12a
0570
(K12a
0570
)
A knot diagram
1
Linearized knot diagam
3 7 9 10 8 12 2 11 5 4 1 6
Solving Sequence
5,9
10 4 11
2,3
1 8 6 7 12
c
9
c
4
c
10
c
3
c
1
c
8
c
5
c
7
c
12
c
2
, c
6
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= hu
40
+ 3u
39
+ ··· + b + 3, −3u
42
− 9u
41
+ ··· + 2a − 11, u
43
+ 3u
42
+ ··· + 11u + 2i
I
u
2
= h190u
31
a + 573u
31
+ ··· − 125a − 709, −u
31
− 14u
29
+ ··· + a
2
+ a, u
32
− u
31
+ ··· − 2u + 1i
I
u
3
= hu
9
+ 4u
7
+ 5u
5
− u
4
+ u
3
− 2u
2
+ b, u
8
+ 4u
6
+ 5u
4
+ 2u
2
+ a + 1, u
10
+ 5u
8
+ 8u
6
+ 3u
4
− u
2
+ 1i
* 3 irreducible components of dim
C
= 0, with total 117 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
=
hu
40
+3u
39
+· · ·+b+3, −3u
42
−9u
41
+· · ·+2a−11, u
43
+3u
42
+· · ·+11u+2i
(i) Arc colorings
a
5
=
0
u
a
9
=
1
0
a
10
=
1
−u
2
a
4
=
−u
u
3
+ u
a
11
=
u
2
+ 1
−u
4
− 2u
2
a
2
=
3
2
u
42
+
9
2
u
41
+ ··· + 23u +
11
2
−u
40
− 3u
39
+ ··· − 10u − 3
a
3
=
−u
3
− 2u
u
3
+ u
a
1
=
5
2
u
42
+
15
2
u
41
+ ··· + 41u +
19
2
−2u
40
− 5u
39
+ ··· − 18u − 5
a
8
=
−u
6
− 3u
4
− 2u
2
+ 1
u
8
+ 4u
6
+ 4u
4
a
6
=
−u
13
− 6u
11
− 13u
9
− 10u
7
+ 2u
5
+ 4u
3
− u
u
15
+ 7u
13
+ 18u
11
+ 19u
9
+ 4u
7
− 4u
5
+ u
a
7
=
1
2
u
42
+
1
2
u
41
+ ··· + u +
1
2
u
41
+ 2u
40
+ ··· + 4u + 1
a
12
=
−
3
2
u
42
−
9
2
u
41
+ ··· − 25u −
9
2
u
40
+ 3u
39
+ ··· + 11u + 3
(ii) Obstruction class = −1
(iii) Cusp Shapes = 12u
42
+ 26u
41
+ ··· + 114u + 38
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
u
43
+ 18u
42
+ ··· − 5u − 1
c
2
, c
6
, c
7
c
12
u
43
+ 9u
41
+ ··· + u − 1
c
3
u
43
+ 3u
42
+ ··· + 79u − 10
c
4
, c
9
, c
10
u
43
− 3u
42
+ ··· + 11u − 2
c
5
u
43
− 21u
42
+ ··· + 18607u − 1058
c
8
u
43
+ 9u
42
+ ··· − 863u − 88
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
43
+ 26y
42
+ ··· + 67y −1
c
2
, c
6
, c
7
c
12
y
43
+ 18y
42
+ ··· − 5y −1
c
3
y
43
+ 3y
42
+ ··· + 241y −100
c
4
, c
9
, c
10
y
43
+ 39y
42
+ ··· + 17y −4
c
5
y
43
+ 3y
42
+ ··· + 10766737y −1119364
c
8
y
43
+ 15y
42
+ ··· + 108705y −7744
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.164014 + 0.946057I
a = 1.282900 − 0.345090I
b = 0.534324 − 0.151237I
2.20216 − 1.04215I 8.70214 + 2.03700I
u = 0.164014 − 0.946057I
a = 1.282900 + 0.345090I
b = 0.534324 + 0.151237I
2.20216 + 1.04215I 8.70214 − 2.03700I
u = 0.243062 + 1.100190I
a = −1.54071 − 0.64105I
b = −1.52314 + 0.64705I
−0.89825 + 9.73279I 4.53563 − 8.30440I
u = 0.243062 − 1.100190I
a = −1.54071 + 0.64105I
b = −1.52314 − 0.64705I
−0.89825 − 9.73279I 4.53563 + 8.30440I
u = −0.722534 + 0.301697I
a = 0.08578 + 3.01066I
b = −0.29124 − 2.70866I
−0.37610 − 13.45560I 5.29575 + 10.36544I
u = −0.722534 − 0.301697I
a = 0.08578 − 3.01066I
b = −0.29124 + 2.70866I
−0.37610 + 13.45560I 5.29575 − 10.36544I
u = −0.404425 + 0.657515I
a = −2.67151 + 0.36651I
b = 0.065501 − 1.014060I
−1.70851 + 9.45730I 2.82665 − 5.31681I
u = −0.404425 − 0.657515I
a = −2.67151 − 0.36651I
b = 0.065501 + 1.014060I
−1.70851 − 9.45730I 2.82665 + 5.31681I
u = −0.204544 + 0.730389I
a = 1.43841 − 0.73472I
b = 0.293207 + 0.580345I
2.08121 − 1.04733I 8.22274 + 3.41589I
u = −0.204544 − 0.730389I
a = 1.43841 + 0.73472I
b = 0.293207 − 0.580345I
2.08121 + 1.04733I 8.22274 − 3.41589I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.644960 + 0.373766I
a = 0.760035 + 0.158019I
b = −1.138310 + 0.047746I
−3.38888 + 1.43692I 3.05929 − 2.01133I
u = −0.644960 − 0.373766I
a = 0.760035 − 0.158019I
b = −1.138310 − 0.047746I
−3.38888 − 1.43692I 3.05929 + 2.01133I
u = −0.703437 + 0.246639I
a = 0.66216 − 1.99434I
b = −0.29319 + 1.70932I
3.84861 − 2.56258I 11.41433 + 1.98438I
u = −0.703437 − 0.246639I
a = 0.66216 + 1.99434I
b = −0.29319 − 1.70932I
3.84861 + 2.56258I 11.41433 − 1.98438I
u = 0.702975 + 0.194251I
a = −0.86374 + 1.45652I
b = 0.330233 − 1.365890I
4.46731 + 4.55873I 11.59252 − 6.90277I
u = 0.702975 − 0.194251I
a = −0.86374 − 1.45652I
b = 0.330233 + 1.365890I
4.46731 − 4.55873I 11.59252 + 6.90277I
u = −0.522120 + 0.491654I
a = −0.240133 − 1.023150I
b = 0.500490 − 0.298029I
−3.88878 − 5.31369I 1.61265 + 8.28245I
u = −0.522120 − 0.491654I
a = −0.240133 + 1.023150I
b = 0.500490 + 0.298029I
−3.88878 + 5.31369I 1.61265 − 8.28245I
u = 0.704270 + 0.097056I
a = −0.35999 − 2.14445I
b = 0.72753 + 1.96810I
2.11782 − 6.17915I 9.04327 + 4.42784I
u = 0.704270 − 0.097056I
a = −0.35999 + 2.14445I
b = 0.72753 − 1.96810I
2.11782 + 6.17915I 9.04327 − 4.42784I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.562309 + 0.373892I
a = −0.425293 − 0.567896I
b = 0.349891 + 0.140060I
−2.01863 + 1.75385I 5.78006 − 4.89342I
u = 0.562309 − 0.373892I
a = −0.425293 + 0.567896I
b = 0.349891 − 0.140060I
−2.01863 − 1.75385I 5.78006 + 4.89342I
u = 0.260662 + 1.303620I
a = 0.878955 + 0.346423I
b = 0.39384 − 2.51915I
−2.24110 − 2.69252I 0
u = 0.260662 − 1.303620I
a = 0.878955 − 0.346423I
b = 0.39384 + 2.51915I
−2.24110 + 2.69252I 0
u = −0.001427 + 1.338340I
a = −0.356373 − 0.037117I
b = 0.518324 − 0.887394I
−3.78341 − 1.46954I 0
u = −0.001427 − 1.338340I
a = −0.356373 + 0.037117I
b = 0.518324 + 0.887394I
−3.78341 + 1.46954I 0
u = −0.126955 + 1.361350I
a = −0.527328 − 0.405446I
b = 0.745333 − 0.463766I
−3.68931 − 1.78526I 0
u = −0.126955 − 1.361350I
a = −0.527328 + 0.405446I
b = 0.745333 + 0.463766I
−3.68931 + 1.78526I 0
u = 0.277378 + 1.369800I
a = −0.295618 − 0.850189I
b = −1.30294 + 1.86794I
−0.48560 + 8.11013I 0
u = 0.277378 − 1.369800I
a = −0.295618 + 0.850189I
b = −1.30294 − 1.86794I
−0.48560 − 8.11013I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.27745 + 1.39855I
a = −1.137110 + 0.389286I
b = −0.19324 − 2.23756I
−1.39190 − 6.12597I 0
u = −0.27745 − 1.39855I
a = −1.137110 − 0.389286I
b = −0.19324 + 2.23756I
−1.39190 + 6.12597I 0
u = 0.21669 + 1.43469I
a = 0.352241 + 0.027500I
b = −0.842082 − 0.581266I
−7.80581 + 4.63802I 0
u = 0.21669 − 1.43469I
a = 0.352241 − 0.027500I
b = −0.842082 + 0.581266I
−7.80581 − 4.63802I 0
u = −0.28325 + 1.42482I
a = 1.35303 − 1.05301I
b = 1.20627 + 3.61742I
−5.8954 − 17.1146I 0
u = −0.28325 − 1.42482I
a = 1.35303 + 1.05301I
b = 1.20627 − 3.61742I
−5.8954 + 17.1146I 0
u = −0.11220 + 1.45113I
a = 1.182720 + 0.686675I
b = −1.55004 − 0.11281I
−8.32121 + 7.81517I 0
u = −0.11220 − 1.45113I
a = 1.182720 − 0.686675I
b = −1.55004 + 0.11281I
−8.32121 − 7.81517I 0
u = −0.24228 + 1.44282I
a = −0.108809 − 0.420814I
b = 1.41781 − 0.62704I
−9.21691 − 1.80423I 0
u = −0.24228 − 1.44282I
a = −0.108809 + 0.420814I
b = 1.41781 + 0.62704I
−9.21691 + 1.80423I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.18017 + 1.45365I
a = −0.205904 + 0.631433I
b = 0.244371 + 0.099729I
−10.10500 − 7.84159I 0
u = −0.18017 − 1.45365I
a = −0.205904 − 0.631433I
b = 0.244371 − 0.099729I
−10.10500 + 7.84159I 0
u = −0.411211
a = 0.972593
b = −0.385880
0.654283 15.3800
9
II. I
u
2
= h190u
31
a + 573u
31
+ · · · − 125a − 709, −u
31
− 14u
29
+ · · · + a
2
+
a, u
32
− u
31
+ · · · − 2u + 1i
(i) Arc colorings
a
5
=
0
u
a
9
=
1
0
a
10
=
1
−u
2
a
4
=
−u
u
3
+ u
a
11
=
u
2
+ 1
−u
4
− 2u
2
a
2
=
a
−0.278592au
31
− 0.840176u
31
+ ··· + 0.183284a + 1.03959
a
3
=
−u
3
− 2u
u
3
+ u
a
1
=
0.140762au
31
− 0.517595u
31
+ ··· + 0.828446a + 0.458944
−0.153959au
31
− 0.293255u
31
+ ··· + 0.140762a + 0.482405
a
8
=
−u
6
− 3u
4
− 2u
2
+ 1
u
8
+ 4u
6
+ 4u
4
a
6
=
−u
13
− 6u
11
− 13u
9
− 10u
7
+ 2u
5
+ 4u
3
− u
u
15
+ 7u
13
+ 18u
11
+ 19u
9
+ 4u
7
− 4u
5
+ u
a
7
=
0.293255au
31
− 1.03666u
31
+ ··· − 0.482405a + 1.24780
−0.214076au
31
− 0.0982405u
31
+ ··· − 0.332845a − 0.895894
a
12
=
0.0982405au
31
− 0.0747801u
31
+ ··· + 0.895894a + 0.325513
−0.0953079au
31
− 0.800587u
31
+ ··· − 0.0557185a + 0.631965
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −4u
31
+4u
30
−60u
29
+52u
28
−392u
27
+292u
26
−1448u
25
+908u
24
−3260u
23
+1640u
22
−
4412u
21
+ 1548u
20
− 3076u
19
+ 248u
18
− 220u
17
− 888u
16
+ 924u
15
− 580u
14
− 60u
13
+
204u
12
−616u
11
+212u
10
−144u
9
−72u
8
+108u
7
−60u
6
+12u
5
+8u
4
−20u
3
+8u
2
−8u+10
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
u
64
+ 35u
63
+ ··· + 52u
2
+ 1
c
2
, c
6
, c
7
c
12
u
64
+ u
63
+ ··· + 2u + 1
c
3
(u
32
− u
31
+ ··· + 20u
3
+ 1)
2
c
4
, c
9
, c
10
(u
32
+ u
31
+ ··· + 2u + 1)
2
c
5
, c
8
(u
32
+ 7u
31
+ ··· + 104u + 17)
2
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
64
− 13y
63
+ ··· + 104y + 1
c
2
, c
6
, c
7
c
12
y
64
+ 35y
63
+ ··· + 52y
2
+ 1
c
3
(y
32
+ y
31
+ ··· + 56y
2
+ 1)
2
c
4
, c
9
, c
10
(y
32
+ 29y
31
+ ··· + 4y
2
+ 1)
2
c
5
, c
8
(y
32
+ 9y
31
+ ··· + 3056y + 289)
2
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.209460 + 1.051390I
a = −0.934884 − 0.232233I
b = −0.533239 − 0.058153I
1.12671 − 4.25629I 7.47389 + 4.09777I
u = −0.209460 + 1.051390I
a = 1.55966 − 0.70578I
b = 1.32202 + 0.52410I
1.12671 − 4.25629I 7.47389 + 4.09777I
u = −0.209460 − 1.051390I
a = −0.934884 + 0.232233I
b = −0.533239 + 0.058153I
1.12671 + 4.25629I 7.47389 − 4.09777I
u = −0.209460 − 1.051390I
a = 1.55966 + 0.70578I
b = 1.32202 − 0.52410I
1.12671 + 4.25629I 7.47389 − 4.09777I
u = 0.089089 + 1.108640I
a = 0.194552 − 0.198501I
b = 0.02787 − 1.84014I
−4.54650 + 1.65846I 3.56019 − 4.42001I
u = 0.089089 + 1.108640I
a = −1.76337 − 1.02559I
b = −1.54639 − 0.20893I
−4.54650 + 1.65846I 3.56019 − 4.42001I
u = 0.089089 − 1.108640I
a = 0.194552 + 0.198501I
b = 0.02787 + 1.84014I
−4.54650 − 1.65846I 3.56019 + 4.42001I
u = 0.089089 − 1.108640I
a = −1.76337 + 1.02559I
b = −1.54639 + 0.20893I
−4.54650 − 1.65846I 3.56019 + 4.42001I
u = 0.714631 + 0.281038I
a = −0.58887 − 1.89058I
b = 0.08278 + 1.63195I
2.12380 + 7.91274I 8.55825 − 6.96002I
u = 0.714631 + 0.281038I
a = −0.44223 + 2.80524I
b = 0.42814 − 2.47045I
2.12380 + 7.91274I 8.55825 − 6.96002I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.714631 − 0.281038I
a = −0.58887 + 1.89058I
b = 0.08278 − 1.63195I
2.12380 − 7.91274I 8.55825 + 6.96002I
u = 0.714631 − 0.281038I
a = −0.44223 − 2.80524I
b = 0.42814 + 2.47045I
2.12380 − 7.91274I 8.55825 + 6.96002I
u = 0.339557 + 0.664733I
a = −1.37593 − 0.63879I
b = −0.035908 + 0.835219I
0.65551 − 4.07051I 5.91410 + 1.89651I
u = 0.339557 + 0.664733I
a = 2.50163 − 0.00413I
b = −0.044254 − 0.702995I
0.65551 − 4.07051I 5.91410 + 1.89651I
u = 0.339557 − 0.664733I
a = −1.37593 + 0.63879I
b = −0.035908 − 0.835219I
0.65551 + 4.07051I 5.91410 − 1.89651I
u = 0.339557 − 0.664733I
a = 2.50163 + 0.00413I
b = −0.044254 + 0.702995I
0.65551 + 4.07051I 5.91410 − 1.89651I
u = −0.672202 + 0.282270I
a = 0.506296 + 0.591013I
b = −1.271420 − 0.532717I
−3.28987 − 4.49550I 4.00000 + 7.21172I
u = −0.672202 + 0.282270I
a = 1.35780 + 3.33899I
b = −1.12075 − 2.55842I
−3.28987 − 4.49550I 4.00000 + 7.21172I
u = −0.672202 − 0.282270I
a = 0.506296 − 0.591013I
b = −1.271420 + 0.532717I
−3.28987 + 4.49550I 4.00000 − 7.21172I
u = −0.672202 − 0.282270I
a = 1.35780 − 3.33899I
b = −1.12075 + 2.55842I
−3.28987 + 4.49550I 4.00000 − 7.21172I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.694439 + 0.142847I
a = 0.789254 + 0.891876I
b = −0.153418 − 0.883404I
3.82740 + 0.78256I 11.62681 + 0.59259I
u = −0.694439 + 0.142847I
a = 0.47492 − 2.22804I
b = −0.62800 + 1.94416I
3.82740 + 0.78256I 11.62681 + 0.59259I
u = −0.694439 − 0.142847I
a = 0.789254 − 0.891876I
b = −0.153418 + 0.883404I
3.82740 − 0.78256I 11.62681 − 0.59259I
u = −0.694439 − 0.142847I
a = 0.47492 + 2.22804I
b = −0.62800 − 1.94416I
3.82740 − 0.78256I 11.62681 − 0.59259I
u = 0.515560 + 0.370610I
a = −0.971553 − 0.576478I
b = 0.521901 + 0.456852I
−2.03323 + 1.65846I 4.43981 − 4.42001I
u = 0.515560 + 0.370610I
a = 0.092361 − 0.506624I
b = 0.160147 − 0.302293I
−2.03323 + 1.65846I 4.43981 − 4.42001I
u = 0.515560 − 0.370610I
a = −0.971553 + 0.576478I
b = 0.521901 − 0.456852I
−2.03323 − 1.65846I 4.43981 + 4.42001I
u = 0.515560 − 0.370610I
a = 0.092361 + 0.506624I
b = 0.160147 + 0.302293I
−2.03323 − 1.65846I 4.43981 + 4.42001I
u = 0.598306 + 0.209645I
a = 0.055218 + 0.713308I
b = 0.864572 − 0.880440I
−2.09042 + 1.01594I 7.95412 − 1.45531I
u = 0.598306 + 0.209645I
a = −1.36702 − 2.81720I
b = 1.01471 + 1.80896I
−2.09042 + 1.01594I 7.95412 − 1.45531I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.598306 − 0.209645I
a = 0.055218 − 0.713308I
b = 0.864572 + 0.880440I
−2.09042 − 1.01594I 7.95412 + 1.45531I
u = 0.598306 − 0.209645I
a = −1.36702 + 2.81720I
b = 1.01471 − 1.80896I
−2.09042 − 1.01594I 7.95412 + 1.45531I
u = −0.265495 + 1.341380I
a = −1.020800 + 0.433430I
b = −0.36050 − 2.59349I
−0.84097 − 2.68301I 6.52130 + 2.36594I
u = −0.265495 + 1.341380I
a = 0.007855 − 0.645958I
b = 0.98543 + 1.23226I
−0.84097 − 2.68301I 6.52130 + 2.36594I
u = −0.265495 − 1.341380I
a = −1.020800 − 0.433430I
b = −0.36050 + 2.59349I
−0.84097 + 2.68301I 6.52130 − 2.36594I
u = −0.265495 − 1.341380I
a = 0.007855 + 0.645958I
b = 0.98543 − 1.23226I
−0.84097 + 2.68301I 6.52130 − 2.36594I
u = −0.323417 + 0.508294I
a = −0.520273 − 1.034610I
b = 0.287125 − 0.913296I
−4.48931 + 1.01594I 0.04588 − 1.45531I
u = −0.323417 + 0.508294I
a = −3.36072 − 0.80274I
b = 0.743295 − 0.386337I
−4.48931 + 1.01594I 0.04588 − 1.45531I
u = −0.323417 − 0.508294I
a = −0.520273 + 1.034610I
b = 0.287125 + 0.913296I
−4.48931 − 1.01594I 0.04588 + 1.45531I
u = −0.323417 − 0.508294I
a = −3.36072 + 0.80274I
b = 0.743295 + 0.386337I
−4.48931 − 1.01594I 0.04588 + 1.45531I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.235723 + 1.392280I
a = 1.45838 + 0.35987I
b = −0.57974 − 2.88435I
−7.23525 + 4.07051I 2.08590 − 1.89651I
u = 0.235723 + 1.392280I
a = −0.320654 − 0.130453I
b = −1.43078 − 0.01572I
−7.23525 + 4.07051I 2.08590 − 1.89651I
u = 0.235723 − 1.392280I
a = 1.45838 − 0.35987I
b = −0.57974 + 2.88435I
−7.23525 − 4.07051I 2.08590 + 1.89651I
u = 0.235723 − 1.392280I
a = −0.320654 + 0.130453I
b = −1.43078 + 0.01572I
−7.23525 − 4.07051I 2.08590 + 1.89651I
u = −0.14428 + 1.41797I
a = 0.182119 + 0.762399I
b = 0.568805 + 0.605729I
−10.40710 − 0.78256I −3.62681 − 0.59259I
u = −0.14428 + 1.41797I
a = 0.86680 + 1.28541I
b = −2.41207 − 0.83594I
−10.40710 − 0.78256I −3.62681 − 0.59259I
u = −0.14428 − 1.41797I
a = 0.182119 − 0.762399I
b = 0.568805 − 0.605729I
−10.40710 + 0.78256I −3.62681 + 0.59259I
u = −0.14428 − 1.41797I
a = 0.86680 − 1.28541I
b = −2.41207 + 0.83594I
−10.40710 + 0.78256I −3.62681 + 0.59259I
u = 0.19271 + 1.41648I
a = 0.691663 − 0.425815I
b = −1.19278 − 0.82150I
−7.70645 + 4.25629I 0. − 4.09777I
u = 0.19271 + 1.41648I
a = −0.066784 + 0.334796I
b = −0.819907 + 0.086970I
−7.70645 + 4.25629I 0. − 4.09777I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.19271 − 1.41648I
a = 0.691663 + 0.425815I
b = −1.19278 + 0.82150I
−7.70645 − 4.25629I 0. + 4.09777I
u = 0.19271 − 1.41648I
a = −0.066784 − 0.334796I
b = −0.819907 − 0.086970I
−7.70645 − 4.25629I 0. + 4.09777I
u = 0.10594 + 1.42756I
a = −0.918714 + 0.715280I
b = 1.54734 − 0.53710I
−5.73877 − 2.68301I 1.47870 + 2.36594I
u = 0.10594 + 1.42756I
a = 0.676636 − 0.372114I
b = −0.756124 − 0.741018I
−5.73877 − 2.68301I 1.47870 + 2.36594I
u = 0.10594 − 1.42756I
a = −0.918714 − 0.715280I
b = 1.54734 + 0.53710I
−5.73877 + 2.68301I 1.47870 − 2.36594I
u = 0.10594 − 1.42756I
a = 0.676636 + 0.372114I
b = −0.756124 + 0.741018I
−5.73877 + 2.68301I 1.47870 − 2.36594I
u = −0.26371 + 1.41237I
a = 0.230081 − 0.417931I
b = 1.66019 − 0.28514I
−8.70354 − 7.91274I 0. + 6.96002I
u = −0.26371 + 1.41237I
a = 1.02067 − 1.69275I
b = 2.33566 + 3.50017I
−8.70354 − 7.91274I 0. + 6.96002I
u = −0.26371 − 1.41237I
a = 0.230081 + 0.417931I
b = 1.66019 + 0.28514I
−8.70354 + 7.91274I 0. − 6.96002I
u = −0.26371 − 1.41237I
a = 1.02067 + 1.69275I
b = 2.33566 − 3.50017I
−8.70354 + 7.91274I 0. − 6.96002I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.28148 + 1.41481I
a = 1.110910 + 0.401180I
b = 0.27105 − 2.03432I
−3.28987 + 11.53570I 4.00000 − 7.26982I
u = 0.28148 + 1.41481I
a = −1.12502 − 1.13544I
b = −1.43575 + 3.33825I
−3.28987 + 11.53570I 4.00000 − 7.26982I
u = 0.28148 − 1.41481I
a = 1.110910 − 0.401180I
b = 0.27105 + 2.03432I
−3.28987 − 11.53570I 4.00000 + 7.26982I
u = 0.28148 − 1.41481I
a = −1.12502 + 1.13544I
b = −1.43575 − 3.33825I
−3.28987 − 11.53570I 4.00000 + 7.26982I
19
III. I
u
3
= hu
9
+ 4u
7
+ 5u
5
− u
4
+ u
3
− 2u
2
+ b, u
8
+ 4u
6
+ 5u
4
+ 2u
2
+ a +
1, u
10
+ 5u
8
+ 8u
6
+ 3u
4
− u
2
+ 1i
(i) Arc colorings
a
5
=
0
u
a
9
=
1
0
a
10
=
1
−u
2
a
4
=
−u
u
3
+ u
a
11
=
u
2
+ 1
−u
4
− 2u
2
a
2
=
−u
8
− 4u
6
− 5u
4
− 2u
2
− 1
−u
9
− 4u
7
− 5u
5
+ u
4
− u
3
+ 2u
2
a
3
=
−u
3
− 2u
u
3
+ u
a
1
=
−u
8
− 4u
6
− 5u
4
+ u
3
− 2u
2
+ 2u − 1
−u
9
− 4u
7
− 5u
5
+ u
4
− 2u
3
+ 2u
2
− u
a
8
=
−u
6
− 3u
4
− 2u
2
+ 1
u
8
+ 4u
6
+ 4u
4
a
6
=
u
7
+ 4u
5
+ 4u
3
−u
7
− 3u
5
− 2u
3
+ u
a
7
=
u
9
+ 5u
7
− u
6
+ 8u
5
− 3u
4
+ 3u
3
− 2u
2
− u + 1
−u
7
− 3u
5
− 2u
3
+ u − 1
a
12
=
−u
8
− 4u
6
− 5u
4
+ u
3
− u
2
+ 2u
−u
9
− 4u
7
− 5u
5
− 2u
3
− u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
6
− 12u
4
− 8u
2
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
(u − 1)
10
c
2
, c
6
, c
7
c
12
(u
2
+ 1)
5
c
3
u
10
+ u
8
+ 8u
6
+ 3u
4
+ 3u
2
+ 1
c
4
, c
9
, c
10
u
10
+ 5u
8
+ 8u
6
+ 3u
4
− u
2
+ 1
c
5
u
10
− 3u
8
+ 4u
6
− u
4
− u
2
+ 1
c
8
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
2
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
(y −1)
10
c
2
, c
6
, c
7
c
12
(y + 1)
10
c
3
(y
5
+ y
4
+ 8y
3
+ 3y
2
+ 3y + 1)
2
c
4
, c
9
, c
10
(y
5
+ 5y
4
+ 8y
3
+ 3y
2
− y + 1)
2
c
5
(y
5
− 3y
4
+ 4y
3
− y
2
− y + 1)
2
c
8
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
2
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.217740I
a = −0.821196
b = −0.76683 − 1.58802I
−5.69095 −1.48110
u = − 1.217740I
a = −0.821196
b = −0.76683 + 1.58802I
−5.69095 −1.48110
u = 0.549911 + 0.309916I
a = −0.77780 − 1.38013I
b = 0.896862 + 0.383681I
−3.61897 + 1.53058I −0.51511 − 4.43065I
u = 0.549911 − 0.309916I
a = −0.77780 + 1.38013I
b = 0.896862 − 0.383681I
−3.61897 − 1.53058I −0.51511 + 4.43065I
u = −0.549911 + 0.309916I
a = −0.77780 + 1.38013I
b = −0.218641 − 1.261070I
−3.61897 − 1.53058I −0.51511 + 4.43065I
u = −0.549911 − 0.309916I
a = −0.77780 − 1.38013I
b = −0.218641 + 1.261070I
−3.61897 + 1.53058I −0.51511 − 4.43065I
u = −0.21917 + 1.41878I
a = 0.688402 − 0.106340I
b = 0.638115 + 0.967447I
−9.16243 − 4.40083I −4.74431 + 3.49859I
u = −0.21917 − 1.41878I
a = 0.688402 + 0.106340I
b = 0.638115 − 0.967447I
−9.16243 + 4.40083I −4.74431 − 3.49859I
u = 0.21917 + 1.41878I
a = 0.688402 + 0.106340I
b = −1.54951 − 1.43286I
−9.16243 + 4.40083I −4.74431 − 3.49859I
u = 0.21917 − 1.41878I
a = 0.688402 − 0.106340I
b = −1.54951 + 1.43286I
−9.16243 − 4.40083I −4.74431 + 3.49859I
23
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
11
((u − 1)
10
)(u
43
+ 18u
42
+ ··· − 5u − 1)(u
64
+ 35u
63
+ ··· + 52u
2
+ 1)
c
2
, c
6
, c
7
c
12
((u
2
+ 1)
5
)(u
43
+ 9u
41
+ ··· + u − 1)(u
64
+ u
63
+ ··· + 2u + 1)
c
3
(u
10
+ u
8
+ 8u
6
+ 3u
4
+ 3u
2
+ 1)(u
32
− u
31
+ ··· + 20u
3
+ 1)
2
· (u
43
+ 3u
42
+ ··· + 79u − 10)
c
4
, c
9
, c
10
(u
10
+ 5u
8
+ 8u
6
+ 3u
4
− u
2
+ 1)(u
32
+ u
31
+ ··· + 2u + 1)
2
· (u
43
− 3u
42
+ ··· + 11u − 2)
c
5
(u
10
− 3u
8
+ 4u
6
− u
4
− u
2
+ 1)(u
32
+ 7u
31
+ ··· + 104u + 17)
2
· (u
43
− 21u
42
+ ··· + 18607u − 1058)
c
8
((u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
2
)(u
32
+ 7u
31
+ ··· + 104u + 17)
2
· (u
43
+ 9u
42
+ ··· − 863u − 88)
24
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
11
((y −1)
10
)(y
43
+ 26y
42
+ ··· + 67y −1)(y
64
− 13y
63
+ ··· + 104y + 1)
c
2
, c
6
, c
7
c
12
((y + 1)
10
)(y
43
+ 18y
42
+ ··· − 5y −1)(y
64
+ 35y
63
+ ··· + 52y
2
+ 1)
c
3
((y
5
+ y
4
+ 8y
3
+ 3y
2
+ 3y + 1)
2
)(y
32
+ y
31
+ ··· + 56y
2
+ 1)
2
· (y
43
+ 3y
42
+ ··· + 241y −100)
c
4
, c
9
, c
10
((y
5
+ 5y
4
+ 8y
3
+ 3y
2
− y + 1)
2
)(y
32
+ 29y
31
+ ··· + 4y
2
+ 1)
2
· (y
43
+ 39y
42
+ ··· + 17y −4)
c
5
((y
5
− 3y
4
+ 4y
3
− y
2
− y + 1)
2
)(y
32
+ 9y
31
+ ··· + 3056y + 289)
2
· (y
43
+ 3y
42
+ ··· + 10766737y −1119364)
c
8
((y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
2
)(y
32
+ 9y
31
+ ··· + 3056y + 289)
2
· (y
43
+ 15y
42
+ ··· + 108705y −7744)
25
