12a
0561
(K12a
0561
)
A knot diagram
1
Linearized knot diagam
3 7 9 8 11 2 1 10 4 12 6 5
Solving Sequence
4,10
9
1,3
2 8 5 7 6 12 11
c
9
c
3
c
1
c
8
c
4
c
7
c
6
c
12
c
10
c
2
, c
5
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−u
5
+ u
3
− u
2
+ b − u, −u
5
+ 2u
3
− u
2
+ a − u + 1, u
7
− 2u
5
+ u
4
+ 2u
3
− u
2
+ u + 1i
I
u
2
= hu
8
− 2u
6
+ 2u
4
+ b, u
23
− u
22
+ ··· + 2a + 3, u
24
+ u
23
+ ··· + 2u + 1i
I
u
3
= hu
23
− 5u
21
+ ··· + 2b − u, 2u
23
+ u
22
+ ··· + 2a + 1, u
24
+ u
23
+ ··· + 2u + 1i
I
u
4
= h−9u
23
+ 30u
22
+ ··· + 4b + 26, u
23
− 10u
22
+ ··· + 8a − 34, u
24
− 4u
23
+ ··· − 12u + 4i
I
u
5
= h−u
2
+ b, −u
3
− u
2
+ a + 1, u
4
− u
2
+ 1i
I
u
6
= h3u
23
a + 2u
23
+ ··· + 2a + 8, 8u
23
a + 2u
22
a + ··· + 6a + 4, u
24
+ u
23
+ ··· + 2u
3
+ 1i
I
u
7
= h−u
2
+ b, u
3
− u
2
+ a − u + 1, u
4
− u
2
+ 1i
I
u
8
= hu
2
+ b − 1, −u
3
+ a − 1, u
4
− u
2
+ 1i
I
u
9
= hu
2
+ b − 1, u
3
+ a − u − 1, u
4
− u
2
+ 1i
I
u
10
= hb + 1, a, u − 1i
* 10 irreducible components of dim
C
= 0, with total 144 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
5
+u
3
−u
2
+b−u, −u
5
+2u
3
−u
2
+a−u+1, u
7
−2u
5
+u
4
+2u
3
−u
2
+u+1i
(i) Arc colorings
a
4
=
0
u
a
10
=
1
0
a
9
=
1
−u
2
a
1
=
u
5
− 2u
3
+ u
2
+ u − 1
u
5
− u
3
+ u
2
+ u
a
3
=
u
−u
3
+ u
a
2
=
u
5
− u
3
+ u
2
+ u − 1
u
2
+ u
a
8
=
−u
2
+ 1
−u
2
a
5
=
u
5
− 2u
3
+ u
u
5
− u
3
+ u
a
7
=
u
6
− u
4
+ u
3
+ u
2
+ 1
u
2
+ u
a
6
=
u + 1
−u
3
+ u
a
12
=
−u
6
+ u
4
− u
3
− u
2
− 1
−u
2
a
11
=
u
6
− u
4
+ u
3
− u + 1
u
4
(ii) Obstruction class = −1
(iii) Cusp Shapes = 6u
4
− 6u
2
+ 6u − 6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
, c
10
u
7
+ 4u
6
+ 8u
5
+ 7u
4
+ 2u
3
− u
2
+ 3u + 1
c
2
, c
3
, c
5
c
6
, c
9
, c
11
u
7
− 2u
5
+ u
4
+ 2u
3
− u
2
+ u + 1
c
4
, c
7
, c
12
u
7
− 3u
6
+ 8u
5
− 10u
4
+ 12u
3
− 6u
2
+ 3u + 3
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
, c
10
y
7
+ 12y
5
− 3y
4
+ 58y
3
− 3y
2
+ 11y −1
c
2
, c
3
, c
5
c
6
, c
9
, c
11
y
7
− 4y
6
+ 8y
5
− 7y
4
+ 2y
3
+ y
2
+ 3y −1
c
4
, c
7
, c
12
y
7
+ 7y
6
+ 28y
5
+ 62y
4
+ 90y
3
+ 96y
2
+ 45y −9
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.323321 + 0.751928I
a = 0.22091 + 1.45384I
b = 0.70630 + 1.26451I
1.50830 + 2.81502I −1.43908 − 1.09480I
u = 0.323321 − 0.751928I
a = 0.22091 − 1.45384I
b = 0.70630 − 1.26451I
1.50830 − 2.81502I −1.43908 + 1.09480I
u = −1.209760 + 0.381906I
a = 1.45272 − 0.50136I
b = 1.21155 + 1.11972I
−10.84690 + 7.59135I −15.8701 − 6.7751I
u = −1.209760 − 0.381906I
a = 1.45272 + 0.50136I
b = 1.21155 − 1.11972I
−10.84690 − 7.59135I −15.8701 + 6.7751I
u = 1.159800 + 0.592772I
a = −2.18871 + 0.23437I
b = −0.85122 + 2.41814I
−5.8285 − 18.2895I −10.4221 + 11.7034I
u = 1.159800 − 0.592772I
a = −2.18871 − 0.23437I
b = −0.85122 − 2.41814I
−5.8285 + 18.2895I −10.4221 − 11.7034I
u = −0.546712
a = −0.969843
b = −0.133251
−0.919438 −10.5380
5
II. I
u
2
= hu
8
− 2u
6
+ 2u
4
+ b, u
23
− u
22
+ · · · + 2a + 3, u
24
+ u
23
+ · · · + 2u + 1i
(i) Arc colorings
a
4
=
0
u
a
10
=
1
0
a
9
=
1
−u
2
a
1
=
−
1
2
u
23
+
1
2
u
22
+ ··· − u −
3
2
−u
8
+ 2u
6
− 2u
4
a
3
=
u
−u
3
+ u
a
2
=
−u
23
+ u
22
+ ··· − 2u − 2
1
2
u
22
−
5
2
u
20
+ ··· +
1
2
u +
1
2
a
8
=
−u
2
+ 1
−u
2
a
5
=
u
5
− 2u
3
+ u
u
5
− u
3
+ u
a
7
=
3
2
u
23
−
21
2
u
21
+ ··· +
5
2
u + 3
1
2
u
22
−
5
2
u
20
+ ··· +
1
2
u +
1
2
a
6
=
1
2
u
23
+
1
2
u
22
+ ··· −
3
2
u
2
+
1
2
−u
3
+ u
a
12
=
−
1
2
u
23
+
1
2
u
22
+ ··· − u −
3
2
−u
2
a
11
=
1
2
u
23
−
7
2
u
21
+ ··· +
3
2
u + 2
u
4
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −2u
23
+ 16u
21
+ 2u
20
−60u
19
−14u
18
+ 132u
17
+ 50u
16
−176u
15
−108u
14
+ 124u
13
+
152u
12
−4u
11
−134u
10
−68u
9
+ 66u
8
+ 50u
7
−8u
6
−16u
5
−2u
4
+ 12u
3
+ 2u
2
−8u −12
6
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
24
+ 10u
23
+ ··· + 24u + 16
c
2
, c
6
u
24
− 4u
23
+ ··· − 12u + 4
c
3
, c
5
, c
9
c
11
u
24
+ u
23
+ ··· + 2u + 1
c
4
, c
12
u
24
+ 3u
23
+ ··· + 8u + 3
c
7
u
24
− 12u
23
+ ··· − 1436u + 276
c
8
, c
10
u
24
+ 13u
23
+ ··· + 4u + 1
7
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
24
+ 6y
23
+ ··· + 1248y + 256
c
2
, c
6
y
24
− 10y
23
+ ··· − 24y + 16
c
3
, c
5
, c
9
c
11
y
24
− 13y
23
+ ··· − 4y + 1
c
4
, c
12
y
24
+ 15y
23
+ ··· − 46y + 9
c
7
y
24
− 2y
23
+ ··· + 176264y + 76176
c
8
, c
10
y
24
− y
23
+ ··· + 4y + 1
8
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.872385 + 0.264900I
a = −0.323474 + 1.214120I
b = −0.415052 − 0.487887I
−1.33365 − 4.85950I −12.45920 + 5.77046I
u = 0.872385 − 0.264900I
a = −0.323474 − 1.214120I
b = −0.415052 + 0.487887I
−1.33365 + 4.85950I −12.45920 − 5.77046I
u = −0.315716 + 0.809370I
a = 0.33853 − 2.31494I
b = 0.75319 − 1.86800I
−0.85756 − 7.78163I −4.85194 + 4.83472I
u = −0.315716 − 0.809370I
a = 0.33853 + 2.31494I
b = 0.75319 + 1.86800I
−0.85756 + 7.78163I −4.85194 − 4.83472I
u = 1.085000 + 0.487361I
a = 0.851652 − 0.459018I
b = −0.280563 + 0.198174I
−1.84490 − 4.33375I −10.12719 + 4.87141I
u = 1.085000 − 0.487361I
a = 0.851652 + 0.459018I
b = −0.280563 − 0.198174I
−1.84490 + 4.33375I −10.12719 − 4.87141I
u = −0.756777 + 0.219796I
a = −0.947046 − 0.628257I
b = −0.293717 + 0.337217I
−0.610616 + 0.203500I −9.13505 + 0.22341I
u = −0.756777 − 0.219796I
a = −0.947046 + 0.628257I
b = −0.293717 − 0.337217I
−0.610616 − 0.203500I −9.13505 − 0.22341I
u = 1.170110 + 0.334879I
a = 1.225630 + 0.246296I
b = 0.357167 − 1.279390I
−6.89501 − 3.48528I −12.35004 + 3.84640I
u = 1.170110 − 0.334879I
a = 1.225630 − 0.246296I
b = 0.357167 + 1.279390I
−6.89501 + 3.48528I −12.35004 − 3.84640I
9
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.100620 + 0.522247I
a = 0.139238 + 0.659699I
b = −0.444574 − 0.623609I
−1.15502 + 9.82269I −8.18318 − 9.91604I
u = −1.100620 − 0.522247I
a = 0.139238 − 0.659699I
b = −0.444574 + 0.623609I
−1.15502 − 9.82269I −8.18318 + 9.91604I
u = −0.192309 + 0.742887I
a = −1.22926 − 1.35826I
b = −0.334849 − 1.104320I
−2.86629 − 0.02006I −7.67881 − 0.81568I
u = −0.192309 − 0.742887I
a = −1.22926 + 1.35826I
b = −0.334849 + 1.104320I
−2.86629 + 0.02006I −7.67881 + 0.81568I
u = −0.516542 + 0.554919I
a = −0.458840 + 0.974457I
b = 0.630180 + 0.307536I
1.74238 + 4.07387I −2.10471 − 4.89426I
u = −0.516542 − 0.554919I
a = −0.458840 − 0.974457I
b = 0.630180 − 0.307536I
1.74238 − 4.07387I −2.10471 + 4.89426I
u = −1.210320 + 0.293868I
a = 1.282240 + 0.074124I
b = 0.16762 + 2.00067I
−10.16720 − 1.16183I −15.8009 + 0.1079I
u = −1.210320 − 0.293868I
a = 1.282240 − 0.074124I
b = 0.16762 − 2.00067I
−10.16720 + 1.16183I −15.8009 − 0.1079I
u = 0.439637 + 0.612670I
a = 0.066881 − 0.351296I
b = 0.791483 + 0.085996I
2.85828 + 0.77209I 0.169658 − 0.914191I
u = 0.439637 − 0.612670I
a = 0.066881 + 0.351296I
b = 0.791483 − 0.085996I
2.85828 − 0.77209I 0.169658 + 0.914191I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.148140 + 0.576039I
a = −1.58681 + 0.02147I
b = −0.67603 − 1.92774I
−3.32912 + 12.94620I −7.81680 − 8.29853I
u = −1.148140 − 0.576039I
a = −1.58681 − 0.02147I
b = −0.67603 + 1.92774I
−3.32912 − 12.94620I −7.81680 + 8.29853I
u = 1.173300 + 0.546469I
a = −0.858733 + 0.794056I
b = 0.24514 + 1.86122I
−8.44001 − 9.78226I −13.6619 + 6.4188I
u = 1.173300 − 0.546469I
a = −0.858733 − 0.794056I
b = 0.24514 − 1.86122I
−8.44001 + 9.78226I −13.6619 − 6.4188I
11
III.
I
u
3
= hu
23
−5u
21
+· · ·+2b−u, 2u
23
+u
22
+· · ·+2a+1, u
24
+u
23
+· · ·+2u+1i
(i) Arc colorings
a
4
=
0
u
a
10
=
1
0
a
9
=
1
−u
2
a
1
=
−u
23
−
1
2
u
22
+ ··· +
3
2
u −
1
2
−
1
2
u
23
+
5
2
u
21
+ ··· −
1
2
u
2
+
1
2
u
a
3
=
u
−u
3
+ u
a
2
=
−u
23
−
1
2
u
22
+ ··· +
3
2
u −
1
2
−
1
2
u
23
+
5
2
u
21
+ ··· −
1
2
u
2
+
1
2
u
a
8
=
−u
2
+ 1
−u
2
a
5
=
u
5
− 2u
3
+ u
u
5
− u
3
+ u
a
7
=
1
2
u
23
−
1
2
u
22
+ ··· + u +
3
2
−
1
2
u
22
+
5
2
u
20
+ ··· −
1
2
u −
1
2
a
6
=
−
1
2
u
22
+
5
2
u
20
+ ··· −
1
2
u +
1
2
−
1
2
u
23
+
7
2
u
21
+ ··· −
3
2
u − 1
a
12
=
−
3
2
u
23
−
1
2
u
22
+ ··· + u −
1
2
−
1
2
u
23
+
5
2
u
21
+ ··· −
1
2
u
2
+
1
2
u
a
11
=
5
2
u
23
+
1
2
u
22
+ ··· + u +
1
2
1
2
u
23
+
1
2
u
22
+ ··· − u −
3
2
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −2u
23
+ 16u
21
+ 2u
20
−60u
19
−14u
18
+ 132u
17
+ 50u
16
−176u
15
−108u
14
+ 124u
13
+
152u
12
−4u
11
−134u
10
−68u
9
+ 66u
8
+ 50u
7
−8u
6
−16u
5
−2u
4
+ 12u
3
+ 2u
2
−8u −12
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
u
24
+ 13u
23
+ ··· + 4u + 1
c
2
, c
3
, c
6
c
9
u
24
+ u
23
+ ··· + 2u + 1
c
4
, c
7
u
24
+ 3u
23
+ ··· + 8u + 3
c
5
, c
11
u
24
− 4u
23
+ ··· − 12u + 4
c
10
u
24
+ 10u
23
+ ··· + 24u + 16
c
12
u
24
− 12u
23
+ ··· − 1436u + 276
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
24
− y
23
+ ··· + 4y + 1
c
2
, c
3
, c
6
c
9
y
24
− 13y
23
+ ··· − 4y + 1
c
4
, c
7
y
24
+ 15y
23
+ ··· − 46y + 9
c
5
, c
11
y
24
− 10y
23
+ ··· − 24y + 16
c
10
y
24
+ 6y
23
+ ··· + 1248y + 256
c
12
y
24
− 2y
23
+ ··· + 176264y + 76176
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.872385 + 0.264900I
a = 0.93475 − 1.40984I
b = −1.23505 − 1.13274I
−1.33365 − 4.85950I −12.45920 + 5.77046I
u = 0.872385 − 0.264900I
a = 0.93475 + 1.40984I
b = −1.23505 + 1.13274I
−1.33365 + 4.85950I −12.45920 − 5.77046I
u = −0.315716 + 0.809370I
a = −0.14253 + 1.46556I
b = −0.65497 + 1.39733I
−0.85756 − 7.78163I −4.85194 + 4.83472I
u = −0.315716 − 0.809370I
a = −0.14253 − 1.46556I
b = −0.65497 − 1.39733I
−0.85756 + 7.78163I −4.85194 − 4.83472I
u = 1.085000 + 0.487361I
a = −2.54924 − 0.76910I
b = −2.05211 + 2.16225I
−1.84490 − 4.33375I −10.12719 + 4.87141I
u = 1.085000 − 0.487361I
a = −2.54924 + 0.76910I
b = −2.05211 − 2.16225I
−1.84490 + 4.33375I −10.12719 − 4.87141I
u = −0.756777 + 0.219796I
a = −1.34088 − 0.49415I
b = 0.283448 − 0.900890I
−0.610616 + 0.203500I −9.13505 + 0.22341I
u = −0.756777 − 0.219796I
a = −1.34088 + 0.49415I
b = 0.283448 + 0.900890I
−0.610616 − 0.203500I −9.13505 − 0.22341I
u = 1.170110 + 0.334879I
a = −1.27442 − 0.69688I
b = −1.38871 + 0.84297I
−6.89501 − 3.48528I −12.35004 + 3.84640I
u = 1.170110 − 0.334879I
a = −1.27442 + 0.69688I
b = −1.38871 − 0.84297I
−6.89501 + 3.48528I −12.35004 − 3.84640I
15
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.100620 + 0.522247I
a = 2.57917 − 0.35492I
b = 1.66695 + 2.42094I
−1.15502 + 9.82269I −8.18318 − 9.91604I
u = −1.100620 − 0.522247I
a = 2.57917 + 0.35492I
b = 1.66695 − 2.42094I
−1.15502 − 9.82269I −8.18318 + 9.91604I
u = −0.192309 + 0.742887I
a = −0.145590 + 1.310270I
b = −0.402626 + 1.200440I
−2.86629 − 0.02006I −7.67881 − 0.81568I
u = −0.192309 − 0.742887I
a = −0.145590 − 1.310270I
b = −0.402626 − 1.200440I
−2.86629 + 0.02006I −7.67881 + 0.81568I
u = −0.516542 + 0.554919I
a = −0.97555 + 1.63616I
b = −1.43709 + 0.58926I
1.74238 + 4.07387I −2.10471 − 4.89426I
u = −0.516542 − 0.554919I
a = −0.97555 − 1.63616I
b = −1.43709 − 0.58926I
1.74238 − 4.07387I −2.10471 + 4.89426I
u = −1.210320 + 0.293868I
a = 1.131960 − 0.521366I
b = 1.152730 + 0.708697I
−10.16720 − 1.16183I −15.8009 + 0.1079I
u = −1.210320 − 0.293868I
a = 1.131960 + 0.521366I
b = 1.152730 − 0.708697I
−10.16720 + 1.16183I −15.8009 − 0.1079I
u = 0.439637 + 0.612670I
a = 0.61309 + 1.54085I
b = 1.11515 + 0.87846I
2.85828 + 0.77209I 0.169658 − 0.914191I
u = 0.439637 − 0.612670I
a = 0.61309 − 1.54085I
b = 1.11515 − 0.87846I
2.85828 − 0.77209I 0.169658 + 0.914191I
16
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.148140 + 0.576039I
a = 2.26759 + 0.13614I
b = 0.99891 + 2.42525I
−3.32912 + 12.94620I −7.81680 − 8.29853I
u = −1.148140 − 0.576039I
a = 2.26759 − 0.13614I
b = 0.99891 − 2.42525I
−3.32912 − 12.94620I −7.81680 + 8.29853I
u = 1.173300 + 0.546469I
a = −2.09835 − 0.02884I
b = −1.04662 + 2.14658I
−8.44001 − 9.78226I −13.6619 + 6.4188I
u = 1.173300 − 0.546469I
a = −2.09835 + 0.02884I
b = −1.04662 − 2.14658I
−8.44001 + 9.78226I −13.6619 − 6.4188I
17
IV. I
u
4
= h−9u
23
+ 30u
22
+ · · · + 4b + 26, u
23
− 10u
22
+ · · · + 8a − 34, u
24
−
4u
23
+ · · · − 12u + 4i
(i) Arc colorings
a
4
=
0
u
a
10
=
1
0
a
9
=
1
−u
2
a
1
=
−
1
8
u
23
+
5
4
u
22
+ ··· −
41
8
u +
17
4
9
4
u
23
−
15
2
u
22
+ ··· +
81
4
u −
13
2
a
3
=
u
−u
3
+ u
a
2
=
−0.625000u
23
+ 5.25000u
22
+ ··· − 22.6250u + 15.2500
−
9
4
u
23
+
15
2
u
22
+ ··· −
93
4
u +
25
2
a
8
=
−u
2
+ 1
−u
2
a
5
=
u
5
− 2u
3
+ u
u
5
− u
3
+ u
a
7
=
9
8
u
23
−
15
4
u
22
+ ··· +
61
8
u −
7
4
5
4
u
23
−
7
2
u
22
+ ··· +
25
4
u −
3
2
a
6
=
49
8
u
23
−
77
4
u
22
+ ··· +
369
8
u −
57
4
15
4
u
23
−
21
2
u
22
+ ··· +
83
4
u −
7
2
a
12
=
3
8
u
23
−
19
4
u
22
+ ··· +
203
8
u −
67
4
11
4
u
23
−
21
2
u
22
+ ··· +
131
4
u −
31
2
a
11
=
−
3
8
u
23
+
5
4
u
22
+ ··· −
55
8
u +
21
4
−
1
4
u
23
+
1
2
u
22
+ ··· −
9
4
u +
3
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
23
− 20u
22
+ 12u
21
+ 78u
20
− 128u
19
− 88u
18
+ 340u
17
−
98u
16
−440u
15
+ 420u
14
+ 232u
13
−598u
12
+ 174u
11
+ 404u
10
−406u
9
−36u
8
+ 290u
7
−
156u
6
− 76u
5
+ 126u
4
− 26u
3
− 58u
2
+ 56u − 18
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
24
+ 13u
23
+ ··· + 4u + 1
c
2
, c
5
, c
6
c
11
u
24
+ u
23
+ ··· + 2u + 1
c
3
, c
9
u
24
− 4u
23
+ ··· − 12u + 4
c
4
u
24
− 12u
23
+ ··· − 1436u + 276
c
7
, c
12
u
24
+ 3u
23
+ ··· + 8u + 3
c
8
u
24
+ 10u
23
+ ··· + 24u + 16
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
24
− y
23
+ ··· + 4y + 1
c
2
, c
5
, c
6
c
11
y
24
− 13y
23
+ ··· − 4y + 1
c
3
, c
9
y
24
− 10y
23
+ ··· − 24y + 16
c
4
y
24
− 2y
23
+ ··· + 176264y + 76176
c
7
, c
12
y
24
+ 15y
23
+ ··· − 46y + 9
c
8
y
24
+ 6y
23
+ ··· + 1248y + 256
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.698657 + 0.763262I
a = 0.140948 + 0.781183I
b = −0.444574 + 0.623609I
−1.15502 − 9.82269I −8.18318 + 9.91604I
u = 0.698657 − 0.763262I
a = 0.140948 − 0.781183I
b = −0.444574 − 0.623609I
−1.15502 + 9.82269I −8.18318 − 9.91604I
u = 0.326549 + 0.852618I
a = −0.25129 − 2.21854I
b = −0.67603 − 1.92774I
−3.32912 + 12.94620I −7.81680 − 8.29853I
u = 0.326549 − 0.852618I
a = −0.25129 + 2.21854I
b = −0.67603 + 1.92774I
−3.32912 − 12.94620I −7.81680 + 8.29853I
u = −0.926567 + 0.601992I
a = −0.021753 + 1.036510I
b = −0.415052 + 0.487887I
−1.33365 + 4.85950I −12.45920 − 5.77046I
u = −0.926567 − 0.601992I
a = −0.021753 − 1.036510I
b = −0.415052 − 0.487887I
−1.33365 − 4.85950I −12.45920 + 5.77046I
u = 0.601776 + 0.655258I
a = 0.279930 − 0.116255I
b = 0.791483 − 0.085996I
2.85828 − 0.77209I 0.169658 + 0.914191I
u = 0.601776 − 0.655258I
a = 0.279930 + 0.116255I
b = 0.791483 + 0.085996I
2.85828 + 0.77209I 0.169658 − 0.914191I
u = −0.678263 + 0.539058I
a = −0.964344 − 0.372340I
b = −0.293717 − 0.337217I
−0.610616 − 0.203500I −9.13505 − 0.22341I
u = −0.678263 − 0.539058I
a = −0.964344 + 0.372340I
b = −0.293717 + 0.337217I
−0.610616 + 0.203500I −9.13505 + 0.22341I
21
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.980297 + 0.588649I
a = 0.113521 + 0.705035I
b = 0.630180 − 0.307536I
1.74238 − 4.07387I −2.10471 + 4.89426I
u = 0.980297 − 0.588649I
a = 0.113521 − 0.705035I
b = 0.630180 + 0.307536I
1.74238 + 4.07387I −2.10471 − 4.89426I
u = −1.121890 + 0.265387I
a = −1.181480 + 0.301677I
b = −0.334849 − 1.104320I
−2.86629 − 0.02006I −7.67881 − 0.81568I
u = −1.121890 − 0.265387I
a = −1.181480 − 0.301677I
b = −0.334849 + 1.104320I
−2.86629 + 0.02006I −7.67881 + 0.81568I
u = 0.931338 + 0.696367I
a = 0.833175 − 0.533883I
b = −0.280563 − 0.198174I
−1.84490 + 4.33375I −10.12719 − 4.87141I
u = 0.931338 − 0.696367I
a = 0.833175 + 0.533883I
b = −0.280563 + 0.198174I
−1.84490 − 4.33375I −10.12719 + 4.87141I
u = 0.085720 + 0.808442I
a = 1.02986 − 1.56270I
b = 0.357167 − 1.279390I
−6.89501 − 3.48528I −12.35004 + 3.84640I
u = 0.085720 − 0.808442I
a = 1.02986 + 1.56270I
b = 0.357167 + 1.279390I
−6.89501 + 3.48528I −12.35004 − 3.84640I
u = −1.215740 + 0.207825I
a = 1.215180 − 0.172607I
b = 0.24514 + 1.86122I
−8.44001 − 9.78226I −13.6619 + 6.4188I
u = −1.215740 − 0.207825I
a = 1.215180 + 0.172607I
b = 0.24514 − 1.86122I
−8.44001 + 9.78226I −13.6619 − 6.4188I
22
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.129130 + 0.560846I
a = 1.60964 + 0.09043I
b = 0.75319 − 1.86800I
−0.85756 − 7.78163I −4.85194 + 4.83472I
u = 1.129130 − 0.560846I
a = 1.60964 − 0.09043I
b = 0.75319 + 1.86800I
−0.85756 + 7.78163I −4.85194 − 4.83472I
u = 1.189000 + 0.481105I
a = −1.053390 + 0.667687I
b = 0.16762 + 2.00067I
−10.16720 − 1.16183I −15.8009 + 0.1079I
u = 1.189000 − 0.481105I
a = −1.053390 − 0.667687I
b = 0.16762 − 2.00067I
−10.16720 + 1.16183I −15.8009 − 0.1079I
23
V. I
u
5
= h−u
2
+ b, −u
3
− u
2
+ a + 1, u
4
− u
2
+ 1i
(i) Arc colorings
a
4
=
0
u
a
10
=
1
0
a
9
=
1
−u
2
a
1
=
u
3
+ u
2
− 1
u
2
a
3
=
u
−u
3
+ u
a
2
=
2u
3
+ u
2
− 1
u
2
+ u
a
8
=
−u
2
+ 1
−u
2
a
5
=
−u
3
0
a
7
=
−u
3
− 2u
2
+ 1
−u
2
− u
a
6
=
−u − 1
u
3
− u
a
12
=
u
3
+ 2u
2
− 1
u
2
a
11
=
u
3
+ u
2
− u − 1
u
2
− 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 12u
2
− 12
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
, c
10
(u
2
− u + 1)
2
c
2
, c
3
, c
4
c
5
, c
6
, c
7
c
9
, c
11
, c
12
u
4
− u
2
+ 1
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
, c
10
(y
2
+ y + 1)
2
c
2
, c
3
, c
4
c
5
, c
6
, c
7
c
9
, c
11
, c
12
(y
2
− y + 1)
2
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.866025 + 0.500000I
a = −0.50000 + 1.86603I
b = 0.500000 + 0.866025I
− 6.08965I −6.00000 + 10.39230I
u = 0.866025 − 0.500000I
a = −0.50000 − 1.86603I
b = 0.500000 − 0.866025I
6.08965I −6.00000 − 10.39230I
u = −0.866025 + 0.500000I
a = −0.500000 + 0.133975I
b = 0.500000 − 0.866025I
6.08965I −6.00000 − 10.39230I
u = −0.866025 − 0.500000I
a = −0.500000 − 0.133975I
b = 0.500000 + 0.866025I
− 6.08965I −6.00000 + 10.39230I
27
VI. I
u
6
=
h3u
23
a+2u
23
+· · ·+2a+8, 8u
23
a+2u
22
a+· · ·+6a+4, u
24
+u
23
+· · ·+2u
3
+1i
(i) Arc colorings
a
4
=
0
u
a
10
=
1
0
a
9
=
1
−u
2
a
1
=
a
−
3
4
u
23
a −
1
2
u
23
+ ··· −
1
2
a − 2
a
3
=
u
−u
3
+ u
a
2
=
1
2
u
22
a −
3
2
u
23
+ ··· +
3
2
a −
1
2
1
4
u
22
a +
3
2
u
23
+ ··· +
1
2
a −
1
2
u
a
8
=
−u
2
+ 1
−u
2
a
5
=
u
5
− 2u
3
+ u
u
5
− u
3
+ u
a
7
=
u
23
a + 2u
23
+ ··· −
3
4
u +
7
4
−
3
2
u
23
a −
1
2
u
23
+ ··· −
3
2
a +
3
4
u
a
6
=
3
2
u
23
a + 4u
23
+ ··· +
3
2
a +
7
2
3
4
u
23
a + u
23
+ ··· − u
2
−
1
2
u
a
12
=
−
3
4
u
22
a − 2u
23
+ ··· + u −
3
2
−
1
2
u
23
a +
1
2
u
23
+ ··· −
3
4
a − 1
a
11
=
1
2
u
23
a + u
23
+ ··· +
3
2
a −
3
4
3
2
u
23
a +
1
2
u
23
+ ··· +
3
2
a +
1
2
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 4u
23
+ 2u
22
−20u
21
−12u
20
+ 52u
19
+ 32u
18
−86u
17
−52u
16
+ 102u
15
+ 54u
14
−92u
13
−
30u
12
+ 70u
11
− 4u
10
− 52u
9
+ 30u
8
+ 38u
7
− 26u
6
− 26u
5
+ 14u
4
+ 8u
3
− 2u
2
− 4u − 2
28
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
, c
10
(u
24
+ 11u
23
+ ··· + 10u
2
+ 1)
2
c
2
, c
3
, c
5
c
6
, c
9
, c
11
(u
24
+ u
23
+ ··· + 2u
3
+ 1)
2
c
4
, c
7
, c
12
(u
24
+ 3u
23
+ ··· + 24u + 16)
2
29
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
, c
10
(y
24
+ 5y
23
+ ··· + 20y + 1)
2
c
2
, c
3
, c
5
c
6
, c
9
, c
11
(y
24
− 11y
23
+ ··· + 10y
2
+ 1)
2
c
4
, c
7
, c
12
(y
24
+ y
23
+ ··· + 1248y + 256)
2
30
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = −0.673584 + 0.693562I
a = −0.187427 + 0.846591I
b = 0.437063 + 0.503858I
1.08130 + 5.29622I −3.89211 − 6.28296I
u = −0.673584 + 0.693562I
a = −0.291150 + 0.030306I
b = −0.835137 − 0.166242I
1.08130 + 5.29622I −3.89211 − 6.28296I
u = −0.673584 − 0.693562I
a = −0.187427 − 0.846591I
b = 0.437063 − 0.503858I
1.08130 − 5.29622I −3.89211 + 6.28296I
u = −0.673584 − 0.693562I
a = −0.291150 − 0.030306I
b = −0.835137 + 0.166242I
1.08130 − 5.29622I −3.89211 + 6.28296I
u = 0.813349 + 0.704643I
a = 0.876273 − 0.562837I
b = −0.149388 − 0.336857I
−2.35506 − 2.67607I −11.61139 + 3.32415I
u = 0.813349 + 0.704643I
a = 0.039587 + 0.868673I
b = −0.189251 + 0.635297I
−2.35506 − 2.67607I −11.61139 + 3.32415I
u = 0.813349 − 0.704643I
a = 0.876273 + 0.562837I
b = −0.149388 + 0.336857I
−2.35506 + 2.67607I −11.61139 − 3.32415I
u = 0.813349 − 0.704643I
a = 0.039587 − 0.868673I
b = −0.189251 − 0.635297I
−2.35506 + 2.67607I −11.61139 − 3.32415I
u = −0.928673 + 0.614578I
a = −0.849267 − 0.512377I
b = 0.195140 − 0.099707I
0.328380 − 0.252703I −5.61015 + 0.96511I
u = −0.928673 + 0.614578I
a = −0.293437 + 0.612548I
b = −0.793906 − 0.293423I
0.328380 − 0.252703I −5.61015 + 0.96511I
31
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = −0.928673 − 0.614578I
a = −0.849267 + 0.512377I
b = 0.195140 + 0.099707I
0.328380 + 0.252703I −5.61015 − 0.96511I
u = −0.928673 − 0.614578I
a = −0.293437 − 0.612548I
b = −0.793906 + 0.293423I
0.328380 + 0.252703I −5.61015 − 0.96511I
u = 1.059150 + 0.358290I
a = 0.894053 − 0.453200I
b = −0.149388 + 0.336857I
−2.35506 + 2.67607I −11.61139 − 3.32415I
u = 1.059150 + 0.358290I
a = −2.07144 + 0.44659I
b = −0.23092 + 2.60789I
−2.35506 + 2.67607I −11.61139 − 3.32415I
u = 1.059150 − 0.358290I
a = 0.894053 + 0.453200I
b = −0.149388 − 0.336857I
−2.35506 − 2.67607I −11.61139 + 3.32415I
u = 1.059150 − 0.358290I
a = −2.07144 − 0.44659I
b = −0.23092 − 2.60789I
−2.35506 − 2.67607I −11.61139 + 3.32415I
u = −1.001220 + 0.511096I
a = −0.855740 − 0.482886I
b = 0.195140 + 0.099707I
0.328380 + 0.252703I −5.61015 − 0.96511I
u = −1.001220 + 0.511096I
a = −1.54622 + 0.71600I
b = −1.34179 − 1.21490I
0.328380 + 0.252703I −5.61015 − 0.96511I
u = −1.001220 − 0.511096I
a = −0.855740 + 0.482886I
b = 0.195140 − 0.099707I
0.328380 − 0.252703I −5.61015 + 0.96511I
u = −1.001220 − 0.511096I
a = −1.54622 − 0.71600I
b = −1.34179 + 1.21490I
0.328380 − 0.252703I −5.61015 + 0.96511I
32
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = −1.065560 + 0.419774I
a = 0.236066 + 0.782241I
b = −0.189251 − 0.635297I
−2.35506 + 2.67607I −11.61139 − 3.32415I
u = −1.065560 + 0.419774I
a = 1.82622 + 0.97204I
b = −0.23092 + 2.60789I
−2.35506 + 2.67607I −11.61139 − 3.32415I
u = −1.065560 − 0.419774I
a = 0.236066 − 0.782241I
b = −0.189251 + 0.635297I
−2.35506 − 2.67607I −11.61139 + 3.32415I
u = −1.065560 − 0.419774I
a = 1.82622 − 0.97204I
b = −0.23092 − 2.60789I
−2.35506 − 2.67607I −11.61139 + 3.32415I
u = 0.228351 + 0.822417I
a = 1.06886 − 1.26863I
b = 0.218871 − 1.132270I
−5.63436 + 4.73566I −10.88636 − 2.91588I
u = 0.228351 + 0.822417I
a = −0.52699 − 2.14743I
b = −0.64283 − 1.72007I
−5.63436 + 4.73566I −10.88636 − 2.91588I
u = 0.228351 − 0.822417I
a = 1.06886 + 1.26863I
b = 0.218871 + 1.132270I
−5.63436 − 4.73566I −10.88636 + 2.91588I
u = 0.228351 − 0.822417I
a = −0.52699 + 2.14743I
b = −0.64283 + 1.72007I
−5.63436 − 4.73566I −10.88636 + 2.91588I
u = 1.051290 + 0.529712I
a = −0.081995 + 0.707393I
b = 0.437063 − 0.503858I
1.08130 − 5.29622I −3.89211 + 6.28296I
u = 1.051290 + 0.529712I
a = 1.68869 + 0.41227I
b = 1.12931 − 1.61414I
1.08130 − 5.29622I −3.89211 + 6.28296I
33
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 1.051290 − 0.529712I
a = −0.081995 − 0.707393I
b = 0.437063 + 0.503858I
1.08130 + 5.29622I −3.89211 − 6.28296I
u = 1.051290 − 0.529712I
a = 1.68869 − 0.41227I
b = 1.12931 + 1.61414I
1.08130 + 5.29622I −3.89211 − 6.28296I
u = 1.177390 + 0.234520I
a = 1.147630 + 0.271970I
b = 0.218871 − 1.132270I
−5.63436 + 4.73566I −10.88636 − 2.91588I
u = 1.177390 + 0.234520I
a = −1.353580 − 0.137275I
b = −0.29717 + 1.94311I
−5.63436 + 4.73566I −10.88636 − 2.91588I
u = 1.177390 − 0.234520I
a = 1.147630 − 0.271970I
b = 0.218871 + 1.132270I
−5.63436 − 4.73566I −10.88636 + 2.91588I
u = 1.177390 − 0.234520I
a = −1.353580 + 0.137275I
b = −0.29717 − 1.94311I
−5.63436 − 4.73566I −10.88636 + 2.91588I
u = −1.152400 + 0.519393I
a = 0.970487 + 0.853116I
b = −0.29717 + 1.94311I
−5.63436 + 4.73566I −10.88636 − 2.91588I
u = −1.152400 + 0.519393I
a = −1.48727 + 0.13129I
b = −0.64283 − 1.72007I
−5.63436 + 4.73566I −10.88636 − 2.91588I
u = −1.152400 − 0.519393I
a = 0.970487 − 0.853116I
b = −0.29717 − 1.94311I
−5.63436 − 4.73566I −10.88636 + 2.91588I
u = −1.152400 − 0.519393I
a = −1.48727 − 0.13129I
b = −0.64283 + 1.72007I
−5.63436 − 4.73566I −10.88636 + 2.91588I
34
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = −0.320890 + 0.627041I
a = 0.167757 − 0.365090I
b = −0.835137 + 0.166242I
1.08130 − 5.29622I −3.89211 + 6.28296I
u = −0.320890 + 0.627041I
a = 0.67130 − 2.82650I
b = 1.12931 − 1.61414I
1.08130 − 5.29622I −3.89211 + 6.28296I
u = −0.320890 − 0.627041I
a = 0.167757 + 0.365090I
b = −0.835137 − 0.166242I
1.08130 + 5.29622I −3.89211 − 6.28296I
u = −0.320890 − 0.627041I
a = 0.67130 + 2.82650I
b = 1.12931 + 1.61414I
1.08130 + 5.29622I −3.89211 − 6.28296I
u = 0.312794 + 0.462406I
a = 1.007250 + 0.906155I
b = −0.793906 + 0.293423I
0.328380 + 0.252703I −5.61015 − 0.96511I
u = 0.312794 + 0.462406I
a = −1.04965 − 3.26660I
b = −1.34179 − 1.21490I
0.328380 + 0.252703I −5.61015 − 0.96511I
u = 0.312794 − 0.462406I
a = 1.007250 − 0.906155I
b = −0.793906 − 0.293423I
0.328380 − 0.252703I −5.61015 + 0.96511I
u = 0.312794 − 0.462406I
a = −1.04965 + 3.26660I
b = −1.34179 + 1.21490I
0.328380 − 0.252703I −5.61015 + 0.96511I
35
VII. I
u
7
= h−u
2
+ b, u
3
− u
2
+ a − u + 1, u
4
− u
2
+ 1i
(i) Arc colorings
a
4
=
0
u
a
10
=
1
0
a
9
=
1
−u
2
a
1
=
−u
3
+ u
2
+ u − 1
u
2
a
3
=
u
−u
3
+ u
a
2
=
−2u
3
+ u
2
+ 2u − 1
−u
3
+ u
2
a
8
=
−u
2
+ 1
−u
2
a
5
=
−u
3
0
a
7
=
u
3
− u
2
− u + 2
u
3
− u
2
a
6
=
u
2
− u
u
3
− u
a
12
=
−u
3
+ 2u
2
+ u − 1
u
2
a
11
=
u
2
+ u − 1
u
2
− 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
2
− 8
36
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
, c
10
(u
2
− u + 1)
2
c
2
, c
3
, c
4
c
5
, c
6
, c
7
c
9
, c
11
, c
12
u
4
− u
2
+ 1
37
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
, c
10
(y
2
+ y + 1)
2
c
2
, c
3
, c
4
c
5
, c
6
, c
7
c
9
, c
11
, c
12
(y
2
− y + 1)
2
38
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = 0.866025 + 0.500000I
a = 0.366025 + 0.366025I
b = 0.500000 + 0.866025I
− 2.02988I −6.00000 + 3.46410I
u = 0.866025 − 0.500000I
a = 0.366025 − 0.366025I
b = 0.500000 − 0.866025I
2.02988I −6.00000 − 3.46410I
u = −0.866025 + 0.500000I
a = −1.36603 − 1.36603I
b = 0.500000 − 0.866025I
2.02988I −6.00000 − 3.46410I
u = −0.866025 − 0.500000I
a = −1.36603 + 1.36603I
b = 0.500000 + 0.866025I
− 2.02988I −6.00000 + 3.46410I
39
VIII. I
u
8
= hu
2
+ b − 1, −u
3
+ a − 1, u
4
− u
2
+ 1i
(i) Arc colorings
a
4
=
0
u
a
10
=
1
0
a
9
=
1
−u
2
a
1
=
u
3
+ 1
−u
2
+ 1
a
3
=
u
−u
3
+ u
a
2
=
2u
3
+ 1
−u
2
+ u + 1
a
8
=
−u
2
+ 1
−u
2
a
5
=
−u
3
0
a
7
=
u
3
− 2u
2
− u + 1
u
3
− u
2
a
6
=
u
3
− 1
u
a
12
=
u
3
− u
2
+ 2
−u
2
+ 1
a
11
=
−2u
2
+ u + 2
−u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
2
− 8
40
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
, c
10
(u
2
− u + 1)
2
c
2
, c
3
, c
4
c
5
, c
6
, c
7
c
9
, c
11
, c
12
u
4
− u
2
+ 1
41
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
, c
10
(y
2
+ y + 1)
2
c
2
, c
3
, c
4
c
5
, c
6
, c
7
c
9
, c
11
, c
12
(y
2
− y + 1)
2
42
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
8
√
−1(vol +
√
−1CS) Cusp shape
u = 0.866025 + 0.500000I
a = 1.00000 + 1.00000I
b = 0.500000 − 0.866025I
− 2.02988I −6.00000 + 3.46410I
u = 0.866025 − 0.500000I
a = 1.00000 − 1.00000I
b = 0.500000 + 0.866025I
2.02988I −6.00000 − 3.46410I
u = −0.866025 + 0.500000I
a = 1.00000 + 1.00000I
b = 0.500000 + 0.866025I
2.02988I −6.00000 − 3.46410I
u = −0.866025 − 0.500000I
a = 1.00000 − 1.00000I
b = 0.500000 − 0.866025I
− 2.02988I −6.00000 + 3.46410I
43
IX. I
u
9
= hu
2
+ b − 1, u
3
+ a − u − 1, u
4
− u
2
+ 1i
(i) Arc colorings
a
4
=
0
u
a
10
=
1
0
a
9
=
1
−u
2
a
1
=
−u
3
+ u + 1
−u
2
+ 1
a
3
=
u
−u
3
+ u
a
2
=
−2u
3
+ 2u + 1
−u
3
− u
2
+ 1
a
8
=
−u
2
+ 1
−u
2
a
5
=
−u
3
0
a
7
=
−u
2
+ u + 2
−u
3
− u
2
+ u
a
6
=
u
3
+ u
2
u
a
12
=
−u
3
− u
2
+ u + 2
−u
2
+ 1
a
11
=
−u
3
− 2u
2
+ 2
−u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
2
− 4
44
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
, c
10
(u
2
− u + 1)
2
c
2
, c
3
, c
4
c
5
, c
6
, c
7
c
9
, c
11
, c
12
u
4
− u
2
+ 1
45
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
, c
10
(y
2
+ y + 1)
2
c
2
, c
3
, c
4
c
5
, c
6
, c
7
c
9
, c
11
, c
12
(y
2
− y + 1)
2
46
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
9
√
−1(vol +
√
−1CS) Cusp shape
u = 0.866025 + 0.500000I
a = 1.86603 − 0.50000I
b = 0.500000 − 0.866025I
2.02988I −6.00000 − 3.46410I
u = 0.866025 − 0.500000I
a = 1.86603 + 0.50000I
b = 0.500000 + 0.866025I
− 2.02988I −6.00000 + 3.46410I
u = −0.866025 + 0.500000I
a = 0.133975 − 0.500000I
b = 0.500000 + 0.866025I
− 2.02988I −6.00000 + 3.46410I
u = −0.866025 − 0.500000I
a = 0.133975 + 0.500000I
b = 0.500000 − 0.866025I
2.02988I −6.00000 − 3.46410I
47
X. I
u
10
= hb + 1, a, u − 1i
(i) Arc colorings
a
4
=
0
1
a
10
=
1
0
a
9
=
1
−1
a
1
=
0
−1
a
3
=
1
0
a
2
=
1
−1
a
8
=
0
−1
a
5
=
0
1
a
7
=
0
−1
a
6
=
−1
0
a
12
=
0
−1
a
11
=
1
1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −18
48
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
, c
10
u + 1
c
2
, c
3
, c
5
c
6
, c
9
, c
11
u − 1
c
4
, c
7
, c
12
u
49
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
5
, c
6
, c
8
c
9
, c
10
, c
11
y − 1
c
4
, c
7
, c
12
y
50
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
10
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0
b = −1.00000
−4.93480 −18.0000
51
XI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
8
, c
10
(u + 1)(u
2
− u + 1)
8
(u
7
+ 4u
6
+ 8u
5
+ 7u
4
+ 2u
3
− u
2
+ 3u + 1)
· (u
24
+ 10u
23
+ ··· + 24u + 16)(u
24
+ 11u
23
+ ··· + 10u
2
+ 1)
2
· (u
24
+ 13u
23
+ ··· + 4u + 1)
2
c
2
, c
3
, c
5
c
6
, c
9
, c
11
(u − 1)(u
4
− u
2
+ 1)
4
(u
7
− 2u
5
+ u
4
+ 2u
3
− u
2
+ u + 1)
· (u
24
− 4u
23
+ ··· − 12u + 4)(u
24
+ u
23
+ ··· + 2u + 1)
2
· (u
24
+ u
23
+ ··· + 2u
3
+ 1)
2
c
4
, c
7
, c
12
u(u
4
− u
2
+ 1)
4
(u
7
− 3u
6
+ 8u
5
− 10u
4
+ 12u
3
− 6u
2
+ 3u + 3)
· (u
24
− 12u
23
+ ··· − 1436u + 276)(u
24
+ 3u
23
+ ··· + 24u + 16)
2
· (u
24
+ 3u
23
+ ··· + 8u + 3)
2
52
XII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
8
, c
10
(y − 1)(y
2
+ y + 1)
8
(y
7
+ 12y
5
− 3y
4
+ 58y
3
− 3y
2
+ 11y − 1)
· ((y
24
− y
23
+ ··· + 4y + 1)
2
)(y
24
+ 5y
23
+ ··· + 20y + 1)
2
· (y
24
+ 6y
23
+ ··· + 1248y + 256)
c
2
, c
3
, c
5
c
6
, c
9
, c
11
(y − 1)(y
2
− y + 1)
8
(y
7
− 4y
6
+ 8y
5
− 7y
4
+ 2y
3
+ y
2
+ 3y − 1)
· ((y
24
− 13y
23
+ ··· − 4y + 1)
2
)(y
24
− 11y
23
+ ··· + 10y
2
+ 1)
2
· (y
24
− 10y
23
+ ··· − 24y + 16)
c
4
, c
7
, c
12
y(y
2
− y + 1)
8
(y
7
+ 7y
6
+ 28y
5
+ 62y
4
+ 90y
3
+ 96y
2
+ 45y − 9)
· (y
24
− 2y
23
+ ··· + 176264y + 76176)
· ((y
24
+ y
23
+ ··· + 1248y + 256)
2
)(y
24
+ 15y
23
+ ··· − 46y + 9)
2
53
