12n
0803
(K12n
0803
)
A knot diagram
1
Linearized knot diagam
4 6 10 12 2 9 12 11 3 7 5 7
Solving Sequence
5,11 7,12
8 9 1 4 2 6 10 3
c
11
c
7
c
8
c
12
c
4
c
1
c
6
c
10
c
3
c
2
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−20967u
23
+ 422302u
22
+ ··· + 119758b + 1936892,
333347u
23
+ 3142111u
22
+ ··· + 119758a + 1463683, u
24
+ 8u
23
+ ··· + 34u + 4i
I
u
2
= h20658081418u
25
a + 11852435996417u
25
+ ··· − 20658081418a + 1592388657005,
− 34939904896u
25
a + 44997972497u
25
+ ··· + 97240087620a + 132117488383,
u
26
− 3u
25
+ ··· + 6u
2
+ 1i
I
u
3
= h−u
11
− 2u
10
− 5u
9
− 5u
8
− 7u
7
− 2u
6
− 2u
5
+ 4u
4
+ u
3
+ 3u
2
+ b − u + 1,
− u
11
− 4u
10
− 11u
9
− 20u
8
− 30u
7
− 34u
6
− 32u
5
− 23u
4
− 13u
3
− 6u
2
+ a − 3u − 3,
u
12
+ 3u
11
+ 8u
10
+ 13u
9
+ 20u
8
+ 21u
7
+ 22u
6
+ 15u
5
+ 12u
4
+ 5u
3
+ 5u
2
+ u + 1i
I
u
4
= hu
5
a + 3u
5
+ 3u
3
a − 5u
4
− 4u
2
a + 9u
3
+ 4au − 7u
2
+ 5b − a + 7u + 2,
u
4
a + 2u
5
− 2u
3
a − 3u
4
+ 3u
2
a + 6u
3
+ a
2
− 3au − 6u
2
+ 2a + 5u, u
6
− u
5
+ 3u
4
− 2u
3
+ 3u
2
+ 1i
* 4 irreducible components of dim
C
= 0, with total 100 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−2.10 × 10
4
u
23
+ 4.22 × 10
5
u
22
+ · · · + 1.20 × 10
5
b + 1.94 × 10
6
, 3.33 ×
10
5
u
23
+3.14×10
6
u
22
+· · ·+1.20×10
5
a+1.46×10
6
, u
24
+8u
23
+· · ·+34u+4i
(i) Arc colorings
a
5
=
0
u
a
11
=
1
0
a
7
=
−2.78351u
23
− 26.2372u
22
+ ··· − 145.274u − 12.2220
0.175078u
23
− 3.52629u
22
+ ··· − 106.512u − 16.1734
a
12
=
1
u
2
a
8
=
8.01248u
23
+ 53.3038u
22
+ ··· + 107.322u + 19.8279
−3.96913u
23
− 20.7820u
22
+ ··· + 82.4172u + 11.1340
a
9
=
4.04335u
23
+ 32.5218u
22
+ ··· + 189.739u + 30.9619
−3.96913u
23
− 20.7820u
22
+ ··· + 82.4172u + 11.1340
a
1
=
8.35351u
23
+ 54.4948u
22
+ ··· − 21.7233u − 14.7332
7.47725u
23
+ 53.9440u
22
+ ··· + 159.286u + 21.2134
a
4
=
u
u
3
+ u
a
2
=
−5.30335u
23
− 34.9495u
22
+ ··· − 94.8437u − 20.0274
−18.2073u
23
− 140.297u
22
+ ··· − 532.766u − 63.3231
a
6
=
0.615082u
23
+ 4.89107u
22
+ ··· + 95.0362u + 24.8300
−11.8092u
23
− 78.8511u
22
+ ··· − 94.1786u − 11.2650
a
10
=
2.17390u
23
+ 18.9945u
22
+ ··· + 64.4428u + 1.18601
0.810526u
23
+ 8.98427u
22
+ ··· + 96.0801u + 14.8004
a
3
=
−3.08556u
23
− 21.2898u
22
+ ··· − 85.1959u − 19.1276
−4.41553u
23
− 33.4970u
22
+ ··· − 93.2357u − 7.87618
(ii) Obstruction class = −1
(iii) Cusp Shapes =
248067
59879
u
23
+
1208199
59879
u
22
+ ··· −
6272226
59879
u −
1406970
59879
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
24
− 29u
23
+ ··· + 8704u − 1024
c
2
, c
3
, c
5
c
9
u
24
− 12u
22
+ ··· + 4u − 1
c
4
, c
11
u
24
+ 8u
23
+ ··· + 34u + 4
c
6
u
24
+ 19u
23
+ ··· + 480u + 16
c
7
, c
12
u
24
+ u
23
+ ··· + 2u + 1
c
8
u
24
+ u
23
+ ··· + 241u + 38
c
10
u
24
+ 2u
23
+ ··· + 66u + 7
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
24
− 19y
23
+ ··· + 52690944y + 1048576
c
2
, c
3
, c
5
c
9
y
24
− 24y
23
+ ··· − 2y + 1
c
4
, c
11
y
24
+ 8y
23
+ ··· − 268y + 16
c
6
y
24
− 5y
23
+ ··· − 88736y + 256
c
7
, c
12
y
24
− 37y
23
+ ··· − 26y + 1
c
8
y
24
+ 27y
23
+ ··· − 37637y + 1444
c
10
y
24
+ 14y
23
+ ··· − 548y + 49
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.328897 + 0.963555I
a = 0.910844 + 0.484743I
b = −0.766113 + 0.751089I
−4.13392 − 1.43705I −8.07864 + 3.13596I
u = 0.328897 − 0.963555I
a = 0.910844 − 0.484743I
b = −0.766113 − 0.751089I
−4.13392 + 1.43705I −8.07864 − 3.13596I
u = 0.939855 + 0.071846I
a = −0.404510 + 0.906423I
b = −0.691190 + 1.173450I
−7.64599 + 2.14568I −13.26685 − 1.01150I
u = 0.939855 − 0.071846I
a = −0.404510 − 0.906423I
b = −0.691190 − 1.173450I
−7.64599 − 2.14568I −13.26685 + 1.01150I
u = −0.746626 + 0.871724I
a = −1.08140 + 1.18930I
b = −0.239897 + 0.846639I
−10.39910 + 0.71995I −14.8370 + 0.2681I
u = −0.746626 − 0.871724I
a = −1.08140 − 1.18930I
b = −0.239897 − 0.846639I
−10.39910 − 0.71995I −14.8370 − 0.2681I
u = −0.778661 + 0.901540I
a = 0.34330 − 1.73842I
b = −0.437819 − 1.055850I
−10.32800 + 5.07117I −14.4995 − 5.6581I
u = −0.778661 − 0.901540I
a = 0.34330 + 1.73842I
b = −0.437819 + 1.055850I
−10.32800 − 5.07117I −14.4995 + 5.6581I
u = −0.973000 + 0.794755I
a = −0.434212 + 0.833754I
b = −0.310872 + 1.186700I
−3.59091 + 0.70472I −5.59047 + 0.17704I
u = −0.973000 − 0.794755I
a = −0.434212 − 0.833754I
b = −0.310872 − 1.186700I
−3.59091 − 0.70472I −5.59047 − 0.17704I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.306537 + 0.623051I
a = −0.22994 − 1.50030I
b = 1.000310 − 0.279529I
1.86738 − 1.10899I 2.50012 + 5.93987I
u = 0.306537 − 0.623051I
a = −0.22994 + 1.50030I
b = 1.000310 + 0.279529I
1.86738 + 1.10899I 2.50012 − 5.93987I
u = −0.143155 + 1.299360I
a = 0.335755 − 0.304928I
b = −0.292872 + 0.366676I
3.50852 + 1.95287I −10.85589 − 6.35743I
u = −0.143155 − 1.299360I
a = 0.335755 + 0.304928I
b = −0.292872 − 0.366676I
3.50852 − 1.95287I −10.85589 + 6.35743I
u = −0.867739 + 1.076530I
a = 0.617487 − 1.083160I
b = −0.735051 − 1.110270I
−2.71430 + 6.07423I −4.21792 − 5.12279I
u = −0.867739 − 1.076530I
a = 0.617487 + 1.083160I
b = −0.735051 + 1.110270I
−2.71430 − 6.07423I −4.21792 + 5.12279I
u = −1.124970 + 0.818587I
a = 0.772531 − 0.690664I
b = 0.92580 − 1.72837I
−13.8026 − 8.9954I −11.74034 + 3.92566I
u = −1.124970 − 0.818587I
a = 0.772531 + 0.690664I
b = 0.92580 + 1.72837I
−13.8026 + 8.9954I −11.74034 − 3.92566I
u = 0.31884 + 1.40808I
a = −0.445331 + 0.435914I
b = −0.006177 − 1.106850I
−2.95010 − 7.04627I −12.05914 + 3.57746I
u = 0.31884 − 1.40808I
a = −0.445331 − 0.435914I
b = −0.006177 + 1.106850I
−2.95010 + 7.04627I −12.05914 − 3.57746I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.91822 + 1.13051I
a = −0.71706 + 1.35307I
b = 1.25897 + 1.53619I
−12.7586 + 16.3728I −10.30097 − 7.90933I
u = −0.91822 − 1.13051I
a = −0.71706 − 1.35307I
b = 1.25897 − 1.53619I
−12.7586 − 16.3728I −10.30097 + 7.90933I
u = −0.429045
a = 0.412338
b = −0.233949
−0.678253 −14.6600
u = −0.254478
a = 4.25274
b = −1.17623
−8.31112 −10.4470
7
II. I
u
2
= h2.07 × 10
10
au
25
+ 1.19 × 10
13
u
25
+ · · · − 2.07 × 10
10
a + 1.59 ×
10
12
, −3.49 × 10
10
au
25
+ 4.50 × 10
10
u
25
+ · · · + 9.72 × 10
10
a + 1.32 ×
10
11
, u
26
− 3u
25
+ · · · + 6u
2
+ 1i
(i) Arc colorings
a
5
=
0
u
a
11
=
1
0
a
7
=
a
−0.00257732au
25
− 1.47872u
25
+ ··· + 0.00257732a − 0.198668
a
12
=
1
u
2
a
8
=
0.00257732au
25
+ 1.47872u
25
+ ··· + 0.997423a + 0.198668
−2.02614u
25
+ 4.93564u
24
+ ··· − 2.35356u − 0.845672
a
9
=
0.00257732au
25
− 0.547418u
25
+ ··· + 0.997423a − 0.647004
−2.02614u
25
+ 4.93564u
24
+ ··· − 2.35356u − 0.845672
a
1
=
0.647004au
25
− 0.0669635u
25
+ ··· − 1.47872a − 0.0221495
0.151236au
25
− 0.930203u
25
+ ··· − 0.931302a + 1.59748
a
4
=
u
u
3
+ u
a
2
=
0.647004au
25
+ 0.0150165u
25
+ ··· − 1.47872a − 0.0947257
0.151236au
25
− 1.17846u
25
+ ··· − 0.931302a + 1.70643
a
6
=
0.198084au
25
− 0.0227350u
25
+ ··· + 0.518890a + 1.13733
0.349848au
25
− 0.457338u
25
+ ··· + 0.00892927a + 1.26221
a
10
=
−0.495767au
25
+ 0.647416u
25
+ ··· + 0.547418a + 0.138652
0.304060au
25
− 0.977539u
25
+ ··· − 0.923265a + 1.73692
a
3
=
0.00515464au
25
+ 0.448336u
25
+ ··· + 0.994845a − 0.603879
−0.187775au
25
+ 1.12169u
25
+ ··· + 0.470801a − 3.06193
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
66478862888
10329040709
u
25
+
217968421278
10329040709
u
24
+ ··· −
74797871360
10329040709
u +
51959996001
10329040709
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
26
+ 7u
25
+ ··· + 104u + 1)
2
c
2
, c
3
, c
5
c
9
u
52
+ u
51
+ ··· + 9u + 1
c
4
, c
11
(u
26
− 3u
25
+ ··· + 6u
2
+ 1)
2
c
6
(u
26
− 5u
25
+ ··· − 114u + 31)
2
c
7
, c
12
u
52
+ 2u
51
+ ··· + 26027u + 12491
c
8
u
52
+ 4u
51
+ ··· − 283294u + 74171
c
10
u
52
− 5u
51
+ ··· − 453512u + 54833
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
26
− 31y
25
+ ··· − 4608y + 1)
2
c
2
, c
3
, c
5
c
9
y
52
− 37y
51
+ ··· − 13y + 1
c
4
, c
11
(y
26
+ 7y
25
+ ··· + 12y + 1)
2
c
6
(y
26
+ 17y
25
+ ··· + 11618y + 961)
2
c
7
, c
12
y
52
− 42y
51
+ ··· − 2616007929y + 156025081
c
8
y
52
+ 38y
51
+ ··· + 245786133074y + 5501337241
c
10
y
52
+ 27y
51
+ ··· − 49791469092y + 3006657889
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.131355 + 0.894729I
a = 0.451077 − 0.150456I
b = −0.998984 − 0.827868I
−3.87482 + 4.61379I −6.13572 − 1.30037I
u = 0.131355 + 0.894729I
a = −1.91778 + 1.70748I
b = 0.443117 − 0.656912I
−3.87482 + 4.61379I −6.13572 − 1.30037I
u = 0.131355 − 0.894729I
a = 0.451077 + 0.150456I
b = −0.998984 + 0.827868I
−3.87482 − 4.61379I −6.13572 + 1.30037I
u = 0.131355 − 0.894729I
a = −1.91778 − 1.70748I
b = 0.443117 + 0.656912I
−3.87482 − 4.61379I −6.13572 + 1.30037I
u = −0.398785 + 0.702857I
a = −0.02931 + 1.44387I
b = 0.514475 + 0.867181I
−0.83541 + 4.01832I −5.46093 − 8.67700I
u = −0.398785 + 0.702857I
a = 1.43554 − 0.33694I
b = −0.856528 − 0.541924I
−0.83541 + 4.01832I −5.46093 − 8.67700I
u = −0.398785 − 0.702857I
a = −0.02931 − 1.44387I
b = 0.514475 − 0.867181I
−0.83541 − 4.01832I −5.46093 + 8.67700I
u = −0.398785 − 0.702857I
a = 1.43554 + 0.33694I
b = −0.856528 + 0.541924I
−0.83541 − 4.01832I −5.46093 + 8.67700I
u = 0.874874 + 0.827469I
a = −0.419640 − 0.908306I
b = −0.485265 − 1.142940I
−6.97798 − 4.77378I −9.07326 + 3.55688I
u = 0.874874 + 0.827469I
a = 0.21817 + 1.45332I
b = −0.539013 + 1.157240I
−6.97798 − 4.77378I −9.07326 + 3.55688I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.874874 − 0.827469I
a = −0.419640 + 0.908306I
b = −0.485265 + 1.142940I
−6.97798 + 4.77378I −9.07326 − 3.55688I
u = 0.874874 − 0.827469I
a = 0.21817 − 1.45332I
b = −0.539013 − 1.157240I
−6.97798 + 4.77378I −9.07326 − 3.55688I
u = 0.509450 + 0.561310I
a = −0.40989 + 1.82180I
b = −0.36665 + 1.55437I
−5.31435 − 7.28077I −10.22138 + 9.25036I
u = 0.509450 + 0.561310I
a = 1.92175 + 0.40718I
b = −0.842568 + 0.445418I
−5.31435 − 7.28077I −10.22138 + 9.25036I
u = 0.509450 − 0.561310I
a = −0.40989 − 1.82180I
b = −0.36665 − 1.55437I
−5.31435 + 7.28077I −10.22138 − 9.25036I
u = 0.509450 − 0.561310I
a = 1.92175 − 0.40718I
b = −0.842568 − 0.445418I
−5.31435 + 7.28077I −10.22138 − 9.25036I
u = 0.808196 + 1.014370I
a = −0.854481 − 0.716975I
b = −0.180742 − 1.005440I
−6.39464 − 1.51730I −7.78325 + 2.91717I
u = 0.808196 + 1.014370I
a = 0.79050 + 1.22544I
b = −0.785952 + 0.988947I
−6.39464 − 1.51730I −7.78325 + 2.91717I
u = 0.808196 − 1.014370I
a = −0.854481 + 0.716975I
b = −0.180742 + 1.005440I
−6.39464 + 1.51730I −7.78325 − 2.91717I
u = 0.808196 − 1.014370I
a = 0.79050 − 1.22544I
b = −0.785952 − 0.988947I
−6.39464 + 1.51730I −7.78325 − 2.91717I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.244374 + 0.651478I
a = −0.296687 − 0.874288I
b = 1.159890 − 0.155610I
1.95982 − 1.10736I −0.80753 + 5.92917I
u = 0.244374 + 0.651478I
a = −0.06047 − 2.05027I
b = 0.735414 − 0.089381I
1.95982 − 1.10736I −0.80753 + 5.92917I
u = 0.244374 − 0.651478I
a = −0.296687 + 0.874288I
b = 1.159890 + 0.155610I
1.95982 + 1.10736I −0.80753 − 5.92917I
u = 0.244374 − 0.651478I
a = −0.06047 + 2.05027I
b = 0.735414 + 0.089381I
1.95982 + 1.10736I −0.80753 − 5.92917I
u = −1.078600 + 0.784353I
a = 0.968849 − 0.380572I
b = 1.79712 − 1.86504I
−11.92070 + 4.73378I −13.8664 − 3.7620I
u = −1.078600 + 0.784353I
a = 0.134340 − 1.178040I
b = −0.619451 − 1.219200I
−11.92070 + 4.73378I −13.8664 − 3.7620I
u = −1.078600 − 0.784353I
a = 0.968849 + 0.380572I
b = 1.79712 + 1.86504I
−11.92070 − 4.73378I −13.8664 + 3.7620I
u = −1.078600 − 0.784353I
a = 0.134340 + 1.178040I
b = −0.619451 + 1.219200I
−11.92070 − 4.73378I −13.8664 + 3.7620I
u = −0.068095 + 1.374870I
a = −0.594304 − 1.280230I
b = 0.50000 + 1.73847I
1.97394 + 0.78097I −7.54315 + 6.50608I
u = −0.068095 + 1.374870I
a = 0.135613 + 0.044884I
b = 0.445532 − 0.369804I
1.97394 + 0.78097I −7.54315 + 6.50608I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.068095 − 1.374870I
a = −0.594304 + 1.280230I
b = 0.50000 − 1.73847I
1.97394 − 0.78097I −7.54315 − 6.50608I
u = −0.068095 − 1.374870I
a = 0.135613 − 0.044884I
b = 0.445532 + 0.369804I
1.97394 − 0.78097I −7.54315 − 6.50608I
u = −0.551572 + 0.242043I
a = −0.91561 − 1.39579I
b = −0.85997 − 1.58919I
−2.14593 + 2.04473I −11.96352 − 3.36744I
u = −0.551572 + 0.242043I
a = −0.25837 + 2.23090I
b = 0.869517 + 0.406486I
−2.14593 + 2.04473I −11.96352 − 3.36744I
u = −0.551572 − 0.242043I
a = −0.91561 + 1.39579I
b = −0.85997 + 1.58919I
−2.14593 − 2.04473I −11.96352 + 3.36744I
u = −0.551572 − 0.242043I
a = −0.25837 − 2.23090I
b = 0.869517 − 0.406486I
−2.14593 − 2.04473I −11.96352 + 3.36744I
u = 1.118310 + 0.840130I
a = 0.933066 + 0.658847I
b = 1.02920 + 2.15726I
−8.03647 + 2.93288I −11.16553 − 3.09783I
u = 1.118310 + 0.840130I
a = −0.414460 − 0.736911I
b = −0.280289 − 1.187630I
−8.03647 + 2.93288I −11.16553 − 3.09783I
u = 1.118310 − 0.840130I
a = 0.933066 − 0.658847I
b = 1.02920 − 2.15726I
−8.03647 − 2.93288I −11.16553 + 3.09783I
u = 1.118310 − 0.840130I
a = −0.414460 + 0.736911I
b = −0.280289 + 1.187630I
−8.03647 − 2.93288I −11.16553 + 3.09783I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.94165 + 1.11572I
a = 0.506918 + 1.031830I
b = −0.723488 + 1.136400I
−7.12929 − 10.36590I −8.80055 + 7.37004I
u = 0.94165 + 1.11572I
a = −0.76431 − 1.34870I
b = 1.39425 − 1.81521I
−7.12929 − 10.36590I −8.80055 + 7.37004I
u = 0.94165 − 1.11572I
a = 0.506918 − 1.031830I
b = −0.723488 − 1.136400I
−7.12929 + 10.36590I −8.80055 − 7.37004I
u = 0.94165 − 1.11572I
a = −0.76431 + 1.34870I
b = 1.39425 + 1.81521I
−7.12929 + 10.36590I −8.80055 − 7.37004I
u = −0.91859 + 1.17812I
a = −0.640700 + 0.507931I
b = −0.129200 + 1.118780I
−10.69780 + 2.56112I −14.5817 − 1.8830I
u = −0.91859 + 1.17812I
a = −0.79513 + 1.47363I
b = 2.17348 + 1.56361I
−10.69780 + 2.56112I −14.5817 − 1.8830I
u = −0.91859 − 1.17812I
a = −0.640700 − 0.507931I
b = −0.129200 − 1.118780I
−10.69780 − 2.56112I −14.5817 + 1.8830I
u = −0.91859 − 1.17812I
a = −0.79513 − 1.47363I
b = 2.17348 − 1.56361I
−10.69780 − 2.56112I −14.5817 + 1.8830I
u = −0.112565 + 0.479367I
a = 0.241569 − 0.802021I
b = −1.22650 + 0.71556I
−1.46888 − 1.74074I −7.09706 − 4.27417I
u = −0.112565 + 0.479367I
a = 2.13374 + 2.67787I
b = 0.332607 − 0.020427I
−1.46888 − 1.74074I −7.09706 − 4.27417I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.112565 − 0.479367I
a = 0.241569 + 0.802021I
b = −1.22650 − 0.71556I
−1.46888 + 1.74074I −7.09706 + 4.27417I
u = −0.112565 − 0.479367I
a = 2.13374 − 2.67787I
b = 0.332607 + 0.020427I
−1.46888 + 1.74074I −7.09706 + 4.27417I
16
III.
I
u
3
= h−u
11
−2u
10
+· · ·+b+1, −u
11
−4u
10
+· · ·+a−3, u
12
+3u
11
+· · ·+u+1i
(i) Arc colorings
a
5
=
0
u
a
11
=
1
0
a
7
=
u
11
+ 4u
10
+ ··· + 3u + 3
u
11
+ 2u
10
+ 5u
9
+ 5u
8
+ 7u
7
+ 2u
6
+ 2u
5
− 4u
4
− u
3
− 3u
2
+ u − 1
a
12
=
1
u
2
a
8
=
u
10
+ 3u
9
+ 8u
8
+ 12u
7
+ 18u
6
+ 16u
5
+ 16u
4
+ 7u
3
+ 6u
2
+ 3
u
11
+ 3u
10
+ 7u
9
+ 10u
8
+ 13u
7
+ 10u
6
+ 8u
5
+ u
4
+ u
3
− 2u
2
+ 2u − 1
a
9
=
u
11
+ 4u
10
+ ··· + 2u + 2
u
11
+ 3u
10
+ 7u
9
+ 10u
8
+ 13u
7
+ 10u
6
+ 8u
5
+ u
4
+ u
3
− 2u
2
+ 2u − 1
a
1
=
4u
11
+ 11u
10
+ ··· + 9u + 1
−u
10
− 3u
9
− 7u
8
− 11u
7
− 15u
6
− 15u
5
− 13u
4
− 9u
3
− 4u
2
− 3u − 2
a
4
=
u
u
3
+ u
a
2
=
2u
11
+ 6u
10
+ ··· + 2u
2
+ 5u
−2u
11
− 7u
10
+ ··· − 6u − 4
a
6
=
2u
11
+ 5u
10
+ ··· + 6u − 1
−2u
11
− 8u
10
+ ··· − 7u − 4
a
10
=
2u
11
+ 5u
10
+ ··· + 2u − 2
−u
11
− 3u
10
+ ··· − 4u − 1
a
3
=
−u
11
− 2u
10
− 5u
9
− 5u
8
− 7u
7
− 2u
6
− 3u
5
+ 3u
4
− u
3
+ 2u
2
− 2u + 2
u
11
+ 3u
10
+ 8u
9
+ 12u
8
+ 18u
7
+ 16u
6
+ 16u
5
+ 7u
4
+ 7u
3
+ 4u
(ii) Obstruction class = 1
(iii) Cusp Shapes
= 10u
11
+ 27u
10
+ 67u
9
+ 97u
8
+ 140u
7
+ 127u
6
+ 122u
5
+ 64u
4
+ 46u
3
+ 7u
2
+ 16u − 9
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
12
+ 9u
9
+ ··· − 56u + 8
c
2
, c
9
u
12
− 5u
10
+ 11u
8
+ u
7
− 12u
6
− 3u
5
+ 7u
4
+ 4u
3
− 2u
2
− 2u + 1
c
3
, c
5
u
12
− 5u
10
+ 11u
8
− u
7
− 12u
6
+ 3u
5
+ 7u
4
− 4u
3
− 2u
2
+ 2u + 1
c
4
u
12
− 3u
11
+ ··· − u + 1
c
6
u
12
+ 6u
11
+ ··· + 55u + 13
c
7
u
12
+ u
11
+ ··· + 2u + 1
c
8
u
12
+ u
11
+ ··· + 26u + 11
c
10
u
12
− 2u
11
+ ··· − 2u + 1
c
11
u
12
+ 3u
11
+ ··· + u + 1
c
12
u
12
− u
11
+ ··· − 2u + 1
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
12
+ 28y
10
+ ··· − 1760y + 64
c
2
, c
3
, c
5
c
9
y
12
− 10y
11
+ ··· − 8y + 1
c
4
, c
11
y
12
+ 7y
11
+ ··· + 9y + 1
c
6
y
12
+ 6y
11
+ ··· − 607y + 169
c
7
, c
12
y
12
− 3y
11
+ ··· + 12y + 1
c
8
y
12
+ 5y
11
+ ··· − 346y + 121
c
10
y
12
+ 4y
11
+ ··· + 2y + 1
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.901514 + 0.798418I
a = 0.140034 − 1.182110I
b = −0.100088 − 1.238220I
−8.12777 + 6.33189I −12.25726 − 6.68709I
u = −0.901514 − 0.798418I
a = 0.140034 + 1.182110I
b = −0.100088 + 1.238220I
−8.12777 − 6.33189I −12.25726 + 6.68709I
u = 0.195818 + 1.216330I
a = −0.178072 − 0.559998I
b = 0.652612 + 0.317914I
3.97699 − 1.74972I 4.29079 + 0.86004I
u = 0.195818 − 1.216330I
a = −0.178072 + 0.559998I
b = 0.652612 − 0.317914I
3.97699 + 1.74972I 4.29079 − 0.86004I
u = −0.218380 + 1.219800I
a = 0.335448 + 0.853839I
b = −0.313935 − 0.677604I
−1.91415 + 7.37706I −3.90229 − 6.46992I
u = −0.218380 − 1.219800I
a = 0.335448 − 0.853839I
b = −0.313935 + 0.677604I
−1.91415 − 7.37706I −3.90229 + 6.46992I
u = 0.388421 + 0.538359I
a = 0.16183 − 1.70410I
b = 1.164420 − 0.293382I
1.55954 − 0.78130I −10.36782 − 6.44455I
u = 0.388421 − 0.538359I
a = 0.16183 + 1.70410I
b = 1.164420 + 0.293382I
1.55954 + 0.78130I −10.36782 + 6.44455I
u = −0.865258 + 1.024720I
a = −0.855063 + 0.838948I
b = 0.193415 + 1.176310I
−7.46101 + 0.19387I −11.77490 + 0.97916I
u = −0.865258 − 1.024720I
a = −0.855063 − 0.838948I
b = 0.193415 − 1.176310I
−7.46101 − 0.19387I −11.77490 − 0.97916I
20
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.099086 + 0.602834I
a = 2.39583 + 0.78317I
b = −0.596419 + 0.848698I
−4.48294 − 5.85264I −8.48852 + 6.46269I
u = −0.099086 − 0.602834I
a = 2.39583 − 0.78317I
b = −0.596419 − 0.848698I
−4.48294 + 5.85264I −8.48852 − 6.46269I
21
IV. I
u
4
=
hu
5
a+3u
5
+· · ·−a +2, u
4
a+2u
5
+· · ·+a
2
+2a, u
6
−u
5
+3u
4
−2u
3
+3u
2
+1i
(i) Arc colorings
a
5
=
0
u
a
11
=
1
0
a
7
=
a
−
1
5
u
5
a −
3
5
u
5
+ ··· +
1
5
a −
2
5
a
12
=
1
u
2
a
8
=
1
5
u
5
a +
3
5
u
5
+ ··· +
4
5
a +
2
5
−u
5
+ 2u
4
− 3u
3
− au + 3u
2
− 2u
a
9
=
1
5
u
5
a −
2
5
u
5
+ ··· +
4
5
a +
2
5
−u
5
+ 2u
4
− 3u
3
− au + 3u
2
− 2u
a
1
=
−
2
5
u
5
a −
6
5
u
5
+ ··· −
3
5
a +
1
5
1
5
u
5
a +
3
5
u
5
+ ··· −
1
5
a −
3
5
a
4
=
u
u
3
+ u
a
2
=
−
2
5
u
5
a −
1
5
u
5
+ ··· −
3
5
a −
4
5
1
5
u
5
a +
3
5
u
5
+ ··· −
1
5
a −
8
5
a
6
=
−
3
5
u
5
a +
1
5
u
5
+ ··· +
3
5
a −
1
5
−
1
5
u
5
a +
2
5
u
5
+ ··· −
4
5
a −
7
5
a
10
=
3
5
u
5
a −
1
5
u
5
+ ··· +
2
5
a −
4
5
−
1
5
u
5
a +
7
5
u
5
+ ··· −
4
5
a −
2
5
a
3
=
−
2
5
u
5
a +
4
5
u
5
+ ··· −
3
5
a −
4
5
4
5
u
5
a +
7
5
u
5
+ ··· −
4
5
a −
2
5
(ii) Obstruction class = 1
(iii) Cusp Shapes = 7u
4
− 8u
3
+ 17u
2
− 9u + 3
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
6
+ u
5
− 4u
4
+ u
3
+ 5u
2
− 8u + 5)
2
c
2
, c
9
u
12
− 4u
10
+ u
9
+ 3u
8
− 7u
7
+ 7u
6
+ 17u
5
− 9u
4
− 18u
3
− 4u
2
+ 7u + 7
c
3
, c
5
u
12
− 4u
10
− u
9
+ 3u
8
+ 7u
7
+ 7u
6
− 17u
5
− 9u
4
+ 18u
3
− 4u
2
− 7u + 7
c
4
(u
6
+ u
5
+ 3u
4
+ 2u
3
+ 3u
2
+ 1)
2
c
6
(u
6
− u
5
− 2u
3
+ 2u
2
+ 1)
2
c
7
u
12
− u
11
+ ··· + 7u + 7
c
8
u
12
− u
11
+ ··· + 10u
2
+ 11
c
10
u
12
+ 6u
11
+ ··· − 4u + 1
c
11
(u
6
− u
5
+ 3u
4
− 2u
3
+ 3u
2
+ 1)
2
c
12
u
12
+ u
11
+ ··· − 7u + 7
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
6
− 9y
5
+ 24y
4
− 15y
3
+ y
2
− 14y + 25)
2
c
2
, c
3
, c
5
c
9
y
12
− 8y
11
+ ··· − 105y + 49
c
4
, c
11
(y
6
+ 5y
5
+ 11y
4
+ 16y
3
+ 15y
2
+ 6y + 1)
2
c
6
(y
6
− y
5
− 2y
3
+ 4y
2
+ 4y + 1)
2
c
7
, c
12
y
12
− 9y
11
+ ··· + 91y + 49
c
8
y
12
+ 3y
11
+ ··· + 220y + 121
c
10
y
12
+ 18y
10
+ ··· − 16y + 1
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.751720 + 0.952459I
a = −0.636694 − 0.705384I
b = −0.573880 − 0.681770I
−8.95401 − 2.84527I −10.14719 + 2.90828I
u = 0.751720 + 0.952459I
a = 0.60954 + 1.74781I
b = −1.17448 + 0.86290I
−8.95401 − 2.84527I −10.14719 + 2.90828I
u = 0.751720 − 0.952459I
a = −0.636694 + 0.705384I
b = −0.573880 + 0.681770I
−8.95401 + 2.84527I −10.14719 − 2.90828I
u = 0.751720 − 0.952459I
a = 0.60954 − 1.74781I
b = −1.17448 − 0.86290I
−8.95401 + 2.84527I −10.14719 − 2.90828I
u = −0.081708 + 1.363140I
a = 0.53017 − 1.32661I
b = −1.01141 + 1.63879I
1.96943 − 1.24964I −7.73074 + 9.76401I
u = −0.081708 + 1.363140I
a = 0.310661 + 0.248175I
b = 0.313585 − 0.116939I
1.96943 − 1.24964I −7.73074 + 9.76401I
u = −0.081708 − 1.363140I
a = 0.53017 + 1.32661I
b = −1.01141 − 1.63879I
1.96943 + 1.24964I −7.73074 − 9.76401I
u = −0.081708 − 1.363140I
a = 0.310661 − 0.248175I
b = 0.313585 + 0.116939I
1.96943 + 1.24964I −7.73074 − 9.76401I
u = −0.170012 + 0.579072I
a = 0.463351 − 0.885770I
b = −1.25941 − 0.96832I
−1.24009 + 2.32699I −1.62207 − 6.56254I
u = −0.170012 + 0.579072I
a = −1.77702 + 2.80509I
b = 0.705591 + 0.260082I
−1.24009 + 2.32699I −1.62207 − 6.56254I
25
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.170012 − 0.579072I
a = 0.463351 + 0.885770I
b = −1.25941 + 0.96832I
−1.24009 − 2.32699I −1.62207 + 6.56254I
u = −0.170012 − 0.579072I
a = −1.77702 − 2.80509I
b = 0.705591 − 0.260082I
−1.24009 − 2.32699I −1.62207 + 6.56254I
26
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
6
+ u
5
− 4u
4
+ u
3
+ 5u
2
− 8u + 5)
2
)(u
12
+ 9u
9
+ ··· − 56u + 8)
· (u
24
− 29u
23
+ ··· + 8704u − 1024)(u
26
+ 7u
25
+ ··· + 104u + 1)
2
c
2
, c
9
(u
12
− 5u
10
+ 11u
8
+ u
7
− 12u
6
− 3u
5
+ 7u
4
+ 4u
3
− 2u
2
− 2u + 1)
· (u
12
− 4u
10
+ u
9
+ 3u
8
− 7u
7
+ 7u
6
+ 17u
5
− 9u
4
− 18u
3
− 4u
2
+ 7u + 7)
· (u
24
− 12u
22
+ ··· + 4u − 1)(u
52
+ u
51
+ ··· + 9u + 1)
c
3
, c
5
(u
12
− 5u
10
+ 11u
8
− u
7
− 12u
6
+ 3u
5
+ 7u
4
− 4u
3
− 2u
2
+ 2u + 1)
· (u
12
− 4u
10
− u
9
+ 3u
8
+ 7u
7
+ 7u
6
− 17u
5
− 9u
4
+ 18u
3
− 4u
2
− 7u + 7)
· (u
24
− 12u
22
+ ··· + 4u − 1)(u
52
+ u
51
+ ··· + 9u + 1)
c
4
((u
6
+ u
5
+ 3u
4
+ 2u
3
+ 3u
2
+ 1)
2
)(u
12
− 3u
11
+ ··· − u + 1)
· (u
24
+ 8u
23
+ ··· + 34u + 4)(u
26
− 3u
25
+ ··· + 6u
2
+ 1)
2
c
6
((u
6
− u
5
− 2u
3
+ 2u
2
+ 1)
2
)(u
12
+ 6u
11
+ ··· + 55u + 13)
· (u
24
+ 19u
23
+ ··· + 480u + 16)(u
26
− 5u
25
+ ··· − 114u + 31)
2
c
7
(u
12
− u
11
+ ··· + 7u + 7)(u
12
+ u
11
+ ··· + 2u + 1)
· (u
24
+ u
23
+ ··· + 2u + 1)(u
52
+ 2u
51
+ ··· + 26027u + 12491)
c
8
(u
12
− u
11
+ ··· + 10u
2
+ 11)(u
12
+ u
11
+ ··· + 26u + 11)
· (u
24
+ u
23
+ ··· + 241u + 38)(u
52
+ 4u
51
+ ··· − 283294u + 74171)
c
10
(u
12
− 2u
11
+ ··· − 2u + 1)(u
12
+ 6u
11
+ ··· − 4u + 1)
· (u
24
+ 2u
23
+ ··· + 66u + 7)(u
52
− 5u
51
+ ··· − 453512u + 54833)
c
11
((u
6
− u
5
+ 3u
4
− 2u
3
+ 3u
2
+ 1)
2
)(u
12
+ 3u
11
+ ··· + u + 1)
· (u
24
+ 8u
23
+ ··· + 34u + 4)(u
26
− 3u
25
+ ··· + 6u
2
+ 1)
2
c
12
(u
12
− u
11
+ ··· − 2u + 1)(u
12
+ u
11
+ ··· − 7u + 7)
· (u
24
+ u
23
+ ··· + 2u + 1)(u
52
+ 2u
51
+ ··· + 26027u + 12491)
27
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
6
− 9y
5
+ 24y
4
− 15y
3
+ y
2
− 14y + 25)
2
· (y
12
+ 28y
10
+ ··· − 1760y + 64)
· (y
24
− 19y
23
+ ··· + 52690944y + 1048576)
· (y
26
− 31y
25
+ ··· − 4608y + 1)
2
c
2
, c
3
, c
5
c
9
(y
12
− 10y
11
+ ··· − 8y + 1)(y
12
− 8y
11
+ ··· − 105y + 49)
· (y
24
− 24y
23
+ ··· − 2y + 1)(y
52
− 37y
51
+ ··· − 13y + 1)
c
4
, c
11
((y
6
+ 5y
5
+ ··· + 6y + 1)
2
)(y
12
+ 7y
11
+ ··· + 9y + 1)
· (y
24
+ 8y
23
+ ··· − 268y + 16)(y
26
+ 7y
25
+ ··· + 12y + 1)
2
c
6
((y
6
− y
5
− 2y
3
+ 4y
2
+ 4y + 1)
2
)(y
12
+ 6y
11
+ ··· − 607y + 169)
· (y
24
− 5y
23
+ ··· − 88736y + 256)
· (y
26
+ 17y
25
+ ··· + 11618y + 961)
2
c
7
, c
12
(y
12
− 9y
11
+ ··· + 91y + 49)(y
12
− 3y
11
+ ··· + 12y + 1)
· (y
24
− 37y
23
+ ··· − 26y + 1)
· (y
52
− 42y
51
+ ··· − 2616007929y + 156025081)
c
8
(y
12
+ 3y
11
+ ··· + 220y + 121)(y
12
+ 5y
11
+ ··· − 346y + 121)
· (y
24
+ 27y
23
+ ··· − 37637y + 1444)
· (y
52
+ 38y
51
+ ··· + 245786133074y + 5501337241)
c
10
(y
12
+ 18y
10
+ ··· − 16y + 1)(y
12
+ 4y
11
+ ··· + 2y + 1)
· (y
24
+ 14y
23
+ ··· − 548y + 49)
· (y
52
+ 27y
51
+ ··· − 49791469092y + 3006657889)
28
