12n
0267
(K12n
0267
)
A knot diagram
1
Linearized knot diagam
3 5 9 2 10 9 11 4 12 5 7 6
Solving Sequence
4,8
9
3,11
7 12 10 6 1 5 2
c
8
c
3
c
7
c
11
c
9
c
6
c
12
c
5
c
2
c
1
, c
4
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h1.63228 × 10
53
u
27
+ 1.02544 × 10
54
u
26
+ ··· + 3.06469 × 10
56
b + 3.90256 × 10
56
,
1.81316 × 10
54
u
27
+ 1.29787 × 10
55
u
26
+ ··· + 2.45175 × 10
57
a − 9.42098 × 10
56
,
u
28
+ 7u
27
+ ··· − 256u − 1024i
I
u
2
= h−15a
5
u
4
− 35a
4
u
4
+ ··· + 62a + 18, 12a
5
u
4
+ 166a
4
u
4
+ ··· + 144010a + 300665,
u
5
− u
4
+ 5u
3
− u
2
+ 2u + 2i
I
u
3
= h−2796800274u
16
+ 1230170348u
15
+ ··· + 5782655035b + 1488757467,
− 115474u
16
+ 4433863u
15
+ ··· + 2844395a − 26311393, u
17
+ 6u
15
+ ··· − 3u − 1i
I
v
1
= ha, 8v
3
− 12v
2
+ b + 10v −3, 8v
4
− 12v
3
+ 12v
2
− 5v + 1i
I
v
2
= ha, b
6
− b
5
+ 2b
4
− 2b
3
+ 2b
2
− 2b + 1, v + 1i
* 5 irreducible components of dim
C
= 0, with total 85 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
=
h1.63×10
53
u
27
+1.03×10
54
u
26
+· · ·+3.06×10
56
b+3.90×10
56
, 1.81×10
54
u
27
+
1.30×10
55
u
26
+· · ·+2.45 ×10
57
a−9.42 × 10
56
, u
28
+7u
27
+· · ·−256u −1024i
(i) Arc colorings
a
4
=
0
u
a
8
=
1
0
a
9
=
1
u
2
a
3
=
u
u
3
+ u
a
11
=
−0.000739535u
27
− 0.00529364u
26
+ ··· + 1.32145u + 0.384255
−0.000532608u
27
− 0.00334597u
26
+ ··· − 0.222903u − 1.27339
a
7
=
−0.0000164451u
27
− 0.000139457u
26
+ ··· + 0.107664u + 0.565098
−0.000174750u
27
− 0.00136950u
26
+ ··· − 0.302799u − 0.594774
a
12
=
−0.000886322u
27
− 0.00613088u
26
+ ··· + 1.06551u − 0.306723
−0.000917462u
27
− 0.00664824u
26
+ ··· + 2.05507u − 0.158393
a
10
=
−0.000128059u
27
− 0.000962696u
26
+ ··· + 0.904215u + 1.23308
0.000823960u
27
+ 0.00616689u
26
+ ··· − 1.24171u − 0.0314143
a
6
=
−0.000282712u
27
− 0.00211501u
26
+ ··· − 0.172064u − 0.00475082
−0.000128885u
27
− 0.000876415u
26
+ ··· − 0.604047u − 0.709139
a
1
=
−0.000661565u
27
− 0.00488332u
26
+ ··· + 2.13497u + 0.559124
−0.000843467u
27
− 0.00643716u
26
+ ··· + 3.43637u + 0.641978
a
5
=
0.000363425u
27
+ 0.00276215u
26
+ ··· − 2.04345u − 0.341280
0.00102499u
27
+ 0.00764547u
26
+ ··· − 4.17842u − 0.900404
a
2
=
−0.000405455u
27
− 0.00320663u
26
+ ··· + 2.56297u + 0.782535
−0.000623273u
27
− 0.00509696u
26
+ ··· + 4.09691u + 0.746524
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.000805991u
27
+ 0.000903953u
26
+ ··· + 16.6786u + 9.73356
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
28
+ 11u
27
+ ··· + 38144u + 4096
c
2
, c
4
u
28
− 5u
27
+ ··· + 368u − 64
c
3
, c
8
u
28
− 7u
27
+ ··· + 256u − 1024
c
5
, c
7
, c
10
c
11
u
28
− u
26
+ ··· + 6u + 1
c
6
, c
12
u
28
− u
27
+ ··· + 5u + 1
c
9
u
28
− 11u
27
+ ··· − 464u + 32
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
28
+ 17y
27
+ ··· − 423952384y + 16777216
c
2
, c
4
y
28
− 11y
27
+ ··· − 38144y + 4096
c
3
, c
8
y
28
+ 21y
27
+ ··· + 7012352y + 1048576
c
5
, c
7
, c
10
c
11
y
28
− 2y
27
+ ··· − 16y + 1
c
6
, c
12
y
28
+ 15y
27
+ ··· + 59y + 1
c
9
y
28
− 9y
27
+ ··· − 57088y + 1024
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.700519 + 0.599156I
a = 0.801515 − 1.064090I
b = 0.037633 − 0.642247I
−3.55837 − 1.15126I −11.39772 − 0.05458I
u = −0.700519 − 0.599156I
a = 0.801515 + 1.064090I
b = 0.037633 + 0.642247I
−3.55837 + 1.15126I −11.39772 + 0.05458I
u = 0.380572 + 0.813474I
a = 0.564232 + 0.751884I
b = −0.166171 + 0.662526I
−0.05630 − 1.72703I −1.78795 + 1.55176I
u = 0.380572 − 0.813474I
a = 0.564232 − 0.751884I
b = −0.166171 − 0.662526I
−0.05630 + 1.72703I −1.78795 − 1.55176I
u = −0.588263 + 1.018270I
a = 0.470372 − 0.902968I
b = −0.094878 − 0.756998I
−2.26210 + 6.12921I −7.94602 + 0.52990I
u = −0.588263 − 1.018270I
a = 0.470372 + 0.902968I
b = −0.094878 + 0.756998I
−2.26210 − 6.12921I −7.94602 − 0.52990I
u = 1.069010 + 0.807521I
a = −0.138524 − 0.648901I
b = 0.903329 − 0.048342I
−0.304442 − 0.720791I −1.85900 + 1.85047I
u = 1.069010 − 0.807521I
a = −0.138524 + 0.648901I
b = 0.903329 + 0.048342I
−0.304442 + 0.720791I −1.85900 − 1.85047I
u = 0.289195 + 0.590850I
a = −0.185649 − 0.370483I
b = 0.454678 − 1.109670I
−4.11561 − 8.14651I −4.6236 + 14.7439I
u = 0.289195 − 0.590850I
a = −0.185649 + 0.370483I
b = 0.454678 + 1.109670I
−4.11561 + 8.14651I −4.6236 − 14.7439I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.008090 + 0.619126I
a = 0.445860 + 0.546608I
b = −0.405809 + 0.656851I
0.33084 − 1.64029I 3.18047 + 4.70949I
u = −0.008090 − 0.619126I
a = 0.445860 − 0.546608I
b = −0.405809 − 0.656851I
0.33084 + 1.64029I 3.18047 − 4.70949I
u = −1.31770 + 0.54916I
a = 0.352145 − 0.329705I
b = −1.100510 − 0.409135I
3.36539 + 1.37186I −0.78063 − 1.56765I
u = −1.31770 − 0.54916I
a = 0.352145 + 0.329705I
b = −1.100510 + 0.409135I
3.36539 − 1.37186I −0.78063 + 1.56765I
u = 0.535945
a = 1.11271
b = 0.260909
−1.18275 −7.92670
u = 0.66539 + 1.38340I
a = 0.420370 + 0.447189I
b = −0.979556 − 0.414826I
−0.93155 + 4.11677I −2.65942 − 4.73683I
u = 0.66539 − 1.38340I
a = 0.420370 − 0.447189I
b = −0.979556 + 0.414826I
−0.93155 − 4.11677I −2.65942 + 4.73683I
u = −1.68431
a = 0.112961
b = 0.309973
−10.2990 −65.2260
u = −1.70473 + 0.38435I
a = −0.204716 + 0.352722I
b = 1.155650 + 0.736871I
2.18156 + 7.22574I −3.09669 − 6.28834I
u = −1.70473 − 0.38435I
a = −0.204716 − 0.352722I
b = 1.155650 − 0.736871I
2.18156 − 7.22574I −3.09669 + 6.28834I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.73389 + 1.71578I
a = −1.098300 + 0.366340I
b = 1.02566 + 1.08507I
9.85046 + 9.25719I −3.57812 − 5.07121I
u = −0.73389 − 1.71578I
a = −1.098300 − 0.366340I
b = 1.02566 − 1.08507I
9.85046 − 9.25719I −3.57812 + 5.07121I
u = −0.84442 + 1.78161I
a = 1.062890 − 0.293393I
b = −1.07966 − 1.38439I
8.3503 + 16.4009I −4.99450 − 7.83007I
u = −0.84442 − 1.78161I
a = 1.062890 + 0.293393I
b = −1.07966 + 1.38439I
8.3503 − 16.4009I −4.99450 + 7.83007I
u = 0.22185 + 2.03555I
a = −0.956969 − 0.026772I
b = 1.27197 − 0.92548I
11.43660 − 1.44441I −1.83528 + 0.I
u = 0.22185 − 2.03555I
a = −0.956969 + 0.026772I
b = 1.27197 + 0.92548I
11.43660 + 1.44441I −1.83528 + 0.I
u = 0.34578 + 2.17004I
a = 0.853942 + 0.002644I
b = −1.30777 + 1.19876I
10.24040 − 8.22431I −4.00000 + 4.11200I
u = 0.34578 − 2.17004I
a = 0.853942 − 0.002644I
b = −1.30777 − 1.19876I
10.24040 + 8.22431I −4.00000 − 4.11200I
7
II. I
u
2
= h−15a
5
u
4
− 35a
4
u
4
+ · · · + 62a + 18, 12a
5
u
4
+ 166a
4
u
4
+ · · · +
144010a + 300665, u
5
− u
4
+ 5u
3
− u
2
+ 2u + 2i
(i) Arc colorings
a
4
=
0
u
a
8
=
1
0
a
9
=
1
u
2
a
3
=
u
u
3
+ u
a
11
=
a
0.535714a
5
u
4
+ 1.25000a
4
u
4
+ ··· − 2.21429a − 0.642857
a
7
=
0.607143a
5
u
4
+ 0.428571a
4
u
4
+ ··· + 0.642857a + 2.71429
−4.67857a
5
u
4
− 3.57143a
4
u
4
+ ··· + 0.928571a + 3.14286
a
12
=
−3.71429a
5
u
4
− 1.03571a
4
u
4
+ ··· − 0.928571a − 2.57143
16.5714a
5
u
4
+ 9.71429a
4
u
4
+ ··· − 7.71429a − 5.42857
a
10
=
−1.21429a
5
u
4
− 0.607143a
4
u
4
+ ··· + 2.78571a + 1.42857
7.07143a
5
u
4
+ 3.64286a
4
u
4
+ ··· − 3.42857a − 2.71429
a
6
=
0.607143a
5
u
4
+ 0.428571a
4
u
4
+ ··· + 0.642857a + 1.71429
−4.67857a
5
u
4
− 3.57143a
4
u
4
+ ··· + 0.928571a + 2.14286
a
1
=
1
4
u
4
−
1
4
u
2
+
3
2
u −
1
2
−u
4
+
1
2
u
3
−
1
2
u
2
a
5
=
−
1
2
u
2
+
1
2
u − 1
−
1
4
u
4
−
1
4
u
2
− u −
1
2
a
2
=
−
1
4
u
4
+
1
2
u
3
+ ··· +
3
2
u −
1
2
1
2
u
3
−
1
2
u
2
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes =
17
7
a
4
u
4
+
5
7
u
4
a
3
+ ··· +
22
7
a −
92
7
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
5
+ 6u
3
+ u
2
− u + 1)
6
c
2
, c
4
(u
5
− 2u
4
+ 2u
3
+ u
2
− u + 1)
6
c
3
, c
8
(u
5
+ u
4
+ 5u
3
+ u
2
+ 2u − 2)
6
c
5
, c
7
, c
10
c
11
u
30
− 2u
29
+ ··· − 20u + 137
c
6
, c
12
u
30
− 6u
29
+ ··· + 392u + 191
c
9
(u
3
+ u
2
− 1)
10
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
5
+ 12y
4
+ 34y
3
− 13y
2
− y −1)
6
c
2
, c
4
(y
5
+ 6y
3
− y
2
− y −1)
6
c
3
, c
8
(y
5
+ 9y
4
+ 27y
3
+ 23y
2
+ 8y −4)
6
c
5
, c
7
, c
10
c
11
y
30
+ 6y
29
+ ··· + 131668y + 18769
c
6
, c
12
y
30
− 2y
29
+ ··· − 47468y + 36481
c
9
(y
3
− y
2
+ 2y −1)
10
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.375669 + 0.888717I
a = 0.674585 + 0.800660I
b = −0.250372 + 0.453019I
−0.05929 − 1.71921I −2.12477 + 0.93832I
u = 0.375669 + 0.888717I
a = 0.150570 − 0.874514I
b = −0.372835 − 1.197460I
−0.05929 + 3.93704I −2.12477 − 5.02057I
u = 0.375669 + 0.888717I
a = 0.865106 + 0.190043I
b = −0.079065 − 1.171220I
−4.19688 + 1.10891I −8.65403 − 2.04112I
u = 0.375669 + 0.888717I
a = 0.500602 + 0.675276I
b = −0.122646 + 0.883622I
−0.05929 − 1.71921I −2.12477 + 0.93832I
u = 0.375669 + 0.888717I
a = −0.790896 − 0.900150I
b = 1.154460 + 0.050802I
−0.05929 + 3.93704I −2.12477 − 5.02057I
u = 0.375669 + 0.888717I
a = −0.156566 − 0.585774I
b = 0.62035 + 1.42290I
−4.19688 + 1.10891I −8.65403 − 2.04112I
u = 0.375669 − 0.888717I
a = 0.674585 − 0.800660I
b = −0.250372 − 0.453019I
−0.05929 + 1.71921I −2.12477 − 0.93832I
u = 0.375669 − 0.888717I
a = 0.150570 + 0.874514I
b = −0.372835 + 1.197460I
−0.05929 − 3.93704I −2.12477 + 5.02057I
u = 0.375669 − 0.888717I
a = 0.865106 − 0.190043I
b = −0.079065 + 1.171220I
−4.19688 − 1.10891I −8.65403 + 2.04112I
u = 0.375669 − 0.888717I
a = 0.500602 − 0.675276I
b = −0.122646 − 0.883622I
−0.05929 + 1.71921I −2.12477 − 0.93832I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.375669 − 0.888717I
a = −0.790896 + 0.900150I
b = 1.154460 − 0.050802I
−0.05929 − 3.93704I −2.12477 + 5.02057I
u = 0.375669 − 0.888717I
a = −0.156566 + 0.585774I
b = 0.62035 − 1.42290I
−4.19688 − 1.10891I −8.65403 + 2.04112I
u = −0.504107
a = −2.97283 + 2.25685I
b = −0.436616 − 0.497956I
−3.11432 + 2.82812I −13.43328 − 2.97945I
u = −0.504107
a = −2.97283 − 2.25685I
b = −0.436616 + 0.497956I
−3.11432 − 2.82812I −13.43328 + 2.97945I
u = −0.504107
a = −2.46586 + 7.51356I
b = −0.07832 + 1.49767I
−7.25191 −19.9625 + 0.I
u = −0.504107
a = −2.46586 − 7.51356I
b = −0.07832 − 1.49767I
−7.25191 −19.9625 + 0.I
u = −0.504107
a = 1.11141 + 9.05588I
b = 0.377491 + 0.857286I
−3.11432 + 2.82812I −13.43328 − 2.97945I
u = −0.504107
a = 1.11141 − 9.05588I
b = 0.377491 − 0.857286I
−3.11432 − 2.82812I −13.43328 + 2.97945I
u = 0.37638 + 2.02979I
a = −0.941568 − 0.072890I
b = 0.99031 − 1.34752I
9.99924 − 6.95303I −3.38420 + 5.13388I
u = 0.37638 + 2.02979I
a = 0.895319 + 0.135542I
b = −1.30155 + 1.31060I
9.99924 − 1.29678I −3.38420 − 0.82502I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.37638 + 2.02979I
a = 0.798012 + 0.078062I
b = −1.64960 + 0.34874I
5.86166 − 4.12490I −9.91347 + 2.15443I
u = 0.37638 + 2.02979I
a = 0.768176 + 0.214026I
b = −1.60645 − 0.98436I
9.99924 − 6.95303I −3.38420 + 5.13388I
u = 0.37638 + 2.02979I
a = −0.750216 + 0.005392I
b = 0.616800 − 0.250072I
5.86166 − 4.12490I −9.91347 + 2.15443I
u = 0.37638 + 2.02979I
a = −0.685847 − 0.213681I
b = 1.13805 + 1.09576I
9.99924 − 1.29678I −3.38420 − 0.82502I
u = 0.37638 − 2.02979I
a = −0.941568 + 0.072890I
b = 0.99031 + 1.34752I
9.99924 + 6.95303I −3.38420 − 5.13388I
u = 0.37638 − 2.02979I
a = 0.895319 − 0.135542I
b = −1.30155 − 1.31060I
9.99924 + 1.29678I −3.38420 + 0.82502I
u = 0.37638 − 2.02979I
a = 0.798012 − 0.078062I
b = −1.64960 − 0.34874I
5.86166 + 4.12490I −9.91347 − 2.15443I
u = 0.37638 − 2.02979I
a = 0.768176 − 0.214026I
b = −1.60645 + 0.98436I
9.99924 + 6.95303I −3.38420 − 5.13388I
u = 0.37638 − 2.02979I
a = −0.750216 − 0.005392I
b = 0.616800 + 0.250072I
5.86166 + 4.12490I −9.91347 − 2.15443I
u = 0.37638 − 2.02979I
a = −0.685847 + 0.213681I
b = 1.13805 − 1.09576I
9.99924 + 1.29678I −3.38420 + 0.82502I
13
III.
I
u
3
= h−2.80 × 10
9
u
16
+ 1.23 × 10
9
u
15
+ · · · + 5.78 × 10
9
b + 1.49 × 10
9
, −1.15 ×
10
5
u
16
+4.43×10
6
u
15
+· · · +2.84×10
6
a−2.63×10
7
, u
17
+6u
15
+· · · − 3u −1i
(i) Arc colorings
a
4
=
0
u
a
8
=
1
0
a
9
=
1
u
2
a
3
=
u
u
3
+ u
a
11
=
0.0405970u
16
− 1.55881u
15
+ ··· − 7.16863u + 9.25026
0.483653u
16
− 0.212735u
15
+ ··· − 1.67509u − 0.257452
a
7
=
3.74840u
16
− 2.16144u
15
+ ··· − 23.4255u − 3.72929
0.0829079u
16
− 0.0995122u
15
+ ··· − 1.83555u − 0.881897
a
12
=
3.61930u
16
− 2.25286u
15
+ ··· − 19.3756u + 0.277471
0.355787u
16
− 0.159534u
15
+ ··· − 2.01409u − 0.833403
a
10
=
0.164018u
16
− 1.84216u
15
+ ··· − 8.28234u + 10.6964
0.483653u
16
− 0.212735u
15
+ ··· − 1.67509u − 0.257452
a
6
=
3.51603u
16
− 2.28526u
15
+ ··· − 22.5251u − 2.44974
0.290525u
16
− 0.147505u
15
+ ··· − 2.43936u − 1.00571
a
1
=
1.23077u
16
− 0.226208u
15
+ ··· − 4.14992u − 2.86754
0.0648607u
16
+ 0.00369480u
15
+ ··· + 0.102878u − 0.137290
a
5
=
−1.08969u
16
+ 0.114263u
15
+ ··· + 3.70066u + 2.95645
0.141079u
16
− 0.111945u
15
+ ··· − 0.449264u + 0.0889186
a
2
=
1.18986u
16
− 0.118103u
15
+ ··· − 3.40302u − 2.98180
0.0172629u
16
+ 0.0956716u
15
+ ··· + 1.13318u − 0.143448
(ii) Obstruction class = 1
(iii) Cusp Shapes =
44404088866
5782655035
u
16
−
1457732737
5782655035
u
15
+ ··· −
34652808542
1156531007
u −
182738550788
5782655035
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
17
− 8u
16
+ ··· + 3u − 1
c
2
u
17
+ 6u
16
+ ··· + u + 1
c
3
u
17
+ 6u
15
+ ··· − 3u + 1
c
4
u
17
− 6u
16
+ ··· + u − 1
c
5
, c
11
u
17
+ 6u
15
+ ··· + 3u − 1
c
6
, c
12
u
17
− 3u
16
+ ··· + 6u − 1
c
7
, c
10
u
17
+ 6u
15
+ ··· + 3u + 1
c
8
u
17
+ 6u
15
+ ··· − 3u − 1
c
9
u
17
− 5u
16
+ ··· + 5u − 1
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
17
+ 8y
16
+ ··· − 25y −1
c
2
, c
4
y
17
− 8y
16
+ ··· + 3y −1
c
3
, c
8
y
17
+ 12y
16
+ ··· + 3y −1
c
5
, c
7
, c
10
c
11
y
17
+ 12y
16
+ ··· − 3y −1
c
6
, c
12
y
17
− 19y
16
+ ··· − 2y −1
c
9
y
17
− 7y
16
+ ··· + 17y −1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.123817 + 0.916477I
a = 0.72791 + 1.22000I
b = −0.302924 + 0.816439I
−0.67196 − 2.40485I −7.80780 + 6.32008I
u = 0.123817 − 0.916477I
a = 0.72791 − 1.22000I
b = −0.302924 − 0.816439I
−0.67196 + 2.40485I −7.80780 − 6.32008I
u = −0.519605 + 0.973810I
a = 0.205092 − 1.101040I
b = −0.199212 − 0.760976I
−2.24497 + 6.61108I −7.2534 − 15.3751I
u = −0.519605 − 0.973810I
a = 0.205092 + 1.101040I
b = −0.199212 + 0.760976I
−2.24497 − 6.61108I −7.2534 + 15.3751I
u = −0.718697 + 0.273065I
a = 0.143920 − 1.236700I
b = −0.503625 + 0.659985I
−2.14035 − 2.21103I −3.32753 + 2.55558I
u = −0.718697 − 0.273065I
a = 0.143920 + 1.236700I
b = −0.503625 − 0.659985I
−2.14035 + 2.21103I −3.32753 − 2.55558I
u = 0.535223 + 1.162140I
a = −0.218207 − 0.016209I
b = −0.154895 − 1.305200I
−4.41311 − 5.07181I −7.38870 + 4.45168I
u = 0.535223 − 1.162140I
a = −0.218207 + 0.016209I
b = −0.154895 + 1.305200I
−4.41311 + 5.07181I −7.38870 − 4.45168I
u = −0.259361 + 1.266310I
a = 0.298735 − 0.200867I
b = −0.27641 + 1.42034I
−2.77350 − 0.30087I −3.43063 − 0.64342I
u = −0.259361 − 1.266310I
a = 0.298735 + 0.200867I
b = −0.27641 − 1.42034I
−2.77350 + 0.30087I −3.43063 + 0.64342I
17
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.642620 + 0.176331I
a = −2.73234 − 3.06072I
b = 0.06025 − 1.48960I
−7.28871 + 0.50220I −14.6902 − 9.4676I
u = 0.642620 − 0.176331I
a = −2.73234 + 3.06072I
b = 0.06025 + 1.48960I
−7.28871 − 0.50220I −14.6902 + 9.4676I
u = −0.314004 + 0.270023I
a = 11.33940 − 1.30281I
b = 0.368087 − 0.696391I
−3.55921 − 3.00568I −21.0214 − 13.1073I
u = −0.314004 − 0.270023I
a = 11.33940 + 1.30281I
b = 0.368087 + 0.696391I
−3.55921 + 3.00568I −21.0214 + 13.1073I
u = 1.73212
a = −0.0334354
b = −0.404382
−10.2300 50.8770
u = −0.35606 + 2.09120I
a = −0.747795 + 0.030202I
b = 1.210930 + 0.258234I
6.82265 + 4.21829I 0.48138 − 3.10222I
u = −0.35606 − 2.09120I
a = −0.747795 − 0.030202I
b = 1.210930 − 0.258234I
6.82265 − 4.21829I 0.48138 + 3.10222I
18
IV. I
v
1
= ha, 8v
3
− 12v
2
+ b + 10v − 3, 8v
4
− 12v
3
+ 12v
2
− 5v + 1i
(i) Arc colorings
a
4
=
v
0
a
8
=
1
0
a
9
=
1
0
a
3
=
v
0
a
11
=
0
−8v
3
+ 12v
2
− 10v + 3
a
7
=
1
−8v
3
+ 8v
2
− 8v + 1
a
12
=
−8v
3
+ 12v
2
− 10v + 3
−8v
3
+ 8v
2
− 6v
a
10
=
8v
3
− 12v
2
+ 10v − 3
16v
3
− 16v
2
+ 14v − 2
a
6
=
−8v
3
+ 8v
2
− 8v + 2
−8v
3
+ 8v
2
− 8v + 1
a
1
=
−1
8v
3
− 12v
2
+ 12v − 5
a
5
=
1
−8v
3
+ 12v
2
− 12v + 5
a
2
=
v − 1
8v
3
− 12v
2
+ 12v − 5
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8v
3
+ 5v
2
− 9
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
4
c
3
, c
8
u
4
c
4
(u + 1)
4
c
5
, c
7
u
4
+ u
2
+ u + 1
c
6
u
4
− 2u
3
+ 3u
2
− u + 1
c
9
u
4
+ 3u
3
+ 4u
2
+ 3u + 2
c
10
, c
11
u
4
+ u
2
− u + 1
c
12
u
4
+ 2u
3
+ 3u
2
+ u + 1
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y − 1)
4
c
3
, c
8
y
4
c
5
, c
7
, c
10
c
11
y
4
+ 2y
3
+ 3y
2
+ y + 1
c
6
, c
12
y
4
+ 2y
3
+ 7y
2
+ 5y + 1
c
9
y
4
− y
3
+ 2y
2
+ 7y + 4
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.447562 + 0.776246I
a = 0
b = −0.547424 + 0.585652I
−0.66484 − 1.39709I −5.25608 + 3.48426I
v = 0.447562 − 0.776246I
a = 0
b = −0.547424 − 0.585652I
−0.66484 + 1.39709I −5.25608 − 3.48426I
v = 0.302438 + 0.253422I
a = 0
b = 0.547424 − 1.120870I
−4.26996 − 7.64338I −8.61892 + 0.34032I
v = 0.302438 − 0.253422I
a = 0
b = 0.547424 + 1.120870I
−4.26996 + 7.64338I −8.61892 − 0.34032I
22
V. I
v
2
= ha, b
6
− b
5
+ 2b
4
− 2b
3
+ 2b
2
− 2b + 1, v + 1i
(i) Arc colorings
a
4
=
−1
0
a
8
=
1
0
a
9
=
1
0
a
3
=
−1
0
a
11
=
0
b
a
7
=
1
b
2
a
12
=
b
b
3
+ b
a
10
=
b
4
+ b
2
+ 1
b
5
+ 2b
3
− b
2
+ 2b − 1
a
6
=
b
2
+ 1
b
2
a
1
=
−b
5
− 2b
3
− b + 1
1
a
5
=
b
5
+ 2b
3
+ b − 1
−1
a
2
=
−b
5
− 2b
3
− b
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4b
3
+ 4b − 8
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
6
c
3
, c
8
u
6
c
4
(u + 1)
6
c
5
, c
7
u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1
c
6
u
6
− 3u
5
+ 4u
4
− 2u
3
+ 1
c
9
(u
3
− u
2
+ 1)
2
c
10
, c
11
u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1
c
12
u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y − 1)
6
c
3
, c
8
y
6
c
5
, c
7
, c
10
c
11
y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1
c
6
, c
12
y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1
c
9
(y
3
− y
2
+ 2y − 1)
2
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
2
√
−1(vol +
√
−1CS) Cusp shape
v = −1.00000
a = 0
b = −0.498832 + 1.001300I
−1.91067 − 2.82812I −4.49024 + 2.97945I
v = −1.00000
a = 0
b = −0.498832 − 1.001300I
−1.91067 + 2.82812I −4.49024 − 2.97945I
v = −1.00000
a = 0
b = 0.284920 + 1.115140I
−6.04826 −11.01951 + 0.I
v = −1.00000
a = 0
b = 0.284920 − 1.115140I
−6.04826 −11.01951 + 0.I
v = −1.00000
a = 0
b = 0.713912 + 0.305839I
−1.91067 − 2.82812I −4.49024 + 2.97945I
v = −1.00000
a = 0
b = 0.713912 − 0.305839I
−1.91067 + 2.82812I −4.49024 − 2.97945I
26
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
10
)(u
5
+ 6u
3
+ u
2
− u + 1)
6
(u
17
− 8u
16
+ ··· + 3u − 1)
· (u
28
+ 11u
27
+ ··· + 38144u + 4096)
c
2
((u − 1)
10
)(u
5
− 2u
4
+ ··· − u + 1)
6
(u
17
+ 6u
16
+ ··· + u + 1)
· (u
28
− 5u
27
+ ··· + 368u − 64)
c
3
u
10
(u
5
+ u
4
+ ··· + 2u − 2)
6
(u
17
+ 6u
15
+ ··· − 3u + 1)
· (u
28
− 7u
27
+ ··· + 256u − 1024)
c
4
((u + 1)
10
)(u
5
− 2u
4
+ ··· − u + 1)
6
(u
17
− 6u
16
+ ··· + u − 1)
· (u
28
− 5u
27
+ ··· + 368u − 64)
c
5
(u
4
+ u
2
+ u + 1)(u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
· (u
17
+ 6u
15
+ ··· + 3u − 1)(u
28
− u
26
+ ··· + 6u + 1)
· (u
30
− 2u
29
+ ··· − 20u + 137)
c
6
(u
4
− 2u
3
+ 3u
2
− u + 1)(u
6
− 3u
5
+ 4u
4
− 2u
3
+ 1)
· (u
17
− 3u
16
+ ··· + 6u − 1)(u
28
− u
27
+ ··· + 5u + 1)
· (u
30
− 6u
29
+ ··· + 392u + 191)
c
7
(u
4
+ u
2
+ u + 1)(u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
· (u
17
+ 6u
15
+ ··· + 3u + 1)(u
28
− u
26
+ ··· + 6u + 1)
· (u
30
− 2u
29
+ ··· − 20u + 137)
c
8
u
10
(u
5
+ u
4
+ ··· + 2u − 2)
6
(u
17
+ 6u
15
+ ··· − 3u − 1)
· (u
28
− 7u
27
+ ··· + 256u − 1024)
c
9
(u
3
− u
2
+ 1)
2
(u
3
+ u
2
− 1)
10
(u
4
+ 3u
3
+ 4u
2
+ 3u + 2)
· (u
17
− 5u
16
+ ··· + 5u − 1)(u
28
− 11u
27
+ ··· − 464u + 32)
c
10
(u
4
+ u
2
− u + 1)(u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)
· (u
17
+ 6u
15
+ ··· + 3u + 1)(u
28
− u
26
+ ··· + 6u + 1)
· (u
30
− 2u
29
+ ··· − 20u + 137)
c
11
(u
4
+ u
2
− u + 1)(u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)
· (u
17
+ 6u
15
+ ··· + 3u − 1)(u
28
− u
26
+ ··· + 6u + 1)
· (u
30
− 2u
29
+ ··· − 20u + 137)
c
12
(u
4
+ 2u
3
+ 3u
2
+ u + 1)(u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1)
· (u
17
− 3u
16
+ ··· + 6u − 1)(u
28
− u
27
+ ··· + 5u + 1)
· (u
30
− 6u
29
+ ··· + 392u + 191)
27
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y − 1)
10
(y
5
+ 12y
4
+ 34y
3
− 13y
2
− y − 1)
6
· (y
17
+ 8y
16
+ ··· − 25y − 1)
· (y
28
+ 17y
27
+ ··· − 423952384y + 16777216)
c
2
, c
4
((y − 1)
10
)(y
5
+ 6y
3
− y
2
− y − 1)
6
(y
17
− 8y
16
+ ··· + 3y − 1)
· (y
28
− 11y
27
+ ··· − 38144y + 4096)
c
3
, c
8
y
10
(y
5
+ 9y
4
+ ··· + 8y − 4)
6
(y
17
+ 12y
16
+ ··· + 3y − 1)
· (y
28
+ 21y
27
+ ··· + 7012352y + 1048576)
c
5
, c
7
, c
10
c
11
(y
4
+ 2y
3
+ 3y
2
+ y + 1)(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
· (y
17
+ 12y
16
+ ··· − 3y − 1)(y
28
− 2y
27
+ ··· − 16y + 1)
· (y
30
+ 6y
29
+ ··· + 131668y + 18769)
c
6
, c
12
(y
4
+ 2y
3
+ 7y
2
+ 5y + 1)(y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1)
· (y
17
− 19y
16
+ ··· − 2y − 1)(y
28
+ 15y
27
+ ··· + 59y + 1)
· (y
30
− 2y
29
+ ··· − 47468y + 36481)
c
9
((y
3
− y
2
+ 2y − 1)
12
)(y
4
− y
3
+ 2y
2
+ 7y + 4)(y
17
− 7y
16
+ ··· + 17y − 1)
· (y
28
− 9y
27
+ ··· − 57088y + 1024)
28
