12n
0602
(K12n
0602
)
A knot diagram
1
Linearized knot diagam
3 7 9 8 10 2 12 4 6 5 7 8
Solving Sequence
3,9 4,7
2 1 6 10 8 5 12 11
c
3
c
2
c
1
c
6
c
9
c
8
c
4
c
12
c
11
c
5
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−u
9
− 3u
8
− 7u
7
− 10u
6
− 9u
5
+ 2u
4
+ 5u
3
+ 11u
2
+ 8b − 6u − 2,
u
8
+ 5u
6
− u
5
+ 6u
4
− 2u
3
+ u
2
+ 4a + 2u − 2, u
10
+ 6u
8
− 3u
7
+ 11u
6
− 13u
5
+ 9u
4
− 12u
3
+ 7u
2
+ 2i
I
u
2
= h−937u
13
− 2472u
12
+ ··· + 1987b − 6836, 12531u
13
+ 27338u
12
+ ··· + 19870a + 85927,
u
14
+ 3u
13
+ ··· + 22u + 5i
I
u
3
= h−u
4
a − u
2
a − u
3
− au + b + a − u − 1,
− 2u
5
a − 2u
4
a + u
5
− 6u
3
a + u
4
− 6u
2
a + 2u
3
+ 2a
2
− 6au + 3u
2
− 6a + u + 3,
u
6
+ 3u
4
+ u
3
+ 2u
2
+ 2u − 1i
I
u
4
= h2u
9
a + 10u
9
+ ··· + 7a + 1, −2u
9
+ 3u
8
+ ··· + a
2
− 4, u
10
− u
9
+ 4u
8
− 4u
7
+ 6u
6
− 6u
5
+ 3u
4
− 3u
3
+ 1i
I
u
5
= hb − 1, 6a − u − 3, u
2
+ 3i
I
u
6
= hb − u, 2a + u + 1, u
2
+ 1i
I
v
1
= ha, b − 1, v + 1i
* 7 irreducible components of dim
C
= 0, with total 61 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−u
9
− 3u
8
+ · · · + 8b − 2, u
8
+ 5u
6
− u
5
+ 6u
4
− 2u
3
+ u
2
+ 4a +
2u − 2, u
10
+ 6u
8
+ · · · + 7u
2
+ 2i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
−u
2
a
7
=
−
1
4
u
8
−
5
4
u
6
+ ··· −
1
2
u +
1
2
1
8
u
9
+
3
8
u
8
+ ··· +
3
4
u +
1
4
a
2
=
−
1
4
u
8
−
5
4
u
6
+ ··· −
1
2
u +
1
2
−
3
8
u
9
+
3
8
u
8
+ ··· −
5
4
u +
1
4
a
1
=
−
3
8
u
9
+
1
8
u
8
+ ··· −
7
4
u +
3
4
−
3
8
u
9
+
3
8
u
8
+ ··· −
5
4
u +
1
4
a
6
=
1
1
2
u
9
+
1
2
u
8
+ ··· + u + 1
a
10
=
u
1
2
u
9
−
1
2
u
8
+ ··· + 2u − 1
a
8
=
−u
u
3
+ u
a
5
=
u
2
+ 1
−u
4
− 2u
2
a
12
=
1
4
u
8
+
5
4
u
6
+ ··· −
3
2
u +
1
2
−
1
8
u
9
+
1
8
u
8
+ ··· −
3
4
u +
3
4
a
11
=
−u
3
− 2u
−
1
2
u
9
+
1
2
u
8
+ ··· − 2u + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes =
3
2
u
9
−
1
2
u
8
+
17
2
u
7
− 8u
6
+
25
2
u
5
− 25u
4
+
17
2
u
3
−
27
2
u
2
+ 13u + 1
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
10
+ u
9
+ 2u
8
− 3u
7
+ 12u
6
+ 24u
5
+ 46u
4
+ 37u
3
+ 7u
2
− 3u + 4
c
2
, c
6
, c
7
c
11
, c
12
u
10
− 3u
9
+ 4u
8
− u
7
− 4u
6
+ 6u
5
− 3u
3
+ u
2
+ u + 2
c
3
, c
4
, c
5
c
8
, c
9
, c
10
u
10
+ 6u
8
+ 3u
7
+ 11u
6
+ 13u
5
+ 9u
4
+ 12u
3
+ 7u
2
+ 2
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
10
+ 3y
9
+ ··· + 47y + 16
c
2
, c
6
, c
7
c
11
, c
12
y
10
− y
9
+ 2y
8
+ 3y
7
+ 12y
6
− 24y
5
+ 46y
4
− 37y
3
+ 7y
2
+ 3y + 4
c
3
, c
4
, c
5
c
8
, c
9
, c
10
y
10
+ 12y
9
+ ··· + 28y + 4
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.849669 + 0.278925I
a = 0.126908 − 1.402190I
b = −0.935978 + 0.707374I
2.59736 + 5.48528I 0.63906 − 6.67204I
u = 0.849669 − 0.278925I
a = 0.126908 + 1.402190I
b = −0.935978 − 0.707374I
2.59736 − 5.48528I 0.63906 + 6.67204I
u = −0.179655 + 1.191160I
a = 0.250838 − 0.636140I
b = −0.46356 + 1.36046I
−2.21767 − 1.59735I −7.51312 + 4.64580I
u = −0.179655 − 1.191160I
a = 0.250838 + 0.636140I
b = −0.46356 − 1.36046I
−2.21767 + 1.59735I −7.51312 − 4.64580I
u = −0.44148 + 1.44610I
a = −0.552527 + 1.275850I
b = −1.28583 − 0.66001I
−8.2686 − 15.1646I −7.51854 + 8.25672I
u = −0.44148 − 1.44610I
a = −0.552527 − 1.275850I
b = −1.28583 + 0.66001I
−8.2686 + 15.1646I −7.51854 − 8.25672I
u = −0.171957 + 0.454648I
a = 0.655512 − 0.286314I
b = 0.281118 + 0.559566I
0.087563 − 1.088810I 1.48967 + 6.22992I
u = −0.171957 − 0.454648I
a = 0.655512 + 0.286314I
b = 0.281118 − 0.559566I
0.087563 + 1.088810I 1.48967 − 6.22992I
u = −0.05658 + 1.78531I
a = 0.519269 + 0.055233I
b = 0.904241 − 0.202548I
−16.0502 + 0.8822I −5.09706 − 8.51458I
u = −0.05658 − 1.78531I
a = 0.519269 − 0.055233I
b = 0.904241 + 0.202548I
−16.0502 − 0.8822I −5.09706 + 8.51458I
5
II. I
u
2
= h−937u
13
− 2472u
12
+ · · · + 1987b − 6836, 12531u
13
+ 27338u
12
+
· · · + 19870a + 85927, u
14
+ 3u
13
+ · · · + 22u + 5i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
−u
2
a
7
=
−0.630649u
13
− 1.37584u
12
+ ··· − 15.3917u − 4.32446
0.471565u
13
+ 1.24409u
12
+ ··· + 9.17765u + 3.44036
a
2
=
0.253296u
13
+ 0.379668u
12
+ ··· + 0.855511u + 0.00558631
−0.425264u
13
− 0.827378u
12
+ ··· − 8.90941u − 2.81228
a
1
=
−0.171968u
13
− 0.447710u
12
+ ··· − 8.05390u − 2.80669
−0.425264u
13
− 0.827378u
12
+ ··· − 8.90941u − 2.81228
a
6
=
−0.693105u
13
− 1.63795u
12
+ ··· − 20.3068u − 6.28908
0.351787u
13
+ 1.16608u
12
+ ··· + 6.24459u + 3.20684
a
10
=
−0.241369u
13
− 0.372320u
12
+ ··· − 0.359235u + 0.934474
0.330649u
13
+ 0.975843u
12
+ ··· + 16.4917u + 5.22446
a
8
=
−u
u
3
+ u
a
5
=
u
2
+ 1
−u
4
− 2u
2
a
12
=
−0.342577u
13
− 0.983191u
12
+ ··· − 14.9880u − 5.16452
−0.112733u
13
− 0.0145949u
12
+ ··· − 3.34877u − 0.572723
a
11
=
−0.0892803u
13
− 0.603523u
12
+ ··· − 14.1325u − 6.15893
−0.537997u
13
− 0.841973u
12
+ ··· − 12.2582u − 3.38500
(ii) Obstruction class = −1
(iii) Cusp Shapes =
2058
1987
u
13
+
6600
1987
u
12
+ ··· +
37538
1987
u +
12194
1987
6
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
7
+ 3u
6
+ 7u
5
+ 8u
4
+ 9u
3
+ 6u
2
+ 5u + 1)
2
c
2
, c
6
, c
7
c
11
, c
12
(u
7
+ u
6
− u
5
− 2u
4
+ u
3
+ 2u
2
+ u − 1)
2
c
3
, c
4
, c
5
c
8
, c
9
, c
10
u
14
− 3u
13
+ ··· − 22u + 5
7
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
7
+ 5y
6
+ 19y
5
+ 36y
4
+ 49y
3
+ 38y
2
+ 13y −1)
2
c
2
, c
6
, c
7
c
11
, c
12
(y
7
− 3y
6
+ 7y
5
− 8y
4
+ 9y
3
− 6y
2
+ 5y −1)
2
c
3
, c
4
, c
5
c
8
, c
9
, c
10
y
14
+ 11y
13
+ ··· − 4y + 25
8
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.370785 + 0.946704I
a = −0.209881 − 0.303567I
b = 0.597306 + 0.773845I
0.562491 − 0.955395I 0.68929 + 2.37083I
u = 0.370785 − 0.946704I
a = −0.209881 + 0.303567I
b = 0.597306 − 0.773845I
0.562491 + 0.955395I 0.68929 − 2.37083I
u = −1.022710 + 0.247588I
a = −0.520411 − 1.220230I
b = 1.139460 + 0.630170I
−2.92618 − 9.93065I −4.46028 + 7.33664I
u = −1.022710 − 0.247588I
a = −0.520411 + 1.220230I
b = 1.139460 − 0.630170I
−2.92618 + 9.93065I −4.46028 − 7.33664I
u = 0.306472 + 1.132160I
a = −0.482637 − 0.675154I
b = −0.502855
−4.24127 −5.93921 + 0.I
u = 0.306472 − 1.132160I
a = −0.482637 + 0.675154I
b = −0.502855
−4.24127 −5.93921 + 0.I
u = −0.736932 + 1.071510I
a = 0.318588 − 0.053278I
b = −0.985336 + 0.506466I
−5.38528 + 3.93070I −6.25941 − 4.87230I
u = −0.736932 − 1.071510I
a = 0.318588 + 0.053278I
b = −0.985336 − 0.506466I
−5.38528 − 3.93070I −6.25941 + 4.87230I
u = −0.538570 + 0.272073I
a = 0.71818 − 1.43908I
b = 0.597306 + 0.773845I
0.562491 − 0.955395I 0.68929 + 2.37083I
u = −0.538570 − 0.272073I
a = 0.71818 + 1.43908I
b = 0.597306 − 0.773845I
0.562491 + 0.955395I 0.68929 − 2.37083I
9
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.36817 + 1.45006I
a = 0.797752 + 1.077130I
b = 1.139460 − 0.630170I
−2.92618 + 9.93065I −4.46028 − 7.33664I
u = 0.36817 − 1.45006I
a = 0.797752 − 1.077130I
b = 1.139460 + 0.630170I
−2.92618 − 9.93065I −4.46028 + 7.33664I
u = −0.24721 + 1.49766I
a = −0.921588 + 0.632363I
b = −0.985336 − 0.506466I
−5.38528 − 3.93070I −6.25941 + 4.87230I
u = −0.24721 − 1.49766I
a = −0.921588 − 0.632363I
b = −0.985336 + 0.506466I
−5.38528 + 3.93070I −6.25941 − 4.87230I
10
III. I
u
3
= h−u
4
a − u
2
a − u
3
− au + b + a − u − 1, −2u
5
a + u
5
+ · · · − 6a +
3, u
6
+ 3u
4
+ u
3
+ 2u
2
+ 2u − 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
−u
2
a
7
=
a
u
4
a + u
2
a + u
3
+ au − a + u + 1
a
2
=
a
u
5
a + 2u
3
a + u
2
a − u
3
− u − 1
a
1
=
u
5
a + 2u
3
a + u
2
a − u
3
+ a − u − 1
u
5
a + 2u
3
a + u
2
a − u
3
− u − 1
a
6
=
1
u
5
+ u
4
+ 2u
3
+ 2u
2
+ u − 1
a
10
=
u
u
5
− u
4
+ u
3
− u
2
− 2u + 1
a
8
=
−u
u
3
+ u
a
5
=
u
2
+ 1
−u
4
− 2u
2
a
12
=
u
3
a − u
3
+ au + a − 2u − 1
−1
a
11
=
−u
3
− 2u
u
4
+ u
3
+ u
2
+ 2u − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
5
+ 4u
4
+ 8u
3
+ 12u
2
+ 4u + 2
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
12
+ 7u
11
+ ··· + 438u + 169
c
2
, c
6
, c
7
c
11
, c
12
u
12
− 3u
11
+ ··· + 42u − 13
c
3
, c
4
, c
5
c
8
, c
9
, c
10
(u
6
+ 3u
4
− u
3
+ 2u
2
− 2u − 1)
2
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
12
− 3y
11
+ ··· − 59686y + 28561
c
2
, c
6
, c
7
c
11
, c
12
y
12
− 7y
11
+ ··· − 438y + 169
c
3
, c
4
, c
5
c
8
, c
9
, c
10
(y
6
+ 6y
5
+ 13y
4
+ 9y
3
− 6y
2
− 8y + 1)
2
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.841864
a = 0.445035 + 1.177780I
b = −0.719261 − 0.742974I
3.23778 2.68180
u = −0.841864
a = 0.445035 − 1.177780I
b = −0.719261 + 0.742974I
3.23778 2.68180
u = −0.126468 + 1.352400I
a = −0.034921 + 1.148040I
b = −1.026470 − 0.870245I
−11.65360 − 3.39374I −10.36018 + 3.51762I
u = −0.126468 + 1.352400I
a = 0.383840 + 0.027542I
b = 1.59190 − 0.18598I
−11.65360 − 3.39374I −10.36018 + 3.51762I
u = −0.126468 − 1.352400I
a = −0.034921 − 1.148040I
b = −1.026470 + 0.870245I
−11.65360 + 3.39374I −10.36018 − 3.51762I
u = −0.126468 − 1.352400I
a = 0.383840 − 0.027542I
b = 1.59190 + 0.18598I
−11.65360 + 3.39374I −10.36018 − 3.51762I
u = 0.376468 + 1.319680I
a = −0.443330 − 1.186910I
b = −1.27617 + 0.73937I
−5.05799 + 8.77346I −5.56216 − 5.90094I
u = 0.376468 + 1.319680I
a = 0.392175 + 0.613857I
b = −0.260915 − 1.156860I
−5.05799 + 8.77346I −5.56216 − 5.90094I
u = 0.376468 − 1.319680I
a = −0.443330 + 1.186910I
b = −1.27617 − 0.73937I
−5.05799 − 8.77346I −5.56216 + 5.90094I
u = 0.376468 − 1.319680I
a = 0.392175 − 0.613857I
b = −0.260915 + 1.156860I
−5.05799 − 8.77346I −5.56216 + 5.90094I
14
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.341865
a = 0.468459
b = 1.13466
−2.71328 5.16290
u = 0.341865
a = 4.04594
b = −0.752839
−2.71328 5.16290
15
IV.
I
u
4
= h2u
9
a+10u
9
+· · ·+7a+1, −2u
9
+3u
8
+· · ·+a
2
−4, u
10
−u
9
+· · ·−3u
3
+1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
−u
2
a
7
=
a
−0.117647au
9
− 0.588235u
9
+ ··· − 0.411765a − 0.0588235
a
2
=
−0.588235au
9
+ 0.0588235u
9
+ ··· − 0.0588235a + 2.70588
0.176471au
9
− 0.117647u
9
+ ··· + 0.117647a − 1.41176
a
1
=
−0.411765au
9
− 0.0588235u
9
+ ··· + 0.0588235a + 1.29412
0.176471au
9
− 0.117647u
9
+ ··· + 0.117647a − 1.41176
a
6
=
−u
9
− 4u
7
− 5u
5
+ 3u
u
9
+ 3u
7
+ 3u
5
− u
a
10
=
2u
9
− u
8
+ 8u
7
− 5u
6
+ 12u
5
− 9u
4
+ 6u
3
− 6u
2
− u − 1
−2u
9
+ u
8
− 8u
7
+ 4u
6
− 12u
5
+ 6u
4
− 5u
3
+ 4u
2
+ 3u + 2
a
8
=
−u
u
3
+ u
a
5
=
u
2
+ 1
−u
4
− 2u
2
a
12
=
−0.588235au
9
+ 0.0588235u
9
+ ··· − 0.0588235a + 0.705882
−1
a
11
=
u
6
+ 3u
4
+ 2u
2
− 1
−u
6
− 2u
4
− u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
9
− 12u
7
− 12u
5
+ 4u
3
+ 8u − 2
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
10
+ 5u
9
+ ··· + 4u + 1)
2
c
2
, c
6
, c
7
c
11
, c
12
(u
10
+ u
9
− 2u
8
− 4u
7
+ 4u
5
+ 3u
4
− u
3
− 2u
2
+ 1)
2
c
3
, c
4
, c
5
c
8
, c
9
, c
10
(u
10
+ u
9
+ 4u
8
+ 4u
7
+ 6u
6
+ 6u
5
+ 3u
4
+ 3u
3
+ 1)
2
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
10
− y
9
− 6y
7
+ 22y
6
+ 6y
5
+ 45y
4
+ 15y
3
+ 22y
2
+ 4y + 1)
2
c
2
, c
6
, c
7
c
11
, c
12
(y
10
− 5y
9
+ ··· − 4y + 1)
2
c
3
, c
4
, c
5
c
8
, c
9
, c
10
(y
10
+ 7y
9
+ 20y
8
+ 26y
7
+ 6y
6
− 22y
5
− 19y
4
+ 3y
3
+ 6y
2
+ 1)
2
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.839548 + 0.070481I
a = −0.900079 + 0.957609I
b = 1.018500 − 0.644891I
−0.70717 + 4.40083I −1.25569 − 3.49859I
u = 0.839548 + 0.070481I
a = 0.01855 − 1.45994I
b = 0.400287 + 0.864056I
−0.70717 + 4.40083I −1.25569 − 3.49859I
u = 0.839548 − 0.070481I
a = −0.900079 − 0.957609I
b = 1.018500 + 0.644891I
−0.70717 − 4.40083I −1.25569 + 3.49859I
u = 0.839548 − 0.070481I
a = 0.01855 + 1.45994I
b = 0.400287 − 0.864056I
−0.70717 − 4.40083I −1.25569 + 3.49859I
u = 0.090539 + 1.215350I
a = −1.57349 + 0.24896I
b = −1.236040 − 0.156723I
−6.25064 + 1.53058I −5.48489 − 4.43065I
u = 0.090539 + 1.215350I
a = 0.23726 + 1.84586I
b = 0.926127 − 0.393188I
−6.25064 + 1.53058I −5.48489 − 4.43065I
u = 0.090539 − 1.215350I
a = −1.57349 − 0.24896I
b = −1.236040 + 0.156723I
−6.25064 − 1.53058I −5.48489 + 4.43065I
u = 0.090539 − 1.215350I
a = 0.23726 − 1.84586I
b = 0.926127 + 0.393188I
−6.25064 − 1.53058I −5.48489 + 4.43065I
u = 0.383413 + 1.200420I
a = −0.734177 − 0.829669I
b = −0.608868 + 0.334904I
−4.17865 −4.51886 + 0.I
u = 0.383413 + 1.200420I
a = −0.073892 − 0.370754I
b = −0.608868 − 0.334904I
−4.17865 −4.51886 + 0.I
19
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.383413 − 1.200420I
a = −0.734177 + 0.829669I
b = −0.608868 − 0.334904I
−4.17865 −4.51886 + 0.I
u = 0.383413 − 1.200420I
a = −0.073892 + 0.370754I
b = −0.608868 + 0.334904I
−4.17865 −4.51886 + 0.I
u = −0.383851 + 1.270630I
a = 0.614423 − 1.130320I
b = 1.018500 + 0.644891I
−0.70717 − 4.40083I −1.25569 + 3.49859I
u = −0.383851 + 1.270630I
a = −0.272551 + 0.291529I
b = 0.400287 − 0.864056I
−0.70717 − 4.40083I −1.25569 + 3.49859I
u = −0.383851 − 1.270630I
a = 0.614423 + 1.130320I
b = 1.018500 − 0.644891I
−0.70717 + 4.40083I −1.25569 − 3.49859I
u = −0.383851 − 1.270630I
a = −0.272551 − 0.291529I
b = 0.400287 + 0.864056I
−0.70717 + 4.40083I −1.25569 − 3.49859I
u = −0.429649 + 0.392970I
a = 1.58670 − 1.31909I
b = −1.236040 + 0.156723I
−6.25064 − 1.53058I −5.48489 + 4.43065I
u = −0.429649 + 0.392970I
a = −2.40274 − 2.38405I
b = 0.926127 + 0.393188I
−6.25064 − 1.53058I −5.48489 + 4.43065I
u = −0.429649 − 0.392970I
a = 1.58670 + 1.31909I
b = −1.236040 − 0.156723I
−6.25064 + 1.53058I −5.48489 − 4.43065I
u = −0.429649 − 0.392970I
a = −2.40274 + 2.38405I
b = 0.926127 − 0.393188I
−6.25064 + 1.53058I −5.48489 − 4.43065I
20
V. I
u
5
= hb − 1, 6a − u − 3, u
2
+ 3i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
3
a
7
=
1
6
u +
1
2
1
a
2
=
−
1
6
u +
1
2
−1
a
1
=
−
1
6
u −
1
2
−1
a
6
=
1
0
a
10
=
u
u
a
8
=
−u
−2u
a
5
=
−2
−3
a
12
=
−
7
6
u −
1
2
−2u − 1
a
11
=
−u
−2u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
(u − 1)
2
c
3
, c
4
, c
5
c
8
, c
9
, c
10
u
2
+ 3
c
6
, c
11
, c
12
(u + 1)
2
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
7
, c
11
, c
12
(y −1)
2
c
3
, c
4
, c
5
c
8
, c
9
, c
10
(y + 3)
2
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 1.73205I
a = 0.500000 + 0.288675I
b = 1.00000
−16.4493 −12.0000
u = − 1.73205I
a = 0.500000 − 0.288675I
b = 1.00000
−16.4493 −12.0000
24
VI. I
u
6
= hb − u, 2a + u + 1, u
2
+ 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
1
a
7
=
−
1
2
u −
1
2
u
a
2
=
1
2
u +
1
2
1
a
1
=
1
2
u +
3
2
1
a
6
=
−1
2u
a
10
=
u
u + 2
a
8
=
−u
0
a
5
=
0
1
a
12
=
1
2
u +
1
2
1
a
11
=
u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u + 1)
2
c
2
, c
3
, c
4
c
5
, c
6
, c
7
c
8
, c
9
, c
10
c
11
, c
12
u
2
+ 1
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y −1)
2
c
2
, c
3
, c
4
c
5
, c
6
, c
7
c
8
, c
9
, c
10
c
11
, c
12
(y + 1)
2
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = −0.500000 − 0.500000I
b = 1.000000I
−1.64493 −4.00000
u = − 1.000000I
a = −0.500000 + 0.500000I
b = − 1.000000I
−1.64493 −4.00000
28
VII. I
v
1
= ha, b − 1, v + 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
−1
0
a
4
=
1
0
a
7
=
0
1
a
2
=
1
−1
a
1
=
0
−1
a
6
=
1
0
a
10
=
−1
0
a
8
=
−1
0
a
5
=
1
0
a
12
=
−1
−1
a
11
=
−1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
29
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
u − 1
c
3
, c
4
, c
5
c
8
, c
9
, c
10
u
c
6
, c
11
, c
12
u + 1
30
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
7
, c
11
, c
12
y −1
c
3
, c
4
, c
5
c
8
, c
9
, c
10
y
31
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −1.00000
a = 0
b = 1.00000
−3.28987 −12.0000
32
VIII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)
3
(u + 1)
2
(u
7
+ 3u
6
+ 7u
5
+ 8u
4
+ 9u
3
+ 6u
2
+ 5u + 1)
2
· (u
10
+ u
9
+ 2u
8
− 3u
7
+ 12u
6
+ 24u
5
+ 46u
4
+ 37u
3
+ 7u
2
− 3u + 4)
· ((u
10
+ 5u
9
+ ··· + 4u + 1)
2
)(u
12
+ 7u
11
+ ··· + 438u + 169)
c
2
, c
7
(u − 1)
3
(u
2
+ 1)(u
7
+ u
6
− u
5
− 2u
4
+ u
3
+ 2u
2
+ u − 1)
2
· (u
10
− 3u
9
+ 4u
8
− u
7
− 4u
6
+ 6u
5
− 3u
3
+ u
2
+ u + 2)
· (u
10
+ u
9
− 2u
8
− 4u
7
+ 4u
5
+ 3u
4
− u
3
− 2u
2
+ 1)
2
· (u
12
− 3u
11
+ ··· + 42u − 13)
c
3
, c
4
, c
5
c
8
, c
9
, c
10
u(u
2
+ 1)(u
2
+ 3)(u
6
+ 3u
4
− u
3
+ 2u
2
− 2u − 1)
2
· (u
10
+ 6u
8
+ 3u
7
+ 11u
6
+ 13u
5
+ 9u
4
+ 12u
3
+ 7u
2
+ 2)
· (u
10
+ u
9
+ 4u
8
+ 4u
7
+ 6u
6
+ 6u
5
+ 3u
4
+ 3u
3
+ 1)
2
· (u
14
− 3u
13
+ ··· − 22u + 5)
c
6
, c
11
, c
12
(u + 1)
3
(u
2
+ 1)(u
7
+ u
6
− u
5
− 2u
4
+ u
3
+ 2u
2
+ u − 1)
2
· (u
10
− 3u
9
+ 4u
8
− u
7
− 4u
6
+ 6u
5
− 3u
3
+ u
2
+ u + 2)
· (u
10
+ u
9
− 2u
8
− 4u
7
+ 4u
5
+ 3u
4
− u
3
− 2u
2
+ 1)
2
· (u
12
− 3u
11
+ ··· + 42u − 13)
33
IX. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y −1)
5
(y
7
+ 5y
6
+ 19y
5
+ 36y
4
+ 49y
3
+ 38y
2
+ 13y −1)
2
· (y
10
− y
9
− 6y
7
+ 22y
6
+ 6y
5
+ 45y
4
+ 15y
3
+ 22y
2
+ 4y + 1)
2
· (y
10
+ 3y
9
+ ··· + 47y + 16)(y
12
− 3y
11
+ ··· − 59686y + 28561)
c
2
, c
6
, c
7
c
11
, c
12
(y −1)
3
(y + 1)
2
(y
7
− 3y
6
+ 7y
5
− 8y
4
+ 9y
3
− 6y
2
+ 5y −1)
2
· (y
10
− 5y
9
+ ··· − 4y + 1)
2
· (y
10
− y
9
+ 2y
8
+ 3y
7
+ 12y
6
− 24y
5
+ 46y
4
− 37y
3
+ 7y
2
+ 3y + 4)
· (y
12
− 7y
11
+ ··· − 438y + 169)
c
3
, c
4
, c
5
c
8
, c
9
, c
10
y(y + 1)
2
(y + 3)
2
(y
6
+ 6y
5
+ 13y
4
+ 9y
3
− 6y
2
− 8y + 1)
2
· (y
10
+ 7y
9
+ 20y
8
+ 26y
7
+ 6y
6
− 22y
5
− 19y
4
+ 3y
3
+ 6y
2
+ 1)
2
· (y
10
+ 12y
9
+ ··· + 28y + 4)(y
14
+ 11y
13
+ ··· − 4y + 25)
34
