56 × 10
10
u
16
+ · · · + 7.86 × 10
9
a + 3.01 × 10
11
, u
18
− 6u
16
+ · · · + 26u − 11i
(i) Arc colorings
a
2
=
0
u
a
9
=
1
0
a
10
=
1
u
2
a
3
=
−u
−u
3
+ u
a
5
=
−2.36280u
17
− 1.98221u
16
+ ··· + 42.9118u − 38.2840
−1.30468u
17
− 1.25019u
16
+ ··· + 25.5466u − 20.8043
a
11
=
2.36280u
17
+ 1.98221u
16
+ ··· − 42.9118u + 39.2840
1.30468u
17
+ 1.25019u
16
+ ··· − 25.5466u + 20.8043
a
6
=
1
u
2
a
4
=
−1.05812u
17
− 0.732017u
16
+ ··· + 17.3652u − 17.4797
−1.30468u
17
− 1.25019u
16
+ ··· + 25.5466u − 20.8043
a
1
=
1.81634u
17
+ 1.25032u
16
+ ··· − 28.5715u + 26.6515
1.00788u
17
+ 0.743283u
16
+ ··· − 9.73596u + 10.2904
a
8
=
−1.14912u
17
− 0.777687u
16
+ ··· + 14.0881u − 13.7093
−1.18839u
17
− 0.728436u
16
+ ··· + 18.1216u − 17.8950
a
7
=
−2.04103u
17
− 1.28781u
16
+ ··· + 25.9391u − 26.4832
−0.673919u
17
− 0.325398u
16
+ ··· + 9.72281u − 10.7326
a
12
=
1.64365u
17
+ 1.02927u
16
+ ··· − 31.3642u + 30.1147
0.504440u
17
+ 0.425894u
16
+ ··· − 5.88815u + 7.85877
(ii) Obstruction class = −1
(iii) Cusp Shapes =
2092315776
714572543
u
17
+
1290870304
714572543
u
16
+ ··· −
28672326560
714572543
u +
31839285294
714572543
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
3
+ u
2
− 1)
6
c
2
, c
3
, c
7
c
9
u
18
− 6u
16
+ ··· − 26u − 11
c
4
, c
8
u
18
+ 2u
16
+ ··· − 2u − 1
c
5
, c
10
(u + 1)
18
c
6
, c
11
, c
12
(u
3
+ u + 1)
6
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
3
− y
2
+ 2y −1)
6
c
2
, c
3
, c
7
c
9
y
18
− 12y
17
+ ··· − 940y + 121
c
4
, c
8
y
18
+ 4y
17
+ ··· − 52y + 1
c
5
, c
10
(y −1)
18
c
6
, c
11
, c
12
(y
3
+ 2y
2
+ y −1)
6
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.975781 + 0.068356I
a = 0.23815 − 1.63160I
b = 1.00799 − 1.57767I
−4.40332 −5.01951 + 0.I
u = −0.975781 − 0.068356I
a = 0.23815 + 1.63160I
b = 1.00799 + 1.57767I
−4.40332 −5.01951 + 0.I
u = 0.866397 + 0.427657I
a = −0.79133 + 1.17259I
b = −0.318215 + 0.079336I
−0.26574 + 2.82812I 1.50976 − 2.97945I
u = 0.866397 − 0.427657I
a = −0.79133 − 1.17259I
b = −0.318215 − 0.079336I
−0.26574 − 2.82812I 1.50976 + 2.97945I
u = 0.725279 + 0.623782I
a = −0.116607 − 0.113262I
b = 1.086520 − 0.121018I
−0.26574 − 2.82812I 1.50976 + 2.97945I
u = 0.725279 − 0.623782I
a = −0.116607 + 0.113262I
b = 1.086520 + 0.121018I
−0.26574 + 2.82812I 1.50976 − 2.97945I
u = 0.788257 + 0.081685I
a = −0.82880 + 2.44549I
b = 0.175633 + 1.396450I
−0.26574 + 2.82812I 1.50976 − 2.97945I
u = 0.788257 − 0.081685I
a = −0.82880 − 2.44549I
b = 0.175633 − 1.396450I
−0.26574 − 2.82812I 1.50976 + 2.97945I
u = −0.227039 + 1.207920I
a = 0.284944 + 0.273008I
b = 0.748674 − 0.540556I
−0.26574 − 2.82812I 1.50976 + 2.97945I
u = −0.227039 − 1.207920I
a = 0.284944 − 0.273008I
b = 0.748674 + 0.540556I
−0.26574 + 2.82812I 1.50976 − 2.97945I
27
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.935012 + 0.810213I
a = 0.524225 − 1.003350I
b = −0.406015 − 1.012790I
−0.26574 + 2.82812I 1.50976 − 2.97945I
u = −0.935012 − 0.810213I
a = 0.524225 + 1.003350I
b = −0.406015 + 1.012790I
−0.26574 − 2.82812I 1.50976 + 2.97945I
u = −1.217880 + 0.512150I
a = −0.45585 − 1.38682I
b = −1.28659 − 1.12457I
−0.26574 + 2.82812I 1.50976 − 2.97945I
u = −1.217880 − 0.512150I
a = −0.45585 + 1.38682I
b = −1.28659 + 1.12457I
−0.26574 − 2.82812I 1.50976 + 2.97945I
u = 1.170190 + 0.730249I
a = 0.249409 + 0.832856I
b = −0.214875 + 1.122590I
−4.40332 −5.01951 + 0.I
u = 1.170190 − 0.730249I
a = 0.249409 − 0.832856I
b = −0.214875 − 1.122590I
−4.40332 −5.01951 + 0.I
u = 1.48728
a = −1.24385
b = −1.75141
−4.40332 −5.01950
u = −1.87610
a = −0.237180
b = 0.165185
−4.40332 −5.01950
28
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
3
+ u
2
− 1)
26
)(u
21
− 9u
20
+ ··· + 6u
2
− 1)
· (u
37
− 30u
36
+ ··· + 159744u − 8192)
c
2
, c
7
(u
18
− 6u
16
+ ··· − 26u − 11)(u
21
+ u
20
+ ··· + u + 1)
· (u
37
− u
36
+ ··· − 2u
2
− 1)(u
60
+ u
59
+ ··· + 152u + 271)
c
3
, c
9
(u
18
− 6u
16
+ ··· − 26u − 11)(u
21
− u
20
+ ··· + u − 1)
· (u
37
− u
36
+ ··· − 2u
2
− 1)(u
60
+ u
59
+ ··· + 152u + 271)
c
4
, c
8
(u
18
+ 2u
16
+ ··· − 2u − 1)(u
21
+ u
19
+ ··· + 2u
2
+ 1)
· (u
37
− 6u
35
+ ··· − u + 1)(u
60
+ 3u
59
+ ··· − 36u + 19)
c
5
(u + 1)
18
· (u
10
− 2u
9
− u
8
+ 5u
7
− 3u
6
− 4u
5
+ 12u
4
− 13u
3
+ 5u
2
− u + 2)
6
· (u
21
− 6u
19
+ ··· + 2u − 1)(u
37
− 7u
36
+ ··· − 3368u + 464)
c
6
(u
3
+ u + 1)
6
(u
10
− u
9
+ 5u
8
− 5u
7
+ 9u
6
− 9u
5
+ 6u
4
− 6u
3
+ u
2
+ 1)
6
· (u
21
+ 10u
19
+ ··· + 3u
2
− 1)(u
37
+ 7u
36
+ ··· + 24u + 8)
c
10
(u + 1)
18
· (u
10
− 2u
9
− u
8
+ 5u
7
− 3u
6
− 4u
5
+ 12u
4
− 13u
3
+ 5u
2
− u + 2)
6
· (u
21
− 6u
19
+ ··· + 2u + 1)(u
37
− 7u
36
+ ··· − 3368u + 464)
c
11
, c
12
(u
3
+ u + 1)
6
(u
10
− u
9
+ 5u
8
− 5u
7
+ 9u
6
− 9u
5
+ 6u
4
− 6u
3
+ u
2
+ 1)
6
· (u
21
+ 10u
19
+ ··· − 3u
2
+ 1)(u
37
+ 7u
36
+ ··· + 24u + 8)
29
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
3
− y
2
+ 2y −1)
26
)(y
21
− 5y
20
+ ··· + 12y −1)
· (y
37
− 6y
36
+ ··· − 16777216y −67108864)
c
2
, c
3
, c
7
c
9
(y
18
− 12y
17
+ ··· − 940y + 121)(y
21
− 21y
20
+ ··· + 19y −1)
· (y
37
− 23y
36
+ ··· − 4y −1)(y
60
− 45y
59
+ ··· + 1471732y + 73441)
c
4
, c
8
(y
18
+ 4y
17
+ ··· − 52y + 1)(y
21
+ 2y
20
+ ··· − 4y −1)
· (y
37
− 12y
36
+ ··· + 25y −1)(y
60
+ 15y
59
+ ··· + 18996y + 361)
c
5
, c
10
((y −1)
18
)(y
10
− 6y
9
+ ··· + 19y + 4)
6
(y
21
− 12y
20
+ ··· + 2y −1)
· (y
37
− 21y
36
+ ··· − 1481536y −215296)
c
6
, c
11
, c
12
(y
3
+ 2y
2
+ y −1)
6
· (y
10
+ 9y
9
+ 33y
8
+ 59y
7
+ 41y
6
− 21y
5
− 44y
4
− 6y
3
+ 13y
2
+ 2y + 1)
6
· (y
21
+ 20y
20
+ ··· + 6y −1)(y
37
+ 31y
36
+ ··· + 96y −64)
30
