12a
0832
(K12a
0832
)
A knot diagram
1
Linearized knot diagam
4 5 8 2 12 9 3 11 6 1 7 10
Solving Sequence
1,4
2 5
3,10
12 6 9 7 8 11
c
1
c
4
c
2
c
12
c
5
c
9
c
6
c
7
c
11
c
3
, c
8
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h1.82100 × 10
145
u
106
+ 1.76856 × 10
146
u
105
+ ··· + 2.34604 × 10
144
b + 1.63398 × 10
145
,
− 9.00860 × 10
144
u
106
− 8.87315 × 10
145
u
105
+ ··· + 3.11583 × 10
143
a − 8.18986 × 10
144
,
u
107
+ 11u
106
+ ··· − u + 1i
I
u
2
= hb
9
− b
8
− 2b
7
+ 3b
6
+ b
5
− 3b
4
+ 2b
3
− b + 1, a − 1, u − 1i
I
u
3
= hb + 1, −12u
2
+ 17a − 11u + 8, u
3
+ u
2
− 1i
* 3 irreducible components of dim
C
= 0, with total 119 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
= h1.82 × 10
145
u
106
+ 1.77 × 10
146
u
105
+ · · · + 2.35 × 10
144
b + 1.63 ×
10
145
, −9.01 × 10
144
u
106
− 8.87 × 10
145
u
105
+ · · · + 3.12 × 10
143
a − 8.19 ×
10
144
, u
107
+ 11u
106
+ · · · − u + 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
5
=
−u
−u
3
+ u
a
3
=
−u
2
+ 1
−u
4
+ 2u
2
a
10
=
28.9123u
106
+ 284.776u
105
+ ··· − 57.4382u + 26.2847
−7.76201u
106
− 75.3850u
105
+ ··· + 12.3022u − 6.96486
a
12
=
35.3044u
106
+ 346.752u
105
+ ··· − 60.1629u + 30.1321
11.0948u
106
+ 107.535u
105
+ ··· − 11.2109u + 7.50499
a
6
=
−225.444u
106
− 2126.33u
105
+ ··· + 217.402u − 139.053
−3.47317u
106
− 15.3113u
105
+ ··· − 22.8525u + 7.66552
a
9
=
152.968u
106
+ 1511.32u
105
+ ··· − 222.234u + 128.653
85.3954u
106
+ 812.499u
105
+ ··· − 90.9059u + 55.8114
a
7
=
−4.74413u
106
− 45.0876u
105
+ ··· + 1.45576u − 3.57826
−1.77398u
106
− 16.9646u
105
+ ··· + 0.374396u − 0.558079
a
8
=
4.11969u
106
+ 39.2305u
105
+ ··· − 8.20858u + 1.92021
2.41999u
106
+ 24.9542u
105
+ ··· − 5.96901u + 3.00759
a
11
=
36.6743u
106
+ 360.161u
105
+ ··· − 69.7404u + 33.2495
−7.76201u
106
− 75.3850u
105
+ ··· + 12.3022u − 6.96486
(ii) Obstruction class = −1
(iii) Cusp Shapes = −205.058u
106
− 2014.48u
105
+ ··· + 295.936u − 174.019
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
4
u
107
− 11u
106
+ ··· − u − 1
c
3
, c
7
u
107
− 2u
106
+ ··· − 512u + 512
c
5
17(17u
107
+ 96u
106
+ ··· − 2.67194 × 10
8
u + 4.35330 × 10
7
)
c
6
, c
9
u
107
+ 3u
106
+ ··· − 3u − 1
c
8
17(17u
107
+ 61u
106
+ ··· + 4.98410 × 10
7
u − 2813417)
c
10
, c
12
u
107
− 5u
106
+ ··· − 5466u − 289
c
11
u
107
+ 2u
106
+ ··· − 10404u + 2312
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
y
107
− 99y
106
+ ··· − 29y −1
c
3
, c
7
y
107
− 54y
106
+ ··· + 7340032y −262144
c
5
289(289y
107
− 19076y
106
+ ··· + 8.77063 × 10
16
y −1.89512 × 10
15
)
c
6
, c
9
y
107
+ 73y
106
+ ··· + 55y −1
c
8
289
· (289y
107
− 7971y
106
+ ··· + 1153422073109755y −7915315215889)
c
10
, c
12
y
107
− 81y
106
+ ··· + 6093612y −83521
c
11
y
107
− 18y
106
+ ··· + 277740560y −5345344
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.346089 + 0.926510I
a = 0.488603 − 1.149700I
b = 1.44877 + 0.53359I
−7.4189 − 13.7965I 0
u = 0.346089 − 0.926510I
a = 0.488603 + 1.149700I
b = 1.44877 − 0.53359I
−7.4189 + 13.7965I 0
u = 0.369955 + 0.942148I
a = 0.573386 − 0.891132I
b = 1.249130 + 0.376668I
−2.55413 − 8.13238I 0
u = 0.369955 − 0.942148I
a = 0.573386 + 0.891132I
b = 1.249130 − 0.376668I
−2.55413 + 8.13238I 0
u = 0.928095 + 0.328024I
a = 1.067700 − 0.348911I
b = 0.122990 + 0.398571I
−0.769990 − 0.237218I 0
u = 0.928095 − 0.328024I
a = 1.067700 + 0.348911I
b = 0.122990 − 0.398571I
−0.769990 + 0.237218I 0
u = 0.319909 + 1.003060I
a = 0.300455 − 0.534456I
b = 1.246370 + 0.010174I
−6.46600 − 1.47782I 0
u = 0.319909 − 1.003060I
a = 0.300455 + 0.534456I
b = 1.246370 − 0.010174I
−6.46600 + 1.47782I 0
u = 0.945816
a = 2.59957
b = −0.936011
−3.02083 0
u = 1.049800 + 0.152492I
a = 2.59795 + 1.35800I
b = −1.182570 − 0.120195I
−5.90093 − 0.77524I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.049800 − 0.152492I
a = 2.59795 − 1.35800I
b = −1.182570 + 0.120195I
−5.90093 + 0.77524I 0
u = 0.771747 + 0.482029I
a = 1.166080 − 0.347003I
b = −0.311412 + 1.048800I
−3.78091 + 2.99219I 0
u = 0.771747 − 0.482029I
a = 1.166080 + 0.347003I
b = −0.311412 − 1.048800I
−3.78091 − 2.99219I 0
u = −0.828331 + 0.756192I
a = 0.891464 + 0.459958I
b = 1.003920 − 0.044300I
1.38178 + 2.91494I 0
u = −0.828331 − 0.756192I
a = 0.891464 − 0.459958I
b = 1.003920 + 0.044300I
1.38178 − 2.91494I 0
u = 0.343042 + 0.788869I
a = −0.336263 + 0.963037I
b = −0.149645 − 1.288650I
−2.37272 − 7.54825I 0
u = 0.343042 − 0.788869I
a = −0.336263 − 0.963037I
b = −0.149645 + 1.288650I
−2.37272 + 7.54825I 0
u = 0.922174 + 0.690097I
a = 0.581180 − 0.416925I
b = 1.43011 − 0.44307I
−9.14754 + 8.24261I 0
u = 0.922174 − 0.690097I
a = 0.581180 + 0.416925I
b = 1.43011 + 0.44307I
−9.14754 − 8.24261I 0
u = 0.448171 + 0.709899I
a = −0.18414 + 1.45497I
b = −1.55514 − 0.73695I
−6.91732 − 4.41662I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.448171 − 0.709899I
a = −0.18414 − 1.45497I
b = −1.55514 + 0.73695I
−6.91732 + 4.41662I 0
u = 0.557495 + 0.610684I
a = 0.362867 + 0.478199I
b = −1.65203 + 0.47475I
−7.33756 − 0.07613I 0
u = 0.557495 − 0.610684I
a = 0.362867 − 0.478199I
b = −1.65203 − 0.47475I
−7.33756 + 0.07613I 0
u = 0.759499 + 0.321795I
a = 1.330620 + 0.358278I
b = −0.378863 − 0.498684I
−3.58750 − 2.31232I 0
u = 0.759499 − 0.321795I
a = 1.330620 − 0.358278I
b = −0.378863 + 0.498684I
−3.58750 + 2.31232I 0
u = 0.289663 + 0.766909I
a = 0.002340 + 0.697636I
b = 0.077224 − 0.771549I
1.09835 − 3.92237I 0
u = 0.289663 − 0.766909I
a = 0.002340 − 0.697636I
b = 0.077224 + 0.771549I
1.09835 + 3.92237I 0
u = 0.926197 + 0.743885I
a = 0.720813 − 0.394658I
b = 1.217190 − 0.229736I
−4.18081 + 2.37986I 0
u = 0.926197 − 0.743885I
a = 0.720813 + 0.394658I
b = 1.217190 + 0.229736I
−4.18081 − 2.37986I 0
u = −1.195860 + 0.071246I
a = 0.834976 + 0.099978I
b = 1.081680 − 0.553383I
−5.80226 + 7.40735I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.195860 − 0.071246I
a = 0.834976 − 0.099978I
b = 1.081680 + 0.553383I
−5.80226 − 7.40735I 0
u = −0.319822 + 0.706800I
a = 0.185472 + 0.770438I
b = 1.180450 + 0.258145I
−3.77986 − 4.80948I 0
u = −0.319822 − 0.706800I
a = 0.185472 − 0.770438I
b = 1.180450 − 0.258145I
−3.77986 + 4.80948I 0
u = 1.012440 + 0.691885I
a = 0.826522 − 0.541378I
b = 1.304000 + 0.146196I
−8.58798 − 4.36356I 0
u = 1.012440 − 0.691885I
a = 0.826522 + 0.541378I
b = 1.304000 − 0.146196I
−8.58798 + 4.36356I 0
u = 0.391589 + 0.655721I
a = −0.43938 + 1.82965I
b = −1.073250 − 0.329860I
−2.56341 − 2.94691I 0
u = 0.391589 − 0.655721I
a = −0.43938 − 1.82965I
b = −1.073250 + 0.329860I
−2.56341 + 2.94691I 0
u = 0.316249 + 0.663493I
a = 1.258330 + 0.584184I
b = −0.209859 + 0.022387I
−2.30486 − 1.44330I 0
u = 0.316249 − 0.663493I
a = 1.258330 − 0.584184I
b = −0.209859 − 0.022387I
−2.30486 + 1.44330I 0
u = −1.263060 + 0.081449I
a = 0.824442 + 0.083550I
b = 0.727801 − 0.763902I
−0.72189 + 2.74860I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.263060 − 0.081449I
a = 0.824442 − 0.083550I
b = 0.727801 + 0.763902I
−0.72189 − 2.74860I 0
u = 1.272250 + 0.106081I
a = 0.98579 + 1.17507I
b = −0.362733 + 0.158221I
−4.76982 + 0.36186I 0
u = 1.272250 − 0.106081I
a = 0.98579 − 1.17507I
b = −0.362733 − 0.158221I
−4.76982 − 0.36186I 0
u = 0.451827 + 0.536220I
a = −0.943034 − 0.499437I
b = −1.144990 + 0.140910I
−2.97691 − 0.95326I 0
u = 0.451827 − 0.536220I
a = −0.943034 + 0.499437I
b = −1.144990 − 0.140910I
−2.97691 + 0.95326I 0
u = 1.302530 + 0.041153I
a = −3.09240 + 1.07743I
b = −1.110650 − 0.240588I
−4.79638 − 0.98699I 0
u = 1.302530 − 0.041153I
a = −3.09240 − 1.07743I
b = −1.110650 + 0.240588I
−4.79638 + 0.98699I 0
u = 1.299920 + 0.168546I
a = −0.107981 − 0.443207I
b = 0.000911 − 0.644871I
−1.66924 − 1.97469I 0
u = 1.299920 − 0.168546I
a = −0.107981 + 0.443207I
b = 0.000911 + 0.644871I
−1.66924 + 1.97469I 0
u = −1.313370 + 0.054285I
a = 0.854577 + 0.008414I
b = 0.476146 − 0.988851I
−3.84509 − 1.95256I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.313370 − 0.054285I
a = 0.854577 − 0.008414I
b = 0.476146 + 0.988851I
−3.84509 + 1.95256I 0
u = −0.408891 + 0.536151I
a = 1.21817 + 1.32334I
b = 1.308990 − 0.468518I
−4.39157 + 8.45275I 0
u = −0.408891 − 0.536151I
a = 1.21817 − 1.32334I
b = 1.308990 + 0.468518I
−4.39157 − 8.45275I 0
u = −0.509411 + 0.390374I
a = 1.43737 + 0.68564I
b = 0.906539 − 0.320701I
0.99398 + 2.92097I −2.14055 − 8.38546I
u = −0.509411 − 0.390374I
a = 1.43737 − 0.68564I
b = 0.906539 + 0.320701I
0.99398 − 2.92097I −2.14055 + 8.38546I
u = 1.352810 + 0.144917I
a = −0.889798 − 1.006880I
b = −0.249790 − 1.218930I
−5.05564 − 5.39819I 0
u = 1.352810 − 0.144917I
a = −0.889798 + 1.006880I
b = −0.249790 + 1.218930I
−5.05564 + 5.39819I 0
u = 1.361330 + 0.043746I
a = −2.95745 − 0.20957I
b = −1.62298 − 0.62301I
−9.17182 − 2.19773I 0
u = 1.361330 − 0.043746I
a = −2.95745 + 0.20957I
b = −1.62298 + 0.62301I
−9.17182 + 2.19773I 0
u = −1.42504 + 0.19094I
a = −0.67013 + 2.22749I
b = −0.879710 − 0.127697I
−8.99268 + 4.16407I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.42504 − 0.19094I
a = −0.67013 − 2.22749I
b = −0.879710 + 0.127697I
−8.99268 − 4.16407I 0
u = −1.43432 + 0.14706I
a = −0.0676959 + 0.0171999I
b = −0.587535 − 0.726567I
−6.76847 + 1.51759I 0
u = −1.43432 − 0.14706I
a = −0.0676959 − 0.0171999I
b = −0.587535 + 0.726567I
−6.76847 − 1.51759I 0
u = −1.42121 + 0.25982I
a = 0.411496 − 0.593144I
b = −0.216513 + 0.240799I
−7.84058 + 4.80609I 0
u = −1.42121 − 0.25982I
a = 0.411496 + 0.593144I
b = −0.216513 − 0.240799I
−7.84058 − 4.80609I 0
u = −0.086365 + 0.547685I
a = −0.300133 − 0.166796I
b = 0.372416 + 0.585011I
2.60177 − 0.62792I −0.78766 + 2.26745I
u = −0.086365 − 0.547685I
a = −0.300133 + 0.166796I
b = 0.372416 − 0.585011I
2.60177 + 0.62792I −0.78766 − 2.26745I
u = 0.233580 + 0.482684I
a = 5.29654 − 3.52833I
b = −0.967668 − 0.083362I
−3.50386 − 1.66896I −16.6348 − 15.7652I
u = 0.233580 − 0.482684I
a = 5.29654 + 3.52833I
b = −0.967668 + 0.083362I
−3.50386 + 1.66896I −16.6348 + 15.7652I
u = −1.43555 + 0.29816I
a = −0.355414 + 0.224137I
b = 0.037878 + 0.954929I
−4.44227 + 7.78550I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.43555 − 0.29816I
a = −0.355414 − 0.224137I
b = 0.037878 − 0.954929I
−4.44227 − 7.78550I 0
u = −1.45576 + 0.20589I
a = −2.32395 − 0.20632I
b = −1.280390 − 0.132160I
−9.07128 + 3.71874I 0
u = −1.45576 − 0.20589I
a = −2.32395 + 0.20632I
b = −1.280390 + 0.132160I
−9.07128 − 3.71874I 0
u = 1.45585 + 0.21194I
a = 2.40050 − 0.71952I
b = 1.45479 + 0.48867I
−10.4011 − 11.2730I 0
u = 1.45585 − 0.21194I
a = 2.40050 + 0.71952I
b = 1.45479 − 0.48867I
−10.4011 + 11.2730I 0
u = −1.47174 + 0.12909I
a = −0.150092 − 0.748850I
b = −0.77291 − 1.28610I
−10.74750 − 1.26365I 0
u = −1.47174 − 0.12909I
a = −0.150092 + 0.748850I
b = −0.77291 + 1.28610I
−10.74750 + 1.26365I 0
u = −1.45743 + 0.24242I
a = −1.77794 − 1.17322I
b = −1.167620 + 0.444078I
−8.52536 + 6.22901I 0
u = −1.45743 − 0.24242I
a = −1.77794 + 1.17322I
b = −1.167620 − 0.444078I
−8.52536 − 6.22901I 0
u = −1.45823 + 0.30150I
a = −0.881779 + 0.470057I
b = −0.12006 + 1.46337I
−8.16809 + 11.50410I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.45823 − 0.30150I
a = −0.881779 − 0.470057I
b = −0.12006 − 1.46337I
−8.16809 − 11.50410I 0
u = 0.504337
a = 1.43138
b = −0.210755
−0.940432 −9.73200
u = 1.48188 + 0.20581I
a = 2.10311 − 0.59020I
b = 1.254090 + 0.304222I
−5.51395 − 5.51248I 0
u = 1.48188 − 0.20581I
a = 2.10311 + 0.59020I
b = 1.254090 − 0.304222I
−5.51395 + 5.51248I 0
u = 1.47936 + 0.26591I
a = 1.67705 − 0.89970I
b = 1.297930 − 0.061100I
−9.67010 + 1.15397I 0
u = 1.47936 − 0.26591I
a = 1.67705 + 0.89970I
b = 1.297930 + 0.061100I
−9.67010 − 1.15397I 0
u = −1.49131 + 0.19909I
a = −1.75436 − 0.92513I
b = −1.93070 − 0.42961I
−13.9537 + 2.9601I 0
u = −1.49131 − 0.19909I
a = −1.75436 + 0.92513I
b = −1.93070 + 0.42961I
−13.9537 − 2.9601I 0
u = −1.48365 + 0.25153I
a = −1.99125 − 0.58447I
b = −1.65104 + 0.93298I
−13.1732 + 7.9062I 0
u = −1.48365 − 0.25153I
a = −1.99125 + 0.58447I
b = −1.65104 − 0.93298I
−13.1732 − 7.9062I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.48073 + 0.36508I
a = 1.89059 + 1.05321I
b = 1.48999 − 0.59218I
−13.2708 + 18.4610I 0
u = −1.48073 − 0.36508I
a = 1.89059 − 1.05321I
b = 1.48999 + 0.59218I
−13.2708 − 18.4610I 0
u = −1.49228 + 0.36576I
a = 1.76452 + 0.89817I
b = 1.323930 − 0.458029I
−8.5253 + 12.8531I 0
u = −1.49228 − 0.36576I
a = 1.76452 − 0.89817I
b = 1.323930 + 0.458029I
−8.5253 − 12.8531I 0
u = −0.141853 + 0.427499I
a = −0.992142 − 0.604973I
b = 0.018620 + 0.994580I
−0.31883 + 3.28324I −5.60431 − 3.66597I
u = −0.141853 − 0.427499I
a = −0.992142 + 0.604973I
b = 0.018620 − 0.994580I
−0.31883 − 3.28324I −5.60431 + 3.66597I
u = −1.50018 + 0.39366I
a = 1.45021 + 0.85922I
b = 1.286570 − 0.159205I
−12.32240 + 6.52710I 0
u = −1.50018 − 0.39366I
a = 1.45021 − 0.85922I
b = 1.286570 + 0.159205I
−12.32240 − 6.52710I 0
u = −1.61494 + 0.01702I
a = 1.95092 + 0.17895I
b = 1.53493 + 0.27322I
−18.4193 − 6.1353I 0
u = −1.61494 − 0.01702I
a = 1.95092 − 0.17895I
b = 1.53493 − 0.27322I
−18.4193 + 6.1353I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.63726
a = 1.84814
b = 1.39245
−13.8071 0
u = −0.135094 + 0.280440I
a = 2.45235 + 0.17022I
b = 0.086578 − 0.492792I
−0.62747 − 1.89102I −3.97049 + 2.88595I
u = −0.135094 − 0.280440I
a = 2.45235 − 0.17022I
b = 0.086578 + 0.492792I
−0.62747 + 1.89102I −3.97049 − 2.88595I
u = 0.105881 + 0.172003I
a = 3.05499 − 3.81158I
b = −0.742474 + 0.130120I
−1.063250 + 0.043134I −7.94611 + 1.24147I
u = 0.105881 − 0.172003I
a = 3.05499 + 3.81158I
b = −0.742474 − 0.130120I
−1.063250 − 0.043134I −7.94611 − 1.24147I
u = −0.131323 + 0.122858I
a = −4.47970 − 3.36732I
b = −1.242240 + 0.474353I
−4.49140 + 1.51008I −9.81598 − 1.55694I
u = −0.131323 − 0.122858I
a = −4.47970 + 3.36732I
b = −1.242240 − 0.474353I
−4.49140 − 1.51008I −9.81598 + 1.55694I
15
II. I
u
2
= hb
9
− b
8
− 2b
7
+ 3b
6
+ b
5
− 3b
4
+ 2b
3
− b + 1, a − 1, u − 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
1
a
2
=
1
1
a
5
=
−1
0
a
3
=
0
1
a
10
=
1
b
a
12
=
−b + 1
−b
2
a
6
=
−b
3
+ b
2
− 1
−b
4
a
9
=
b
6
− b
5
− b
4
+ 2b
3
− b + 1
b
7
− b
5
+ b
a
7
=
0
−b
8
+ b
7
+ 3b
6
− 2b
5
− 3b
4
+ 2b
3
+ 1
a
8
=
0
−b
8
+ b
7
+ 3b
6
− 2b
5
− 3b
4
+ 2b
3
+ 1
a
11
=
−b + 1
b
(ii) Obstruction class = 1
(iii) Cusp Shapes = b
8
− b
7
+ 2b
6
− b
5
− 3b
4
+ 5b
3
+ 2b
2
− 3b − 5
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
9
c
3
, c
7
u
9
c
4
(u + 1)
9
c
5
u
9
− 5u
8
+ 12u
7
− 15u
6
+ 9u
5
+ u
4
− 4u
3
+ 2u
2
+ u − 1
c
6
u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1
c
8
u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1
c
9
u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1
c
10
u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1
c
11
u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1
c
12
u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
9
c
3
, c
7
y
9
c
5
y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1
c
6
, c
9
y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1
c
8
, c
11
y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1
c
10
, c
12
y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 1.00000
b = 0.772920 + 0.510351I
0.13850 − 2.09337I −6.02684 + 1.69698I
u = 1.00000
a = 1.00000
b = 0.772920 − 0.510351I
0.13850 + 2.09337I −6.02684 − 1.69698I
u = 1.00000
a = 1.00000
b = −0.825933
−2.84338 −3.87310
u = 1.00000
a = 1.00000
b = −1.173910 + 0.391555I
−6.01628 + 1.33617I −16.4774 − 4.4812I
u = 1.00000
a = 1.00000
b = −1.173910 − 0.391555I
−6.01628 − 1.33617I −16.4774 + 4.4812I
u = 1.00000
a = 1.00000
b = 0.141484 + 0.739668I
−2.26187 + 2.45442I −8.53903 − 2.82066I
u = 1.00000
a = 1.00000
b = 0.141484 − 0.739668I
−2.26187 − 2.45442I −8.53903 + 2.82066I
u = 1.00000
a = 1.00000
b = 1.172470 + 0.500383I
−5.24306 − 7.08493I −9.02021 + 2.94778I
u = 1.00000
a = 1.00000
b = 1.172470 − 0.500383I
−5.24306 + 7.08493I −9.02021 − 2.94778I
19
III. I
u
3
= hb + 1, −12u
2
+ 17a − 11u + 8, u
3
+ u
2
− 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
5
=
−u
u
2
+ u − 1
a
3
=
−u
2
+ 1
u
2
− u + 1
a
10
=
12
17
u
2
+
11
17
u −
8
17
−1
a
12
=
12
17
u
2
+
11
17
u +
9
17
−1
a
6
=
−0.00346021u
2
− 0.733564u + 0.217993
14
17
u
2
+
10
17
u −
15
17
a
9
=
0.484429u
2
− 0.301038u + 0.480969
29
17
u
2
+
11
17
u −
42
17
a
7
=
−2u + 1
5u
2
+ 2u − 4
a
8
=
−u
2u
2
+ u − 2
a
11
=
12
17
u
2
+
11
17
u +
9
17
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
8258
289
u
2
+
2667
289
u +
54
289
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
u
3
+ u
2
− 1
c
3
u
3
− u
2
+ 2u − 1
c
4
u
3
− u
2
+ 1
c
5
17(17u
3
+ 10u
2
− u − 1)
c
6
u
3
+ 3u
2
+ 2u − 1
c
7
u
3
+ u
2
+ 2u + 1
c
8
17(17u
3
− 23u
2
+ 8u − 1)
c
9
u
3
− 3u
2
+ 2u + 1
c
10
(u − 1)
3
c
11
u
3
c
12
(u + 1)
3
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
y
3
− y
2
+ 2y −1
c
3
, c
7
y
3
+ 3y
2
+ 2y −1
c
5
289(289y
3
− 134y
2
+ 21y −1)
c
6
, c
9
y
3
− 5y
2
+ 10y −1
c
8
289(289y
3
− 257y
2
+ 18y −1)
c
10
, c
12
(y −1)
3
c
11
y
3
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.877439 + 0.744862I
a = −0.886522 − 0.440719I
b = −1.00000
1.37919 + 2.82812I −14.0563 + 44.2246I
u = −0.877439 − 0.744862I
a = −0.886522 + 0.440719I
b = −1.00000
1.37919 − 2.82812I −14.0563 − 44.2246I
u = 0.754878
a = 0.420102
b = −1.00000
−2.75839 −9.12970
23
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
2
((u − 1)
9
)(u
3
+ u
2
− 1)(u
107
− 11u
106
+ ··· − u − 1)
c
3
u
9
(u
3
− u
2
+ 2u − 1)(u
107
− 2u
106
+ ··· − 512u + 512)
c
4
((u + 1)
9
)(u
3
− u
2
+ 1)(u
107
− 11u
106
+ ··· − u − 1)
c
5
289(17u
3
+ 10u
2
− u − 1)
· (u
9
− 5u
8
+ 12u
7
− 15u
6
+ 9u
5
+ u
4
− 4u
3
+ 2u
2
+ u − 1)
· (17u
107
+ 96u
106
+ ··· − 267194040u + 43532959)
c
6
(u
3
+ 3u
2
+ 2u − 1)
· (u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
· (u
107
+ 3u
106
+ ··· − 3u − 1)
c
7
u
9
(u
3
+ u
2
+ 2u + 1)(u
107
− 2u
106
+ ··· − 512u + 512)
c
8
289(17u
3
− 23u
2
+ 8u − 1)(u
9
+ u
8
+ ··· + u − 1)
· (17u
107
+ 61u
106
+ ··· + 49840983u − 2813417)
c
9
(u
3
− 3u
2
+ 2u + 1)
· (u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1)
· (u
107
+ 3u
106
+ ··· − 3u − 1)
c
10
(u − 1)
3
(u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1)
· (u
107
− 5u
106
+ ··· − 5466u − 289)
c
11
u
3
(u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1)
· (u
107
+ 2u
106
+ ··· − 10404u + 2312)
c
12
(u + 1)
3
(u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1)
· (u
107
− 5u
106
+ ··· − 5466u − 289)
24
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
((y −1)
9
)(y
3
− y
2
+ 2y −1)(y
107
− 99y
106
+ ··· − 29y −1)
c
3
, c
7
y
9
(y
3
+ 3y
2
+ 2y −1)(y
107
− 54y
106
+ ··· + 7340032y −262144)
c
5
83521(289y
3
− 134y
2
+ 21y −1)
· (y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1)
· (289y
107
− 1.91 × 10
4
y
106
+ ··· + 8.77 × 10
16
y −1.90 × 10
15
)
c
6
, c
9
(y
3
− 5y
2
+ 10y −1)
· (y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1)
· (y
107
+ 73y
106
+ ··· + 55y −1)
c
8
83521(289y
3
− 257y
2
+ 18y −1)
· (y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1)
· (289y
107
− 7971y
106
+ ··· + 1153422073109755y −7915315215889)
c
10
, c
12
(y −1)
3
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1)
· (y
107
− 81y
106
+ ··· + 6093612y −83521)
c
11
y
3
(y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1)
· (y
107
− 18y
106
+ ··· + 277740560y −5345344)
25
