12n
0831
(K12n
0831
)
A knot diagram
1
Linearized knot diagam
4 6 12 8 2 10 1 5 6 7 3 7
Solving Sequence
7,12 1,4
2 8 5 3 11 10 6 9
c
12
c
1
c
7
c
4
c
3
c
11
c
10
c
6
c
9
c
2
, c
5
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h−396999u
17
− 586653u
16
+ ··· + 343642b − 1550584,
− 523933u
17
− 696379u
16
+ ··· + 343642a − 2066672, u
18
+ u
17
+ ··· + 6u − 1i
I
u
2
= h−3.98523 × 10
90
u
43
+ 1.45733 × 10
90
u
42
+ ··· + 3.76570 × 10
90
b + 3.66878 × 10
91
,
3.76232 × 10
91
u
43
− 6.44638 × 10
90
u
42
+ ··· + 5.27198 × 10
90
a − 6.67170 × 10
92
,
2u
44
− 29u
42
+ ··· − 88u − 7i
I
u
3
= h−u
5
+ u
4
+ 2u
3
− 3u
2
+ 2b − 4u + 4, −u
5
+ 2u
4
+ u
3
− 3u
2
+ 2a − 3u + 6,
u
6
− 2u
5
− u
4
+ 4u
3
+ 2u
2
− 6u + 1i
I
u
4
= hb − 1, a + 4u − 6, 2u
2
− 4u + 1i
I
u
5
= hb − 1, a
2
− 2, u + 1i
I
u
6
= hb − a + 2, 2a
2
− 4a + 1, u + 1i
I
u
7
= hb − 1, a, u − 1i
* 7 irreducible components of dim
C
= 0, with total 75 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−3.97 × 10
5
u
17
− 5.87 × 10
5
u
16
+ · · · + 3.44 × 10
5
b − 1.55 × 10
6
, −5.24 ×
10
5
u
17
− 6.96× 10
5
u
16
+ · · · + 3.44 × 10
5
a −2.07 × 10
6
, u
18
+ u
17
+ · · · + 6u − 1i
(i) Arc colorings
a
7
=
0
u
a
12
=
1
0
a
1
=
1
−u
2
a
4
=
1.52465u
17
+ 2.02647u
16
+ ··· − 13.8141u + 6.01403
1.15527u
17
+ 1.70716u
16
+ ··· − 12.3278u + 4.51221
a
2
=
−0.325219u
17
+ 0.133368u
16
+ ··· − 5.76386u + 3.29663
−1.39846u
17
− 1.87149u
16
+ ··· + 11.1270u − 3.17599
a
8
=
u
−u
3
+ u
a
5
=
1.52465u
17
+ 2.02647u
16
+ ··· − 13.8141u + 6.01403
1.15527u
17
+ 1.70716u
16
+ ··· − 12.3278u + 4.51221
a
3
=
2.67992u
17
+ 3.73363u
16
+ ··· − 26.1419u + 10.5262
1.15527u
17
+ 1.70716u
16
+ ··· − 12.3278u + 4.51221
a
11
=
1.29270u
17
+ 1.81223u
16
+ ··· − 10.6425u + 2.91863
1.04950u
17
+ 1.64790u
16
+ ··· − 11.8434u + 3.25485
a
10
=
1.29270u
17
+ 1.81223u
16
+ ··· − 10.6425u + 2.91863
0.901071u
17
+ 1.31644u
16
+ ··· − 10.0189u + 2.73532
a
6
=
−1.44262u
17
− 1.82416u
16
+ ··· + 15.3771u − 4.47443
−1.41888u
17
− 1.96720u
16
+ ··· + 13.3296u − 3.75667
a
9
=
−0.501819u
17
− 0.871197u
16
+ ··· + 2.13386u − 1.52465
−0.551894u
17
− 0.465700u
16
+ ··· + 1.41941u − 1.15527
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
2646884
171821
u
17
−
7468939
343642
u
16
+ ··· +
54604739
343642
u −
10027319
171821
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
18
− 11u
17
+ ··· + 160u − 32
c
2
, c
3
, c
5
c
11
u
18
− u
17
+ ··· − 3u
3
+ 1
c
4
, c
7
, c
8
c
12
u
18
− u
17
+ ··· − 6u − 1
c
6
, c
9
, c
10
u
18
+ 10u
17
+ ··· − 16u + 16
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
18
− 7y
17
+ ··· + 3584y + 1024
c
2
, c
3
, c
5
c
11
y
18
− 3y
17
+ ··· − 14y
2
+ 1
c
4
, c
7
, c
8
c
12
y
18
− 17y
17
+ ··· − 28y + 1
c
6
, c
9
, c
10
y
18
− 8y
17
+ ··· − 10880y + 256
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.191738 + 1.076920I
a = 0.164769 − 0.216172I
b = −0.739470 − 0.526977I
−2.66808 − 4.00314I −9.75217 + 7.89932I
u = 0.191738 − 1.076920I
a = 0.164769 + 0.216172I
b = −0.739470 + 0.526977I
−2.66808 + 4.00314I −9.75217 − 7.89932I
u = 0.856890
a = 1.85099
b = −0.508119
−3.70252 0.540670
u = −1.268520 + 0.068652I
a = −0.20738 + 1.47520I
b = −1.13159 − 0.92777I
6.81521 − 6.56774I −2.02682 + 4.35412I
u = −1.268520 − 0.068652I
a = −0.20738 − 1.47520I
b = −1.13159 + 0.92777I
6.81521 + 6.56774I −2.02682 − 4.35412I
u = 0.099241 + 0.636465I
a = 0.938741 + 0.442143I
b = 0.365623 + 0.498306I
−0.56691 − 1.59781I −4.88738 + 2.87220I
u = 0.099241 − 0.636465I
a = 0.938741 − 0.442143I
b = 0.365623 − 0.498306I
−0.56691 + 1.59781I −4.88738 − 2.87220I
u = 1.384510 + 0.061181I
a = −0.025694 + 1.290750I
b = −0.757872 − 1.174240I
9.74101 + 0.20067I 0.876554 + 0.056243I
u = 1.384510 − 0.061181I
a = −0.025694 − 1.290750I
b = −0.757872 + 1.174240I
9.74101 − 0.20067I 0.876554 − 0.056243I
u = −0.598117
a = 2.91842
b = 0.874375
−6.04349 −17.8030
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.36280 + 0.56912I
a = 0.123467 − 0.674233I
b = −0.019982 + 0.551107I
2.28034 − 2.61810I −1.94443 − 3.90509I
u = −1.36280 − 0.56912I
a = 0.123467 + 0.674233I
b = −0.019982 − 0.551107I
2.28034 + 2.61810I −1.94443 + 3.90509I
u = −1.53449 + 0.53389I
a = −0.200699 − 1.249540I
b = 1.26204 + 1.00770I
6.5797 − 16.1278I −3.35911 + 8.29974I
u = −1.53449 − 0.53389I
a = −0.200699 + 1.249540I
b = 1.26204 − 1.00770I
6.5797 + 16.1278I −3.35911 − 8.29974I
u = 1.56750 + 0.44100I
a = −0.207302 + 1.123790I
b = 0.815416 − 1.132280I
9.08495 + 8.48084I −0.38289 − 5.34256I
u = 1.56750 − 0.44100I
a = −0.207302 − 1.123790I
b = 0.815416 + 1.132280I
9.08495 − 8.48084I −0.38289 + 5.34256I
u = 0.348681
a = −0.719922
b = −1.63240
−10.4921 19.6160
u = 0.238190
a = 1.77872
b = 0.677803
−1.17090 −9.40150
6
II. I
u
2
= h−3.99 × 10
90
u
43
+ 1.46 × 10
90
u
42
+ · · · + 3.77 × 10
90
b + 3.67 ×
10
91
, 3.76 × 10
91
u
43
− 6.45 × 10
90
u
42
+ · · · + 5.27 × 10
90
a − 6.67 ×
10
92
, 2u
44
− 29u
42
+ · · · − 88u − 7i
(i) Arc colorings
a
7
=
0
u
a
12
=
1
0
a
1
=
1
−u
2
a
4
=
−7.13643u
43
+ 1.22276u
42
+ ··· + 1065.91u + 126.550
1.05830u
43
− 0.387000u
42
+ ··· − 112.988u − 9.74262
a
2
=
0.806957u
43
− 0.114485u
42
+ ··· − 142.855u − 24.2057
−0.107399u
43
− 0.0284322u
42
+ ··· + 28.3132u + 2.84251
a
8
=
u
−u
3
+ u
a
5
=
−6.86544u
43
+ 1.11246u
42
+ ··· + 1029.07u + 121.406
1.23457u
43
− 0.400196u
42
+ ··· − 145.917u − 14.5004
a
3
=
−6.07814u
43
+ 0.835762u
42
+ ··· + 952.920u + 116.808
1.05830u
43
− 0.387000u
42
+ ··· − 112.988u − 9.74262
a
11
=
−1.21508u
43
+ 0.317864u
42
+ ··· + 169.292u + 27.9292
0.208421u
43
− 0.0153784u
42
+ ··· − 37.9937u − 4.00886
a
10
=
−1.21508u
43
+ 0.317864u
42
+ ··· + 169.292u + 27.9292
0.326622u
43
− 0.0913778u
42
+ ··· − 47.7269u − 5.12139
a
6
=
0.738865u
43
− 0.0945014u
42
+ ··· − 100.491u − 22.2900
−0.0713589u
43
− 0.0325985u
42
+ ··· + 7.91982u + 0.387737
a
9
=
−1.57557u
43
+ 0.540452u
42
+ ··· + 85.6799u + 8.24586
0.457009u
43
− 0.0873987u
42
+ ··· − 54.0595u − 7.38741
(ii) Obstruction class = −1
(iii) Cusp Shapes = −1.66800u
43
+ 0.434075u
42
+ ··· + 217.610u + 37.4599
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
22
+ 7u
21
+ ··· − 6u − 2)
2
c
2
, c
3
, c
5
c
11
2(2u
44
− u
42
+ ··· − 24u + 1)
c
4
, c
7
, c
8
c
12
2(2u
44
− 29u
42
+ ··· + 88u − 7)
c
6
, c
9
, c
10
(u
22
− 4u
21
+ ··· + 2u − 2)
2
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
22
+ y
21
+ ··· + 48y + 4)
2
c
2
, c
3
, c
5
c
11
4(4y
44
− 4y
43
+ ··· − 214y + 1)
c
4
, c
7
, c
8
c
12
4(4y
44
− 116y
43
+ ··· − 4454y + 49)
c
6
, c
9
, c
10
(y
22
− 8y
21
+ ··· − 40y + 4)
2
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00768
a = 0.540189
b = 1.30858
−3.29588 −2.01200
u = −0.959621 + 0.038327I
a = 0.51386 + 2.68354I
b = −0.56442 − 2.02765I
0.186770 + 0.086750I −6.26765 + 6.36021I
u = −0.959621 − 0.038327I
a = 0.51386 − 2.68354I
b = −0.56442 + 2.02765I
0.186770 − 0.086750I −6.26765 − 6.36021I
u = 0.188755 + 0.896184I
a = 0.385957 − 0.105829I
b = 0.738143 + 0.476023I
−1.36349 − 1.79115I −8.68124 + 6.28577I
u = 0.188755 − 0.896184I
a = 0.385957 + 0.105829I
b = 0.738143 − 0.476023I
−1.36349 + 1.79115I −8.68124 − 6.28577I
u = 1.091200 + 0.395456I
a = 0.347759 + 0.568798I
b = 0.993160 − 0.453337I
−0.580514 + 1.104780I −4.00000 − 5.65044I
u = 1.091200 − 0.395456I
a = 0.347759 − 0.568798I
b = 0.993160 + 0.453337I
−0.580514 − 1.104780I −4.00000 + 5.65044I
u = −1.065490 + 0.625029I
a = −0.376962 + 1.132670I
b = −0.503539 − 0.055689I
2.05974 − 7.04859I 0
u = −1.065490 − 0.625029I
a = −0.376962 − 1.132670I
b = −0.503539 + 0.055689I
2.05974 + 7.04859I 0
u = −1.262810 + 0.021566I
a = −0.086610 + 1.327570I
b = 1.26751 − 0.99085I
7.73724 − 0.72368I 0
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.262810 − 0.021566I
a = −0.086610 − 1.327570I
b = 1.26751 + 0.99085I
7.73724 + 0.72368I 0
u = 0.693940 + 0.232041I
a = 0.33396 − 1.93120I
b = −0.287053 + 0.030616I
−1.36349 + 1.79115I −8.68124 − 6.28577I
u = 0.693940 − 0.232041I
a = 0.33396 + 1.93120I
b = −0.287053 − 0.030616I
−1.36349 − 1.79115I −8.68124 + 6.28577I
u = −1.32704
a = 1.09776
b = −0.0760743
−3.29588 0
u = 1.221150 + 0.530023I
a = 0.017428 + 1.394390I
b = 1.08731 − 1.10905I
0.55910 + 9.58499I 0
u = 1.221150 − 0.530023I
a = 0.017428 − 1.394390I
b = 1.08731 + 1.10905I
0.55910 − 9.58499I 0
u = −1.212660 + 0.590602I
a = 0.240876 − 0.883836I
b = 0.312263 + 0.853014I
1.85821 − 2.76391I 0
u = −1.212660 − 0.590602I
a = 0.240876 + 0.883836I
b = 0.312263 − 0.853014I
1.85821 + 2.76391I 0
u = 1.343550 + 0.163045I
a = −0.18872 − 1.40724I
b = 0.75925 + 1.39471I
8.21251 + 7.73197I 0
u = 1.343550 − 0.163045I
a = −0.18872 + 1.40724I
b = 0.75925 − 1.39471I
8.21251 − 7.73197I 0
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.884535 + 1.031500I
a = 0.227336 − 0.088919I
b = −0.457268 − 0.093641I
1.85821 − 2.76391I 0
u = −0.884535 − 1.031500I
a = 0.227336 + 0.088919I
b = −0.457268 + 0.093641I
1.85821 + 2.76391I 0
u = 1.271690 + 0.520977I
a = −0.16546 − 1.41673I
b = −0.930159 + 0.836061I
2.05974 + 7.04859I 0
u = 1.271690 − 0.520977I
a = −0.16546 + 1.41673I
b = −0.930159 − 0.836061I
2.05974 − 7.04859I 0
u = −0.613961 + 0.057476I
a = −0.959684 + 0.038453I
b = 1.217830 − 0.517219I
−0.580514 − 1.104780I −5.89293 + 5.65044I
u = −0.613961 − 0.057476I
a = −0.959684 − 0.038453I
b = 1.217830 + 0.517219I
−0.580514 + 1.104780I −5.89293 − 5.65044I
u = 1.346020 + 0.430624I
a = −0.093856 − 1.127210I
b = −1.105420 + 0.843659I
3.25581 + 6.25880I 0
u = 1.346020 − 0.430624I
a = −0.093856 + 1.127210I
b = −1.105420 − 0.843659I
3.25581 − 6.25880I 0
u = 0.45146 + 1.34717I
a = −0.0697853 − 0.0952976I
b = −0.924940 + 0.532455I
0.55910 + 9.58499I 0
u = 0.45146 − 1.34717I
a = −0.0697853 + 0.0952976I
b = −0.924940 − 0.532455I
0.55910 − 9.58499I 0
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.42044 + 0.15034I
a = 0.185356 + 0.976083I
b = −0.751350 − 0.962354I
4.35834 − 0.41728I 0
u = −1.42044 − 0.15034I
a = 0.185356 − 0.976083I
b = −0.751350 + 0.962354I
4.35834 + 0.41728I 0
u = 1.46909
a = −0.934519
b = 0.929346
−6.50325 0
u = 1.62269 + 0.27689I
a = 0.443344 − 1.014190I
b = −0.843009 + 1.064050I
7.73724 + 0.72368I 0
u = 1.62269 − 0.27689I
a = 0.443344 + 1.014190I
b = −0.843009 − 1.064050I
7.73724 − 0.72368I 0
u = −1.61575 + 0.49113I
a = 0.250844 + 1.051830I
b = −1.22355 − 0.90329I
8.21251 − 7.73197I 0
u = −1.61575 − 0.49113I
a = 0.250844 − 1.051830I
b = −1.22355 + 0.90329I
8.21251 + 7.73197I 0
u = −0.223680 + 0.077265I
a = 5.50128 + 1.65439I
b = −0.264264 − 0.788553I
4.35834 + 0.41728I 1.220508 + 0.567857I
u = −0.223680 − 0.077265I
a = 5.50128 − 1.65439I
b = −0.264264 + 0.788553I
4.35834 − 0.41728I 1.220508 − 0.567857I
u = 0.224841
a = 5.44634
b = −1.36290
−6.50325 −14.7860
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.179416 + 0.100194I
a = −6.69182 − 0.26567I
b = 0.206450 + 0.863665I
3.25581 − 6.25880I −1.71216 + 4.44144I
u = −0.179416 − 0.100194I
a = −6.69182 + 0.26567I
b = 0.206450 − 0.863665I
3.25581 + 6.25880I −1.71216 − 4.44144I
u = −0.47940 + 2.17394I
a = 0.181439 + 0.022852I
b = 0.873580 + 0.079126I
0.186770 − 0.086750I 0
u = −0.47940 − 2.17394I
a = 0.181439 − 0.022852I
b = 0.873580 − 0.079126I
0.186770 + 0.086750I 0
14
III. I
u
3
= h−u
5
+ u
4
+ 2u
3
− 3u
2
+ 2b − 4u + 4, −u
5
+ 2u
4
+ u
3
− 3u
2
+ 2a −
3u + 6, u
6
− 2u
5
− u
4
+ 4u
3
+ 2u
2
− 6u + 1i
(i) Arc colorings
a
7
=
0
u
a
12
=
1
0
a
1
=
1
−u
2
a
4
=
1
2
u
5
− u
4
+ ··· +
3
2
u − 3
1
2
u
5
−
1
2
u
4
− u
3
+
3
2
u
2
+ 2u − 2
a
2
=
−u
5
+ 2u
4
+ u
3
− 4u
2
− 2u + 6
−
1
2
u
5
+ u
4
+ ··· −
3
2
u + 3
a
8
=
u
−u
3
+ u
a
5
=
1
2
u
5
− u
4
+ ··· +
3
2
u − 3
1
2
u
5
−
3
2
u
4
− u
3
+
5
2
u
2
+ 2u − 2
a
3
=
u
5
−
3
2
u
4
−
3
2
u
3
+ 3u
2
+
7
2
u − 5
1
2
u
5
−
1
2
u
4
− u
3
+
3
2
u
2
+ 2u − 2
a
11
=
u
5
− 2u
4
−
3
2
u
3
+
9
2
u
2
+ 3u −
13
2
−
1
2
u
4
+
3
2
u
2
−
1
2
u −
5
2
a
10
=
u
5
− 2u
4
−
3
2
u
3
+
9
2
u
2
+ 3u −
13
2
1
2
u
5
− u
4
− u
3
+ 2u
2
+
1
2
u −
5
2
a
6
=
−
3
2
u
5
+
5
2
u
4
+ 2u
3
−
9
2
u
2
− 4u + 7
−
1
2
u
3
−
1
2
u
2
+ u +
5
2
a
9
=
−
1
2
u
3
−
1
2
u
2
+ u +
1
2
1
2
u
5
+
1
2
u
4
−
3
2
u
3
− u
2
+
1
2
(ii) Obstruction class = 1
(iii) Cusp Shapes =
17
2
u
5
− 16u
4
− 12u
3
+ 27u
2
+
55
2
u −
81
2
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
6
− u
5
+ 3u
3
− 5u
2
+ 4u − 1
c
2
, c
11
u
6
+ 2u
5
− 3u
3
− 4u
2
− 2u − 1
c
3
, c
5
u
6
− 2u
5
+ 3u
3
− 4u
2
+ 2u − 1
c
4
, c
7
u
6
+ 2u
5
− u
4
− 4u
3
+ 2u
2
+ 6u + 1
c
6
u
6
+ 3u
5
+ 3u
4
− 2u
3
− 5u
2
− 2u + 1
c
8
, c
12
u
6
− 2u
5
− u
4
+ 4u
3
+ 2u
2
− 6u + 1
c
9
, c
10
u
6
− 3u
5
+ 3u
4
+ 2u
3
− 5u
2
+ 2u + 1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
6
− y
5
− 4y
4
− 3y
3
+ y
2
− 6y + 1
c
2
, c
3
, c
5
c
11
y
6
− 4y
5
+ 4y
4
− 3y
3
+ 4y
2
+ 4y + 1
c
4
, c
7
, c
8
c
12
y
6
− 6y
5
+ 21y
4
− 42y
3
+ 50y
2
− 32y + 1
c
6
, c
9
, c
10
y
6
− 3y
5
+ 11y
4
− 20y
3
+ 23y
2
− 14y + 1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.123340 + 0.626153I
a = −0.656989 + 1.205750I
b = −0.781728 − 0.767267I
2.95967 − 8.51727I −2.49626 + 9.75541I
u = −1.123340 − 0.626153I
a = −0.656989 − 1.205750I
b = −0.781728 + 0.767267I
2.95967 + 8.51727I −2.49626 − 9.75541I
u = 1.31922
a = −0.589573
b = 1.43649
−0.237758 0.719370
u = 1.37304 + 0.80106I
a = −0.206939 − 0.540853I
b = −0.139351 + 0.586947I
2.47933 + 2.98689I 8.4923 − 12.8795I
u = 1.37304 − 0.80106I
a = −0.206939 + 0.540853I
b = −0.139351 − 0.586947I
2.47933 − 2.98689I 8.4923 + 12.8795I
u = 0.181369
a = −2.68257
b = −1.59433
−10.6403 −34.7110
18
IV. I
u
4
= hb − 1, a + 4u − 6, 2u
2
− 4u + 1i
(i) Arc colorings
a
7
=
0
u
a
12
=
1
0
a
1
=
1
−2u +
1
2
a
4
=
−4u + 6
1
a
2
=
−4u + 9
−4u +
5
2
a
8
=
u
−
5
2
u + 1
a
5
=
−5u + 6
5
2
u
a
3
=
−4u + 7
1
a
11
=
4u − 6
−1
a
10
=
4u − 6
−2u
a
6
=
−4u + 8
−3u + 2
a
9
=
−4u + 6
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
, c
9
c
10
u
2
− 2
c
2
, c
7
2(2u
2
+ 4u + 1)
c
3
, c
8
(u + 1)
2
c
4
, c
11
(u − 1)
2
c
5
, c
12
2(2u
2
− 4u + 1)
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
, c
9
c
10
(y − 2)
2
c
2
, c
5
, c
7
c
12
4(4y
2
− 12y + 1)
c
3
, c
4
, c
8
c
11
(y − 1)
2
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.292893
a = 4.82843
b = 1.00000
−4.93480 −8.00000
u = 1.70711
a = −0.828427
b = 1.00000
−4.93480 −8.00000
22
V. I
u
5
= hb − 1, a
2
− 2, u + 1i
(i) Arc colorings
a
7
=
0
−1
a
12
=
1
0
a
1
=
1
−1
a
4
=
a
1
a
2
=
a + 3
a
a
8
=
−1
0
a
5
=
a + 1
1
a
3
=
a + 1
1
a
11
=
−a
−1
a
10
=
−a
a − 1
a
6
=
−2
−a + 1
a
9
=
a
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
2
− 2u − 1
c
2
, c
4
, c
7
c
11
(u − 1)
2
c
3
, c
5
, c
8
c
12
(u + 1)
2
c
6
, c
9
, c
10
u
2
− 2
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
2
− 6y + 1
c
2
, c
3
, c
4
c
5
, c
7
, c
8
c
11
, c
12
(y − 1)
2
c
6
, c
9
, c
10
(y − 2)
2
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 1.41421
b = 1.00000
−4.93480 −8.00000
u = −1.00000
a = −1.41421
b = 1.00000
−4.93480 −8.00000
26
VI. I
u
6
= hb − a + 2, 2a
2
− 4a + 1, u + 1i
(i) Arc colorings
a
7
=
0
−1
a
12
=
1
0
a
1
=
1
−1
a
4
=
a
a − 2
a
2
=
2a
−2a + 2
a
8
=
−1
0
a
5
=
2a − 2
a − 2
a
3
=
2a − 2
a − 2
a
11
=
2a − 2
2a −
7
2
a
10
=
2a − 2
−1.5
a
6
=
−2
3a − 4
a
9
=
−2a + 2
−2a +
7
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8
27
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
, c
9
c
10
u
2
− 2
c
2
, c
7
(u − 1)
2
c
3
, c
8
2(2u
2
− 4u + 1)
c
4
, c
11
2(2u
2
+ 4u + 1)
c
5
, c
12
(u + 1)
2
28
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
, c
9
c
10
(y − 2)
2
c
2
, c
5
, c
7
c
12
(y − 1)
2
c
3
, c
4
, c
8
c
11
4(4y
2
− 12y + 1)
29
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 0.292893
b = −1.70711
−4.93480 −8.00000
u = −1.00000
a = 1.70711
b = −0.292893
−4.93480 −8.00000
30
VII. I
u
7
= hb − 1, a, u − 1i
(i) Arc colorings
a
7
=
0
1
a
12
=
1
0
a
1
=
1
−1
a
4
=
0
1
a
2
=
1
0
a
8
=
1
0
a
5
=
1
1
a
3
=
1
1
a
11
=
0
−1
a
10
=
0
−1
a
6
=
0
1
a
9
=
0
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
31
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
8
c
11
, c
12
u − 1
c
3
, c
4
, c
5
c
7
u + 1
c
6
, c
9
, c
10
u
32
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
7
c
8
, c
11
, c
12
y − 1
c
6
, c
9
, c
10
y
33
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0
b = 1.00000
0 0
34
VIII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)(u
2
− 2)
2
(u
2
− 2u − 1)(u
6
− u
5
+ 3u
3
− 5u
2
+ 4u − 1)
· (u
18
− 11u
17
+ ··· + 160u − 32)(u
22
+ 7u
21
+ ··· − 6u − 2)
2
c
2
, c
11
4(u − 1)
5
(2u
2
+ 4u + 1)(u
6
+ 2u
5
− 3u
3
− 4u
2
− 2u − 1)
· (u
18
− u
17
+ ··· − 3u
3
+ 1)(2u
44
− u
42
+ ··· − 24u + 1)
c
3
, c
5
4(u + 1)
5
(2u
2
− 4u + 1)(u
6
− 2u
5
+ 3u
3
− 4u
2
+ 2u − 1)
· (u
18
− u
17
+ ··· − 3u
3
+ 1)(2u
44
− u
42
+ ··· − 24u + 1)
c
4
, c
7
4(u − 1)
4
(u + 1)(2u
2
+ 4u + 1)(u
6
+ 2u
5
+ ··· + 6u + 1)
· (u
18
− u
17
+ ··· − 6u − 1)(2u
44
− 29u
42
+ ··· + 88u − 7)
c
6
u(u
2
− 2)
3
(u
6
+ 3u
5
+ 3u
4
− 2u
3
− 5u
2
− 2u + 1)
· (u
18
+ 10u
17
+ ··· − 16u + 16)(u
22
− 4u
21
+ ··· + 2u − 2)
2
c
8
, c
12
4(u − 1)(u + 1)
4
(2u
2
− 4u + 1)(u
6
− 2u
5
+ ··· − 6u + 1)
· (u
18
− u
17
+ ··· − 6u − 1)(2u
44
− 29u
42
+ ··· + 88u − 7)
c
9
, c
10
u(u
2
− 2)
3
(u
6
− 3u
5
+ 3u
4
+ 2u
3
− 5u
2
+ 2u + 1)
· (u
18
+ 10u
17
+ ··· − 16u + 16)(u
22
− 4u
21
+ ··· + 2u − 2)
2
35
IX. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y − 2)
4
(y − 1)(y
2
− 6y + 1)(y
6
− y
5
− 4y
4
− 3y
3
+ y
2
− 6y + 1)
· (y
18
− 7y
17
+ ··· + 3584y + 1024)(y
22
+ y
21
+ ··· + 48y + 4)
2
c
2
, c
3
, c
5
c
11
16(y − 1)
5
(4y
2
− 12y + 1)(y
6
− 4y
5
+ 4y
4
− 3y
3
+ 4y
2
+ 4y + 1)
· (y
18
− 3y
17
+ ··· − 14y
2
+ 1)(4y
44
− 4y
43
+ ··· − 214y + 1)
c
4
, c
7
, c
8
c
12
16(y − 1)
5
(4y
2
− 12y + 1)(y
6
− 6y
5
+ ··· − 32y + 1)
· (y
18
− 17y
17
+ ··· − 28y + 1)(4y
44
− 116y
43
+ ··· − 4454y + 49)
c
6
, c
9
, c
10
y(y − 2)
6
(y
6
− 3y
5
+ 11y
4
− 20y
3
+ 23y
2
− 14y + 1)
· (y
18
− 8y
17
+ ··· − 10880y + 256)(y
22
− 8y
21
+ ··· − 40y + 4)
2
36
