12a
0023
(K12a
0023
)
A knot diagram
1
Linearized knot diagam
3 5 6 9 2 11 10 12 4 7 1 8
Solving Sequence
6,11 2,7
5 3 4 1 10 8 9 12
c
6
c
5
c
2
c
3
c
1
c
10
c
7
c
9
c
12
c
4
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h1.54404 × 10
97
u
81
− 3.41633 × 10
97
u
80
+ ··· + 2.29518 × 10
98
b − 3.85065 × 10
98
,
− 1.38710 × 10
99
u
81
+ 4.21392 × 10
99
u
80
+ ··· + 3.35096 × 10
100
a + 5.51614 × 10
101
,
u
82
− 3u
81
+ ··· − 360u + 73i
I
u
2
= h−u
6
− 2u
4
− u
3
− u
2
+ b − u − 1, u
10
+ 3u
8
+ 2u
7
+ 3u
6
+ 4u
5
+ 3u
4
+ 3u
3
+ 2u
2
+ a + u,
u
12
+ 4u
10
+ 2u
9
+ 6u
8
+ 6u
7
+ 7u
6
+ 6u
5
+ 7u
4
+ 3u
3
+ 3u
2
+ u + 1i
I
u
3
= hu
2
a − au + u
2
+ b − u, 2u
3
a − 4u
2
a − 5u
3
+ 4a
2
+ 6au + 6u
2
− 2a − 13u + 15, u
4
− u
3
+ 3u
2
− 2u + 1i
I
u
4
= h89a
4
u + 27a
4
− 332a
3
u + 255a
3
+ 238a
2
u − 336a
2
− 693au + 173b + 93a + 205u − 208,
a
5
− 5a
4
u − 4a
4
+ 13a
3
u − 12a
2
u − 2a
2
+ 18au + 3a − 6u + 5, u
2
+ 1i
I
u
5
= hu
12
+ 4u
10
+ 2u
9
+ 6u
8
+ 6u
7
+ 6u
6
+ 6u
5
+ 5u
4
+ 2u
3
+ 2u
2
+ b,
u
12
+ 5u
10
+ 2u
9
+ 9u
8
+ 8u
7
+ 10u
6
+ 10u
5
+ 10u
4
+ 6u
3
+ 5u
2
+ a + 2u + 1, u
18
+ 6u
16
+ ··· + 2u
3
+ 1i
* 5 irreducible components of dim
C
= 0, with total 130 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
= h1.54 × 10
97
u
81
− 3.42 × 10
97
u
80
+ · · · + 2.30 × 10
98
b − 3.85 ×
10
98
, −1.39 × 10
99
u
81
+ 4.21 × 10
99
u
80
+ · · · + 3.35 × 10
100
a + 5.52 ×
10
101
, u
82
− 3u
81
+ · · · − 360u + 73i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
2
=
0.0413941u
81
− 0.125753u
80
+ ··· + 42.8841u − 16.4614
−0.0672732u
81
+ 0.148848u
80
+ ··· − 8.13184u + 1.67771
a
7
=
1
u
2
a
5
=
−0.0821417u
81
+ 0.264163u
80
+ ··· − 69.1648u + 27.9833
0.128564u
81
− 0.295774u
80
+ ··· + 10.3237u − 0.432825
a
3
=
0.129775u
81
− 0.321359u
80
+ ··· + 96.0521u − 36.0885
−0.134314u
81
+ 0.328329u
80
+ ··· − 16.2930u + 0.328601
a
4
=
0.264088u
81
− 0.649687u
80
+ ··· + 112.345u − 36.4171
−0.134314u
81
+ 0.328329u
80
+ ··· − 16.2930u + 0.328601
a
1
=
0.0708172u
81
− 0.216816u
80
+ ··· + 43.2679u − 15.8971
−0.0495787u
81
+ 0.0950525u
80
+ ··· − 4.54197u + 2.12782
a
10
=
u
u
3
+ u
a
8
=
u
2
+ 1
u
4
+ 2u
2
a
9
=
0.0784673u
81
− 0.196720u
80
+ ··· + 47.2231u − 14.7403
0.0892485u
81
− 0.257911u
80
+ ··· + 33.5150u − 11.6127
a
12
=
0.153951u
81
− 0.394472u
80
+ ··· + 69.7949u − 26.5441
−0.00512662u
81
− 0.00648671u
80
+ ··· + 9.47710u − 2.79106
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.0994831u
81
− 0.402830u
80
+ ··· − 10.5235u + 2.17824
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
82
+ 40u
81
+ ··· − 49u + 16
c
2
, c
5
u
82
+ 4u
81
+ ··· + 35u + 4
c
3
u
82
− 4u
81
+ ··· + 198067u + 62564
c
4
, c
9
u
82
− 2u
81
+ ··· − 1536u + 2048
c
6
, c
7
, c
10
u
82
− 3u
81
+ ··· − 360u + 73
c
8
, c
12
u
82
− 3u
81
+ ··· − 494u + 73
c
11
u
82
+ 33u
81
+ ··· + 157464u + 5329
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
82
+ 8y
81
+ ··· + 20543y + 256
c
2
, c
5
y
82
+ 40y
81
+ ··· − 49y + 16
c
3
y
82
− 24y
81
+ ··· − 66737549857y + 3914254096
c
4
, c
9
y
82
+ 40y
81
+ ··· + 81002496y + 4194304
c
6
, c
7
, c
10
y
82
+ 85y
81
+ ··· − 1704y + 5329
c
8
, c
12
y
82
+ 33y
81
+ ··· + 157464y + 5329
c
11
y
82
+ 45y
81
+ ··· − 920479712y + 28398241
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.931867 + 0.288264I
a = 0.74456 + 2.19168I
b = −0.578133 + 1.146860I
−4.73439 − 13.08270I 0
u = 0.931867 − 0.288264I
a = 0.74456 − 2.19168I
b = −0.578133 − 1.146860I
−4.73439 + 13.08270I 0
u = −0.716067 + 0.747461I
a = −0.032611 + 1.086440I
b = −0.496263 + 1.079110I
−1.68085 − 2.38669I 0
u = −0.716067 − 0.747461I
a = −0.032611 − 1.086440I
b = −0.496263 − 1.079110I
−1.68085 + 2.38669I 0
u = 0.881772 + 0.288043I
a = −0.567238 + 0.105365I
b = −0.812359 − 0.318846I
−2.27548 − 7.90430I 0
u = 0.881772 − 0.288043I
a = −0.567238 − 0.105365I
b = −0.812359 + 0.318846I
−2.27548 + 7.90430I 0
u = −0.552972 + 0.923521I
a = 1.04759 − 1.44828I
b = −0.404154 − 1.082810I
−2.30869 + 4.66431I 0
u = −0.552972 − 0.923521I
a = 1.04759 + 1.44828I
b = −0.404154 + 1.082810I
−2.30869 − 4.66431I 0
u = 0.865905 + 0.193943I
a = −0.21817 − 2.33698I
b = −0.225527 − 1.181770I
−7.10693 − 4.86870I 0
u = 0.865905 − 0.193943I
a = −0.21817 + 2.33698I
b = −0.225527 + 1.181770I
−7.10693 + 4.86870I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.629083 + 0.592688I
a = 0.557418 − 0.631931I
b = −0.462219 − 0.392158I
0.35733 + 1.72933I 0
u = −0.629083 − 0.592688I
a = 0.557418 + 0.631931I
b = −0.462219 + 0.392158I
0.35733 − 1.72933I 0
u = −0.757316 + 0.260733I
a = −0.54770 + 3.02690I
b = 0.514202 + 1.095290I
−2.21702 + 6.90031I −3.45370 − 7.38488I
u = −0.757316 − 0.260733I
a = −0.54770 − 3.02690I
b = 0.514202 − 1.095290I
−2.21702 − 6.90031I −3.45370 + 7.38488I
u = 0.708061 + 0.318172I
a = 0.036016 − 0.721055I
b = 0.702828 − 0.691781I
−0.26229 − 5.35525I −1.75979 + 8.80201I
u = 0.708061 − 0.318172I
a = 0.036016 + 0.721055I
b = 0.702828 + 0.691781I
−0.26229 + 5.35525I −1.75979 − 8.80201I
u = 0.102266 + 1.220550I
a = 0.346306 − 1.356210I
b = −0.485285 − 1.241660I
−4.87377 + 3.17759I 0
u = 0.102266 − 1.220550I
a = 0.346306 + 1.356210I
b = −0.485285 + 1.241660I
−4.87377 − 3.17759I 0
u = −0.331871 + 0.700232I
a = 0.496451 − 0.036342I
b = −0.301233 + 0.157524I
0.204488 + 1.398330I 2.03862 − 5.44556I
u = −0.331871 − 0.700232I
a = 0.496451 + 0.036342I
b = −0.301233 − 0.157524I
0.204488 − 1.398330I 2.03862 + 5.44556I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.674373 + 0.346981I
a = 1.073310 + 0.123315I
b = 0.578755 − 0.306719I
0.00632 + 2.50124I 0.80512 − 3.77203I
u = −0.674373 − 0.346981I
a = 1.073310 − 0.123315I
b = 0.578755 + 0.306719I
0.00632 − 2.50124I 0.80512 + 3.77203I
u = 0.186356 + 1.239000I
a = 0.56436 + 1.53697I
b = −0.407486 + 1.256420I
−5.40817 − 6.29101I 0
u = 0.186356 − 1.239000I
a = 0.56436 − 1.53697I
b = −0.407486 − 1.256420I
−5.40817 + 6.29101I 0
u = 0.131448 + 1.261180I
a = 0.0126024 + 0.1044920I
b = −0.894097 + 0.065764I
−1.27320 − 1.76086I 0
u = 0.131448 − 1.261180I
a = 0.0126024 − 0.1044920I
b = −0.894097 − 0.065764I
−1.27320 + 1.76086I 0
u = 0.000944 + 0.700428I
a = 0.836733 − 0.250241I
b = 0.453431 + 0.652167I
0.85090 + 1.37273I 5.63231 − 4.46237I
u = 0.000944 − 0.700428I
a = 0.836733 + 0.250241I
b = 0.453431 − 0.652167I
0.85090 − 1.37273I 5.63231 + 4.46237I
u = 0.600384 + 0.298134I
a = −0.26365 + 1.53064I
b = 0.645915 + 0.903317I
−0.883850 − 0.200745I −5.12754 + 3.53229I
u = 0.600384 − 0.298134I
a = −0.26365 − 1.53064I
b = 0.645915 − 0.903317I
−0.883850 + 0.200745I −5.12754 − 3.53229I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.044049 + 1.339840I
a = 0.38952 + 1.43290I
b = 0.201452 + 1.108560I
2.76790 + 2.04513I 0
u = 0.044049 − 1.339840I
a = 0.38952 − 1.43290I
b = 0.201452 − 1.108560I
2.76790 − 2.04513I 0
u = 0.638837 + 0.095613I
a = −1.03149 − 2.03244I
b = −0.360549 − 1.188300I
−8.84527 + 3.38561I −9.80482 − 3.21851I
u = 0.638837 − 0.095613I
a = −1.03149 + 2.03244I
b = −0.360549 + 1.188300I
−8.84527 − 3.38561I −9.80482 + 3.21851I
u = −0.217222 + 1.359330I
a = 0.41987 − 1.65460I
b = 0.309949 − 1.160650I
1.51647 + 2.63898I 0
u = −0.217222 − 1.359330I
a = 0.41987 + 1.65460I
b = 0.309949 + 1.160650I
1.51647 − 2.63898I 0
u = −0.580389 + 0.144752I
a = −0.08898 − 3.84967I
b = 0.368006 − 1.071140I
−3.26708 − 0.25890I −6.56949 − 0.34009I
u = −0.580389 − 0.144752I
a = −0.08898 + 3.84967I
b = 0.368006 + 1.071140I
−3.26708 + 0.25890I −6.56949 + 0.34009I
u = −0.293167 + 1.373670I
a = −0.364644 + 0.989732I
b = −0.155107 + 1.157470I
0.62942 + 3.86909I 0
u = −0.293167 − 1.373670I
a = −0.364644 − 0.989732I
b = −0.155107 − 1.157470I
0.62942 − 3.86909I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.10157 + 1.41564I
a = −1.007610 − 0.291358I
b = 0.672906 − 0.991984I
6.01806 − 2.03585I 0
u = −0.10157 − 1.41564I
a = −1.007610 + 0.291358I
b = 0.672906 + 0.991984I
6.01806 + 2.03585I 0
u = 0.19353 + 1.40902I
a = −1.56362 − 1.41156I
b = 0.571655 − 1.099770I
5.20020 − 5.30195I 0
u = 0.19353 − 1.40902I
a = −1.56362 + 1.41156I
b = 0.571655 + 1.099770I
5.20020 + 5.30195I 0
u = 0.23431 + 1.41260I
a = −0.563863 + 0.112880I
b = 0.720598 + 0.946524I
4.58279 − 3.27171I 0
u = 0.23431 − 1.41260I
a = −0.563863 − 0.112880I
b = 0.720598 − 0.946524I
4.58279 + 3.27171I 0
u = 0.141385 + 0.546620I
a = −1.17091 − 2.94774I
b = 0.537230 − 0.935250I
0.01009 − 2.82413I 1.52552 − 1.31964I
u = 0.141385 − 0.546620I
a = −1.17091 + 2.94774I
b = 0.537230 + 0.935250I
0.01009 + 2.82413I 1.52552 + 1.31964I
u = 0.35574 + 1.39551I
a = −0.589303 − 1.191880I
b = −0.181803 − 1.231480I
−2.06157 − 9.25202I 0
u = 0.35574 − 1.39551I
a = −0.589303 + 1.191880I
b = −0.181803 + 1.231480I
−2.06157 + 9.25202I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.15745 + 1.43439I
a = −0.807625 − 0.077038I
b = 0.768058 + 0.620750I
7.11638 + 3.39177I 0
u = −0.15745 − 1.43439I
a = −0.807625 + 0.077038I
b = 0.768058 − 0.620750I
7.11638 − 3.39177I 0
u = 0.13510 + 1.43944I
a = −0.028780 − 0.593948I
b = 0.730607 + 0.374401I
7.31677 − 0.34373I 0
u = 0.13510 − 1.43944I
a = −0.028780 + 0.593948I
b = 0.730607 − 0.374401I
7.31677 + 0.34373I 0
u = −0.29944 + 1.41443I
a = −1.42686 + 1.79453I
b = 0.543220 + 1.143100I
3.13401 + 10.72870I 0
u = −0.29944 − 1.41443I
a = −1.42686 − 1.79453I
b = 0.543220 − 1.143100I
3.13401 − 10.72870I 0
u = −0.25420 + 1.43282I
a = 0.217341 + 0.561259I
b = 0.743632 − 0.257984I
5.70142 + 5.87245I 0
u = −0.25420 − 1.43282I
a = 0.217341 − 0.561259I
b = 0.743632 + 0.257984I
5.70142 − 5.87245I 0
u = 0.27241 + 1.42956I
a = −0.908143 − 0.308634I
b = 0.793344 − 0.693334I
5.33290 − 8.91870I 0
u = 0.27241 − 1.42956I
a = −0.908143 + 0.308634I
b = 0.793344 + 0.693334I
5.33290 + 8.91870I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.475745 + 0.209145I
a = 2.03995 + 2.38629I
b = −0.499651 + 1.175680I
−7.90191 − 5.12885I −9.18084 + 4.19654I
u = 0.475745 − 0.209145I
a = 2.03995 − 2.38629I
b = −0.499651 − 1.175680I
−7.90191 + 5.12885I −9.18084 − 4.19654I
u = 0.35661 + 1.44636I
a = 0.035317 + 0.650934I
b = −0.867997 − 0.346788I
3.26342 − 12.37470I 0
u = 0.35661 − 1.44636I
a = 0.035317 − 0.650934I
b = −0.867997 + 0.346788I
3.26342 + 12.37470I 0
u = −0.27471 + 1.46687I
a = 0.253358 − 0.576940I
b = −0.818333 + 0.377304I
5.76778 + 6.48991I 0
u = −0.27471 − 1.46687I
a = 0.253358 + 0.576940I
b = −0.818333 − 0.377304I
5.76778 − 6.48991I 0
u = 0.493335 + 0.088573I
a = −0.704097 + 1.043790I
b = −0.778342 − 0.137458I
−4.86017 − 0.43404I −6.11324 + 0.16498I
u = 0.493335 − 0.088573I
a = −0.704097 − 1.043790I
b = −0.778342 + 0.137458I
−4.86017 + 0.43404I −6.11324 − 0.16498I
u = 0.38104 + 1.45468I
a = 1.56176 + 1.40425I
b = −0.605715 + 1.158280I
0.8212 − 17.8110I 0
u = 0.38104 − 1.45468I
a = 1.56176 − 1.40425I
b = −0.605715 − 1.158280I
0.8212 + 17.8110I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.31053 + 1.48595I
a = 1.53155 − 1.11523I
b = −0.598642 − 1.130360I
3.51847 + 11.77520I 0
u = −0.31053 − 1.48595I
a = 1.53155 + 1.11523I
b = −0.598642 + 1.130360I
3.51847 − 11.77520I 0
u = 0.03211 + 1.54530I
a = 0.827192 + 0.027538I
b = −0.614172 + 0.556963I
8.23836 + 1.61654I 0
u = 0.03211 − 1.54530I
a = 0.827192 − 0.027538I
b = −0.614172 − 0.556963I
8.23836 − 1.61654I 0
u = −0.18029 + 1.54523I
a = 0.998658 − 0.285530I
b = −0.517302 − 0.643049I
7.43559 + 4.67815I 0
u = −0.18029 − 1.54523I
a = 0.998658 + 0.285530I
b = −0.517302 + 0.643049I
7.43559 − 4.67815I 0
u = −0.01098 + 1.60996I
a = 0.915198 − 0.352984I
b = −0.530424 − 1.010100I
6.89596 + 6.13785I 0
u = −0.01098 − 1.60996I
a = 0.915198 + 0.352984I
b = −0.530424 + 1.010100I
6.89596 − 6.13785I 0
u = −0.14411 + 1.60864I
a = 0.643410 + 0.262050I
b = −0.477631 + 0.979007I
6.41976 + 0.62950I 0
u = −0.14411 − 1.60864I
a = 0.643410 − 0.262050I
b = −0.477631 − 0.979007I
6.41976 − 0.62950I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.177461 + 0.198624I
a = 3.73067 + 4.25469I
b = 0.216638 + 0.860749I
−1.89160 + 1.79439I −7.98709 − 4.10659I
u = −0.177461 − 0.198624I
a = 3.73067 − 4.25469I
b = 0.216638 − 0.860749I
−1.89160 − 1.79439I −7.98709 + 4.10659I
13
II.
I
u
2
= h−u
6
−2u
4
−u
3
−u
2
+b−u−1, u
10
+3u
8
+· · ·+a+u, u
12
+4u
10
+· · ·+u+1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
2
=
−u
10
− 3u
8
− 2u
7
− 3u
6
− 4u
5
− 3u
4
− 3u
3
− 2u
2
− u
u
6
+ 2u
4
+ u
3
+ u
2
+ u + 1
a
7
=
1
u
2
a
5
=
−u
9
− 3u
7
− u
6
− 3u
5
− 2u
4
− 2u
3
− u
2
+ 1
u
3
+ u
a
3
=
−u
10
− 3u
8
− u
7
− 3u
6
− 2u
5
− 2u
4
− u
3
− u
2
+ u + 1
u
9
+ 3u
7
+ 2u
6
+ 3u
5
+ 4u
4
+ 3u
3
+ 2u
2
+ 2u + 1
a
4
=
−u
10
− u
9
− 3u
8
− 4u
7
− 5u
6
− 5u
5
− 6u
4
− 4u
3
− 3u
2
− u
u
9
+ 3u
7
+ 2u
6
+ 3u
5
+ 4u
4
+ 3u
3
+ 2u
2
+ 2u + 1
a
1
=
u
u
3
+ u
a
10
=
u
u
3
+ u
a
8
=
u
2
+ 1
u
4
+ 2u
2
a
9
=
−u
4
− u
2
− 1
−u
6
− 2u
4
− u
2
a
12
=
−u
3
−u
5
− u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
9
− 12u
7
− 4u
6
− 12u
5
− 8u
4
− 12u
3
− 4u
2
− 8u + 2
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
4
+ 2u
3
+ 3u
2
+ u + 1)
3
c
2
, c
4
, c
5
c
9
(u
4
+ u
2
− u + 1)
3
c
3
(u
4
− 3u
3
+ 4u
2
− 3u + 2)
3
c
6
, c
7
, c
8
c
10
, c
12
u
12
+ 4u
10
+ 2u
9
+ 6u
8
+ 6u
7
+ 7u
6
+ 6u
5
+ 7u
4
+ 3u
3
+ 3u
2
+ u + 1
c
11
u
12
+ 8u
11
+ ··· + 5u + 1
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
4
+ 2y
3
+ 7y
2
+ 5y + 1)
3
c
2
, c
4
, c
5
c
9
(y
4
+ 2y
3
+ 3y
2
+ y + 1)
3
c
3
(y
4
− y
3
+ 2y
2
+ 7y + 4)
3
c
6
, c
7
, c
8
c
10
, c
12
y
12
+ 8y
11
+ ··· + 5y + 1
c
11
y
12
− 8y
11
+ ··· + 9y + 1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.831200 + 0.424235I
a = 0.94351 − 1.97518I
b = −0.547424 − 1.120870I
−2.62503 + 7.64338I −1.77019 − 6.51087I
u = −0.831200 − 0.424235I
a = 0.94351 + 1.97518I
b = −0.547424 + 1.120870I
−2.62503 − 7.64338I −1.77019 + 6.51087I
u = 0.636602 + 0.984558I
a = 0.023505 − 1.114990I
b = −0.547424 − 1.120870I
−2.62503 + 7.64338I −1.77019 − 6.51087I
u = 0.636602 − 0.984558I
a = 0.023505 + 1.114990I
b = −0.547424 + 1.120870I
−2.62503 − 7.64338I −1.77019 + 6.51087I
u = 0.012163 + 1.233070I
a = −1.07001 + 1.70262I
b = 0.547424 − 0.585652I
0.98010 − 1.39709I 3.77019 + 3.86736I
u = 0.012163 − 1.233070I
a = −1.07001 − 1.70262I
b = 0.547424 + 0.585652I
0.98010 + 1.39709I 3.77019 − 3.86736I
u = 0.369581 + 0.646475I
a = 0.947255 − 0.427323I
b = 0.547424 + 0.585652I
0.98010 + 1.39709I 3.77019 − 3.86736I
u = 0.369581 − 0.646475I
a = 0.947255 + 0.427323I
b = 0.547424 − 0.585652I
0.98010 − 1.39709I 3.77019 + 3.86736I
u = −0.381744 + 0.586589I
a = 0.252697 + 0.206342I
b = 0.547424 + 0.585652I
0.98010 + 1.39709I 3.77019 − 3.86736I
u = −0.381744 − 0.586589I
a = 0.252697 − 0.206342I
b = 0.547424 − 0.585652I
0.98010 − 1.39709I 3.77019 + 3.86736I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.19460 + 1.40879I
a = 1.90304 + 0.59138I
b = −0.547424 + 1.120870I
−2.62503 − 7.64338I −1.77019 + 6.51087I
u = 0.19460 − 1.40879I
a = 1.90304 − 0.59138I
b = −0.547424 − 1.120870I
−2.62503 + 7.64338I −1.77019 − 6.51087I
18
III.
I
u
3
= hu
2
a − au + u
2
+ b − u, 2u
3
a − 5u
3
+ · · · − 2a +15, u
4
− u
3
+ 3u
2
− 2u + 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
2
=
a
−u
2
a + au − u
2
+ u
a
7
=
1
u
2
a
5
=
u
2
a +
1
2
u
3
− au + a +
1
2
u −
1
2
−u
2
a + au − u
2
+ u − 1
a
3
=
1
2
u
3
− u
2
+ a +
3
2
u −
3
2
−u
2
a + au − u
2
+ u − 1
a
4
=
u
2
a +
1
2
u
3
− au + a +
1
2
u −
1
2
−u
2
a + au − u
2
+ u − 1
a
1
=
−1
0
a
10
=
u
u
3
+ u
a
8
=
u
2
+ 1
u
3
− u
2
+ 2u − 1
a
9
=
u
u
3
+ u
a
12
=
−u
u
(ii) Obstruction class = 1
(iii) Cusp Shapes =
3
2
u
3
a − 3u
2
a +
9
2
u
3
−
1
2
au − 5u
2
−
5
2
a +
21
2
u −
9
2
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
(u
2
− u + 1)
4
c
2
(u
2
+ u + 1)
4
c
4
, c
9
u
8
c
6
, c
7
, c
11
(u
4
− u
3
+ 3u
2
− 2u + 1)
2
c
8
(u
4
− u
3
+ u
2
+ 1)
2
c
10
(u
4
+ u
3
+ 3u
2
+ 2u + 1)
2
c
12
(u
4
+ u
3
+ u
2
+ 1)
2
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
5
(y
2
+ y + 1)
4
c
4
, c
9
y
8
c
6
, c
7
, c
10
c
11
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
2
c
8
, c
12
(y
4
+ y
3
+ 3y
2
+ 2y + 1)
2
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.395123 + 0.506844I
a = 0.32193 + 1.46300I
b = 0.500000 + 0.866025I
−0.211005 + 0.614778I 0.065036 − 0.652246I
u = 0.395123 + 0.506844I
a = −0.39397 − 1.87632I
b = 0.500000 − 0.866025I
−0.21101 − 3.44499I −2.28131 + 9.48913I
u = 0.395123 − 0.506844I
a = 0.32193 − 1.46300I
b = 0.500000 − 0.866025I
−0.211005 − 0.614778I 0.065036 + 0.652246I
u = 0.395123 − 0.506844I
a = −0.39397 + 1.87632I
b = 0.500000 + 0.866025I
−0.21101 + 3.44499I −2.28131 − 9.48913I
u = 0.10488 + 1.55249I
a = −0.975620 − 0.357786I
b = 0.500000 − 0.866025I
6.79074 − 5.19385I −0.84181 + 3.92087I
u = 0.10488 + 1.55249I
a = −0.702338 + 0.200007I
b = 0.500000 + 0.866025I
6.79074 − 1.13408I 4.18309 + 3.88645I
u = 0.10488 − 1.55249I
a = −0.975620 + 0.357786I
b = 0.500000 + 0.866025I
6.79074 + 5.19385I −0.84181 − 3.92087I
u = 0.10488 − 1.55249I
a = −0.702338 − 0.200007I
b = 0.500000 − 0.866025I
6.79074 + 1.13408I 4.18309 − 3.88645I
22
IV.
I
u
4
= h89a
4
u − 332a
3
u + · · · + 93a − 208, −5a
4
u + 13a
3
u + · · · + 3a + 5, u
2
+ 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
2
=
a
−0.514451a
4
u + 1.91908a
3
u + ··· − 0.537572a + 1.20231
a
7
=
1
−1
a
5
=
−0.919075a
4
u + 0.653179a
3
u + ··· − 7.58960a + 4.86705
0.0173410a
4
u − 1.50289a
3
u + ··· − 3.55491a + 0.757225
a
3
=
−0.0115607a
4
u − 0.664740a
3
u + ··· + 0.369942a − 0.838150
0.254335a
4
u + 1.62428a
3
u + ··· + 5.86127a − 2.56069
a
4
=
−0.265896a
4
u − 2.28902a
3
u + ··· − 5.49133a + 1.72254
0.254335a
4
u + 1.62428a
3
u + ··· + 5.86127a − 2.56069
a
1
=
u
−0.156069a
4
u − 1.47399a
3
u + ··· − 4.00578a − 0.815029
a
10
=
u
0
a
8
=
0
−1
a
9
=
1
−0.514451a
4
u + 1.91908a
3
u + ··· − 1.53757a + 2.20231
a
12
=
u
−0.156069a
4
u − 1.47399a
3
u + ··· − 4.00578a − 0.815029
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −
188
173
a
4
u +
184
173
a
4
−
84
173
a
3
u −
1184
173
a
3
+
648
173
a
2
u +
1324
173
a
2
+
352
173
au −
1596
173
a +
500
173
u +
556
173
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
5
− 3u
4
+ 4u
3
− u
2
− u + 1)
2
c
2
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
2
c
3
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
2
c
4
, c
9
u
10
+ 5u
8
+ 8u
6
+ 3u
4
− u
2
+ 1
c
5
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
2
c
6
, c
7
, c
8
c
10
, c
12
(u
2
+ 1)
5
c
11
(u − 1)
10
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)
2
c
2
, c
5
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
2
c
3
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
2
c
4
, c
9
(y
5
+ 5y
4
+ 8y
3
+ 3y
2
− y + 1)
2
c
6
, c
7
, c
8
c
10
, c
12
(y + 1)
10
c
11
(y −1)
10
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = −0.077593 − 1.165070I
b = −0.455697 − 1.200150I
−5.87256 + 4.40083I −4.74431 − 3.49859I
u = 1.000000I
a = 0.233174 + 0.517119I
b = −0.766826
−2.40108 −1.48114 + 0.I
u = 1.000000I
a = 1.16620 + 1.23524I
b = −0.455697 + 1.200150I
−5.87256 − 4.40083I −4.74431 + 3.49859I
u = 1.000000I
a = 1.67996 + 1.38398I
b = 0.339110 − 0.822375I
−0.32910 − 1.53058I −0.51511 + 4.43065I
u = 1.000000I
a = 0.99826 + 3.02873I
b = 0.339110 + 0.822375I
−0.32910 + 1.53058I −0.51511 − 4.43065I
u = − 1.000000I
a = −0.077593 + 1.165070I
b = −0.455697 + 1.200150I
−5.87256 − 4.40083I −4.74431 + 3.49859I
u = − 1.000000I
a = 0.233174 − 0.517119I
b = −0.766826
−2.40108 −1.48114 + 0.I
u = − 1.000000I
a = 1.16620 − 1.23524I
b = −0.455697 − 1.200150I
−5.87256 + 4.40083I −4.74431 − 3.49859I
u = − 1.000000I
a = 1.67996 − 1.38398I
b = 0.339110 + 0.822375I
−0.32910 + 1.53058I −0.51511 − 4.43065I
u = − 1.000000I
a = 0.99826 − 3.02873I
b = 0.339110 − 0.822375I
−0.32910 − 1.53058I −0.51511 + 4.43065I
26
V.
I
u
5
= hu
12
+4u
10
+· · ·+2u
2
+b, u
12
+5u
10
+· · ·+a+1, u
18
+6u
16
+· · ·+2u
3
+1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
2
=
−u
12
− 5u
10
+ ··· − 2u − 1
−u
12
− 4u
10
− 2u
9
− 6u
8
− 6u
7
− 6u
6
− 6u
5
− 5u
4
− 2u
3
− 2u
2
a
7
=
1
u
2
a
5
=
u
16
+ 5u
14
+ ··· − 2u − 1
−u
15
− 5u
13
+ ··· − u − 1
a
3
=
u
15
+ 6u
13
+ ··· − 2u − 1
u
15
+ 5u
13
+ ··· − u
2
− u
a
4
=
u
13
+ 4u
11
+ 2u
10
+ 7u
9
+ 6u
8
+ 8u
7
+ 7u
6
+ 6u
5
+ 3u
4
+ 2u
3
− u − 1
u
15
+ 5u
13
+ ··· − u
2
− u
a
1
=
u
u
3
+ u
a
10
=
u
u
3
+ u
a
8
=
u
2
+ 1
u
4
+ 2u
2
a
9
=
−u
4
− u
2
− 1
−u
6
− 2u
4
− u
2
a
12
=
−u
3
−u
5
− u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −4u
15
−20u
13
−8u
12
−40u
11
−32u
10
−44u
9
−48u
8
−32u
7
−28u
6
−16u
5
+4u
2
+4u −2
27
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1)
3
c
2
, c
4
, c
5
c
9
(u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)
3
c
3
(u
3
+ u
2
− 1)
6
c
6
, c
7
, c
8
c
10
, c
12
u
18
+ 6u
16
+ ··· + 2u
3
+ 1
c
11
u
18
+ 12u
17
+ ··· + 8u
2
+ 1
28
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1)
3
c
2
, c
4
, c
5
c
9
(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
3
c
3
(y
3
− y
2
+ 2y −1)
6
c
6
, c
7
, c
8
c
10
, c
12
y
18
+ 12y
17
+ ··· + 8y
2
+ 1
c
11
y
18
− 12y
17
+ ··· + 16y + 1
29
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.313259 + 0.899357I
a = 0.45015 − 2.25952I
b = 0.498832 − 1.001300I
−0.26574 − 2.82812I 1.50976 + 2.97945I
u = −0.313259 − 0.899357I
a = 0.45015 + 2.25952I
b = 0.498832 + 1.001300I
−0.26574 + 2.82812I 1.50976 − 2.97945I
u = 0.561896 + 0.941136I
a = 0.236041 + 0.494044I
b = −0.713912 + 0.305839I
−0.26574 + 2.82812I 1.50976 − 2.97945I
u = 0.561896 − 0.941136I
a = 0.236041 − 0.494044I
b = −0.713912 − 0.305839I
−0.26574 − 2.82812I 1.50976 + 2.97945I
u = −0.731365 + 0.409982I
a = −0.296941 − 0.190639I
b = −0.713912 + 0.305839I
−0.26574 + 2.82812I 1.50976 − 2.97945I
u = −0.731365 − 0.409982I
a = −0.296941 + 0.190639I
b = −0.713912 − 0.305839I
−0.26574 − 2.82812I 1.50976 + 2.97945I
u = −0.789849 + 0.225271I
a = −0.23233 + 1.95687I
b = −0.284920 + 1.115140I
−4.40332 −5.01951 + 0.I
u = −0.789849 − 0.225271I
a = −0.23233 − 1.95687I
b = −0.284920 − 1.115140I
−4.40332 −5.01951 + 0.I
u = −0.128706 + 1.190210I
a = −3.31018 + 1.26239I
b = 0.498832 + 1.001300I
−0.26574 + 2.82812I 1.50976 − 2.97945I
u = −0.128706 − 1.190210I
a = −3.31018 − 1.26239I
b = 0.498832 − 1.001300I
−0.26574 − 2.82812I 1.50976 + 2.97945I
30
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.506047 + 1.088270I
a = 1.08391 + 1.64474I
b = −0.284920 + 1.115140I
−4.40332 −5.01951 + 0.I
u = 0.506047 − 1.088270I
a = 1.08391 − 1.64474I
b = −0.284920 − 1.115140I
−4.40332 −5.01951 + 0.I
u = 0.283803 + 1.313550I
a = −0.574018 − 0.362840I
b = −0.284920 − 1.115140I
−4.40332 −5.01951 + 0.I
u = 0.283803 − 1.313550I
a = −0.574018 + 0.362840I
b = −0.284920 + 1.115140I
−4.40332 −5.01951 + 0.I
u = 0.169470 + 1.351120I
a = 0.731066 + 0.861716I
b = −0.713912 − 0.305839I
−0.26574 − 2.82812I 1.50976 + 2.97945I
u = 0.169470 − 1.351120I
a = 0.731066 − 0.861716I
b = −0.713912 + 0.305839I
−0.26574 + 2.82812I 1.50976 − 2.97945I
u = 0.441965 + 0.290850I
a = −1.08769 − 3.19240I
b = 0.498832 − 1.001300I
−0.26574 − 2.82812I 1.50976 + 2.97945I
u = 0.441965 − 0.290850I
a = −1.08769 + 3.19240I
b = 0.498832 + 1.001300I
−0.26574 + 2.82812I 1.50976 − 2.97945I
31
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
2
− u + 1)
4
(u
4
+ 2u
3
+ 3u
2
+ u + 1)
3
(u
5
− 3u
4
+ 4u
3
− u
2
− u + 1)
2
· ((u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1)
3
)(u
82
+ 40u
81
+ ··· − 49u + 16)
c
2
(u
2
+ u + 1)
4
(u
4
+ u
2
− u + 1)
3
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
2
· ((u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)
3
)(u
82
+ 4u
81
+ ··· + 35u + 4)
c
3
(u
2
− u + 1)
4
(u
3
+ u
2
− 1)
6
(u
4
− 3u
3
+ 4u
2
− 3u + 2)
3
· ((u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
2
)(u
82
− 4u
81
+ ··· + 198067u + 62564)
c
4
, c
9
u
8
(u
4
+ u
2
− u + 1)
3
(u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)
3
· (u
10
+ 5u
8
+ 8u
6
+ 3u
4
− u
2
+ 1)(u
82
− 2u
81
+ ··· − 1536u + 2048)
c
5
(u
2
− u + 1)
4
(u
4
+ u
2
− u + 1)
3
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
2
· ((u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)
3
)(u
82
+ 4u
81
+ ··· + 35u + 4)
c
6
, c
7
(u
2
+ 1)
5
(u
4
− u
3
+ 3u
2
− 2u + 1)
2
· (u
12
+ 4u
10
+ 2u
9
+ 6u
8
+ 6u
7
+ 7u
6
+ 6u
5
+ 7u
4
+ 3u
3
+ 3u
2
+ u + 1)
· (u
18
+ 6u
16
+ ··· + 2u
3
+ 1)(u
82
− 3u
81
+ ··· − 360u + 73)
c
8
(u
2
+ 1)
5
(u
4
− u
3
+ u
2
+ 1)
2
· (u
12
+ 4u
10
+ 2u
9
+ 6u
8
+ 6u
7
+ 7u
6
+ 6u
5
+ 7u
4
+ 3u
3
+ 3u
2
+ u + 1)
· (u
18
+ 6u
16
+ ··· + 2u
3
+ 1)(u
82
− 3u
81
+ ··· − 494u + 73)
c
10
(u
2
+ 1)
5
(u
4
+ u
3
+ 3u
2
+ 2u + 1)
2
· (u
12
+ 4u
10
+ 2u
9
+ 6u
8
+ 6u
7
+ 7u
6
+ 6u
5
+ 7u
4
+ 3u
3
+ 3u
2
+ u + 1)
· (u
18
+ 6u
16
+ ··· + 2u
3
+ 1)(u
82
− 3u
81
+ ··· − 360u + 73)
c
11
((u − 1)
10
)(u
4
− u
3
+ 3u
2
− 2u + 1)
2
(u
12
+ 8u
11
+ ··· + 5u + 1)
· (u
18
+ 12u
17
+ ··· + 8u
2
+ 1)(u
82
+ 33u
81
+ ··· + 157464u + 5329)
c
12
(u
2
+ 1)
5
(u
4
+ u
3
+ u
2
+ 1)
2
· (u
12
+ 4u
10
+ 2u
9
+ 6u
8
+ 6u
7
+ 7u
6
+ 6u
5
+ 7u
4
+ 3u
3
+ 3u
2
+ u + 1)
· (u
18
+ 6u
16
+ ··· + 2u
3
+ 1)(u
82
− 3u
81
+ ··· − 494u + 73)
32
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
2
+ y + 1)
4
(y
4
+ 2y
3
+ 7y
2
+ 5y + 1)
3
· (y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)
2
(y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1)
3
· (y
82
+ 8y
81
+ ··· + 20543y + 256)
c
2
, c
5
(y
2
+ y + 1)
4
(y
4
+ 2y
3
+ 3y
2
+ y + 1)
3
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
2
· ((y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
3
)(y
82
+ 40y
81
+ ··· − 49y + 16)
c
3
(y
2
+ y + 1)
4
(y
3
− y
2
+ 2y −1)
6
(y
4
− y
3
+ 2y
2
+ 7y + 4)
3
· (y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
2
· (y
82
− 24y
81
+ ··· − 66737549857y + 3914254096)
c
4
, c
9
y
8
(y
4
+ 2y
3
+ 3y
2
+ y + 1)
3
(y
5
+ 5y
4
+ 8y
3
+ 3y
2
− y + 1)
2
· (y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
3
· (y
82
+ 40y
81
+ ··· + 81002496y + 4194304)
c
6
, c
7
, c
10
((y + 1)
10
)(y
4
+ 5y
3
+ ··· + 2y + 1)
2
(y
12
+ 8y
11
+ ··· + 5y + 1)
· (y
18
+ 12y
17
+ ··· + 8y
2
+ 1)(y
82
+ 85y
81
+ ··· − 1704y + 5329)
c
8
, c
12
((y + 1)
10
)(y
4
+ y
3
+ 3y
2
+ 2y + 1)
2
(y
12
+ 8y
11
+ ··· + 5y + 1)
· (y
18
+ 12y
17
+ ··· + 8y
2
+ 1)(y
82
+ 33y
81
+ ··· + 157464y + 5329)
c
11
((y −1)
10
)(y
4
+ 5y
3
+ ··· + 2y + 1)
2
(y
12
− 8y
11
+ ··· + 9y + 1)
· (y
18
− 12y
17
+ ··· + 16y + 1)
· (y
82
+ 45y
81
+ ··· − 920479712y + 28398241)
33
