12n
0350
(K12n
0350
)
A knot diagram
1
Linearized knot diagam
3 5 8 10 2 11 3 4 1 12 6 4
Solving Sequence
3,5
2 6
1,10
4 9 8 12 11 7
c
2
c
5
c
1
c
4
c
9
c
8
c
12
c
11
c
6
c
3
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−5.29491 × 10
120
u
72
− 5.67691 × 10
120
u
71
+ ··· + 2.16404 × 10
120
b + 3.26172 × 10
122
,
− 1.13483 × 10
122
u
72
− 2.62988 × 10
122
u
71
+ ··· + 3.09458 × 10
122
a − 3.19287 × 10
124
,
u
73
+ u
72
+ ··· − 54u + 143i
I
u
2
= hu
21
+ 2u
20
+ ··· + b + 2, −6u
21
− 7u
20
+ ··· + a + 7, u
22
+ 2u
21
+ ··· + 2u + 1i
* 2 irreducible components of dim
C
= 0, with total 95 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−5.29 × 10
120
u
72
− 5.68 × 10
120
u
71
+ · · · + 2.16 × 10
120
b + 3.26 ×
10
122
, −1.13 × 10
122
u
72
− 2.63 × 10
122
u
71
+ · · · + 3.09 × 10
122
a − 3.19 ×
10
124
, u
73
+ u
72
+ · · · − 54u + 143i
(i) Arc colorings
a
3
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
6
=
u
u
3
+ u
a
1
=
u
2
+ 1
u
2
a
10
=
0.366715u
72
+ 0.849834u
71
+ ··· + 93.7582u + 103.176
2.44677u
72
+ 2.62329u
71
+ ··· + 404.194u − 150.723
a
4
=
−0.0790626u
72
− 0.0854014u
71
+ ··· − 11.2736u − 52.6707
−0.461261u
72
+ 0.201291u
71
+ ··· − 91.3359u + 152.246
a
9
=
0.103382u
72
+ 0.154811u
71
+ ··· + 68.5103u + 78.0723
1.59212u
72
+ 1.90881u
71
+ ··· + 288.755u − 68.9470
a
8
=
−0.555398u
72
− 1.64164u
71
+ ··· − 56.7111u − 118.525
0.235819u
72
+ 0.648309u
71
+ ··· + 33.9399u + 52.7633
a
12
=
−0.420761u
72
− 0.753968u
71
+ ··· − 88.3251u + 21.7494
0.826324u
72
+ 0.838782u
71
+ ··· + 168.780u − 9.30641
a
11
=
−1.42862u
72
− 1.96581u
71
+ ··· − 265.577u + 38.5749
0.600156u
72
+ 0.832821u
71
+ ··· + 124.638u + 36.6878
a
7
=
0.791216u
72
+ 2.28995u
71
+ ··· + 90.6511u + 171.289
−0.235819u
72
− 0.648309u
71
+ ··· − 33.9399u − 52.7633
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2.47879u
72
− 1.95242u
71
+ ··· − 309.552u + 200.317
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
73
+ 43u
72
+ ··· − 318262u − 20449
c
2
, c
5
u
73
− u
72
+ ··· − 54u − 143
c
3
, c
7
, c
8
u
73
+ u
72
+ ··· − 18u − 1
c
4
u
73
− u
72
+ ··· − 26u − 3
c
6
, c
11
u
73
+ u
72
+ ··· + 280u − 119
c
9
u
73
− 5u
72
+ ··· + 22u − 1
c
10
u
73
− 25u
72
+ ··· − 219576u + 14161
c
12
u
73
+ 5u
72
+ ··· − 14u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
73
− 13y
72
+ ··· + 6813662274y −418161601
c
2
, c
5
y
73
+ 43y
72
+ ··· − 318262y −20449
c
3
, c
7
, c
8
y
73
− 19y
72
+ ··· + 78y −1
c
4
y
73
− 9y
72
+ ··· − 140y −9
c
6
, c
11
y
73
+ 25y
72
+ ··· − 219576y −14161
c
9
y
73
− 71y
72
+ ··· + 74y −1
c
10
y
73
+ 45y
72
+ ··· + 7780282916y −200533921
c
12
y
73
+ 65y
72
+ ··· − 124y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.683574 + 0.741540I
a = 1.24911 − 0.93513I
b = 1.63585 + 0.41682I
6.62976 + 3.45446I 12.33941 + 0.I
u = 0.683574 − 0.741540I
a = 1.24911 + 0.93513I
b = 1.63585 − 0.41682I
6.62976 − 3.45446I 12.33941 + 0.I
u = −0.986818 + 0.037483I
a = 1.21894 − 0.96902I
b = 1.38473 − 0.39776I
−3.56549 − 3.25751I 4.00000 + 2.71745I
u = −0.986818 − 0.037483I
a = 1.21894 + 0.96902I
b = 1.38473 + 0.39776I
−3.56549 + 3.25751I 4.00000 − 2.71745I
u = −0.535723 + 0.826575I
a = 0.676203 + 0.430293I
b = 0.919141 − 0.126022I
1.71374 − 1.35709I 6.26252 + 3.77195I
u = −0.535723 − 0.826575I
a = 0.676203 − 0.430293I
b = 0.919141 + 0.126022I
1.71374 + 1.35709I 6.26252 − 3.77195I
u = 0.249076 + 0.988123I
a = 0.963692 − 0.195170I
b = 1.215860 − 0.565099I
−0.10064 + 5.52882I 4.00000 − 5.78158I
u = 0.249076 − 0.988123I
a = 0.963692 + 0.195170I
b = 1.215860 + 0.565099I
−0.10064 − 5.52882I 4.00000 + 5.78158I
u = −0.171086 + 1.013120I
a = −1.240710 + 0.320252I
b = 0.183330 + 0.223602I
−2.89227 − 2.61557I 4.00000 + 0.I
u = −0.171086 − 1.013120I
a = −1.240710 − 0.320252I
b = 0.183330 − 0.223602I
−2.89227 + 2.61557I 4.00000 + 0.I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.948455 + 0.085623I
a = −0.82199 + 1.24099I
b = −1.332150 + 0.245893I
−4.43555 − 4.42989I 3.57907 + 2.45374I
u = 0.948455 − 0.085623I
a = −0.82199 − 1.24099I
b = −1.332150 − 0.245893I
−4.43555 + 4.42989I 3.57907 − 2.45374I
u = 0.230974 + 1.025990I
a = −0.529050 + 1.197620I
b = −2.28839 − 0.58000I
2.79792 + 3.70869I 0
u = 0.230974 − 1.025990I
a = −0.529050 − 1.197620I
b = −2.28839 + 0.58000I
2.79792 − 3.70869I 0
u = −0.753813 + 0.569849I
a = 0.007602 − 0.307173I
b = −0.253666 + 0.408703I
2.13347 − 0.67945I 9.13563 + 0.70093I
u = −0.753813 − 0.569849I
a = 0.007602 + 0.307173I
b = −0.253666 − 0.408703I
2.13347 + 0.67945I 9.13563 − 0.70093I
u = 0.228817 + 0.896549I
a = 0.273889 − 0.255136I
b = −1.97284 + 3.60878I
−4.04258 + 1.08271I 11.21709 − 7.54652I
u = 0.228817 − 0.896549I
a = 0.273889 + 0.255136I
b = −1.97284 − 3.60878I
−4.04258 − 1.08271I 11.21709 + 7.54652I
u = 0.451538 + 0.991597I
a = −0.661238 + 0.590058I
b = −1.04730 − 2.04932I
1.15731 + 7.06397I 0
u = 0.451538 − 0.991597I
a = −0.661238 − 0.590058I
b = −1.04730 + 2.04932I
1.15731 − 7.06397I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.072770 + 0.230198I
a = 0.85636 − 1.12907I
b = 1.38317 − 0.30370I
−3.02705 − 10.41650I 0
u = 1.072770 − 0.230198I
a = 0.85636 + 1.12907I
b = 1.38317 + 0.30370I
−3.02705 + 10.41650I 0
u = −0.612070 + 0.941386I
a = 0.565613 − 0.052080I
b = 1.02901 − 1.19145I
1.08635 − 4.46104I 0
u = −0.612070 − 0.941386I
a = 0.565613 + 0.052080I
b = 1.02901 + 1.19145I
1.08635 + 4.46104I 0
u = −0.836204 + 0.261291I
a = −1.33600 + 1.06634I
b = −1.35173 + 0.47656I
−4.10363 + 2.39606I 3.81600 − 2.35228I
u = −0.836204 − 0.261291I
a = −1.33600 − 1.06634I
b = −1.35173 − 0.47656I
−4.10363 − 2.39606I 3.81600 + 2.35228I
u = 0.291875 + 1.098960I
a = −0.464893 − 0.352121I
b = −1.62372 + 0.26942I
−3.74319 + 0.35423I 0
u = 0.291875 − 1.098960I
a = −0.464893 + 0.352121I
b = −1.62372 − 0.26942I
−3.74319 − 0.35423I 0
u = −0.814736 + 0.183028I
a = −0.960227 + 0.069320I
b = −0.330314 + 0.069183I
3.36781 − 3.36881I 14.2825 + 3.4147I
u = −0.814736 − 0.183028I
a = −0.960227 − 0.069320I
b = −0.330314 − 0.069183I
3.36781 + 3.36881I 14.2825 − 3.4147I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.090816 + 0.822219I
a = −1.43478 + 0.31964I
b = −1.180510 + 0.536261I
−2.10787 + 1.28735I −0.94828 + 1.56152I
u = −0.090816 − 0.822219I
a = −1.43478 − 0.31964I
b = −1.180510 − 0.536261I
−2.10787 − 1.28735I −0.94828 − 1.56152I
u = 0.686083 + 0.978905I
a = −0.765292 + 1.051350I
b = −1.57564 − 0.25864I
5.92171 + 1.85310I 0
u = 0.686083 − 0.978905I
a = −0.765292 − 1.051350I
b = −1.57564 + 0.25864I
5.92171 − 1.85310I 0
u = 0.348220 + 0.717099I
a = 0.633784 + 1.212890I
b = 0.300550 − 0.658677I
0.72632 − 2.98385I 2.65867 − 1.61148I
u = 0.348220 − 0.717099I
a = 0.633784 − 1.212890I
b = 0.300550 + 0.658677I
0.72632 + 2.98385I 2.65867 + 1.61148I
u = 0.559248 + 0.542007I
a = 0.304713 − 0.769105I
b = 1.63410 − 0.28852I
2.49213 − 2.99410I 10.23774 + 2.77464I
u = 0.559248 − 0.542007I
a = 0.304713 + 0.769105I
b = 1.63410 + 0.28852I
2.49213 + 2.99410I 10.23774 − 2.77464I
u = 0.071021 + 0.771811I
a = 0.03076 − 1.73667I
b = 1.51208 + 1.30733I
3.99461 − 2.09346I 4.40638 + 4.85697I
u = 0.071021 − 0.771811I
a = 0.03076 + 1.73667I
b = 1.51208 − 1.30733I
3.99461 + 2.09346I 4.40638 − 4.85697I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.550268 + 1.099350I
a = 0.621185 + 0.125940I
b = 2.03807 + 0.21438I
−1.98384 + 7.01266I 0
u = 0.550268 − 1.099350I
a = 0.621185 − 0.125940I
b = 2.03807 − 0.21438I
−1.98384 − 7.01266I 0
u = −0.851304 + 0.913176I
a = 0.798557 + 0.326350I
b = 1.068680 − 0.466872I
2.18546 − 1.63429I 0
u = −0.851304 − 0.913176I
a = 0.798557 − 0.326350I
b = 1.068680 + 0.466872I
2.18546 + 1.63429I 0
u = 0.656597 + 0.322411I
a = 0.009722 + 1.058680I
b = −0.153000 − 0.490916I
0.19655 − 2.31294I 2.63030 + 3.93885I
u = 0.656597 − 0.322411I
a = 0.009722 − 1.058680I
b = −0.153000 + 0.490916I
0.19655 + 2.31294I 2.63030 − 3.93885I
u = −0.910749 + 0.899481I
a = −0.681027 − 0.535163I
b = −0.994698 + 0.400858I
2.24214 − 4.81846I 0
u = −0.910749 − 0.899481I
a = −0.681027 + 0.535163I
b = −0.994698 − 0.400858I
2.24214 + 4.81846I 0
u = −0.347418 + 1.242890I
a = 0.897027 + 0.556994I
b = 2.36861 − 1.55566I
−8.62556 − 1.39524I 0
u = −0.347418 − 1.242890I
a = 0.897027 − 0.556994I
b = 2.36861 + 1.55566I
−8.62556 + 1.39524I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.327113 + 1.269160I
a = −0.447376 − 0.279699I
b = −0.885740 + 0.124459I
−3.06231 − 3.20525I 0
u = −0.327113 − 1.269160I
a = −0.447376 + 0.279699I
b = −0.885740 − 0.124459I
−3.06231 + 3.20525I 0
u = 0.307931 + 0.612364I
a = −1.29884 − 0.76584I
b = −0.944065 + 0.409129I
−2.61771 + 1.38695I 0.42548 − 4.72459I
u = 0.307931 − 0.612364I
a = −1.29884 + 0.76584I
b = −0.944065 − 0.409129I
−2.61771 − 1.38695I 0.42548 + 4.72459I
u = −0.585251 + 1.199500I
a = −0.552128 + 1.160950I
b = 0.338923 + 0.505424I
−6.87606 − 7.71394I 0
u = −0.585251 − 1.199500I
a = −0.552128 − 1.160950I
b = 0.338923 − 0.505424I
−6.87606 + 7.71394I 0
u = 0.526112 + 1.266110I
a = 0.986760 − 0.358538I
b = 2.22186 + 1.40051I
−8.04182 + 9.70758I 0
u = 0.526112 − 1.266110I
a = 0.986760 + 0.358538I
b = 2.22186 − 1.40051I
−8.04182 − 9.70758I 0
u = 0.417829 + 1.314000I
a = −0.640898 − 0.878070I
b = −0.077620 − 0.324517I
−8.85194 + 0.38418I 0
u = 0.417829 − 1.314000I
a = −0.640898 + 0.878070I
b = −0.077620 + 0.324517I
−8.85194 − 0.38418I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.154627 + 1.375210I
a = 0.222651 − 0.081323I
b = −0.502565 + 0.009919I
−4.25898 − 3.13951I 0
u = −0.154627 − 1.375210I
a = 0.222651 + 0.081323I
b = −0.502565 − 0.009919I
−4.25898 + 3.13951I 0
u = −0.472127 + 1.305790I
a = −0.970835 − 0.577427I
b = −2.14130 + 1.05133I
−7.75277 − 8.37018I 0
u = −0.472127 − 1.305790I
a = −0.970835 + 0.577427I
b = −2.14130 − 1.05133I
−7.75277 + 8.37018I 0
u = −0.485385 + 1.325740I
a = 0.538637 + 0.179909I
b = 0.864234 − 0.172690I
−1.09461 − 8.18682I 0
u = −0.485385 − 1.325740I
a = 0.538637 − 0.179909I
b = 0.864234 + 0.172690I
−1.09461 + 8.18682I 0
u = −0.50188 + 1.32442I
a = 0.375415 − 0.996617I
b = −0.455184 − 0.473111I
−7.57640 − 2.11236I 0
u = −0.50188 − 1.32442I
a = 0.375415 + 0.996617I
b = −0.455184 + 0.473111I
−7.57640 + 2.11236I 0
u = 0.62233 + 1.28194I
a = −1.069290 + 0.406801I
b = −2.07922 − 1.15092I
−6.3009 + 16.4753I 0
u = 0.62233 − 1.28194I
a = −1.069290 − 0.406801I
b = −2.07922 + 1.15092I
−6.3009 − 16.4753I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.548644
a = 0.938206
b = 0.336065
0.951713 10.2780
u = 0.30872 + 1.43489I
a = 0.479050 + 0.788819I
b = −0.076582 + 0.370238I
−8.67982 − 5.51516I 0
u = 0.30872 − 1.43489I
a = 0.479050 − 0.788819I
b = −0.076582 − 0.370238I
−8.67982 + 5.51516I 0
12
II.
I
u
2
= hu
21
+2u
20
+· · ·+b+2, −6u
21
−7u
20
+· · ·+a+7, u
22
+2u
21
+· · ·+2u+1i
(i) Arc colorings
a
3
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
6
=
u
u
3
+ u
a
1
=
u
2
+ 1
u
2
a
10
=
6u
21
+ 7u
20
+ ··· + 7u − 7
−u
21
− 2u
20
+ ··· + 5u − 2
a
4
=
−6u
21
− 13u
20
+ ··· − 35u − 9
−u
20
− 2u
19
+ ··· − 3u − 2
a
9
=
10u
21
+ 12u
20
+ ··· + 13u − 11
u
21
+ 2u
20
+ ··· + 9u + 1
a
8
=
2u
21
− 4u
20
+ ··· − 18u − 19
u
21
+ u
20
+ ··· − 5u − 6
a
12
=
8u
21
+ 11u
20
+ ··· + 13u − 11
2u
21
+ 4u
20
+ ··· + 10u + 1
a
11
=
8u
21
+ 10u
20
+ ··· + 10u − 15
3u
21
+ 5u
20
+ ··· + 9u − 2
a
7
=
u
21
− 5u
20
+ ··· − 13u − 13
u
21
+ u
20
+ ··· − 5u − 6
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −6u
21
−9u
20
−34u
19
−38u
18
−100u
17
−95u
16
−208u
15
−158u
14
−307u
13
−182u
12
−
348u
11
− 137u
10
− 288u
9
− 36u
8
− 183u
7
+ 43u
6
− 64u
5
+ 69u
4
− 21u
3
+ 45u
2
− 4u + 20
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
22
− 12u
21
+ ··· − 16u + 1
c
2
u
22
+ 2u
21
+ ··· + 2u + 1
c
3
u
22
− 9u
20
+ ··· − 8u
2
+ 1
c
4
u
22
− 6u
20
+ ··· + 5u
2
+ 1
c
5
u
22
− 2u
21
+ ··· − 2u + 1
c
6
u
22
− 2u
21
+ ··· − 2u + 1
c
7
, c
8
u
22
− 9u
20
+ ··· − 8u
2
+ 1
c
9
u
22
− 2u
21
+ ··· + 4u
2
+ 1
c
10
u
22
+ 10u
21
+ ··· + 18u + 1
c
11
u
22
+ 2u
21
+ ··· + 2u + 1
c
12
u
22
+ 9u
20
+ ··· + 7u
2
+ 1
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
22
+ 8y
21
+ ··· − 8y + 1
c
2
, c
5
y
22
+ 12y
21
+ ··· + 16y + 1
c
3
, c
7
, c
8
y
22
− 18y
21
+ ··· − 16y + 1
c
4
y
22
− 12y
21
+ ··· + 10y + 1
c
6
, c
11
y
22
+ 10y
21
+ ··· + 18y + 1
c
9
y
22
− 14y
21
+ ··· + 8y + 1
c
10
y
22
+ 2y
21
+ ··· − 18y + 1
c
12
y
22
+ 18y
21
+ ··· + 14y + 1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.241973 + 0.958544I
a = −0.490866 + 0.123430I
b = −2.10277 − 2.55701I
−4.38986 − 0.97753I −11.44106 + 0.80561I
u = −0.241973 − 0.958544I
a = −0.490866 − 0.123430I
b = −2.10277 + 2.55701I
−4.38986 + 0.97753I −11.44106 − 0.80561I
u = 0.680342 + 0.808019I
a = −1.11141 + 1.19166I
b = −1.44518 − 0.36748I
6.14692 + 4.23019I 6.87486 − 8.22378I
u = 0.680342 − 0.808019I
a = −1.11141 − 1.19166I
b = −1.44518 + 0.36748I
6.14692 − 4.23019I 6.87486 + 8.22378I
u = 0.381053 + 0.993854I
a = 0.485823 − 0.931803I
b = 2.51178 + 0.40690I
3.50530 + 4.41296I 8.17984 − 7.57278I
u = 0.381053 − 0.993854I
a = 0.485823 + 0.931803I
b = 2.51178 − 0.40690I
3.50530 − 4.41296I 8.17984 + 7.57278I
u = −0.864576 + 0.756693I
a = −0.705540 − 0.375538I
b = −0.712469 + 0.591982I
3.13466 − 4.55728I 13.4598 + 7.0179I
u = −0.864576 − 0.756693I
a = −0.705540 + 0.375538I
b = −0.712469 − 0.591982I
3.13466 + 4.55728I 13.4598 − 7.0179I
u = 0.344344 + 0.775789I
a = −0.23930 + 1.47914I
b = −1.60383 − 1.37208I
4.32626 − 1.33597I 9.03146 − 2.86152I
u = 0.344344 − 0.775789I
a = −0.23930 − 1.47914I
b = −1.60383 + 1.37208I
4.32626 + 1.33597I 9.03146 + 2.86152I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.683857 + 0.953567I
a = 0.986932 − 0.976839I
b = 1.58711 + 0.21263I
5.68936 + 1.04482I 6.35421 + 3.19394I
u = 0.683857 − 0.953567I
a = 0.986932 + 0.976839I
b = 1.58711 − 0.21263I
5.68936 − 1.04482I 6.35421 − 3.19394I
u = −0.483198 + 1.148360I
a = 0.511255 − 0.042735I
b = 1.178750 + 0.403621I
−1.14942 − 7.14765I 5.07018 + 7.28569I
u = −0.483198 − 1.148360I
a = 0.511255 + 0.042735I
b = 1.178750 − 0.403621I
−1.14942 + 7.14765I 5.07018 − 7.28569I
u = −0.887565 + 0.930577I
a = 0.669634 + 0.226011I
b = 0.920717 − 0.461715I
2.63405 − 1.92174I 16.1641 + 7.0514I
u = −0.887565 − 0.930577I
a = 0.669634 − 0.226011I
b = 0.920717 + 0.461715I
2.63405 + 1.92174I 16.1641 − 7.0514I
u = −0.182700 + 1.302970I
a = −0.532890 + 0.197172I
b = 0.140687 + 0.127074I
−4.66681 − 2.93382I −4.96536 − 0.66259I
u = −0.182700 − 1.302970I
a = −0.532890 − 0.197172I
b = 0.140687 − 0.127074I
−4.66681 + 2.93382I −4.96536 + 0.66259I
u = −0.321038 + 0.588930I
a = 0.76251 − 1.19934I
b = 0.970661 + 0.503731I
1.05601 + 3.62165I 7.15284 − 7.64302I
u = −0.321038 − 0.588930I
a = 0.76251 + 1.19934I
b = 0.970661 − 0.503731I
1.05601 − 3.62165I 7.15284 + 7.64302I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.108546 + 0.545335I
a = −2.33615 + 0.39651I
b = −0.945452 + 0.497914I
−1.48208 + 1.54693I 10.61918 − 2.30760I
u = −0.108546 − 0.545335I
a = −2.33615 − 0.39651I
b = −0.945452 − 0.497914I
−1.48208 − 1.54693I 10.61918 + 2.30760I
18
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
22
− 12u
21
+ ··· − 16u + 1)(u
73
+ 43u
72
+ ··· − 318262u − 20449)
c
2
(u
22
+ 2u
21
+ ··· + 2u + 1)(u
73
− u
72
+ ··· − 54u − 143)
c
3
(u
22
− 9u
20
+ ··· − 8u
2
+ 1)(u
73
+ u
72
+ ··· − 18u − 1)
c
4
(u
22
− 6u
20
+ ··· + 5u
2
+ 1)(u
73
− u
72
+ ··· − 26u − 3)
c
5
(u
22
− 2u
21
+ ··· − 2u + 1)(u
73
− u
72
+ ··· − 54u − 143)
c
6
(u
22
− 2u
21
+ ··· − 2u + 1)(u
73
+ u
72
+ ··· + 280u − 119)
c
7
, c
8
(u
22
− 9u
20
+ ··· − 8u
2
+ 1)(u
73
+ u
72
+ ··· − 18u − 1)
c
9
(u
22
− 2u
21
+ ··· + 4u
2
+ 1)(u
73
− 5u
72
+ ··· + 22u − 1)
c
10
(u
22
+ 10u
21
+ ··· + 18u + 1)(u
73
− 25u
72
+ ··· − 219576u + 14161)
c
11
(u
22
+ 2u
21
+ ··· + 2u + 1)(u
73
+ u
72
+ ··· + 280u − 119)
c
12
(u
22
+ 9u
20
+ ··· + 7u
2
+ 1)(u
73
+ 5u
72
+ ··· − 14u − 1)
19
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
22
+ 8y
21
+ ··· − 8y + 1)
· (y
73
− 13y
72
+ ··· + 6813662274y −418161601)
c
2
, c
5
(y
22
+ 12y
21
+ ··· + 16y + 1)(y
73
+ 43y
72
+ ··· − 318262y −20449)
c
3
, c
7
, c
8
(y
22
− 18y
21
+ ··· − 16y + 1)(y
73
− 19y
72
+ ··· + 78y −1)
c
4
(y
22
− 12y
21
+ ··· + 10y + 1)(y
73
− 9y
72
+ ··· − 140y −9)
c
6
, c
11
(y
22
+ 10y
21
+ ··· + 18y + 1)(y
73
+ 25y
72
+ ··· − 219576y −14161)
c
9
(y
22
− 14y
21
+ ··· + 8y + 1)(y
73
− 71y
72
+ ··· + 74y −1)
c
10
(y
22
+ 2y
21
+ ··· − 18y + 1)
· (y
73
+ 45y
72
+ ··· + 7780282916y −200533921)
c
12
(y
22
+ 18y
21
+ ··· + 14y + 1)(y
73
+ 65y
72
+ ··· − 124y −1)
20
