12a
0298
(K12a
0298
)
A knot diagram
1
Linearized knot diagam
3 6 8 10 2 12 1 5 11 4 9 7
Solving Sequence
4,11
10
2,5
6 9 12 7 8 3 1
c
10
c
4
c
5
c
9
c
11
c
6
c
8
c
3
c
1
c
2
, c
7
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−u
66
− 10u
64
+ ··· + 4b − 4u, −u
66
− 11u
64
+ ··· + 4a − 2, u
69
+ 2u
68
+ ··· − 2u
2
+ 2i
I
u
2
= h−412u
8
a
2
+ 444u
8
a + ··· − 624a + 202, 2u
8
a
2
− u
8
a + ··· − a + 1,
u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1i
I
u
3
= h2u
3
+ u
2
+ b + u + 1, u
3
+ 2a + 3u + 2, u
4
+ u
2
+ 2i
I
u
4
= hb + u, a + 2u − 1, u
2
+ 1i
I
u
5
= h−u
3
− u
2
+ b − 2u + 1, u
3
− u
2
+ a − u, u
4
+ 1i
I
v
1
= ha, b + 1, v −1i
* 6 irreducible components of dim
C
= 0, with total 107 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
=
h−u
66
−10u
64
+· · ·+4b−4u, −u
66
−11u
64
+· · ·+4a−2, u
69
+2u
68
+· · ·−2u
2
+2i
(i) Arc colorings
a
4
=
0
u
a
11
=
1
0
a
10
=
1
u
2
a
2
=
1
4
u
66
+
11
4
u
64
+ ··· −
1
2
u +
1
2
1
4
u
66
+
5
2
u
64
+ ··· −
9
2
u
4
+ u
a
5
=
u
u
3
+ u
a
6
=
1
2
u
68
+
11
2
u
66
+ ··· + u −
3
2
u
68
+ u
67
+ ··· +
1
2
u + 1
a
9
=
u
2
+ 1
u
2
a
12
=
u
4
+ u
2
+ 1
u
4
a
7
=
−
1
4
u
63
−
5
2
u
61
+ ··· +
1
2
u − 1
−
1
4
u
65
−
11
4
u
63
+ ··· −
5
2
u
2
+
1
2
u
a
8
=
u
6
+ u
4
+ 2u
2
+ 1
u
8
+ 2u
6
+ 2u
4
+ 2u
2
a
3
=
−u
13
− 2u
11
− 5u
9
− 6u
7
− 6u
5
− 4u
3
− u
−u
15
− 3u
13
− 6u
11
− 9u
9
− 8u
7
− 6u
5
− 2u
3
+ u
a
1
=
1
4
u
61
+
5
2
u
59
+ ··· − u
2
+ 1
1
4
u
61
+
9
4
u
59
+ ··· −
1
2
u
2
+
1
2
u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 2u
68
+ 4u
67
+ ··· − 10u + 8
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
69
+ 26u
68
+ ··· + 3481u + 256
c
2
, c
5
u
69
+ 2u
68
+ ··· − 5u − 16
c
3
u
69
− 2u
68
+ ··· − 188076u − 54322
c
4
, c
10
u
69
− 2u
68
+ ··· + 2u
2
− 2
c
6
, c
7
, c
12
u
69
− 2u
68
+ ··· − 37u − 16
c
8
u
69
+ 10u
68
+ ··· − 2116u − 86
c
9
, c
11
u
69
+ 22u
68
+ ··· + 8u − 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
69
+ 46y
68
+ ··· − 2589327y −65536
c
2
, c
5
y
69
− 26y
68
+ ··· + 3481y −256
c
3
y
69
− 26y
68
+ ··· + 15690417448y −2950879684
c
4
, c
10
y
69
+ 22y
68
+ ··· + 8y −4
c
6
, c
7
, c
12
y
69
− 74y
68
+ ··· − 10919y −256
c
8
y
69
− 2y
68
+ ··· − 1189944y −7396
c
9
, c
11
y
69
+ 50y
68
+ ··· + 768y −16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.735899 + 0.688576I
a = −1.41058 − 0.11854I
b = −0.96277 + 2.11478I
−0.240515 + 0.033439I −1.48136 + 0.I
u = −0.735899 − 0.688576I
a = −1.41058 + 0.11854I
b = −0.96277 − 2.11478I
−0.240515 − 0.033439I −1.48136 + 0.I
u = 0.338664 + 0.953969I
a = 0.259722 + 0.602753I
b = 0.242668 + 1.080750I
5.18981 + 0.99757I 4.76342 − 3.46084I
u = 0.338664 − 0.953969I
a = 0.259722 − 0.602753I
b = 0.242668 − 1.080750I
5.18981 − 0.99757I 4.76342 + 3.46084I
u = 0.484849 + 0.860276I
a = 1.27015 + 0.75092I
b = −0.89181 + 2.10893I
−1.85693 − 1.13119I −2.07731 + 1.47337I
u = 0.484849 − 0.860276I
a = 1.27015 − 0.75092I
b = −0.89181 − 2.10893I
−1.85693 + 1.13119I −2.07731 − 1.47337I
u = 0.058334 + 1.021690I
a = 0.24060 − 2.11026I
b = 0.529272 − 0.918124I
−5.74447 − 0.01900I −8.65927 + 0.I
u = 0.058334 − 1.021690I
a = 0.24060 + 2.11026I
b = 0.529272 + 0.918124I
−5.74447 + 0.01900I −8.65927 + 0.I
u = 0.154964 + 1.031240I
a = −0.85296 + 1.99168I
b = −0.216276 + 0.724886I
−3.54966 + 6.72812I −3.30535 − 7.86468I
u = 0.154964 − 1.031240I
a = −0.85296 − 1.99168I
b = −0.216276 − 0.724886I
−3.54966 − 6.72812I −3.30535 + 7.86468I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.718154 + 0.761613I
a = 0.040869 + 0.875751I
b = −0.531478 + 0.949465I
3.60394 − 0.19911I 9.90804 + 0.I
u = 0.718154 − 0.761613I
a = 0.040869 − 0.875751I
b = −0.531478 − 0.949465I
3.60394 + 0.19911I 9.90804 + 0.I
u = −0.422383 + 0.968673I
a = −0.599532 + 1.252790I
b = 1.85369 + 1.47586I
3.61056 + 4.51985I 0
u = −0.422383 − 0.968673I
a = −0.599532 − 1.252790I
b = 1.85369 − 1.47586I
3.61056 − 4.51985I 0
u = 0.193872 + 1.039360I
a = −0.624526 + 0.079575I
b = −0.927525 − 0.005005I
4.24263 + 5.04361I 0. − 4.03426I
u = 0.193872 − 1.039360I
a = −0.624526 − 0.079575I
b = −0.927525 + 0.005005I
4.24263 − 5.04361I 0. + 4.03426I
u = 0.721986 + 0.582383I
a = 1.020400 − 0.497911I
b = 1.35891 + 1.25471I
3.90829 + 1.18050I 7.40920 − 3.02522I
u = 0.721986 − 0.582383I
a = 1.020400 + 0.497911I
b = 1.35891 − 1.25471I
3.90829 − 1.18050I 7.40920 + 3.02522I
u = −0.814686 + 0.705728I
a = 2.39011 + 0.79666I
b = 2.59506 − 2.01293I
2.93810 + 6.44249I 0
u = −0.814686 − 0.705728I
a = 2.39011 − 0.79666I
b = 2.59506 + 2.01293I
2.93810 − 6.44249I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.028573 + 1.077810I
a = −0.61215 − 1.87207I
b = −0.511359 − 0.452462I
−1.60521 + 2.06429I 0
u = −0.028573 − 1.077810I
a = −0.61215 + 1.87207I
b = −0.511359 + 0.452462I
−1.60521 − 2.06429I 0
u = −0.170360 + 1.066470I
a = 0.37501 + 2.28994I
b = 0.350653 + 0.759401I
2.10642 − 10.83270I 0. + 7.91871I
u = −0.170360 − 1.066470I
a = 0.37501 − 2.28994I
b = 0.350653 − 0.759401I
2.10642 + 10.83270I 0. − 7.91871I
u = 0.836381 + 0.694622I
a = −2.53666 + 0.36324I
b = −2.27305 − 2.69677I
8.89008 − 10.76610I 0
u = 0.836381 − 0.694622I
a = −2.53666 − 0.36324I
b = −2.27305 + 2.69677I
8.89008 + 10.76610I 0
u = −0.833721 + 0.715169I
a = −0.612597 + 0.721125I
b = 0.402951 + 0.631456I
11.06750 + 4.64835I 0
u = −0.833721 − 0.715169I
a = −0.612597 − 0.721125I
b = 0.402951 − 0.631456I
11.06750 − 4.64835I 0
u = −0.788117 + 0.777559I
a = −0.860399 − 0.145200I
b = −1.208460 − 0.042361I
4.23303 − 3.52292I 0
u = −0.788117 − 0.777559I
a = −0.860399 + 0.145200I
b = −1.208460 + 0.042361I
4.23303 + 3.52292I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.821959 + 0.782703I
a = 1.141410 + 0.345243I
b = 0.680996 − 0.881071I
12.26590 − 0.79570I 0
u = −0.821959 − 0.782703I
a = 1.141410 − 0.345243I
b = 0.680996 + 0.881071I
12.26590 + 0.79570I 0
u = 0.611116 + 0.956461I
a = −0.49978 − 2.05095I
b = 2.42886 − 2.48221I
−2.54832 + 5.58402I 0
u = 0.611116 − 0.956461I
a = −0.49978 + 2.05095I
b = 2.42886 + 2.48221I
−2.54832 − 5.58402I 0
u = 0.814707 + 0.809092I
a = 0.295475 − 0.322981I
b = 0.913082 − 1.062150I
10.93290 + 7.02859I 0
u = 0.814707 − 0.809092I
a = 0.295475 + 0.322981I
b = 0.913082 + 1.062150I
10.93290 − 7.02859I 0
u = 0.695607 + 0.941949I
a = −0.886074 − 0.080146I
b = −0.262992 − 0.787216I
3.05990 + 5.61567I 0
u = 0.695607 − 0.941949I
a = −0.886074 + 0.080146I
b = −0.262992 + 0.787216I
3.05990 − 5.61567I 0
u = −0.044024 + 0.818063I
a = 0.652335 − 0.322162I
b = −0.167905 + 0.623453I
−1.27770 − 1.44146I 0.19549 + 5.54807I
u = −0.044024 − 0.818063I
a = 0.652335 + 0.322162I
b = −0.167905 − 0.623453I
−1.27770 + 1.44146I 0.19549 − 5.54807I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.613808 + 1.009340I
a = 0.84248 − 1.87193I
b = −2.04716 − 2.64513I
1.96131 − 8.32605I 0
u = −0.613808 − 1.009340I
a = 0.84248 + 1.87193I
b = −2.04716 + 2.64513I
1.96131 + 8.32605I 0
u = −0.662707 + 0.477450I
a = −1.86190 + 0.54426I
b = −0.57360 + 1.90850I
3.39108 + 3.42806I 6.35256 − 3.02642I
u = −0.662707 − 0.477450I
a = −1.86190 − 0.54426I
b = −0.57360 − 1.90850I
3.39108 − 3.42806I 6.35256 + 3.02642I
u = −0.737691 + 0.955567I
a = −0.388118 − 0.820537I
b = −0.573332 + 0.251331I
3.68498 − 2.23055I 0
u = −0.737691 − 0.955567I
a = −0.388118 + 0.820537I
b = −0.573332 − 0.251331I
3.68498 + 2.23055I 0
u = −0.689892 + 0.991018I
a = 0.09117 − 1.66872I
b = −2.85026 − 1.61053I
−1.14588 − 5.49156I 0
u = −0.689892 − 0.991018I
a = 0.09117 + 1.66872I
b = −2.85026 + 1.61053I
−1.14588 + 5.49156I 0
u = 0.659252 + 1.016190I
a = 0.137976 − 1.363260I
b = 2.56392 − 0.66959I
2.66779 + 4.10740I 0
u = 0.659252 − 1.016190I
a = 0.137976 + 1.363260I
b = 2.56392 + 0.66959I
2.66779 − 4.10740I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.771414 + 0.943358I
a = 0.552899 − 0.216552I
b = −0.327428 + 0.913552I
10.51840 − 1.09087I 0
u = 0.771414 − 0.943358I
a = 0.552899 + 0.216552I
b = −0.327428 − 0.913552I
10.51840 + 1.09087I 0
u = −0.764178 + 0.965173I
a = 0.412858 + 1.010290I
b = 1.49440 + 0.94058I
11.70390 − 5.14096I 0
u = −0.764178 − 0.965173I
a = 0.412858 − 1.010290I
b = 1.49440 − 0.94058I
11.70390 + 5.14096I 0
u = −0.729127 + 1.006320I
a = 0.85456 + 2.40770I
b = 4.06882 + 0.97788I
2.02182 − 12.24190I 0
u = −0.729127 − 1.006320I
a = 0.85456 − 2.40770I
b = 4.06882 − 0.97788I
2.02182 + 12.24190I 0
u = −0.741771 + 1.008840I
a = 0.545247 − 0.543242I
b = 0.321004 − 1.292670I
10.1674 − 10.5435I 0
u = −0.741771 − 1.008840I
a = 0.545247 + 0.543242I
b = 0.321004 + 1.292670I
10.1674 + 10.5435I 0
u = 0.734769 + 1.019640I
a = −0.36453 + 2.55787I
b = −4.11635 + 1.81421I
7.8960 + 16.6434I 0
u = 0.734769 − 1.019640I
a = −0.36453 − 2.55787I
b = −4.11635 − 1.81421I
7.8960 − 16.6434I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.670400 + 0.147828I
a = 1.80229 + 0.50503I
b = 1.30651 − 0.96838I
6.05766 − 8.22168I 7.69702 + 5.92932I
u = −0.670400 − 0.147828I
a = 1.80229 − 0.50503I
b = 1.30651 + 0.96838I
6.05766 + 8.22168I 7.69702 − 5.92932I
u = 0.656891 + 0.088355I
a = −0.868107 − 1.024770I
b = −0.163464 − 0.301668I
7.87968 + 2.33195I 10.31373 − 1.18340I
u = 0.656891 − 0.088355I
a = −0.868107 + 1.024770I
b = −0.163464 + 0.301668I
7.87968 − 2.33195I 10.31373 + 1.18340I
u = 0.412551 + 0.453150I
a = 1.75896 − 0.29485I
b = 0.385319 + 1.182700I
−1.61119 − 1.13122I −1.25895 + 1.21665I
u = 0.412551 − 0.453150I
a = 1.75896 + 0.29485I
b = 0.385319 − 1.182700I
−1.61119 + 1.13122I −1.25895 − 1.21665I
u = 0.591730 + 0.129745I
a = −1.49243 + 0.30843I
b = −0.650903 − 1.070410I
0.12986 + 4.40376I 4.64576 − 6.38172I
u = 0.591730 − 0.129745I
a = −1.49243 − 0.30843I
b = −0.650903 + 1.070410I
0.12986 − 4.40376I 4.64576 + 6.38172I
u = −0.371894
a = 0.571634
b = −0.480013
0.931539 11.9680
11
II. I
u
2
= h−412u
8
a
2
+ 444u
8
a + · · · − 624a + 202, 2u
8
a
2
− u
8
a + · · · − a +
1, u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1i
(i) Arc colorings
a
4
=
0
u
a
11
=
1
0
a
10
=
1
u
2
a
2
=
a
0.235026a
2
u
8
− 0.253280au
8
+ ··· + 0.355961a − 0.115231
a
5
=
u
u
3
+ u
a
6
=
1.13862a
2
u
8
+ 0.287507au
8
+ ··· + 0.190531a − 0.247576
0.854535a
2
u
8
+ 1.25385au
8
+ ··· − 1.11352a + 0.309184
a
9
=
u
2
+ 1
u
2
a
12
=
u
4
+ u
2
+ 1
u
4
a
7
=
0.983457a
2
u
8
− 0.108386au
8
+ ··· − 0.0638905a − 0.851112
0.826013a
2
u
8
+ 1.34284au
8
+ ··· − 1.29264a + 0.565887
a
8
=
u
6
+ u
4
+ 2u
2
+ 1
u
8
+ 2u
6
+ 2u
4
+ 2u
2
a
3
=
u
4
+ u
2
+ 1
u
4
a
1
=
−0.142042a
2
u
8
+ 0.483172au
8
+ ··· − 0.652025a + 0.278380
0.157444a
2
u
8
− 0.451226au
8
+ ··· − 0.771249a − 1.41700
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
7
+ 4u
6
− 4u
5
+ 4u
4
− 8u
3
+ 4u
2
+ 6
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
27
+ 18u
26
+ ··· + u + 1
c
2
, c
5
, c
6
c
7
, c
12
u
27
− 9u
25
+ ··· + u + 1
c
3
(u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1)
3
c
4
, c
10
(u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1)
3
c
8
(u
9
− 5u
8
+ 12u
7
− 15u
6
+ 9u
5
+ u
4
− 4u
3
+ 2u
2
+ u − 1)
3
c
9
, c
11
(u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
3
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
27
− 18y
26
+ ··· + y − 1
c
2
, c
5
, c
6
c
7
, c
12
y
27
− 18y
26
+ ··· + y − 1
c
3
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y − 1)
3
c
4
, c
10
(y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y − 1)
3
c
8
(y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y − 1)
3
c
9
, c
11
(y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y − 1)
3
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.140343 + 0.966856I
a = 1.25673 + 1.05313I
b = 0.049646 + 0.706168I
−1.78344 − 2.09337I −0.51499 + 4.16283I
u = −0.140343 + 0.966856I
a = 0.163898 − 0.278866I
b = 0.601292 + 0.256808I
−1.78344 − 2.09337I −0.51499 + 4.16283I
u = −0.140343 + 0.966856I
a = −0.01736 − 2.34952I
b = −0.95932 − 1.47752I
−1.78344 − 2.09337I −0.51499 + 4.16283I
u = −0.140343 − 0.966856I
a = 1.25673 − 1.05313I
b = 0.049646 − 0.706168I
−1.78344 + 2.09337I −0.51499 − 4.16283I
u = −0.140343 − 0.966856I
a = 0.163898 + 0.278866I
b = 0.601292 − 0.256808I
−1.78344 + 2.09337I −0.51499 − 4.16283I
u = −0.140343 − 0.966856I
a = −0.01736 + 2.34952I
b = −0.95932 + 1.47752I
−1.78344 + 2.09337I −0.51499 − 4.16283I
u = −0.628449 + 0.875112I
a = 0.0738554 + 0.0112823I
b = −0.329184 + 0.287114I
0.61694 − 2.45442I 2.32792 + 2.91298I
u = −0.628449 + 0.875112I
a = −2.10033 + 0.25220I
b = −0.22682 + 3.11202I
0.61694 − 2.45442I 2.32792 + 2.91298I
u = −0.628449 + 0.875112I
a = 0.05733 − 2.33941I
b = −2.96621 − 2.53925I
0.61694 − 2.45442I 2.32792 + 2.91298I
u = −0.628449 − 0.875112I
a = 0.0738554 − 0.0112823I
b = −0.329184 − 0.287114I
0.61694 + 2.45442I 2.32792 − 2.91298I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.628449 − 0.875112I
a = −2.10033 − 0.25220I
b = −0.22682 − 3.11202I
0.61694 + 2.45442I 2.32792 − 2.91298I
u = −0.628449 − 0.875112I
a = 0.05733 + 2.33941I
b = −2.96621 + 2.53925I
0.61694 + 2.45442I 2.32792 − 2.91298I
u = 0.796005 + 0.733148I
a = 0.897099 + 0.478488I
b = 0.366734 + 0.756648I
4.37135 − 1.33617I 7.28409 + 0.70175I
u = 0.796005 + 0.733148I
a = 1.64130 − 0.08440I
b = 1.01907 + 2.73861I
4.37135 − 1.33617I 7.28409 + 0.70175I
u = 0.796005 + 0.733148I
a = −1.69292 + 1.13699I
b = −2.24611 − 0.83019I
4.37135 − 1.33617I 7.28409 + 0.70175I
u = 0.796005 − 0.733148I
a = 0.897099 − 0.478488I
b = 0.366734 − 0.756648I
4.37135 + 1.33617I 7.28409 − 0.70175I
u = 0.796005 − 0.733148I
a = 1.64130 + 0.08440I
b = 1.01907 − 2.73861I
4.37135 + 1.33617I 7.28409 − 0.70175I
u = 0.796005 − 0.733148I
a = −1.69292 − 1.13699I
b = −2.24611 + 0.83019I
4.37135 + 1.33617I 7.28409 − 0.70175I
u = 0.728966 + 0.986295I
a = −0.280859 − 0.864363I
b = 0.366463 − 0.892237I
3.59813 + 7.08493I 5.57680 − 5.91335I
u = 0.728966 + 0.986295I
a = −0.12458 − 1.78606I
b = 3.23510 − 2.02570I
3.59813 + 7.08493I 5.57680 − 5.91335I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.728966 + 0.986295I
a = −1.25383 + 1.67614I
b = −3.12748 − 0.01225I
3.59813 + 7.08493I 5.57680 − 5.91335I
u = 0.728966 − 0.986295I
a = −0.280859 + 0.864363I
b = 0.366463 + 0.892237I
3.59813 − 7.08493I 5.57680 + 5.91335I
u = 0.728966 − 0.986295I
a = −0.12458 + 1.78606I
b = 3.23510 + 2.02570I
3.59813 − 7.08493I 5.57680 + 5.91335I
u = 0.728966 − 0.986295I
a = −1.25383 − 1.67614I
b = −3.12748 + 0.01225I
3.59813 − 7.08493I 5.57680 + 5.91335I
u = −0.512358
a = 0.923120 + 0.394259I
b = −0.085863 − 0.444563I
1.19845 8.65230
u = −0.512358
a = 0.923120 − 0.394259I
b = −0.085863 + 0.444563I
1.19845 8.65230
u = −0.512358
a = −3.08692
b = −1.39464
1.19845 8.65230
17
III. I
u
3
= h2u
3
+ u
2
+ b + u + 1, u
3
+ 2a + 3u + 2, u
4
+ u
2
+ 2i
(i) Arc colorings
a
4
=
0
u
a
11
=
1
0
a
10
=
1
u
2
a
2
=
−
1
2
u
3
−
3
2
u − 1
−2u
3
− u
2
− u − 1
a
5
=
u
u
3
+ u
a
6
=
−
1
2
u
3
−
1
2
u − 1
−u
3
− u
2
− 1
a
9
=
u
2
+ 1
u
2
a
12
=
−1
−u
2
− 2
a
7
=
−
1
2
u
3
−
1
2
u
−u
3
+ 1
a
8
=
1
u
2
+ 2
a
3
=
−u
−u
3
− u
a
1
=
−
1
2
u
3
−
1
2
u − 1
−u
3
− u
2
− 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
2
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
6
c
7
(u − 1)
4
c
2
, c
12
(u + 1)
4
c
3
, c
4
, c
8
c
10
u
4
+ u
2
+ 2
c
9
(u
2
− u + 2)
2
c
11
(u
2
+ u + 2)
2
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
7
, c
12
(y − 1)
4
c
3
, c
4
, c
8
c
10
(y
2
+ y + 2)
2
c
9
, c
11
(y
2
+ 3y + 4)
2
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.676097 + 0.978318I
a = −1.19802 − 1.67009I
b = 2.08839 − 3.11166I
0.82247 + 5.33349I 2.00000 − 5.29150I
u = 0.676097 − 0.978318I
a = −1.19802 + 1.67009I
b = 2.08839 + 3.11166I
0.82247 − 5.33349I 2.00000 + 5.29150I
u = −0.676097 + 0.978318I
a = −0.80198 − 1.67009I
b = −3.08839 − 0.46591I
0.82247 − 5.33349I 2.00000 + 5.29150I
u = −0.676097 − 0.978318I
a = −0.80198 + 1.67009I
b = −3.08839 + 0.46591I
0.82247 + 5.33349I 2.00000 − 5.29150I
21
IV. I
u
4
= hb + u, a + 2u − 1, u
2
+ 1i
(i) Arc colorings
a
4
=
0
u
a
11
=
1
0
a
10
=
1
−1
a
2
=
−2u + 1
−u
a
5
=
u
0
a
6
=
−u + 1
−u
a
9
=
0
−1
a
12
=
1
1
a
7
=
−u
−u − 1
a
8
=
−1
−1
a
3
=
−u
0
a
1
=
−u + 1
−u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
6
c
7
, c
9
(u − 1)
2
c
2
, c
11
, c
12
(u + 1)
2
c
3
, c
4
, c
8
c
10
u
2
+ 1
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
7
, c
9
c
11
, c
12
(y − 1)
2
c
3
, c
4
, c
8
c
10
(y + 1)
2
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = 1.00000 − 2.00000I
b = − 1.000000I
−3.28987 −4.00000
u = − 1.000000I
a = 1.00000 + 2.00000I
b = 1.000000I
−3.28987 −4.00000
25
V. I
u
5
= h−u
3
− u
2
+ b − 2u + 1, u
3
− u
2
+ a − u, u
4
+ 1i
(i) Arc colorings
a
4
=
0
u
a
11
=
1
0
a
10
=
1
u
2
a
2
=
−u
3
+ u
2
+ u
u
3
+ u
2
+ 2u − 1
a
5
=
u
u
3
+ u
a
6
=
u
3
− u
2
−u
2
− u + 1
a
9
=
u
2
+ 1
u
2
a
12
=
u
2
−1
a
7
=
u
3
−u
2
− u
a
8
=
u
2
−1
a
3
=
u
u
3
+ u
a
1
=
−u
3
+ u
2
u
2
+ u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4
26
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
12
(u − 1)
4
c
3
, c
4
, c
8
c
10
u
4
+ 1
c
5
, c
6
, c
7
(u + 1)
4
c
9
, c
11
(u
2
+ 1)
2
27
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
7
, c
12
(y − 1)
4
c
3
, c
4
, c
8
c
10
(y
2
+ 1)
2
c
9
, c
11
(y + 1)
4
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.707107 + 0.707107I
a = 1.41421 + 1.00000I
b = −0.29289 + 3.12132I
1.64493 4.00000
u = 0.707107 − 0.707107I
a = 1.41421 − 1.00000I
b = −0.29289 − 3.12132I
1.64493 4.00000
u = −0.707107 + 0.707107I
a = −1.41421 − 1.00000I
b = −1.70711 + 1.12132I
1.64493 4.00000
u = −0.707107 − 0.707107I
a = −1.41421 + 1.00000I
b = −1.70711 − 1.12132I
1.64493 4.00000
29
VI. I
v
1
= ha, b + 1, v − 1i
(i) Arc colorings
a
4
=
1
0
a
11
=
1
0
a
10
=
1
0
a
2
=
0
−1
a
5
=
1
0
a
6
=
1
1
a
9
=
1
0
a
12
=
1
0
a
7
=
2
1
a
8
=
1
0
a
3
=
1
0
a
1
=
−1
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
30
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
12
u − 1
c
3
, c
4
, c
8
c
9
, c
10
, c
11
u
c
5
, c
6
, c
7
u + 1
31
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
7
, c
12
y − 1
c
3
, c
4
, c
8
c
9
, c
10
, c
11
y
32
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 1.00000
a = 0
b = −1.00000
0 0
33
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
11
)(u
27
+ 18u
26
+ ··· + u + 1)(u
69
+ 26u
68
+ ··· + 3481u + 256)
c
2
((u − 1)
5
)(u + 1)
6
(u
27
− 9u
25
+ ··· + u + 1)(u
69
+ 2u
68
+ ··· − 5u − 16)
c
3
u(u
2
+ 1)(u
4
+ 1)(u
4
+ u
2
+ 2)
· (u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1)
3
· (u
69
− 2u
68
+ ··· − 188076u − 54322)
c
4
, c
10
u(u
2
+ 1)(u
4
+ 1)(u
4
+ u
2
+ 2)(u
9
+ u
8
+ ··· + u − 1)
3
· (u
69
− 2u
68
+ ··· + 2u
2
− 2)
c
5
((u − 1)
6
)(u + 1)
5
(u
27
− 9u
25
+ ··· + u + 1)(u
69
+ 2u
68
+ ··· − 5u − 16)
c
6
, c
7
((u − 1)
6
)(u + 1)
5
(u
27
− 9u
25
+ ··· + u + 1)
· (u
69
− 2u
68
+ ··· − 37u − 16)
c
8
u(u
2
+ 1)(u
4
+ 1)(u
4
+ u
2
+ 2)
· (u
9
− 5u
8
+ 12u
7
− 15u
6
+ 9u
5
+ u
4
− 4u
3
+ 2u
2
+ u − 1)
3
· (u
69
+ 10u
68
+ ··· − 2116u − 86)
c
9
u(u − 1)
2
(u
2
+ 1)
2
(u
2
− u + 2)
2
· (u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
3
· (u
69
+ 22u
68
+ ··· + 8u − 4)
c
11
u(u + 1)
2
(u
2
+ 1)
2
(u
2
+ u + 2)
2
· (u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
3
· (u
69
+ 22u
68
+ ··· + 8u − 4)
c
12
((u − 1)
5
)(u + 1)
6
(u
27
− 9u
25
+ ··· + u + 1)
· (u
69
− 2u
68
+ ··· − 37u − 16)
34
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y − 1)
11
)(y
27
− 18y
26
+ ··· + y − 1)
· (y
69
+ 46y
68
+ ··· − 2589327y − 65536)
c
2
, c
5
((y − 1)
11
)(y
27
− 18y
26
+ ··· + y − 1)(y
69
− 26y
68
+ ··· + 3481y − 256)
c
3
y(y + 1)
2
(y
2
+ 1)
2
(y
2
+ y + 2)
2
· (y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y − 1)
3
· (y
69
− 26y
68
+ ··· + 15690417448y − 2950879684)
c
4
, c
10
y(y + 1)
2
(y
2
+ 1)
2
(y
2
+ y + 2)
2
· (y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y − 1)
3
· (y
69
+ 22y
68
+ ··· + 8y − 4)
c
6
, c
7
, c
12
((y − 1)
11
)(y
27
− 18y
26
+ ··· + y − 1)
· (y
69
− 74y
68
+ ··· − 10919y − 256)
c
8
y(y + 1)
2
(y
2
+ 1)
2
(y
2
+ y + 2)
2
· (y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y − 1)
3
· (y
69
− 2y
68
+ ··· − 1189944y − 7396)
c
9
, c
11
y(y − 1)
2
(y + 1)
4
(y
2
+ 3y + 4)
2
· (y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y − 1)
3
· (y
69
+ 50y
68
+ ··· + 768y − 16)
35
