12a
0685
(K12a
0685
)
A knot diagram
1
Linearized knot diagam
3 7 11 1 9 2 6 12 5 4 8 10
Solving Sequence
5,9
6
10,12
1 4 8 7 11 3 2
c
5
c
9
c
12
c
4
c
8
c
7
c
11
c
3
c
2
c
1
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.88356 × 10
553
u
121
+ 1.21209 × 10
554
u
120
+ ··· + 8.71696 × 10
553
b − 3.64779 × 10
555
,
4.27797 × 10
555
u
121
− 1.73052 × 10
556
u
120
+ ··· + 2.72841 × 10
556
a + 1.06739 × 10
558
,
u
122
− 5u
121
+ ··· − 2671u + 313i
I
u
2
= h5u
19
− 5u
18
+ ··· + b − 13u, −4u
19
+ 4u
18
+ ··· + a + 13u, u
20
− u
19
+ ··· − 4u
2
− 1i
I
u
3
= hb + 1, a − u − 1, u
2
+ u + 1i
* 3 irreducible components of dim
C
= 0, with total 144 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−2.88 × 10
553
u
121
+ 1.21 × 10
554
u
120
+ · · · + 8.72 × 10
553
b − 3.65 ×
10
555
, 4.28 × 10
555
u
121
− 1.73 × 10
556
u
120
+ · · · + 2.73 × 10
556
a + 1.07 ×
10
558
, u
122
− 5u
121
+ · · · − 2671u + 313i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
6
=
1
u
2
a
10
=
−u
u
a
12
=
−0.156793u
121
+ 0.634260u
120
+ ··· + 256.687u − 39.1212
0.330799u
121
− 1.39049u
120
+ ··· − 256.314u + 41.8470
a
1
=
−0.0146363u
121
+ 0.105168u
120
+ ··· + 7.19887u − 3.50278
0.188642u
121
− 0.861399u
120
+ ··· − 6.82568u + 6.22859
a
4
=
0.560056u
121
− 2.92442u
120
+ ··· + 643.200u − 60.0524
−0.342976u
121
+ 1.55630u
120
+ ··· + 93.8076u − 22.7278
a
8
=
0.101891u
121
− 0.649364u
120
+ ··· + 517.201u − 55.0592
−0.436544u
121
+ 2.01244u
120
+ ··· − 9.53506u − 14.2558
a
7
=
−0.229119u
121
+ 0.737054u
120
+ ··· + 913.255u − 113.107
−0.130498u
121
+ 0.841269u
120
+ ··· − 623.444u + 69.8259
a
11
=
0.423648u
121
− 1.77534u
120
+ ··· − 508.989u + 67.2783
−0.822229u
121
+ 3.70501u
120
+ ··· + 315.069u − 65.2216
a
3
=
−0.149715u
121
+ 0.0244993u
120
+ ··· + 1701.15u − 213.253
0.0916345u
121
+ 0.419588u
120
+ ··· − 2068.61u + 254.915
a
2
=
−0.0978973u
121
+ 0.243033u
120
+ ··· + 277.019u − 36.7654
−0.183988u
121
+ 1.22389u
120
+ ··· − 801.640u + 90.3639
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.345389u
121
− 0.408893u
120
+ ··· − 2814.41u + 346.625
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
122
+ 41u
121
+ ··· + 33207u + 121
c
2
, c
6
u
122
− u
121
+ ··· + 223u + 11
c
3
, c
10
u
122
− 2u
121
+ ··· + 169938u + 8767
c
4
u
122
− 6u
121
+ ··· + 12u − 8
c
5
, c
9
u
122
− 5u
121
+ ··· − 2671u + 313
c
8
, c
11
u
122
+ u
121
+ ··· + 4149u + 108
c
12
u
122
− 2u
121
+ ··· + 29u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
122
+ 91y
121
+ ··· − 1012244039y + 14641
c
2
, c
6
y
122
− 41y
121
+ ··· − 33207y + 121
c
3
, c
10
y
122
+ 70y
121
+ ··· + 180016550y + 76860289
c
4
y
122
+ 20y
121
+ ··· + 720y + 64
c
5
, c
9
y
122
+ 73y
121
+ ··· + 3716843y + 97969
c
8
, c
11
y
122
− 73y
121
+ ··· − 13689081y + 11664
c
12
y
122
− 12y
121
+ ··· − 81y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.507146 + 0.855992I
a = 1.39763 + 0.38908I
b = −1.58922 − 0.73202I
0.15714 + 3.46101I 0
u = −0.507146 − 0.855992I
a = 1.39763 − 0.38908I
b = −1.58922 + 0.73202I
0.15714 − 3.46101I 0
u = 0.242227 + 0.979225I
a = 0.651388 − 0.786992I
b = −1.76441 + 0.84561I
−1.76184 − 1.89377I 0
u = 0.242227 − 0.979225I
a = 0.651388 + 0.786992I
b = −1.76441 − 0.84561I
−1.76184 + 1.89377I 0
u = 0.369913 + 0.912696I
a = −1.21901 + 0.99429I
b = 1.33892 − 1.30519I
−5.98273 − 3.58080I 0
u = 0.369913 − 0.912696I
a = −1.21901 − 0.99429I
b = 1.33892 + 1.30519I
−5.98273 + 3.58080I 0
u = −0.721993 + 0.658333I
a = −0.524412 − 1.175230I
b = −0.362442 + 0.593749I
−0.417036 + 1.284330I 0
u = −0.721993 − 0.658333I
a = −0.524412 + 1.175230I
b = −0.362442 − 0.593749I
−0.417036 − 1.284330I 0
u = 0.648403 + 0.720029I
a = 0.41433 − 1.40827I
b = 0.393075 + 0.699599I
−1.05367 + 4.67798I 0
u = 0.648403 − 0.720029I
a = 0.41433 + 1.40827I
b = 0.393075 − 0.699599I
−1.05367 − 4.67798I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.227753 + 1.007340I
a = 0.479723 + 0.520123I
b = −1.72903 + 0.21460I
1.31833 − 3.84074I 0
u = 0.227753 − 1.007340I
a = 0.479723 − 0.520123I
b = −1.72903 − 0.21460I
1.31833 + 3.84074I 0
u = −0.523794 + 0.893580I
a = 0.413860 + 0.269007I
b = −0.395349 + 0.457081I
−1.71998 + 0.88588I 0
u = −0.523794 − 0.893580I
a = 0.413860 − 0.269007I
b = −0.395349 − 0.457081I
−1.71998 − 0.88588I 0
u = 0.036474 + 0.957207I
a = 0.01900 − 2.30092I
b = 0.028206 + 1.126470I
−3.98184 − 2.64884I 0
u = 0.036474 − 0.957207I
a = 0.01900 + 2.30092I
b = 0.028206 − 1.126470I
−3.98184 + 2.64884I 0
u = 0.144312 + 1.033520I
a = −0.43604 + 1.42034I
b = 0.47698 − 1.68915I
−3.56343 + 2.07493I 0
u = 0.144312 − 1.033520I
a = −0.43604 − 1.42034I
b = 0.47698 + 1.68915I
−3.56343 − 2.07493I 0
u = 0.618887 + 0.841397I
a = 0.233538 − 0.401885I
b = −1.47477 + 0.40985I
0.75469 − 3.02592I 0
u = 0.618887 − 0.841397I
a = 0.233538 + 0.401885I
b = −1.47477 − 0.40985I
0.75469 + 3.02592I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.477079 + 0.822515I
a = −1.59165 + 0.48054I
b = 1.76249 − 0.84223I
−0.77649 − 9.14865I 0
u = 0.477079 − 0.822515I
a = −1.59165 − 0.48054I
b = 1.76249 + 0.84223I
−0.77649 + 9.14865I 0
u = 1.054680 + 0.094255I
a = 1.218420 − 0.371226I
b = −0.244011 − 0.244100I
−9.21798 + 6.22997I 0
u = 1.054680 − 0.094255I
a = 1.218420 + 0.371226I
b = −0.244011 + 0.244100I
−9.21798 − 6.22997I 0
u = 0.138610 + 1.058360I
a = −0.532185 + 1.199180I
b = 1.139570 + 0.187880I
3.72323 − 4.84674I 0
u = 0.138610 − 1.058360I
a = −0.532185 − 1.199180I
b = 1.139570 − 0.187880I
3.72323 + 4.84674I 0
u = −0.359693 + 1.007070I
a = 0.432069 − 0.378673I
b = −1.106490 + 0.143329I
1.61424 + 3.30812I 0
u = −0.359693 − 1.007070I
a = 0.432069 + 0.378673I
b = −1.106490 − 0.143329I
1.61424 − 3.30812I 0
u = −0.917118 + 0.113358I
a = −1.316600 − 0.058252I
b = 0.079637 + 0.366292I
−5.18540 + 3.19989I 0
u = −0.917118 − 0.113358I
a = −1.316600 + 0.058252I
b = 0.079637 − 0.366292I
−5.18540 − 3.19989I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.071921 + 1.074860I
a = 0.536466 + 1.102590I
b = −1.298910 + 0.214239I
4.53635 − 1.19512I 0
u = −0.071921 − 1.074860I
a = 0.536466 − 1.102590I
b = −1.298910 − 0.214239I
4.53635 + 1.19512I 0
u = 0.065495 + 1.084360I
a = −0.548966 − 0.588478I
b = 1.45908 + 0.28829I
3.18981 + 0.55992I 0
u = 0.065495 − 1.084360I
a = −0.548966 + 0.588478I
b = 1.45908 − 0.28829I
3.18981 − 0.55992I 0
u = −0.017047 + 0.888778I
a = −0.134366 + 0.929996I
b = 1.99375 + 0.51223I
−3.06363 + 1.21973I 0
u = −0.017047 − 0.888778I
a = −0.134366 − 0.929996I
b = 1.99375 − 0.51223I
−3.06363 − 1.21973I 0
u = 0.154471 + 1.105440I
a = 0.487434 − 0.720037I
b = −2.23947 + 1.00600I
−1.92977 − 1.78813I 0
u = 0.154471 − 1.105440I
a = 0.487434 + 0.720037I
b = −2.23947 − 1.00600I
−1.92977 + 1.78813I 0
u = 0.501989 + 1.014050I
a = 1.062520 − 0.427536I
b = −2.01893 + 0.65151I
0.94916 − 7.19297I 0
u = 0.501989 − 1.014050I
a = 1.062520 + 0.427536I
b = −2.01893 − 0.65151I
0.94916 + 7.19297I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.228489 + 1.128820I
a = 0.706469 − 0.874340I
b = −2.01056 − 0.09616I
2.72426 − 9.72933I 0
u = 0.228489 − 1.128820I
a = 0.706469 + 0.874340I
b = −2.01056 + 0.09616I
2.72426 + 9.72933I 0
u = −0.177121 + 1.149440I
a = −0.686607 − 0.798525I
b = 1.93922 + 0.07899I
4.31675 + 3.76010I 0
u = −0.177121 − 1.149440I
a = −0.686607 + 0.798525I
b = 1.93922 − 0.07899I
4.31675 − 3.76010I 0
u = −0.517454 + 1.053270I
a = −1.097670 − 0.227427I
b = 2.04032 + 0.50754I
1.10043 + 2.28207I 0
u = −0.517454 − 1.053270I
a = −1.097670 + 0.227427I
b = 2.04032 − 0.50754I
1.10043 − 2.28207I 0
u = 0.630953 + 0.484428I
a = −0.50591 + 1.37090I
b = 0.0151728 − 0.1063120I
−0.57666 + 2.76411I 0
u = 0.630953 − 0.484428I
a = −0.50591 − 1.37090I
b = 0.0151728 + 0.1063120I
−0.57666 − 2.76411I 0
u = −0.558023 + 0.560799I
a = 0.258704 − 0.470798I
b = 1.296390 + 0.185115I
0.13015 + 7.94791I 0
u = −0.558023 − 0.560799I
a = 0.258704 + 0.470798I
b = 1.296390 − 0.185115I
0.13015 − 7.94791I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.461375 + 1.117550I
a = 0.667723 + 0.692906I
b = −0.806009 − 0.913075I
−2.12629 + 1.69618I 0
u = −0.461375 − 1.117550I
a = 0.667723 − 0.692906I
b = −0.806009 + 0.913075I
−2.12629 − 1.69618I 0
u = −0.418495 + 1.134790I
a = −0.962800 + 0.236257I
b = 1.92529 + 0.23170I
−1.08991 + 6.40452I 0
u = −0.418495 − 1.134790I
a = −0.962800 − 0.236257I
b = 1.92529 − 0.23170I
−1.08991 − 6.40452I 0
u = −0.686573 + 0.377263I
a = 0.41902 + 1.35088I
b = 0.146460 − 0.125587I
−0.83065 + 2.29413I 0
u = −0.686573 − 0.377263I
a = 0.41902 − 1.35088I
b = 0.146460 + 0.125587I
−0.83065 − 2.29413I 0
u = −0.767024
a = 1.11830
b = −0.231853
−1.42025 0
u = 0.202430 + 0.728860I
a = 0.33510 − 2.39306I
b = 0.116223 + 0.950572I
−6.96114 + 0.72996I 0
u = 0.202430 − 0.728860I
a = 0.33510 + 2.39306I
b = 0.116223 − 0.950572I
−6.96114 − 0.72996I 0
u = −1.258190 + 0.026736I
a = −0.904118 + 0.330926I
b = 0.131425 + 0.086046I
−1.97565 + 6.21374I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.258190 − 0.026736I
a = −0.904118 − 0.330926I
b = 0.131425 − 0.086046I
−1.97565 − 6.21374I 0
u = 0.305764 + 1.244400I
a = 0.993398 + 0.584367I
b = −1.85645 + 0.04560I
5.33674 − 5.20139I 0
u = 0.305764 − 1.244400I
a = 0.993398 − 0.584367I
b = −1.85645 − 0.04560I
5.33674 + 5.20139I 0
u = 1.287590 + 0.035022I
a = 0.912763 − 0.412908I
b = −0.178807 − 0.058045I
−2.99067 + 12.22930I 0
u = 1.287590 − 0.035022I
a = 0.912763 + 0.412908I
b = −0.178807 + 0.058045I
−2.99067 − 12.22930I 0
u = −0.342892 + 1.258960I
a = −1.058540 + 0.547415I
b = 1.90413 + 0.04316I
4.64137 + 11.06510I 0
u = −0.342892 − 1.258960I
a = −1.058540 − 0.547415I
b = 1.90413 − 0.04316I
4.64137 − 11.06510I 0
u = 0.288069 + 0.630674I
a = −0.53746 + 1.64812I
b = 0.254099 + 0.152010I
−2.92024 − 0.76437I 0
u = 0.288069 − 0.630674I
a = −0.53746 − 1.64812I
b = 0.254099 − 0.152010I
−2.92024 + 0.76437I 0
u = −0.413630 + 1.245240I
a = −0.666885 − 0.534985I
b = 1.63416 + 0.81728I
2.24606 + 4.27656I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.413630 − 1.245240I
a = −0.666885 + 0.534985I
b = 1.63416 − 0.81728I
2.24606 − 4.27656I 0
u = 0.359238 + 1.296200I
a = −0.415506 + 0.695099I
b = 1.58193 − 1.69623I
−4.17814 − 3.10881I 0
u = 0.359238 − 1.296200I
a = −0.415506 − 0.695099I
b = 1.58193 + 1.69623I
−4.17814 + 3.10881I 0
u = 0.630864 + 0.069124I
a = 2.18441 − 0.27617I
b = −0.221149 − 0.599419I
−8.04418 − 0.71542I −17.0967 + 1.7392I
u = 0.630864 − 0.069124I
a = 2.18441 + 0.27617I
b = −0.221149 + 0.599419I
−8.04418 + 0.71542I −17.0967 − 1.7392I
u = 0.628713 + 1.212980I
a = 0.628761 − 0.556862I
b = −1.56682 + 0.70226I
−0.58676 − 7.14016I 0
u = 0.628713 − 1.212980I
a = 0.628761 + 0.556862I
b = −1.56682 − 0.70226I
−0.58676 + 7.14016I 0
u = 0.244179 + 1.377560I
a = −0.719476 − 0.333457I
b = 1.43445 − 0.11358I
9.18175 + 0.11415I 0
u = 0.244179 − 1.377560I
a = −0.719476 + 0.333457I
b = 1.43445 + 0.11358I
9.18175 − 0.11415I 0
u = −0.074484 + 1.403190I
a = −0.574464 − 0.350721I
b = 1.29544 + 0.97751I
5.81324 + 1.62511I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.074484 − 1.403190I
a = −0.574464 + 0.350721I
b = 1.29544 − 0.97751I
5.81324 − 1.62511I 0
u = 0.073608 + 0.584728I
a = −0.156648 − 1.117150I
b = −0.88013 + 1.20164I
2.29915 + 3.56926I −1.92611 − 0.98363I
u = 0.073608 − 0.584728I
a = −0.156648 + 1.117150I
b = −0.88013 − 1.20164I
2.29915 − 3.56926I −1.92611 + 0.98363I
u = −0.025684 + 1.413150I
a = 0.555704 − 0.268203I
b = −1.15630 + 0.93671I
5.06356 + 4.48557I 0
u = −0.025684 − 1.413150I
a = 0.555704 + 0.268203I
b = −1.15630 − 0.93671I
5.06356 − 4.48557I 0
u = −0.30282 + 1.38844I
a = 0.697396 − 0.277292I
b = −1.390550 − 0.164891I
8.98982 + 6.01349I 0
u = −0.30282 − 1.38844I
a = 0.697396 + 0.277292I
b = −1.390550 + 0.164891I
8.98982 − 6.01349I 0
u = −0.575887 + 0.053854I
a = 0.43797 + 1.36280I
b = 0.586028 + 0.053066I
−4.09960 − 2.58603I −15.3423 + 3.8817I
u = −0.575887 − 0.053854I
a = 0.43797 − 1.36280I
b = 0.586028 − 0.053066I
−4.09960 + 2.58603I −15.3423 − 3.8817I
u = 0.54142 + 1.31566I
a = −0.685592 + 0.695747I
b = 1.78060 − 1.26482I
−5.38333 − 11.88530I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.54142 − 1.31566I
a = −0.685592 − 0.695747I
b = 1.78060 + 1.26482I
−5.38333 + 11.88530I 0
u = −0.45512 + 1.36440I
a = 0.560970 + 0.598672I
b = −1.56394 − 1.34093I
−0.59437 + 8.14708I 0
u = −0.45512 − 1.36440I
a = 0.560970 − 0.598672I
b = −1.56394 + 1.34093I
−0.59437 − 8.14708I 0
u = −0.521685
a = 0.0566446
b = −0.400783
−1.05875 −8.98480
u = −0.59026 + 1.39756I
a = 0.797067 + 0.590410I
b = −1.75850 − 1.08987I
2.45491 + 12.60890I 0
u = −0.59026 − 1.39756I
a = 0.797067 − 0.590410I
b = −1.75850 + 1.08987I
2.45491 − 12.60890I 0
u = 0.61662 + 1.38795I
a = −0.831695 + 0.620331I
b = 1.80616 − 1.08473I
1.2324 − 18.7981I 0
u = 0.61662 − 1.38795I
a = −0.831695 − 0.620331I
b = 1.80616 + 1.08473I
1.2324 + 18.7981I 0
u = −0.018266 + 0.473866I
a = 0.670205 − 0.917153I
b = 0.475830 + 1.181720I
2.86428 + 1.80692I −0.18499 − 4.21230I
u = −0.018266 − 0.473866I
a = 0.670205 + 0.917153I
b = 0.475830 − 1.181720I
2.86428 − 1.80692I −0.18499 + 4.21230I
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.60919 + 1.42322I
a = −0.712375 − 0.571819I
b = 1.53522 + 0.76204I
6.20510 + 6.08526I 0
u = −0.60919 − 1.42322I
a = −0.712375 + 0.571819I
b = 1.53522 − 0.76204I
6.20510 − 6.08526I 0
u = 0.66085 + 1.41665I
a = 0.710039 − 0.593401I
b = −1.53047 + 0.75564I
5.46010 − 12.01240I 0
u = 0.66085 − 1.41665I
a = 0.710039 + 0.593401I
b = −1.53047 − 0.75564I
5.46010 + 12.01240I 0
u = −0.06933 + 1.56209I
a = 0.059047 + 0.435793I
b = −0.20208 − 1.61254I
7.59602 + 3.60881I 0
u = −0.06933 − 1.56209I
a = 0.059047 − 0.435793I
b = −0.20208 + 1.61254I
7.59602 − 3.60881I 0
u = 0.308470 + 0.299676I
a = 0.256000 + 1.188170I
b = −0.226868 + 0.493468I
−0.49377 + 1.38538I −4.82093 − 5.16315I
u = 0.308470 − 0.299676I
a = 0.256000 − 1.188170I
b = −0.226868 − 0.493468I
−0.49377 − 1.38538I −4.82093 + 5.16315I
u = −0.087457 + 0.356516I
a = 1.70937 + 0.74743I
b = 1.45278 − 0.50533I
0.18833 + 8.05722I −8.94518 − 5.79512I
u = −0.087457 − 0.356516I
a = 1.70937 − 0.74743I
b = 1.45278 + 0.50533I
0.18833 − 8.05722I −8.94518 + 5.79512I
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.24933 + 1.18864I
a = 0.582356 + 0.281378I
b = −0.617452 + 0.046696I
0.86161 − 1.79317I 0
u = −1.24933 − 1.18864I
a = 0.582356 − 0.281378I
b = −0.617452 − 0.046696I
0.86161 + 1.79317I 0
u = −1.33504 + 1.09767I
a = 0.256971 + 0.354347I
b = −0.482895 − 0.312137I
2.04741 + 1.84177I 0
u = −1.33504 − 1.09767I
a = 0.256971 − 0.354347I
b = −0.482895 + 0.312137I
2.04741 − 1.84177I 0
u = 0.146999 + 0.118246I
a = −3.40056 − 1.80387I
b = −1.041310 − 0.634427I
1.27269 − 2.64482I −5.70753 + 1.40210I
u = 0.146999 − 0.118246I
a = −3.40056 + 1.80387I
b = −1.041310 + 0.634427I
1.27269 + 2.64482I −5.70753 − 1.40210I
u = 1.38605 + 1.21593I
a = −0.560619 + 0.303873I
b = 0.607412 − 0.024097I
0.66862 − 3.59542I 0
u = 1.38605 − 1.21593I
a = −0.560619 − 0.303873I
b = 0.607412 + 0.024097I
0.66862 + 3.59542I 0
u = 1.45579 + 1.17501I
a = −0.272961 + 0.386992I
b = 0.471732 − 0.314653I
1.66775 + 3.85576I 0
u = 1.45579 − 1.17501I
a = −0.272961 − 0.386992I
b = 0.471732 + 0.314653I
1.66775 − 3.85576I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.81331 + 1.30001I
a = −0.382421 + 0.280846I
b = 0.427458 − 0.169329I
−3.05641 + 0.12266I 0
u = 1.81331 − 1.30001I
a = −0.382421 − 0.280846I
b = 0.427458 + 0.169329I
−3.05641 − 0.12266I 0
17
II. I
u
2
=
h5u
19
−5u
18
+· · ·+b−13u, −4u
19
+4u
18
+· · ·+a+13u, u
20
−u
19
+· · ·−4u
2
−1i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
6
=
1
u
2
a
10
=
−u
u
a
12
=
4u
19
− 4u
18
+ ··· + u
2
− 13u
−5u
19
+ 5u
18
+ ··· − u
2
+ 13u
a
1
=
3u
19
− 3u
18
+ ··· + u
2
− 12u
−4u
19
+ 4u
18
+ ··· − u
2
+ 12u
a
4
=
−u
19
+ 13u
18
+ ··· + 5u − 30
u
19
− 12u
18
+ ··· − 5u + 26
a
8
=
13u
19
− 13u
18
+ ··· − 34u − 1
−13u
19
+ 13u
18
+ ··· + 31u + 1
a
7
=
4u
19
− 4u
18
+ ··· + u
2
− 16u
−9u
19
+ 9u
18
+ ··· + 22u + 1
a
11
=
−30u
19
+ 29u
18
+ ··· + 70u + 5
26u
19
− 25u
18
+ ··· − 57u − 5
a
3
=
4u
19
− 22u
18
+ ··· − 13u + 40
−4u
19
+ 19u
18
+ ··· + 12u − 31
a
2
=
−42u
19
+ 24u
18
+ ··· + 76u + 40
23u
19
− 8u
18
+ ··· − 42u − 31
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −55u
19
+ 78u
18
− 215u
17
+ 218u
16
− 126u
15
+ 14u
14
+ 368u
13
− 370u
12
+ 511u
11
−
293u
10
− 163u
9
+ 207u
8
− 487u
7
+ 303u
6
− 151u
5
+ 37u
4
+ 218u
3
− 95u
2
+ 106u − 54
18
(iv) u-Polynomials at the component
19
Crossings u-Polynomials at each crossing
c
1
u
20
− 8u
19
+ ··· − 11u + 1
c
2
u
20
− 4u
18
+ ··· + u + 1
c
3
u
20
+ 4u
18
+ ··· + u − 1
c
4
u
20
+ u
19
+ ··· + 29u + 3
c
5
u
20
− u
19
+ ··· − 4u
2
− 1
c
6
u
20
− 4u
18
+ ··· − u + 1
c
7
u
20
+ 8u
19
+ ··· + 11u + 1
c
8
u
20
+ 8u
19
+ ··· + 7u + 1
c
9
u
20
+ u
19
+ ··· − 4u
2
− 1
c
10
u
20
+ 4u
18
+ ··· − u − 1
c
11
u
20
− 8u
19
+ ··· − 7u + 1
c
12
u
20
+ 8u
19
+ ··· + 12u + 1
20
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
20
+ 16y
19
+ ··· + 9y + 1
c
2
, c
6
y
20
− 8y
19
+ ··· − 11y + 1
c
3
, c
10
y
20
+ 8y
19
+ ··· + 7y + 1
c
4
y
20
+ 11y
19
+ ··· − 475y + 9
c
5
, c
9
y
20
+ 7y
19
+ ··· + 8y + 1
c
8
, c
11
y
20
− 20y
19
+ ··· − 17y + 1
c
12
y
20
− 6y
19
+ ··· − 24y + 1
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.440461 + 0.887093I
a = 1.011110 − 0.192582I
b = −2.13494 + 0.17080I
1.63580 − 3.99791I −4.05237 + 6.97033I
u = 0.440461 − 0.887093I
a = 1.011110 + 0.192582I
b = −2.13494 − 0.17080I
1.63580 + 3.99791I −4.05237 − 6.97033I
u = 1.002750 + 0.180612I
a = −0.813503 + 0.481706I
b = 0.305552 − 0.479994I
1.56279 − 1.47094I −8.44352 + 3.39464I
u = 1.002750 − 0.180612I
a = −0.813503 − 0.481706I
b = 0.305552 + 0.479994I
1.56279 + 1.47094I −8.44352 − 3.39464I
u = −0.968414
a = 1.10107
b = −0.601331
−3.16321 −11.6810
u = −0.952644 + 0.151565I
a = 0.991608 + 0.507864I
b = −0.485665 − 0.510762I
1.12978 − 4.10891I −8.64390 + 2.63626I
u = −0.952644 − 0.151565I
a = 0.991608 − 0.507864I
b = −0.485665 + 0.510762I
1.12978 + 4.10891I −8.64390 − 2.63626I
u = −0.365639 + 0.861904I
a = −1.137270 − 0.437397I
b = 2.38481 + 0.24397I
0.60943 + 9.23667I −6.79031 − 11.19751I
u = −0.365639 − 0.861904I
a = −1.137270 + 0.437397I
b = 2.38481 − 0.24397I
0.60943 − 9.23667I −6.79031 + 11.19751I
u = −0.269639 + 1.073570I
a = −0.496198 − 0.545379I
b = 2.25289 + 1.25338I
−2.47111 + 2.51451I −10.96980 − 7.14864I
23
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.269639 − 1.073570I
a = −0.496198 + 0.545379I
b = 2.25289 − 1.25338I
−2.47111 − 2.51451I −10.96980 + 7.14864I
u = 1.14484
a = −0.666442
b = 0.170982
−1.95989 −25.7520
u = 0.516360 + 1.079540I
a = 0.567855 − 0.134368I
b = −1.56996 + 0.50655I
0.30729 − 5.12932I −9.17717 + 5.16594I
u = 0.516360 − 1.079540I
a = 0.567855 + 0.134368I
b = −1.56996 − 0.50655I
0.30729 + 5.12932I −9.17717 − 5.16594I
u = −0.026852 + 0.751387I
a = −0.25165 − 2.33927I
b = 0.470745 + 0.636723I
−6.66011 + 1.32977I −10.28878 − 6.51476I
u = −0.026852 − 0.751387I
a = −0.25165 + 2.33927I
b = 0.470745 − 0.636723I
−6.66011 − 1.32977I −10.28878 + 6.51476I
u = −0.010454 + 0.694976I
a = −0.13434 − 2.97510I
b = 0.19228 + 1.63279I
−4.80260 − 2.45770I −17.1646 + 2.6654I
u = −0.010454 − 0.694976I
a = −0.13434 + 2.97510I
b = 0.19228 − 1.63279I
−4.80260 + 2.45770I −17.1646 − 2.6654I
u = 0.07745 + 1.50340I
a = 0.045081 − 0.289638I
b = −0.20053 + 1.45946I
7.96041 − 3.52390I 5.24692 + 0.37074I
u = 0.07745 − 1.50340I
a = 0.045081 + 0.289638I
b = −0.20053 − 1.45946I
7.96041 + 3.52390I 5.24692 − 0.37074I
24
III. I
u
3
= hb + 1, a − u − 1, u
2
+ u + 1i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
6
=
1
−u − 1
a
10
=
−u
u
a
12
=
u + 1
−1
a
1
=
u
0
a
4
=
1
0
a
8
=
−u − 1
u + 1
a
7
=
−u
0
a
11
=
0
u
a
3
=
1
−u − 1
a
2
=
u + 1
−u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −15
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
8
(u − 1)
2
c
3
, c
5
, c
12
u
2
+ u + 1
c
4
u
2
c
6
, c
7
, c
11
(u + 1)
2
c
9
, c
10
u
2
− u + 1
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
7
, c
8
, c
11
(y −1)
2
c
3
, c
5
, c
9
c
10
, c
12
y
2
+ y + 1
c
4
y
2
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = 0.500000 + 0.866025I
b = −1.00000
−3.28987 −15.0000
u = −0.500000 − 0.866025I
a = 0.500000 − 0.866025I
b = −1.00000
−3.28987 −15.0000
28
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
2
)(u
20
− 8u
19
+ ··· − 11u + 1)
· (u
122
+ 41u
121
+ ··· + 33207u + 121)
c
2
((u − 1)
2
)(u
20
− 4u
18
+ ··· + u + 1)(u
122
− u
121
+ ··· + 223u + 11)
c
3
(u
2
+ u + 1)(u
20
+ 4u
18
+ ··· + u − 1)
· (u
122
− 2u
121
+ ··· + 169938u + 8767)
c
4
u
2
(u
20
+ u
19
+ ··· + 29u + 3)(u
122
− 6u
121
+ ··· + 12u − 8)
c
5
(u
2
+ u + 1)(u
20
− u
19
+ ··· − 4u
2
− 1)(u
122
− 5u
121
+ ··· − 2671u + 313)
c
6
((u + 1)
2
)(u
20
− 4u
18
+ ··· − u + 1)(u
122
− u
121
+ ··· + 223u + 11)
c
7
((u + 1)
2
)(u
20
+ 8u
19
+ ··· + 11u + 1)
· (u
122
+ 41u
121
+ ··· + 33207u + 121)
c
8
((u − 1)
2
)(u
20
+ 8u
19
+ ··· + 7u + 1)(u
122
+ u
121
+ ··· + 4149u + 108)
c
9
(u
2
− u + 1)(u
20
+ u
19
+ ··· − 4u
2
− 1)(u
122
− 5u
121
+ ··· − 2671u + 313)
c
10
(u
2
− u + 1)(u
20
+ 4u
18
+ ··· − u − 1)
· (u
122
− 2u
121
+ ··· + 169938u + 8767)
c
11
((u + 1)
2
)(u
20
− 8u
19
+ ··· − 7u + 1)(u
122
+ u
121
+ ··· + 4149u + 108)
c
12
(u
2
+ u + 1)(u
20
+ 8u
19
+ ··· + 12u + 1)(u
122
− 2u
121
+ ··· + 29u − 1)
29
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
((y −1)
2
)(y
20
+ 16y
19
+ ··· + 9y + 1)
· (y
122
+ 91y
121
+ ··· − 1012244039y + 14641)
c
2
, c
6
((y −1)
2
)(y
20
− 8y
19
+ ··· − 11y + 1)
· (y
122
− 41y
121
+ ··· − 33207y + 121)
c
3
, c
10
(y
2
+ y + 1)(y
20
+ 8y
19
+ ··· + 7y + 1)
· (y
122
+ 70y
121
+ ··· + 180016550y + 76860289)
c
4
y
2
(y
20
+ 11y
19
+ ··· − 475y + 9)(y
122
+ 20y
121
+ ··· + 720y + 64)
c
5
, c
9
(y
2
+ y + 1)(y
20
+ 7y
19
+ ··· + 8y + 1)
· (y
122
+ 73y
121
+ ··· + 3716843y + 97969)
c
8
, c
11
((y −1)
2
)(y
20
− 20y
19
+ ··· − 17y + 1)
· (y
122
− 73y
121
+ ··· − 13689081y + 11664)
c
12
(y
2
+ y + 1)(y
20
− 6y
19
+ ··· − 24y + 1)(y
122
− 12y
121
+ ··· − 81y + 1)
30
