12a
0228
(K12a
0228
)
A knot diagram
1
Linearized knot diagam
3 6 7 9 11 2 1 5 12 8 4 10
Solving Sequence
3,6
2 7 4 1
8,10
11 5 12 9
c
2
c
6
c
3
c
1
c
7
c
10
c
5
c
12
c
9
c
4
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h5.75581 × 10
60
u
115
+ 1.98417 × 10
61
u
114
+ ··· + 6.45264 × 10
60
b − 1.60343 × 10
61
,
5.07246 × 10
60
u
115
+ 7.72531 × 10
60
u
114
+ ··· + 2.15088 × 10
60
a − 6.26357 × 10
60
, u
116
+ 2u
115
+ ··· − 5u − 1i
I
u
2
= h6u
4
− 24u
3
+ 33u
2
+ 17b − 20u − 2, u
4
− 4u
3
+ 14u
2
+ 17a − 9u + 11, u
5
− u
4
+ 2u
3
− u
2
+ u − 1i
* 2 irreducible components of dim
C
= 0, with total 121 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
= h5.76 × 10
60
u
115
+ 1.98 × 10
61
u
114
+ · · · + 6.45 × 10
60
b − 1.60 ×
10
61
, 5.07 × 10
60
u
115
+ 7.73 × 10
60
u
114
+ · · · + 2.15 × 10
60
a − 6.26 ×
10
60
, u
116
+ 2u
115
+ · · · − 5u − 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
u
2
a
7
=
u
u
3
+ u
a
4
=
u
4
+ u
2
+ 1
u
6
+ 2u
4
+ u
2
a
1
=
u
2
+ 1
u
2
a
8
=
−u
7
− 2u
5
− 2u
3
−u
7
− u
5
+ u
a
10
=
−2.35832u
115
− 3.59170u
114
+ ··· + 5.62431u + 2.91210
−0.892009u
115
− 3.07497u
114
+ ··· + 6.78907u + 2.48492
a
11
=
−0.666357u
115
− 0.411615u
114
+ ··· − 1.02339u + 1.71894
0.244543u
115
− 0.720314u
114
+ ··· + 1.56448u + 1.23807
a
5
=
−2.30584u
115
− 3.63509u
114
+ ··· + 5.89997u + 2.09097
−0.964992u
115
− 1.49301u
114
+ ··· + 3.05675u + 0.534737
a
12
=
−2.56113u
115
− 3.41397u
114
+ ··· + 3.10597u + 3.15038
−0.809371u
115
− 2.81370u
114
+ ··· + 6.08982u + 2.24085
a
9
=
−0.00487807u
115
− 1.44058u
114
+ ··· + 9.57972u + 1.72391
−0.539615u
115
− 1.54506u
114
+ ··· + 5.14801u + 1.34085
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4.97176u
115
+ 8.14134u
114
+ ··· − 7.30434u + 7.67511
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
116
+ 54u
115
+ ··· − 11u + 1
c
2
, c
6
u
116
− 2u
115
+ ··· + 5u − 1
c
3
u
116
+ 2u
115
+ ··· + 35u − 425
c
4
, c
8
u
116
+ 2u
115
+ ··· + u − 1
c
5
u
116
+ u
115
+ ··· − 76160u + 9248
c
7
u
116
− 10u
115
+ ··· + 3962235u − 436275
c
9
, c
12
u
116
+ 6u
115
+ ··· + 3349u − 289
c
10
17(17u
116
− 49u
115
+ ··· + 4.80276 × 10
8
u + 5.07692 × 10
7
)
c
11
17(17u
116
+ 127u
115
+ ··· − 6.60670 × 10
8
u + 1.85956 × 10
8
)
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
116
+ 18y
115
+ ··· − 203y + 1
c
2
, c
6
y
116
+ 54y
115
+ ··· − 11y + 1
c
3
y
116
− 18y
115
+ ··· − 14809075y + 180625
c
4
, c
8
y
116
+ 78y
115
+ ··· − 11y + 1
c
5
y
116
− 33y
115
+ ··· − 5184058880y + 85525504
c
7
y
116
+ 54y
115
+ ··· + 2904898639725y + 190335875625
c
9
, c
12
y
116
− 94y
115
+ ··· − 10562661y + 83521
c
10
289(289y
116
− 735y
115
+ ··· − 8.40142 × 10
16
y + 2.57752 × 10
15
)
c
11
289(289y
116
− 35645y
115
+ ··· − 9.53692 × 10
17
y + 3.45798 × 10
16
)
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.213726 + 0.979678I
a = 1.60090 + 0.53449I
b = 1.83411 − 0.89425I
0.167995 + 0.526081I 0
u = −0.213726 − 0.979678I
a = 1.60090 − 0.53449I
b = 1.83411 + 0.89425I
0.167995 − 0.526081I 0
u = 0.125887 + 0.978569I
a = 1.70020 − 0.61531I
b = 1.366030 + 0.140718I
4.35805 − 1.96715I 0
u = 0.125887 − 0.978569I
a = 1.70020 + 0.61531I
b = 1.366030 − 0.140718I
4.35805 + 1.96715I 0
u = 0.309540 + 0.933467I
a = 0.112007 − 0.737693I
b = 1.93325 − 1.81475I
0.77750 + 1.28815I 0
u = 0.309540 − 0.933467I
a = 0.112007 + 0.737693I
b = 1.93325 + 1.81475I
0.77750 − 1.28815I 0
u = 0.743846 + 0.630403I
a = 1.90685 + 1.03273I
b = −0.22355 + 1.92834I
10.83050 − 1.67305I 0
u = 0.743846 − 0.630403I
a = 1.90685 − 1.03273I
b = −0.22355 − 1.92834I
10.83050 + 1.67305I 0
u = −0.751758 + 0.607698I
a = 1.95762 − 1.27271I
b = −0.39410 − 1.79230I
6.55718 − 4.78302I 0
u = −0.751758 − 0.607698I
a = 1.95762 + 1.27271I
b = −0.39410 + 1.79230I
6.55718 + 4.78302I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.738019 + 0.605133I
a = 2.08860 + 1.33989I
b = −0.58143 + 1.83889I
11.3529 + 10.6244I 0
u = 0.738019 − 0.605133I
a = 2.08860 − 1.33989I
b = −0.58143 − 1.83889I
11.3529 − 10.6244I 0
u = −0.236713 + 1.018870I
a = 0.376854 − 0.678326I
b = −0.900450 − 1.066460I
−0.027406 − 1.051670I 0
u = −0.236713 − 1.018870I
a = 0.376854 + 0.678326I
b = −0.900450 + 1.066460I
−0.027406 + 1.051670I 0
u = 0.319760 + 1.015070I
a = −2.16164 + 3.60624I
b = −7.18790 − 1.77810I
1.33619 + 0.84695I 0
u = 0.319760 − 1.015070I
a = −2.16164 − 3.60624I
b = −7.18790 + 1.77810I
1.33619 − 0.84695I 0
u = 0.447876 + 0.971546I
a = −0.044939 + 1.030310I
b = −0.0173674 − 0.0369021I
2.76198 + 4.91396I 0
u = 0.447876 − 0.971546I
a = −0.044939 − 1.030310I
b = −0.0173674 + 0.0369021I
2.76198 − 4.91396I 0
u = −0.387226 + 0.997733I
a = −0.479626 − 0.904983I
b = −0.853551 + 0.688235I
−0.83470 − 2.75967I 0
u = −0.387226 − 0.997733I
a = −0.479626 + 0.904983I
b = −0.853551 − 0.688235I
−0.83470 + 2.75967I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.180477 + 1.077350I
a = 0.552778 + 1.052860I
b = 0.411909 − 0.007067I
−0.03499 + 4.92088I 0
u = −0.180477 − 1.077350I
a = 0.552778 − 1.052860I
b = 0.411909 + 0.007067I
−0.03499 − 4.92088I 0
u = −0.826428 + 0.374638I
a = 1.16217 − 2.07695I
b = −0.69074 − 1.49489I
9.38100 + 1.35019I 0
u = −0.826428 − 0.374638I
a = 1.16217 + 2.07695I
b = −0.69074 + 1.49489I
9.38100 − 1.35019I 0
u = −0.371827 + 0.824359I
a = 0.707381 − 0.378871I
b = 1.156950 + 0.662434I
4.93896 − 1.72487I 0
u = −0.371827 − 0.824359I
a = 0.707381 + 0.378871I
b = 1.156950 − 0.662434I
4.93896 + 1.72487I 0
u = 0.813710 + 0.390654I
a = 1.65938 + 2.30133I
b = −0.47737 + 1.91274I
5.35441 − 7.81379I 0
u = 0.813710 − 0.390654I
a = 1.65938 − 2.30133I
b = −0.47737 − 1.91274I
5.35441 + 7.81379I 0
u = 0.214588 + 1.080830I
a = 0.237087 − 0.533447I
b = 0.002009 + 0.228143I
−3.44211 − 1.31744I 0
u = 0.214588 − 1.080830I
a = 0.237087 + 0.533447I
b = 0.002009 − 0.228143I
−3.44211 + 1.31744I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.806147 + 0.384835I
a = 1.75293 − 2.64831I
b = −0.59316 − 2.20336I
10.1438 + 13.5286I 0
u = −0.806147 − 0.384835I
a = 1.75293 + 2.64831I
b = −0.59316 + 2.20336I
10.1438 − 13.5286I 0
u = 0.684803 + 0.538931I
a = 0.356592 − 0.731019I
b = 1.144010 + 0.473688I
5.38099 + 4.74367I 0
u = 0.684803 − 0.538931I
a = 0.356592 + 0.731019I
b = 1.144010 − 0.473688I
5.38099 − 4.74367I 0
u = −0.716074 + 0.485984I
a = −1.56043 + 1.94624I
b = 1.28088 + 1.50181I
9.28238 − 1.11602I 13.84835 + 0.I
u = −0.716074 − 0.485984I
a = −1.56043 − 1.94624I
b = 1.28088 − 1.50181I
9.28238 + 1.11602I 13.84835 + 0.I
u = 0.735710 + 0.444784I
a = −2.10447 − 2.13484I
b = 0.58715 − 2.40571I
9.06427 − 3.60222I 13.25447 + 0.I
u = 0.735710 − 0.444784I
a = −2.10447 + 2.13484I
b = 0.58715 + 2.40571I
9.06427 + 3.60222I 13.25447 + 0.I
u = −0.751426 + 0.398872I
a = −1.331980 + 0.280135I
b = −0.65647 + 1.33074I
4.65190 + 7.12858I 8.00466 − 6.45034I
u = −0.751426 − 0.398872I
a = −1.331980 − 0.280135I
b = −0.65647 − 1.33074I
4.65190 − 7.12858I 8.00466 + 6.45034I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.158418 + 1.151430I
a = −1.74281 − 0.26217I
b = −1.73088 + 0.55675I
5.05609 + 10.97800I 0
u = −0.158418 − 1.151430I
a = −1.74281 + 0.26217I
b = −1.73088 − 0.55675I
5.05609 − 10.97800I 0
u = −0.407944 + 1.088610I
a = −0.970445 − 0.729417I
b = −0.746780 + 0.242375I
−2.10001 − 6.03359I 0
u = −0.407944 − 1.088610I
a = −0.970445 + 0.729417I
b = −0.746780 − 0.242375I
−2.10001 + 6.03359I 0
u = 0.647035 + 0.966883I
a = 0.60997 + 1.62296I
b = −1.15036 + 2.56312I
9.82905 + 6.94446I 0
u = 0.647035 − 0.966883I
a = 0.60997 − 1.62296I
b = −1.15036 − 2.56312I
9.82905 − 6.94446I 0
u = −0.644975 + 0.529795I
a = 0.317585 − 0.144452I
b = 0.444610 − 0.522513I
1.80492 − 1.53618I 3.15801 + 3.61737I
u = −0.644975 − 0.529795I
a = 0.317585 + 0.144452I
b = 0.444610 + 0.522513I
1.80492 + 1.53618I 3.15801 − 3.61737I
u = 0.689493 + 0.467421I
a = −2.87010 − 1.03664I
b = 0.09768 − 1.55760I
4.67202 + 0.02612I 5.05104 + 0.I
u = 0.689493 − 0.467421I
a = −2.87010 + 1.03664I
b = 0.09768 + 1.55760I
4.67202 − 0.02612I 5.05104 + 0.I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.710222 + 0.434714I
a = −1.75555 + 2.99422I
b = 0.84628 + 2.17663I
4.49672 + 2.23779I 5.47097 − 1.27314I
u = −0.710222 − 0.434714I
a = −1.75555 − 2.99422I
b = 0.84628 − 2.17663I
4.49672 − 2.23779I 5.47097 + 1.27314I
u = 0.374555 + 1.106800I
a = −0.745632 + 0.391856I
b = −0.565566 − 0.009069I
−4.95014 + 1.97544I 0
u = 0.374555 − 1.106800I
a = −0.745632 − 0.391856I
b = −0.565566 + 0.009069I
−4.95014 − 1.97544I 0
u = 0.145684 + 1.159730I
a = −1.47907 + 0.20648I
b = −1.61847 − 0.35202I
0.17052 − 5.27151I 0
u = 0.145684 − 1.159730I
a = −1.47907 − 0.20648I
b = −1.61847 + 0.35202I
0.17052 + 5.27151I 0
u = −0.552992 + 1.030300I
a = 0.343583 − 0.419278I
b = −0.529664 − 0.227199I
0.31815 − 3.15390I 0
u = −0.552992 − 1.030300I
a = 0.343583 + 0.419278I
b = −0.529664 + 0.227199I
0.31815 + 3.15390I 0
u = −0.449021 + 1.080700I
a = 0.697371 − 0.733803I
b = −0.81172 − 1.64241I
−1.83928 − 1.16536I 0
u = −0.449021 − 1.080700I
a = 0.697371 + 0.733803I
b = −0.81172 + 1.64241I
−1.83928 + 1.16536I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.734193 + 0.382672I
a = −0.363486 − 0.221446I
b = −0.252124 − 0.679881I
1.04420 − 3.63453I 2.00000 + 3.37564I
u = 0.734193 − 0.382672I
a = −0.363486 + 0.221446I
b = −0.252124 + 0.679881I
1.04420 + 3.63453I 2.00000 − 3.37564I
u = 0.636595 + 0.984802I
a = 0.71956 + 1.68566I
b = −0.73241 + 2.95425I
10.22580 − 5.40240I 0
u = 0.636595 − 0.984802I
a = 0.71956 − 1.68566I
b = −0.73241 − 2.95425I
10.22580 + 5.40240I 0
u = 0.826337
a = 0.752087
b = −0.356164
−0.424621 19.7700
u = 0.578311 + 1.021470I
a = −0.325740 + 0.405044I
b = −1.47077 − 0.57548I
3.95182 + 0.14125I 0
u = 0.578311 − 1.021470I
a = −0.325740 − 0.405044I
b = −1.47077 + 0.57548I
3.95182 − 0.14125I 0
u = −0.648829 + 0.986349I
a = 0.69438 − 1.65109I
b = −0.81010 − 2.70604I
5.43273 − 0.51549I 0
u = −0.648829 − 0.986349I
a = 0.69438 + 1.65109I
b = −0.81010 + 2.70604I
5.43273 + 0.51549I 0
u = −0.341593 + 0.739889I
a = 0.491846 − 0.519334I
b = −0.650693 − 0.657690I
−0.07351 − 1.53899I −0.35735 + 4.62669I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.341593 − 0.739889I
a = 0.491846 + 0.519334I
b = −0.650693 + 0.657690I
−0.07351 + 1.53899I −0.35735 − 4.62669I
u = −0.702246 + 0.400107I
a = 1.66196 + 0.97308I
b = 1.088350 + 0.037803I
4.18759 + 0.99207I 8.76986 + 0.I
u = −0.702246 − 0.400107I
a = 1.66196 − 0.97308I
b = 1.088350 − 0.037803I
4.18759 − 0.99207I 8.76986 + 0.I
u = 0.551493 + 1.056650I
a = 2.34626 + 0.85733I
b = 1.41245 + 2.07391I
2.91340 + 5.62132I 0
u = 0.551493 − 1.056650I
a = 2.34626 − 0.85733I
b = 1.41245 − 2.07391I
2.91340 − 5.62132I 0
u = −0.170661 + 1.184020I
a = −1.317040 + 0.124672I
b = −1.237580 + 0.310417I
4.20227 − 1.40731I 0
u = −0.170661 − 1.184020I
a = −1.317040 − 0.124672I
b = −1.237580 − 0.310417I
4.20227 + 1.40731I 0
u = 0.637926 + 0.481213I
a = 0.31869 + 2.12232I
b = −0.247274 + 0.566263I
4.62411 − 0.94935I 11.70670 + 0.13383I
u = 0.637926 − 0.481213I
a = 0.31869 − 2.12232I
b = −0.247274 − 0.566263I
4.62411 + 0.94935I 11.70670 − 0.13383I
u = 0.573566 + 1.061840I
a = −0.29785 − 2.25510I
b = 1.55526 − 3.19666I
2.91832 + 4.85580I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.573566 − 1.061840I
a = −0.29785 + 2.25510I
b = 1.55526 + 3.19666I
2.91832 − 4.85580I 0
u = −0.589394 + 1.056650I
a = −1.20022 + 1.15722I
b = −0.28853 + 3.39941I
7.59396 − 3.88847I 0
u = −0.589394 − 1.056650I
a = −1.20022 − 1.15722I
b = −0.28853 − 3.39941I
7.59396 + 3.88847I 0
u = 0.476904 + 1.120410I
a = 0.501150 + 0.454538I
b = −0.31692 + 1.52578I
−4.25414 + 5.60705I 0
u = 0.476904 − 1.120410I
a = 0.501150 − 0.454538I
b = −0.31692 − 1.52578I
−4.25414 − 5.60705I 0
u = −0.577539 + 1.078690I
a = −2.11320 + 1.66372I
b = −0.17083 + 4.02607I
2.60273 − 7.18374I 0
u = −0.577539 − 1.078690I
a = −2.11320 − 1.66372I
b = −0.17083 − 4.02607I
2.60273 + 7.18374I 0
u = −0.566964 + 1.089470I
a = −1.05362 − 1.05257I
b = −1.68561 + 0.12365I
2.17207 − 5.87574I 0
u = −0.566964 − 1.089470I
a = −1.05362 + 1.05257I
b = −1.68561 − 0.12365I
2.17207 + 5.87574I 0
u = 0.589893 + 1.079910I
a = −1.51806 − 1.70782I
b = 0.76044 − 3.88756I
7.18842 + 8.65606I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.589893 − 1.079910I
a = −1.51806 + 1.70782I
b = 0.76044 + 3.88756I
7.18842 − 8.65606I 0
u = −0.402416 + 1.170640I
a = −0.558708 + 0.087620I
b = −0.013361 − 0.491838I
1.32732 + 2.51230I 0
u = −0.402416 − 1.170640I
a = −0.558708 − 0.087620I
b = −0.013361 + 0.491838I
1.32732 − 2.51230I 0
u = −0.443018 + 1.159920I
a = 0.275598 + 0.078688I
b = 0.17555 − 1.44020I
1.60686 − 10.79070I 0
u = −0.443018 − 1.159920I
a = 0.275598 − 0.078688I
b = 0.17555 + 1.44020I
1.60686 + 10.79070I 0
u = 0.574854 + 1.102970I
a = −0.311171 − 0.375018I
b = 0.672540 − 0.546778I
−1.06723 + 8.62177I 0
u = 0.574854 − 1.102970I
a = −0.311171 + 0.375018I
b = 0.672540 + 0.546778I
−1.06723 − 8.62177I 0
u = −0.584507 + 1.101830I
a = −0.289837 + 1.073540I
b = 1.64161 + 1.26609I
2.58041 − 12.19620I 0
u = −0.584507 − 1.101830I
a = −0.289837 − 1.073540I
b = 1.64161 − 1.26609I
2.58041 + 12.19620I 0
u = −0.746532 + 0.035193I
a = 0.300992 − 0.466186I
b = −0.724441 − 0.419011I
4.88516 + 6.54091I 7.04632 − 5.66501I
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.746532 − 0.035193I
a = 0.300992 + 0.466186I
b = −0.724441 + 0.419011I
4.88516 − 6.54091I 7.04632 + 5.66501I
u = −0.599085 + 1.123350I
a = 1.78094 − 1.65645I
b = −0.02174 − 3.95945I
7.9462 − 18.7856I 0
u = −0.599085 − 1.123350I
a = 1.78094 + 1.65645I
b = −0.02174 + 3.95945I
7.9462 + 18.7856I 0
u = 0.603607 + 1.123490I
a = 1.49343 + 1.57396I
b = −0.10145 + 3.52882I
3.16983 + 13.10760I 0
u = 0.603607 − 1.123490I
a = 1.49343 − 1.57396I
b = −0.10145 − 3.52882I
3.16983 − 13.10760I 0
u = −0.604196 + 1.133820I
a = 1.29900 − 1.15047I
b = 0.30017 − 3.00439I
7.11642 − 6.67701I 0
u = −0.604196 − 1.133820I
a = 1.29900 + 1.15047I
b = 0.30017 + 3.00439I
7.11642 + 6.67701I 0
u = 0.447930 + 1.216100I
a = −0.196025 + 0.331108I
b = −0.322401 + 1.165090I
−4.07214 + 4.51567I 0
u = 0.447930 − 1.216100I
a = −0.196025 − 0.331108I
b = −0.322401 − 1.165090I
−4.07214 − 4.51567I 0
u = 0.631815 + 0.152180I
a = 0.838584 + 0.735490I
b = −0.128293 + 0.612715I
−1.56177 − 1.36213I −2.43526 + 3.51072I
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.631815 − 0.152180I
a = 0.838584 − 0.735490I
b = −0.128293 − 0.612715I
−1.56177 + 1.36213I −2.43526 − 3.51072I
u = −0.540848 + 0.029673I
a = 1.30352 − 0.93076I
b = 0.298046 − 0.822427I
0.80862 − 2.54444I 2.28912 + 3.32919I
u = −0.540848 − 0.029673I
a = 1.30352 + 0.93076I
b = 0.298046 + 0.822427I
0.80862 + 2.54444I 2.28912 − 3.32919I
u = 0.370358 + 0.278693I
a = 2.36180 + 0.08518I
b = 1.151130 − 0.099955I
4.31697 − 1.33395I 7.26914 − 0.12263I
u = 0.370358 − 0.278693I
a = 2.36180 − 0.08518I
b = 1.151130 + 0.099955I
4.31697 + 1.33395I 7.26914 + 0.12263I
u = −0.255830
a = 1.95257
b = 0.902295
1.20356 8.93350
16
II. I
u
2
= h6u
4
− 24u
3
+ 33u
2
+ 17b − 20u − 2, u
4
− 4u
3
+ 14u
2
+ 17a − 9u +
11, u
5
− u
4
+ 2u
3
− u
2
+ u − 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
u
2
a
7
=
u
u
3
+ u
a
4
=
u
4
+ u
2
+ 1
u
4
− u
3
+ u
2
+ 1
a
1
=
u
2
+ 1
u
2
a
8
=
−u
2
− 1
u
4
a
10
=
−0.0588235u
4
+ 0.235294u
3
+ ··· + 0.529412u − 0.647059
−0.352941u
4
+ 1.41176u
3
+ ··· + 1.17647u + 0.117647
a
11
=
0
−0.529412u
4
+ 1.11765u
3
+ ··· + 0.764706u + 0.176471
a
5
=
0
u
a
12
=
−0.0588235u
4
+ 0.235294u
3
+ ··· + 0.529412u + 0.352941
−0.352941u
4
+ 1.41176u
3
+ ··· + 1.17647u + 0.117647
a
9
=
−u
2
− 1
−u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
3058
289
u
4
+
4089
289
u
3
−
4307
289
u
2
+
2549
289
u −
1576
289
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
5
− 3u
4
+ 4u
3
− u
2
− u + 1
c
2
u
5
− u
4
+ 2u
3
− u
2
+ u − 1
c
3
, c
4
u
5
+ u
4
− 2u
3
− u
2
+ u − 1
c
5
u
5
c
6
u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1
c
7
u
5
+ 5u
4
+ 8u
3
+ 3u
2
− u + 1
c
8
u
5
− u
4
− 2u
3
+ u
2
+ u + 1
c
9
(u + 1)
5
c
10
17(17u
5
− 54u
4
+ 67u
3
− 38u
2
+ 10u − 1)
c
11
17(17u
5
+ 12u
4
− 4u
3
− 7u
2
+ 1)
c
12
(u − 1)
5
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1
c
2
, c
6
y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1
c
3
, c
4
, c
8
y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1
c
5
y
5
c
7
y
5
− 9y
4
+ 32y
3
− 35y
2
− 5y −1
c
9
, c
12
(y −1)
5
c
10
289(289y
5
− 638y
4
+ 725y
3
− 212y
2
+ 24y −1)
c
11
289(289y
5
− 280y
4
+ 184y
3
− 73y
2
+ 14y −1)
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.339110 + 0.822375I
a = −0.211858 + 0.793759I
b = 1.72316 + 1.44455I
1.31583 − 1.53058I 9.06178 + 5.08523I
u = −0.339110 − 0.822375I
a = −0.211858 − 0.793759I
b = 1.72316 − 1.44455I
1.31583 + 1.53058I 9.06178 − 5.08523I
u = 0.766826
a = −0.639588
b = 0.392884
−0.756147 −4.73200
u = 0.455697 + 1.200150I
a = 0.149299 − 0.337603I
b = 0.286285 − 1.144490I
−4.22763 + 4.40083I −13.0037 + 8.9390I
u = 0.455697 − 1.200150I
a = 0.149299 + 0.337603I
b = 0.286285 + 1.144490I
−4.22763 − 4.40083I −13.0037 − 8.9390I
20
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
5
− 3u
4
+ 4u
3
− u
2
− u + 1)(u
116
+ 54u
115
+ ··· − 11u + 1)
c
2
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)(u
116
− 2u
115
+ ··· + 5u − 1)
c
3
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)(u
116
+ 2u
115
+ ··· + 35u − 425)
c
4
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)(u
116
+ 2u
115
+ ··· + u − 1)
c
5
u
5
(u
116
+ u
115
+ ··· − 76160u + 9248)
c
6
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)(u
116
− 2u
115
+ ··· + 5u − 1)
c
7
(u
5
+ 5u
4
+ 8u
3
+ 3u
2
− u + 1)
· (u
116
− 10u
115
+ ··· + 3962235u − 436275)
c
8
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)(u
116
+ 2u
115
+ ··· + u − 1)
c
9
((u + 1)
5
)(u
116
+ 6u
115
+ ··· + 3349u − 289)
c
10
289(17u
5
− 54u
4
+ 67u
3
− 38u
2
+ 10u − 1)
· (17u
116
− 49u
115
+ ··· + 480276280u + 50769239)
c
11
289(17u
5
+ 12u
4
− 4u
3
− 7u
2
+ 1)
· (17u
116
+ 127u
115
+ ··· − 660669734u + 185956423)
c
12
((u − 1)
5
)(u
116
+ 6u
115
+ ··· + 3349u − 289)
21
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)(y
116
+ 18y
115
+ ··· − 203y + 1)
c
2
, c
6
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)(y
116
+ 54y
115
+ ··· − 11y + 1)
c
3
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
· (y
116
− 18y
115
+ ··· − 14809075y + 180625)
c
4
, c
8
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)(y
116
+ 78y
115
+ ··· − 11y + 1)
c
5
y
5
(y
116
− 33y
115
+ ··· − 5.18406 × 10
9
y + 8.55255 × 10
7
)
c
7
(y
5
− 9y
4
+ 32y
3
− 35y
2
− 5y −1)
· (y
116
+ 54y
115
+ ··· + 2904898639725y + 190335875625)
c
9
, c
12
((y −1)
5
)(y
116
− 94y
115
+ ··· − 1.05627 × 10
7
y + 83521)
c
10
83521(289y
5
− 638y
4
+ 725y
3
− 212y
2
+ 24y −1)
· (289y
116
− 735y
115
+ ··· − 8.40 × 10
16
y + 2.58 × 10
15
)
c
11
83521(289y
5
− 280y
4
+ 184y
3
− 73y
2
+ 14y −1)
· (289y
116
− 3.56 × 10
4
y
115
+ ··· − 9.54 × 10
17
y + 3.46 × 10
16
)
22
