12a
1052
(K12a
1052
)
A knot diagram
1
Linearized knot diagam
4 7 9 10 11 12 3 1 2 6 5 8
Solving Sequence
6,10
11 5 12 7
2,4
1 9 3 8
c
10
c
5
c
11
c
6
c
4
c
1
c
9
c
3
c
8
c
2
, c
7
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h7.32033 × 10
90
u
113
− 1.93522 × 10
90
u
112
+ ··· + 6.70656 × 10
90
b + 1.59902 × 10
90
,
3.53856 × 10
91
u
113
− 2.33564 × 10
91
u
112
+ ··· + 6.70656 × 10
90
a + 2.28699 × 10
92
, u
114
− u
113
+ ··· + 17u − 1i
I
u
2
= hu
20
+ 9u
18
+ ··· + 6u
2
+ b, u
19
+ u
18
+ ··· + a + 1, u
21
+ 10u
19
+ ··· + 3u
2
− 1i
* 2 irreducible components of dim
C
= 0, with total 135 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
= h7.32 × 10
90
u
113
− 1.94 × 10
90
u
112
+ · · · + 6.71 × 10
90
b + 1.60 ×
10
90
, 3.54 × 10
91
u
113
− 2.34 × 10
91
u
112
+ · · · + 6.71 × 10
90
a + 2.29 ×
10
92
, u
114
− u
113
+ · · · + 17u − 1i
(i) Arc colorings
a
6
=
0
u
a
10
=
1
0
a
11
=
1
u
2
a
5
=
u
u
3
+ u
a
12
=
u
2
+ 1
u
4
+ 2u
2
a
7
=
−u
5
− 2u
3
− u
−u
7
− 3u
5
− 2u
3
+ u
a
2
=
−5.27627u
113
+ 3.48262u
112
+ ··· + 314.505u − 34.1008
−1.09152u
113
+ 0.288557u
112
+ ··· − 2.59648u − 0.238427
a
4
=
u
3
+ 2u
u
3
+ u
a
1
=
−4.61041u
113
+ 3.67810u
112
+ ··· + 314.574u − 33.6140
−1.20888u
113
− 0.656988u
112
+ ··· − 18.5266u + 0.967100
a
9
=
4.25189u
113
− 5.29865u
112
+ ··· − 335.802u + 36.0515
−1.87637u
113
+ 2.53372u
112
+ ··· − 19.8731u + 1.91709
a
3
=
−4.87644u
113
+ 4.31876u
112
+ ··· + 334.488u − 35.6095
−1.22567u
113
− 0.772076u
112
+ ··· − 22.9954u + 1.24478
a
8
=
4.47862u
113
− 6.30012u
112
+ ··· − 385.534u + 47.2150
−0.612792u
113
+ 0.596277u
112
+ ··· − 36.3318u + 4.07133
(ii) Obstruction class = −1
(iii) Cusp Shapes = 3.96121u
113
− 4.24884u
112
+ ··· − 488.686u + 44.0315
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
114
− 13u
113
+ ··· − 76092u + 7999
c
2
, c
7
u
114
− 33u
112
+ ··· + 2u + 1
c
3
u
114
− u
113
+ ··· + 7u + 1
c
4
, c
6
u
114
+ u
113
+ ··· + 60449u − 3737
c
5
, c
10
, c
11
u
114
− u
113
+ ··· + 17u − 1
c
8
, c
12
u
114
− 40u
112
+ ··· + 934u + 509
c
9
u
114
+ 3u
113
+ ··· − 2304u + 416
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
114
− 41y
113
+ ··· − 1109681576y + 63984001
c
2
, c
7
y
114
− 66y
113
+ ··· − 42y + 1
c
3
y
114
+ 11y
113
+ ··· + 15y + 1
c
4
, c
6
y
114
− 85y
113
+ ··· − 1006282569y + 13965169
c
5
, c
10
, c
11
y
114
+ 95y
113
+ ··· − 89y + 1
c
8
, c
12
y
114
− 80y
113
+ ··· − 10221668y + 259081
c
9
y
114
+ 13y
113
+ ··· + 3856896y + 173056
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.887561 + 0.033463I
a = 0.667047 − 0.840543I
b = 0.761693 − 0.542709I
−8.87011 − 0.11224I 0
u = 0.887561 − 0.033463I
a = 0.667047 + 0.840543I
b = 0.761693 + 0.542709I
−8.87011 + 0.11224I 0
u = 0.884055
a = 1.57119
b = 1.32521
−8.83336 0
u = 0.861941 + 0.130288I
a = 0.66446 − 2.36238I
b = 1.12530 − 1.26937I
−6.2381 − 13.5633I 0
u = 0.861941 − 0.130288I
a = 0.66446 + 2.36238I
b = 1.12530 + 1.26937I
−6.2381 + 13.5633I 0
u = −0.855647 + 0.157410I
a = −0.36775 + 1.65160I
b = 0.174619 + 1.137200I
−6.26667 + 4.41214I 0
u = −0.855647 − 0.157410I
a = −0.36775 − 1.65160I
b = 0.174619 − 1.137200I
−6.26667 − 4.41214I 0
u = −0.420494 + 1.077840I
a = −0.472262 + 0.757702I
b = 0.009418 + 1.138830I
−3.43938 + 0.18223I 0
u = −0.420494 − 1.077840I
a = −0.472262 − 0.757702I
b = 0.009418 − 1.138830I
−3.43938 − 0.18223I 0
u = −0.838651 + 0.073965I
a = 0.35169 + 2.00996I
b = 0.986139 + 0.983905I
−9.16090 + 6.43907I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.838651 − 0.073965I
a = 0.35169 − 2.00996I
b = 0.986139 − 0.983905I
−9.16090 − 6.43907I 0
u = −0.836559 + 0.094115I
a = −1.11752 − 2.62098I
b = −1.21368 − 1.37230I
−2.01821 + 6.94038I 0
u = −0.836559 − 0.094115I
a = −1.11752 + 2.62098I
b = −1.21368 + 1.37230I
−2.01821 − 6.94038I 0
u = −0.034680 + 1.171200I
a = −1.05610 + 0.95379I
b = 1.114310 − 0.346505I
1.35481 + 2.41007I 0
u = −0.034680 − 1.171200I
a = −1.05610 − 0.95379I
b = 1.114310 + 0.346505I
1.35481 − 2.41007I 0
u = −0.799088 + 0.028521I
a = 1.61160 − 2.64644I
b = 1.34739 − 1.59685I
−5.95563 + 3.80586I −11.44875 − 3.61947I
u = −0.799088 − 0.028521I
a = 1.61160 + 2.64644I
b = 1.34739 + 1.59685I
−5.95563 − 3.80586I −11.44875 + 3.61947I
u = −0.631624 + 0.489717I
a = 0.972513 + 0.063768I
b = 0.544420 − 0.666919I
−1.07011 − 4.46542I 0. + 4.95137I
u = −0.631624 − 0.489717I
a = 0.972513 − 0.063768I
b = 0.544420 + 0.666919I
−1.07011 + 4.46542I 0. − 4.95137I
u = −0.194897 + 1.186990I
a = −0.384797 + 0.465226I
b = 0.374866 − 0.496573I
2.30672 + 2.64556I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.194897 − 1.186990I
a = −0.384797 − 0.465226I
b = 0.374866 + 0.496573I
2.30672 − 2.64556I 0
u = 0.302875 + 1.165030I
a = 0.338380 + 0.916390I
b = 0.332156 + 1.047030I
−0.924303 − 0.501252I 0
u = 0.302875 − 1.165030I
a = 0.338380 − 0.916390I
b = 0.332156 − 1.047030I
−0.924303 + 0.501252I 0
u = 0.433363 + 1.126810I
a = −0.937304 − 0.439869I
b = −1.00068 − 1.24442I
−3.18527 + 8.92336I 0
u = 0.433363 − 1.126810I
a = −0.937304 + 0.439869I
b = −1.00068 + 1.24442I
−3.18527 − 8.92336I 0
u = −0.559272 + 0.553878I
a = 0.046469 − 0.925572I
b = −0.781859 − 0.851553I
−0.82179 + 8.69014I −4.00000 − 9.28919I
u = −0.559272 − 0.553878I
a = 0.046469 + 0.925572I
b = −0.781859 + 0.851553I
−0.82179 − 8.69014I −4.00000 + 9.28919I
u = −0.772600 + 0.037228I
a = 0.61904 + 1.35329I
b = 0.011448 + 0.359945I
−1.70108 + 1.04212I −5.52078 − 1.15687I
u = −0.772600 − 0.037228I
a = 0.61904 − 1.35329I
b = 0.011448 − 0.359945I
−1.70108 − 1.04212I −5.52078 + 1.15687I
u = 0.764051 + 0.115411I
a = 0.31036 + 2.12630I
b = −0.446089 + 1.030000I
−4.09501 − 3.38991I −10.58127 + 2.23573I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.764051 − 0.115411I
a = 0.31036 − 2.12630I
b = −0.446089 − 1.030000I
−4.09501 + 3.38991I −10.58127 − 2.23573I
u = 0.769870
a = 0.648054
b = 1.32831
−0.697644 −8.68980
u = 0.762064 + 0.089577I
a = −0.30317 + 2.09043I
b = −0.339727 + 0.412420I
−2.72396 − 5.39723I −4.97222 + 8.97168I
u = 0.762064 − 0.089577I
a = −0.30317 − 2.09043I
b = −0.339727 − 0.412420I
−2.72396 + 5.39723I −4.97222 − 8.97168I
u = −0.385495 + 1.171350I
a = 1.341730 − 0.444799I
b = 1.04075 − 1.34482I
1.28099 − 2.53613I 0
u = −0.385495 − 1.171350I
a = 1.341730 + 0.444799I
b = 1.04075 + 1.34482I
1.28099 + 2.53613I 0
u = 0.283143 + 1.201940I
a = 0.55050 + 1.52618I
b = 0.168272 + 0.232893I
0.62179 + 1.60000I 0
u = 0.283143 − 1.201940I
a = 0.55050 − 1.52618I
b = 0.168272 − 0.232893I
0.62179 − 1.60000I 0
u = 0.756287 + 0.034907I
a = −0.01534 + 2.83346I
b = −0.55058 + 1.35141I
−4.02624 − 3.05369I −8.42676 + 2.90164I
u = 0.756287 − 0.034907I
a = −0.01534 − 2.83346I
b = −0.55058 − 1.35141I
−4.02624 + 3.05369I −8.42676 − 2.90164I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.368655 + 0.653613I
a = 0.362791 + 0.342465I
b = 0.315800 + 0.964205I
−2.18652 + 0.53327I −7.37777 + 1.33068I
u = 0.368655 − 0.653613I
a = 0.362791 − 0.342465I
b = 0.315800 − 0.964205I
−2.18652 − 0.53327I −7.37777 − 1.33068I
u = −0.389371 + 1.194790I
a = −0.417451 + 0.445391I
b = −0.900074 + 1.060790I
−5.71894 − 2.02281I 0
u = −0.389371 − 1.194790I
a = −0.417451 − 0.445391I
b = −0.900074 − 1.060790I
−5.71894 + 2.02281I 0
u = −0.312733 + 1.245960I
a = −0.788461 + 0.880942I
b = 0.226218 + 0.195802I
2.01023 + 2.87194I 0
u = −0.312733 − 1.245960I
a = −0.788461 − 0.880942I
b = 0.226218 − 0.195802I
2.01023 − 2.87194I 0
u = 0.033169 + 1.286540I
a = −0.475286 + 0.111459I
b = 0.45164 + 1.73582I
2.83720 − 3.54184I 0
u = 0.033169 − 1.286540I
a = −0.475286 − 0.111459I
b = 0.45164 − 1.73582I
2.83720 + 3.54184I 0
u = 0.019067 + 1.288260I
a = −0.86674 − 1.65349I
b = 0.859718 − 0.367698I
6.84727 − 0.41254I 0
u = 0.019067 − 1.288260I
a = −0.86674 + 1.65349I
b = 0.859718 + 0.367698I
6.84727 + 0.41254I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.348064 + 1.245640I
a = 1.07973 − 2.09369I
b = −1.44236 − 1.42499I
−2.19698 + 0.32673I 0
u = −0.348064 − 1.245640I
a = 1.07973 + 2.09369I
b = −1.44236 + 1.42499I
−2.19698 − 0.32673I 0
u = 0.314287 + 1.257980I
a = 0.98429 + 1.16072I
b = 0.39966 + 1.57679I
−0.241377 − 0.796662I 0
u = 0.314287 − 1.257980I
a = 0.98429 − 1.16072I
b = 0.39966 − 1.57679I
−0.241377 + 0.796662I 0
u = 0.446966 + 1.234100I
a = −0.288788 − 0.032285I
b = −0.433345 − 0.625329I
−5.16161 − 4.65132I 0
u = 0.446966 − 1.234100I
a = −0.288788 + 0.032285I
b = −0.433345 + 0.625329I
−5.16161 + 4.65132I 0
u = 0.329032 + 1.273180I
a = 0.672769 + 0.766233I
b = −1.335070 − 0.128239I
3.25821 − 3.96182I 0
u = 0.329032 − 1.273180I
a = 0.672769 − 0.766233I
b = −1.335070 + 0.128239I
3.25821 + 3.96182I 0
u = 0.118691 + 1.310740I
a = −1.86300 + 0.21647I
b = 0.590937 − 0.530944I
1.60694 − 5.76070I 0
u = 0.118691 − 1.310740I
a = −1.86300 − 0.21647I
b = 0.590937 + 0.530944I
1.60694 + 5.76070I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.040353 + 1.316630I
a = 1.193600 + 0.254814I
b = −0.664084 − 0.488787I
4.67481 + 1.79142I 0
u = −0.040353 − 1.316630I
a = 1.193600 − 0.254814I
b = −0.664084 + 0.488787I
4.67481 − 1.79142I 0
u = −0.350707 + 1.289720I
a = −1.49684 + 0.06917I
b = −1.26736 + 1.75060I
−1.84646 + 7.94723I 0
u = −0.350707 − 1.289720I
a = −1.49684 − 0.06917I
b = −1.26736 − 1.75060I
−1.84646 − 7.94723I 0
u = −0.336746 + 1.293450I
a = −0.125394 − 1.215930I
b = −0.148005 − 0.510473I
2.45095 + 5.04973I 0
u = −0.336746 − 1.293450I
a = −0.125394 + 1.215930I
b = −0.148005 + 0.510473I
2.45095 − 5.04973I 0
u = 0.329752 + 1.298790I
a = −1.46795 − 1.54358I
b = 0.74460 − 1.22192I
0.15037 − 6.98175I 0
u = 0.329752 − 1.298790I
a = −1.46795 + 1.54358I
b = 0.74460 + 1.22192I
0.15037 + 6.98175I 0
u = 0.417386 + 1.276610I
a = −0.557000 + 0.889935I
b = −1.338270 − 0.222985I
−4.86969 − 4.65741I 0
u = 0.417386 − 1.276610I
a = −0.557000 − 0.889935I
b = −1.338270 + 0.222985I
−4.86969 + 4.65741I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.274471 + 1.318860I
a = −0.644135 + 0.621966I
b = 1.059720 − 0.139345I
3.34166 + 3.14281I 0
u = −0.274471 − 1.318860I
a = −0.644135 − 0.621966I
b = 1.059720 + 0.139345I
3.34166 − 3.14281I 0
u = 0.405592 + 1.294220I
a = 0.256254 + 1.094430I
b = −1.014100 + 0.529729I
−4.73797 − 4.73329I 0
u = 0.405592 − 1.294220I
a = 0.256254 − 1.094430I
b = −1.014100 − 0.529729I
−4.73797 + 4.73329I 0
u = 0.180288 + 1.348920I
a = 0.047717 − 1.084830I
b = 1.069820 + 0.119273I
8.05571 − 1.71787I 0
u = 0.180288 − 1.348920I
a = 0.047717 + 1.084830I
b = 1.069820 − 0.119273I
8.05571 + 1.71787I 0
u = −0.030908 + 1.363840I
a = 1.25211 − 0.87845I
b = −0.814496 − 0.347039I
6.34340 + 3.23650I 0
u = −0.030908 − 1.363840I
a = 1.25211 + 0.87845I
b = −0.814496 + 0.347039I
6.34340 − 3.23650I 0
u = 0.330308 + 1.325050I
a = −0.53730 − 1.74794I
b = 0.419800 − 0.520125I
1.71717 − 9.35311I 0
u = 0.330308 − 1.325050I
a = −0.53730 + 1.74794I
b = 0.419800 + 0.520125I
1.71717 + 9.35311I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.373340 + 1.320330I
a = 1.21371 − 1.55752I
b = −1.042950 − 0.908818I
−4.79616 + 10.79540I 0
u = −0.373340 − 1.320330I
a = 1.21371 + 1.55752I
b = −1.042950 + 0.908818I
−4.79616 − 10.79540I 0
u = 0.108689 + 1.371010I
a = 1.061600 + 0.206574I
b = −1.33473 + 0.73220I
8.86434 − 5.29938I 0
u = 0.108689 − 1.371010I
a = 1.061600 − 0.206574I
b = −1.33473 − 0.73220I
8.86434 + 5.29938I 0
u = −0.370406 + 1.333370I
a = −0.93236 + 1.98221I
b = 1.33934 + 1.36558I
2.46011 + 11.28260I 0
u = −0.370406 − 1.333370I
a = −0.93236 − 1.98221I
b = 1.33934 − 1.36558I
2.46011 − 11.28260I 0
u = −0.603702 + 0.119908I
a = −0.568367 − 0.079694I
b = −0.984828 + 0.073067I
−1.118330 − 0.146384I −7.95111 − 0.77273I
u = −0.603702 − 0.119908I
a = −0.568367 + 0.079694I
b = −0.984828 − 0.073067I
−1.118330 + 0.146384I −7.95111 + 0.77273I
u = 0.328033 + 1.346520I
a = −1.25207 − 1.10692I
b = 0.527323 − 1.006500I
0.51996 − 7.34154I 0
u = 0.328033 − 1.346520I
a = −1.25207 + 1.10692I
b = 0.527323 + 1.006500I
0.51996 + 7.34154I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.416646 + 0.435532I
a = 0.260901 − 1.084610I
b = 0.979372 − 0.738723I
3.22241 − 3.59528I 0.10104 + 7.41453I
u = 0.416646 − 0.435532I
a = 0.260901 + 1.084610I
b = 0.979372 + 0.738723I
3.22241 + 3.59528I 0.10104 − 7.41453I
u = 0.379205 + 1.357300I
a = 1.07109 + 1.73396I
b = −1.21519 + 1.25837I
−1.5579 − 18.0236I 0
u = 0.379205 − 1.357300I
a = 1.07109 − 1.73396I
b = −1.21519 − 1.25837I
−1.5579 + 18.0236I 0
u = −0.37524 + 1.37204I
a = 0.967313 − 0.718309I
b = −0.307967 − 1.103800I
−1.44531 + 8.84515I 0
u = −0.37524 − 1.37204I
a = 0.967313 + 0.718309I
b = −0.307967 + 1.103800I
−1.44531 − 8.84515I 0
u = −0.13255 + 1.42840I
a = −0.916140 + 0.104632I
b = 1.063870 + 0.779304I
5.55804 + 10.90110I 0
u = −0.13255 − 1.42840I
a = −0.916140 − 0.104632I
b = 1.063870 − 0.779304I
5.55804 − 10.90110I 0
u = 0.487522 + 0.286146I
a = 1.23842 + 1.37284I
b = −0.489413 + 0.866012I
−3.26040 − 3.77688I −9.45106 + 6.46344I
u = 0.487522 − 0.286146I
a = 1.23842 − 1.37284I
b = −0.489413 − 0.866012I
−3.26040 + 3.77688I −9.45106 − 6.46344I
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.438175 + 0.317808I
a = −1.65447 + 0.85222I
b = −0.798715 − 0.331573I
2.97321 + 0.57316I 0.65978 + 1.46059I
u = 0.438175 − 0.317808I
a = −1.65447 − 0.85222I
b = −0.798715 + 0.331573I
2.97321 − 0.57316I 0.65978 − 1.46059I
u = −0.135646 + 0.515904I
a = −0.69934 + 1.68522I
b = 0.741027 + 0.101363I
0.66930 + 2.73386I −0.07956 − 6.07456I
u = −0.135646 − 0.515904I
a = −0.69934 − 1.68522I
b = 0.741027 − 0.101363I
0.66930 − 2.73386I −0.07956 + 6.07456I
u = −0.530416
a = −0.298864
b = −0.599772
−1.23397 −8.01990
u = 0.02591 + 1.46972I
a = 0.162162 + 0.238122I
b = −0.217407 − 0.693830I
4.73023 − 0.42053I 0
u = 0.02591 − 1.46972I
a = 0.162162 − 0.238122I
b = −0.217407 + 0.693830I
4.73023 + 0.42053I 0
u = −0.16103 + 1.46411I
a = −0.095768 − 0.559743I
b = −0.537984 + 0.322029I
5.32575 − 1.73856I 0
u = −0.16103 − 1.46411I
a = −0.095768 + 0.559743I
b = −0.537984 − 0.322029I
5.32575 + 1.73856I 0
u = −0.238747 + 0.339224I
a = −0.919861 + 0.508205I
b = 0.271657 + 0.619291I
−0.297429 + 0.992589I −5.42028 − 6.49573I
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.238747 − 0.339224I
a = −0.919861 − 0.508205I
b = 0.271657 − 0.619291I
−0.297429 − 0.992589I −5.42028 + 6.49573I
u = 0.154183 + 0.111813I
a = 3.03466 − 2.70612I
b = −0.547828 − 1.159590I
−1.43517 − 2.95501I −9.6375 + 11.3747I
u = 0.154183 − 0.111813I
a = 3.03466 + 2.70612I
b = −0.547828 + 1.159590I
−1.43517 + 2.95501I −9.6375 − 11.3747I
u = 0.116826
a = −12.1443
b = −0.822751
2.72265 12.9620
16
II.
I
u
2
= hu
20
+9u
18
+· · ·+6u
2
+b, u
19
+u
18
+· · ·+a+1, u
21
+10u
19
+· · ·+3u
2
−1i
(i) Arc colorings
a
6
=
0
u
a
10
=
1
0
a
11
=
1
u
2
a
5
=
u
u
3
+ u
a
12
=
u
2
+ 1
u
4
+ 2u
2
a
7
=
−u
5
− 2u
3
− u
−u
7
− 3u
5
− 2u
3
+ u
a
2
=
−u
19
− u
18
+ ··· − 7u − 1
−u
20
− 9u
18
+ ··· − 3u
3
− 6u
2
a
4
=
u
3
+ 2u
u
3
+ u
a
1
=
−u
18
− 9u
16
+ ··· − 7u − 1
−u
20
− u
19
+ ··· − 8u
2
+ 1
a
9
=
−2u
19
+ u
18
+ ··· + 5u + 4
u
19
+ 9u
17
+ ··· + 2u − 1
a
3
=
−u
18
− 9u
16
+ ··· − 8u − 2
−u
20
− 9u
18
+ ··· − 6u
2
+ u
a
8
=
u
20
− u
19
+ ··· + 9u + 3
−u
20
− u
19
+ ··· + 5u
2
+ 2u
(ii) Obstruction class = 1
(iii) Cusp Shapes
= u
20
+ 5u
19
+ 6u
18
+ 43u
17
+ 8u
16
+ 148u
15
− 24u
14
+ 234u
13
− 92u
12
+ 92u
11
−
106u
10
− 199u
9
− 13u
8
− 203u
7
+ 70u
6
+ 56u
5
+ 43u
4
+ 91u
3
− 12u
2
− 19u − 15
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
21
− 6u
19
+ ··· + 9u − 1
c
2
u
21
+ u
20
+ ··· + u + 1
c
3
u
21
+ 2u
19
+ ··· − u
2
− 1
c
4
, c
6
u
21
− 6u
19
+ ··· + 2u + 1
c
5
u
21
+ 10u
19
+ ··· − 3u
2
+ 1
c
7
u
21
− u
20
+ ··· + u − 1
c
8
u
21
− u
20
+ ··· + u − 1
c
9
u
21
+ u
19
+ ··· − 2u
2
− 1
c
10
, c
11
u
21
+ 10u
19
+ ··· + 3u
2
− 1
c
12
u
21
+ u
20
+ ··· + u + 1
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
21
− 12y
20
+ ··· + 5y −1
c
2
, c
7
y
21
− 21y
20
+ ··· + 19y −1
c
3
y
21
+ 4y
20
+ ··· − 2y −1
c
4
, c
6
y
21
− 12y
20
+ ··· + 2y −1
c
5
, c
10
, c
11
y
21
+ 20y
20
+ ··· + 6y −1
c
8
, c
12
y
21
− 19y
20
+ ··· + 21y −1
c
9
y
21
+ 2y
20
+ ··· − 4y −1
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.904293
a = −1.42467
b = −1.18397
−8.48711 5.04120
u = −0.076972 + 1.189930I
a = 1.006270 − 0.805513I
b = −0.565251 + 1.149290I
1.39138 + 3.54794I −6.10052 − 7.16362I
u = −0.076972 − 1.189930I
a = 1.006270 + 0.805513I
b = −0.565251 − 1.149290I
1.39138 − 3.54794I −6.10052 + 7.16362I
u = −0.760358 + 0.100576I
a = −0.65190 + 2.51046I
b = 0.052448 + 1.117880I
−3.83535 + 4.58464I −8.80266 − 6.89397I
u = −0.760358 − 0.100576I
a = −0.65190 − 2.51046I
b = 0.052448 − 1.117880I
−3.83535 − 4.58464I −8.80266 + 6.89397I
u = −0.296928 + 1.197740I
a = −0.76878 + 1.67924I
b = 0.080602 + 1.224810I
−0.520443 − 0.759678I −5.59489 + 3.00147I
u = −0.296928 − 1.197740I
a = −0.76878 − 1.67924I
b = 0.080602 − 1.224810I
−0.520443 + 0.759678I −5.59489 − 3.00147I
u = 0.709431
a = 0.0961397
b = 1.08690
0.407384 0.329430
u = 0.289693 + 1.282470I
a = 0.990631 + 0.460119I
b = −1.100200 − 0.092788I
4.40522 − 3.60581I 4.85190 + 2.94987I
u = 0.289693 − 1.282470I
a = 0.990631 − 0.460119I
b = −1.100200 + 0.092788I
4.40522 + 3.60581I 4.85190 − 2.94987I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.099228 + 1.315090I
a = −0.22166 − 1.47776I
b = 0.782001 − 0.220049I
6.69676 − 1.50889I 0.02014 + 3.74098I
u = 0.099228 − 1.315090I
a = −0.22166 + 1.47776I
b = 0.782001 + 0.220049I
6.69676 + 1.50889I 0.02014 − 3.74098I
u = 0.434962 + 1.273550I
a = 0.565779 − 0.772032I
b = 1.163530 + 0.233492I
−4.53652 − 4.78275I 7.22141 + 6.57103I
u = 0.434962 − 1.273550I
a = 0.565779 + 0.772032I
b = 1.163530 − 0.233492I
−4.53652 + 4.78275I 7.22141 − 6.57103I
u = −0.329270 + 1.336270I
a = 1.24760 − 1.14044I
b = −0.172630 − 1.063930I
0.69087 + 8.53235I −3.78246 − 8.49503I
u = −0.329270 − 1.336270I
a = 1.24760 + 1.14044I
b = −0.172630 + 1.063930I
0.69087 − 8.53235I −3.78246 + 8.49503I
u = −0.06876 + 1.45018I
a = −0.153482 + 0.129522I
b = −0.156384 − 0.514490I
4.68874 − 1.20750I −5.08024 + 4.24177I
u = −0.06876 − 1.45018I
a = −0.153482 − 0.129522I
b = −0.156384 + 0.514490I
4.68874 + 1.20750I −5.08024 − 4.24177I
u = −0.261219 + 0.323597I
a = 1.004950 − 0.044950I
b = 0.358070 + 0.842385I
−1.23671 − 2.41016I −4.09983 − 1.07265I
u = −0.261219 − 0.323597I
a = 1.004950 + 0.044950I
b = 0.358070 − 0.842385I
−1.23671 + 2.41016I −4.09983 + 1.07265I
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.325517
a = −4.71029
b = −0.787304
2.46145 −18.6360
22
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
21
− 6u
19
+ ··· + 9u − 1)(u
114
− 13u
113
+ ··· − 76092u + 7999)
c
2
(u
21
+ u
20
+ ··· + u + 1)(u
114
− 33u
112
+ ··· + 2u + 1)
c
3
(u
21
+ 2u
19
+ ··· − u
2
− 1)(u
114
− u
113
+ ··· + 7u + 1)
c
4
, c
6
(u
21
− 6u
19
+ ··· + 2u + 1)(u
114
+ u
113
+ ··· + 60449u − 3737)
c
5
(u
21
+ 10u
19
+ ··· − 3u
2
+ 1)(u
114
− u
113
+ ··· + 17u − 1)
c
7
(u
21
− u
20
+ ··· + u − 1)(u
114
− 33u
112
+ ··· + 2u + 1)
c
8
(u
21
− u
20
+ ··· + u − 1)(u
114
− 40u
112
+ ··· + 934u + 509)
c
9
(u
21
+ u
19
+ ··· − 2u
2
− 1)(u
114
+ 3u
113
+ ··· − 2304u + 416)
c
10
, c
11
(u
21
+ 10u
19
+ ··· + 3u
2
− 1)(u
114
− u
113
+ ··· + 17u − 1)
c
12
(u
21
+ u
20
+ ··· + u + 1)(u
114
− 40u
112
+ ··· + 934u + 509)
23
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
21
− 12y
20
+ ··· + 5y −1)
· (y
114
− 41y
113
+ ··· − 1109681576y + 63984001)
c
2
, c
7
(y
21
− 21y
20
+ ··· + 19y −1)(y
114
− 66y
113
+ ··· − 42y + 1)
c
3
(y
21
+ 4y
20
+ ··· − 2y −1)(y
114
+ 11y
113
+ ··· + 15y + 1)
c
4
, c
6
(y
21
− 12y
20
+ ··· + 2y −1)
· (y
114
− 85y
113
+ ··· − 1006282569y + 13965169)
c
5
, c
10
, c
11
(y
21
+ 20y
20
+ ··· + 6y −1)(y
114
+ 95y
113
+ ··· − 89y + 1)
c
8
, c
12
(y
21
− 19y
20
+ ··· + 21y −1)
· (y
114
− 80y
113
+ ··· − 10221668y + 259081)
c
9
(y
21
+ 2y
20
+ ··· − 4y −1)(y
114
+ 13y
113
+ ··· + 3856896y + 173056)
24
