12n
0507
(K12n
0507
)
A knot diagram
1
Linearized knot diagam
3 5 11 7 2 9 12 3 5 8 4 10
Solving Sequence
4,11
12
3,8
7 5 2 6 10 1 9
c
11
c
3
c
7
c
4
c
2
c
5
c
10
c
12
c
9
c
1
, c
6
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h1.00284 × 10
74
u
51
− 5.06570 × 10
74
u
50
+ ··· + 2.45946 × 10
74
b − 5.12443 × 10
75
,
1.96421 × 10
74
u
51
− 1.03477 × 10
75
u
50
+ ··· + 5.81327 × 10
74
a − 1.34829 × 10
76
,
u
52
− 6u
51
+ ··· − 168u + 52i
I
u
2
= h117054u
17
− 360970u
16
+ ··· + 246977b + 230480,
207914u
17
− 537859u
16
+ ··· + 740931a − 581924, u
18
− 2u
17
+ ··· + 8u + 3i
I
u
3
= h7a
4
+ 16a
3
− 4a
2
+ 11b − 40a + 8, a
5
+ 2a
4
− a
3
− 6a
2
+ 3a − 1, u + 1i
I
v
1
= ha, b
2
− b + 1, v −1i
* 4 irreducible components of dim
C
= 0, with total 77 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
=
h1.00×10
74
u
51
−5.07×10
74
u
50
+· · ·+2.46×10
74
b−5.12×10
75
, 1.96×10
74
u
51
−
1.03 × 10
75
u
50
+ · · · + 5.81 × 10
74
a − 1.35 × 10
76
, u
52
− 6u
51
+ · · · − 168u + 52i
(i) Arc colorings
a
4
=
0
u
a
11
=
1
0
a
12
=
1
−u
2
a
3
=
−u
u
a
8
=
−0.337885u
51
+ 1.78002u
50
+ ··· − 47.5713u + 23.1933
−0.407746u
51
+ 2.05968u
50
+ ··· − 49.5998u + 20.8356
a
7
=
0.231416u
51
− 1.16982u
50
+ ··· + 26.0026u − 10.5013
−0.746564u
51
+ 3.90831u
50
+ ··· − 98.2781u + 45.0657
a
5
=
−0.483569u
51
+ 2.46254u
50
+ ··· − 59.1117u + 30.0174
−0.138554u
51
+ 0.761537u
50
+ ··· − 19.4741u + 10.6533
a
2
=
0.136698u
51
− 0.735393u
50
+ ··· + 21.0106u − 6.84353
0.189414u
51
− 0.720852u
50
+ ··· + 9.10899u + 1.55169
a
6
=
−0.924358u
51
+ 4.32805u
50
+ ··· − 89.5677u + 26.2032
2.94505u
51
− 14.5616u
50
+ ··· + 329.171u − 146.279
a
10
=
−0.558793u
51
+ 2.71369u
50
+ ··· − 59.1474u + 26.7302
0.449141u
51
− 2.26958u
50
+ ··· + 53.1092u − 22.9509
a
1
=
0.805085u
51
− 3.90019u
50
+ ··· + 88.1248u − 32.8658
−0.478973u
51
+ 2.44395u
50
+ ··· − 58.0052u + 27.5740
a
9
=
0.161202u
51
− 0.874376u
50
+ ··· + 20.1820u − 9.77912
−0.906833u
51
+ 4.71408u
50
+ ··· − 117.353u + 53.8080
(ii) Obstruction class = −1
(iii) Cusp Shapes = −1.43996u
51
+ 6.82741u
50
+ ··· − 140.681u + 61.5443
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
52
+ 79u
51
+ ··· + 126u + 1
c
2
, c
5
u
52
+ u
51
+ ··· − 16u + 1
c
3
, c
11
u
52
+ 6u
51
+ ··· + 168u + 52
c
4
u
52
− 7u
51
+ ··· − 729u + 449
c
6
u
52
− u
51
+ ··· − 32223752u + 2811556
c
7
u
52
− 3u
51
+ ··· − 97u + 49
c
8
u
52
− u
51
+ ··· − 248316u + 85849
c
9
u
52
− 2u
51
+ ··· + 172169u + 39973
c
10
u
52
+ 11u
51
+ ··· + 560u + 49
c
12
u
52
− 15u
51
+ ··· − 112029u + 100799
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
52
− 209y
51
+ ··· + 2042y + 1
c
2
, c
5
y
52
+ 79y
51
+ ··· + 126y + 1
c
3
, c
11
y
52
− 40y
51
+ ··· − 11792y + 2704
c
4
y
52
+ 27y
51
+ ··· + 5239107y + 201601
c
6
y
52
+ 93y
51
+ ··· − 26572892374864y + 7904847141136
c
7
y
52
− 15y
51
+ ··· − 35575y + 2401
c
8
y
52
− 15y
51
+ ··· − 75223432574y + 7370050801
c
9
y
52
+ 80y
51
+ ··· + 24550030999y + 1597840729
c
10
y
52
+ 7y
51
+ ··· + 23618y + 2401
c
12
y
52
− 45y
51
+ ··· + 108799403279y + 10160438401
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.072076 + 1.073670I
a = 0.422821 + 0.107445I
b = −0.157151 + 0.717710I
−0.08598 − 3.46440I 0. + 3.76930I
u = −0.072076 − 1.073670I
a = 0.422821 − 0.107445I
b = −0.157151 − 0.717710I
−0.08598 + 3.46440I 0. − 3.76930I
u = 1.068700 + 0.176322I
a = 0.99400 − 1.18957I
b = −0.471542 − 1.119630I
−7.77272 + 4.78722I 5.62286 − 4.46937I
u = 1.068700 − 0.176322I
a = 0.99400 + 1.18957I
b = −0.471542 + 1.119630I
−7.77272 − 4.78722I 5.62286 + 4.46937I
u = −0.269878 + 0.867397I
a = −0.065611 − 0.173550I
b = 0.680688 − 0.688393I
0.88668 − 2.29079I 4.46889 + 2.66895I
u = −0.269878 − 0.867397I
a = −0.065611 + 0.173550I
b = 0.680688 + 0.688393I
0.88668 + 2.29079I 4.46889 − 2.66895I
u = 1.048260 + 0.371285I
a = 1.55261 + 0.09090I
b = −0.733122 − 0.676797I
−0.94506 + 3.54563I 1.62965 − 5.75409I
u = 1.048260 − 0.371285I
a = 1.55261 − 0.09090I
b = −0.733122 + 0.676797I
−0.94506 − 3.54563I 1.62965 + 5.75409I
u = 1.104730 + 0.182136I
a = 0.839035 − 0.685937I
b = −0.615619 + 1.264700I
3.12675 + 4.09577I 11.1869 − 8.8133I
u = 1.104730 − 0.182136I
a = 0.839035 + 0.685937I
b = −0.615619 − 1.264700I
3.12675 − 4.09577I 11.1869 + 8.8133I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.132840 + 0.177320I
a = −1.42486 + 0.17109I
b = 1.32434 − 1.18522I
2.29045 − 1.02276I 4.00000 + 0.I
u = −1.132840 − 0.177320I
a = −1.42486 − 0.17109I
b = 1.32434 + 1.18522I
2.29045 + 1.02276I 4.00000 + 0.I
u = −0.280215 + 0.778839I
a = −0.567039 + 0.203024I
b = −0.80247 − 1.29034I
−12.44140 + 2.96434I −0.898916 − 0.509328I
u = −0.280215 − 0.778839I
a = −0.567039 − 0.203024I
b = −0.80247 + 1.29034I
−12.44140 − 2.96434I −0.898916 + 0.509328I
u = 0.495944 + 0.659946I
a = −0.93403 + 1.16897I
b = −0.782553 + 0.575131I
−8.85362 + 2.74417I 1.62020 − 2.60444I
u = 0.495944 − 0.659946I
a = −0.93403 − 1.16897I
b = −0.782553 − 0.575131I
−8.85362 − 2.74417I 1.62020 + 2.60444I
u = 0.383796 + 0.722249I
a = 0.0394551 + 0.0110081I
b = −0.141872 + 0.858570I
−3.00681 + 0.54202I −3.07092 − 1.78302I
u = 0.383796 − 0.722249I
a = 0.0394551 − 0.0110081I
b = −0.141872 − 0.858570I
−3.00681 − 0.54202I −3.07092 + 1.78302I
u = −1.118520 + 0.405885I
a = −1.99263 − 0.26808I
b = 0.607693 − 0.824065I
2.47983 − 5.59777I 0. + 7.04199I
u = −1.118520 − 0.405885I
a = −1.99263 + 0.26808I
b = 0.607693 + 0.824065I
2.47983 + 5.59777I 0. − 7.04199I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.989819 + 0.690556I
a = 0.738252 − 1.108280I
b = −0.493528 − 1.071940I
−7.62938 + 2.46347I 0
u = 0.989819 − 0.690556I
a = 0.738252 + 1.108280I
b = −0.493528 + 1.071940I
−7.62938 − 2.46347I 0
u = 1.209340 + 0.050765I
a = −1.57890 − 0.62627I
b = 1.37163 + 1.27972I
5.14318 + 1.81368I 18.0333 + 0.I
u = 1.209340 − 0.050765I
a = −1.57890 + 0.62627I
b = 1.37163 − 1.27972I
5.14318 − 1.81368I 18.0333 + 0.I
u = −1.142540 + 0.409057I
a = 1.98363 − 0.31458I
b = −1.28875 + 1.59470I
−9.77699 − 7.32778I 0
u = −1.142540 − 0.409057I
a = 1.98363 + 0.31458I
b = −1.28875 − 1.59470I
−9.77699 + 7.32778I 0
u = 0.038697 + 1.225180I
a = 0.060632 − 0.219112I
b = −0.787773 − 1.095970I
−10.30200 + 8.83554I 0
u = 0.038697 − 1.225180I
a = 0.060632 + 0.219112I
b = −0.787773 + 1.095970I
−10.30200 − 8.83554I 0
u = −1.298120 + 0.219749I
a = 1.57172 + 0.70746I
b = −2.01283 − 0.85764I
−3.60868 − 5.39855I 0
u = −1.298120 − 0.219749I
a = 1.57172 − 0.70746I
b = −2.01283 + 0.85764I
−3.60868 + 5.39855I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.435814 + 0.497980I
a = −0.144770 + 1.329400I
b = 0.406646 + 0.837607I
0.35496 + 1.82856I 2.55368 − 2.81717I
u = −0.435814 − 0.497980I
a = −0.144770 − 1.329400I
b = 0.406646 − 0.837607I
0.35496 − 1.82856I 2.55368 + 2.81717I
u = −1.325900 + 0.415407I
a = 1.133880 + 0.064846I
b = −0.593152 + 0.351949I
5.15254 − 2.08012I 0
u = −1.325900 − 0.415407I
a = 1.133880 − 0.064846I
b = −0.593152 − 0.351949I
5.15254 + 2.08012I 0
u = 0.594624 + 0.117518I
a = −2.93422 − 1.82812I
b = −0.610865 + 0.355975I
−9.27919 − 3.18450I 2.07898 − 0.42481I
u = 0.594624 − 0.117518I
a = −2.93422 + 1.82812I
b = −0.610865 − 0.355975I
−9.27919 + 3.18450I 2.07898 + 0.42481I
u = 1.34204 + 0.52912I
a = 1.308500 − 0.013301I
b = −0.646221 − 0.811256I
4.19597 + 9.10494I 0
u = 1.34204 − 0.52912I
a = 1.308500 + 0.013301I
b = −0.646221 + 0.811256I
4.19597 − 9.10494I 0
u = 1.38606 + 0.43784I
a = −1.47210 − 0.00392I
b = 1.21303 + 1.00411I
5.90548 + 7.10957I 0
u = 1.38606 − 0.43784I
a = −1.47210 + 0.00392I
b = 1.21303 − 1.00411I
5.90548 − 7.10957I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.163645 + 0.500729I
a = 1.48155 − 0.11869I
b = −0.210860 − 0.434892I
0.61514 − 1.70536I 3.89799 + 3.77276I
u = 0.163645 − 0.500729I
a = 1.48155 + 0.11869I
b = −0.210860 + 0.434892I
0.61514 + 1.70536I 3.89799 − 3.77276I
u = −1.40514 + 0.56979I
a = 1.50502 − 0.02569I
b = −1.02860 + 1.37422I
−5.7801 − 15.0850I 0
u = −1.40514 − 0.56979I
a = 1.50502 + 0.02569I
b = −1.02860 − 1.37422I
−5.7801 + 15.0850I 0
u = −0.334164 + 0.327190I
a = 0.80947 − 1.27346I
b = 0.454762 − 0.337305I
0.700125 − 1.067100I 7.65429 + 6.43905I
u = −0.334164 − 0.327190I
a = 0.80947 + 1.27346I
b = 0.454762 + 0.337305I
0.700125 + 1.067100I 7.65429 − 6.43905I
u = −1.54216 + 0.53974I
a = −0.817027 + 0.067290I
b = 0.805620 − 0.732243I
4.04363 − 5.57601I 0
u = −1.54216 − 0.53974I
a = −0.817027 − 0.067290I
b = 0.805620 + 0.732243I
4.04363 + 5.57601I 0
u = 1.82542 + 0.12353I
a = 0.180716 − 0.464332I
b = −0.529222 + 0.477306I
−5.59317 + 0.61259I 0
u = 1.82542 − 0.12353I
a = 0.180716 + 0.464332I
b = −0.529222 − 0.477306I
−5.59317 − 0.61259I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.70629 + 0.88313I
a = 0.040681 − 0.244589I
b = −0.458284 + 0.504879I
−5.74740 − 1.53118I 0
u = 1.70629 − 0.88313I
a = 0.040681 + 0.244589I
b = −0.458284 − 0.504879I
−5.74740 + 1.53118I 0
10
II. I
u
2
= h1.17 × 10
5
u
17
− 3.61 × 10
5
u
16
+ · · · + 2.47 × 10
5
b + 2.30 × 10
5
, 2.08 ×
10
5
u
17
−5.38×10
5
u
16
+· · · +7.41×10
5
a−5.82×10
5
, u
18
−2u
17
+· · · +8u +3i
(i) Arc colorings
a
4
=
0
u
a
11
=
1
0
a
12
=
1
−u
2
a
3
=
−u
u
a
8
=
−0.280612u
17
+ 0.725923u
16
+ ··· − 3.10639u + 0.785396
−0.473947u
17
+ 1.46155u
16
+ ··· − 2.24939u − 0.933204
a
7
=
0.237918u
17
− 0.825679u
16
+ ··· − 0.381241u + 2.21270
−0.894460u
17
+ 2.94986u
16
+ ··· − 4.81013u − 2.47683
a
5
=
−0.605086u
17
+ 1.13512u
16
+ ··· − 3.56873u − 1.00410
0.513671u
17
− 0.344639u
16
+ ··· − 4.46092u − 1.91207
a
2
=
0.758081u
17
− 1.12381u
16
+ ··· − 3.30368u − 1.75050
−0.800844u
17
+ 1.20535u
16
+ ··· + 9.72215u + 2.40419
a
6
=
−0.210071u
17
+ 1.20477u
16
+ ··· − 7.21760u − 1.54346
−0.623933u
17
+ 0.206902u
16
+ ··· + 7.78891u + 2.25446
a
10
=
−0.457344u
17
− 0.485917u
16
+ ··· + 1.87185u + 1.65301
0.188467u
17
+ 1.56389u
16
+ ··· − 12.1388u − 4.59404
a
1
=
0.852110u
17
− 1.08511u
16
+ ··· − 3.14348u − 1.73854
−0.894873u
17
+ 1.16664u
16
+ ··· + 9.56196u + 2.39223
a
9
=
0.132791u
17
− 0.992322u
16
+ ··· + 0.0568042u + 2.82047
−0.887350u
17
+ 3.17980u
16
+ ··· − 5.41258u − 2.96828
(ii) Obstruction class = 1
(iii) Cusp Shapes =
39445
246977
u
17
−
1167483
246977
u
16
+ ··· +
8666107
246977
u +
3104388
246977
11
(iv) u-Polynomials at the component
12
Crossings u-Polynomials at each crossing
c
1
u
18
− 21u
17
+ ··· − 23u + 1
c
2
u
18
− u
17
+ ··· + u + 1
c
3
u
18
+ 2u
17
+ ··· − 8u + 3
c
4
u
18
− 5u
17
+ ··· − 10u + 11
c
5
u
18
+ u
17
+ ··· − u + 1
c
6
u
18
+ 4u
17
+ ··· + 8u + 3
c
7
u
18
− 3u
17
+ ··· − 22u + 5
c
8
u
18
− u
17
+ ··· + u + 5
c
9
u
18
+ 5u
16
+ ··· − 4u + 1
c
10
u
18
− 9u
17
+ ··· − u + 1
c
11
u
18
− 2u
17
+ ··· + 8u + 3
c
12
u
18
− 7u
17
+ ··· − 14u + 11
13
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
18
− 47y
17
+ ··· − 89y + 1
c
2
, c
5
y
18
+ 21y
17
+ ··· + 23y + 1
c
3
, c
11
y
18
− 20y
17
+ ··· − 58y + 9
c
4
y
18
+ 9y
17
+ ··· + 956y + 121
c
6
y
18
+ 18y
17
+ ··· + 68y + 9
c
7
y
18
− 5y
17
+ ··· − 104y + 25
c
8
y
18
+ 7y
17
+ ··· + 29y + 25
c
9
y
18
+ 10y
17
+ ··· − 8y + 1
c
10
y
18
− 3y
17
+ ··· + 3y + 1
c
12
y
18
− 15y
17
+ ··· + 1256y + 121
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.005450 + 0.295263I
a = 1.203530 + 0.437285I
b = −0.335827 − 0.487120I
2.17303 − 3.53081I 4.11221 + 3.61845I
u = −1.005450 − 0.295263I
a = 1.203530 − 0.437285I
b = −0.335827 + 0.487120I
2.17303 + 3.53081I 4.11221 − 3.61845I
u = −0.207208 + 0.849001I
a = −0.282886 + 0.138697I
b = 0.549633 − 0.563104I
1.17142 − 3.80180I 6.45298 + 6.93246I
u = −0.207208 − 0.849001I
a = −0.282886 − 0.138697I
b = 0.549633 + 0.563104I
1.17142 + 3.80180I 6.45298 − 6.93246I
u = 1.161860 + 0.107310I
a = −2.23789 − 0.78537I
b = 2.15942 + 1.58054I
3.02525 + 1.29728I 13.4543 − 5.0288I
u = 1.161860 − 0.107310I
a = −2.23789 + 0.78537I
b = 2.15942 − 1.58054I
3.02525 − 1.29728I 13.4543 + 5.0288I
u = 0.751188 + 0.315078I
a = 1.51622 − 2.08382I
b = −0.655881 − 0.938092I
−9.23443 + 4.41108I 1.12625 − 5.00994I
u = 0.751188 − 0.315078I
a = 1.51622 + 2.08382I
b = −0.655881 + 0.938092I
−9.23443 − 4.41108I 1.12625 + 5.00994I
u = −1.218070 + 0.029447I
a = −1.184950 + 0.350003I
b = 0.820578 − 1.114160I
4.34167 − 2.03661I 7.20835 + 3.90028I
u = −1.218070 − 0.029447I
a = −1.184950 − 0.350003I
b = 0.820578 + 1.114160I
4.34167 + 2.03661I 7.20835 − 3.90028I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.38134 + 0.46176I
a = −1.399010 + 0.094856I
b = 1.182680 + 0.724988I
6.00324 + 8.77263I 8.55851 − 6.89757I
u = 1.38134 − 0.46176I
a = −1.399010 − 0.094856I
b = 1.182680 − 0.724988I
6.00324 − 8.77263I 8.55851 + 6.89757I
u = −1.40929 + 0.49254I
a = −1.140630 − 0.031844I
b = 0.703194 − 0.839704I
5.15223 − 3.52976I 7.05597 + 3.81806I
u = −1.40929 − 0.49254I
a = −1.140630 + 0.031844I
b = 0.703194 + 0.839704I
5.15223 + 3.52976I 7.05597 − 3.81806I
u = −0.282235 + 0.273085I
a = 2.34179 − 1.33257I
b = 0.414830 − 0.603446I
−0.0620604 − 0.0079783I −0.270726 + 0.542760I
u = −0.282235 − 0.273085I
a = 2.34179 + 1.33257I
b = 0.414830 + 0.603446I
−0.0620604 + 0.0079783I −0.270726 − 0.542760I
u = 1.82787 + 0.56276I
a = −0.149506 − 0.193772I
b = −0.338633 + 0.304616I
−5.99061 − 1.24449I −6.19786 − 0.78651I
u = 1.82787 − 0.56276I
a = −0.149506 + 0.193772I
b = −0.338633 − 0.304616I
−5.99061 + 1.24449I −6.19786 + 0.78651I
17
III.
I
u
3
= h7a
4
+ 16a
3
− 4a
2
+ 11b − 40a + 8, a
5
+ 2a
4
− a
3
− 6a
2
+ 3a − 1, u + 1i
(i) Arc colorings
a
4
=
0
−1
a
11
=
1
0
a
12
=
1
−1
a
3
=
1
−1
a
8
=
a
−0.636364a
4
− 1.45455a
3
+ ··· + 3.63636a − 0.727273
a
7
=
0.636364a
4
+ 1.45455a
3
+ ··· − 3.63636a + 0.727273
−1.27273a
4
− 2.90909a
3
+ ··· + 8.27273a − 1.45455
a
5
=
−0.181818a
4
− 0.272727a
3
+ ··· + 1.18182a − 1.63636
0.545455a
4
+ 0.818182a
3
+ ··· − 3.54545a + 2.90909
a
2
=
−0.636364a
4
− 1.45455a
3
+ ··· + 4.63636a − 0.727273
1.27273a
4
+ 2.90909a
3
+ ··· − 8.27273a + 1.45455
a
6
=
−0.636364a
4
− 1.45455a
3
+ ··· + 3.63636a − 0.727273
1.27273a
4
+ 2.90909a
3
+ ··· − 8.27273a + 1.45455
a
10
=
−0.181818a
4
− 0.272727a
3
+ ··· + 1.18182a + 0.363636
−0.181818a
4
− 0.272727a
3
+ ··· + 1.18182a − 1.63636
a
1
=
a
0.636364a
4
+ 1.45455a
3
+ ··· − 4.63636a + 0.727273
a
9
=
0.636364a
4
+ 1.45455a
3
+ ··· − 3.63636a + 0.727273
−1.27273a
4
− 2.90909a
3
+ ··· + 8.27273a − 1.45455
(ii) Obstruction class = −1
(iii) Cusp Shapes = 6
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
9
u
5
+ 2u
4
+ 3u
3
+ 2u
2
+ u − 1
c
2
, c
5
, c
12
u
5
+ u
3
+ u − 1
c
3
, c
11
(u − 1)
5
c
6
u
5
c
7
, c
8
u
5
+ u
3
+ 2u
2
− u − 2
c
10
u
5
− 2u
4
+ 3u
3
− 2u
2
+ u + 1
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
9
c
10
y
5
+ 2y
4
+ 3y
3
+ 6y
2
+ 5y −1
c
2
, c
5
, c
12
y
5
+ 2y
4
+ 3y
3
+ 2y
2
+ y −1
c
3
, c
11
(y −1)
5
c
6
y
5
c
7
, c
8
y
5
+ 2y
4
− y
3
− 6y
2
+ 9y −4
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 1.30084
b = −0.405620
1.64493 6.00000
u = −1.00000
a = 0.234877 + 0.318507I
b = 0.208008 + 1.191750I
1.64493 6.00000
u = −1.00000
a = 0.234877 − 0.318507I
b = 0.208008 − 1.191750I
1.64493 6.00000
u = −1.00000
a = −1.88529 + 1.16368I
b = 0.994802 − 0.833601I
1.64493 6.00000
u = −1.00000
a = −1.88529 − 1.16368I
b = 0.994802 + 0.833601I
1.64493 6.00000
21
IV. I
v
1
= ha, b
2
− b + 1, v − 1i
(i) Arc colorings
a
4
=
1
0
a
11
=
1
0
a
12
=
1
0
a
3
=
1
0
a
8
=
0
b
a
7
=
−b
b
a
5
=
−b + 2
b − 1
a
2
=
2b
−b
a
6
=
−b
b
a
10
=
1
b − 1
a
1
=
b
−b
a
9
=
−b
b
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
c
10
u
2
− u + 1
c
2
, c
7
, c
8
c
9
, c
12
u
2
+ u + 1
c
3
, c
6
, c
11
u
2
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
7
, c
8
c
9
, c
10
, c
12
y
2
+ y + 1
c
3
, c
6
, c
11
y
2
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 1.00000
a = 0
b = 0.500000 + 0.866025I
0 0
v = 1.00000
a = 0
b = 0.500000 − 0.866025I
0 0
25
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
2
− u + 1)(u
5
+ 2u
4
+ ··· + u − 1)(u
18
− 21u
17
+ ··· − 23u + 1)
· (u
52
+ 79u
51
+ ··· + 126u + 1)
c
2
(u
2
+ u + 1)(u
5
+ u
3
+ u − 1)(u
18
− u
17
+ ··· + u + 1)
· (u
52
+ u
51
+ ··· − 16u + 1)
c
3
u
2
(u − 1)
5
(u
18
+ 2u
17
+ ··· − 8u + 3)(u
52
+ 6u
51
+ ··· + 168u + 52)
c
4
(u
2
− u + 1)(u
5
+ 2u
4
+ ··· + u − 1)(u
18
− 5u
17
+ ··· − 10u + 11)
· (u
52
− 7u
51
+ ··· − 729u + 449)
c
5
(u
2
− u + 1)(u
5
+ u
3
+ u − 1)(u
18
+ u
17
+ ··· − u + 1)
· (u
52
+ u
51
+ ··· − 16u + 1)
c
6
u
7
(u
18
+ 4u
17
+ ··· + 8u + 3)(u
52
− u
51
+ ··· − 3.22238 × 10
7
u + 2811556)
c
7
(u
2
+ u + 1)(u
5
+ u
3
+ 2u
2
− u − 2)(u
18
− 3u
17
+ ··· − 22u + 5)
· (u
52
− 3u
51
+ ··· − 97u + 49)
c
8
(u
2
+ u + 1)(u
5
+ u
3
+ 2u
2
− u − 2)(u
18
− u
17
+ ··· + u + 5)
· (u
52
− u
51
+ ··· − 248316u + 85849)
c
9
(u
2
+ u + 1)(u
5
+ 2u
4
+ ··· + u − 1)(u
18
+ 5u
16
+ ··· − 4u + 1)
· (u
52
− 2u
51
+ ··· + 172169u + 39973)
c
10
(u
2
− u + 1)(u
5
− 2u
4
+ ··· + u + 1)(u
18
− 9u
17
+ ··· − u + 1)
· (u
52
+ 11u
51
+ ··· + 560u + 49)
c
11
u
2
(u − 1)
5
(u
18
− 2u
17
+ ··· + 8u + 3)(u
52
+ 6u
51
+ ··· + 168u + 52)
c
12
(u
2
+ u + 1)(u
5
+ u
3
+ u − 1)(u
18
− 7u
17
+ ··· − 14u + 11)
· (u
52
− 15u
51
+ ··· − 112029u + 100799)
26
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
2
+ y + 1)(y
5
+ 2y
4
+ ··· + 5y −1)(y
18
− 47y
17
+ ··· − 89y + 1)
· (y
52
− 209y
51
+ ··· + 2042y + 1)
c
2
, c
5
(y
2
+ y + 1)(y
5
+ 2y
4
+ ··· + y −1)(y
18
+ 21y
17
+ ··· + 23y + 1)
· (y
52
+ 79y
51
+ ··· + 126y + 1)
c
3
, c
11
y
2
(y −1)
5
(y
18
− 20y
17
+ ··· − 58y + 9)
· (y
52
− 40y
51
+ ··· − 11792y + 2704)
c
4
(y
2
+ y + 1)(y
5
+ 2y
4
+ 3y
3
+ 6y
2
+ 5y −1)
· (y
18
+ 9y
17
+ ··· + 956y + 121)
· (y
52
+ 27y
51
+ ··· + 5239107y + 201601)
c
6
y
7
(y
18
+ 18y
17
+ ··· + 68y + 9)
· (y
52
+ 93y
51
+ ··· − 26572892374864y + 7904847141136)
c
7
(y
2
+ y + 1)(y
5
+ 2y
4
+ ··· + 9y −4)(y
18
− 5y
17
+ ··· − 104y + 25)
· (y
52
− 15y
51
+ ··· − 35575y + 2401)
c
8
(y
2
+ y + 1)(y
5
+ 2y
4
+ ··· + 9y −4)(y
18
+ 7y
17
+ ··· + 29y + 25)
· (y
52
− 15y
51
+ ··· − 75223432574y + 7370050801)
c
9
(y
2
+ y + 1)(y
5
+ 2y
4
+ ··· + 5y −1)(y
18
+ 10y
17
+ ··· − 8y + 1)
· (y
52
+ 80y
51
+ ··· + 24550030999y + 1597840729)
c
10
(y
2
+ y + 1)(y
5
+ 2y
4
+ ··· + 5y −1)(y
18
− 3y
17
+ ··· + 3y + 1)
· (y
52
+ 7y
51
+ ··· + 23618y + 2401)
c
12
(y
2
+ y + 1)(y
5
+ 2y
4
+ 3y
3
+ 2y
2
+ y −1)
· (y
18
− 15y
17
+ ··· + 1256y + 121)
· (y
52
− 45y
51
+ ··· + 108799403279y + 10160438401)
27
