12n
0882
(K12n
0882
)
A knot diagram
1
Linearized knot diagam
4 11 7 10 11 12 4 12 1 5 3 9
Solving Sequence
4,10 5,7
8 11 3 12 2 1 6 9
c
4
c
7
c
10
c
3
c
11
c
2
c
1
c
6
c
9
c
5
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h4u
12
− 8u
11
− 26u
10
+ 41u
9
+ 59u
8
− 69u
7
− 42u
6
+ 9u
5
− 10u
4
+ 56u
3
+ u
2
+ 13b − 5u + 10,
− 4u
12
+ 8u
11
+ 26u
10
− 41u
9
− 59u
8
+ 69u
7
+ 42u
6
− 9u
5
+ 10u
4
− 69u
3
− u
2
+ 13a + 31u − 10,
u
13
+ u
12
− 6u
11
− 6u
10
+ 13u
9
+ 14u
8
− 7u
7
− 13u
6
− 12u
5
+ 13u
3
+ 6u
2
+ 2u + 1i
I
u
2
= h−5.18174 × 10
46
u
47
− 1.01683 × 10
47
u
46
+ ··· + 3.77343 × 10
47
b − 4.53377 × 10
47
,
2.81502 × 10
47
u
47
+ 3.21473 × 10
47
u
46
+ ··· + 1.25781 × 10
47
a + 4.62967 × 10
48
, u
48
+ u
47
+ ··· + 20u + 1i
I
u
3
= h−u
2
+ b + 1, −u
3
+ u
2
+ a + 2u − 1, u
5
− 3u
3
+ 2u + 1i
I
u
4
= h−u
2
+ b + 1, −2u
7
− u
6
+ 11u
5
+ 3u
4
− 18u
3
+ 3u
2
+ a + 8u − 9,
u
8
− 5u
6
+ u
5
+ 7u
4
− 4u
3
− 2u
2
+ 4u − 1i
I
u
5
= hb + 1, a, u − 1i
* 5 irreducible components of dim
C
= 0, with total 75 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
=
h4u
12
−8u
11
+· · ·+13b+10, −4u
12
+8u
11
+· · ·+13a−10, u
13
+u
12
+· · ·+2u+1i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
5
=
1
−u
2
a
7
=
0.307692u
12
− 0.615385u
11
+ ··· − 2.38462u + 0.769231
−0.307692u
12
+ 0.615385u
11
+ ··· + 0.384615u − 0.769231
a
8
=
u
3
− 2u
−0.307692u
12
+ 0.615385u
11
+ ··· + 0.384615u − 0.769231
a
11
=
u
−u
3
+ u
a
3
=
0.538462u
12
− 0.0769231u
11
+ ··· + 3.07692u + 1.84615
−1.07692u
12
+ 0.153846u
11
+ ··· − 2.15385u − 0.692308
a
12
=
u
2
− 1
−0.692308u
12
+ 0.384615u
11
+ ··· + 1.61538u − 0.230769
a
2
=
1.46154u
12
+ 0.0769231u
11
+ ··· + 2.92308u + 2.15385
−1.46154u
12
− 0.0769231u
11
+ ··· − 2.92308u − 1.15385
a
1
=
1
−1.46154u
12
− 0.0769231u
11
+ ··· − 2.92308u − 1.15385
a
6
=
−u
2
+ 1
u
4
− 2u
2
a
9
=
−u
−1.38462u
12
+ 0.769231u
11
+ ··· − 0.769231u − 1.46154
(ii) Obstruction class = −1
(iii) Cusp Shapes =
42
13
u
12
+
20
13
u
11
− 18u
10
−
122
13
u
9
+
483
13
u
8
+
309
13
u
7
−
285
13
u
6
−
367
13
u
5
−
300
13
u
4
+
94
13
u
3
+
394
13
u
2
+
162
13
u +
157
13
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
13
− 12u
12
+ ··· + 352u − 32
c
2
, c
3
, c
7
c
11
u
13
− 3u
11
+ 9u
9
+ u
8
− 12u
7
+ u
6
+ 16u
5
− u
4
− 11u
3
+ 3u
2
+ 4u − 1
c
4
, c
5
, c
8
c
9
, c
10
, c
12
u
13
− u
12
+ ··· + 2u − 1
c
6
u
13
+ 11u
12
+ ··· − 208u − 56
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
13
+ 8y
12
+ ··· + 42496y −1024
c
2
, c
3
, c
7
c
11
y
13
− 6y
12
+ ··· + 22y −1
c
4
, c
5
, c
8
c
9
, c
10
, c
12
y
13
− 13y
12
+ ··· − 8y −1
c
6
y
13
+ y
12
+ ··· + 5408y −3136
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.171620 + 0.859681I
a = −0.34697 − 1.56070I
b = 1.065670 − 0.718049I
−2.17962 − 5.84511I 7.45794 + 6.04290I
u = −0.171620 − 0.859681I
a = −0.34697 + 1.56070I
b = 1.065670 + 0.718049I
−2.17962 + 5.84511I 7.45794 − 6.04290I
u = −1.309140 + 0.064534I
a = −0.581299 − 0.674191I
b = 0.972284 + 0.876654I
8.82263 + 2.58229I 16.9820 − 3.0015I
u = −1.309140 − 0.064534I
a = −0.581299 + 0.674191I
b = 0.972284 − 0.876654I
8.82263 − 2.58229I 16.9820 + 3.0015I
u = 1.356440 + 0.275517I
a = 0.256447 + 0.156488I
b = −0.782477 + 0.792358I
5.13873 + 2.17385I 13.57691 − 0.52106I
u = 1.356440 − 0.275517I
a = 0.256447 − 0.156488I
b = −0.782477 − 0.792358I
5.13873 − 2.17385I 13.57691 + 0.52106I
u = 1.356860 + 0.395151I
a = −1.72651 + 1.21374I
b = 0.875267 + 0.116755I
9.39305 + 5.41911I 19.2364 − 4.1129I
u = 1.356860 − 0.395151I
a = −1.72651 − 1.21374I
b = 0.875267 − 0.116755I
9.39305 − 5.41911I 19.2364 + 4.1129I
u = −0.537178
a = 1.16207
b = −0.242725
0.805138 11.7720
u = −1.48836 + 0.39264I
a = 1.67676 + 0.98279I
b = −1.30871 + 0.78070I
8.6054 − 15.1865I 15.2811 + 7.9689I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.48836 − 0.39264I
a = 1.67676 − 0.98279I
b = −1.30871 − 0.78070I
8.6054 + 15.1865I 15.2811 − 7.9689I
u = 0.024401 + 0.393610I
a = 0.640545 − 1.244220I
b = −0.700673 + 0.396722I
1.07099 − 1.38837I 7.07977 + 4.85651I
u = 0.024401 − 0.393610I
a = 0.640545 + 1.244220I
b = −0.700673 − 0.396722I
1.07099 + 1.38837I 7.07977 − 4.85651I
6
II.
I
u
2
= h−5.18×10
46
u
47
−1.02×10
47
u
46
+· · ·+3.77×10
47
b−4.53×10
47
, 2.82×
10
47
u
47
+3.21×10
47
u
46
+· · ·+1.26×10
47
a+4.63×10
48
, u
48
+u
47
+· · ·+20u+1i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
5
=
1
−u
2
a
7
=
−2.23803u
47
− 2.55582u
46
+ ··· − 95.9559u − 36.8074
0.137322u
47
+ 0.269470u
46
+ ··· + 10.2860u + 1.20150
a
8
=
−2.10071u
47
− 2.28635u
46
+ ··· − 85.6699u − 35.6059
0.137322u
47
+ 0.269470u
46
+ ··· + 10.2860u + 1.20150
a
11
=
u
−u
3
+ u
a
3
=
−1.66504u
47
− 1.59037u
46
+ ··· − 127.758u − 32.3177
0.0330654u
47
+ 0.122014u
46
+ ··· − 10.8225u + 0.0377011
a
12
=
−2.91125u
47
− 2.61233u
46
+ ··· − 182.706u − 53.5737
0.168578u
47
+ 0.0577104u
46
+ ··· − 0.407278u + 0.897363
a
2
=
−1.68717u
47
− 1.75245u
46
+ ··· − 125.467u − 32.2876
0.0461378u
47
+ 0.188914u
46
+ ··· − 11.3519u − 0.0721935
a
1
=
−1.64103u
47
− 1.56354u
46
+ ··· − 136.819u − 32.3598
0.0461378u
47
+ 0.188914u
46
+ ··· − 11.3519u − 0.0721935
a
6
=
−u
2
+ 1
u
4
− 2u
2
a
9
=
2.76666u
47
+ 2.69855u
46
+ ··· + 205.087u + 52.5080
−0.111644u
47
+ 0.153944u
46
+ ··· + 8.10592u − 0.451941
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2.00373u
47
− 2.03203u
46
+ ··· − 42.9306u − 8.93702
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
24
+ 2u
23
+ ··· − 20u − 1)
2
c
2
, c
3
, c
7
c
11
u
48
− u
47
+ ··· − 197u + 73
c
4
, c
5
, c
8
c
9
, c
10
, c
12
u
48
− u
47
+ ··· − 20u + 1
c
6
(u
24
− 5u
23
+ ··· + 15u − 1)
2
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
24
+ 4y
23
+ ··· − 522y + 1)
2
c
2
, c
3
, c
7
c
11
y
48
− 23y
47
+ ··· − 76039y + 5329
c
4
, c
5
, c
8
c
9
, c
10
, c
12
y
48
− 43y
47
+ ··· − 216y + 1
c
6
(y
24
− 3y
23
+ ··· − 135y + 1)
2
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.379137 + 0.976493I
a = −0.471549 + 1.157640I
b = 1.29469 + 0.67005I
2.67292 + 10.25690I 12.1975 − 7.6788I
u = 0.379137 − 0.976493I
a = −0.471549 − 1.157640I
b = 1.29469 − 0.67005I
2.67292 − 10.25690I 12.1975 + 7.6788I
u = −0.021423 + 0.948358I
a = 0.401732 + 0.737665I
b = −0.856499 + 0.135005I
4.94291 − 0.58720I 16.0412 − 0.8168I
u = −0.021423 − 0.948358I
a = 0.401732 − 0.737665I
b = −0.856499 − 0.135005I
4.94291 + 0.58720I 16.0412 + 0.8168I
u = −1.023260 + 0.490646I
a = 0.476231 + 0.027830I
b = −1.044720 − 0.584882I
0.464120 + 1.081590I 8.00000 − 2.00672I
u = −1.023260 − 0.490646I
a = 0.476231 − 0.027830I
b = −1.044720 + 0.584882I
0.464120 − 1.081590I 8.00000 + 2.00672I
u = −0.379291 + 0.739173I
a = 0.316811 + 0.748267I
b = 0.248462 + 1.064600I
−0.51929 − 4.00862I 8.65058 + 5.80685I
u = −0.379291 − 0.739173I
a = 0.316811 − 0.748267I
b = 0.248462 − 1.064600I
−0.51929 + 4.00862I 8.65058 − 5.80685I
u = 1.135680 + 0.336882I
a = 0.864140 − 0.699527I
b = −0.713544 − 0.730081I
−0.51929 + 4.00862I 8.00000 − 5.80685I
u = 1.135680 − 0.336882I
a = 0.864140 + 0.699527I
b = −0.713544 + 0.730081I
−0.51929 − 4.00862I 8.00000 + 5.80685I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.750478 + 0.292577I
a = 1.176600 + 0.468222I
b = −0.319389 + 0.477318I
0.664158 9.39053 + 0.I
u = −0.750478 − 0.292577I
a = 1.176600 − 0.468222I
b = −0.319389 − 0.477318I
0.664158 9.39053 + 0.I
u = 1.163220 + 0.303346I
a = −0.223618 − 0.467491I
b = −1.004700 + 0.471049I
4.64466 15.0647 + 0.I
u = 1.163220 − 0.303346I
a = −0.223618 + 0.467491I
b = −1.004700 − 0.471049I
4.64466 15.0647 + 0.I
u = 0.141459 + 0.765036I
a = 0.561104 − 0.769052I
b = 0.623240 − 0.846147I
−3.53422 4.26168 + 0.I
u = 0.141459 − 0.765036I
a = 0.561104 + 0.769052I
b = 0.623240 + 0.846147I
−3.53422 4.26168 + 0.I
u = 0.068175 + 0.762824I
a = 0.696604 + 1.029800I
b = 0.970507 + 0.650047I
1.27885 + 3.92180I 9.29302 − 3.73808I
u = 0.068175 − 0.762824I
a = 0.696604 − 1.029800I
b = 0.970507 − 0.650047I
1.27885 − 3.92180I 9.29302 + 3.73808I
u = 1.235930 + 0.167013I
a = −0.657445 − 0.412560I
b = 0.705420 + 0.391760I
4.65694 + 3.47868I 0
u = 1.235930 − 0.167013I
a = −0.657445 + 0.412560I
b = 0.705420 − 0.391760I
4.65694 − 3.47868I 0
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.916403 + 0.885493I
a = 0.391708 − 0.248635I
b = −1.329710 + 0.460814I
4.14619 − 4.10761I 0
u = 0.916403 − 0.885493I
a = 0.391708 + 0.248635I
b = −1.329710 − 0.460814I
4.14619 + 4.10761I 0
u = −1.265470 + 0.153865I
a = −2.80490 − 0.73050I
b = 0.791562 + 0.363762I
4.94291 − 0.58720I 0
u = −1.265470 − 0.153865I
a = −2.80490 + 0.73050I
b = 0.791562 − 0.363762I
4.94291 + 0.58720I 0
u = −1.263720 + 0.231617I
a = 2.48042 + 2.19572I
b = −0.811085 + 0.535687I
4.14619 − 4.10761I 0
u = −1.263720 − 0.231617I
a = 2.48042 − 2.19572I
b = −0.811085 − 0.535687I
4.14619 + 4.10761I 0
u = −1.28856
a = −0.869778
b = −0.755603
14.0810 25.5770
u = 1.32785
a = 4.15788
b = −0.885530
14.6478 0
u = 1.330000 + 0.048649I
a = −2.39749 + 0.12309I
b = 1.065850 + 0.841425I
9.08685 + 4.24572I 0
u = 1.330000 − 0.048649I
a = −2.39749 − 0.12309I
b = 1.065850 − 0.841425I
9.08685 − 4.24572I 0
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.309300 + 0.318007I
a = 0.889440 + 0.821935I
b = −0.928244 + 0.711653I
5.58448 − 7.81589I 0
u = −1.309300 − 0.318007I
a = 0.889440 − 0.821935I
b = −0.928244 − 0.711653I
5.58448 + 7.81589I 0
u = −1.316980 + 0.405826I
a = −0.548637 + 0.081279I
b = 0.803853 + 0.148006I
9.08685 − 4.24572I 0
u = −1.316980 − 0.405826I
a = −0.548637 − 0.081279I
b = 0.803853 − 0.148006I
9.08685 + 4.24572I 0
u = −0.087131 + 0.611347I
a = 0.35264 + 2.45893I
b = 0.721176 + 0.611639I
0.464120 + 1.081590I 8.16075 − 2.00672I
u = −0.087131 − 0.611347I
a = 0.35264 − 2.45893I
b = 0.721176 − 0.611639I
0.464120 − 1.081590I 8.16075 + 2.00672I
u = −1.373810 + 0.321857I
a = −0.344264 + 0.528075I
b = −0.621802 − 0.993232I
1.27885 − 3.92180I 0
u = −1.373810 − 0.321857I
a = −0.344264 − 0.528075I
b = −0.621802 + 0.993232I
1.27885 + 3.92180I 0
u = 1.36990 + 0.36882I
a = 1.75795 − 1.37725I
b = −1.073560 − 0.763448I
2.67292 + 10.25690I 0
u = 1.36990 − 0.36882I
a = 1.75795 + 1.37725I
b = −1.073560 + 0.763448I
2.67292 − 10.25690I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.49633 + 0.29266I
a = −0.376487 − 0.561865I
b = −0.34302 + 1.38502I
5.58448 + 7.81589I 0
u = 1.49633 − 0.29266I
a = −0.376487 + 0.561865I
b = −0.34302 − 1.38502I
5.58448 − 7.81589I 0
u = 1.65947
a = −1.72670
b = 1.72233
10.1445 0
u = −1.66105
a = −1.80640
b = 2.14588
14.0810 0
u = −1.81988
a = −1.44716
b = 1.67660
14.6478 0
u = −0.024167 + 0.177554I
a = −0.54655 + 4.54825I
b = −1.041510 + 0.853951I
4.65694 − 3.47868I 16.3031 + 8.4838I
u = −0.024167 − 0.177554I
a = −0.54655 − 4.54825I
b = −1.041510 − 0.853951I
4.65694 + 3.47868I 16.3031 − 8.4838I
u = −0.0602179
a = −35.2967
b = 0.822371
10.1445 −9.41450
14
III. I
u
3
= h−u
2
+ b + 1, −u
3
+ u
2
+ a + 2u − 1, u
5
− 3u
3
+ 2u + 1i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
5
=
1
−u
2
a
7
=
u
3
− u
2
− 2u + 1
u
2
− 1
a
8
=
u
3
− 2u
u
2
− 1
a
11
=
u
−u
3
+ u
a
3
=
−u
4
+ 2u
2
− 1
u
4
− 2u
2
+ 1
a
12
=
u
2
− 1
−u
3
− u
2
+ 2u + 1
a
2
=
−u
4
− u
3
+ 2u
2
+ u − 1
u
4
+ u
3
− 2u
2
− u
a
1
=
−1
u
4
+ u
3
− 2u
2
− u
a
6
=
−u
2
+ 1
u
4
− 2u
2
a
9
=
−u
u
4
+ u
3
− u
2
− u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −2u
4
− 3u
3
+ 3u
2
+ 2u + 17
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
5
− 2u
4
+ 5u
3
− 4u
2
− 1
c
2
, c
7
u
5
+ u
4
− u
3
− u
2
+ 1
c
3
, c
11
u
5
− u
4
− u
3
+ u
2
− 1
c
4
, c
5
, c
8
c
9
u
5
− 3u
3
+ 2u + 1
c
6
u
5
+ 2u
4
+ 3u
3
+ 3u
2
+ 3u + 1
c
10
, c
12
u
5
− 3u
3
+ 2u − 1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
5
+ 6y
4
+ 9y
3
− 20y
2
− 8y −1
c
2
, c
3
, c
7
c
11
y
5
− 3y
4
+ 3y
3
− 3y
2
+ 2y −1
c
4
, c
5
, c
8
c
9
, c
10
, c
12
y
5
− 6y
4
+ 13y
3
− 12y
2
+ 4y −1
c
6
y
5
+ 2y
4
+ 3y
3
+ 5y
2
+ 3y −1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.297630 + 0.272489I
a = −1.308900 + 0.104091I
b = 0.609585 + 0.707177I
7.56155 + 5.69445I 14.5549 − 5.9553I
u = 1.297630 − 0.272489I
a = −1.308900 − 0.104091I
b = 0.609585 − 0.707177I
7.56155 − 5.69445I 14.5549 + 5.9553I
u = −0.516079 + 0.312340I
a = 1.87697 − 0.08320I
b = −0.831219 − 0.322384I
2.00050 + 0.85728I 16.5843 − 0.7821I
u = −0.516079 − 0.312340I
a = 1.87697 + 0.08320I
b = −0.831219 + 0.322384I
2.00050 − 0.85728I 16.5843 + 0.7821I
u = −1.56310
a = −2.13614
b = 1.44327
17.0644 20.7220
18
IV.
I
u
4
= h−u
2
+b+1, −2u
7
−u
6
+· · ·+a−9, u
8
−5u
6
+u
5
+7u
4
−4u
3
−2u
2
+4u−1i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
5
=
1
−u
2
a
7
=
2u
7
+ u
6
− 11u
5
− 3u
4
+ 18u
3
− 3u
2
− 8u + 9
u
2
− 1
a
8
=
2u
7
+ u
6
− 11u
5
− 3u
4
+ 18u
3
− 2u
2
− 8u + 8
u
2
− 1
a
11
=
u
−u
3
+ u
a
3
=
−3u
7
− u
6
+ 14u
5
+ u
4
− 18u
3
+ 6u
2
+ 6u − 7
u
4
− 2u
2
+ 1
a
12
=
4u
7
+ 2u
6
− 19u
5
− 5u
4
+ 26u
3
− 5u
2
− 11u + 12
u
5
− 4u
3
+ u
2
+ 3u − 2
a
2
=
−3u
7
+ 14u
5
− 2u
4
− 17u
3
+ 7u
2
+ 4u − 7
−u
6
+ 4u
4
− u
3
− 3u
2
+ 2u
a
1
=
−3u
7
− u
6
+ 14u
5
+ 2u
4
− 18u
3
+ 4u
2
+ 6u − 7
−u
6
+ 4u
4
− u
3
− 3u
2
+ 2u
a
6
=
−u
2
+ 1
u
4
− 2u
2
a
9
=
−3u
7
+ 15u
5
− 2u
4
− 21u
3
+ 9u
2
+ 7u − 11
u
7
+ u
6
− 4u
5
− 3u
4
+ 4u
3
+ u
2
− u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 10u
7
+ 5u
6
− 45u
5
− 10u
4
+ 60u
3
− 15u
2
− 25u + 42
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
4
+ 3u
3
+ 4u
2
+ 4u + 1)
2
c
2
, c
7
u
8
+ 2u
7
− 3u
6
− 5u
5
+ 5u
4
+ 6u
3
− u
2
− 3u − 1
c
3
, c
11
u
8
− 2u
7
− 3u
6
+ 5u
5
+ 5u
4
− 6u
3
− u
2
+ 3u − 1
c
4
, c
5
, c
8
c
9
u
8
− 5u
6
+ u
5
+ 7u
4
− 4u
3
− 2u
2
+ 4u − 1
c
6
(u
4
− u
3
+ u
2
+ u − 1)
2
c
10
, c
12
u
8
− 5u
6
− u
5
+ 7u
4
+ 4u
3
− 2u
2
− 4u − 1
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
4
− y
3
− 6y
2
− 8y + 1)
2
c
2
, c
3
, c
7
c
11
y
8
− 10y
7
+ 39y
6
− 81y
5
+ 101y
4
− 70y
3
+ 27y
2
− 7y + 1
c
4
, c
5
, c
8
c
9
, c
10
, c
12
y
8
− 10y
7
+ 39y
6
− 75y
5
+ 75y
4
− 42y
3
+ 22y
2
− 12y + 1
c
6
(y
4
+ y
3
+ y
2
− 3y + 1)
2
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.220530 + 0.143929I
a = −0.57045 + 1.41533I
b = 0.468985 − 0.351339I
4.50609 − 2.52742I 14.9376 + 0.3938I
u = −1.220530 − 0.143929I
a = −0.57045 − 1.41533I
b = 0.468985 + 0.351339I
4.50609 + 2.52742I 14.9376 − 0.3938I
u = 0.475131 + 0.605600I
a = 0.0796516 + 0.0837240I
b = −1.141000 + 0.575478I
4.50609 − 2.52742I 14.9376 + 0.3938I
u = 0.475131 − 0.605600I
a = 0.0796516 − 0.0837240I
b = −1.141000 − 0.575478I
4.50609 + 2.52742I 14.9376 − 0.3938I
u = 1.26429
a = 1.67924
b = 0.598434
13.5577 8.81150
u = 1.63636
a = −1.79185
b = 1.67768
10.3288 34.3130
u = 0.313425
a = 6.69143
b = −0.901765
10.3288 34.3130
u = −1.72328
a = −1.59721
b = 1.96968
13.5577 8.81150
22
V. I
u
5
= hb + 1, a, u − 1i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
1
a
5
=
1
−1
a
7
=
0
−1
a
8
=
−1
−1
a
11
=
1
0
a
3
=
1
1
a
12
=
0
−1
a
2
=
0
1
a
1
=
1
1
a
6
=
0
−1
a
9
=
−1
0
(ii) Obstruction class = −1
(iii) Cusp Shapes = 18
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
7
, c
11
u − 1
c
4
, c
5
, c
8
c
9
, c
10
, c
12
u + 1
c
6
u
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
7
c
8
, c
9
, c
10
c
11
, c
12
y −1
c
6
y
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0
b = −1.00000
4.93480 18.0000
26
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)(u
4
+ 3u
3
+ 4u
2
+ 4u + 1)
2
(u
5
− 2u
4
+ 5u
3
− 4u
2
− 1)
· (u
13
− 12u
12
+ ··· + 352u − 32)(u
24
+ 2u
23
+ ··· − 20u − 1)
2
c
2
, c
7
(u − 1)(u
5
+ u
4
− u
3
− u
2
+ 1)
· (u
8
+ 2u
7
− 3u
6
− 5u
5
+ 5u
4
+ 6u
3
− u
2
− 3u − 1)
· (u
13
− 3u
11
+ 9u
9
+ u
8
− 12u
7
+ u
6
+ 16u
5
− u
4
− 11u
3
+ 3u
2
+ 4u − 1)
· (u
48
− u
47
+ ··· − 197u + 73)
c
3
, c
11
(u − 1)(u
5
− u
4
− u
3
+ u
2
− 1)
· (u
8
− 2u
7
− 3u
6
+ 5u
5
+ 5u
4
− 6u
3
− u
2
+ 3u − 1)
· (u
13
− 3u
11
+ 9u
9
+ u
8
− 12u
7
+ u
6
+ 16u
5
− u
4
− 11u
3
+ 3u
2
+ 4u − 1)
· (u
48
− u
47
+ ··· − 197u + 73)
c
4
, c
5
, c
8
c
9
(u + 1)(u
5
− 3u
3
+ 2u + 1)(u
8
− 5u
6
+ ··· + 4u − 1)
· (u
13
− u
12
+ ··· + 2u − 1)(u
48
− u
47
+ ··· − 20u + 1)
c
6
u(u
4
− u
3
+ u
2
+ u − 1)
2
(u
5
+ 2u
4
+ 3u
3
+ 3u
2
+ 3u + 1)
· (u
13
+ 11u
12
+ ··· − 208u − 56)(u
24
− 5u
23
+ ··· + 15u − 1)
2
c
10
, c
12
(u + 1)(u
5
− 3u
3
+ 2u − 1)(u
8
− 5u
6
+ ··· − 4u − 1)
· (u
13
− u
12
+ ··· + 2u − 1)(u
48
− u
47
+ ··· − 20u + 1)
27
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y −1)(y
4
− y
3
− 6y
2
− 8y + 1)
2
(y
5
+ 6y
4
+ 9y
3
− 20y
2
− 8y −1)
· (y
13
+ 8y
12
+ ··· + 42496y −1024)(y
24
+ 4y
23
+ ··· − 522y + 1)
2
c
2
, c
3
, c
7
c
11
(y −1)(y
5
− 3y
4
+ 3y
3
− 3y
2
+ 2y −1)
· (y
8
− 10y
7
+ 39y
6
− 81y
5
+ 101y
4
− 70y
3
+ 27y
2
− 7y + 1)
· (y
13
− 6y
12
+ ··· + 22y −1)(y
48
− 23y
47
+ ··· − 76039y + 5329)
c
4
, c
5
, c
8
c
9
, c
10
, c
12
(y −1)(y
5
− 6y
4
+ 13y
3
− 12y
2
+ 4y −1)
· (y
8
− 10y
7
+ 39y
6
− 75y
5
+ 75y
4
− 42y
3
+ 22y
2
− 12y + 1)
· (y
13
− 13y
12
+ ··· − 8y −1)(y
48
− 43y
47
+ ··· − 216y + 1)
c
6
y(y
4
+ y
3
+ y
2
− 3y + 1)
2
(y
5
+ 2y
4
+ 3y
3
+ 5y
2
+ 3y −1)
· (y
13
+ y
12
+ ··· + 5408y −3136)(y
24
− 3y
23
+ ··· − 135y + 1)
2
28
