11a
170
(K11a
170
)
A knot diagram
1
Linearized knot diagam
5 1 7 8 2 11 10 6 3 4 9
Solving Sequence
7,10 4,8
5 11 3 6 9 1 2
c
7
c
4
c
10
c
3
c
6
c
9
c
11
c
2
c
1
, c
5
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.47044 × 10
43
u
38
+ 4.27047 × 10
44
u
37
+ ··· + 9.58937 × 10
43
b − 1.14769 × 10
44
,
5.73844 × 10
43
u
38
− 1.63474 × 10
45
u
37
+ ··· + 1.91787 × 10
44
a + 3.56267 × 10
43
, u
39
− 29u
38
+ ··· + 14u − 4i
I
u
2
= h2430u
18
a
3
− 5190u
18
a
2
+ ··· + 12488a
2
− 9913, 24u
18
a
3
+ 64u
18
a
2
+ ··· + 58a + 349,
u
19
+ 9u
18
+ ··· − u − 2i
I
u
3
= h1560902u
18
+ 15217104u
17
+ ··· + 4517673b + 1159923,
− 386641u
18
+ 43014u
17
+ ··· + 13553019a − 28935738, u
19
+ 12u
18
+ ··· + 51u + 9i
I
v
1
= ha, b + 1, v
2
− v + 1i
I
v
2
= ha, b + v −1, v
2
− v + 1i
* 5 irreducible components of dim
C
= 0, with total 138 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−1.47 × 10
43
u
38
+ 4.27 × 10
44
u
37
+ · · · + 9.59 × 10
43
b − 1.15 ×
10
44
, 5.74 × 10
43
u
38
− 1.63 × 10
45
u
37
+ · · · + 1.92 × 10
44
a + 3.56 ×
10
43
, u
39
− 29u
38
+ · · · + 14u − 4i
(i) Arc colorings
a
7
=
1
0
a
10
=
0
u
a
4
=
−0.299208u
38
+ 8.52370u
37
+ ··· + 2.19933u − 0.185762
0.153341u
38
− 4.45334u
37
+ ··· − 4.00316u + 1.19683
a
8
=
1
−u
2
a
5
=
−0.139409u
38
+ 3.92433u
37
+ ··· − 0.853890u + 0.397710
0.126095u
38
− 3.74672u
37
+ ··· − 4.15512u + 1.05762
a
11
=
−0.238011u
38
+ 7.00101u
37
+ ··· + 10.6223u + 0.765363
−0.0987012u
38
+ 2.65437u
37
+ ··· − 3.09751u + 0.952043
a
3
=
−0.145868u
38
+ 4.07037u
37
+ ··· − 1.80383u + 1.01107
0.153341u
38
− 4.45334u
37
+ ··· − 4.00316u + 1.19683
a
6
=
−0.0442803u
38
+ 1.19691u
37
+ ··· + 8.27899u − 3.04017
0.295182u
38
− 8.17668u
37
+ ··· + 1.08639u + 0.571926
a
9
=
−0.227449u
38
+ 6.41835u
37
+ ··· + 0.0934401u + 3.06425
0.109263u
38
− 3.23703u
37
+ ··· − 5.43137u + 1.34685
a
1
=
−0.0331425u
38
+ 1.03976u
37
+ ··· + 0.307399u + 0.302283
−0.247066u
38
+ 6.86896u
37
+ ··· + 0.529326u − 0.320849
a
2
=
−0.150801u
38
+ 4.40571u
37
+ ··· + 1.28760u − 0.423103
−0.240955u
38
+ 6.61929u
37
+ ··· − 0.756100u + 0.338269
a
2
=
−0.150801u
38
+ 4.40571u
37
+ ··· + 1.28760u − 0.423103
−0.240955u
38
+ 6.61929u
37
+ ··· − 0.756100u + 0.338269
(ii) Obstruction class = −1
(iii) Cusp Shapes = −1.44324u
38
+ 40.0008u
37
+ ··· − 2.64538u − 0.932055
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
39
+ 9u
38
+ ··· − 124u − 16
c
2
u
39
+ 17u
38
+ ··· + 1200u + 256
c
3
, c
10
u
39
− 4u
37
+ ··· + u − 1
c
4
, c
9
u
39
− u
38
+ ··· + 47u + 17
c
6
u
39
+ 37u
38
+ ··· + 5505024u + 262144
c
7
u
39
+ 29u
38
+ ··· + 14u + 4
c
8
, c
11
u
39
− u
38
+ ··· − u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
39
− 17y
38
+ ··· + 1200y −256
c
2
y
39
+ 11y
38
+ ··· − 231680y −65536
c
3
, c
10
y
39
− 8y
38
+ ··· + 9y −1
c
4
, c
9
y
39
− 19y
38
+ ··· + 3399y −289
c
6
y
39
− 5y
38
+ ··· + 515396075520y −68719476736
c
7
y
39
− 11y
38
+ ··· − 276y −16
c
8
, c
11
y
39
+ y
38
+ ··· + 37y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.331870 + 0.943428I
a = −0.133268 − 0.994133I
b = −0.893665 + 0.455652I
−3.26169 − 3.52438I 0
u = 0.331870 − 0.943428I
a = −0.133268 + 0.994133I
b = −0.893665 − 0.455652I
−3.26169 + 3.52438I 0
u = 0.841757 + 0.821032I
a = −0.625635 − 0.086146I
b = 0.455904 + 0.586181I
−1.14633 − 4.05626I 0
u = 0.841757 − 0.821032I
a = −0.625635 + 0.086146I
b = 0.455904 − 0.586181I
−1.14633 + 4.05626I 0
u = 0.817409 + 0.895529I
a = 0.147866 − 0.842126I
b = −0.875015 + 0.555944I
−5.58025 + 3.26982I 0
u = 0.817409 − 0.895529I
a = 0.147866 + 0.842126I
b = −0.875015 − 0.555944I
−5.58025 − 3.26982I 0
u = 0.419302 + 0.634476I
a = −0.038397 + 1.226960I
b = 0.794577 − 0.490104I
−1.48621 + 0.90379I −4.25055 − 1.87469I
u = 0.419302 − 0.634476I
a = −0.038397 − 1.226960I
b = 0.794577 + 0.490104I
−1.48621 − 0.90379I −4.25055 + 1.87469I
u = −0.562878 + 1.206500I
a = 0.021414 − 0.311325I
b = −0.363558 − 0.201074I
1.74925 − 1.27793I 0
u = −0.562878 − 1.206500I
a = 0.021414 + 0.311325I
b = −0.363558 + 0.201074I
1.74925 + 1.27793I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.301200 + 0.541325I
a = −0.372119 + 0.962153I
b = 1.00504 − 1.05051I
4.42472 + 1.39638I 0
u = 1.301200 − 0.541325I
a = −0.372119 − 0.962153I
b = 1.00504 + 1.05051I
4.42472 − 1.39638I 0
u = 1.09375 + 0.89879I
a = −0.048210 + 1.101960I
b = 1.04316 − 1.16194I
−0.36330 + 10.93520I 0
u = 1.09375 − 0.89879I
a = −0.048210 − 1.101960I
b = 1.04316 + 1.16194I
−0.36330 − 10.93520I 0
u = 1.27453 + 0.71084I
a = 0.227363 − 1.011290I
b = −1.00865 + 1.12730I
6.38619 + 7.86261I 0
u = 1.27453 − 0.71084I
a = 0.227363 + 1.011290I
b = −1.00865 − 1.12730I
6.38619 − 7.86261I 0
u = 1.49152
a = 0.906411
b = −1.35193
−6.30934 0
u = −0.034630 + 0.476179I
a = 0.57531 + 1.32639I
b = 0.651520 − 0.228017I
−1.40805 + 0.45537I −6.68789 − 0.37229I
u = −0.034630 − 0.476179I
a = 0.57531 − 1.32639I
b = 0.651520 + 0.228017I
−1.40805 − 0.45537I −6.68789 + 0.37229I
u = −0.305932 + 0.311045I
a = 1.08603 + 1.91133I
b = 0.926761 + 0.246934I
−0.07010 − 4.24589I −2.71126 + 7.01324I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.305932 − 0.311045I
a = 1.08603 − 1.91133I
b = 0.926761 − 0.246934I
−0.07010 + 4.24589I −2.71126 − 7.01324I
u = 0.166848 + 0.352846I
a = 0.73742 + 2.79209I
b = 0.862139 − 0.726050I
−0.162274 + 0.211332I −1.308088 + 0.536675I
u = 0.166848 − 0.352846I
a = 0.73742 − 2.79209I
b = 0.862139 + 0.726050I
−0.162274 − 0.211332I −1.308088 − 0.536675I
u = 1.24696 + 1.01994I
a = 0.026843 − 0.978351I
b = −1.03133 + 1.19259I
6.6772 + 13.2005I 0
u = 1.24696 − 1.01994I
a = 0.026843 + 0.978351I
b = −1.03133 − 1.19259I
6.6772 − 13.2005I 0
u = 1.22434 + 1.08925I
a = 0.011484 + 0.970890I
b = 1.04348 − 1.20121I
4.8624 + 19.2051I 0
u = 1.22434 − 1.08925I
a = 0.011484 − 0.970890I
b = 1.04348 + 1.20121I
4.8624 − 19.2051I 0
u = −0.318547 + 0.066288I
a = −2.76662 − 1.78349I
b = −0.999521 − 0.384730I
0.0975477 − 0.0620158I −2.09239 + 0.09201I
u = −0.318547 − 0.066288I
a = −2.76662 + 1.78349I
b = −0.999521 + 0.384730I
0.0975477 + 0.0620158I −2.09239 − 0.09201I
u = −0.103070 + 0.291494I
a = −2.92237 − 2.35332I
b = −0.987188 + 0.609296I
−0.09530 + 3.97123I −1.67802 − 6.97168I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.103070 − 0.291494I
a = −2.92237 + 2.35332I
b = −0.987188 − 0.609296I
−0.09530 − 3.97123I −1.67802 + 6.97168I
u = 1.76013 + 0.77135I
a = −0.314047 + 0.368852I
b = 0.837278 − 0.406987I
2.84675 + 3.80672I 0
u = 1.76013 − 0.77135I
a = −0.314047 − 0.368852I
b = 0.837278 + 0.406987I
2.84675 − 3.80672I 0
u = 1.62789 + 1.03730I
a = 0.210948 − 0.444220I
b = −0.804192 + 0.504323I
1.25508 + 10.27040I 0
u = 1.62789 − 1.03730I
a = 0.210948 + 0.444220I
b = −0.804192 − 0.504323I
1.25508 − 10.27040I 0
u = 1.55330 + 1.50941I
a = −0.261427 − 0.177739I
b = 0.137795 + 0.670683I
4.32938 − 9.77720I 0
u = 1.55330 − 1.50941I
a = −0.261427 + 0.177739I
b = 0.137795 − 0.670683I
4.32938 + 9.77720I 0
u = 1.42000 + 1.74003I
a = 0.234216 + 0.122995I
b = −0.118571 − 0.582195I
5.48378 − 3.90827I 0
u = 1.42000 − 1.74003I
a = 0.234216 − 0.122995I
b = −0.118571 + 0.582195I
5.48378 + 3.90827I 0
8
II. I
u
2
= h2430u
18
a
3
− 5190u
18
a
2
+ · · · + 12488a
2
− 9913, 24u
18
a
3
+
64u
18
a
2
+ · · · + 58a + 349, u
19
+ 9u
18
+ · · · − u − 2i
(i) Arc colorings
a
7
=
1
0
a
10
=
0
u
a
4
=
a
−0.332968a
3
u
18
+ 0.711154a
2
u
18
+ ··· − 1.71115a
2
+ 1.35832
a
8
=
1
−u
2
a
5
=
−0.332968a
3
u
18
+ 0.711154a
2
u
18
+ ··· + a + 1.35832
−1.00110a
3
u
18
− 0.133461a
2
u
18
+ ··· + 1.13346a
2
+ 1.92505
a
11
=
−a
2
u
0.711154a
3
u
18
+ 0.332968a
2
u
18
+ ··· − 4a − 0.999863
a
3
=
−0.332968a
3
u
18
+ 0.711154a
2
u
18
+ ··· + a + 1.35832
−0.332968a
3
u
18
+ 0.711154a
2
u
18
+ ··· − 1.71115a
2
+ 1.35832
a
6
=
−0.144423a
3
u
18
− 0.333516a
2
u
18
+ ··· − 0.666484a
2
+ 0.500069
0.711154a
3
u
18
+ 0.332968a
2
u
18
+ ··· − 4a + 0.000137024
a
9
=
0.155385a
3
u
18
+ 0.668128a
2
u
18
+ ··· − 0.668128a
2
− 0.000548095
−0.555769a
3
u
18
+ 0.335160a
2
u
18
+ ··· + 4a + 0.999315
a
1
=
−0.411346a
3
u
18
+ 0.668676a
2
u
18
+ ··· − 0.668676a
2
+ 0.499246
−0.133461a
3
u
18
+ 1.00110a
2
u
18
+ ··· − 2a − 0.000411072
a
2
=
−0.676350a
3
u
18
+ 0.654426a
2
u
18
+ ··· − a + 1.50459
−0.338449a
3
u
18
+ 1.04385a
2
u
18
+ ··· − 6a + 0.983557
a
2
=
−0.676350a
3
u
18
+ 0.654426a
2
u
18
+ ··· − a + 1.50459
−0.338449a
3
u
18
+ 1.04385a
2
u
18
+ ··· − 6a + 0.983557
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
10380
3649
u
18
a
3
−
4860
3649
u
18
a
2
+ ··· + 16a +
62031
3649
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
(u
19
− 2u
18
+ ··· − 4u + 1)
4
c
2
(u
19
+ 8u
18
+ ··· + 4u + 1)
4
c
3
, c
10
u
76
+ 4u
75
+ ··· − 13u + 1
c
4
, c
9
u
76
+ 2u
75
+ ··· − 461147u + 92641
c
6
(u
2
− u + 1)
38
c
7
(u
19
− 9u
18
+ ··· − u + 2)
4
c
8
, c
11
u
76
− 3u
75
+ ··· + 7318u + 1741
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
19
− 8y
18
+ ··· + 4y −1)
4
c
2
(y
19
+ 8y
18
+ ··· − 16y −1)
4
c
3
, c
10
y
76
+ 26y
75
+ ··· + 75y + 1
c
4
, c
9
y
76
− 34y
75
+ ··· − 289799457437y + 8582354881
c
6
(y
2
+ y + 1)
38
c
7
(y
19
− 3y
18
+ ··· + 37y −4)
4
c
8
, c
11
y
76
− 31y
75
+ ··· − 27023766y + 3031081
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.488744 + 1.038280I
a = −0.046618 + 0.988356I
b = −0.79374 − 1.47743I
0.05398 − 9.62803I −3.53397 + 12.41778I
u = −0.488744 + 1.038280I
a = −0.293242 + 0.933326I
b = −0.111329 − 0.106061I
0.05398 − 5.56826I −3.53397 + 5.48958I
u = −0.488744 + 1.038280I
a = 0.87027 − 1.17413I
b = 1.003410 + 0.531456I
0.05398 − 9.62803I −3.53397 + 12.41778I
u = −0.488744 + 1.038280I
a = 0.0423036 − 0.1271370I
b = 0.825736 + 0.760626I
0.05398 − 5.56826I −3.53397 + 5.48958I
u = −0.488744 − 1.038280I
a = −0.046618 − 0.988356I
b = −0.79374 + 1.47743I
0.05398 + 9.62803I −3.53397 − 12.41778I
u = −0.488744 − 1.038280I
a = −0.293242 − 0.933326I
b = −0.111329 + 0.106061I
0.05398 + 5.56826I −3.53397 − 5.48958I
u = −0.488744 − 1.038280I
a = 0.87027 + 1.17413I
b = 1.003410 − 0.531456I
0.05398 + 9.62803I −3.53397 − 12.41778I
u = −0.488744 − 1.038280I
a = 0.0423036 + 0.1271370I
b = 0.825736 − 0.760626I
0.05398 + 5.56826I −3.53397 − 5.48958I
u = −0.752606 + 0.874521I
a = 0.009232 − 0.929025I
b = 0.89425 + 1.37563I
1.75286 − 5.17897I 0.41778 + 7.25838I
u = −0.752606 + 0.874521I
a = 0.130623 − 0.587298I
b = −0.207899 + 0.298912I
1.75286 − 1.11920I 0.417778 + 0.330175I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.752606 + 0.874521I
a = −0.39813 + 1.36519I
b = −0.805505 − 0.707263I
1.75286 − 5.17897I 0.41778 + 7.25838I
u = −0.752606 + 0.874521I
a = −0.313905 + 0.032415I
b = −0.415297 − 0.556237I
1.75286 − 1.11920I 0.417778 + 0.330175I
u = −0.752606 − 0.874521I
a = 0.009232 + 0.929025I
b = 0.89425 − 1.37563I
1.75286 + 5.17897I 0.41778 − 7.25838I
u = −0.752606 − 0.874521I
a = 0.130623 + 0.587298I
b = −0.207899 − 0.298912I
1.75286 + 1.11920I 0.417778 − 0.330175I
u = −0.752606 − 0.874521I
a = −0.39813 − 1.36519I
b = −0.805505 + 0.707263I
1.75286 + 5.17897I 0.41778 − 7.25838I
u = −0.752606 − 0.874521I
a = −0.313905 − 0.032415I
b = −0.415297 + 0.556237I
1.75286 + 1.11920I 0.417778 − 0.330175I
u = −1.211130 + 0.137559I
a = −0.836689 + 0.841595I
b = 0.089876 − 0.698008I
4.59520 − 0.63634I 7.58619 − 0.25531I
u = −1.211130 + 0.137559I
a = 0.695655 + 1.094640I
b = −0.211353 − 0.748765I
4.59520 − 4.69611I 7.58619 + 6.67289I
u = −1.211130 + 0.137559I
a = −0.102962 − 0.629929I
b = 0.99311 + 1.23007I
4.59520 − 4.69611I 7.58619 + 6.67289I
u = −1.211130 + 0.137559I
a = 0.137888 − 0.560665I
b = −0.89757 + 1.13438I
4.59520 − 0.63634I 7.58619 − 0.25531I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.211130 − 0.137559I
a = −0.836689 − 0.841595I
b = 0.089876 + 0.698008I
4.59520 + 0.63634I 7.58619 + 0.25531I
u = −1.211130 − 0.137559I
a = 0.695655 − 1.094640I
b = −0.211353 + 0.748765I
4.59520 + 4.69611I 7.58619 − 6.67289I
u = −1.211130 − 0.137559I
a = −0.102962 + 0.629929I
b = 0.99311 − 1.23007I
4.59520 + 4.69611I 7.58619 − 6.67289I
u = −1.211130 − 0.137559I
a = 0.137888 + 0.560665I
b = −0.89757 − 1.13438I
4.59520 + 0.63634I 7.58619 + 0.25531I
u = 0.687103 + 0.235969I
a = 0.041834 − 0.923046I
b = 1.52253 + 1.30009I
4.06740 + 10.25010I 5.86786 − 12.03410I
u = 0.687103 + 0.235969I
a = 0.61351 + 1.33915I
b = 1.13417 − 1.00234I
4.06740 + 6.19033I 5.86786 − 5.10589I
u = 0.687103 + 0.235969I
a = −1.02838 + 1.81197I
b = −0.105545 − 1.064900I
4.06740 + 6.19033I 5.86786 − 5.10589I
u = 0.687103 + 0.235969I
a = −2.56334 − 1.01181I
b = −0.246555 + 0.624356I
4.06740 + 10.25010I 5.86786 − 12.03410I
u = 0.687103 − 0.235969I
a = 0.041834 + 0.923046I
b = 1.52253 − 1.30009I
4.06740 − 10.25010I 5.86786 + 12.03410I
u = 0.687103 − 0.235969I
a = 0.61351 − 1.33915I
b = 1.13417 + 1.00234I
4.06740 − 6.19033I 5.86786 + 5.10589I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.687103 − 0.235969I
a = −1.02838 − 1.81197I
b = −0.105545 + 1.064900I
4.06740 − 6.19033I 5.86786 + 5.10589I
u = 0.687103 − 0.235969I
a = −2.56334 + 1.01181I
b = −0.246555 − 0.624356I
4.06740 − 10.25010I 5.86786 + 12.03410I
u = 0.689008 + 0.139635I
a = −0.095129 + 1.010870I
b = −1.45640 − 1.29970I
5.90964 + 4.35931I 9.40004 − 6.47018I
u = 0.689008 + 0.139635I
a = −0.409287 − 1.280010I
b = −1.19567 + 1.13465I
5.90964 + 0.29954I 9.40004 + 0.45802I
u = 0.689008 + 0.139635I
a = 1.34631 − 1.91963I
b = 0.103269 + 0.939085I
5.90964 + 0.29954I 9.40004 + 0.45802I
u = 0.689008 + 0.139635I
a = 2.39759 + 1.40044I
b = 0.206697 − 0.683213I
5.90964 + 4.35931I 9.40004 − 6.47018I
u = 0.689008 − 0.139635I
a = −0.095129 − 1.010870I
b = −1.45640 + 1.29970I
5.90964 − 4.35931I 9.40004 + 6.47018I
u = 0.689008 − 0.139635I
a = −0.409287 + 1.280010I
b = −1.19567 − 1.13465I
5.90964 − 0.29954I 9.40004 − 0.45802I
u = 0.689008 − 0.139635I
a = 1.34631 + 1.91963I
b = 0.103269 − 0.939085I
5.90964 − 0.29954I 9.40004 − 0.45802I
u = 0.689008 − 0.139635I
a = 2.39759 − 1.40044I
b = 0.206697 + 0.683213I
5.90964 − 4.35931I 9.40004 + 6.47018I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.378245 + 0.567353I
a = 0.131552 + 1.078100I
b = −1.01749 − 1.65463I
−2.19784 − 2.79119I −7.49818 + 10.51788I
u = −0.378245 + 0.567353I
a = −0.324334 + 0.098555I
b = 1.389240 + 0.131080I
−2.19784 + 1.26857I −7.49818 + 3.58967I
u = −0.378245 + 0.567353I
a = 0.97020 + 1.80181I
b = −0.066762 + 0.221290I
−2.19784 + 1.26857I −7.49818 + 3.58967I
u = −0.378245 + 0.567353I
a = 1.19128 − 2.58761I
b = 0.661419 + 0.333147I
−2.19784 − 2.79119I −7.49818 + 10.51788I
u = −0.378245 − 0.567353I
a = 0.131552 − 1.078100I
b = −1.01749 + 1.65463I
−2.19784 + 2.79119I −7.49818 − 10.51788I
u = −0.378245 − 0.567353I
a = −0.324334 − 0.098555I
b = 1.389240 − 0.131080I
−2.19784 − 1.26857I −7.49818 − 3.58967I
u = −0.378245 − 0.567353I
a = 0.97020 − 1.80181I
b = −0.066762 − 0.221290I
−2.19784 − 1.26857I −7.49818 − 3.58967I
u = −0.378245 − 0.567353I
a = 1.19128 + 2.58761I
b = 0.661419 − 0.333147I
−2.19784 + 2.79119I −7.49818 − 10.51788I
u = −0.865146 + 1.042810I
a = 0.045926 − 0.937417I
b = 0.80203 + 1.30087I
1.73711 − 5.29191I −1.82857 + 8.05106I
u = −0.865146 + 1.042810I
a = −0.360952 + 1.068560I
b = −0.937819 − 0.858895I
1.73711 − 5.29191I −1.82857 + 8.05106I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.865146 + 1.042810I
a = 0.296569 − 0.571023I
b = 0.024029 + 0.464704I
1.73711 − 1.23215I −1.82857 + 1.12286I
u = −0.865146 + 1.042810I
a = −0.252629 + 0.232631I
b = −0.338895 − 0.803284I
1.73711 − 1.23215I −1.82857 + 1.12286I
u = −0.865146 − 1.042810I
a = 0.045926 + 0.937417I
b = 0.80203 − 1.30087I
1.73711 + 5.29191I −1.82857 − 8.05106I
u = −0.865146 − 1.042810I
a = −0.360952 − 1.068560I
b = −0.937819 + 0.858895I
1.73711 + 5.29191I −1.82857 − 8.05106I
u = −0.865146 − 1.042810I
a = 0.296569 + 0.571023I
b = 0.024029 − 0.464704I
1.73711 + 1.23215I −1.82857 − 1.12286I
u = −0.865146 − 1.042810I
a = −0.252629 − 0.232631I
b = −0.338895 + 0.803284I
1.73711 + 1.23215I −1.82857 − 1.12286I
u = 0.494703
a = −0.050248 + 1.334190I
b = 1.25357 − 1.55428I
−0.73172 − 2.02988I 13.11408 + 3.46410I
u = 0.494703
a = −0.050248 − 1.334190I
b = 1.25357 + 1.55428I
−0.73172 + 2.02988I 13.11408 − 3.46410I
u = 0.494703
a = −2.53399 + 3.14184I
b = 0.024858 − 0.660026I
−0.73172 − 2.02988I 13.11408 + 3.46410I
u = 0.494703
a = −2.53399 − 3.14184I
b = 0.024858 + 0.660026I
−0.73172 + 2.02988I 13.11408 − 3.46410I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.23842 + 1.01885I
a = 0.057902 + 1.004440I
b = −0.547319 − 1.129000I
4.33121 − 3.93186I 7.62421 + 4.84403I
u = −1.23842 + 1.01885I
a = 0.183718 − 0.760502I
b = 1.09508 + 1.18492I
4.33121 − 3.93186I 7.62421 + 4.84403I
u = −1.23842 + 1.01885I
a = −0.490134 + 0.482986I
b = −0.207412 − 0.651096I
4.33121 + 0.12791I 7.62421 − 2.08417I
u = −1.23842 + 1.01885I
a = 0.158068 − 0.395706I
b = −0.114899 + 1.097510I
4.33121 + 0.12791I 7.62421 − 2.08417I
u = −1.23842 − 1.01885I
a = 0.057902 − 1.004440I
b = −0.547319 + 1.129000I
4.33121 + 3.93186I 7.62421 − 4.84403I
u = −1.23842 − 1.01885I
a = 0.183718 + 0.760502I
b = 1.09508 − 1.18492I
4.33121 + 3.93186I 7.62421 − 4.84403I
u = −1.23842 − 1.01885I
a = −0.490134 − 0.482986I
b = −0.207412 + 0.651096I
4.33121 − 0.12791I 7.62421 + 2.08417I
u = −1.23842 − 1.01885I
a = 0.158068 + 0.395706I
b = −0.114899 − 1.097510I
4.33121 − 0.12791I 7.62421 + 2.08417I
u = −1.18917 + 1.13858I
a = −0.024921 − 0.964193I
b = 0.580828 + 1.201930I
3.96785 − 8.80564I 5.90760 + 12.35499I
u = −1.18917 + 1.13858I
a = −0.250062 + 0.771309I
b = −1.12744 − 1.11822I
3.96785 − 8.80564I 5.90760 + 12.35499I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.18917 + 1.13858I
a = 0.463313 − 0.506844I
b = 0.226931 + 0.615001I
3.96785 − 4.74587I 5.90760 + 5.42679I
u = −1.18917 + 1.13858I
a = −0.158778 + 0.365144I
b = −0.026123 − 1.130240I
3.96785 − 4.74587I 5.90760 + 5.42679I
u = −1.18917 − 1.13858I
a = −0.024921 + 0.964193I
b = 0.580828 − 1.201930I
3.96785 + 8.80564I 5.90760 − 12.35499I
u = −1.18917 − 1.13858I
a = −0.250062 − 0.771309I
b = −1.12744 + 1.11822I
3.96785 + 8.80564I 5.90760 − 12.35499I
u = −1.18917 − 1.13858I
a = 0.463313 + 0.506844I
b = 0.226931 − 0.615001I
3.96785 + 4.74587I 5.90760 − 5.42679I
u = −1.18917 − 1.13858I
a = −0.158778 − 0.365144I
b = −0.026123 + 1.130240I
3.96785 + 4.74587I 5.90760 − 5.42679I
19
III.
I
u
3
= h1.56 × 10
6
u
18
+ 1.52 × 10
7
u
17
+ · · · + 4.52 × 10
6
b + 1.16 × 10
6
, −3.87 ×
10
5
u
18
+4.30×10
4
u
17
+· · ·+1.36×10
7
a−2.89×10
7
, u
19
+12u
18
+· · ·+51u+9i
(i) Arc colorings
a
7
=
1
0
a
10
=
0
u
a
4
=
0.0285280u
18
− 0.00317376u
17
+ ··· − 3.85295u + 2.13500
−0.345510u
18
− 3.36835u
17
+ ··· + 0.680073u − 0.256752
a
8
=
1
−u
2
a
5
=
0.460790u
18
+ 4.84379u
17
+ ··· + 14.1914u + 4.98784
−0.291696u
18
− 3.42901u
17
+ ··· − 12.7785u − 3.31832
a
11
=
0.0849012u
18
+ 0.801365u
17
+ ··· − 14.2478u − 1.23217
−0.217450u
18
− 2.32098u
17
+ ··· − 4.56214u − 0.764111
a
3
=
−0.316982u
18
− 3.37152u
17
+ ··· − 3.17288u + 1.87825
−0.345510u
18
− 3.36835u
17
+ ··· + 0.680073u − 0.256752
a
6
=
0.739359u
18
+ 7.93694u
17
+ ··· + 24.6242u + 3.21974
−1.22379u
18
− 13.0814u
17
+ ··· − 45.8134u − 8.61129
a
9
=
−0.0615806u
18
− 0.830822u
17
+ ··· − 15.0462u − 0.803344
0.0709684u
18
+ 0.688798u
17
+ ··· + 5.76371u + 1.19294
a
1
=
0.159691u
18
+ 1.66506u
17
+ ··· + 2.28727u + 1.05357
−0.508449u
18
− 5.42759u
17
+ ··· − 14.2274u − 3.22952
a
2
=
−0.113233u
18
− 1.38897u
17
+ ··· − 4.56154u + 2.35178
−0.539522u
18
− 5.73993u
17
+ ··· − 4.17334u − 1.57028
a
2
=
−0.113233u
18
− 1.38897u
17
+ ··· − 4.56154u + 2.35178
−0.539522u
18
− 5.73993u
17
+ ··· − 4.17334u − 1.57028
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
34181122
4517673
u
18
−
118384024
1505891
u
17
+ ··· −
772349428
4517673
u −
55184665
1505891
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
19
+ 4u
18
+ ··· − 2u
2
+ 1
c
2
u
19
+ 10u
18
+ ··· + 4u + 1
c
3
, c
10
u
19
+ 3u
17
+ ··· − u + 1
c
4
, c
9
u
19
− u
18
+ ··· − 3u − 1
c
5
u
19
− 4u
18
+ ··· + 2u
2
− 1
c
6
u
19
+ 6u
18
+ ··· + 10u + 1
c
7
u
19
+ 12u
18
+ ··· + 51u + 9
c
8
, c
11
u
19
− 5u
18
+ ··· + 9u − 1
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
19
− 10y
18
+ ··· + 4y −1
c
2
y
19
+ 2y
18
+ ··· − 88y −1
c
3
, c
10
y
19
+ 6y
18
+ ··· − 9y −1
c
4
, c
9
y
19
− 9y
18
+ ··· + y −1
c
6
y
19
− 6y
18
+ ··· + 18y −1
c
7
y
19
− 8y
18
+ ··· − 1467y −81
c
8
, c
11
y
19
− 9y
18
+ ··· + 47y −1
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.763973 + 0.707293I
a = −0.016917 − 0.602834I
b = 0.413456 − 0.472514I
4.82041 − 3.45939I 2.24813 + 1.36505I
u = 0.763973 − 0.707293I
a = −0.016917 + 0.602834I
b = 0.413456 + 0.472514I
4.82041 + 3.45939I 2.24813 − 1.36505I
u = 0.787742 + 0.364961I
a = −0.300275 + 0.783661I
b = −0.522544 + 0.507734I
3.28624 − 9.25767I 0.20658 + 5.93399I
u = 0.787742 − 0.364961I
a = −0.300275 − 0.783661I
b = −0.522544 − 0.507734I
3.28624 + 9.25767I 0.20658 − 5.93399I
u = −0.780232 + 0.960591I
a = −0.259815 + 1.112610I
b = −0.866049 − 1.117670I
1.44789 − 8.17017I 1.07066 + 8.69229I
u = −0.780232 − 0.960591I
a = −0.259815 − 1.112610I
b = −0.866049 + 1.117670I
1.44789 + 8.17017I 1.07066 − 8.69229I
u = −1.299810 + 0.166754I
a = −0.071862 + 0.781904I
b = −0.036979 − 1.028310I
4.55790 − 2.62916I 7.70901 + 3.24676I
u = −1.299810 − 0.166754I
a = −0.071862 − 0.781904I
b = −0.036979 + 1.028310I
4.55790 + 2.62916I 7.70901 − 3.24676I
u = −0.92391 + 1.10552I
a = 0.220440 − 0.953370I
b = 0.850301 + 1.124530I
2.35431 − 4.44658I 3.29197 + 0.64229I
u = −0.92391 − 1.10552I
a = 0.220440 + 0.953370I
b = 0.850301 − 1.124530I
2.35431 + 4.44658I 3.29197 − 0.64229I
23
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.48175
a = −0.897373
b = 1.32968
−6.35573 −86.5700
u = −1.35468 + 0.82893I
a = 0.103212 + 0.748589I
b = −0.760347 − 0.928541I
3.44755 − 2.31743I 3.03564 + 2.58655I
u = −1.35468 − 0.82893I
a = 0.103212 − 0.748589I
b = −0.760347 + 0.928541I
3.44755 + 2.31743I 3.03564 − 2.58655I
u = −1.23165 + 1.02181I
a = 0.056424 − 0.827648I
b = 0.776207 + 1.077030I
3.52042 − 7.51917I 2.67994 + 6.56347I
u = −1.23165 − 1.02181I
a = 0.056424 + 0.827648I
b = 0.776207 − 1.077030I
3.52042 + 7.51917I 2.67994 − 6.56347I
u = −1.13680 + 1.22450I
a = −0.214225 + 0.319199I
b = −0.147330 − 0.625185I
2.48354 − 1.43560I 12.35059 + 4.73480I
u = −1.13680 − 1.22450I
a = −0.214225 − 0.319199I
b = −0.147330 + 0.625185I
2.48354 + 1.43560I 12.35059 − 4.73480I
u = −0.083759 + 0.261720I
a = 3.26504 + 0.37475I
b = −0.371555 + 0.823137I
−1.35625 − 2.07457I −3.80759 + 4.22380I
u = −0.083759 − 0.261720I
a = 3.26504 − 0.37475I
b = −0.371555 − 0.823137I
−1.35625 + 2.07457I −3.80759 − 4.22380I
24
IV. I
v
1
= ha, b + 1, v
2
− v + 1i
(i) Arc colorings
a
7
=
1
0
a
10
=
v
0
a
4
=
0
−1
a
8
=
1
0
a
5
=
−1
−1
a
11
=
v
v
a
3
=
−1
−1
a
6
=
−v + 2
−v + 1
a
9
=
2v
v
a
1
=
v − 2
v − 1
a
2
=
v − 3
v − 2
a
2
=
v − 3
v − 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4v − 5
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
(u − 1)
2
c
2
, c
5
(u + 1)
2
c
6
, c
8
, c
11
u
2
− u + 1
c
7
u
2
c
9
, c
10
u
2
+ u + 1
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
(y − 1)
2
c
6
, c
8
, c
9
c
10
, c
11
y
2
+ y + 1
c
7
y
2
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.500000 + 0.866025I
a = 0
b = −1.00000
−1.64493 − 2.02988I −3.00000 + 3.46410I
v = 0.500000 − 0.866025I
a = 0
b = −1.00000
−1.64493 + 2.02988I −3.00000 − 3.46410I
28
V. I
v
2
= ha, b + v − 1, v
2
− v + 1i
(i) Arc colorings
a
7
=
1
0
a
10
=
v
0
a
4
=
0
−v + 1
a
8
=
1
0
a
5
=
−v + 1
−v + 1
a
11
=
v
−v + 1
a
3
=
−v + 1
−v + 1
a
6
=
0
v
a
9
=
1
−v + 1
a
1
=
0
−v
a
2
=
−v + 1
−2v + 1
a
2
=
−v + 1
−2v + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4v − 1
29
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
, c
10
(u − 1)
2
c
2
, c
5
(u + 1)
2
c
3
, c
4
u
2
+ u + 1
c
6
, c
8
, c
11
u
2
− u + 1
c
7
u
2
30
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
9
, c
10
(y − 1)
2
c
3
, c
4
, c
6
c
8
, c
11
y
2
+ y + 1
c
7
y
2
31
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
2
√
−1(vol +
√
−1CS) Cusp shape
v = 0.500000 + 0.866025I
a = 0
b = 0.500000 − 0.866025I
−1.64493 + 2.02988I −3.00000 − 3.46410I
v = 0.500000 − 0.866025I
a = 0
b = 0.500000 + 0.866025I
−1.64493 − 2.02988I −3.00000 + 3.46410I
32
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
4
)(u
19
− 2u
18
+ ··· − 4u + 1)
4
(u
19
+ 4u
18
+ ··· − 2u
2
+ 1)
· (u
39
+ 9u
38
+ ··· − 124u − 16)
c
2
((u + 1)
4
)(u
19
+ 8u
18
+ ··· + 4u + 1)
4
(u
19
+ 10u
18
+ ··· + 4u + 1)
· (u
39
+ 17u
38
+ ··· + 1200u + 256)
c
3
, c
10
((u − 1)
2
)(u
2
+ u + 1)(u
19
+ 3u
17
+ ··· − u + 1)(u
39
− 4u
37
+ ··· + u − 1)
· (u
76
+ 4u
75
+ ··· − 13u + 1)
c
4
, c
9
((u − 1)
2
)(u
2
+ u + 1)(u
19
− u
18
+ ··· − 3u − 1)
· (u
39
− u
38
+ ··· + 47u + 17)(u
76
+ 2u
75
+ ··· − 461147u + 92641)
c
5
((u + 1)
4
)(u
19
− 4u
18
+ ··· + 2u
2
− 1)(u
19
− 2u
18
+ ··· − 4u + 1)
4
· (u
39
+ 9u
38
+ ··· − 124u − 16)
c
6
((u
2
− u + 1)
40
)(u
19
+ 6u
18
+ ··· + 10u + 1)
· (u
39
+ 37u
38
+ ··· + 5505024u + 262144)
c
7
u
4
(u
19
− 9u
18
+ ··· − u + 2)
4
(u
19
+ 12u
18
+ ··· + 51u + 9)
· (u
39
+ 29u
38
+ ··· + 14u + 4)
c
8
, c
11
((u
2
− u + 1)
2
)(u
19
− 5u
18
+ ··· + 9u − 1)(u
39
− u
38
+ ··· − u − 1)
· (u
76
− 3u
75
+ ··· + 7318u + 1741)
33
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
((y − 1)
4
)(y
19
− 10y
18
+ ··· + 4y − 1)(y
19
− 8y
18
+ ··· + 4y − 1)
4
· (y
39
− 17y
38
+ ··· + 1200y − 256)
c
2
((y − 1)
4
)(y
19
+ 2y
18
+ ··· − 88y − 1)(y
19
+ 8y
18
+ ··· − 16y − 1)
4
· (y
39
+ 11y
38
+ ··· − 231680y − 65536)
c
3
, c
10
((y − 1)
2
)(y
2
+ y + 1)(y
19
+ 6y
18
+ ··· − 9y − 1)
· (y
39
− 8y
38
+ ··· + 9y − 1)(y
76
+ 26y
75
+ ··· + 75y + 1)
c
4
, c
9
((y − 1)
2
)(y
2
+ y + 1)(y
19
− 9y
18
+ ··· + y − 1)
· (y
39
− 19y
38
+ ··· + 3399y − 289)
· (y
76
− 34y
75
+ ··· − 289799457437y + 8582354881)
c
6
((y
2
+ y + 1)
40
)(y
19
− 6y
18
+ ··· + 18y − 1)
· (y
39
− 5y
38
+ ··· + 515396075520y − 68719476736)
c
7
y
4
(y
19
− 8y
18
+ ··· − 1467y − 81)(y
19
− 3y
18
+ ··· + 37y − 4)
4
· (y
39
− 11y
38
+ ··· − 276y − 16)
c
8
, c
11
((y
2
+ y + 1)
2
)(y
19
− 9y
18
+ ··· + 47y − 1)(y
39
+ y
38
+ ··· + 37y − 1)
· (y
76
− 31y
75
+ ··· − 27023766y + 3031081)
34
