12a
0233
(K12a
0233
)
A knot diagram
1
Linearized knot diagam
3 6 7 9 12 2 11 5 8 1 4 10
Solving Sequence
4,9 5,12
6 8 10 1 11 7 3 2
c
4
c
5
c
8
c
9
c
12
c
11
c
7
c
3
c
2
c
1
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h4.18488 × 10
227
u
127
+ 5.48646 × 10
227
u
126
+ ··· + 2.24973 × 10
228
b + 1.02313 × 10
228
,
1.34465 × 10
228
u
127
+ 5.19412 × 10
228
u
126
+ ··· + 7.31163 × 10
228
a + 8.12721 × 10
228
, u
128
+ 2u
127
+ ··· + 4u + 1i
I
u
2
= hb, 21u
3
− 14u
2
+ 13a + 54u − 24, u
4
− u
3
+ 3u
2
− 2u + 1i
* 2 irreducible components of dim
C
= 0, with total 132 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
= h4.18 × 10
227
u
127
+ 5.49 × 10
227
u
126
+ · · · + 2.25 × 10
228
b + 1.02 ×
10
228
, 1.34 × 10
228
u
127
+ 5.19 × 10
228
u
126
+ · · · + 7.31 × 10
228
a + 8.13 ×
10
228
, u
128
+ 2u
127
+ · · · + 4u + 1i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
5
=
1
u
2
a
12
=
−0.183906u
127
− 0.710391u
126
+ ··· − 2.82573u − 1.11155
−0.186017u
127
− 0.243872u
126
+ ··· + 0.364001u − 0.454777
a
6
=
2.12621u
127
+ 7.12324u
126
+ ··· + 18.8467u + 7.04245
−0.141375u
127
− 0.0767156u
126
+ ··· + 0.384787u + 0.310717
a
8
=
u
u
3
+ u
a
10
=
u
3
u
5
+ u
3
+ u
a
1
=
−0.0809780u
127
− 0.414723u
126
+ ··· − 2.39257u − 0.955381
u
5
+ u
3
+ u
a
11
=
−0.369923u
127
− 0.954263u
126
+ ··· − 2.46172u − 1.56632
−0.186017u
127
− 0.243872u
126
+ ··· + 0.364001u − 0.454777
a
7
=
−0.272534u
127
− 4.23409u
126
+ ··· − 10.9206u − 2.04342
0.306137u
127
+ 0.382329u
126
+ ··· + 1.78713u + 0.793514
a
3
=
−2.12817u
127
− 3.27752u
126
+ ··· − 6.67846u − 1.39973
0.0958762u
127
+ 0.310460u
126
+ ··· + 2.02656u + 0.685172
a
2
=
0.289840u
127
+ 0.491603u
126
+ ··· + 2.31147u + 0.795233
0.413994u
127
+ 0.479323u
126
+ ··· + 1.65330u + 0.537177
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.987890u
127
− 5.81033u
126
+ ··· − 41.3925u − 15.5122
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
128
+ 62u
127
+ ··· + 4u + 1
c
2
, c
6
u
128
− 2u
127
+ ··· − 2u + 1
c
3
u
128
+ 2u
127
+ ··· + 4224656u + 1446152
c
4
, c
8
u
128
+ 2u
127
+ ··· + 4u + 1
c
5
13(13u
128
− 13u
127
+ ··· − 23585u + 12601)
c
7
13(13u
128
+ 104u
127
+ ··· + 257066u + 17686)
c
9
u
128
− 58u
127
+ ··· − 4u + 1
c
10
, c
12
u
128
+ 5u
127
+ ··· + 1642u + 169
c
11
u
128
+ 5u
127
+ ··· + 25272u + 2704
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
128
+ 10y
127
+ ··· + 16y + 1
c
2
, c
6
y
128
+ 62y
127
+ ··· + 4y + 1
c
3
y
128
− 42y
127
+ ··· − 15693533191440y + 2091355607104
c
4
, c
8
y
128
+ 58y
127
+ ··· + 4y + 1
c
5
169(169y
128
+ 5603y
127
+ ··· − 9.11953 × 10
8
y + 1.58785 × 10
8
)
c
7
169(169y
128
+ 11180y
127
+ ··· + 1.65779 × 10
10
y + 3.12795 × 10
8
)
c
9
y
128
+ 26y
127
+ ··· + 64y + 1
c
10
, c
12
y
128
− 75y
127
+ ··· + 85914y + 28561
c
11
y
128
− 27y
127
+ ··· + 238719936y + 7311616
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.632351 + 0.776627I
a = 0.384670 + 0.174926I
b = 0.468234 + 0.140402I
−0.40228 + 1.86126I 0
u = −0.632351 − 0.776627I
a = 0.384670 − 0.174926I
b = 0.468234 − 0.140402I
−0.40228 − 1.86126I 0
u = 0.898979 + 0.430780I
a = 0.129023 + 0.106373I
b = 1.16662 − 0.85267I
−0.07280 + 8.63391I 0
u = 0.898979 − 0.430780I
a = 0.129023 − 0.106373I
b = 1.16662 + 0.85267I
−0.07280 − 8.63391I 0
u = −0.895363 + 0.438019I
a = −0.156897 + 0.105804I
b = −1.24502 − 0.90117I
−2.65354 − 13.84350I 0
u = −0.895363 − 0.438019I
a = −0.156897 − 0.105804I
b = −1.24502 + 0.90117I
−2.65354 + 13.84350I 0
u = 0.929547 + 0.405477I
a = 0.0413716 + 0.0807925I
b = 0.848325 − 0.738830I
2.38568 + 6.03387I 0
u = 0.929547 − 0.405477I
a = 0.0413716 − 0.0807925I
b = 0.848325 + 0.738830I
2.38568 − 6.03387I 0
u = −0.885131 + 0.421262I
a = −0.115650 + 0.156423I
b = −1.221290 − 0.694121I
−4.91627 − 5.37289I 0
u = −0.885131 − 0.421262I
a = −0.115650 − 0.156423I
b = −1.221290 + 0.694121I
−4.91627 + 5.37289I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.952929 + 0.376629I
a = 0.0036938 + 0.0791327I
b = −0.702715 − 0.596805I
2.00855 − 0.71097I 0
u = −0.952929 − 0.376629I
a = 0.0036938 − 0.0791327I
b = −0.702715 + 0.596805I
2.00855 + 0.71097I 0
u = 0.818015 + 0.622461I
a = −0.186819 + 0.231456I
b = −1.110050 − 0.108095I
−6.18849 − 1.43861I 0
u = 0.818015 − 0.622461I
a = −0.186819 − 0.231456I
b = −1.110050 + 0.108095I
−6.18849 + 1.43861I 0
u = −0.274045 + 0.926878I
a = −0.92575 − 2.27337I
b = −0.602160 + 1.228960I
1.73156 + 2.55640I 0
u = −0.274045 − 0.926878I
a = −0.92575 + 2.27337I
b = −0.602160 − 1.228960I
1.73156 − 2.55640I 0
u = −0.322986 + 0.983840I
a = −0.41115 − 2.42512I
b = −1.34793 + 1.14806I
2.69083 − 3.89242I 0
u = −0.322986 − 0.983840I
a = −0.41115 + 2.42512I
b = −1.34793 − 1.14806I
2.69083 + 3.89242I 0
u = 0.346007 + 0.977002I
a = 0.31122 − 2.15276I
b = 1.36159 + 0.83379I
4.67825 − 0.54660I 0
u = 0.346007 − 0.977002I
a = 0.31122 + 2.15276I
b = 1.36159 − 0.83379I
4.67825 + 0.54660I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.426686 + 0.862947I
a = −2.03486 − 3.06355I
b = −0.329659 + 0.305677I
1.78616 + 1.80735I 0
u = −0.426686 − 0.862947I
a = −2.03486 + 3.06355I
b = −0.329659 − 0.305677I
1.78616 − 1.80735I 0
u = 0.526025 + 0.894900I
a = −3.64824 + 6.31543I
b = −0.057519 − 0.285480I
−0.91250 + 1.67927I 0
u = 0.526025 − 0.894900I
a = −3.64824 − 6.31543I
b = −0.057519 + 0.285480I
−0.91250 − 1.67927I 0
u = −0.500220 + 0.917179I
a = −0.90698 + 3.81295I
b = −0.208222 − 0.324824I
1.63645 + 2.27841I 0
u = −0.500220 − 0.917179I
a = −0.90698 − 3.81295I
b = −0.208222 + 0.324824I
1.63645 − 2.27841I 0
u = 0.384306 + 0.990713I
a = −0.11804 − 1.66145I
b = 1.57928 + 0.30620I
4.93867 − 1.81136I 0
u = 0.384306 − 0.990713I
a = −0.11804 + 1.66145I
b = 1.57928 − 0.30620I
4.93867 + 1.81136I 0
u = −0.037841 + 0.932887I
a = −1.66931 − 1.32141I
b = 0.613399 + 1.108330I
−0.95705 − 6.55438I 0
u = −0.037841 − 0.932887I
a = −1.66931 + 1.32141I
b = 0.613399 − 1.108330I
−0.95705 + 6.55438I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.535878 + 0.927976I
a = −2.05775 + 2.73591I
b = 0.015290 − 0.533756I
−1.26429 − 5.66383I 0
u = 0.535878 − 0.927976I
a = −2.05775 − 2.73591I
b = 0.015290 + 0.533756I
−1.26429 + 5.66383I 0
u = −0.745382 + 0.545622I
a = 0.077721 + 0.386047I
b = 1.42048 + 0.54522I
−7.27264 + 0.58083I 0
u = −0.745382 − 0.545622I
a = 0.077721 − 0.386047I
b = 1.42048 − 0.54522I
−7.27264 − 0.58083I 0
u = 0.883502 + 0.625066I
a = −0.191745 + 0.163487I
b = −0.948287 − 0.428041I
−3.74142 − 9.48538I 0
u = 0.883502 − 0.625066I
a = −0.191745 − 0.163487I
b = −0.948287 + 0.428041I
−3.74142 + 9.48538I 0
u = −0.400087 + 1.007720I
a = 0.57220 − 1.45592I
b = −1.80895 − 0.00572I
3.23788 + 6.12295I 0
u = −0.400087 − 1.007720I
a = 0.57220 + 1.45592I
b = −1.80895 + 0.00572I
3.23788 − 6.12295I 0
u = −0.873555 + 0.658407I
a = 0.163345 + 0.182698I
b = 0.860741 − 0.290075I
−1.37571 + 4.26938I 0
u = −0.873555 − 0.658407I
a = 0.163345 − 0.182698I
b = 0.860741 + 0.290075I
−1.37571 − 4.26938I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.096379 + 0.890392I
a = −1.36267 − 0.83058I
b = 0.566969 + 0.647022I
−2.01309 + 1.15458I 0
u = 0.096379 − 0.890392I
a = −1.36267 + 0.83058I
b = 0.566969 − 0.647022I
−2.01309 − 1.15458I 0
u = 0.718201 + 0.533561I
a = 0.019695 + 0.390470I
b = −1.30885 + 0.75980I
−3.18770 + 2.76839I 0
u = 0.718201 − 0.533561I
a = 0.019695 − 0.390470I
b = −1.30885 − 0.75980I
−3.18770 − 2.76839I 0
u = −0.727223 + 0.517544I
a = −0.015327 + 0.459392I
b = 1.44559 + 0.83679I
−5.85757 − 7.54109I 0
u = −0.727223 − 0.517544I
a = −0.015327 − 0.459392I
b = 1.44559 − 0.83679I
−5.85757 + 7.54109I 0
u = 0.200788 + 0.867511I
a = 1.08886 − 1.93715I
b = 0.099058 + 1.157480I
2.81820 + 1.20231I 0
u = 0.200788 − 0.867511I
a = 1.08886 + 1.93715I
b = 0.099058 − 1.157480I
2.81820 − 1.20231I 0
u = 0.492212 + 0.740960I
a = −2.20367 − 1.81776I
b = −0.101543 + 0.598383I
−1.38202 − 5.91758I 0
u = 0.492212 − 0.740960I
a = −2.20367 + 1.81776I
b = −0.101543 − 0.598383I
−1.38202 + 5.91758I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.448235 + 1.016420I
a = 1.120110 − 0.326616I
b = −1.52198 − 0.89095I
2.92272 + 0.14341I 0
u = −0.448235 − 1.016420I
a = 1.120110 + 0.326616I
b = −1.52198 + 0.89095I
2.92272 − 0.14341I 0
u = 0.471306 + 1.015550I
a = −1.220560 + 0.267213I
b = 1.16705 − 1.18281I
4.35010 − 4.32900I 0
u = 0.471306 − 1.015550I
a = −1.220560 − 0.267213I
b = 1.16705 + 1.18281I
4.35010 + 4.32900I 0
u = 0.054445 + 0.874045I
a = 1.38644 − 1.39055I
b = −0.390969 + 1.030140I
1.56973 + 2.00866I 0
u = 0.054445 − 0.874045I
a = 1.38644 + 1.39055I
b = −0.390969 − 1.030140I
1.56973 − 2.00866I 0
u = −0.449444 + 0.749502I
a = 1.16998 − 2.30692I
b = −0.000337 + 0.566212I
1.08929 + 1.73625I 0
u = −0.449444 − 0.749502I
a = 1.16998 + 2.30692I
b = −0.000337 − 0.566212I
1.08929 − 1.73625I 0
u = −0.578952 + 0.966012I
a = 0.95852 + 1.19777I
b = 0.373143 − 0.693459I
0.30632 + 2.86178I 0
u = −0.578952 − 0.966012I
a = 0.95852 − 1.19777I
b = 0.373143 + 0.693459I
0.30632 − 2.86178I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.793240 + 0.356284I
a = −0.107941 + 0.280203I
b = 1.071670 − 0.042848I
−6.33619 + 3.32794I 0
u = 0.793240 − 0.356284I
a = −0.107941 − 0.280203I
b = 1.071670 + 0.042848I
−6.33619 − 3.32794I 0
u = 0.497702 + 1.025980I
a = −1.52817 + 0.84837I
b = 0.77404 − 1.61636I
3.64882 − 5.60532I 0
u = 0.497702 − 1.025980I
a = −1.52817 − 0.84837I
b = 0.77404 + 1.61636I
3.64882 + 5.60532I 0
u = −0.528951 + 1.014510I
a = 1.29255 + 1.35472I
b = −0.12714 − 1.48116I
0.08476 + 3.28264I 0
u = −0.528951 − 1.014510I
a = 1.29255 − 1.35472I
b = −0.12714 + 1.48116I
0.08476 − 3.28264I 0
u = 0.630037 + 0.571249I
a = 0.119204 + 0.091100I
b = −0.731769 + 0.766308I
−1.01345 + 1.95971I 0
u = 0.630037 − 0.571249I
a = 0.119204 − 0.091100I
b = −0.731769 − 0.766308I
−1.01345 − 1.95971I 0
u = −0.504744 + 1.035910I
a = 1.72928 + 1.01611I
b = −0.67860 − 1.87767I
1.48535 + 10.17420I 0
u = −0.504744 − 1.035910I
a = 1.72928 − 1.01611I
b = −0.67860 + 1.87767I
1.48535 − 10.17420I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.464624 + 0.685655I
a = −1.27292 − 0.93048I
b = 0.025724 + 0.647128I
−1.99473 + 1.41613I 0
u = 0.464624 − 0.685655I
a = −1.27292 + 0.93048I
b = 0.025724 − 0.647128I
−1.99473 − 1.41613I 0
u = 0.589028 + 1.017350I
a = −0.78540 + 1.70504I
b = −0.83917 − 1.14462I
0.31608 − 6.78721I 0
u = 0.589028 − 1.017350I
a = −0.78540 − 1.70504I
b = −0.83917 + 1.14462I
0.31608 + 6.78721I 0
u = 0.707936 + 0.362323I
a = −0.275552 + 0.323362I
b = 0.974206 + 0.241415I
−5.25090 − 5.17198I 0
u = 0.707936 − 0.362323I
a = −0.275552 − 0.323362I
b = 0.974206 − 0.241415I
−5.25090 + 5.17198I 0
u = −0.760118 + 0.936366I
a = 0.003216 + 0.528381I
b = 0.672054 + 0.027651I
−0.49600 + 1.69688I 0
u = −0.760118 − 0.936366I
a = 0.003216 − 0.528381I
b = 0.672054 − 0.027651I
−0.49600 − 1.69688I 0
u = −0.734325 + 0.300986I
a = 0.224525 + 0.220536I
b = −0.872585 + 0.091595I
−2.28361 + 0.47581I 0
u = −0.734325 − 0.300986I
a = 0.224525 − 0.220536I
b = −0.872585 − 0.091595I
−2.28361 − 0.47581I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.610855 + 1.041230I
a = −0.40502 + 2.02467I
b = −1.41825 − 1.06966I
−1.68060 − 7.86822I 0
u = 0.610855 − 1.041230I
a = −0.40502 − 2.02467I
b = −1.41825 + 1.06966I
−1.68060 + 7.86822I 0
u = −0.625131 + 1.041040I
a = 0.16613 + 1.93058I
b = 1.50137 − 0.80100I
−5.79503 + 4.63683I 0
u = −0.625131 − 1.041040I
a = 0.16613 − 1.93058I
b = 1.50137 + 0.80100I
−5.79503 − 4.63683I 0
u = −0.611400 + 1.049250I
a = 0.35391 + 2.17037I
b = 1.58312 − 1.12574I
−4.28254 + 12.66350I 0
u = −0.611400 − 1.049250I
a = 0.35391 − 2.17037I
b = 1.58312 + 1.12574I
−4.28254 − 12.66350I 0
u = 0.679144 + 1.007210I
a = 0.086544 + 1.125410I
b = −1.051820 − 0.135293I
−5.02581 − 4.14807I 0
u = 0.679144 − 1.007210I
a = 0.086544 − 1.125410I
b = −1.051820 + 0.135293I
−5.02581 + 4.14807I 0
u = −0.065310 + 1.260480I
a = 1.10987 + 1.17405I
b = −0.904424 − 0.933478I
3.43285 − 11.15210I 0
u = −0.065310 − 1.260480I
a = 1.10987 − 1.17405I
b = −0.904424 + 0.933478I
3.43285 + 11.15210I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.101203 + 1.262340I
a = 1.072270 + 0.805770I
b = −0.831818 − 0.644666I
0.97764 − 2.56762I 0
u = −0.101203 − 1.262340I
a = 1.072270 − 0.805770I
b = −0.831818 + 0.644666I
0.97764 + 2.56762I 0
u = 0.763272 + 1.016450I
a = 0.302516 + 0.578936I
b = −0.761657 + 0.212115I
−2.57086 + 3.46847I 0
u = 0.763272 − 1.016450I
a = 0.302516 − 0.578936I
b = −0.761657 − 0.212115I
−2.57086 − 3.46847I 0
u = 0.071409 + 1.271830I
a = −0.97930 + 1.09070I
b = 0.789462 − 0.879460I
6.01140 + 5.85590I 0
u = 0.071409 − 1.271830I
a = −0.97930 − 1.09070I
b = 0.789462 + 0.879460I
6.01140 − 5.85590I 0
u = 0.528327 + 1.163720I
a = −0.728580 − 0.906768I
b = 0.746221 + 0.117323I
−2.85021 + 0.40649I 0
u = 0.528327 − 1.163720I
a = −0.728580 + 0.906768I
b = 0.746221 − 0.117323I
−2.85021 − 0.40649I 0
u = 0.594955 + 1.152750I
a = −0.41766 − 1.37163I
b = 0.959140 + 0.350193I
−3.95846 − 8.56048I 0
u = 0.594955 − 1.152750I
a = −0.41766 + 1.37163I
b = 0.959140 − 0.350193I
−3.95846 + 8.56048I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.643161 + 1.137780I
a = −0.21745 − 1.93403I
b = −1.26228 + 0.86867I
−2.75261 + 11.00610I 0
u = −0.643161 − 1.137780I
a = −0.21745 + 1.93403I
b = −1.26228 − 0.86867I
−2.75261 − 11.00610I 0
u = −0.651207 + 1.135620I
a = −0.42713 − 2.03646I
b = −1.31308 + 1.04434I
−0.5375 + 19.5357I 0
u = −0.651207 − 1.135620I
a = −0.42713 + 2.03646I
b = −1.31308 − 1.04434I
−0.5375 − 19.5357I 0
u = 0.650004 + 1.138880I
a = 0.40382 − 1.93633I
b = 1.23809 + 1.01206I
2.0745 − 14.3290I 0
u = 0.650004 − 1.138880I
a = 0.40382 + 1.93633I
b = 1.23809 − 1.01206I
2.0745 + 14.3290I 0
u = −0.575489 + 1.189130I
a = 0.389298 − 1.000600I
b = −0.736345 + 0.304703I
0.38762 + 4.55179I 0
u = −0.575489 − 1.189130I
a = 0.389298 + 1.000600I
b = −0.736345 − 0.304703I
0.38762 − 4.55179I 0
u = 0.651021 + 1.154090I
a = 0.41737 − 1.56021I
b = 0.946995 + 0.959821I
4.66018 − 11.80060I 0
u = 0.651021 − 1.154090I
a = 0.41737 + 1.56021I
b = 0.946995 − 0.959821I
4.66018 + 11.80060I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.649273 + 1.165840I
a = −0.340607 − 1.351870I
b = −0.806556 + 0.860138I
4.40266 + 6.51601I 0
u = −0.649273 − 1.165840I
a = −0.340607 + 1.351870I
b = −0.806556 − 0.860138I
4.40266 − 6.51601I 0
u = 0.051760 + 1.351390I
a = −0.323387 + 0.865265I
b = 0.256174 − 0.739354I
8.69485 + 2.85046I 0
u = 0.051760 − 1.351390I
a = −0.323387 − 0.865265I
b = 0.256174 + 0.739354I
8.69485 − 2.85046I 0
u = −0.485376 + 0.423733I
a = −1.006980 − 0.316764I
b = 0.020564 + 1.180970I
−1.48749 + 0.97090I −3.81000 − 0.30668I
u = −0.485376 − 0.423733I
a = −1.006980 + 0.316764I
b = 0.020564 − 1.180970I
−1.48749 − 0.97090I −3.81000 + 0.30668I
u = −0.480842 + 0.307056I
a = −1.66540 − 0.20548I
b = −0.439562 + 1.314170I
−0.38770 − 6.08787I −1.35496 + 6.52586I
u = −0.480842 − 0.307056I
a = −1.66540 + 0.20548I
b = −0.439562 − 1.314170I
−0.38770 + 6.08787I −1.35496 − 6.52586I
u = 0.421069 + 0.301666I
a = 1.75107 − 0.54964I
b = 0.443775 + 1.063820I
1.85296 + 1.65232I 2.94839 − 2.48371I
u = 0.421069 − 0.301666I
a = 1.75107 + 0.54964I
b = 0.443775 − 1.063820I
1.85296 − 1.65232I 2.94839 + 2.48371I
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.305943 + 0.360032I
a = 0.456966 − 0.223325I
b = −0.297089 + 0.365052I
−0.348286 + 1.187860I −3.96956 − 5.64798I
u = −0.305943 − 0.360032I
a = 0.456966 + 0.223325I
b = −0.297089 − 0.365052I
−0.348286 − 1.187860I −3.96956 + 5.64798I
u = −0.14095 + 1.53124I
a = 0.200951 + 0.272306I
b = −0.165297 − 0.276738I
8.49675 + 3.09124I 0
u = −0.14095 − 1.53124I
a = 0.200951 − 0.272306I
b = −0.165297 + 0.276738I
8.49675 − 3.09124I 0
u = −0.394568 + 0.069063I
a = −2.99712 − 0.25955I
b = −1.056850 + 0.326869I
0.80465 + 3.21848I −1.53035 − 4.61809I
u = −0.394568 − 0.069063I
a = −2.99712 + 0.25955I
b = −1.056850 − 0.326869I
0.80465 − 3.21848I −1.53035 + 4.61809I
u = 0.348442 + 0.164860I
a = 2.69769 − 0.80106I
b = 0.711422 + 0.592619I
2.47813 + 0.76089I 3.69985 − 0.16469I
u = 0.348442 − 0.164860I
a = 2.69769 + 0.80106I
b = 0.711422 − 0.592619I
2.47813 − 0.76089I 3.69985 + 0.16469I
17
II. I
u
2
= hb, 21u
3
− 14u
2
+ 13a + 54u − 24, u
4
− u
3
+ 3u
2
− 2u + 1i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
5
=
1
u
2
a
12
=
−1.61538u
3
+ 1.07692u
2
− 4.15385u + 1.84615
0
a
6
=
1.06509u
3
− 1.01775u
2
+ 2.72781u − 0.964497
u
2
a
8
=
u
u
3
+ u
a
10
=
u
3
−u
3
− u
2
+ 2u − 1
a
1
=
−2.61538u
3
+ 1.07692u
2
− 4.15385u + 1.84615
u
3
+ u
2
− 2u + 1
a
11
=
−1.61538u
3
+ 1.07692u
2
− 4.15385u + 1.84615
0
a
7
=
2.01183u
3
− 1.36686u
2
+ 6.04142u − 2.26627
u
3
+ u
a
3
=
−1.11834u
3
+ 2.66864u
2
− 2.41420u + 3.66272
u
3
− 2u
2
+ u
a
2
=
−1.06509u
3
+ 2.01775u
2
− 2.72781u + 2.96450
−u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
1555
169
u
3
+
2575
169
u
2
−
626
169
u −
80
169
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
4
− u
3
+ 3u
2
− 2u + 1
c
2
u
4
− u
3
+ u
2
+ 1
c
3
u
4
+ u
3
+ 5u
2
− u + 2
c
5
13(13u
4
+ 16u
3
+ 7u
2
+ u + 1)
c
6
u
4
+ u
3
+ u
2
+ 1
c
7
13(13u
4
+ 23u
3
− 9u + 2)
c
8
u
4
+ u
3
+ 3u
2
+ 2u + 1
c
9
u
4
− 5u
3
+ 7u
2
− 2u + 1
c
10
(u + 1)
4
c
11
u
4
c
12
(u − 1)
4
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
8
y
4
+ 5y
3
+ 7y
2
+ 2y + 1
c
2
, c
6
y
4
+ y
3
+ 3y
2
+ 2y + 1
c
3
y
4
+ 9y
3
+ 31y
2
+ 19y + 4
c
5
169(169y
4
− 74y
3
+ 43y
2
+ 13y + 1)
c
7
169(169y
4
− 529y
3
+ 466y
2
− 81y + 4)
c
9
y
4
− 11y
3
+ 31y
2
+ 10y + 1
c
10
, c
12
(y −1)
4
c
11
y
4
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.395123 + 0.506844I
a = 0.48860 − 1.84716I
b = 0
1.43393 − 1.41510I −1.23808 + 3.23912I
u = 0.395123 − 0.506844I
a = 0.48860 + 1.84716I
b = 0
1.43393 + 1.41510I −1.23808 − 3.23912I
u = 0.10488 + 1.55249I
a = 0.049857 − 0.136327I
b = 0
8.43568 − 3.16396I −30.4513 + 33.1692I
u = 0.10488 − 1.55249I
a = 0.049857 + 0.136327I
b = 0
8.43568 + 3.16396I −30.4513 − 33.1692I
21
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
4
− u
3
+ 3u
2
− 2u + 1)(u
128
+ 62u
127
+ ··· + 4u + 1)
c
2
(u
4
− u
3
+ u
2
+ 1)(u
128
− 2u
127
+ ··· − 2u + 1)
c
3
(u
4
+ u
3
+ 5u
2
− u + 2)(u
128
+ 2u
127
+ ··· + 4224656u + 1446152)
c
4
(u
4
− u
3
+ 3u
2
− 2u + 1)(u
128
+ 2u
127
+ ··· + 4u + 1)
c
5
169(13u
4
+ 16u
3
+ 7u
2
+ u + 1)
· (13u
128
− 13u
127
+ ··· − 23585u + 12601)
c
6
(u
4
+ u
3
+ u
2
+ 1)(u
128
− 2u
127
+ ··· − 2u + 1)
c
7
169(13u
4
+ 23u
3
− 9u + 2)
· (13u
128
+ 104u
127
+ ··· + 257066u + 17686)
c
8
(u
4
+ u
3
+ 3u
2
+ 2u + 1)(u
128
+ 2u
127
+ ··· + 4u + 1)
c
9
(u
4
− 5u
3
+ 7u
2
− 2u + 1)(u
128
− 58u
127
+ ··· − 4u + 1)
c
10
((u + 1)
4
)(u
128
+ 5u
127
+ ··· + 1642u + 169)
c
11
u
4
(u
128
+ 5u
127
+ ··· + 25272u + 2704)
c
12
((u − 1)
4
)(u
128
+ 5u
127
+ ··· + 1642u + 169)
22
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)(y
128
+ 10y
127
+ ··· + 16y + 1)
c
2
, c
6
(y
4
+ y
3
+ 3y
2
+ 2y + 1)(y
128
+ 62y
127
+ ··· + 4y + 1)
c
3
(y
4
+ 9y
3
+ 31y
2
+ 19y + 4)
· (y
128
− 42y
127
+ ··· − 15693533191440y + 2091355607104)
c
4
, c
8
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)(y
128
+ 58y
127
+ ··· + 4y + 1)
c
5
28561(169y
4
− 74y
3
+ 43y
2
+ 13y + 1)
· (169y
128
+ 5603y
127
+ ··· − 911953253y + 158785201)
c
7
28561(169y
4
− 529y
3
+ 466y
2
− 81y + 4)
· (169y
128
+ 11180y
127
+ ··· + 16577933816y + 312794596)
c
9
(y
4
− 11y
3
+ 31y
2
+ 10y + 1)(y
128
+ 26y
127
+ ··· + 64y + 1)
c
10
, c
12
((y −1)
4
)(y
128
− 75y
127
+ ··· + 85914y + 28561)
c
11
y
4
(y
128
− 27y
127
+ ··· + 2.38720 × 10
8
y + 7311616)
23
