12a
0413
(K12a
0413
)
A knot diagram
1
Linearized knot diagam
3 6 9 12 2 1 4 11 7 5 8 10
Solving Sequence
5,12 4,8
7 11 9 3 10 1 2 6
c
4
c
7
c
11
c
8
c
3
c
10
c
12
c
1
c
6
c
2
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.42965 × 10
227
u
80
− 1.46174 × 10
227
u
79
+ ··· + 3.55353 × 10
227
b − 1.26641 × 10
227
,
3.52326 × 10
227
u
80
+ 1.26641 × 10
227
u
79
+ ··· + 3.55353 × 10
227
a + 1.44105 × 10
228
, u
81
− 24u
79
+ ··· + 5u − 1i
I
u
2
= h1.14895 × 10
438
u
95
− 2.47031 × 10
438
u
94
+ ··· + 3.83896 × 10
439
b + 6.50354 × 10
438
,
− 2.04308 × 10
439
u
95
+ 6.01402 × 10
439
u
94
+ ··· + 3.83896 × 10
439
a − 8.80804 × 10
438
,
u
96
− 3u
95
+ ··· + 16u
2
+ 2i
I
u
3
= h−1.02996 × 10
27
u
33
− 6.93582 × 10
26
u
32
+ ··· + 5.98975 × 10
27
b + 1.50476 × 10
27
,
− 3.25125 × 10
27
u
33
+ 1.50476 × 10
27
u
32
+ ··· + 5.98975 × 10
27
a + 2.04748 × 10
27
, u
34
+ 6u
32
+ ··· − u + 1i
I
u
4
= h−u
3
− u
2
+ b − 1, u
3
+ 2u
2
+ 2a + u, u
4
+ 2u
3
− u
2
− 2u + 2i
* 4 irreducible components of dim
C
= 0, with total 215 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−1.43 × 10
227
u
80
− 1.46 × 10
227
u
79
+ · · · + 3.55 × 10
227
b − 1.27 ×
10
227
, 3.52 × 10
227
u
80
+ 1.27 × 10
227
u
79
+ · · · + 3.55 × 10
227
a + 1.44 ×
10
228
, u
81
− 24u
79
+ · · · + 5u − 1i
(i) Arc colorings
a
5
=
1
0
a
12
=
0
u
a
4
=
1
−u
2
a
8
=
−0.991483u
80
− 0.356381u
79
+ ··· − 65.8302u − 4.05525
0.402319u
80
+ 0.411350u
79
+ ··· + 0.209580u + 0.356381
a
7
=
−0.991483u
80
− 0.356381u
79
+ ··· − 64.8302u − 4.05525
0.402319u
80
+ 0.411350u
79
+ ··· + 0.209580u + 0.356381
a
11
=
1.07654u
80
+ 0.931549u
79
+ ··· − 83.1510u + 0.150529
−0.127897u
80
+ 0.0324780u
79
+ ··· + 3.79078u − 0.575168
a
9
=
2.59787u
80
+ 1.73504u
79
+ ··· − 168.401u + 2.68154
−0.947267u
80
− 0.463794u
79
+ ··· + 9.86812u − 2.31021
a
3
=
−5.73123u
80
− 1.06854u
79
+ ··· + 39.9455u − 17.0848
0.433762u
80
− 0.169396u
79
+ ··· − 3.97706u + 3.13069
a
10
=
0.948644u
80
+ 0.964026u
79
+ ··· − 79.3602u − 0.424639
−0.127897u
80
+ 0.0324780u
79
+ ··· + 3.79078u − 0.575168
a
1
=
−2.13921u
80
− 0.0773816u
79
+ ··· + 95.7701u − 7.62114
0.208044u
80
− 0.323011u
79
+ ··· − 3.13771u + 1.93467
a
2
=
−12.5649u
80
− 1.86559u
79
+ ··· − 8.88741u − 70.4314
0.506624u
80
+ 0.0528748u
79
+ ··· + 9.81585u + 3.89395
a
6
=
−16.1275u
80
− 3.64845u
79
+ ··· − 7.40160u − 63.9727
1.38353u
80
+ 0.167871u
79
+ ··· + 1.18482u + 6.65535
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4.39444u
80
+ 0.0171805u
79
+ ··· − 42.0156u + 41.6462
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
81
+ 40u
80
+ ··· + 25u + 4
c
2
, c
5
u
81
+ 8u
80
+ ··· + 17u + 2
c
3
, c
10
u
81
− u
79
+ ··· − 166u + 43
c
4
, c
7
u
81
− 24u
79
+ ··· + 5u + 1
c
6
u
81
+ 24u
80
+ ··· + 358010u + 19264
c
8
, c
11
u
81
+ 20u
80
+ ··· + 11513u + 416
c
9
, c
12
u
81
+ 2u
80
+ ··· + 5u + 2
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
81
+ 8y
80
+ ··· − 239y −16
c
2
, c
5
y
81
− 40y
80
+ ··· + 25y −4
c
3
, c
10
y
81
− 2y
80
+ ··· + 40714y −1849
c
4
, c
7
y
81
− 48y
80
+ ··· + 141y −1
c
6
y
81
+ 24y
80
+ ··· + 2334897828y −371101696
c
8
, c
11
y
81
+ 44y
80
+ ··· + 10855025y −173056
c
9
, c
12
y
81
+ 44y
80
+ ··· − 283y −4
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.903079 + 0.550850I
a = 0.429159 − 0.337361I
b = 0.347652 + 0.296638I
−1.95520 − 1.19929I 0
u = 0.903079 − 0.550850I
a = 0.429159 + 0.337361I
b = 0.347652 − 0.296638I
−1.95520 + 1.19929I 0
u = −1.083920 + 0.041793I
a = −0.579989 + 1.117260I
b = −0.50474 − 1.32145I
−8.88772 − 0.47155I 0
u = −1.083920 − 0.041793I
a = −0.579989 − 1.117260I
b = −0.50474 + 1.32145I
−8.88772 + 0.47155I 0
u = −0.878110 + 0.192771I
a = 0.12922 − 1.46095I
b = −0.478343 + 1.308730I
−3.72693 − 2.92513I 0
u = −0.878110 − 0.192771I
a = 0.12922 + 1.46095I
b = −0.478343 − 1.308730I
−3.72693 + 2.92513I 0
u = 0.893405 + 0.013006I
a = 0.43587 − 1.65249I
b = 0.50718 + 1.32157I
−10.03340 + 0.38814I 0
u = 0.893405 − 0.013006I
a = 0.43587 + 1.65249I
b = 0.50718 − 1.32157I
−10.03340 − 0.38814I 0
u = 0.969990 + 0.536933I
a = −0.460171 − 0.857076I
b = 0.37753 + 1.57558I
−3.51679 − 0.43160I 0
u = 0.969990 − 0.536933I
a = −0.460171 + 0.857076I
b = 0.37753 − 1.57558I
−3.51679 + 0.43160I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.006130 + 0.470317I
a = −0.293775 − 0.438445I
b = −0.358781 + 0.539142I
−4.68916 − 3.35217I 0
u = −1.006130 − 0.470317I
a = −0.293775 + 0.438445I
b = −0.358781 − 0.539142I
−4.68916 + 3.35217I 0
u = −0.861433 + 0.051722I
a = −0.26645 − 1.73774I
b = −0.509575 + 1.312850I
−5.94203 − 3.76063I 0
u = −0.861433 − 0.051722I
a = −0.26645 + 1.73774I
b = −0.509575 − 1.312850I
−5.94203 + 3.76063I 0
u = −0.980345 + 0.615042I
a = −0.518246 − 0.465904I
b = −0.116475 + 0.261615I
−5.91291 + 4.69549I 0
u = −0.980345 − 0.615042I
a = −0.518246 + 0.465904I
b = −0.116475 − 0.261615I
−5.91291 − 4.69549I 0
u = 0.839001 + 0.031227I
a = 0.32065 − 1.84947I
b = 0.516689 + 1.314510I
−8.62816 + 8.54082I 0
u = 0.839001 − 0.031227I
a = 0.32065 + 1.84947I
b = 0.516689 − 1.314510I
−8.62816 − 8.54082I 0
u = 1.162140 + 0.230832I
a = 0.156751 − 0.894141I
b = 0.479067 + 1.306700I
−3.03442 − 0.89093I 0
u = 1.162140 − 0.230832I
a = 0.156751 + 0.894141I
b = 0.479067 − 1.306700I
−3.03442 + 0.89093I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.970022 + 0.698699I
a = −0.805602 − 0.341776I
b = −0.141996 − 0.238556I
1.96549 + 7.02940I 0
u = −0.970022 − 0.698699I
a = −0.805602 + 0.341776I
b = −0.141996 + 0.238556I
1.96549 − 7.02940I 0
u = 0.960828 + 0.712083I
a = 0.753196 − 0.275712I
b = 0.270124 − 0.203842I
1.55787 − 1.96344I 0
u = 0.960828 − 0.712083I
a = 0.753196 + 0.275712I
b = 0.270124 + 0.203842I
1.55787 + 1.96344I 0
u = −1.141990 + 0.355379I
a = −0.022029 − 0.642644I
b = −0.594423 + 1.094440I
−4.74824 − 3.47457I 0
u = −1.141990 − 0.355379I
a = −0.022029 + 0.642644I
b = −0.594423 − 1.094440I
−4.74824 + 3.47457I 0
u = −0.974870 + 0.694526I
a = −0.843489 − 0.462950I
b = 0.046789 − 0.231017I
−0.32356 + 9.29303I 0
u = −0.974870 − 0.694526I
a = −0.843489 + 0.462950I
b = 0.046789 + 0.231017I
−0.32356 − 9.29303I 0
u = 0.978304 + 0.690962I
a = 0.785381 − 0.489695I
b = −0.060443 − 0.135945I
−4.99194 − 6.09651I 0
u = 0.978304 − 0.690962I
a = 0.785381 + 0.489695I
b = −0.060443 + 0.135945I
−4.99194 + 6.09651I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.975319 + 0.696384I
a = 0.862768 − 0.491837I
b = −0.095096 − 0.246252I
−2.8881 − 14.4050I 0
u = 0.975319 − 0.696384I
a = 0.862768 + 0.491837I
b = −0.095096 + 0.246252I
−2.8881 + 14.4050I 0
u = −1.200610 + 0.135296I
a = −0.663574 + 0.864477I
b = −0.53709 − 1.31057I
−6.37178 − 8.44892I 0
u = −1.200610 − 0.135296I
a = −0.663574 − 0.864477I
b = −0.53709 + 1.31057I
−6.37178 + 8.44892I 0
u = 1.219070 + 0.053782I
a = 0.544832 + 0.888452I
b = 0.52746 − 1.33544I
−4.07346 + 3.22609I 0
u = 1.219070 − 0.053782I
a = 0.544832 − 0.888452I
b = 0.52746 + 1.33544I
−4.07346 − 3.22609I 0
u = −1.169330 + 0.379709I
a = 0.231493 − 0.620798I
b = −0.90121 + 1.34461I
−5.09366 + 3.39097I 0
u = −1.169330 − 0.379709I
a = 0.231493 + 0.620798I
b = −0.90121 − 1.34461I
−5.09366 − 3.39097I 0
u = 1.152460 + 0.435758I
a = −0.305450 − 0.699799I
b = 0.79728 + 1.53911I
−3.10119 + 0.19958I 0
u = 1.152460 − 0.435758I
a = −0.305450 + 0.699799I
b = 0.79728 − 1.53911I
−3.10119 − 0.19958I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.613617 + 0.423176I
a = −1.03569 − 1.08690I
b = 0.253643 + 1.175650I
−3.80121 − 0.19494I 0
u = 0.613617 − 0.423176I
a = −1.03569 + 1.08690I
b = 0.253643 − 1.175650I
−3.80121 + 0.19494I 0
u = 1.158590 + 0.508165I
a = −0.384496 − 0.720116I
b = 0.72748 + 1.74159I
−3.49408 + 0.28112I 0
u = 1.158590 − 0.508165I
a = −0.384496 + 0.720116I
b = 0.72748 − 1.74159I
−3.49408 − 0.28112I 0
u = −1.173590 + 0.570860I
a = 0.427375 − 0.725476I
b = −0.65087 + 1.90628I
−6.45309 + 3.20546I 0
u = −1.173590 − 0.570860I
a = 0.427375 + 0.725476I
b = −0.65087 − 1.90628I
−6.45309 − 3.20546I 0
u = −1.202720 + 0.521369I
a = 0.409907 − 0.693687I
b = −0.81427 + 1.85032I
−6.07010 − 4.33648I 0
u = −1.202720 − 0.521369I
a = 0.409907 + 0.693687I
b = −0.81427 − 1.85032I
−6.07010 + 4.33648I 0
u = −0.13101 + 1.42903I
a = 0.507329 − 0.241819I
b = 0.98685 + 1.12932I
2.74929 − 1.56105I 0
u = −0.13101 − 1.42903I
a = 0.507329 + 0.241819I
b = 0.98685 − 1.12932I
2.74929 + 1.56105I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.397723 + 0.375405I
a = 1.72040 − 0.69997I
b = −0.218386 + 0.901221I
0.03236 − 2.49515I 0.44371 + 2.70738I
u = −0.397723 − 0.375405I
a = 1.72040 + 0.69997I
b = −0.218386 − 0.901221I
0.03236 + 2.49515I 0.44371 − 2.70738I
u = 0.444303 + 0.311469I
a = −1.84853 − 1.09502I
b = 0.326808 + 0.933026I
−2.33464 + 7.11407I −3.06794 − 6.14015I
u = 0.444303 − 0.311469I
a = −1.84853 + 1.09502I
b = 0.326808 − 0.933026I
−2.33464 − 7.11407I −3.06794 + 6.14015I
u = 0.456913
a = 0.253678
b = 0.403953
−0.942905 −11.1650
u = 0.51889 + 1.52238I
a = −0.446848 − 0.338033I
b = −0.93049 + 1.53593I
2.46516 − 4.28325I 0
u = 0.51889 − 1.52238I
a = −0.446848 + 0.338033I
b = −0.93049 − 1.53593I
2.46516 + 4.28325I 0
u = −1.28578 + 1.02589I
a = 0.300936 − 0.698163I
b = 0.37528 + 2.23926I
−8.73798 − 0.20568I 0
u = −1.28578 − 1.02589I
a = 0.300936 + 0.698163I
b = 0.37528 − 2.23926I
−8.73798 + 0.20568I 0
u = −0.172413 + 0.277440I
a = 2.25399 + 0.95734I
b = −0.157507 + 0.538306I
1.32239 − 1.55771I 2.58702 + 5.50475I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.172413 − 0.277440I
a = 2.25399 − 0.95734I
b = −0.157507 − 0.538306I
1.32239 + 1.55771I 2.58702 − 5.50475I
u = 1.39144 + 0.93444I
a = −0.151774 − 0.865162I
b = −0.69703 + 2.24874I
−6.7665 − 20.6415I 0
u = 1.39144 − 0.93444I
a = −0.151774 + 0.865162I
b = −0.69703 − 2.24874I
−6.7665 + 20.6415I 0
u = −1.39492 + 0.93638I
a = 0.148970 − 0.852295I
b = 0.67232 + 2.23665I
−4.0945 + 15.3933I 0
u = −1.39492 − 0.93638I
a = 0.148970 + 0.852295I
b = 0.67232 − 2.23665I
−4.0945 − 15.3933I 0
u = 1.39156 + 0.94333I
a = −0.170590 − 0.842332I
b = −0.64135 + 2.27276I
−8.9687 − 11.9497I 0
u = 1.39156 − 0.94333I
a = −0.170590 + 0.842332I
b = −0.64135 − 2.27276I
−8.9687 + 11.9497I 0
u = −1.35748 + 0.99485I
a = 0.243220 − 0.748871I
b = 0.45774 + 2.29058I
−10.01880 + 8.98125I 0
u = −1.35748 − 0.99485I
a = 0.243220 + 0.748871I
b = 0.45774 − 2.29058I
−10.01880 − 8.98125I 0
u = 1.34234 + 1.04798I
a = −0.250789 − 0.693209I
b = −0.43153 + 2.24133I
−5.50274 − 4.90115I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.34234 − 1.04798I
a = −0.250789 + 0.693209I
b = −0.43153 − 2.24133I
−5.50274 + 4.90115I 0
u = −1.41876 + 0.94350I
a = 0.124214 − 0.801178I
b = 0.58669 + 2.17551I
−1.24782 + 12.75560I 0
u = −1.41876 − 0.94350I
a = 0.124214 + 0.801178I
b = 0.58669 − 2.17551I
−1.24782 − 12.75560I 0
u = 1.43602 + 0.96116I
a = −0.124783 − 0.763025I
b = −0.52826 + 2.17418I
−1.39931 − 7.33732I 0
u = 1.43602 − 0.96116I
a = −0.124783 + 0.763025I
b = −0.52826 − 2.17418I
−1.39931 + 7.33732I 0
u = 0.191879 + 0.136262I
a = −4.57848 + 1.23371I
b = 0.339950 + 0.353163I
0.04190 − 2.04058I 2.67481 + 0.29939I
u = 0.191879 − 0.136262I
a = −4.57848 − 1.23371I
b = 0.339950 − 0.353163I
0.04190 + 2.04058I 2.67481 − 0.29939I
u = 0.199528 + 0.058202I
a = −6.15885 + 0.67502I
b = 0.439537 + 0.176661I
0.60362 + 4.61374I 6.36261 − 6.48089I
u = 0.199528 − 0.058202I
a = −6.15885 − 0.67502I
b = 0.439537 − 0.176661I
0.60362 − 4.61374I 6.36261 + 6.48089I
u = −0.169065 + 0.033618I
a = 6.99710 + 0.79348I
b = −0.370174 + 0.091371I
2.60987 − 0.42182I 12.11739 + 2.00022I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.169065 − 0.033618I
a = 6.99710 − 0.79348I
b = −0.370174 − 0.091371I
2.60987 + 0.42182I 12.11739 − 2.00022I
13
II. I
u
2
= h1.15 × 10
438
u
95
− 2.47 × 10
438
u
94
+ · · · + 3.84 × 10
439
b + 6.50 ×
10
438
, −2.04 × 10
439
u
95
+ 6.01 × 10
439
u
94
+ · · · + 3.84 × 10
439
a − 8.81 ×
10
438
, u
96
− 3u
95
+ · · · + 16u
2
+ 2i
(i) Arc colorings
a
5
=
1
0
a
12
=
0
u
a
4
=
1
−u
2
a
8
=
0.532197u
95
− 1.56658u
94
+ ··· + 8.79516u + 0.229438
−0.0299288u
95
+ 0.0643484u
94
+ ··· + 0.269231u − 0.169409
a
7
=
1
2
u
95
−
3
2
u
94
+ ··· −
41
2
u
2
+ 8u
−0.0321972u
95
+ 0.0665767u
94
+ ··· + 0.204837u − 0.229438
a
11
=
0.575081u
95
− 1.66673u
94
+ ··· + 9.69187u + 0.527136
−0.0360635u
95
+ 0.0883803u
94
+ ··· + 1.25346u − 0.180674
a
9
=
1.15647u
95
− 3.35032u
94
+ ··· + 19.4650u + 1.10864
−0.0633405u
95
+ 0.149731u
94
+ ··· + 1.60421u − 0.283309
a
3
=
0.609013u
95
− 1.98147u
94
+ ··· + 10.7863u − 0.679440
0.144780u
95
− 0.460723u
94
+ ··· + 1.48348u − 0.352848
a
10
=
0.539018u
95
− 1.57835u
94
+ ··· + 10.9453u + 0.346462
−0.0360635u
95
+ 0.0883803u
94
+ ··· + 1.25346u − 0.180674
a
1
=
−0.624301u
95
+ 1.78526u
94
+ ··· − 14.3857u − 1.06687
0.0271219u
95
− 0.0569288u
94
+ ··· − 0.226824u + 0.185505
a
2
=
−0.240992u
95
+ 0.679703u
94
+ ··· − 7.35020u − 1.71513
−0.129481u
95
+ 0.427106u
94
+ ··· − 0.741908u + 0.241757
a
6
=
0.107195u
95
− 0.543300u
94
+ ··· + 1.75034u − 3.48636
−0.142490u
95
+ 0.417692u
94
+ ··· − 0.328294u − 0.440229
(ii) Obstruction class = −1
(iii) Cusp Shapes = 1.18779u
95
− 3.29337u
94
+ ··· + 3.37341u + 9.33011
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
48
+ 25u
47
+ ··· + 3u + 1)
2
c
2
, c
5
(u
48
− 3u
47
+ ··· − 3u + 1)
2
c
3
, c
10
u
96
− u
95
+ ··· + 3112u + 446
c
4
, c
7
u
96
+ 3u
95
+ ··· + 16u
2
+ 2
c
6
(u
48
− 15u
47
+ ··· − 536u + 48)
2
c
8
, c
11
(u
48
− 15u
47
+ ··· − 19u + 3)
2
c
9
, c
12
u
96
+ 15u
95
+ ··· + 380u + 113
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
48
− y
47
+ ··· + 21y + 1)
2
c
2
, c
5
(y
48
− 25y
47
+ ··· − 3y + 1)
2
c
3
, c
10
y
96
− 15y
95
+ ··· − 3527960y + 198916
c
4
, c
7
y
96
+ 9y
95
+ ··· + 64y + 4
c
6
(y
48
+ 21y
47
+ ··· − 2752y + 2304)
2
c
8
, c
11
(y
48
+ 31y
47
+ ··· + 281y + 9)
2
c
9
, c
12
y
96
− 21y
95
+ ··· − 876866y + 12769
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.642886 + 0.769233I
a = −0.526834 + 1.245750I
b = −0.159604 − 0.779166I
−2.64526 + 1.62822I 0
u = −0.642886 − 0.769233I
a = −0.526834 − 1.245750I
b = −0.159604 + 0.779166I
−2.64526 − 1.62822I 0
u = −0.881612 + 0.504458I
a = −0.284621 + 1.359290I
b = 0.07887 − 1.83409I
−3.39889 + 6.05165I 0
u = −0.881612 − 0.504458I
a = −0.284621 − 1.359290I
b = 0.07887 + 1.83409I
−3.39889 − 6.05165I 0
u = −0.550537 + 0.862614I
a = −0.353146 + 0.068121I
b = 0.658429 + 0.450242I
−4.39871 + 0.53615I 0
u = −0.550537 − 0.862614I
a = −0.353146 − 0.068121I
b = 0.658429 − 0.450242I
−4.39871 − 0.53615I 0
u = 0.591865 + 0.735838I
a = −0.530706 − 0.763908I
b = −0.89983 + 1.90530I
2.33675 − 3.85987I 0
u = 0.591865 − 0.735838I
a = −0.530706 + 0.763908I
b = −0.89983 − 1.90530I
2.33675 + 3.85987I 0
u = 0.744875 + 0.808215I
a = 0.499652 + 1.192210I
b = 0.368377 − 1.007510I
−1.16841 − 5.60646I 0
u = 0.744875 − 0.808215I
a = 0.499652 − 1.192210I
b = 0.368377 + 1.007510I
−1.16841 + 5.60646I 0
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.692565 + 0.869229I
a = 0.403178 − 0.593267I
b = 0.98304 + 1.61871I
2.56945 − 1.35665I 0
u = −0.692565 − 0.869229I
a = 0.403178 + 0.593267I
b = 0.98304 − 1.61871I
2.56945 + 1.35665I 0
u = 1.006670 + 0.476250I
a = 0.129614 + 1.347410I
b = 0.24871 − 2.14752I
−5.00099 − 3.47007I 0
u = 1.006670 − 0.476250I
a = 0.129614 − 1.347410I
b = 0.24871 + 2.14752I
−5.00099 + 3.47007I 0
u = 0.466684 + 1.016830I
a = 0.512670 − 0.003710I
b = −0.470600 + 0.326451I
0.20357 − 3.69554I 0
u = 0.466684 − 1.016830I
a = 0.512670 + 0.003710I
b = −0.470600 − 0.326451I
0.20357 + 3.69554I 0
u = −1.121980 + 0.006018I
a = 0.496967 + 0.635037I
b = −0.23987 − 1.42293I
0.31882 + 3.05575I 0
u = −1.121980 − 0.006018I
a = 0.496967 − 0.635037I
b = −0.23987 + 1.42293I
0.31882 − 3.05575I 0
u = 1.052960 + 0.479633I
a = 0.050990 + 1.321560I
b = 0.45256 − 2.17603I
−4.17993 − 10.74180I 0
u = 1.052960 − 0.479633I
a = 0.050990 − 1.321560I
b = 0.45256 + 2.17603I
−4.17993 + 10.74180I 0
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.788187 + 0.296245I
a = 0.30429 + 1.58700I
b = −0.83719 − 2.15789I
−8.27561 − 9.88494I −13.0154 + 9.0074I
u = 0.788187 − 0.296245I
a = 0.30429 − 1.58700I
b = −0.83719 + 2.15789I
−8.27561 + 9.88494I −13.0154 − 9.0074I
u = 0.878872 + 0.755618I
a = −0.103691 − 0.300136I
b = −0.928283 + 1.060800I
−4.39871 + 0.53615I 0
u = 0.878872 − 0.755618I
a = −0.103691 + 0.300136I
b = −0.928283 − 1.060800I
−4.39871 − 0.53615I 0
u = 1.145610 + 0.196711I
a = −0.424922 + 0.824724I
b = 0.48997 − 1.53810I
−1.75049 − 7.70855I 0
u = 1.145610 − 0.196711I
a = −0.424922 − 0.824724I
b = 0.48997 + 1.53810I
−1.75049 + 7.70855I 0
u = −0.539373 + 1.036980I
a = −0.482926 − 0.045604I
b = 0.549913 + 0.228608I
−2.36747 + 8.78466I 0
u = −0.539373 − 1.036980I
a = −0.482926 + 0.045604I
b = 0.549913 − 0.228608I
−2.36747 − 8.78466I 0
u = −1.054550 + 0.505113I
a = −0.069236 + 1.271350I
b = −0.45452 − 2.06511I
−1.83280 + 6.39539I 0
u = −1.054550 − 0.505113I
a = −0.069236 − 1.271350I
b = −0.45452 + 2.06511I
−1.83280 − 6.39539I 0
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.744926 + 0.330366I
a = −0.36118 + 1.57550I
b = 0.86851 − 1.95808I
−5.28131 + 5.31478I −9.91001 − 5.90435I
u = −0.744926 − 0.330366I
a = −0.36118 − 1.57550I
b = 0.86851 + 1.95808I
−5.28131 − 5.31478I −9.91001 + 5.90435I
u = 0.877709 + 0.804600I
a = −0.079711 − 0.469464I
b = −1.19264 + 1.20731I
−2.36747 + 8.78466I 0
u = 0.877709 − 0.804600I
a = −0.079711 + 0.469464I
b = −1.19264 − 1.20731I
−2.36747 − 8.78466I 0
u = −0.422974 + 0.679133I
a = −0.484849 + 1.257640I
b = 0.286203 − 0.120211I
−1.75049 + 7.70855I −2.00000 − 9.19551I
u = −0.422974 − 0.679133I
a = −0.484849 − 1.257640I
b = 0.286203 + 0.120211I
−1.75049 − 7.70855I −2.00000 + 9.19551I
u = −0.885497 + 0.816043I
a = 0.143990 − 0.454057I
b = 1.10587 + 1.27859I
0.20357 − 3.69554I 0
u = −0.885497 − 0.816043I
a = 0.143990 + 0.454057I
b = 1.10587 − 1.27859I
0.20357 + 3.69554I 0
u = −0.617010 + 0.458737I
a = 0.510585 − 1.251970I
b = 1.15497 + 2.53019I
−3.82102 + 11.41630I −6.42715 − 12.30916I
u = −0.617010 − 0.458737I
a = 0.510585 + 1.251970I
b = 1.15497 − 2.53019I
−3.82102 − 11.41630I −6.42715 + 12.30916I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.116250 + 0.523188I
a = −0.010373 + 1.152480I
b = −0.59115 − 1.94086I
−1.16841 + 5.60646I 0
u = −1.116250 − 0.523188I
a = −0.010373 − 1.152480I
b = −0.59115 + 1.94086I
−1.16841 − 5.60646I 0
u = 0.840551 + 0.901899I
a = 0.501532 + 1.098490I
b = 0.664576 − 1.148100I
−1.83280 − 6.39539I 0
u = 0.840551 − 0.901899I
a = 0.501532 − 1.098490I
b = 0.664576 + 1.148100I
−1.83280 + 6.39539I 0
u = 0.582207 + 0.492020I
a = −0.583632 − 1.188390I
b = −1.04267 + 2.48467I
−1.02590 − 6.16550I −2.65535 + 9.33427I
u = 0.582207 − 0.492020I
a = −0.583632 + 1.188390I
b = −1.04267 − 2.48467I
−1.02590 + 6.16550I −2.65535 − 9.33427I
u = 0.700142 + 0.267722I
a = 0.37070 + 1.66660I
b = −1.14715 − 2.02661I
−9.07400 − 1.45077I −14.9364 + 2.5761I
u = 0.700142 − 0.267722I
a = 0.37070 − 1.66660I
b = −1.14715 + 2.02661I
−9.07400 + 1.45077I −14.9364 − 2.5761I
u = 0.394288 + 0.630257I
a = 0.408579 + 1.146370I
b = −0.453451 + 0.068064I
0.31882 − 3.05575I 1.65755 + 4.94037I
u = 0.394288 − 0.630257I
a = 0.408579 − 1.146370I
b = −0.453451 − 0.068064I
0.31882 + 3.05575I 1.65755 − 4.94037I
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.166510 + 0.480358I
a = −0.090082 + 1.071060I
b = 0.65923 − 1.87858I
−2.64526 − 1.62822I 0
u = 1.166510 − 0.480358I
a = −0.090082 − 1.071060I
b = 0.65923 + 1.87858I
−2.64526 + 1.62822I 0
u = −0.837500 + 0.963295I
a = −0.538952 + 1.070850I
b = −0.796961 − 1.106660I
−4.17993 + 10.74180I 0
u = −0.837500 − 0.963295I
a = −0.538952 − 1.070850I
b = −0.796961 + 1.106660I
−4.17993 − 10.74180I 0
u = 0.157511 + 1.296980I
a = 0.600289 − 0.109413I
b = 0.257618 + 0.442631I
2.56945 − 1.35665I 0
u = 0.157511 − 1.296980I
a = 0.600289 + 0.109413I
b = 0.257618 − 0.442631I
2.56945 + 1.35665I 0
u = −0.671540 + 0.083180I
a = 1.140730 − 0.312113I
b = −0.145785 + 0.759806I
1.36929 − 1.70556I 1.97914 + 5.99044I
u = −0.671540 − 0.083180I
a = 1.140730 + 0.312113I
b = −0.145785 − 0.759806I
1.36929 + 1.70556I 1.97914 − 5.99044I
u = −0.498384 + 0.440768I
a = 0.77114 − 1.30300I
b = 0.88548 + 2.70801I
−5.85125 + 2.47327I −7.62799 − 9.67832I
u = −0.498384 − 0.440768I
a = 0.77114 + 1.30300I
b = 0.88548 − 2.70801I
−5.85125 − 2.47327I −7.62799 + 9.67832I
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.941314 + 0.963403I
a = −0.487817 + 1.007280I
b = −0.84079 − 1.31864I
−5.00099 + 3.47007I 0
u = −0.941314 − 0.963403I
a = −0.487817 − 1.007280I
b = −0.84079 + 1.31864I
−5.00099 − 3.47007I 0
u = −0.274245 + 0.532196I
a = −1.13951 + 0.85490I
b = 1.41801 + 0.47506I
−4.30194 + 0.88213I −1.07264 − 5.83713I
u = −0.274245 − 0.532196I
a = −1.13951 − 0.85490I
b = 1.41801 − 0.47506I
−4.30194 − 0.88213I −1.07264 + 5.83713I
u = 0.325884 + 0.493774I
a = −0.259522 + 1.327550I
b = −0.280013 + 0.349388I
1.36929 − 1.70556I 1.97914 + 5.99044I
u = 0.325884 − 0.493774I
a = −0.259522 − 1.327550I
b = −0.280013 − 0.349388I
1.36929 + 1.70556I 1.97914 − 5.99044I
u = 1.13913 + 0.87034I
a = 0.327320 + 0.927958I
b = 0.78160 − 1.65470I
−3.39889 − 6.05165I 0
u = 1.13913 − 0.87034I
a = 0.327320 − 0.927958I
b = 0.78160 + 1.65470I
−3.39889 + 6.05165I 0
u = 0.490861 + 0.153450I
a = −1.74121 + 1.04697I
b = 0.421596 − 0.432102I
0.10142 + 2.05601I 0.137930 + 0.873851I
u = 0.490861 − 0.153450I
a = −1.74121 − 1.04697I
b = 0.421596 + 0.432102I
0.10142 − 2.05601I 0.137930 − 0.873851I
23
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.114659 + 0.466798I
a = 0.00540 + 2.17381I
b = 0.259270 + 0.292223I
0.10142 − 2.05601I 0.137930 − 0.873851I
u = −0.114659 − 0.466798I
a = 0.00540 − 2.17381I
b = 0.259270 − 0.292223I
0.10142 + 2.05601I 0.137930 + 0.873851I
u = 0.351745 + 0.304220I
a = −1.69203 + 1.85365I
b = 0.515101 − 0.142675I
0.59444 − 4.56975I 2.71553 + 7.39575I
u = 0.351745 − 0.304220I
a = −1.69203 − 1.85365I
b = 0.515101 + 0.142675I
0.59444 + 4.56975I 2.71553 − 7.39575I
u = 0.065642 + 0.447008I
a = −0.67332 + 2.49409I
b = 0.366472 + 0.222908I
0.59444 + 4.56975I 2.71553 − 7.39575I
u = 0.065642 − 0.447008I
a = −0.67332 − 2.49409I
b = 0.366472 − 0.222908I
0.59444 − 4.56975I 2.71553 + 7.39575I
u = −0.13300 + 1.58906I
a = −0.539562 − 0.110912I
b = −0.714161 + 0.229672I
2.33675 − 3.85987I 0
u = −0.13300 − 1.58906I
a = −0.539562 + 0.110912I
b = −0.714161 − 0.229672I
2.33675 + 3.85987I 0
u = −0.250425 + 0.276302I
a = 1.90195 + 2.34062I
b = −0.399041 − 0.058517I
2.59741 + 0.40649I 8.69780 − 2.37814I
u = −0.250425 − 0.276302I
a = 1.90195 − 2.34062I
b = −0.399041 + 0.058517I
2.59741 − 0.40649I 8.69780 + 2.37814I
24
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.101058 + 0.353624I
a = 0.99755 + 2.89065I
b = −0.342472 + 0.126951I
2.59741 − 0.40649I 8.69780 + 2.37814I
u = −0.101058 − 0.353624I
a = 0.99755 − 2.89065I
b = −0.342472 − 0.126951I
2.59741 + 0.40649I 8.69780 − 2.37814I
u = 1.48296 + 1.07800I
a = 0.303733 + 0.651079I
b = 1.02175 − 1.97671I
−5.28131 − 5.31478I 0
u = 1.48296 − 1.07800I
a = 0.303733 − 0.651079I
b = 1.02175 + 1.97671I
−5.28131 + 5.31478I 0
u = −1.41597 + 1.16916I
a = −0.368256 + 0.642979I
b = −1.10576 − 1.92579I
−8.27561 + 9.88494I 0
u = −1.41597 − 1.16916I
a = −0.368256 − 0.642979I
b = −1.10576 + 1.92579I
−8.27561 − 9.88494I 0
u = 1.90461 + 0.62984I
a = −0.199040 − 0.375683I
b = −0.53252 + 2.22350I
−4.30194 + 0.88213I 0
u = 1.90461 − 0.62984I
a = −0.199040 + 0.375683I
b = −0.53252 − 2.22350I
−4.30194 − 0.88213I 0
u = −1.61679 + 1.19012I
a = −0.298993 + 0.563009I
b = −1.10844 − 2.09261I
−9.07400 + 1.45077I 0
u = −1.61679 − 1.19012I
a = −0.298993 − 0.563009I
b = −1.10844 + 2.09261I
−9.07400 − 1.45077I 0
25
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.41836 + 2.03517I
a = −0.485295 − 0.020582I
b = −1.307860 − 0.416026I
−1.02590 − 6.16550I 0
u = −0.41836 − 2.03517I
a = −0.485295 + 0.020582I
b = −1.307860 + 0.416026I
−1.02590 + 6.16550I 0
u = 0.53318 + 2.02799I
a = 0.495751 + 0.002483I
b = 1.28632 − 0.60384I
−3.82102 + 11.41630I 0
u = 0.53318 − 2.02799I
a = 0.495751 − 0.002483I
b = 1.28632 + 0.60384I
−3.82102 − 11.41630I 0
u = 0.35474 + 2.29871I
a = 0.432812 − 0.015862I
b = 1.70830 − 0.34692I
−5.85125 + 2.47327I 0
u = 0.35474 − 2.29871I
a = 0.432812 + 0.015862I
b = 1.70830 + 0.34692I
−5.85125 − 2.47327I 0
26
III.
I
u
3
= h−1.03×10
27
u
33
−6.94×10
26
u
32
+· · ·+5.99×10
27
b+1.50×10
27
, −3.25×
10
27
u
33
+1.50×10
27
u
32
+· · ·+5.99×10
27
a+2.05×10
27
, u
34
+6u
32
+· · ·−u+1i
(i) Arc colorings
a
5
=
1
0
a
12
=
0
u
a
4
=
1
−u
2
a
8
=
0.542802u
33
− 0.251223u
32
+ ··· − 7.53898u − 0.341831
0.171955u
33
+ 0.115795u
32
+ ··· − 0.205975u − 0.251223
a
7
=
0.542802u
33
− 0.251223u
32
+ ··· − 8.53898u − 0.341831
0.171955u
33
+ 0.115795u
32
+ ··· − 0.205975u − 0.251223
a
11
=
−0.576385u
33
− 0.909392u
32
+ ··· − 7.25965u + 1.35157
0.457198u
33
+ 0.251223u
32
+ ··· + 0.538981u − 0.658169
a
9
=
−2.54912u
33
− 2.60279u
32
+ ··· − 12.8894u + 4.80790
1.29114u
33
+ 0.773964u
32
+ ··· − 0.485310u − 1.94462
a
3
=
−9.51283u
33
− 6.25014u
32
+ ··· + 8.83020u + 15.8107
2.51171u
33
+ 1.68159u
32
+ ··· − 2.35329u − 4.39660
a
10
=
−0.119187u
33
− 0.658169u
32
+ ··· − 6.72066u + 0.693397
0.457198u
33
+ 0.251223u
32
+ ··· + 0.538981u − 0.658169
a
1
=
3.85380u
33
+ 2.76293u
32
+ ··· + 3.33199u − 6.40806
−1.85354u
33
− 1.03523u
32
+ ··· + 2.09086u + 2.76293
a
2
=
28.8164u
33
+ 13.5114u
32
+ ··· − 50.1688u − 53.5858
−3.73654u
33
− 1.38453u
32
+ ··· + 9.57389u + 7.50993
a
6
=
23.9720u
33
+ 12.4863u
32
+ ··· − 39.6641u − 37.8422
−6.11197u
33
− 3.30169u
32
+ ··· + 8.60080u + 9.97463
(ii) Obstruction class = 1
(iii) Cusp Shapes = −19.0859u
33
− 9.51134u
32
+ ··· + 12.5905u + 3.71374
27
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
34
− 17u
33
+ ··· − 7u + 1
c
2
u
34
+ 5u
33
+ ··· + 5u + 1
c
3
, c
10
u
34
− 7u
32
+ ··· − 4u
2
+ 1
c
4
, c
7
u
34
+ 6u
32
+ ··· − u + 1
c
5
u
34
− 5u
33
+ ··· − 5u + 1
c
6
u
34
− 15u
33
+ ··· − 253u + 41
c
8
u
34
+ 17u
33
+ ··· + 182u + 13
c
9
, c
12
u
34
− 2u
33
+ ··· − 2u + 1
c
11
u
34
− 17u
33
+ ··· − 182u + 13
28
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
34
+ 7y
33
+ ··· + 17y + 1
c
2
, c
5
y
34
− 17y
33
+ ··· − 7y + 1
c
3
, c
10
y
34
− 14y
33
+ ··· − 8y + 1
c
4
, c
7
y
34
+ 12y
33
+ ··· − 15y + 1
c
6
y
34
+ 3y
33
+ ··· − 16039y + 1681
c
8
, c
11
y
34
+ 15y
33
+ ··· + 1144y + 169
c
9
, c
12
y
34
− 20y
33
+ ··· + 6y + 1
29
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.076965 + 0.959190I
a = 0.199225 + 0.316284I
b = 0.212383 − 0.640653I
3.01771 + 2.35559I 5.29885 − 4.36590I
u = −0.076965 − 0.959190I
a = 0.199225 − 0.316284I
b = 0.212383 + 0.640653I
3.01771 − 2.35559I 5.29885 + 4.36590I
u = −0.221363 + 1.051030I
a = −0.698305 − 0.023770I
b = −0.50475 − 1.40105I
−3.23998 − 10.01620I −5.90505 + 7.69289I
u = −0.221363 − 1.051030I
a = −0.698305 + 0.023770I
b = −0.50475 + 1.40105I
−3.23998 + 10.01620I −5.90505 − 7.69289I
u = 0.910809 + 0.570273I
a = 0.25175 + 1.40507I
b = 0.42183 − 1.54046I
−4.12026 − 2.43542I −5.73530 + 1.04188I
u = 0.910809 − 0.570273I
a = 0.25175 − 1.40507I
b = 0.42183 + 1.54046I
−4.12026 + 2.43542I −5.73530 − 1.04188I
u = 0.744415 + 0.819249I
a = 0.773157 + 0.987622I
b = 0.55068 − 1.64672I
−6.62866 − 9.86389I −7.02161 + 9.02410I
u = 0.744415 − 0.819249I
a = 0.773157 − 0.987622I
b = 0.55068 + 1.64672I
−6.62866 + 9.86389I −7.02161 − 9.02410I
u = 0.216752 + 1.094920I
a = 0.650118 + 0.031422I
b = 0.54701 − 1.36730I
−0.54668 + 4.75082I −3.33000 − 4.96647I
u = 0.216752 − 1.094920I
a = 0.650118 − 0.031422I
b = 0.54701 + 1.36730I
−0.54668 − 4.75082I −3.33000 + 4.96647I
30
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.903788 + 0.664614I
a = −0.392135 + 1.248020I
b = −0.44841 − 1.60386I
−2.47123 + 5.82267I −1.63689 − 7.40519I
u = −0.903788 − 0.664614I
a = −0.392135 − 1.248020I
b = −0.44841 + 1.60386I
−2.47123 − 5.82267I −1.63689 + 7.40519I
u = 1.026410 + 0.507331I
a = −0.000680 + 1.282540I
b = 0.30984 − 1.52769I
−3.62865 − 8.99227I −5.79625 + 8.92125I
u = 1.026410 − 0.507331I
a = −0.000680 − 1.282540I
b = 0.30984 + 1.52769I
−3.62865 + 8.99227I −5.79625 − 8.92125I
u = −0.306702 + 1.109860I
a = −0.720577 + 0.136270I
b = −0.60588 − 1.44538I
−5.48119 − 1.27072I −10.02892 + 2.21325I
u = −0.306702 − 1.109860I
a = −0.720577 − 0.136270I
b = −0.60588 + 1.44538I
−5.48119 + 1.27072I −10.02892 − 2.21325I
u = 0.708053 + 0.959890I
a = 0.745477 + 0.726510I
b = 0.59263 − 1.66805I
−7.45480 − 1.41493I −9.16439 + 2.56140I
u = 0.708053 − 0.959890I
a = 0.745477 − 0.726510I
b = 0.59263 + 1.66805I
−7.45480 + 1.41493I −9.16439 − 2.56140I
u = −0.819992 + 0.874421I
a = −0.621157 + 0.908271I
b = −0.53979 − 1.68142I
−3.64019 + 5.34500I −3.82482 − 5.95522I
u = −0.819992 − 0.874421I
a = −0.621157 − 0.908271I
b = −0.53979 + 1.68142I
−3.64019 − 5.34500I −3.82482 + 5.95522I
31
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.097760 + 0.622980I
a = −0.098367 + 1.085070I
b = −0.30600 − 1.64399I
−1.99445 + 4.85533I −2.92313 − 3.18673I
u = −1.097760 − 0.622980I
a = −0.098367 − 1.085070I
b = −0.30600 + 1.64399I
−1.99445 − 4.85533I −2.92313 + 3.18673I
u = −0.515077 + 0.372282I
a = 1.57892 + 0.43037I
b = 0.149961 + 0.178715I
1.000570 − 0.744743I −1.95626 − 4.02928I
u = −0.515077 − 0.372282I
a = 1.57892 − 0.43037I
b = 0.149961 − 0.178715I
1.000570 + 0.744743I −1.95626 + 4.02928I
u = 0.570770 + 0.142323I
a = −2.25846 − 0.09273I
b = 0.104173 + 0.252933I
−0.35565 − 2.26022I −13.9823 + 8.9210I
u = 0.570770 − 0.142323I
a = −2.25846 + 0.09273I
b = 0.104173 − 0.252933I
−0.35565 + 2.26022I −13.9823 − 8.9210I
u = 0.549236 + 0.056659I
a = −2.65564 − 0.14508I
b = 0.234310 + 0.151924I
0.26818 + 4.54432I −17.1303 − 1.6797I
u = 0.549236 − 0.056659I
a = −2.65564 + 0.14508I
b = 0.234310 − 0.151924I
0.26818 − 4.54432I −17.1303 + 1.6797I
u = −0.506040 + 0.041856I
a = 2.71268 − 0.00120I
b = −0.183809 + 0.073362I
2.33418 − 0.36984I −16.4229 − 3.2359I
u = −0.506040 − 0.041856I
a = 2.71268 + 0.00120I
b = −0.183809 − 0.073362I
2.33418 + 0.36984I −16.4229 + 3.2359I
32
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.23699 + 1.52014I
a = 0.479159 + 0.229975I
b = 1.00905 − 1.34686I
2.66327 + 1.73847I −14.9980 − 19.9197I
u = 0.23699 − 1.52014I
a = 0.479159 − 0.229975I
b = 1.00905 + 1.34686I
2.66327 − 1.73847I −14.9980 + 19.9197I
u = −0.51575 + 1.61254I
a = −0.445169 + 0.312529I
b = −1.04324 − 1.62347I
2.31395 + 4.27658I 0
u = −0.51575 − 1.61254I
a = −0.445169 − 0.312529I
b = −1.04324 + 1.62347I
2.31395 − 4.27658I 0
33
IV. I
u
4
= h−u
3
− u
2
+ b − 1, u
3
+ 2u
2
+ 2a + u, u
4
+ 2u
3
− u
2
− 2u + 2i
(i) Arc colorings
a
5
=
1
0
a
12
=
0
u
a
4
=
1
−u
2
a
8
=
−
1
2
u
3
− u
2
−
1
2
u
u
3
+ u
2
+ 1
a
7
=
−
1
2
u
3
− u
2
+
1
2
u + 1
1
a
11
=
−
1
2
u
3
− u
2
+
1
2
u + 1
u
3
+ 2u
2
− 1
a
9
=
0
u
3
+ u
2
− u
a
3
=
1
0
a
10
=
1
2
u
3
+ u
2
+
1
2
u
u
3
+ 2u
2
− 1
a
1
=
1
2
u
3
+ u
2
−
1
2
u − 1
−1
a
2
=
1
2
u
3
+ u
2
−
1
2
u
−1
a
6
=
−
1
2
u
3
− u
2
+
1
2
u + 1
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
34
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
4
c
3
, c
10
u
4
+ 3u
2
+ 2u + 2
c
4
, c
7
u
4
+ 2u
3
− u
2
− 2u + 2
c
5
(u + 1)
4
c
6
u
4
c
8
, c
9
, c
11
c
12
(u
2
+ 1)
2
35
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y −1)
4
c
3
, c
10
y
4
+ 6y
3
+ 13y
2
+ 8y + 4
c
4
, c
7
y
4
− 6y
3
+ 13y
2
− 8y + 4
c
6
y
4
c
8
, c
9
, c
11
c
12
(y + 1)
4
36
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.693897 + 0.418797I
a = −0.637550 − 1.056350I
b = 1.27510 + 1.11269I
−4.93480 −12.0000
u = 0.693897 − 0.418797I
a = −0.637550 + 1.056350I
b = 1.27510 − 1.11269I
−4.93480 −12.0000
u = −1.69390 + 0.41880I
a = 0.137550 − 0.556347I
b = −0.27510 + 2.11269I
−4.93480 −12.0000
u = −1.69390 − 0.41880I
a = 0.137550 + 0.556347I
b = −0.27510 − 2.11269I
−4.93480 −12.0000
37
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
4
)(u
34
− 17u
33
+ ··· − 7u + 1)(u
48
+ 25u
47
+ ··· + 3u + 1)
2
· (u
81
+ 40u
80
+ ··· + 25u + 4)
c
2
((u − 1)
4
)(u
34
+ 5u
33
+ ··· + 5u + 1)(u
48
− 3u
47
+ ··· − 3u + 1)
2
· (u
81
+ 8u
80
+ ··· + 17u + 2)
c
3
, c
10
(u
4
+ 3u
2
+ 2u + 2)(u
34
− 7u
32
+ ··· − 4u
2
+ 1)
· (u
81
− u
79
+ ··· − 166u + 43)(u
96
− u
95
+ ··· + 3112u + 446)
c
4
, c
7
(u
4
+ 2u
3
− u
2
− 2u + 2)(u
34
+ 6u
32
+ ··· − u + 1)
· (u
81
− 24u
79
+ ··· + 5u + 1)(u
96
+ 3u
95
+ ··· + 16u
2
+ 2)
c
5
((u + 1)
4
)(u
34
− 5u
33
+ ··· − 5u + 1)(u
48
− 3u
47
+ ··· − 3u + 1)
2
· (u
81
+ 8u
80
+ ··· + 17u + 2)
c
6
u
4
(u
34
− 15u
33
+ ··· − 253u + 41)(u
48
− 15u
47
+ ··· − 536u + 48)
2
· (u
81
+ 24u
80
+ ··· + 358010u + 19264)
c
8
((u
2
+ 1)
2
)(u
34
+ 17u
33
+ ··· + 182u + 13)
· ((u
48
− 15u
47
+ ··· − 19u + 3)
2
)(u
81
+ 20u
80
+ ··· + 11513u + 416)
c
9
, c
12
((u
2
+ 1)
2
)(u
34
− 2u
33
+ ··· − 2u + 1)(u
81
+ 2u
80
+ ··· + 5u + 2)
· (u
96
+ 15u
95
+ ··· + 380u + 113)
c
11
((u
2
+ 1)
2
)(u
34
− 17u
33
+ ··· − 182u + 13)
· ((u
48
− 15u
47
+ ··· − 19u + 3)
2
)(u
81
+ 20u
80
+ ··· + 11513u + 416)
38
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
4
)(y
34
+ 7y
33
+ ··· + 17y + 1)(y
48
− y
47
+ ··· + 21y + 1)
2
· (y
81
+ 8y
80
+ ··· − 239y −16)
c
2
, c
5
((y −1)
4
)(y
34
− 17y
33
+ ··· − 7y + 1)(y
48
− 25y
47
+ ··· − 3y + 1)
2
· (y
81
− 40y
80
+ ··· + 25y −4)
c
3
, c
10
(y
4
+ 6y
3
+ 13y
2
+ 8y + 4)(y
34
− 14y
33
+ ··· − 8y + 1)
· (y
81
− 2y
80
+ ··· + 40714y −1849)
· (y
96
− 15y
95
+ ··· − 3527960y + 198916)
c
4
, c
7
(y
4
− 6y
3
+ 13y
2
− 8y + 4)(y
34
+ 12y
33
+ ··· − 15y + 1)
· (y
81
− 48y
80
+ ··· + 141y −1)(y
96
+ 9y
95
+ ··· + 64y + 4)
c
6
y
4
(y
34
+ 3y
33
+ ··· − 16039y + 1681)
· (y
48
+ 21y
47
+ ··· − 2752y + 2304)
2
· (y
81
+ 24y
80
+ ··· + 2334897828y −371101696)
c
8
, c
11
((y + 1)
4
)(y
34
+ 15y
33
+ ··· + 1144y + 169)
· (y
48
+ 31y
47
+ ··· + 281y + 9)
2
· (y
81
+ 44y
80
+ ··· + 10855025y −173056)
c
9
, c
12
((y + 1)
4
)(y
34
− 20y
33
+ ··· + 6y + 1)(y
81
+ 44y
80
+ ··· − 283y −4)
· (y
96
− 21y
95
+ ··· − 876866y + 12769)
39
