12a
1183
(K12a
1183
)
A knot diagram
1
Linearized knot diagam
4 10 8 1 12 11 3 5 2 7 6 9
Solving Sequence
1,5
4
2,9
10 8 3 7 12 6 11
c
4
c
1
c
9
c
8
c
3
c
7
c
12
c
5
c
11
c
2
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h7u
26
− 128u
25
+ ··· + 8b + 328, −41u
26
+ 628u
25
+ ··· + 32a + 816, u
27
− 16u
26
+ ··· + 448u − 32i
I
u
2
= h3830888122431a
9
u
4
− 2857501004595a
8
u
4
+ ··· + 8963993636290a − 1366272633452,
− a
9
u
4
− 4a
8
u
4
+ ··· − 5a − 10, u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1i
I
u
3
= h4u
16
+ 12u
15
+ ··· + b − 2, 2u
16
+ 18u
15
+ ··· + 3a + 32, u
17
+ 3u
16
+ ··· + 7u + 3i
* 3 irreducible components of dim
C
= 0, with total 94 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
= h7u
26
− 128u
25
+ · · · + 8b + 328, −41u
26
+ 628u
25
+ · · · + 32a +
816, u
27
− 16u
26
+ · · · + 448u − 32i
(i) Arc colorings
a
1
=
0
u
a
5
=
1
0
a
4
=
1
−u
2
a
2
=
−u
u
3
+ u
a
9
=
1.28125u
26
− 19.6250u
25
+ ··· + 254.500u − 25.5000
−
7
8
u
26
+ 16u
25
+ ··· +
1199
2
u − 41
a
10
=
−1.46875u
26
+ 22.1250u
25
+ ··· + 361.500u − 29.5000
−
9
8
u
26
+
57
4
u
25
+ ··· −
855
2
u + 35
a
8
=
13
32
u
26
−
29
8
u
25
+ ··· + 854u −
133
2
−
7
8
u
26
+ 16u
25
+ ··· +
1199
2
u − 41
a
3
=
1
32
u
26
−
5
16
u
25
+ ··· + 33u − 2
−
9
16
u
26
+
69
8
u
25
+ ··· + 250u − 19
a
7
=
−2.68750u
26
+ 44.4375u
25
+ ··· + 1475.75u − 109.500
−
61
16
u
26
+
449
8
u
25
+ ··· +
777
2
u − 24
a
12
=
45
32
u
26
−
337
16
u
25
+ ··· − 233u + 15
−
23
16
u
26
+
179
8
u
25
+ ··· + 616u − 45
a
6
=
53
32
u
26
−
213
8
u
25
+ ··· −
821
2
u + 25
3
4
u
26
−
81
8
u
25
+ ··· + 119u − 7
a
11
=
−
11
4
u
26
+
309
8
u
25
+ ··· − 967u + 82
33
8
u
26
−
519
8
u
25
+ ··· − 1569u + 110
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
9
4
u
26
+ 37u
25
+ ··· + 348u − 10
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
27
− 16u
26
+ ··· + 448u − 32
c
2
, c
3
, c
7
c
9
u
27
− u
26
+ ··· + 4u
2
+ 1
c
5
, c
6
, c
10
c
11
u
27
− 11u
26
+ ··· + 416u − 32
c
8
, c
12
u
27
+ u
26
+ ··· + 5u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
27
+ 16y
26
+ ··· − 9728y −1024
c
2
, c
3
, c
7
c
9
y
27
− 27y
26
+ ··· − 8y −1
c
5
, c
6
, c
10
c
11
y
27
+ 31y
26
+ ··· − 3584y −1024
c
8
, c
12
y
27
− 5y
26
+ ··· + 3y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.326738 + 0.973251I
a = 1.36638 − 0.75273I
b = −1.17904 − 1.08389I
−5.90216 − 5.12959I −5.71356 − 0.71345I
u = 0.326738 − 0.973251I
a = 1.36638 + 0.75273I
b = −1.17904 + 1.08389I
−5.90216 + 5.12959I −5.71356 + 0.71345I
u = 0.257668 + 1.013350I
a = −1.094370 + 0.580330I
b = 0.870061 + 0.959444I
1.67867 − 3.20907I −3.00867 + 3.20014I
u = 0.257668 − 1.013350I
a = −1.094370 − 0.580330I
b = 0.870061 − 0.959444I
1.67867 + 3.20907I −3.00867 − 3.20014I
u = 0.156189 + 1.077390I
a = 0.815391 − 0.397247I
b = −0.555344 − 0.816446I
3.09390 + 0.00363I 1.18580 − 2.67864I
u = 0.156189 − 1.077390I
a = 0.815391 + 0.397247I
b = −0.555344 + 0.816446I
3.09390 − 0.00363I 1.18580 + 2.67864I
u = 1.165660 + 0.184416I
a = −0.911038 + 0.705453I
b = 1.192060 − 0.654307I
−19.4453 + 9.1728I −13.26883 − 4.48783I
u = 1.165660 − 0.184416I
a = −0.911038 − 0.705453I
b = 1.192060 + 0.654307I
−19.4453 − 9.1728I −13.26883 + 4.48783I
u = −0.135256 + 1.225450I
a = −0.369172 + 0.209810I
b = 0.207180 + 0.480781I
−0.53153 + 2.11620I −4.00000 − 3.37376I
u = −0.135256 − 1.225450I
a = −0.369172 − 0.209810I
b = 0.207180 − 0.480781I
−0.53153 − 2.11620I −4.00000 + 3.37376I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.296730 + 0.234088I
a = 0.629855 − 0.468322I
b = −0.926383 + 0.459847I
−9.64040 + 5.83308I −13.1962 − 6.2251I
u = 1.296730 − 0.234088I
a = 0.629855 + 0.468322I
b = −0.926383 − 0.459847I
−9.64040 − 5.83308I −13.1962 + 6.2251I
u = 0.401898 + 0.513270I
a = 0.05616 − 1.60013I
b = −0.843872 + 0.614264I
−7.16168 + 2.04670I −4.62828 − 4.92551I
u = 0.401898 − 0.513270I
a = 0.05616 + 1.60013I
b = −0.843872 − 0.614264I
−7.16168 − 2.04670I −4.62828 + 4.92551I
u = 0.63266 + 1.30092I
a = −1.110240 + 0.483598I
b = 1.33153 + 1.13838I
−15.9655 − 15.4642I 0
u = 0.63266 − 1.30092I
a = −1.110240 − 0.483598I
b = 1.33153 − 1.13838I
−15.9655 + 15.4642I 0
u = 0.67380 + 1.29759I
a = 0.990312 − 0.341657I
b = −1.11060 − 1.05481I
−6.30603 − 12.55790I 0
u = 0.67380 − 1.29759I
a = 0.990312 + 0.341657I
b = −1.11060 + 1.05481I
−6.30603 + 12.55790I 0
u = 0.75681 + 1.30765I
a = −0.790458 + 0.172262I
b = 0.823487 + 0.903270I
−2.55975 − 7.75483I 0
u = 0.75681 − 1.30765I
a = −0.790458 − 0.172262I
b = 0.823487 − 0.903270I
−2.55975 + 7.75483I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.58357
a = −0.438551
b = 0.694476
−6.13943 0
u = 0.202392 + 0.231714I
a = 0.26309 + 1.63520I
b = 0.325651 − 0.391913I
−0.150445 + 0.974739I −2.92263 − 7.14002I
u = 0.202392 − 0.231714I
a = 0.26309 − 1.63520I
b = 0.325651 + 0.391913I
−0.150445 − 0.974739I −2.92263 + 7.14002I
u = 0.89228 + 1.45430I
a = 0.440805 − 0.117681I
b = −0.564466 − 0.536060I
−4.37833 − 2.08868I 0
u = 0.89228 − 1.45430I
a = 0.440805 + 0.117681I
b = −0.564466 + 0.536060I
−4.37833 + 2.08868I 0
u = 0.58063 + 1.74046I
a = −0.067440 + 0.312189I
b = 0.582509 − 0.063892I
−13.55330 + 2.79514I 0
u = 0.58063 − 1.74046I
a = −0.067440 − 0.312189I
b = 0.582509 + 0.063892I
−13.55330 − 2.79514I 0
7
II. I
u
2
= h3.83 × 10
12
a
9
u
4
− 2.86 × 10
12
a
8
u
4
+ · · · + 8.96 × 10
12
a − 1.37 ×
10
12
, −a
9
u
4
− 4a
8
u
4
+ · · · − 5a − 10, u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1i
(i) Arc colorings
a
1
=
0
u
a
5
=
1
0
a
4
=
1
−u
2
a
2
=
−u
u
3
+ u
a
9
=
a
−1.30396a
9
u
4
+ 0.972636a
8
u
4
+ ··· − 3.05116a + 0.465052
a
10
=
−1.34977a
9
u
4
+ 2.51833a
8
u
4
+ ··· + 0.382620a + 0.196848
0.275845a
9
u
4
+ 1.98098a
8
u
4
+ ··· − 0.891259a + 0.748114
a
8
=
−1.30396a
9
u
4
+ 0.972636a
8
u
4
+ ··· − 2.05116a + 0.465052
−1.30396a
9
u
4
+ 0.972636a
8
u
4
+ ··· − 3.05116a + 0.465052
a
3
=
0.978965a
9
u
4
− 1.44213a
8
u
4
+ ··· − 0.0881825a + 0.194750
−0.311779a
9
u
4
− 0.827493a
8
u
4
+ ··· − 0.104852a − 0.728899
a
7
=
−1.32778a
9
u
4
+ 0.504526a
8
u
4
+ ··· − 0.111225a − 0.415918
−3.49328a
9
u
4
+ 0.486696a
8
u
4
+ ··· + 1.37737a − 1.28533
a
12
=
a
2
u
1.16482a
9
u
4
− 0.841308a
8
u
4
+ ··· − 0.639242a + 0.155880
a
6
=
0.598958a
9
u
4
− 0.536641a
8
u
4
+ ··· − 0.100841a + 0.898935
2.00856a
9
u
4
− 0.391347a
8
u
4
+ ··· − 0.420272a + 1.38748
a
11
=
−0.269881a
9
u
4
− 0.151648a
8
u
4
+ ··· + 0.391092a − 0.370194
−2.37370a
9
u
4
+ 2.91763a
8
u
4
+ ··· + 0.705077a − 0.305615
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
3336817308298
1468946744399
a
9
u
4
+
8995916260558
1468946744399
a
8
u
4
+ ··· −
6523463258754
1468946744399
a −
5778728076718
1468946744399
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
10
c
2
, c
3
, c
7
c
9
u
50
− u
49
+ ··· + 3504u − 928
c
5
, c
6
, c
10
c
11
(u
5
+ u
4
+ 4u
3
+ 3u
2
+ 3u + 1)
10
c
8
, c
12
u
50
+ 5u
49
+ ··· − 80u − 32
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
10
c
2
, c
3
, c
7
c
9
y
50
− 45y
49
+ ··· − 84632320y + 861184
c
5
, c
6
, c
10
c
11
(y
5
+ 7y
4
+ 16y
3
+ 13y
2
+ 3y −1)
10
c
8
, c
12
y
50
− 9y
49
+ ··· − 40704y + 1024
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.339110 + 0.822375I
a = −0.941072 − 0.102065I
b = 1.188350 − 0.588608I
−3.72352 − 1.53058I −3.87605 + 4.43065I
u = 0.339110 + 0.822375I
a = 0.368837 − 1.146040I
b = −0.40610 − 1.63231I
−6.42551 + 0.68339I −12.37057 + 0.20776I
u = 0.339110 + 0.822375I
a = −0.630435 + 1.098070I
b = 0.63922 + 2.16713I
−15.5640 + 1.8012I −13.40362 + 2.06837I
u = 0.339110 + 0.822375I
a = 0.10246 + 1.48727I
b = 0.235191 + 0.808525I
−3.72352 − 1.53058I −3.87605 + 4.43065I
u = 0.339110 + 0.822375I
a = 0.051054 + 0.421661I
b = 2.04277 − 1.49049I
−15.5640 − 4.8623I −13.4036 + 6.7929I
u = 0.339110 + 0.822375I
a = 0.255094 − 0.199412I
b = −1.62129 + 1.17233I
−6.42551 − 3.74455I −12.3706 + 8.6535I
u = 0.339110 + 0.822375I
a = 1.87045 + 0.27748I
b = −1.067550 + 0.085312I
−6.42551 + 0.68339I −12.37057 + 0.20776I
u = 0.339110 + 0.822375I
a = −0.52357 − 2.18737I
b = −0.250496 − 0.142160I
−6.42551 − 3.74455I −12.3706 + 8.6535I
u = 0.339110 + 0.822375I
a = −2.52618 − 0.26440I
b = 1.116810 + 0.146089I
−15.5640 + 1.8012I −13.40362 + 2.06837I
u = 0.339110 + 0.822375I
a = 0.67360 + 2.76175I
b = 0.329451 − 0.184975I
−15.5640 − 4.8623I −13.4036 + 6.7929I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.339110 − 0.822375I
a = −0.941072 + 0.102065I
b = 1.188350 + 0.588608I
−3.72352 + 1.53058I −3.87605 − 4.43065I
u = 0.339110 − 0.822375I
a = 0.368837 + 1.146040I
b = −0.40610 + 1.63231I
−6.42551 − 0.68339I −12.37057 − 0.20776I
u = 0.339110 − 0.822375I
a = −0.630435 − 1.098070I
b = 0.63922 − 2.16713I
−15.5640 − 1.8012I −13.40362 − 2.06837I
u = 0.339110 − 0.822375I
a = 0.10246 − 1.48727I
b = 0.235191 − 0.808525I
−3.72352 + 1.53058I −3.87605 − 4.43065I
u = 0.339110 − 0.822375I
a = 0.051054 − 0.421661I
b = 2.04277 + 1.49049I
−15.5640 + 4.8623I −13.4036 − 6.7929I
u = 0.339110 − 0.822375I
a = 0.255094 + 0.199412I
b = −1.62129 − 1.17233I
−6.42551 + 3.74455I −12.3706 − 8.6535I
u = 0.339110 − 0.822375I
a = 1.87045 − 0.27748I
b = −1.067550 − 0.085312I
−6.42551 − 0.68339I −12.37057 − 0.20776I
u = 0.339110 − 0.822375I
a = −0.52357 + 2.18737I
b = −0.250496 + 0.142160I
−6.42551 + 3.74455I −12.3706 − 8.6535I
u = 0.339110 − 0.822375I
a = −2.52618 + 0.26440I
b = 1.116810 − 0.146089I
−15.5640 − 1.8012I −13.40362 − 2.06837I
u = 0.339110 − 0.822375I
a = 0.67360 − 2.76175I
b = 0.329451 + 0.184975I
−15.5640 + 4.8623I −13.4036 − 6.7929I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.766826
a = 1.01971
b = −0.448297
−1.65154 −2.91000
u = −0.766826
a = 0.888970 + 0.810814I
b = −1.073730 − 0.319738I
−4.35353 − 2.21397I −11.40454 + 4.22289I
u = −0.766826
a = 0.888970 − 0.810814I
b = −1.073730 + 0.319738I
−4.35353 + 2.21397I −11.40454 − 4.22289I
u = −0.766826
a = −0.584614
b = 0.781942
−1.65154 −2.91000
u = −0.766826
a = −1.40023 + 0.41696I
b = 0.681685 − 0.621753I
−4.35353 + 2.21397I −11.40454 − 4.22289I
u = −0.766826
a = −1.40023 − 0.41696I
b = 0.681685 + 0.621753I
−4.35353 − 2.21397I −11.40454 + 4.22289I
u = −0.766826
a = −1.12618 + 1.23565I
b = 1.34736 − 0.48010I
−13.49200 + 3.33174I −12.43759 − 2.36228I
u = −0.766826
a = −1.12618 − 1.23565I
b = 1.34736 + 0.48010I
−13.49200 − 3.33174I −12.43759 + 2.36228I
u = −0.766826
a = 1.75707 + 0.62609I
b = −0.863581 − 0.947532I
−13.49200 − 3.33174I −12.43759 + 2.36228I
u = −0.766826
a = 1.75707 − 0.62609I
b = −0.863581 + 0.947532I
−13.49200 + 3.33174I −12.43759 − 2.36228I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.455697 + 1.200150I
a = 0.259834 − 0.944414I
b = 0.485723 + 0.128685I
−10.02050 + 1.06909I −9.17442 − 1.13631I
u = −0.455697 + 1.200150I
a = 0.929129 + 0.303128I
b = −0.764563 + 0.575714I
1.81994 + 4.40083I 0.35315 − 3.49859I
u = −0.455697 + 1.200150I
a = −0.924621 − 0.502186I
b = 1.61901 − 1.43093I
−10.02050 + 7.73258I −9.17442 − 5.86086I
u = −0.455697 + 1.200150I
a = 0.807918 + 0.442221I
b = −1.28871 + 1.21910I
−0.88204 + 6.61480I −8.14137 − 7.72148I
u = −0.455697 + 1.200150I
a = −0.630666 − 0.397591I
b = 0.787201 − 0.976962I
1.81994 + 4.40083I 0.35315 − 3.49859I
u = −0.455697 + 1.200150I
a = −1.244130 − 0.601390I
b = 0.898898 − 0.768106I
−0.88204 + 6.61480I −8.14137 − 7.72148I
u = −0.455697 + 1.200150I
a = 0.174801 + 0.486058I
b = −0.326391 + 0.480267I
−0.88204 + 2.18686I −8.14137 + 0.72431I
u = −0.455697 + 1.200150I
a = −0.439999 − 0.104891I
b = 0.663000 + 0.011708I
−0.88204 + 2.18686I −8.14137 + 0.72431I
u = −0.455697 + 1.200150I
a = 0.040595 + 0.389304I
b = −1.015040 − 0.742207I
−10.02050 + 1.06909I −9.17442 − 1.13631I
u = −0.455697 + 1.200150I
a = 1.48973 + 0.78335I
b = −1.024050 + 0.880841I
−10.02050 + 7.73258I −9.17442 − 5.86086I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.455697 − 1.200150I
a = 0.259834 + 0.944414I
b = 0.485723 − 0.128685I
−10.02050 − 1.06909I −9.17442 + 1.13631I
u = −0.455697 − 1.200150I
a = 0.929129 − 0.303128I
b = −0.764563 − 0.575714I
1.81994 − 4.40083I 0.35315 + 3.49859I
u = −0.455697 − 1.200150I
a = −0.924621 + 0.502186I
b = 1.61901 + 1.43093I
−10.02050 − 7.73258I −9.17442 + 5.86086I
u = −0.455697 − 1.200150I
a = 0.807918 − 0.442221I
b = −1.28871 − 1.21910I
−0.88204 − 6.61480I −8.14137 + 7.72148I
u = −0.455697 − 1.200150I
a = −0.630666 + 0.397591I
b = 0.787201 + 0.976962I
1.81994 − 4.40083I 0.35315 + 3.49859I
u = −0.455697 − 1.200150I
a = −1.244130 + 0.601390I
b = 0.898898 + 0.768106I
−0.88204 − 6.61480I −8.14137 + 7.72148I
u = −0.455697 − 1.200150I
a = 0.174801 − 0.486058I
b = −0.326391 − 0.480267I
−0.88204 − 2.18686I −8.14137 − 0.72431I
u = −0.455697 − 1.200150I
a = −0.439999 + 0.104891I
b = 0.663000 − 0.011708I
−0.88204 − 2.18686I −8.14137 − 0.72431I
u = −0.455697 − 1.200150I
a = 0.040595 − 0.389304I
b = −1.015040 + 0.742207I
−10.02050 − 1.06909I −9.17442 + 1.13631I
u = −0.455697 − 1.200150I
a = 1.48973 − 0.78335I
b = −1.024050 − 0.880841I
−10.02050 − 7.73258I −9.17442 + 5.86086I
15
III. I
u
3
=
h4u
16
+12u
15
+· · ·+b−2, 2u
16
+18u
15
+· · ·+3a+32, u
17
+3u
16
+· · ·+7u+3i
(i) Arc colorings
a
1
=
0
u
a
5
=
1
0
a
4
=
1
−u
2
a
2
=
−u
u
3
+ u
a
9
=
−
2
3
u
16
− 6u
15
+ ··· −
103
3
u −
32
3
−4u
16
− 12u
15
+ ··· − 6u + 2
a
10
=
−
11
3
u
16
− 15u
15
+ ··· −
145
3
u −
32
3
−2u
16
− 6u
15
+ ··· − u + 2
a
8
=
−
14
3
u
16
− 18u
15
+ ··· −
121
3
u −
26
3
−4u
16
− 12u
15
+ ··· − 6u + 2
a
3
=
4
3
u
16
+ 5u
15
+ ··· +
53
3
u +
16
3
u
16
+ 3u
15
+ ··· + 3u − 1
a
7
=
8u
16
+ 23u
15
+ ··· + 8u − 12
−3u
15
− 9u
14
+ ··· − 37u − 15
a
12
=
2
3
u
16
+ u
15
+ ··· −
26
3
u −
19
3
−u
16
− 3u
15
+ ··· − 10u − 2
a
6
=
−
14
3
u
16
− 14u
15
+ ··· −
109
3
u −
14
3
u
15
+ 3u
14
+ ··· + 22u + 11
a
11
=
1
3
u
16
+ 6u
15
+ ··· +
230
3
u +
94
3
4u
16
+ 12u
15
+ ··· + 24u + 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −2u
16
− 2u
15
− 11u
14
− 6u
13
− 21u
12
− u
11
− 8u
10
+ 21u
9
+
25u
8
+ 41u
7
+ 51u
6
+ 51u
5
+ 47u
4
+ 35u
3
+ 25u
2
+ 10u − 3
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
17
− 3u
16
+ ··· + 7u − 3
c
2
, c
7
u
17
+ u
16
+ ··· − 5u
2
+ 1
c
3
, c
9
u
17
− u
16
+ ··· + 5u
2
− 1
c
4
u
17
+ 3u
16
+ ··· + 7u + 3
c
5
, c
6
u
17
+ 12u
15
+ ··· + 3u + 1
c
8
, c
12
u
17
− u
16
+ ··· + u + 1
c
10
, c
11
u
17
+ 12u
15
+ ··· + 3u − 1
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
17
+ 13y
16
+ ··· − 71y −9
c
2
, c
3
, c
7
c
9
y
17
− 17y
16
+ ··· + 10y −1
c
5
, c
6
, c
10
c
11
y
17
+ 24y
16
+ ··· − y −1
c
8
, c
12
y
17
− 3y
16
+ ··· + y −1
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.593894 + 0.802495I
a = −0.180639 − 0.594767I
b = 0.370017 − 0.498191I
−4.67950 − 0.64322I −10.55963 − 0.15588I
u = 0.593894 − 0.802495I
a = −0.180639 + 0.594767I
b = 0.370017 + 0.498191I
−4.67950 + 0.64322I −10.55963 + 0.15588I
u = −0.906544
a = −0.854243
b = 0.774409
−2.37375 −16.8760
u = −0.735692 + 0.527270I
a = 0.520506 + 1.068180I
b = −0.946153 − 0.511408I
−7.87303 − 1.51903I −13.64272 − 0.09514I
u = −0.735692 − 0.527270I
a = 0.520506 − 1.068180I
b = −0.946153 + 0.511408I
−7.87303 + 1.51903I −13.64272 + 0.09514I
u = −0.458344 + 1.062210I
a = 1.265050 + 0.613512I
b = −1.23151 + 1.06256I
−6.20697 + 5.92549I −9.60300 − 7.59115I
u = −0.458344 − 1.062210I
a = 1.265050 − 0.613512I
b = −1.23151 − 1.06256I
−6.20697 − 5.92549I −9.60300 + 7.59115I
u = 0.096850 + 0.818804I
a = −1.20033 − 1.49411I
b = 1.10713 − 1.12754I
−14.9635 − 3.6269I −8.98825 + 1.04806I
u = 0.096850 − 0.818804I
a = −1.20033 + 1.49411I
b = 1.10713 + 1.12754I
−14.9635 + 3.6269I −8.98825 − 1.04806I
u = 0.177512 + 0.760501I
a = 0.83863 + 1.36734I
b = −0.890995 + 0.880497I
−6.11660 − 2.68617I −9.52611 + 0.92826I
19
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.177512 − 0.760501I
a = 0.83863 − 1.36734I
b = −0.890995 − 0.880497I
−6.11660 + 2.68617I −9.52611 − 0.92826I
u = −0.479649 + 1.148250I
a = −0.902382 − 0.459289I
b = 0.960206 − 0.815864I
0.69293 + 4.86005I −8.33294 − 6.22017I
u = −0.479649 − 1.148250I
a = −0.902382 + 0.459289I
b = 0.960206 + 0.815864I
0.69293 − 4.86005I −8.33294 + 6.22017I
u = 0.27357 + 1.41350I
a = 0.387595 − 0.159279I
b = 0.331176 + 0.504291I
−12.89620 + 2.38711I −8.51735 + 0.78017I
u = 0.27357 − 1.41350I
a = 0.387595 + 0.159279I
b = 0.331176 − 0.504291I
−12.89620 − 2.38711I −8.51735 − 0.78017I
u = −0.51487 + 1.41784I
a = 0.365354 + 0.281395I
b = −0.587082 + 0.373130I
−1.05312 + 3.04104I −10.39187 − 9.53113I
u = −0.51487 − 1.41784I
a = 0.365354 − 0.281395I
b = −0.587082 − 0.373130I
−1.05312 − 3.04104I −10.39187 + 9.53113I
20
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
10
)(u
17
− 3u
16
+ ··· + 7u − 3)
· (u
27
− 16u
26
+ ··· + 448u − 32)
c
2
, c
7
(u
17
+ u
16
+ ··· − 5u
2
+ 1)(u
27
− u
26
+ ··· + 4u
2
+ 1)
· (u
50
− u
49
+ ··· + 3504u − 928)
c
3
, c
9
(u
17
− u
16
+ ··· + 5u
2
− 1)(u
27
− u
26
+ ··· + 4u
2
+ 1)
· (u
50
− u
49
+ ··· + 3504u − 928)
c
4
((u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
10
)(u
17
+ 3u
16
+ ··· + 7u + 3)
· (u
27
− 16u
26
+ ··· + 448u − 32)
c
5
, c
6
((u
5
+ u
4
+ 4u
3
+ 3u
2
+ 3u + 1)
10
)(u
17
+ 12u
15
+ ··· + 3u + 1)
· (u
27
− 11u
26
+ ··· + 416u − 32)
c
8
, c
12
(u
17
− u
16
+ ··· + u + 1)(u
27
+ u
26
+ ··· + 5u + 1)
· (u
50
+ 5u
49
+ ··· − 80u − 32)
c
10
, c
11
((u
5
+ u
4
+ 4u
3
+ 3u
2
+ 3u + 1)
10
)(u
17
+ 12u
15
+ ··· + 3u − 1)
· (u
27
− 11u
26
+ ··· + 416u − 32)
21
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
10
)(y
17
+ 13y
16
+ ··· − 71y −9)
· (y
27
+ 16y
26
+ ··· − 9728y −1024)
c
2
, c
3
, c
7
c
9
(y
17
− 17y
16
+ ··· + 10y −1)(y
27
− 27y
26
+ ··· − 8y −1)
· (y
50
− 45y
49
+ ··· − 84632320y + 861184)
c
5
, c
6
, c
10
c
11
((y
5
+ 7y
4
+ 16y
3
+ 13y
2
+ 3y −1)
10
)(y
17
+ 24y
16
+ ··· − y −1)
· (y
27
+ 31y
26
+ ··· − 3584y −1024)
c
8
, c
12
(y
17
− 3y
16
+ ··· + y −1)(y
27
− 5y
26
+ ··· + 3y −1)
· (y
50
− 9y
49
+ ··· − 40704y + 1024)
22
