12n
0886
(K12n
0886
)
A knot diagram
1
Linearized knot diagam
5 6 7 9 8 10 12 2 4 3 8 7
Solving Sequence
8,11
12
3,7
4 1 10 6 2 5 9
c
11
c
7
c
3
c
12
c
10
c
6
c
2
c
5
c
9
c
1
, c
4
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h2.28947 × 10
47
u
38
+ 4.04764 × 10
47
u
37
+ ··· + 2.48782 × 10
48
b − 5.46868 × 10
48
,
4.40280 × 10
48
u
38
+ 1.28334 × 10
49
u
37
+ ··· + 3.48294 × 10
49
a + 1.28461 × 10
49
, u
39
+ 3u
38
+ ··· + 97u + 28i
I
u
2
= h−3.16826 × 10
23
au
35
+ 4.21892 × 10
23
u
35
+ ··· + 6.95896 × 10
24
a + 5.71717 × 10
24
,
5.19604 × 10
24
au
35
− 8.48983 × 10
24
u
35
+ ··· + 6.84613 × 10
24
a + 1.19689 × 10
26
,
u
36
− 2u
35
+ ··· − 48u + 19i
I
u
3
= h−22u
12
a + 31u
12
+ ··· + 12a + 9, 6u
12
a + 4u
12
+ ··· − 6a + 38,
u
13
− 2u
12
+ 8u
11
− 12u
10
+ 25u
9
− 27u
8
+ 40u
7
− 31u
6
+ 36u
5
− 18u
4
+ 17u
3
− 2u
2
+ 3u + 1i
I
u
4
= h−u
5
− 2u
4
− 3u
3
− 3u
2
+ b − 2u, −u
4
− 2u
3
− 4u
2
+ a − 3u − 3, u
6
+ 2u
5
+ 4u
4
+ 4u
3
+ 4u
2
+ u + 1i
* 4 irreducible components of dim
C
= 0, with total 143 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
=
h2.29×10
47
u
38
+4.05×10
47
u
37
+· · ·+2.49×10
48
b−5.47×10
48
, 4.40×10
48
u
38
+
1.28 × 10
49
u
37
+ · · · + 3.48 × 10
49
a + 1.28 × 10
49
, u
39
+ 3u
38
+ · · · + 97u + 28i
(i) Arc colorings
a
8
=
0
u
a
11
=
1
0
a
12
=
1
u
2
a
3
=
−0.126410u
38
− 0.368465u
37
+ ··· − 11.5215u − 0.368828
−0.0920273u
38
− 0.162698u
37
+ ··· + 2.33867u + 2.19819
a
7
=
u
u
3
+ u
a
4
=
−0.126011u
38
− 0.302424u
37
+ ··· − 3.73851u + 1.95256
−0.104356u
38
− 0.190877u
37
+ ··· + 3.82088u + 2.70401
a
1
=
u
2
+ 1
u
4
+ 2u
2
a
10
=
−0.194866u
38
− 0.476802u
37
+ ··· − 9.00949u − 1.31112
0.0407147u
38
− 0.0606632u
37
+ ··· − 11.8899u − 6.06492
a
6
=
−0.0785067u
38
− 0.327547u
37
+ ··· − 14.6147u − 5.27648
0.0107661u
38
+ 0.0759285u
37
+ ··· + 11.8930u + 3.53949
a
2
=
−0.113492u
38
− 0.284012u
37
+ ··· − 2.11951u + 1.73553
0.195599u
38
+ 0.486101u
37
+ ··· + 11.1853u + 0.740865
a
5
=
−0.0785067u
38
− 0.327547u
37
+ ··· − 14.6147u − 5.27648
0.124150u
38
+ 0.411280u
37
+ ··· + 23.0178u + 6.11626
a
9
=
−0.0241106u
38
+ 0.0681245u
37
+ ··· + 15.3829u + 6.23920
0.225516u
38
+ 0.613536u
37
+ ··· + 12.0478u + 0.558854
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.711169u
38
− 3.04251u
37
+ ··· − 97.9978u − 38.0725
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
39
− u
38
+ ··· − 288u + 24
c
2
u
39
− 6u
38
+ ··· + 577u + 284
c
4
, c
9
3(3u
39
− 9u
38
+ ··· + 384u + 128)
c
5
, c
10
3(3u
39
− 15u
38
+ ··· + 24u + 17)
c
6
, c
8
u
39
+ 4u
37
+ ··· − 21u + 3
c
7
, c
11
, c
12
u
39
+ 3u
38
+ ··· + 97u + 28
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
39
− 13y
38
+ ··· + 9024y −576
c
2
y
39
+ 10y
38
+ ··· + 1402473y −80656
c
4
, c
9
9(9y
39
+ 165y
38
+ ··· + 188416y −16384)
c
5
, c
10
9(9y
39
+ 147y
38
+ ··· − 7176y −289)
c
6
, c
8
y
39
+ 8y
38
+ ··· + 69y −9
c
7
, c
11
, c
12
y
39
+ 19y
38
+ ··· + 3249y −784
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.916514 + 0.441237I
a = 0.247881 − 0.833626I
b = 0.207591 − 1.107760I
−2.80770 + 1.03926I −7.88545 − 0.44169I
u = −0.916514 − 0.441237I
a = 0.247881 + 0.833626I
b = 0.207591 + 1.107760I
−2.80770 − 1.03926I −7.88545 + 0.44169I
u = −0.135804 + 0.949926I
a = −0.160880 − 1.247510I
b = 0.883058 + 0.239291I
4.06880 + 6.12048I 0.19446 − 7.21984I
u = −0.135804 − 0.949926I
a = −0.160880 + 1.247510I
b = 0.883058 − 0.239291I
4.06880 − 6.12048I 0.19446 + 7.21984I
u = −0.328914 + 0.888085I
a = −0.161668 − 1.131530I
b = −1.237060 − 0.045140I
1.48517 + 2.10751I −1.96614 − 8.73804I
u = −0.328914 − 0.888085I
a = −0.161668 + 1.131530I
b = −1.237060 + 0.045140I
1.48517 − 2.10751I −1.96614 + 8.73804I
u = −0.483608 + 0.797162I
a = 0.47424 − 2.55899I
b = −1.82147 − 1.40610I
1.57165 + 2.07582I 13.4964 + 12.8859I
u = −0.483608 − 0.797162I
a = 0.47424 + 2.55899I
b = −1.82147 + 1.40610I
1.57165 − 2.07582I 13.4964 − 12.8859I
u = 0.923741 + 0.613959I
a = −0.890068 − 0.882613I
b = −0.80569 − 1.43771I
−3.92945 + 6.07851I −7.89096 − 4.82336I
u = 0.923741 − 0.613959I
a = −0.890068 + 0.882613I
b = −0.80569 + 1.43771I
−3.92945 − 6.07851I −7.89096 + 4.82336I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.752187 + 0.832147I
a = 1.13539 − 0.96953I
b = −0.190145 − 0.615515I
−0.10015 − 2.41578I −8.63287 + 3.83598I
u = −0.752187 − 0.832147I
a = 1.13539 + 0.96953I
b = −0.190145 + 0.615515I
−0.10015 + 2.41578I −8.63287 − 3.83598I
u = −0.711955 + 0.900911I
a = −0.089276 − 1.410670I
b = −0.089221 − 0.908822I
0.11878 + 7.97565I −8.57990 − 9.49272I
u = −0.711955 − 0.900911I
a = −0.089276 + 1.410670I
b = −0.089221 + 0.908822I
0.11878 − 7.97565I −8.57990 + 9.49272I
u = 0.800506 + 0.823754I
a = 0.212411 + 1.237080I
b = −0.125997 + 1.041490I
−4.29233 − 4.38952I −12.7464 + 8.5386I
u = 0.800506 − 0.823754I
a = 0.212411 − 1.237080I
b = −0.125997 − 1.041490I
−4.29233 + 4.38952I −12.7464 − 8.5386I
u = 0.713165 + 0.944690I
a = 0.925475 + 0.938504I
b = −0.208623 + 0.798757I
−3.87382 − 1.34228I −11.55865 − 0.85858I
u = 0.713165 − 0.944690I
a = 0.925475 − 0.938504I
b = −0.208623 − 0.798757I
−3.87382 + 1.34228I −11.55865 + 0.85858I
u = −0.177652 + 0.777872I
a = 1.70436 + 0.68558I
b = −0.822667 + 0.609797I
3.36049 − 4.70428I 0.07633 + 7.03063I
u = −0.177652 − 0.777872I
a = 1.70436 − 0.68558I
b = −0.822667 − 0.609797I
3.36049 + 4.70428I 0.07633 − 7.03063I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.146750 + 0.440730I
a = −0.565258 + 0.986647I
b = −0.89775 + 1.37606I
0.05936 − 12.21210I −4.60084 + 6.75366I
u = −1.146750 − 0.440730I
a = −0.565258 − 0.986647I
b = −0.89775 − 1.37606I
0.05936 + 12.21210I −4.60084 − 6.75366I
u = 0.735638 + 1.075410I
a = −0.76266 − 1.50039I
b = 1.16251 − 1.43644I
−2.50894 − 12.16870I −6.00000 + 9.67889I
u = 0.735638 − 1.075410I
a = −0.76266 + 1.50039I
b = 1.16251 + 1.43644I
−2.50894 + 12.16870I −6.00000 − 9.67889I
u = −0.617583 + 1.166490I
a = 0.802084 − 0.731744I
b = −0.520402 − 0.991081I
−0.54733 + 4.60938I −6.00000 − 4.32150I
u = −0.617583 − 1.166490I
a = 0.802084 + 0.731744I
b = −0.520402 + 0.991081I
−0.54733 − 4.60938I −6.00000 + 4.32150I
u = 0.177150 + 1.362390I
a = −0.738434 + 0.517093I
b = 0.110360 − 0.283380I
8.80818 − 3.56269I 0
u = 0.177150 − 1.362390I
a = −0.738434 − 0.517093I
b = 0.110360 + 0.283380I
8.80818 + 3.56269I 0
u = −0.09539 + 1.41424I
a = −0.264813 − 0.436944I
b = 0.341868 + 0.804996I
3.95195 + 4.10222I −13.18136 + 0.I
u = −0.09539 − 1.41424I
a = −0.264813 + 0.436944I
b = 0.341868 − 0.804996I
3.95195 − 4.10222I −13.18136 + 0.I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.74692 + 1.23578I
a = −0.84084 + 1.29226I
b = 1.11567 + 1.33283I
2.5485 + 18.9404I 0
u = −0.74692 − 1.23578I
a = −0.84084 − 1.29226I
b = 1.11567 − 1.33283I
2.5485 − 18.9404I 0
u = 1.11970 + 0.93154I
a = 0.408674 + 0.839692I
b = −0.125452 + 1.366430I
−3.17217 − 3.88150I 0
u = 1.11970 − 0.93154I
a = 0.408674 − 0.839692I
b = −0.125452 − 1.366430I
−3.17217 + 3.88150I 0
u = 0.442258 + 0.222040I
a = 1.168930 − 0.401308I
b = −0.226973 + 0.541420I
3.75967 − 1.17014I −3.19480 + 5.79771I
u = 0.442258 − 0.222040I
a = 1.168930 + 0.401308I
b = −0.226973 − 0.541420I
3.75967 + 1.17014I −3.19480 − 5.79771I
u = −0.13386 + 1.60465I
a = −0.048505 + 0.218993I
b = 0.580718 − 1.138840I
7.49768 − 7.41295I 0
u = −0.13386 − 1.60465I
a = −0.048505 − 0.218993I
b = 0.580718 + 1.138840I
7.49768 + 7.41295I 0
u = −0.330056
a = 1.27880
b = 0.339349
−0.743035 −13.5950
8
II. I
u
2
= h−3.17 × 10
23
au
35
+ 4.22 × 10
23
u
35
+ · · · + 6.96 × 10
24
a + 5.72 ×
10
24
, 5.20 × 10
24
au
35
− 8.49 × 10
24
u
35
+ · · · + 6.85 × 10
24
a + 1.20 ×
10
26
, u
36
− 2u
35
+ · · · − 48u + 19i
(i) Arc colorings
a
8
=
0
u
a
11
=
1
0
a
12
=
1
u
2
a
3
=
a
2.06053au
35
− 2.74385u
35
+ ··· − 45.2588a − 37.1826
a
7
=
u
u
3
+ u
a
4
=
1.48264au
35
− 1.81640u
35
+ ··· − 25.3448a − 27.0290
2.57849au
35
− 3.07539u
35
+ ··· − 56.3149a − 44.1527
a
1
=
u
2
+ 1
u
4
+ 2u
2
a
10
=
1.06765au
35
− 0.157828u
35
+ ··· − 25.9276a + 24.1903
−1.00977au
35
+ 2.51580u
35
+ ··· + 30.5478a − 48.9528
a
6
=
−2.38204au
35
+ 1.36461u
35
+ ··· − 49.5905a + 25.0494
0.374254u
35
+ 0.716994u
34
+ ··· − 189.282u + 72.9225
a
2
=
−0.913044au
35
+ 2.61003u
35
+ ··· + 28.4338a − 73.4659
−1.71093au
35
+ 2.45734u
35
+ ··· − 0.462668a − 176.281
a
5
=
−2.38204au
35
+ 1.36461u
35
+ ··· − 49.5905a + 25.0494
1.38657au
35
− 1.10162u
35
+ ··· + 39.1501a + 52.6371
a
9
=
−0.995475au
35
− 0.534403u
35
+ ··· − 10.4404a + 39.4763
0.860915au
35
+ 2.29603u
35
+ ··· − 34.0245a − 24.9123
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
93144148804390001398740
3750225582640850341841
u
35
+
92757417872856011479263
3750225582640850341841
u
34
+ ··· +
3062243866116418648517160
3750225582640850341841
u −
2323290663795802739504375
3750225582640850341841
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
72
+ u
71
+ ··· + 2338u + 157
c
2
(u
36
+ 3u
35
+ ··· − 4u + 1)
2
c
4
, c
9
(u
36
− u
35
+ ··· − 414u + 81)
2
c
5
, c
10
u
72
− 10u
70
+ ··· − 504u + 281
c
6
, c
8
u
72
+ u
71
+ ··· + 112u + 263
c
7
, c
11
, c
12
(u
36
− 2u
35
+ ··· − 48u + 19)
2
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
72
+ 31y
71
+ ··· − 3034000y + 24649
c
2
(y
36
− 5y
35
+ ··· − 12y + 1)
2
c
4
, c
9
(y
36
+ 25y
35
+ ··· + 64638y + 6561)
2
c
5
, c
10
y
72
− 20y
71
+ ··· + 2867332y + 78961
c
6
, c
8
y
72
+ 35y
71
+ ··· + 2571694y + 69169
c
7
, c
11
, c
12
(y
36
+ 18y
35
+ ··· + 5182y + 361)
2
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.964482 + 0.279763I
a = −0.083033 − 0.734831I
b = −0.294363 − 1.055310I
−2.40362 + 4.79530I −7.96169 − 4.74931I
u = 0.964482 + 0.279763I
a = 0.444907 + 1.284300I
b = 0.885771 + 1.064060I
−2.40362 + 4.79530I −7.96169 − 4.74931I
u = 0.964482 − 0.279763I
a = −0.083033 + 0.734831I
b = −0.294363 + 1.055310I
−2.40362 − 4.79530I −7.96169 + 4.74931I
u = 0.964482 − 0.279763I
a = 0.444907 − 1.284300I
b = 0.885771 − 1.064060I
−2.40362 − 4.79530I −7.96169 + 4.74931I
u = 0.554516 + 0.760407I
a = −1.32940 − 0.80475I
b = 0.958462 − 0.405342I
0.46960 − 5.37963I −4.19743 + 9.12512I
u = 0.554516 + 0.760407I
a = 0.05645 + 1.69365I
b = −0.58307 + 1.32126I
0.46960 − 5.37963I −4.19743 + 9.12512I
u = 0.554516 − 0.760407I
a = −1.32940 + 0.80475I
b = 0.958462 + 0.405342I
0.46960 + 5.37963I −4.19743 − 9.12512I
u = 0.554516 − 0.760407I
a = 0.05645 − 1.69365I
b = −0.58307 − 1.32126I
0.46960 + 5.37963I −4.19743 − 9.12512I
u = 0.830035 + 0.659658I
a = −0.713804 − 0.720140I
b = −0.595408 − 0.656952I
3.07705 + 3.54112I −1.03463 − 4.96095I
u = 0.830035 + 0.659658I
a = 0.147631 + 1.213210I
b = −1.71953 + 0.43289I
3.07705 + 3.54112I −1.03463 − 4.96095I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.830035 − 0.659658I
a = −0.713804 + 0.720140I
b = −0.595408 + 0.656952I
3.07705 − 3.54112I −1.03463 + 4.96095I
u = 0.830035 − 0.659658I
a = 0.147631 − 1.213210I
b = −1.71953 − 0.43289I
3.07705 − 3.54112I −1.03463 + 4.96095I
u = 0.649973 + 0.864864I
a = 0.697455 + 1.027760I
b = −0.42990 + 1.55194I
3.83685 − 2.52949I 4.23245 + 4.01766I
u = 0.649973 + 0.864864I
a = −0.31224 − 1.76739I
b = 0.211989 − 0.294922I
3.83685 − 2.52949I 4.23245 + 4.01766I
u = 0.649973 − 0.864864I
a = 0.697455 − 1.027760I
b = −0.42990 − 1.55194I
3.83685 + 2.52949I 4.23245 − 4.01766I
u = 0.649973 − 0.864864I
a = −0.31224 + 1.76739I
b = 0.211989 + 0.294922I
3.83685 + 2.52949I 4.23245 − 4.01766I
u = −0.493988 + 0.765361I
a = 0.382874 + 1.353590I
b = 1.86841 − 0.17622I
0.54175 + 1.53117I −4.65772 − 1.00690I
u = −0.493988 + 0.765361I
a = 0.10514 + 2.22225I
b = 1.14356 + 0.92471I
0.54175 + 1.53117I −4.65772 − 1.00690I
u = −0.493988 − 0.765361I
a = 0.382874 − 1.353590I
b = 1.86841 + 0.17622I
0.54175 − 1.53117I −4.65772 + 1.00690I
u = −0.493988 − 0.765361I
a = 0.10514 − 2.22225I
b = 1.14356 − 0.92471I
0.54175 − 1.53117I −4.65772 + 1.00690I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.931263 + 0.577928I
a = 0.061833 + 0.835364I
b = −0.053936 + 0.791398I
−4.03363 + 0.42238I −8.84374 + 0.22152I
u = −0.931263 + 0.577928I
a = 0.798239 − 1.005660I
b = 0.64545 − 1.53598I
−4.03363 + 0.42238I −8.84374 + 0.22152I
u = −0.931263 − 0.577928I
a = 0.061833 − 0.835364I
b = −0.053936 − 0.791398I
−4.03363 − 0.42238I −8.84374 − 0.22152I
u = −0.931263 − 0.577928I
a = 0.798239 + 1.005660I
b = 0.64545 + 1.53598I
−4.03363 − 0.42238I −8.84374 − 0.22152I
u = 0.050425 + 0.902306I
a = −0.971105 − 0.521470I
b = 1.266010 + 0.433022I
8.53562 + 4.47679I 4.25634 − 2.05619I
u = 0.050425 + 0.902306I
a = −0.25070 − 3.19402I
b = 0.195047 − 1.195970I
8.53562 + 4.47679I 4.25634 − 2.05619I
u = 0.050425 − 0.902306I
a = −0.971105 + 0.521470I
b = 1.266010 − 0.433022I
8.53562 − 4.47679I 4.25634 + 2.05619I
u = 0.050425 − 0.902306I
a = −0.25070 + 3.19402I
b = 0.195047 + 1.195970I
8.53562 − 4.47679I 4.25634 + 2.05619I
u = 0.240873 + 0.823070I
a = −0.435832 − 0.301124I
b = −1.350300 − 0.295675I
6.13385 − 1.04825I 5.57209 + 2.15226I
u = 0.240873 + 0.823070I
a = −2.01054 − 0.70373I
b = 0.952566 + 0.034574I
6.13385 − 1.04825I 5.57209 + 2.15226I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.240873 − 0.823070I
a = −0.435832 + 0.301124I
b = −1.350300 + 0.295675I
6.13385 + 1.04825I 5.57209 − 2.15226I
u = 0.240873 − 0.823070I
a = −2.01054 + 0.70373I
b = 0.952566 − 0.034574I
6.13385 + 1.04825I 5.57209 − 2.15226I
u = −0.451409 + 1.054230I
a = −0.296134 − 0.843172I
b = −1.43433 + 0.61656I
1.41758 + 2.33776I −3.67843 − 8.45528I
u = −0.451409 + 1.054230I
a = −0.757663 − 0.010345I
b = −0.462494 + 0.485912I
1.41758 + 2.33776I −3.67843 − 8.45528I
u = −0.451409 − 1.054230I
a = −0.296134 + 0.843172I
b = −1.43433 − 0.61656I
1.41758 − 2.33776I −3.67843 + 8.45528I
u = −0.451409 − 1.054230I
a = −0.757663 + 0.010345I
b = −0.462494 − 0.485912I
1.41758 − 2.33776I −3.67843 + 8.45528I
u = 0.049435 + 0.845861I
a = 0.207488 − 1.277230I
b = −0.258187 + 0.328423I
1.91410 + 1.92268I −2.04106 − 3.51220I
u = 0.049435 + 0.845861I
a = 0.337984 − 0.000584I
b = −1.048350 − 0.385024I
1.91410 + 1.92268I −2.04106 − 3.51220I
u = 0.049435 − 0.845861I
a = 0.207488 + 1.277230I
b = −0.258187 − 0.328423I
1.91410 − 1.92268I −2.04106 + 3.51220I
u = 0.049435 − 0.845861I
a = 0.337984 + 0.000584I
b = −1.048350 + 0.385024I
1.91410 − 1.92268I −2.04106 + 3.51220I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.897625 + 0.782315I
a = 0.832278 − 0.699415I
b = 0.201018 − 1.010950I
2.09110 − 1.58939I −6 − 0.989186 + 0.10I
u = −0.897625 + 0.782315I
a = 0.470717 − 0.079989I
b = −1.183550 + 0.290183I
2.09110 − 1.58939I −6 − 0.989186 + 0.10I
u = −0.897625 − 0.782315I
a = 0.832278 + 0.699415I
b = 0.201018 + 1.010950I
2.09110 + 1.58939I −6 − 0.989186 + 0.10I
u = −0.897625 − 0.782315I
a = 0.470717 + 0.079989I
b = −1.183550 − 0.290183I
2.09110 + 1.58939I −6 − 0.989186 + 0.10I
u = 0.703597 + 1.001610I
a = 0.499128 − 0.446788I
b = 1.78903 + 0.93549I
4.09740 − 9.24115I 0.36103 + 8.46138I
u = 0.703597 + 1.001610I
a = −0.33466 − 1.59173I
b = 0.869174 − 0.879755I
4.09740 − 9.24115I 0.36103 + 8.46138I
u = 0.703597 − 1.001610I
a = 0.499128 + 0.446788I
b = 1.78903 − 0.93549I
4.09740 + 9.24115I 0.36103 − 8.46138I
u = 0.703597 − 1.001610I
a = −0.33466 + 1.59173I
b = 0.869174 + 0.879755I
4.09740 + 9.24115I 0.36103 − 8.46138I
u = 0.581465 + 1.085270I
a = 0.844122 + 0.246524I
b = −0.133944 + 1.010430I
1.52771 + 0.98450I −3.57694 − 0.95161I
u = 0.581465 + 1.085270I
a = 0.416357 + 0.032259I
b = −1.091040 − 0.625348I
1.52771 + 0.98450I −3.57694 − 0.95161I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.581465 − 1.085270I
a = 0.844122 − 0.246524I
b = −0.133944 − 1.010430I
1.52771 − 0.98450I −3.57694 + 0.95161I
u = 0.581465 − 1.085270I
a = 0.416357 − 0.032259I
b = −1.091040 + 0.625348I
1.52771 − 0.98450I −3.57694 + 0.95161I
u = 0.012887 + 0.754972I
a = 0.425777 + 0.051147I
b = −1.48025 + 0.48236I
7.88452 − 4.75608I 13.5087 + 12.0607I
u = 0.012887 + 0.754972I
a = −0.99123 + 5.52698I
b = −0.108726 − 0.155625I
7.88452 − 4.75608I 13.5087 + 12.0607I
u = 0.012887 − 0.754972I
a = 0.425777 − 0.051147I
b = −1.48025 − 0.48236I
7.88452 + 4.75608I 13.5087 − 12.0607I
u = 0.012887 − 0.754972I
a = −0.99123 − 5.52698I
b = −0.108726 + 0.155625I
7.88452 + 4.75608I 13.5087 − 12.0607I
u = −0.784875 + 0.966998I
a = −1.139390 + 0.687511I
b = 0.964426 + 0.159897I
2.67417 + 7.77252I 3.94128 − 5.80679I
u = −0.784875 + 0.966998I
a = 0.290769 − 1.311760I
b = −0.62633 − 1.30213I
2.67417 + 7.77252I 3.94128 − 5.80679I
u = −0.784875 − 0.966998I
a = −1.139390 − 0.687511I
b = 0.964426 − 0.159897I
2.67417 − 7.77252I 3.94128 + 5.80679I
u = −0.784875 − 0.966998I
a = 0.290769 + 1.311760I
b = −0.62633 + 1.30213I
2.67417 − 7.77252I 3.94128 + 5.80679I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.752748 + 1.104470I
a = −0.602310 + 0.801496I
b = 0.435953 + 0.655547I
−2.43760 + 5.76392I −6.00000 − 5.84184I
u = −0.752748 + 1.104470I
a = 0.82699 − 1.30167I
b = −1.00751 − 1.53836I
−2.43760 + 5.76392I −6.00000 − 5.84184I
u = −0.752748 − 1.104470I
a = −0.602310 − 0.801496I
b = 0.435953 − 0.655547I
−2.43760 − 5.76392I −6.00000 + 5.84184I
u = −0.752748 − 1.104470I
a = 0.82699 + 1.30167I
b = −1.00751 + 1.53836I
−2.43760 − 5.76392I −6.00000 + 5.84184I
u = 0.64868 + 1.27209I
a = −0.668947 − 0.583415I
b = 0.624552 − 0.835714I
0.62783 − 10.73630I 0
u = 0.64868 + 1.27209I
a = 1.02496 + 1.32516I
b = −1.09433 + 1.14792I
0.62783 − 10.73630I 0
u = 0.64868 − 1.27209I
a = −0.668947 + 0.583415I
b = 0.624552 + 0.835714I
0.62783 + 10.73630I 0
u = 0.64868 − 1.27209I
a = 1.02496 − 1.32516I
b = −1.09433 − 1.14792I
0.62783 + 10.73630I 0
u = 0.02554 + 1.66020I
a = −1.70704 − 0.04770I
b = 1.78182 − 0.29395I
11.74880 + 0.92694I 0
u = 0.02554 + 1.66020I
a = −0.1091770 + 0.0135728I
b = 0.162309 + 0.239459I
11.74880 + 0.92694I 0
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.02554 − 1.66020I
a = −1.70704 + 0.04770I
b = 1.78182 + 0.29395I
11.74880 − 0.92694I 0
u = 0.02554 − 1.66020I
a = −0.1091770 − 0.0135728I
b = 0.162309 − 0.239459I
11.74880 − 0.92694I 0
19
III. I
u
3
= h−22u
12
a + 31u
12
+ · · · + 12a + 9, 6u
12
a + 4u
12
+ · · · − 6a +
38, u
13
− 2u
12
+ · · · + 3u + 1i
(i) Arc colorings
a
8
=
0
u
a
11
=
1
0
a
12
=
1
u
2
a
3
=
a
1.15789au
12
− 1.63158u
12
+ ··· − 0.631579a − 0.473684
a
7
=
u
u
3
+ u
a
4
=
0.0526316au
12
− 1.21053u
12
+ ··· + 1.78947a − 1.15789
3.52632au
12
− 5.10526u
12
+ ··· − 1.10526a + 1.42105
a
1
=
u
2
+ 1
u
4
+ 2u
2
a
10
=
0.631579au
12
− 0.192982u
12
+ ··· − 1.52632a + 1.77193
−1.68421au
12
+ 2.40351u
12
+ ··· + 0.736842a + 0.385965
a
6
=
−0.631579au
12
+ 1.52632u
12
+ ··· − 0.473684a + 1.89474
2u
11
− 4u
10
+ ··· + 8u + 2
a
2
=
−1.10526au
12
− 0.578947u
12
+ ··· + 2.42105a − 3.68421
1.15789au
12
− 3.63158u
12
+ ··· − 0.631579a + 5.52632
a
5
=
−0.631579au
12
+ 1.52632u
12
+ ··· − 0.473684a + 1.89474
−0.789474au
12
+ 0.157895u
12
+ ··· + 1.15789a + 1.36842
a
9
=
−1.42105au
12
+ 0.684211u
12
+ ··· + 0.684211a − 3.73684
−0.736842au
12
− 1.05263u
12
+ ··· + 3.94737a − 0.789474
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −u
12
−u
11
+ 3u
10
−14u
9
+ 36u
8
−53u
7
+ 81u
6
−77u
5
+ 87u
4
−51u
3
+ 43u
2
−9u −3
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
26
+ 4u
25
+ ··· + 72u + 24
c
2
(u
13
− 5u
12
+ ··· + 20u + 7)
2
c
4
, c
9
3(3u
26
+ 44u
24
+ ··· + 25358u
2
+ 3901)
c
5
, c
10
3(3u
26
+ 3u
25
+ ··· − 8u + 1)
c
6
, c
8
u
26
+ 11u
24
+ ··· + 17u
2
+ 3
c
7
(u
13
+ 2u
12
+ ··· + 3u − 1)
2
c
11
, c
12
(u
13
− 2u
12
+ ··· + 3u + 1)
2
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
26
+ 24y
25
+ ··· + 1344y + 576
c
2
(y
13
− y
12
+ ··· + 176y −49)
2
c
4
, c
9
9(3y
13
+ 44y
12
+ ··· + 25358y + 3901)
2
c
5
, c
10
9(9y
26
− 159y
25
+ ··· − 26y + 1)
c
6
, c
8
y
26
+ 22y
25
+ ··· + 102y + 9
c
7
, c
11
, c
12
(y
13
+ 12y
12
+ ··· + 13y −1)
2
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.456698 + 0.978502I
a = 1.091760 + 0.643230I
b = 1.25818 − 0.77830I
1.70610 + 1.75748I 3.25753 + 1.63211I
u = −0.456698 + 0.978502I
a = −1.24923 − 0.92903I
b = −1.68596 + 1.20474I
1.70610 + 1.75748I 3.25753 + 1.63211I
u = −0.456698 − 0.978502I
a = 1.091760 − 0.643230I
b = 1.25818 + 0.77830I
1.70610 − 1.75748I 3.25753 − 1.63211I
u = −0.456698 − 0.978502I
a = −1.24923 + 0.92903I
b = −1.68596 − 1.20474I
1.70610 − 1.75748I 3.25753 − 1.63211I
u = 0.780947 + 0.875360I
a = 0.939523 + 0.590319I
b = 0.050081 + 0.784745I
1.59722 + 2.60071I −4.14222 − 5.54834I
u = 0.780947 + 0.875360I
a = 0.701024 + 0.533622I
b = −1.148630 − 0.151348I
1.59722 + 2.60071I −4.14222 − 5.54834I
u = 0.780947 − 0.875360I
a = 0.939523 − 0.590319I
b = 0.050081 − 0.784745I
1.59722 − 2.60071I −4.14222 + 5.54834I
u = 0.780947 − 0.875360I
a = 0.701024 − 0.533622I
b = −1.148630 + 0.151348I
1.59722 − 2.60071I −4.14222 + 5.54834I
u = 0.690962 + 0.954550I
a = −0.803327 − 0.072506I
b = 0.847547 + 0.024766I
1.87579 − 8.12356I −4.48580 + 9.21675I
u = 0.690962 + 0.954550I
a = 0.24451 + 1.54178I
b = −0.573849 + 1.111810I
1.87579 − 8.12356I −4.48580 + 9.21675I
23
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.690962 − 0.954550I
a = −0.803327 + 0.072506I
b = 0.847547 − 0.024766I
1.87579 + 8.12356I −4.48580 − 9.21675I
u = 0.690962 − 0.954550I
a = 0.24451 − 1.54178I
b = −0.573849 − 1.111810I
1.87579 + 8.12356I −4.48580 − 9.21675I
u = 0.064732 + 1.235320I
a = −0.383941 + 0.050840I
b = 1.020450 − 0.441007I
9.78578 − 5.01236I 6.45767 + 6.26552I
u = 0.064732 + 1.235320I
a = −0.75059 + 1.99999I
b = −0.107730 − 0.435609I
9.78578 − 5.01236I 6.45767 + 6.26552I
u = 0.064732 − 1.235320I
a = −0.383941 − 0.050840I
b = 1.020450 + 0.441007I
9.78578 + 5.01236I 6.45767 − 6.26552I
u = 0.064732 − 1.235320I
a = −0.75059 − 1.99999I
b = −0.107730 + 0.435609I
9.78578 + 5.01236I 6.45767 − 6.26552I
u = 0.030983 + 0.707445I
a = 0.705239 + 0.334856I
b = −1.43425 − 0.44103I
7.63535 + 4.59295I −10.45011 + 2.14951I
u = 0.030983 + 0.707445I
a = −0.68314 − 5.26527I
b = 0.223276 − 0.607048I
7.63535 + 4.59295I −10.45011 + 2.14951I
u = 0.030983 − 0.707445I
a = 0.705239 − 0.334856I
b = −1.43425 + 0.44103I
7.63535 − 4.59295I −10.45011 − 2.14951I
u = 0.030983 − 0.707445I
a = −0.68314 + 5.26527I
b = 0.223276 + 0.607048I
7.63535 − 4.59295I −10.45011 − 2.14951I
24
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.00114 + 1.63210I
a = −1.76445 + 0.00971I
b = 1.72434 − 0.28475I
11.84210 + 0.83470I 21.9422 + 18.2258I
u = −0.00114 + 1.63210I
a = −0.084459 − 0.134146I
b = 0.245040 − 0.012226I
11.84210 + 0.83470I 21.9422 + 18.2258I
u = −0.00114 − 1.63210I
a = −1.76445 − 0.00971I
b = 1.72434 + 0.28475I
11.84210 − 0.83470I 21.9422 − 18.2258I
u = −0.00114 − 1.63210I
a = −0.084459 + 0.134146I
b = 0.245040 + 0.012226I
11.84210 − 0.83470I 21.9422 − 18.2258I
u = −0.219578
a = 2.03709 + 4.15875I
b = −0.918493 − 0.193390I
5.13740 1.84150
u = −0.219578
a = 2.03709 − 4.15875I
b = −0.918493 + 0.193390I
5.13740 1.84150
25
IV. I
u
4
= h−u
5
− 2u
4
− 3u
3
− 3u
2
+ b − 2u, −u
4
− 2u
3
− 4u
2
+ a − 3u −
3, u
6
+ 2u
5
+ 4u
4
+ 4u
3
+ 4u
2
+ u + 1i
(i) Arc colorings
a
8
=
0
u
a
11
=
1
0
a
12
=
1
u
2
a
3
=
u
4
+ 2u
3
+ 4u
2
+ 3u + 3
u
5
+ 2u
4
+ 3u
3
+ 3u
2
+ 2u
a
7
=
u
u
3
+ u
a
4
=
u
4
+ 2u
3
+ 3u
2
+ 3u + 2
u
5
+ u
4
+ 3u
3
+ u
2
+ 2u − 1
a
1
=
u
2
+ 1
u
4
+ 2u
2
a
10
=
u
5
+ 2u
4
+ 3u
3
+ 2u
2
+ u − 1
−u
5
− 2u
4
− 4u
3
− 4u
2
− 3u − 1
a
6
=
u
4
+ 2u
3
+ 3u
2
+ 3u + 2
u
5
+ 2u
4
+ 4u
3
+ 3u
2
+ 3u
a
2
=
u
5
+ 2u
4
+ 4u
3
+ 4u
2
+ 3u
−u
4
− 2u
3
− 3u
2
− 3u − 2
a
5
=
u
4
+ 2u
3
+ 3u
2
+ 3u + 2
u
5
+ u
4
+ 3u
3
+ u
2
+ 2u − 1
a
9
=
u
5
+ 2u
4
+ 3u
3
+ 2u
2
+ u − 1
−u
5
− 2u
4
− 4u
3
− 4u
2
− 3u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
5
+ 14u
4
+ 21u
3
+ 23u
2
+ 18u + 3
26
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
6
− 3u
5
+ 4u
4
− 5u
3
+ 5u
2
− 2u + 1
c
2
u
6
+ 3u
5
+ 4u
4
+ u
3
− u
2
+ 1
c
4
, c
9
u
6
c
5
, c
10
u
6
+ u
5
+ 2u
4
+ u
3
+ u
2
+ 1
c
6
, c
8
u
6
+ u
4
− u
3
+ 2u
2
− u + 1
c
7
u
6
− 2u
5
+ 4u
4
− 4u
3
+ 4u
2
− u + 1
c
11
, c
12
u
6
+ 2u
5
+ 4u
4
+ 4u
3
+ 4u
2
+ u + 1
27
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
6
− y
5
− 4y
4
+ 5y
3
+ 13y
2
+ 6y + 1
c
2
y
6
− y
5
+ 8y
4
− 7y
3
+ 9y
2
− 2y + 1
c
4
, c
9
y
6
c
5
, c
10
y
6
+ 3y
5
+ 4y
4
+ 5y
3
+ 5y
2
+ 2y + 1
c
6
, c
8
y
6
+ 2y
5
+ 5y
4
+ 5y
3
+ 4y
2
+ 3y + 1
c
7
, c
11
, c
12
y
6
+ 4y
5
+ 8y
4
+ 14y
3
+ 16y
2
+ 7y + 1
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.937424 + 0.916243I
a = 0.469690 − 0.964836I
b = −0.155981 − 1.227730I
−3.99825 + 3.41127I −10.42820 − 0.63715I
u = −0.937424 − 0.916243I
a = 0.469690 + 0.964836I
b = −0.155981 + 1.227730I
−3.99825 − 3.41127I −10.42820 + 0.63715I
u = −0.096993 + 1.308890I
a = −0.272522 − 0.634620I
b = 0.456483 + 0.601395I
4.36362 + 4.05299I 6.62312 − 1.95617I
u = −0.096993 − 1.308890I
a = −0.272522 + 0.634620I
b = 0.456483 − 0.601395I
4.36362 − 4.05299I 6.62312 + 1.95617I
u = 0.034417 + 0.580231I
a = 1.80283 + 1.48709I
b = −0.800501 + 0.710292I
1.27956 − 3.69612I −3.19491 + 7.18248I
u = 0.034417 − 0.580231I
a = 1.80283 − 1.48709I
b = −0.800501 − 0.710292I
1.27956 + 3.69612I −3.19491 − 7.18248I
29
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
3
(u
6
− 3u
5
+ ··· − 2u + 1)(u
26
+ 4u
25
+ ··· + 72u + 24)
· (u
39
− u
38
+ ··· − 288u + 24)(u
72
+ u
71
+ ··· + 2338u + 157)
c
2
(u
6
+ 3u
5
+ 4u
4
+ u
3
− u
2
+ 1)(u
13
− 5u
12
+ ··· + 20u + 7)
2
· ((u
36
+ 3u
35
+ ··· − 4u + 1)
2
)(u
39
− 6u
38
+ ··· + 577u + 284)
c
4
, c
9
9u
6
(3u
26
+ 44u
24
+ ··· + 25358u
2
+ 3901)
· ((u
36
− u
35
+ ··· − 414u + 81)
2
)(3u
39
− 9u
38
+ ··· + 384u + 128)
c
5
, c
10
9(u
6
+ u
5
+ ··· + u
2
+ 1)(3u
26
+ 3u
25
+ ··· − 8u + 1)
· (3u
39
− 15u
38
+ ··· + 24u + 17)(u
72
− 10u
70
+ ··· − 504u + 281)
c
6
, c
8
(u
6
+ u
4
− u
3
+ 2u
2
− u + 1)(u
26
+ 11u
24
+ ··· + 17u
2
+ 3)
· (u
39
+ 4u
37
+ ··· − 21u + 3)(u
72
+ u
71
+ ··· + 112u + 263)
c
7
(u
6
− 2u
5
+ 4u
4
− 4u
3
+ 4u
2
− u + 1)(u
13
+ 2u
12
+ ··· + 3u − 1)
2
· ((u
36
− 2u
35
+ ··· − 48u + 19)
2
)(u
39
+ 3u
38
+ ··· + 97u + 28)
c
11
, c
12
(u
6
+ 2u
5
+ 4u
4
+ 4u
3
+ 4u
2
+ u + 1)(u
13
− 2u
12
+ ··· + 3u + 1)
2
· ((u
36
− 2u
35
+ ··· − 48u + 19)
2
)(u
39
+ 3u
38
+ ··· + 97u + 28)
30
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
3
(y
6
− y
5
+ ··· + 6y + 1)(y
26
+ 24y
25
+ ··· + 1344y + 576)
· (y
39
− 13y
38
+ ··· + 9024y −576)
· (y
72
+ 31y
71
+ ··· − 3034000y + 24649)
c
2
(y
6
− y
5
+ 8y
4
− 7y
3
+ 9y
2
− 2y + 1)(y
13
− y
12
+ ··· + 176y −49)
2
· (y
36
− 5y
35
+ ··· − 12y + 1)
2
· (y
39
+ 10y
38
+ ··· + 1402473y −80656)
c
4
, c
9
81y
6
(3y
13
+ 44y
12
+ ··· + 25358y + 3901)
2
· (y
36
+ 25y
35
+ ··· + 64638y + 6561)
2
· (9y
39
+ 165y
38
+ ··· + 188416y −16384)
c
5
, c
10
81(y
6
+ 3y
5
+ ··· + 2y + 1)(9y
26
− 159y
25
+ ··· − 26y + 1)
· (9y
39
+ 147y
38
+ ··· − 7176y −289)
· (y
72
− 20y
71
+ ··· + 2867332y + 78961)
c
6
, c
8
(y
6
+ 2y
5
+ ··· + 3y + 1)(y
26
+ 22y
25
+ ··· + 102y + 9)
· (y
39
+ 8y
38
+ ··· + 69y −9)(y
72
+ 35y
71
+ ··· + 2571694y + 69169)
c
7
, c
11
, c
12
(y
6
+ 4y
5
+ 8y
4
+ 14y
3
+ 16y
2
+ 7y + 1)
· ((y
13
+ 12y
12
+ ··· + 13y −1)
2
)(y
36
+ 18y
35
+ ··· + 5182y + 361)
2
· (y
39
+ 19y
38
+ ··· + 3249y −784)
31
