12a
0562
(K12a
0562
)
A knot diagram
1
Linearized knot diagam
3 7 9 8 11 10 2 4 1 12 6 5
Solving Sequence
5,11
6 12
1,3
2 10 7 8 4 9
c
5
c
11
c
12
c
1
c
10
c
6
c
7
c
4
c
9
c
2
, c
3
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h3u
60
− 48u
58
+ ··· + 4b + 4, 2u
67
− 36u
65
+ ··· + 4a − 4, u
68
+ 2u
67
+ ··· + 5u + 2i
I
u
2
= h−2319u
8
a
2
− 1264u
8
a + ··· + 708a + 1030, 5u
8
a + u
8
+ ··· − 3a − 3,
u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1i
I
u
3
= hb − 1, u
8
+ u
7
− 2u
6
− 2u
5
+ 2u
4
+ 2u
3
+ u
2
+ a + u − 1, u
10
− 3u
8
+ 4u
6
− u
4
− u
2
+ 1i
* 3 irreducible components of dim
C
= 0, with total 105 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
=
h3u
60
−48u
58
+· · ·+4b+4, 2u
67
−36u
65
+· · ·+4a−4, u
68
+2u
67
+· · ·+5u+2i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
6
=
1
u
2
a
12
=
−u
−u
3
+ u
a
1
=
−u
3
−u
3
+ u
a
3
=
−
1
2
u
67
+ 9u
65
+ ··· −
1
4
u + 1
−
3
4
u
60
+ 12u
58
+ ··· +
1
2
u − 1
a
2
=
−
1
4
u
60
+
15
4
u
58
+ ··· −
1
2
u +
1
2
−
1
4
u
60
+ 4u
58
+ ··· −
5
4
u
2
+ u
a
10
=
u
3
u
5
− u
3
+ u
a
7
=
u
6
− u
4
+ 1
u
8
− 2u
6
+ 2u
4
a
8
=
−
1
2
u
67
−
1
4
u
66
+ ··· −
11
4
u
2
−
7
4
u
−
1
2
u
67
−
1
2
u
66
+ ··· −
9
4
u −
1
2
a
4
=
1
4
u
55
−
7
2
u
53
+ ··· +
3
4
u + 1
1
4
u
57
−
15
4
u
55
+ ··· −
1
2
u
2
+
1
2
u
a
9
=
u
11
− 2u
9
+ 2u
7
+ u
3
u
11
− 3u
9
+ 4u
7
− u
5
− u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2u
67
+ 36u
65
+ ··· − 12u − 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
68
+ 27u
67
+ ··· + 7896u + 289
c
2
, c
7
u
68
+ u
67
+ ··· − 20u + 17
c
3
, c
4
, c
8
u
68
+ u
67
+ ··· − 42u + 17
c
5
, c
11
u
68
+ 2u
67
+ ··· + 5u + 2
c
6
, c
12
u
68
+ 6u
67
+ ··· + 160u + 128
c
9
u
68
− 8u
67
+ ··· + 28469u + 10016
c
10
u
68
+ 36u
67
+ ··· − 19u + 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
68
+ 39y
67
+ ··· + 6510324y + 83521
c
2
, c
7
y
68
+ 27y
67
+ ··· + 7896y + 289
c
3
, c
4
, c
8
y
68
+ 71y
67
+ ··· − 7272y + 289
c
5
, c
11
y
68
− 36y
67
+ ··· + 19y + 4
c
6
, c
12
y
68
+ 52y
67
+ ··· + 1088512y + 16384
c
9
y
68
+ 8y
67
+ ··· + 482721863y + 100320256
c
10
y
68
− 8y
67
+ ··· − 417y + 16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.840906 + 0.541453I
a = −1.68268 − 0.94647I
b = −0.79895 + 1.76961I
0.64575 + 6.76137I −3.02362 − 9.36135I
u = −0.840906 − 0.541453I
a = −1.68268 + 0.94647I
b = −0.79895 − 1.76961I
0.64575 − 6.76137I −3.02362 + 9.36135I
u = 0.996210 + 0.105534I
a = −0.88720 − 1.68128I
b = −0.755001 − 0.743583I
−3.62273 − 3.17922I −12.49077 + 5.37603I
u = 0.996210 − 0.105534I
a = −0.88720 + 1.68128I
b = −0.755001 + 0.743583I
−3.62273 + 3.17922I −12.49077 − 5.37603I
u = −0.827181 + 0.584200I
a = 0.631027 + 0.169558I
b = −0.131814 − 1.265700I
8.49998 + 4.71847I 2.64745 − 4.37235I
u = −0.827181 − 0.584200I
a = 0.631027 − 0.169558I
b = −0.131814 + 1.265700I
8.49998 − 4.71847I 2.64745 + 4.37235I
u = 0.865742 + 0.583006I
a = 1.67800 − 0.77268I
b = 0.55259 + 1.85985I
6.64125 − 10.66220I 0. + 8.92755I
u = 0.865742 − 0.583006I
a = 1.67800 + 0.77268I
b = 0.55259 − 1.85985I
6.64125 + 10.66220I 0. − 8.92755I
u = −0.884770 + 0.361343I
a = 1.31924 − 0.62047I
b = −0.0505122 − 0.1233410I
−2.02149 + 1.35661I −10.70049 − 3.21023I
u = −0.884770 − 0.361343I
a = 1.31924 + 0.62047I
b = −0.0505122 + 0.1233410I
−2.02149 − 1.35661I −10.70049 + 3.21023I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.704686 + 0.598885I
a = −1.231360 − 0.615484I
b = −0.287687 + 1.027190I
8.85003 − 0.06365I 3.56810 − 2.34699I
u = −0.704686 − 0.598885I
a = −1.231360 + 0.615484I
b = −0.287687 − 1.027190I
8.85003 + 0.06365I 3.56810 + 2.34699I
u = 0.654533 + 0.611050I
a = −1.293350 + 0.557244I
b = 0.37269 − 1.71190I
7.24282 + 5.98050I 1.58701 − 2.73296I
u = 0.654533 − 0.611050I
a = −1.293350 − 0.557244I
b = 0.37269 + 1.71190I
7.24282 − 5.98050I 1.58701 + 2.73296I
u = −1.097730 + 0.129973I
a = 0.66528 − 1.74507I
b = 0.610710 − 1.198750I
1.58150 + 6.31789I 0
u = −1.097730 − 0.129973I
a = 0.66528 + 1.74507I
b = 0.610710 + 1.198750I
1.58150 − 6.31789I 0
u = 1.088810 + 0.220966I
a = −0.577505 + 0.470525I
b = 0.156355 + 0.374983I
2.95364 − 1.17645I 0
u = 1.088810 − 0.220966I
a = −0.577505 − 0.470525I
b = 0.156355 − 0.374983I
2.95364 + 1.17645I 0
u = −0.675962 + 0.538934I
a = 1.46405 + 0.27481I
b = −0.45008 − 1.66037I
1.11309 − 2.39299I −1.31545 + 2.74693I
u = −0.675962 − 0.538934I
a = 1.46405 − 0.27481I
b = −0.45008 + 1.66037I
1.11309 + 2.39299I −1.31545 − 2.74693I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.753612 + 0.388922I
a = −0.003675 − 0.950130I
b = 0.929815 − 0.107409I
1.24035 − 1.74892I 3.03511 + 5.28030I
u = 0.753612 − 0.388922I
a = −0.003675 + 0.950130I
b = 0.929815 + 0.107409I
1.24035 + 1.74892I 3.03511 − 5.28030I
u = 0.165754 + 0.823138I
a = 1.002930 + 0.124969I
b = 0.98242 − 1.90847I
3.07394 + 11.57570I −1.74839 − 6.82824I
u = 0.165754 − 0.823138I
a = 1.002930 − 0.124969I
b = 0.98242 + 1.90847I
3.07394 − 11.57570I −1.74839 + 6.82824I
u = 0.029718 + 0.835469I
a = −0.311656 + 0.504146I
b = 0.691747 + 0.421141I
−1.00288 − 1.92318I −1.79190 + 3.81342I
u = 0.029718 − 0.835469I
a = −0.311656 − 0.504146I
b = 0.691747 − 0.421141I
−1.00288 + 1.92318I −1.79190 − 3.81342I
u = −0.183684 + 0.797547I
a = 0.279594 − 0.071647I
b = 0.35544 + 1.52101I
5.39105 − 5.75675I 1.12004 + 2.96362I
u = −0.183684 − 0.797547I
a = 0.279594 + 0.071647I
b = 0.35544 − 1.52101I
5.39105 + 5.75675I 1.12004 − 2.96362I
u = 1.072680 + 0.514608I
a = −2.06130 − 0.56028I
b = −0.090665 − 1.048220I
3.97397 − 0.25739I 0
u = 1.072680 − 0.514608I
a = −2.06130 + 0.56028I
b = −0.090665 + 1.048220I
3.97397 + 0.25739I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.151153 + 0.793214I
a = −1.085160 + 0.133068I
b = −1.39874 − 1.64237I
−2.51385 − 7.29843I −5.32805 + 6.53927I
u = −0.151153 − 0.793214I
a = −1.085160 − 0.133068I
b = −1.39874 + 1.64237I
−2.51385 + 7.29843I −5.32805 − 6.53927I
u = −0.061331 + 0.780735I
a = 0.330547 + 0.805383I
b = −0.502018 − 0.085930I
−4.88006 − 0.19763I −10.23533 − 0.14539I
u = −0.061331 − 0.780735I
a = 0.330547 − 0.805383I
b = −0.502018 + 0.085930I
−4.88006 + 0.19763I −10.23533 + 0.14539I
u = 1.147840 + 0.446072I
a = 0.78870 − 2.15745I
b = 1.10678 − 0.89125I
−3.04492 − 5.41261I 0
u = 1.147840 − 0.446072I
a = 0.78870 + 2.15745I
b = 1.10678 + 0.89125I
−3.04492 + 5.41261I 0
u = −1.116720 + 0.521286I
a = −1.57151 − 0.51789I
b = −0.573997 + 0.218690I
4.70746 + 6.09415I 0
u = −1.116720 − 0.521286I
a = −1.57151 + 0.51789I
b = −0.573997 − 0.218690I
4.70746 − 6.09415I 0
u = −1.142120 + 0.472829I
a = 2.64269 − 0.71234I
b = 0.73682 − 1.37957I
−2.86459 + 2.56142I 0
u = −1.142120 − 0.472829I
a = 2.64269 + 0.71234I
b = 0.73682 + 1.37957I
−2.86459 − 2.56142I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.288870 + 0.702347I
a = −0.974335 + 0.183643I
b = −0.386475 − 0.456700I
7.11141 − 1.43004I 2.66134 + 2.04753I
u = −0.288870 − 0.702347I
a = −0.974335 − 0.183643I
b = −0.386475 + 0.456700I
7.11141 + 1.43004I 2.66134 − 2.04753I
u = 0.357888 + 0.667374I
a = −0.889683 − 0.281502I
b = 0.141604 + 1.285040I
6.03868 − 4.30670I 1.46994 + 3.45796I
u = 0.357888 − 0.667374I
a = −0.889683 + 0.281502I
b = 0.141604 − 1.285040I
6.03868 + 4.30670I 1.46994 − 3.45796I
u = 1.197530 + 0.346738I
a = −0.11563 − 1.85593I
b = 0.55742 − 1.36973I
1.21003 + 2.01792I 0
u = 1.197530 − 0.346738I
a = −0.11563 + 1.85593I
b = 0.55742 + 1.36973I
1.21003 − 2.01792I 0
u = 1.202190 + 0.372091I
a = −1.56784 + 2.63243I
b = −1.49112 + 1.42833I
−6.55660 + 3.40545I 0
u = 1.202190 − 0.372091I
a = −1.56784 − 2.63243I
b = −1.49112 − 1.42833I
−6.55660 − 3.40545I 0
u = −1.221200 + 0.356970I
a = 0.89428 + 2.61237I
b = 1.06051 + 1.77150I
−1.16641 − 7.64309I 0
u = −1.221200 − 0.356970I
a = 0.89428 − 2.61237I
b = 1.06051 − 1.77150I
−1.16641 + 7.64309I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.204100 + 0.423605I
a = −0.348738 − 0.171647I
b = −0.652313 + 0.123062I
−8.58591 − 4.02293I 0
u = 1.204100 − 0.423605I
a = −0.348738 + 0.171647I
b = −0.652313 − 0.123062I
−8.58591 + 4.02293I 0
u = −1.197470 + 0.478507I
a = −0.235493 − 0.884755I
b = −0.457387 + 0.202512I
−8.19611 + 4.78252I 0
u = −1.197470 − 0.478507I
a = −0.235493 + 0.884755I
b = −0.457387 − 0.202512I
−8.19611 − 4.78252I 0
u = −1.180790 + 0.525663I
a = 2.06732 − 0.85708I
b = 0.42377 − 1.66754I
2.45212 + 10.65030I 0
u = −1.180790 − 0.525663I
a = 2.06732 + 0.85708I
b = 0.42377 + 1.66754I
2.45212 − 10.65030I 0
u = −1.187140 + 0.513961I
a = −3.70852 − 0.08255I
b = −1.53628 + 1.72826I
−5.55900 + 12.12010I 0
u = −1.187140 − 0.513961I
a = −3.70852 + 0.08255I
b = −1.53628 − 1.72826I
−5.55900 − 12.12010I 0
u = 1.194400 + 0.526145I
a = 3.44519 + 0.50306I
b = 1.06198 + 1.98167I
0.0245 − 16.5311I 0
u = 1.194400 − 0.526145I
a = 3.44519 − 0.50306I
b = 1.06198 − 1.98167I
0.0245 + 16.5311I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.231000 + 0.440784I
a = 0.823478 − 0.382539I
b = 0.770134 − 0.469099I
−4.78562 + 6.43179I 0
u = −1.231000 − 0.440784I
a = 0.823478 + 0.382539I
b = 0.770134 + 0.469099I
−4.78562 − 6.43179I 0
u = 1.224950 + 0.470945I
a = 0.064399 − 1.290010I
b = 0.726960 − 0.347094I
−4.57008 − 2.76226I 0
u = 1.224950 − 0.470945I
a = 0.064399 + 1.290010I
b = 0.726960 + 0.347094I
−4.57008 + 2.76226I 0
u = −0.225662 + 0.547625I
a = 0.984096 + 0.221334I
b = 0.140194 + 1.076410I
−0.15904 + 1.57803I −1.93957 − 4.05866I
u = −0.225662 − 0.547625I
a = 0.984096 − 0.221334I
b = 0.140194 − 1.076410I
−0.15904 − 1.57803I −1.93957 + 4.05866I
u = 0.062422 + 0.547904I
a = 0.714824 + 0.515000I
b = 0.685106 + 0.637373I
−0.06279 + 1.44675I −0.83204 − 5.13904I
u = 0.062422 − 0.547904I
a = 0.714824 − 0.515000I
b = 0.685106 − 0.637373I
−0.06279 − 1.44675I −0.83204 + 5.13904I
11
II. I
u
2
= h−2319u
8
a
2
− 1264u
8
a + · · · + 708a + 1030, 5u
8
a + u
8
+ · · · − 3a −
3, u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
6
=
1
u
2
a
12
=
−u
−u
3
+ u
a
1
=
−u
3
−u
3
+ u
a
3
=
a
1.00346a
2
u
8
+ 0.546949au
8
+ ··· − 0.306361a − 0.445695
a
2
=
0.0207702a
2
u
8
− 0.718304au
8
+ ··· + 1.16183a + 1.32583
−0.0562527a
2
u
8
+ 1.11207au
8
+ ··· − 0.0216357a − 1.25746
a
10
=
u
3
u
5
− u
3
+ u
a
7
=
u
6
− u
4
+ 1
u
8
− 2u
6
+ 2u
4
a
8
=
1.60623a
2
u
8
− 0.215491au
8
+ ··· − 3.15145a + 1.19775
−0.526179a
2
u
8
− 1.13630au
8
+ ··· + 0.566854a + 1.74556
a
4
=
0.0207702a
2
u
8
− 0.718304au
8
+ ··· + 1.16183a + 1.32583
−0.0562527a
2
u
8
+ 1.11207au
8
+ ··· − 0.0216357a − 1.25746
a
9
=
−u
6
+ u
4
− 1
−u
8
+ 2u
6
− 2u
4
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
7
− 8u
5
+ 4u
4
+ 8u
3
− 4u
2
+ 4u − 2
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
27
+ 18u
26
+ ··· + u − 1
c
2
, c
3
, c
4
c
7
, c
8
u
27
+ 9u
25
+ ··· + u + 1
c
5
, c
11
(u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1)
3
c
6
, c
12
(u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1)
3
c
9
(u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1)
3
c
10
(u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
2
+ u + 1)
3
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
27
− 18y
26
+ ··· + 17y − 1
c
2
, c
3
, c
4
c
7
, c
8
y
27
+ 18y
26
+ ··· + y − 1
c
5
, c
11
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y − 1)
3
c
6
, c
12
(y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y − 1)
3
c
9
(y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y − 1)
3
c
10
(y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y − 1)
3
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.772920 + 0.510351I
a = −1.015990 − 0.216914I
b = 0.53465 − 1.31702I
1.78344 − 2.09337I 0.51499 + 4.16283I
u = 0.772920 + 0.510351I
a = −1.49846 − 0.72657I
b = 0.466265 + 0.129322I
1.78344 − 2.09337I 0.51499 + 4.16283I
u = 0.772920 + 0.510351I
a = 1.25695 − 1.13794I
b = 0.99909 + 1.18770I
1.78344 − 2.09337I 0.51499 + 4.16283I
u = 0.772920 − 0.510351I
a = −1.015990 + 0.216914I
b = 0.53465 + 1.31702I
1.78344 + 2.09337I 0.51499 − 4.16283I
u = 0.772920 − 0.510351I
a = −1.49846 + 0.72657I
b = 0.466265 − 0.129322I
1.78344 + 2.09337I 0.51499 − 4.16283I
u = 0.772920 − 0.510351I
a = 1.25695 + 1.13794I
b = 0.99909 − 1.18770I
1.78344 + 2.09337I 0.51499 − 4.16283I
u = −0.825933
a = 0.164740
b = −0.407730
−1.19845 −8.65230
u = −0.825933
a = 1.58072 + 1.94080I
b = 1.203870 − 0.085974I
−1.19845 −8.65230
u = −0.825933
a = 1.58072 − 1.94080I
b = 1.203870 + 0.085974I
−1.19845 −8.65230
u = −1.173910 + 0.391555I
a = 0.060301 + 0.267806I
b = 0.850678 + 0.663233I
−4.37135 + 1.33617I −7.28409 − 0.70175I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.173910 + 0.391555I
a = −0.02187 − 1.90349I
b = −0.677531 − 1.190630I
−4.37135 + 1.33617I −7.28409 − 0.70175I
u = −1.173910 + 0.391555I
a = 2.60362 + 1.98656I
b = 1.82685 + 0.52740I
−4.37135 + 1.33617I −7.28409 − 0.70175I
u = −1.173910 − 0.391555I
a = 0.060301 − 0.267806I
b = 0.850678 − 0.663233I
−4.37135 − 1.33617I −7.28409 + 0.70175I
u = −1.173910 − 0.391555I
a = −0.02187 + 1.90349I
b = −0.677531 + 1.190630I
−4.37135 − 1.33617I −7.28409 + 0.70175I
u = −1.173910 − 0.391555I
a = 2.60362 − 1.98656I
b = 1.82685 − 0.52740I
−4.37135 − 1.33617I −7.28409 + 0.70175I
u = 0.141484 + 0.739668I
a = 1.137900 + 0.280832I
b = 1.68535 − 0.81163I
−0.61694 + 2.45442I −2.32792 − 2.91298I
u = 0.141484 + 0.739668I
a = −0.610565 + 1.028440I
b = 0.652744 − 0.562733I
−0.61694 + 2.45442I −2.32792 − 2.91298I
u = 0.141484 + 0.739668I
a = −0.363377 + 0.147221I
b = −0.33809 + 1.37436I
−0.61694 + 2.45442I −2.32792 − 2.91298I
u = 0.141484 − 0.739668I
a = 1.137900 − 0.280832I
b = 1.68535 + 0.81163I
−0.61694 − 2.45442I −2.32792 + 2.91298I
u = 0.141484 − 0.739668I
a = −0.610565 − 1.028440I
b = 0.652744 + 0.562733I
−0.61694 − 2.45442I −2.32792 + 2.91298I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.141484 − 0.739668I
a = −0.363377 − 0.147221I
b = −0.33809 − 1.37436I
−0.61694 − 2.45442I −2.32792 + 2.91298I
u = 1.172470 + 0.500383I
a = 0.589040 − 0.774213I
b = 0.578755 + 0.699902I
−3.59813 − 7.08493I −5.57680 + 5.91335I
u = 1.172470 + 0.500383I
a = −2.17609 − 1.01614I
b = −0.46969 − 1.60732I
−3.59813 − 7.08493I −5.57680 + 5.91335I
u = 1.172470 + 0.500383I
a = 3.37545 − 1.16633I
b = 1.89094 + 0.90742I
−3.59813 − 7.08493I −5.57680 + 5.91335I
u = 1.172470 − 0.500383I
a = 0.589040 + 0.774213I
b = 0.578755 − 0.699902I
−3.59813 + 7.08493I −5.57680 − 5.91335I
u = 1.172470 − 0.500383I
a = −2.17609 + 1.01614I
b = −0.46969 + 1.60732I
−3.59813 + 7.08493I −5.57680 − 5.91335I
u = 1.172470 − 0.500383I
a = 3.37545 + 1.16633I
b = 1.89094 − 0.90742I
−3.59813 + 7.08493I −5.57680 − 5.91335I
17
III. I
u
3
= hb − 1, u
8
+ u
7
+ · · · + a − 1, u
10
− 3u
8
+ 4u
6
− u
4
− u
2
+ 1i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
6
=
1
u
2
a
12
=
−u
−u
3
+ u
a
1
=
−u
3
−u
3
+ u
a
3
=
−u
8
− u
7
+ 2u
6
+ 2u
5
− 2u
4
− 2u
3
− u
2
− u + 1
1
a
2
=
−u
8
− u
7
+ 2u
6
+ 2u
5
− 2u
4
− 3u
3
− u
2
− u + 1
−u
3
+ u + 1
a
10
=
u
3
u
5
− u
3
+ u
a
7
=
u
6
− u
4
+ 1
u
8
− 2u
6
+ 2u
4
a
8
=
u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− u
3
+ u
2
− u − 2
−u
9
+ 2u
7
− u
5
− 2u
3
+ u
a
4
=
−u
8
− u
7
+ 2u
6
+ 2u
5
− 2u
4
− 2u
3
− u
2
− u + 2
1
a
9
=
u
9
− 2u
7
+ u
5
+ 2u
3
− u
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
8
− 8u
6
+ 8u
4
+ 4u
2
− 8
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
10
c
2
, c
3
, c
4
c
7
, c
8
(u
2
+ 1)
5
c
5
, c
11
u
10
− 3u
8
+ 4u
6
− u
4
− u
2
+ 1
c
6
, c
12
u
10
+ 5u
8
+ 8u
6
+ 3u
4
− u
2
+ 1
c
9
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
2
c
10
(u
5
− 3u
4
+ 4u
3
− u
2
− u + 1)
2
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y − 1)
10
c
2
, c
3
, c
4
c
7
, c
8
(y + 1)
10
c
5
, c
11
(y
5
− 3y
4
+ 4y
3
− y
2
− y + 1)
2
c
6
, c
12
(y
5
+ 5y
4
+ 8y
3
+ 3y
2
− y + 1)
2
c
9
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y − 1)
2
c
10
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y − 1)
2
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.822375 + 0.339110I
a = 1.50891 + 0.32986I
b = 1.00000
−0.32910 + 1.53058I −4.51511 − 4.43065I
u = −0.822375 − 0.339110I
a = 1.50891 − 0.32986I
b = 1.00000
−0.32910 − 1.53058I −4.51511 + 4.43065I
u = 0.822375 + 0.339110I
a = −1.25135 − 1.88547I
b = 1.00000
−0.32910 − 1.53058I −4.51511 + 4.43065I
u = 0.822375 − 0.339110I
a = −1.25135 + 1.88547I
b = 1.00000
−0.32910 + 1.53058I −4.51511 − 4.43065I
u = 0.766826I
a = 0.370286 + 0.821196I
b = 1.00000
−2.40108 −5.48110
u = − 0.766826I
a = 0.370286 − 0.821196I
b = 1.00000
−2.40108 −5.48110
u = −1.200150 + 0.455697I
a = 1.292420 + 0.186244I
b = 1.00000
−5.87256 + 4.40083I −8.74431 − 3.49859I
u = −1.200150 − 0.455697I
a = 1.292420 − 0.186244I
b = 1.00000
−5.87256 − 4.40083I −8.74431 + 3.49859I
u = 1.200150 + 0.455697I
a = 1.07974 − 1.56305I
b = 1.00000
−5.87256 − 4.40083I −8.74431 + 3.49859I
u = 1.200150 − 0.455697I
a = 1.07974 + 1.56305I
b = 1.00000
−5.87256 + 4.40083I −8.74431 − 3.49859I
21
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
10
)(u
27
+ 18u
26
+ ··· + u − 1)(u
68
+ 27u
67
+ ··· + 7896u + 289)
c
2
, c
7
((u
2
+ 1)
5
)(u
27
+ 9u
25
+ ··· + u + 1)(u
68
+ u
67
+ ··· − 20u + 17)
c
3
, c
4
, c
8
((u
2
+ 1)
5
)(u
27
+ 9u
25
+ ··· + u + 1)(u
68
+ u
67
+ ··· − 42u + 17)
c
5
, c
11
(u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1)
3
· (u
10
− 3u
8
+ 4u
6
− u
4
− u
2
+ 1)(u
68
+ 2u
67
+ ··· + 5u + 2)
c
6
, c
12
(u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1)
3
· (u
10
+ 5u
8
+ 8u
6
+ 3u
4
− u
2
+ 1)(u
68
+ 6u
67
+ ··· + 160u + 128)
c
9
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
2
· (u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1)
3
· (u
68
− 8u
67
+ ··· + 28469u + 10016)
c
10
(u
5
− 3u
4
+ 4u
3
− u
2
− u + 1)
2
· (u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
2
+ u + 1)
3
· (u
68
+ 36u
67
+ ··· − 19u + 4)
22
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y − 1)
10
)(y
27
− 18y
26
+ ··· + 17y − 1)
· (y
68
+ 39y
67
+ ··· + 6510324y + 83521)
c
2
, c
7
((y + 1)
10
)(y
27
+ 18y
26
+ ··· + y − 1)(y
68
+ 27y
67
+ ··· + 7896y + 289)
c
3
, c
4
, c
8
((y + 1)
10
)(y
27
+ 18y
26
+ ··· + y − 1)(y
68
+ 71y
67
+ ··· − 7272y + 289)
c
5
, c
11
(y
5
− 3y
4
+ 4y
3
− y
2
− y + 1)
2
· (y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y − 1)
3
· (y
68
− 36y
67
+ ··· + 19y + 4)
c
6
, c
12
(y
5
+ 5y
4
+ 8y
3
+ 3y
2
− y + 1)
2
· (y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y − 1)
3
· (y
68
+ 52y
67
+ ··· + 1088512y + 16384)
c
9
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y − 1)
2
· (y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y − 1)
3
· (y
68
+ 8y
67
+ ··· + 482721863y + 100320256)
c
10
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y − 1)
2
· (y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y − 1)
3
· (y
68
− 8y
67
+ ··· − 417y + 16)
23
