12a
0381
(K12a
0381
)
A knot diagram
1
Linearized knot diagam
3 6 9 10 7 2 12 5 4 1 8 11
Solving Sequence
7,12 2,8
6 3 5 9 11 1 10 4
c
7
c
6
c
2
c
5
c
8
c
11
c
12
c
10
c
4
c
1
, c
3
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= hb − u, u
22
− u
21
+ ··· + 2a + u, u
23
− u
22
+ ··· + 4u
2
+ 1i
I
u
2
= h−1.58008 × 10
30
u
65
+ 4.09523 × 10
30
u
64
+ ··· + 2.14580 × 10
30
b + 1.44290 × 10
31
,
− 1.35351 × 10
31
u
65
+ 4.37094 × 10
31
u
64
+ ··· + 3.00412 × 10
31
a − 1.14573 × 10
30
,
u
66
− 2u
65
+ ··· + 19u + 7i
I
u
3
= hb + u, a
2
+ 2au − 4a − 3u + 1, u
2
− u + 1i
I
u
4
= hb + u, a + u + 2, u
2
+ u + 1i
I
u
5
= hb − u + 1, a
2
+ 2u, u
2
− u + 1i
I
u
6
= hb − u − 1, a, u
2
+ u + 1i
* 6 irreducible components of dim
C
= 0, with total 101 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
= hb − u, u
22
− u
21
+ · · · + 2a + u, u
23
− u
22
+ · · · + 4u
2
+ 1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
2
=
−
1
2
u
22
+
1
2
u
21
+ ··· − 4u
3
−
1
2
u
u
a
8
=
1
−u
2
a
6
=
1
2
u
19
−
1
2
u
18
+ ··· +
3
2
u
2
+
3
2
u
2
a
3
=
−
1
2
u
22
+
1
2
u
21
+ ··· −
5
2
u
3
+ u
u
3
+ u
a
5
=
1
2
u
19
−
1
2
u
18
+ ··· +
5
2
u
2
+
3
2
u
2
a
9
=
−
1
2
u
22
+ u
21
+ ··· + 2u
2
+
1
2
−
1
2
u
21
+
1
2
u
20
+ ··· − 3u
2
−
1
2
a
11
=
−u
u
3
+ u
a
1
=
−u
3
u
5
+ u
3
+ u
a
10
=
−u
5
− u
u
7
+ u
5
+ 2u
3
+ u
a
4
=
1
2
u
21
−
1
2
u
20
+ ··· + 4u
2
+
3
2
1
2
u
21
−
1
2
u
20
+ ··· + 2u
2
+
1
2
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −5u
22
+3u
21
−16u
20
+6u
19
−53u
18
+17u
17
−101u
16
+17u
15
−174u
14
+7u
13
−224u
12
−
20u
11
− 239u
10
− 75u
9
− 209u
8
− 97u
7
− 132u
6
− 106u
5
− 73u
4
− 72u
3
− 27u
2
− 17u − 9
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
10
c
12
u
23
+ 7u
22
+ ··· − 8u − 1
c
2
, c
6
, c
7
c
11
u
23
− u
22
+ ··· + 4u
2
+ 1
c
3
, c
4
, c
9
u
23
+ 5u
22
+ ··· + 4u + 4
c
8
u
23
− 15u
22
+ ··· + 2004u − 332
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
10
c
12
y
23
+ 23y
22
+ ··· − 4y −1
c
2
, c
6
, c
7
c
11
y
23
+ 7y
22
+ ··· − 8y −1
c
3
, c
4
, c
9
y
23
− 21y
22
+ ··· − 48y −16
c
8
y
23
− y
22
+ ··· + 356048y −110224
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.108766 + 1.038960I
a = −0.14445 + 2.16071I
b = −0.108766 + 1.038960I
−9.31458 − 4.23664I −14.9374 + 4.2518I
u = −0.108766 − 1.038960I
a = −0.14445 − 2.16071I
b = −0.108766 − 1.038960I
−9.31458 + 4.23664I −14.9374 − 4.2518I
u = 0.062381 + 0.953110I
a = 0.17223 + 1.91880I
b = 0.062381 + 0.953110I
−3.67662 + 1.63978I −11.45625 − 4.68535I
u = 0.062381 − 0.953110I
a = 0.17223 − 1.91880I
b = 0.062381 − 0.953110I
−3.67662 − 1.63978I −11.45625 + 4.68535I
u = 0.878988 + 0.705166I
a = −1.38624 − 0.52383I
b = 0.878988 + 0.705166I
4.20055 − 4.17420I −1.40540 + 0.69157I
u = 0.878988 − 0.705166I
a = −1.38624 + 0.52383I
b = 0.878988 − 0.705166I
4.20055 + 4.17420I −1.40540 − 0.69157I
u = −0.709127 + 0.898384I
a = 3.06567 − 0.32207I
b = −0.709127 + 0.898384I
−2.78113 − 5.44900I −3.47285 + 6.34023I
u = −0.709127 − 0.898384I
a = 3.06567 + 0.32207I
b = −0.709127 − 0.898384I
−2.78113 + 5.44900I −3.47285 − 6.34023I
u = −0.868691 + 0.769532I
a = 1.60761 − 0.45900I
b = −0.868691 + 0.769532I
9.09763 − 0.31187I 2.24462 + 1.40830I
u = −0.868691 − 0.769532I
a = 1.60761 + 0.45900I
b = −0.868691 − 0.769532I
9.09763 + 0.31187I 2.24462 − 1.40830I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.838998 + 0.838326I
a = −1.91420 − 0.34412I
b = 0.838998 + 0.838326I
6.46982 + 5.13305I −0.60159 − 5.77161I
u = 0.838998 − 0.838326I
a = −1.91420 + 0.34412I
b = 0.838998 − 0.838326I
6.46982 − 5.13305I −0.60159 + 5.77161I
u = 0.780652 + 0.967249I
a = −2.39587 + 0.31250I
b = 0.780652 + 0.967249I
5.63176 + 7.01945I −1.80788 − 4.37801I
u = 0.780652 − 0.967249I
a = −2.39587 − 0.31250I
b = 0.780652 − 0.967249I
5.63176 − 7.01945I −1.80788 + 4.37801I
u = −0.320435 + 0.678319I
a = −1.41963 + 0.05223I
b = −0.320435 + 0.678319I
−5.40470 − 2.53254I −9.43035 + 2.23223I
u = −0.320435 − 0.678319I
a = −1.41963 − 0.05223I
b = −0.320435 − 0.678319I
−5.40470 + 2.53254I −9.43035 − 2.23223I
u = −0.770543 + 1.018970I
a = 2.33411 + 0.64664I
b = −0.770543 + 1.018970I
7.50703 − 11.94160I −0.51059 + 8.65040I
u = −0.770543 − 1.018970I
a = 2.33411 − 0.64664I
b = −0.770543 − 1.018970I
7.50703 + 11.94160I −0.51059 − 8.65040I
u = 0.748511 + 1.049130I
a = −2.32792 + 0.88202I
b = 0.748511 + 1.049130I
2.0337 + 16.3152I −4.71784 − 9.86318I
u = 0.748511 − 1.049130I
a = −2.32792 − 0.88202I
b = 0.748511 − 1.049130I
2.0337 − 16.3152I −4.71784 + 9.86318I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.538161
a = 0.226955
b = −0.538161
−2.63402 −1.54930
u = 0.237113 + 0.441635I
a = 0.295194 − 0.025537I
b = 0.237113 + 0.441635I
−0.109440 + 0.967023I −2.12980 − 6.92815I
u = 0.237113 − 0.441635I
a = 0.295194 + 0.025537I
b = 0.237113 − 0.441635I
−0.109440 − 0.967023I −2.12980 + 6.92815I
7
II. I
u
2
= h−1.58 × 10
30
u
65
+ 4.10 × 10
30
u
64
+ · · · + 2.15 × 10
30
b + 1.44 ×
10
31
, −1.35 × 10
31
u
65
+ 4.37 × 10
31
u
64
+ · · · + 3.00 × 10
31
a − 1.15 ×
10
30
, u
66
− 2u
65
+ · · · + 19u + 7i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
2
=
0.450551u
65
− 1.45498u
64
+ ··· + 0.601985u + 0.0381388
0.736361u
65
− 1.90849u
64
+ ··· − 17.1039u − 6.72429
a
8
=
1
−u
2
a
6
=
0.880632u
65
− 0.628257u
64
+ ··· + 10.5151u + 7.47661
0.134748u
65
− 0.326968u
64
+ ··· + 19.1692u + 3.77720
a
3
=
0.541655u
65
− 1.07474u
64
+ ··· + 13.2018u + 5.03970
0.859372u
65
− 2.24529u
64
+ ··· + 1.06882u − 2.22730
a
5
=
1.01538u
65
− 0.955224u
64
+ ··· + 29.6843u + 11.2538
0.134748u
65
− 0.326968u
64
+ ··· + 19.1692u + 3.77720
a
9
=
−0.644879u
65
+ 1.15798u
64
+ ··· + 2.59190u + 1.58917
−0.317784u
65
− 0.0128892u
64
+ ··· − 7.61429u − 2.11502
a
11
=
−u
u
3
+ u
a
1
=
−u
3
u
5
+ u
3
+ u
a
10
=
−u
5
− u
u
7
+ u
5
+ 2u
3
+ u
a
4
=
1.40413u
65
− 1.90048u
64
+ ··· + 6.61630u + 4.46567
0.103837u
65
− 0.390389u
64
+ ··· + 18.6949u + 4.37292
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.117014u
65
+ 1.08091u
64
+ ··· − 52.4974u − 13.7114
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
10
c
12
u
66
+ 22u
65
+ ··· + 591u + 49
c
2
, c
6
, c
7
c
11
u
66
− 2u
65
+ ··· + 19u + 7
c
3
, c
4
, c
9
(u
33
− 2u
32
+ ··· + 5u
3
− 2)
2
c
8
(u
33
+ 6u
32
+ ··· + 84u + 22)
2
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
10
c
12
y
66
+ 46y
65
+ ··· + 47227y + 2401
c
2
, c
6
, c
7
c
11
y
66
+ 22y
65
+ ··· + 591y + 49
c
3
, c
4
, c
9
(y
33
− 30y
32
+ ··· − 72y
2
− 4)
2
c
8
(y
33
+ 10y
32
+ ··· + 808y −484)
2
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.780007 + 0.702896I
a = 0.060274 + 0.274900I
b = −0.217053 + 1.123410I
−3.25939 − 4.10922I −6.90114 + 3.20990I
u = 0.780007 − 0.702896I
a = 0.060274 − 0.274900I
b = −0.217053 − 1.123410I
−3.25939 + 4.10922I −6.90114 − 3.20990I
u = −0.711321 + 0.791297I
a = −0.056822 + 0.187212I
b = 0.331350 + 1.060870I
1.24121 + 0.80287I 0
u = −0.711321 − 0.791297I
a = −0.056822 − 0.187212I
b = 0.331350 − 1.060870I
1.24121 − 0.80287I 0
u = 0.718922 + 0.797842I
a = 1.47367 − 0.63983I
b = −0.435907 − 1.078550I
−1.97159 + 3.23829I −4.00000 − 3.70582I
u = 0.718922 − 0.797842I
a = 1.47367 + 0.63983I
b = −0.435907 + 1.078550I
−1.97159 − 3.23829I −4.00000 + 3.70582I
u = −0.252240 + 0.890572I
a = −0.682248 + 0.144403I
b = −0.442341 + 0.328309I
−5.30265 − 2.57775I −8.82504 + 3.79477I
u = −0.252240 − 0.890572I
a = −0.682248 − 0.144403I
b = −0.442341 − 0.328309I
−5.30265 + 2.57775I −8.82504 − 3.79477I
u = −0.713764 + 0.843003I
a = 1.58827 + 1.87585I
b = −0.713764 − 0.843003I
−2.60888 0
u = −0.713764 − 0.843003I
a = 1.58827 − 1.87585I
b = −0.713764 + 0.843003I
−2.60888 0
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.587924 + 0.938053I
a = 1.54849 − 0.69333I
b = −0.233499 − 0.806742I
−0.73076 + 3.39395I 0
u = 0.587924 − 0.938053I
a = 1.54849 + 0.69333I
b = −0.233499 + 0.806742I
−0.73076 − 3.39395I 0
u = 0.786418 + 0.782314I
a = 0.842464 − 0.449392I
b = −0.769109 + 0.132418I
0.933995 − 0.933678I 0
u = 0.786418 − 0.782314I
a = 0.842464 + 0.449392I
b = −0.769109 − 0.132418I
0.933995 + 0.933678I 0
u = 0.331350 + 1.060870I
a = −0.181882 + 0.044732I
b = −0.711321 + 0.791297I
1.24121 + 0.80287I 0
u = 0.331350 − 1.060870I
a = −0.181882 − 0.044732I
b = −0.711321 − 0.791297I
1.24121 − 0.80287I 0
u = 0.884836 + 0.675520I
a = −1.46006 + 0.36957I
b = 0.759584 − 1.033520I
3.18615 − 10.25700I 0
u = 0.884836 − 0.675520I
a = −1.46006 − 0.36957I
b = 0.759584 + 1.033520I
3.18615 + 10.25700I 0
u = 0.258928 + 1.090430I
a = 1.03310 − 1.35443I
b = −0.704139 − 0.938636I
0.78565 + 6.23956I 0
u = 0.258928 − 1.090430I
a = 1.03310 + 1.35443I
b = −0.704139 + 0.938636I
0.78565 − 6.23956I 0
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.572109 + 0.986999I
a = −1.90024 − 0.84110I
b = −0.026298 − 0.856856I
−6.63294 − 1.73715I 0
u = −0.572109 − 0.986999I
a = −1.90024 + 0.84110I
b = −0.026298 + 0.856856I
−6.63294 + 1.73715I 0
u = 0.511863 + 0.689377I
a = 0.553781 − 0.103147I
b = −0.239361 + 0.530434I
0.050783 + 1.125010I −3.91132 − 5.66806I
u = 0.511863 − 0.689377I
a = 0.553781 + 0.103147I
b = −0.239361 − 0.530434I
0.050783 − 1.125010I −3.91132 + 5.66806I
u = −0.875841 + 0.733268I
a = 1.41304 + 0.58667I
b = −0.784228 − 0.996367I
8.39261 + 5.82817I 0
u = −0.875841 − 0.733268I
a = 1.41304 − 0.58667I
b = −0.784228 + 0.996367I
8.39261 − 5.82817I 0
u = −0.026298 + 0.856856I
a = 1.55713 − 2.28540I
b = −0.572109 − 0.986999I
−6.63294 + 1.73715I −11.77893 − 2.62669I
u = −0.026298 − 0.856856I
a = 1.55713 + 2.28540I
b = −0.572109 + 0.986999I
−6.63294 − 1.73715I −11.77893 + 2.62669I
u = −0.217053 + 1.123410I
a = 0.244597 + 0.082892I
b = 0.780007 + 0.702896I
−3.25939 − 4.10922I 0
u = −0.217053 − 1.123410I
a = 0.244597 − 0.082892I
b = 0.780007 − 0.702896I
−3.25939 + 4.10922I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.233499 + 0.806742I
a = −1.71181 − 1.43920I
b = 0.587924 − 0.938053I
−0.73076 − 3.39395I −8.06022 + 0.66822I
u = −0.233499 − 0.806742I
a = −1.71181 + 1.43920I
b = 0.587924 + 0.938053I
−0.73076 + 3.39395I −8.06022 − 0.66822I
u = −0.760681 + 0.877322I
a = −0.884877 − 0.473302I
b = 0.759107 − 0.044308I
4.54074 − 2.87533I 0
u = −0.760681 − 0.877322I
a = −0.884877 + 0.473302I
b = 0.759107 + 0.044308I
4.54074 + 2.87533I 0
u = 0.843301 + 0.798735I
a = −1.35150 + 0.89613I
b = 0.797643 − 0.937164I
6.15793 − 0.96390I 0
u = 0.843301 − 0.798735I
a = −1.35150 − 0.89613I
b = 0.797643 + 0.937164I
6.15793 + 0.96390I 0
u = −0.182118 + 1.148190I
a = −0.87619 − 1.47269I
b = 0.715657 − 0.997367I
−4.14648 − 9.77183I 0
u = −0.182118 − 1.148190I
a = −0.87619 + 1.47269I
b = 0.715657 + 0.997367I
−4.14648 + 9.77183I 0
u = 0.707507 + 0.923188I
a = −0.016161 + 0.150604I
b = −0.475703 + 1.094070I
−2.34954 + 2.22028I 0
u = 0.707507 − 0.923188I
a = −0.016161 − 0.150604I
b = −0.475703 − 1.094070I
−2.34954 − 2.22028I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.435907 + 1.078550I
a = −1.07615 − 1.02066I
b = 0.718922 − 0.797842I
−1.97159 − 3.23829I 0
u = −0.435907 − 1.078550I
a = −1.07615 + 1.02066I
b = 0.718922 + 0.797842I
−1.97159 + 3.23829I 0
u = −0.704139 + 0.938636I
a = −1.42101 − 0.79245I
b = 0.258928 − 1.090430I
0.78565 − 6.23956I 0
u = −0.704139 − 0.938636I
a = −1.42101 + 0.79245I
b = 0.258928 + 1.090430I
0.78565 + 6.23956I 0
u = −0.793318 + 0.194870I
a = −1.54496 + 0.21724I
b = 0.745981 − 0.954952I
0.40872 − 6.71347I −2.25632 + 6.01205I
u = −0.793318 − 0.194870I
a = −1.54496 − 0.21724I
b = 0.745981 + 0.954952I
0.40872 + 6.71347I −2.25632 − 6.01205I
u = −0.475703 + 1.094070I
a = 0.120730 + 0.085039I
b = 0.707507 + 0.923188I
−2.34954 + 2.22028I 0
u = −0.475703 − 1.094070I
a = 0.120730 − 0.085039I
b = 0.707507 − 0.923188I
−2.34954 − 2.22028I 0
u = 0.745981 + 0.954952I
a = 0.909008 − 0.529042I
b = −0.793318 − 0.194870I
0.40872 + 6.71347I 0
u = 0.745981 − 0.954952I
a = 0.909008 + 0.529042I
b = −0.793318 + 0.194870I
0.40872 − 6.71347I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.769109 + 0.132418I
a = −1.214120 − 0.606459I
b = 0.786418 + 0.782314I
0.933995 − 0.933678I −1.133669 + 0.682217I
u = −0.769109 − 0.132418I
a = −1.214120 + 0.606459I
b = 0.786418 − 0.782314I
0.933995 + 0.933678I −1.133669 − 0.682217I
u = 0.715657 + 0.997367I
a = 1.36718 − 0.87437I
b = −0.182118 − 1.148190I
−4.14648 + 9.77183I 0
u = 0.715657 − 0.997367I
a = 1.36718 + 0.87437I
b = −0.182118 + 1.148190I
−4.14648 − 9.77183I 0
u = 0.797643 + 0.937164I
a = −0.77688 + 1.31869I
b = 0.843301 − 0.798735I
6.15793 + 0.96390I 0
u = 0.797643 − 0.937164I
a = −0.77688 − 1.31869I
b = 0.843301 + 0.798735I
6.15793 − 0.96390I 0
u = 0.759107 + 0.044308I
a = 1.46075 + 0.46313I
b = −0.760681 − 0.877322I
4.54074 + 2.87533I 2.79872 − 3.16413I
u = 0.759107 − 0.044308I
a = 1.46075 − 0.46313I
b = −0.760681 + 0.877322I
4.54074 − 2.87533I 2.79872 + 3.16413I
u = −0.784228 + 0.996367I
a = 0.489817 + 1.288340I
b = −0.875841 − 0.733268I
8.39261 − 5.82817I 0
u = −0.784228 − 0.996367I
a = 0.489817 − 1.288340I
b = −0.875841 + 0.733268I
8.39261 + 5.82817I 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.759584 + 1.033520I
a = −0.297584 + 1.272870I
b = 0.884836 − 0.675520I
3.18615 + 10.25700I 0
u = 0.759584 − 1.033520I
a = −0.297584 − 1.272870I
b = 0.884836 + 0.675520I
3.18615 − 10.25700I 0
u = −0.239361 + 0.530434I
a = 0.264651 − 0.787874I
b = 0.511863 + 0.689377I
0.050783 + 1.125010I −3.91132 − 5.66806I
u = −0.239361 − 0.530434I
a = 0.264651 + 0.787874I
b = 0.511863 − 0.689377I
0.050783 − 1.125010I −3.91132 + 5.66806I
u = −0.442341 + 0.328309I
a = −0.760163 + 0.891727I
b = −0.252240 + 0.890572I
−5.30265 − 2.57775I −8.82504 + 3.79477I
u = −0.442341 − 0.328309I
a = −0.760163 − 0.891727I
b = −0.252240 − 0.890572I
−5.30265 + 2.57775I −8.82504 − 3.79477I
17
III. I
u
3
= hb + u, a
2
+ 2au − 4a − 3u + 1, u
2
− u + 1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
2
=
a
−u
a
8
=
1
−u + 1
a
6
=
−au + 1
u − 1
a
3
=
au − u
−u + 1
a
5
=
−au + u
u − 1
a
9
=
−a − 3u + 3
au − a − 3u + 2
a
11
=
−u
u − 1
a
1
=
1
0
a
10
=
−1
u − 1
a
4
=
−au + a + 2u − 2
−au + a + 3u − 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8u − 4
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
c
7
, c
10
(u
2
− u + 1)
2
c
3
, c
4
, c
8
c
9
(u
2
− 2)
2
c
6
, c
11
, c
12
(u
2
+ u + 1)
2
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
7
, c
10
c
11
, c
12
(y
2
+ y + 1)
2
c
3
, c
4
, c
8
c
9
(y −2)
4
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = 0.085786 − 0.866025I
b = −0.500000 − 0.866025I
−4.93480 + 4.05977I −8.00000 − 6.92820I
u = 0.500000 + 0.866025I
a = 2.91421 − 0.86603I
b = −0.500000 − 0.866025I
−4.93480 + 4.05977I −8.00000 − 6.92820I
u = 0.500000 − 0.866025I
a = 0.085786 + 0.866025I
b = −0.500000 + 0.866025I
−4.93480 − 4.05977I −8.00000 + 6.92820I
u = 0.500000 − 0.866025I
a = 2.91421 + 0.86603I
b = −0.500000 + 0.866025I
−4.93480 − 4.05977I −8.00000 + 6.92820I
21
IV. I
u
4
= hb + u, a + u + 2, u
2
+ u + 1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
2
=
−u − 2
−u
a
8
=
1
u + 1
a
6
=
u
−u − 1
a
3
=
−1
−u − 1
a
5
=
−1
−u − 1
a
9
=
1
u + 1
a
11
=
−u
u + 1
a
1
=
−1
0
a
10
=
1
u + 1
a
4
=
−1
−u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 8u + 4
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
6
c
10
, c
11
u
2
− u + 1
c
2
, c
7
, c
12
u
2
+ u + 1
c
3
, c
4
, c
8
c
9
u
2
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
7
, c
10
c
11
, c
12
y
2
+ y + 1
c
3
, c
4
, c
8
c
9
y
2
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = −1.50000 − 0.86603I
b = 0.500000 − 0.866025I
− 4.05977I 0. + 6.92820I
u = −0.500000 − 0.866025I
a = −1.50000 + 0.86603I
b = 0.500000 + 0.866025I
4.05977I 0. − 6.92820I
25
V. I
u
5
= hb − u + 1, a
2
+ 2u, u
2
− u + 1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
2
=
a
u − 1
a
8
=
1
−u + 1
a
6
=
au − a + 1
−u
a
3
=
−au + a + u − 1
u
a
5
=
au − a − u + 1
−u
a
9
=
−a − 2u + 1
au − a − u + 1
a
11
=
−u
u − 1
a
1
=
1
0
a
10
=
−1
u − 1
a
4
=
−a − u + 1
−a − u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8
26
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
c
7
, c
10
(u
2
− u + 1)
2
c
3
, c
4
, c
8
c
9
(u
2
− 2)
2
c
6
, c
11
, c
12
(u
2
+ u + 1)
2
27
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
7
, c
10
c
11
, c
12
(y
2
+ y + 1)
2
c
3
, c
4
, c
8
c
9
(y −2)
4
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = 0.707110 − 1.224740I
b = −0.500000 + 0.866025I
−4.93480 −8.00000
u = 0.500000 + 0.866025I
a = −0.707110 + 1.224740I
b = −0.500000 + 0.866025I
−4.93480 −8.00000
u = 0.500000 − 0.866025I
a = 0.707110 + 1.224740I
b = −0.500000 − 0.866025I
−4.93480 −8.00000
u = 0.500000 − 0.866025I
a = −0.707110 − 1.224740I
b = −0.500000 − 0.866025I
−4.93480 −8.00000
29
VI. I
u
6
= hb − u − 1, a, u
2
+ u + 1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
2
=
0
u + 1
a
8
=
1
u + 1
a
6
=
1
u
a
3
=
u + 1
u
a
5
=
u + 1
u
a
9
=
1
u + 1
a
11
=
−u
u + 1
a
1
=
−1
0
a
10
=
1
u + 1
a
4
=
u + 1
u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −6
30
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
6
c
10
, c
11
u
2
− u + 1
c
2
, c
7
, c
12
u
2
+ u + 1
c
3
, c
4
, c
8
c
9
u
2
31
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
7
, c
10
c
11
, c
12
y
2
+ y + 1
c
3
, c
4
, c
8
c
9
y
2
32
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = 0
b = 0.500000 + 0.866025I
0 −6.00000
u = −0.500000 − 0.866025I
a = 0
b = 0.500000 − 0.866025I
0 −6.00000
33
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
10
((u
2
− u + 1)
6
)(u
23
+ 7u
22
+ ··· − 8u − 1)
· (u
66
+ 22u
65
+ ··· + 591u + 49)
c
2
, c
7
((u
2
− u + 1)
4
)(u
2
+ u + 1)
2
(u
23
− u
22
+ ··· + 4u
2
+ 1)
· (u
66
− 2u
65
+ ··· + 19u + 7)
c
3
, c
4
, c
9
u
4
(u
2
− 2)
4
(u
23
+ 5u
22
+ ··· + 4u + 4)(u
33
− 2u
32
+ ··· + 5u
3
− 2)
2
c
6
, c
11
((u
2
− u + 1)
2
)(u
2
+ u + 1)
4
(u
23
− u
22
+ ··· + 4u
2
+ 1)
· (u
66
− 2u
65
+ ··· + 19u + 7)
c
8
u
4
(u
2
− 2)
4
(u
23
− 15u
22
+ ··· + 2004u − 332)
· (u
33
+ 6u
32
+ ··· + 84u + 22)
2
c
12
((u
2
+ u + 1)
6
)(u
23
+ 7u
22
+ ··· − 8u − 1)
· (u
66
+ 22u
65
+ ··· + 591u + 49)
34
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
10
c
12
((y
2
+ y + 1)
6
)(y
23
+ 23y
22
+ ··· − 4y −1)
· (y
66
+ 46y
65
+ ··· + 47227y + 2401)
c
2
, c
6
, c
7
c
11
((y
2
+ y + 1)
6
)(y
23
+ 7y
22
+ ··· − 8y −1)
· (y
66
+ 22y
65
+ ··· + 591y + 49)
c
3
, c
4
, c
9
y
4
(y −2)
8
(y
23
− 21y
22
+ ··· − 48y −16)
· (y
33
− 30y
32
+ ··· − 72y
2
− 4)
2
c
8
y
4
(y −2)
8
(y
23
− y
22
+ ··· + 356048y −110224)
· (y
33
+ 10y
32
+ ··· + 808y −484)
2
35
