12n
0538
(K12n
0538
)
A knot diagram
1
Linearized knot diagam
3 6 8 7 2 9 11 12 6 3 4 10
Solving Sequence
2,6 3,9
7 10 11 1 5 4 12 8
c
2
c
6
c
9
c
10
c
1
c
5
c
4
c
12
c
8
c
3
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= hb − u, −1.88153 × 10
15
u
21
− 8.14124 × 10
14
u
20
+ ··· + 7.04162 × 10
15
a − 1.77167 × 10
16
,
u
22
+ u
21
+ ··· − u − 1i
I
u
2
= h3.24728 × 10
55
u
29
+ 4.53015 × 10
55
u
28
+ ··· + 1.62069 × 10
57
b + 2.03912 × 10
58
,
− 4.46743 × 10
57
u
29
− 5.44501 × 10
57
u
28
+ ··· + 9.44863 × 10
59
a − 4.18593 × 10
60
,
u
30
+ 2u
29
+ ··· + 4496u + 583i
I
u
3
= hb + u, −2u
10
− 10u
9
− 13u
8
+ 10u
7
+ 31u
6
+ 4u
5
− 27u
4
− 5u
3
+ 17u
2
+ a + 5u − 4,
u
11
+ 4u
10
+ 2u
9
− 9u
8
− 8u
7
+ 9u
6
+ 9u
5
− 7u
4
− 6u
3
+ 3u
2
+ 2u − 1i
I
u
4
= hb + 1, u
2
+ a − u, u
3
− u − 1i
I
u
5
= ha
2
+ b + 1, a
3
+ a
2
+ 2a + 1, u − 1i
I
u
6
= hb + 1, a
3
+ a
2
+ 2a + 1, u − 1i
* 6 irreducible components of dim
C
= 0, with total 72 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
= hb − u, −1.88 × 10
15
u
21
− 8.14 × 10
14
u
20
+ · · · + 7.04 × 10
15
a −
1.77 × 10
16
, u
22
+ u
21
+ · · · − u − 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
u
2
a
9
=
0.267202u
21
+ 0.115616u
20
+ ··· + 5.41231u + 2.51601
u
a
7
=
0.617336u
21
+ 0.765365u
20
+ ··· − 1.29850u + 1.66021
0.155989u
21
+ 0.149710u
20
+ ··· + 0.884384u + 0.151586
a
10
=
0.267202u
21
+ 0.115616u
20
+ ··· + 5.41231u + 2.51601
−0.155989u
21
− 0.149710u
20
+ ··· + 1.11562u − 0.151586
a
11
=
0.267202u
21
+ 0.115616u
20
+ ··· + 4.41231u + 2.51601
−0.155989u
21
− 0.149710u
20
+ ··· + 1.11562u − 0.151586
a
1
=
−u
2
+ 1
−u
4
a
5
=
u
u
a
4
=
−0.322075u
21
− 0.212786u
20
+ ··· − 6.89909u − 3.09806
−0.193421u
21
− 0.0467415u
20
+ ··· − 0.323268u − 0.397732
a
12
=
0.305894u
21
+ 0.558047u
20
+ ··· − 0.813238u + 1.19414
−0.124057u
21
− 0.268999u
20
+ ··· + 0.865623u + 0.408142
a
8
=
0.536796u
21
+ 0.450130u
20
+ ··· + 6.96025u + 3.15781
−0.105547u
21
− 0.0829132u
20
+ ··· + 1.39238u + 0.00872824
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
2868088365347525
4694410161939152
u
21
−
18112778300119
586801270242394
u
20
+ ··· −
981896352987059
586801270242394
u −
17835381551211165
4694410161939152
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
22
+ 33u
21
+ ··· − 15u + 1
c
2
, c
5
, c
10
u
22
+ u
21
+ ··· − u − 1
c
3
, c
8
u
22
+ u
21
+ ··· + 5u + 1
c
4
u
22
+ 2u
21
+ ··· − 126u + 103
c
6
, c
9
u
22
− 10u
21
+ ··· − 80u + 16
c
7
u
22
+ u
21
+ ··· + 36u + 8
c
11
u
22
− 13u
21
+ ··· + 2u + 4
c
12
u
22
+ 4u
21
+ ··· − 281u − 83
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
22
− 113y
21
+ ··· + 107y + 1
c
2
, c
5
, c
10
y
22
− 33y
21
+ ··· + 15y + 1
c
3
, c
8
y
22
− 9y
21
+ ··· − 25y + 1
c
4
y
22
+ 24y
21
+ ··· + 134916y + 10609
c
6
, c
9
y
22
+ 6y
21
+ ··· − 672y + 256
c
7
y
22
+ 13y
21
+ ··· + 368y + 64
c
11
y
22
− y
21
+ ··· − 460y + 16
c
12
y
22
− 60y
21
+ ··· − 67175y + 6889
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.748970 + 0.444444I
a = −0.19228 + 1.51718I
b = −0.748970 + 0.444444I
0.13615 − 1.92714I −10.34642 + 1.92836I
u = −0.748970 − 0.444444I
a = −0.19228 − 1.51718I
b = −0.748970 − 0.444444I
0.13615 + 1.92714I −10.34642 − 1.92836I
u = −0.130611 + 0.725732I
a = −1.39284 − 0.49810I
b = −0.130611 + 0.725732I
−0.18292 + 6.65611I −5.95007 − 7.18766I
u = −0.130611 − 0.725732I
a = −1.39284 + 0.49810I
b = −0.130611 − 0.725732I
−0.18292 − 6.65611I −5.95007 + 7.18766I
u = 0.401084 + 0.542056I
a = 1.24737 + 1.06824I
b = 0.401084 + 0.542056I
3.54902 + 1.72435I 1.79964 − 0.73697I
u = 0.401084 − 0.542056I
a = 1.24737 − 1.06824I
b = 0.401084 − 0.542056I
3.54902 − 1.72435I 1.79964 + 0.73697I
u = −1.33424
a = −0.431084
b = −1.33424
−2.34301 2.73470
u = −0.056775 + 0.629497I
a = 0.785309 − 1.011460I
b = −0.056775 + 0.629497I
−1.31504 + 2.14729I −8.96814 − 3.55690I
u = −0.056775 − 0.629497I
a = 0.785309 + 1.011460I
b = −0.056775 − 0.629497I
−1.31504 − 2.14729I −8.96814 + 3.55690I
u = −0.287480 + 0.350556I
a = 1.135910 + 0.180293I
b = −0.287480 + 0.350556I
−0.788001 + 1.021190I −5.92604 − 5.41331I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.287480 − 0.350556I
a = 1.135910 − 0.180293I
b = −0.287480 − 0.350556I
−0.788001 − 1.021190I −5.92604 + 5.41331I
u = 0.181344 + 0.303051I
a = 1.69533 + 2.92707I
b = 0.181344 + 0.303051I
0.04653 + 2.94961I −5.40179 + 1.97738I
u = 0.181344 − 0.303051I
a = 1.69533 − 2.92707I
b = 0.181344 − 0.303051I
0.04653 − 2.94961I −5.40179 − 1.97738I
u = 1.76598
a = 0.362139
b = 1.76598
−9.32648 −9.85720
u = 1.88020 + 0.16813I
a = 0.593976 + 0.598808I
b = 1.88020 + 0.16813I
−13.59180 − 1.67864I −10.72705 − 0.48573I
u = 1.88020 − 0.16813I
a = 0.593976 − 0.598808I
b = 1.88020 − 0.16813I
−13.59180 + 1.67864I −10.72705 + 0.48573I
u = −1.95173 + 0.18984I
a = −0.792024 + 0.526959I
b = −1.95173 + 0.18984I
−15.4135 − 5.6943I −10.05870 + 3.46761I
u = −1.95173 − 0.18984I
a = −0.792024 − 0.526959I
b = −1.95173 − 0.18984I
−15.4135 + 5.6943I −10.05870 − 3.46761I
u = 1.97172 + 0.33031I
a = 0.661105 + 0.393921I
b = 1.97172 + 0.33031I
−14.3712 − 6.4475I −12.31821 + 5.34631I
u = 1.97172 − 0.33031I
a = 0.661105 − 0.393921I
b = 1.97172 − 0.33031I
−14.3712 + 6.4475I −12.31821 − 5.34631I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.97465 + 0.36872I
a = −0.707383 + 0.533233I
b = −1.97465 + 0.36872I
−14.7419 + 15.2513I −9.04193 − 6.95312I
u = −1.97465 − 0.36872I
a = −0.707383 − 0.533233I
b = −1.97465 − 0.36872I
−14.7419 − 15.2513I −9.04193 + 6.95312I
7
II. I
u
2
= h3.25 × 10
55
u
29
+ 4.53 × 10
55
u
28
+ · · · + 1.62 × 10
57
b + 2.04 ×
10
58
, −4.47 × 10
57
u
29
− 5.45 × 10
57
u
28
+ · · · + 9.45 × 10
59
a − 4.19 ×
10
60
, u
30
+ 2u
29
+ · · · + 4496u + 583i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
u
2
a
9
=
0.00472813u
29
+ 0.00576275u
28
+ ··· + 27.0557u + 4.43020
−0.0200364u
29
− 0.0279520u
28
+ ··· − 67.4156u − 12.5818
a
7
=
0.00410451u
29
+ 0.0121031u
28
+ ··· + 6.61203u + 1.98039
0.00745135u
29
+ 0.0160502u
28
+ ··· + 0.792830u + 0.0832540
a
10
=
0.00472813u
29
+ 0.00576275u
28
+ ··· + 27.0557u + 4.43020
−0.0171807u
29
− 0.0229105u
28
+ ··· − 53.5661u − 10.4285
a
11
=
0.0247645u
29
+ 0.0337147u
28
+ ··· + 94.4714u + 17.0120
−0.00141883u
29
− 0.00143599u
28
+ ··· − 10.7523u − 3.36205
a
1
=
−u
2
+ 1
−u
4
a
5
=
u
u
a
4
=
−0.00504933u
29
− 0.00945349u
28
+ ··· − 40.1713u − 6.41129
0.00262810u
29
+ 0.00887618u
28
+ ··· − 27.9565u − 3.77015
a
12
=
0.00260386u
29
+ 0.00679584u
28
+ ··· − 7.78421u + 2.10200
−0.0131077u
29
− 0.00690705u
28
+ ··· − 102.987u − 16.3636
a
8
=
0.00606568u
29
+ 0.0116476u
28
+ ··· + 9.85622u − 0.550040
0.00608037u
29
+ 0.0164677u
28
+ ··· − 17.2937u − 1.45033
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.261146u
29
+ 0.287455u
28
+ ··· + 1402.90u + 219.809
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
30
+ 46u
29
+ ··· + 11608936u + 339889
c
2
, c
5
, c
10
u
30
+ 2u
29
+ ··· + 4496u + 583
c
3
, c
8
u
30
+ u
29
+ ··· + 58u − 11
c
4
u
30
+ 8u
29
+ ··· + 2447u + 271
c
6
, c
9
(u
15
+ 7u
14
+ ··· + 4u + 1)
2
c
7
u
30
+ 3u
29
+ ··· + 356u + 88
c
11
(u
15
+ 8u
14
+ ··· + 5u + 1)
2
c
12
u
30
+ 2u
29
+ ··· + 197368u − 32296
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
30
− 50y
29
+ ··· − 48946220611468y + 115524532321
c
2
, c
5
, c
10
y
30
− 46y
29
+ ··· − 11608936y + 339889
c
3
, c
8
y
30
− 3y
29
+ ··· − 3056y + 121
c
4
y
30
+ 64y
29
+ ··· − 1263195y + 73441
c
6
, c
9
(y
15
− 3y
14
+ ··· + 36y −1)
2
c
7
y
30
+ 17y
29
+ ··· + 280176y + 7744
c
11
(y
15
+ 28y
13
+ ··· − 9y −1)
2
c
12
y
30
− 22y
29
+ ··· − 9540868384y + 1043031616
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.733366 + 0.760399I
a = −0.932743 + 0.643875I
b = −1.086660 + 0.495175I
−3.92076 − 0.11084I −19.2470 + 2.6115I
u = 0.733366 − 0.760399I
a = −0.932743 − 0.643875I
b = −1.086660 − 0.495175I
−3.92076 + 0.11084I −19.2470 − 2.6115I
u = 1.102460 + 0.135538I
a = 0.850106 − 0.383862I
b = 1.20887 − 1.10475I
−4.14672 + 8.45942I −10.28669 − 6.66978I
u = 1.102460 − 0.135538I
a = 0.850106 + 0.383862I
b = 1.20887 + 1.10475I
−4.14672 − 8.45942I −10.28669 + 6.66978I
u = −0.873450 + 0.022311I
a = −0.450314 − 0.183725I
b = −1.86355 + 1.25575I
−2.83938 + 0.15495I −69.8860 − 16.0941I
u = −0.873450 − 0.022311I
a = −0.450314 + 0.183725I
b = −1.86355 − 1.25575I
−2.83938 − 0.15495I −69.8860 + 16.0941I
u = −0.965004 + 0.592094I
a = 0.798906 + 0.014589I
b = 1.027040 + 0.648501I
−2.16274 + 2.22327I −10.93751 − 4.89170I
u = −0.965004 − 0.592094I
a = 0.798906 − 0.014589I
b = 1.027040 − 0.648501I
−2.16274 − 2.22327I −10.93751 + 4.89170I
u = 1.133110 + 0.242313I
a = −0.356690 − 1.137480I
b = −0.340336 − 0.281341I
1.41649 − 4.96313I −5.21468 + 7.56800I
u = 1.133110 − 0.242313I
a = −0.356690 + 1.137480I
b = −0.340336 + 0.281341I
1.41649 + 4.96313I −5.21468 − 7.56800I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.086660 + 0.495175I
a = 0.812020 + 0.588181I
b = 0.733366 + 0.760399I
−3.92076 − 0.11084I −19.2470 + 2.6115I
u = −1.086660 − 0.495175I
a = 0.812020 − 0.588181I
b = 0.733366 − 0.760399I
−3.92076 + 0.11084I −19.2470 − 2.6115I
u = 1.027040 + 0.648501I
a = −0.340958 + 0.662159I
b = −0.965004 + 0.592094I
−2.16274 + 2.22327I −10.93751 − 4.89170I
u = 1.027040 − 0.648501I
a = −0.340958 − 0.662159I
b = −0.965004 − 0.592094I
−2.16274 − 2.22327I −10.93751 + 4.89170I
u = −1.24424
a = 0.162086
b = −0.214799
−2.25644 3.80230
u = −0.340336 + 0.281341I
a = 2.20884 − 2.21512I
b = 1.133110 − 0.242313I
1.41649 + 4.96313I −5.21468 − 7.56800I
u = −0.340336 − 0.281341I
a = 2.20884 + 2.21512I
b = 1.133110 + 0.242313I
1.41649 − 4.96313I −5.21468 + 7.56800I
u = 1.20887 + 1.10475I
a = 0.572773 − 0.268684I
b = 1.102460 − 0.135538I
−4.14672 − 8.45942I −6.00000 + 6.66978I
u = 1.20887 − 1.10475I
a = 0.572773 + 0.268684I
b = 1.102460 + 0.135538I
−4.14672 + 8.45942I −6.00000 − 6.66978I
u = −0.214799
a = 0.938895
b = −1.24424
−2.25644 3.80230
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.81586 + 0.25309I
a = −0.879383 − 0.431389I
b = −2.13925 − 0.18775I
−14.0337 − 3.5387I 0
u = 1.81586 − 0.25309I
a = −0.879383 + 0.431389I
b = −2.13925 + 0.18775I
−14.0337 + 3.5387I 0
u = 1.88905 + 0.21159I
a = −0.720062 − 0.679808I
b = −1.91198 − 0.46830I
−12.66340 − 6.19285I 0
u = 1.88905 − 0.21159I
a = −0.720062 + 0.679808I
b = −1.91198 + 0.46830I
−12.66340 + 6.19285I 0
u = −1.91198 + 0.46830I
a = 0.773799 − 0.561815I
b = 1.88905 − 0.21159I
−12.66340 + 6.19285I 0
u = −1.91198 − 0.46830I
a = 0.773799 + 0.561815I
b = 1.88905 + 0.21159I
−12.66340 − 6.19285I 0
u = −2.13925 + 0.18775I
a = 0.731046 − 0.406052I
b = 1.81586 − 0.25309I
−14.0337 + 3.5387I 0
u = −2.13925 − 0.18775I
a = 0.731046 + 0.406052I
b = 1.81586 + 0.25309I
−14.0337 − 3.5387I 0
u = −1.86355 + 1.25575I
a = −0.109258 − 0.154344I
b = −0.873450 + 0.022311I
−2.83938 + 0.15495I 0
u = −1.86355 − 1.25575I
a = −0.109258 + 0.154344I
b = −0.873450 − 0.022311I
−2.83938 − 0.15495I 0
13
III. I
u
3
= hb + u, −2u
10
− 10u
9
+ · · · + a − 4, u
11
+ 4u
10
+ · · · + 2u − 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
u
2
a
9
=
2u
10
+ 10u
9
+ ··· − 5u + 4
−u
a
7
=
4u
10
+ 17u
9
+ ··· + u + 6
u
10
+ 4u
9
+ 3u
8
− 6u
7
− 9u
6
+ u
5
+ 9u
4
+ u
3
− 6u
2
− u + 2
a
10
=
2u
10
+ 10u
9
+ ··· − 5u + 4
u
10
+ 4u
9
+ 3u
8
− 6u
7
− 9u
6
+ u
5
+ 9u
4
+ u
3
− 6u
2
− 3u + 2
a
11
=
2u
10
+ 10u
9
+ ··· − 4u + 4
u
10
+ 4u
9
+ 3u
8
− 6u
7
− 9u
6
+ u
5
+ 9u
4
+ 2u
3
− 6u
2
− 3u + 2
a
1
=
−u
2
+ 1
−u
4
a
5
=
u
u
a
4
=
−4u
10
− 18u
9
+ ··· + 3u − 5
−2u
9
− 7u
8
− u
7
+ 16u
6
+ 6u
5
− 15u
4
− 4u
3
+ 10u
2
+ 2u − 2
a
12
=
3u
10
+ 13u
9
+ ··· − 2u + 6
u
10
+ 5u
9
+ 5u
8
− 10u
7
− 16u
6
+ 8u
5
+ 16u
4
− 5u
3
− 10u
2
+ u + 2
a
8
=
6u
10
+ 25u
9
+ ··· − 4u + 8
2u
10
+ 8u
9
+ 5u
8
− 14u
7
− 14u
6
+ 10u
5
+ 12u
4
− 7u
3
− 7u
2
+ u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −11u
10
− 54u
9
− 64u
8
+ 66u
7
+ 156u
6
− 8u
5
− 139u
4
− 6u
3
+ 92u
2
+ 14u − 33
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
11
− 12u
10
+ ··· + 10u − 1
c
2
, c
10
u
11
+ 4u
10
+ 2u
9
− 9u
8
− 8u
7
+ 9u
6
+ 9u
5
− 7u
4
− 6u
3
+ 3u
2
+ 2u − 1
c
3
, c
8
u
11
− u
9
+ u
8
+ 3u
7
− u
6
− u
5
− 2u
4
− 2u
3
+ 3u
2
+ u − 1
c
4
u
11
+ u
10
+ 4u
9
+ u
8
+ 7u
7
− 4u
6
− 3u
5
− 7u
4
+ 5u
3
+ u
2
− 1
c
5
u
11
− 4u
10
+ 2u
9
+ 9u
8
− 8u
7
− 9u
6
+ 9u
5
+ 7u
4
− 6u
3
− 3u
2
+ 2u + 1
c
6
u
11
− 4u
10
+ ··· + 4u − 1
c
7
u
11
+ u
10
+ ··· + 9u + 1
c
9
u
11
+ 4u
10
+ ··· + 4u + 1
c
11
u
11
− 5u
10
+ 13u
9
− 20u
8
+ 20u
7
− 13u
6
+ 7u
5
− 5u
4
+ 3u
3
− u
2
− 1
c
12
u
11
+ 7u
10
+ ··· + 7u + 1
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
11
− 24y
10
+ ··· + 6y −1
c
2
, c
5
, c
10
y
11
− 12y
10
+ ··· + 10y −1
c
3
, c
8
y
11
− 2y
10
+ ··· + 7y −1
c
4
y
11
+ 7y
10
+ ··· + 2y −1
c
6
, c
9
y
11
+ 6y
10
+ ··· − 6y −1
c
7
y
11
+ 7y
10
+ ··· + 59y −1
c
11
y
11
+ y
10
+ ··· − 2y −1
c
12
y
11
− 17y
10
+ ··· − 7y −1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.783748 + 0.507589I
a = −0.655301 + 0.652413I
b = 0.783748 − 0.507589I
−1.51867 + 8.25174I −7.26021 − 7.31178I
u = −0.783748 − 0.507589I
a = −0.655301 − 0.652413I
b = 0.783748 + 0.507589I
−1.51867 − 8.25174I −7.26021 + 7.31178I
u = 1.09593
a = −0.532565
b = −1.09593
−2.75997 −16.4390
u = −1.038820 + 0.472232I
a = 0.374208 − 1.064480I
b = 1.038820 − 0.472232I
0.22754 + 6.88359I −6.74283 − 7.96199I
u = −1.038820 − 0.472232I
a = 0.374208 + 1.064480I
b = 1.038820 + 0.472232I
0.22754 − 6.88359I −6.74283 + 7.96199I
u = 0.688260 + 0.474217I
a = 0.128118 + 0.656640I
b = −0.688260 − 0.474217I
−2.33645 − 0.11538I −12.41153 + 0.34745I
u = 0.688260 − 0.474217I
a = 0.128118 − 0.656640I
b = −0.688260 + 0.474217I
−2.33645 + 0.11538I −12.41153 − 0.34745I
u = 0.526465 + 0.148349I
a = −1.33892 − 1.68823I
b = −0.526465 − 0.148349I
−0.17031 − 3.59582I −8.70170 + 8.76278I
u = 0.526465 − 0.148349I
a = −1.33892 + 1.68823I
b = −0.526465 + 0.148349I
−0.17031 + 3.59582I −8.70170 − 8.76278I
u = −1.94012 + 0.28522I
a = 0.758182 − 0.505152I
b = 1.94012 − 0.28522I
−12.91640 + 4.72001I −9.66405 − 2.38742I
17
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.94012 − 0.28522I
a = 0.758182 + 0.505152I
b = 1.94012 + 0.28522I
−12.91640 − 4.72001I −9.66405 + 2.38742I
18
IV. I
u
4
= hb + 1, u
2
+ a − u, u
3
− u − 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
u
2
a
9
=
−u
2
+ u
−1
a
7
=
u
2
− 2
u
2
− 1
a
10
=
−u
2
+ u
−u
2
a
11
=
−u
2
+ u + 1
0
a
1
=
−u
2
+ 1
−u
2
− u
a
5
=
u
u
a
4
=
1
u + 1
a
12
=
−u
2
+ 1
−u
2
− u
a
8
=
0
u
2
− 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −7u
2
− u − 5
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
3
− 2u
2
+ u − 1
c
2
, c
4
, c
11
u
3
− u − 1
c
3
u
3
+ u
2
− 1
c
5
u
3
− u + 1
c
6
, c
8
u
3
− u
2
+ 2u − 1
c
7
u
3
+ 2u
2
+ 3u + 1
c
9
u
3
+ u
2
+ 2u + 1
c
10
(u − 1)
3
c
12
u
3
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
3
− 2y
2
− 3y −1
c
2
, c
4
, c
5
c
11
y
3
− 2y
2
+ y −1
c
3
y
3
− y
2
+ 2y −1
c
6
, c
8
, c
9
y
3
+ 3y
2
+ 2y −1
c
7
y
3
+ 2y
2
+ 5y −1
c
10
(y −1)
3
c
12
y
3
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.662359 + 0.562280I
a = −0.78492 + 1.30714I
b = −1.00000
1.37919 − 2.82812I −5.19557 + 4.65175I
u = −0.662359 − 0.562280I
a = −0.78492 − 1.30714I
b = −1.00000
1.37919 + 2.82812I −5.19557 − 4.65175I
u = 1.32472
a = −0.430160
b = −1.00000
−2.75839 −18.6090
22
V. I
u
5
= ha
2
+ b + 1, a
3
+ a
2
+ 2a + 1, u − 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
1
a
3
=
1
1
a
9
=
a
−a
2
− 1
a
7
=
−a
2
−a
2
− a
a
10
=
a
−a
2
+ a − 1
a
11
=
a
2
+ a + 1
a
a
1
=
0
−1
a
5
=
1
1
a
4
=
−a
2
− 2a
−2a
a
12
=
−a
2
−2a
2
− a − 2
a
8
=
−a
2
−a
2
− a
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8a
2
− 7a − 20
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
3
c
3
, c
4
, c
6
u
3
− u
2
+ 2u − 1
c
5
(u + 1)
3
c
7
u
3
c
8
u
3
+ u
2
− 1
c
9
, c
12
u
3
+ u
2
+ 2u + 1
c
10
, c
11
u
3
− u − 1
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y −1)
3
c
3
, c
4
, c
6
c
9
, c
12
y
3
+ 3y
2
+ 2y −1
c
7
y
3
c
8
y
3
− y
2
+ 2y −1
c
10
, c
11
y
3
− 2y
2
+ y −1
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −0.215080 + 1.307140I
b = 0.662359 + 0.562280I
1.37919 + 2.82812I −5.19557 − 4.65175I
u = 1.00000
a = −0.215080 − 1.307140I
b = 0.662359 − 0.562280I
1.37919 − 2.82812I −5.19557 + 4.65175I
u = 1.00000
a = −0.569840
b = −1.32472
−2.75839 −18.6090
26
VI. I
u
6
= hb + 1, a
3
+ a
2
+ 2a + 1, u − 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
1
a
3
=
1
1
a
9
=
a
−1
a
7
=
−a
2
a + 1
a
10
=
a
a − 1
a
11
=
a + 1
a
a
1
=
0
−1
a
5
=
1
1
a
4
=
a
2
+ a + 1
a
2
+ 1
a
12
=
−a
2
−a
2
+ a − 1
a
8
=
−a
2
a + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −5a
2
− 4a − 16
27
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
10
c
11
(u − 1)
3
c
3
, c
4
, c
8
u
3
+ u
2
− 1
c
5
(u + 1)
3
c
6
u
3
− u
2
+ 2u − 1
c
7
u
3
c
9
, c
12
u
3
+ u
2
+ 2u + 1
28
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
10
, c
11
(y −1)
3
c
3
, c
4
, c
8
y
3
− y
2
+ 2y −1
c
6
, c
9
, c
12
y
3
+ 3y
2
+ 2y −1
c
7
y
3
29
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −0.215080 + 1.307140I
b = −1.00000
1.37919 + 2.82812I −6.82789 − 2.41717I
u = 1.00000
a = −0.215080 − 1.307140I
b = −1.00000
1.37919 − 2.82812I −6.82789 + 2.41717I
u = 1.00000
a = −0.569840
b = −1.00000
−2.75839 −15.3440
30
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
6
)(u
3
− 2u
2
+ u − 1)(u
11
− 12u
10
+ ··· + 10u − 1)
· (u
22
+ 33u
21
+ ··· − 15u + 1)
· (u
30
+ 46u
29
+ ··· + 11608936u + 339889)
c
2
, c
10
(u − 1)
6
(u
3
− u − 1)
· (u
11
+ 4u
10
+ 2u
9
− 9u
8
− 8u
7
+ 9u
6
+ 9u
5
− 7u
4
− 6u
3
+ 3u
2
+ 2u − 1)
· (u
22
+ u
21
+ ··· − u − 1)(u
30
+ 2u
29
+ ··· + 4496u + 583)
c
3
, c
8
(u
3
− u
2
+ 2u − 1)(u
3
+ u
2
− 1)
2
· (u
11
− u
9
+ u
8
+ 3u
7
− u
6
− u
5
− 2u
4
− 2u
3
+ 3u
2
+ u − 1)
· (u
22
+ u
21
+ ··· + 5u + 1)(u
30
+ u
29
+ ··· + 58u − 11)
c
4
(u
3
− u − 1)(u
3
− u
2
+ 2u − 1)(u
3
+ u
2
− 1)
· (u
11
+ u
10
+ 4u
9
+ u
8
+ 7u
7
− 4u
6
− 3u
5
− 7u
4
+ 5u
3
+ u
2
− 1)
· (u
22
+ 2u
21
+ ··· − 126u + 103)(u
30
+ 8u
29
+ ··· + 2447u + 271)
c
5
(u + 1)
6
(u
3
− u + 1)
· (u
11
− 4u
10
+ 2u
9
+ 9u
8
− 8u
7
− 9u
6
+ 9u
5
+ 7u
4
− 6u
3
− 3u
2
+ 2u + 1)
· (u
22
+ u
21
+ ··· − u − 1)(u
30
+ 2u
29
+ ··· + 4496u + 583)
c
6
((u
3
− u
2
+ 2u − 1)
3
)(u
11
− 4u
10
+ ··· + 4u − 1)
· ((u
15
+ 7u
14
+ ··· + 4u + 1)
2
)(u
22
− 10u
21
+ ··· − 80u + 16)
c
7
u
6
(u
3
+ 2u
2
+ 3u + 1)(u
11
+ u
10
+ ··· + 9u + 1)(u
22
+ u
21
+ ··· + 36u + 8)
· (u
30
+ 3u
29
+ ··· + 356u + 88)
c
9
((u
3
+ u
2
+ 2u + 1)
3
)(u
11
+ 4u
10
+ ··· + 4u + 1)
· ((u
15
+ 7u
14
+ ··· + 4u + 1)
2
)(u
22
− 10u
21
+ ··· − 80u + 16)
c
11
(u − 1)
3
(u
3
− u − 1)
2
· (u
11
− 5u
10
+ 13u
9
− 20u
8
+ 20u
7
− 13u
6
+ 7u
5
− 5u
4
+ 3u
3
− u
2
− 1)
· ((u
15
+ 8u
14
+ ··· + 5u + 1)
2
)(u
22
− 13u
21
+ ··· + 2u + 4)
c
12
u
3
(u
3
+ u
2
+ 2u + 1)
2
(u
11
+ 7u
10
+ ··· + 7u + 1)
· (u
22
+ 4u
21
+ ··· − 281u − 83)(u
30
+ 2u
29
+ ··· + 197368u − 32296)
31
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
6
)(y
3
− 2y
2
− 3y −1)(y
11
− 24y
10
+ ··· + 6y −1)
· (y
22
− 113y
21
+ ··· + 107y + 1)
· (y
30
− 50y
29
+ ··· − 48946220611468y + 115524532321)
c
2
, c
5
, c
10
((y −1)
6
)(y
3
− 2y
2
+ y −1)(y
11
− 12y
10
+ ··· + 10y −1)
· (y
22
− 33y
21
+ ··· + 15y + 1)
· (y
30
− 46y
29
+ ··· − 11608936y + 339889)
c
3
, c
8
((y
3
− y
2
+ 2y −1)
2
)(y
3
+ 3y
2
+ 2y −1)(y
11
− 2y
10
+ ··· + 7y −1)
· (y
22
− 9y
21
+ ··· − 25y + 1)(y
30
− 3y
29
+ ··· − 3056y + 121)
c
4
(y
3
− 2y
2
+ y −1)(y
3
− y
2
+ 2y −1)(y
3
+ 3y
2
+ 2y −1)
· (y
11
+ 7y
10
+ ··· + 2y −1)(y
22
+ 24y
21
+ ··· + 134916y + 10609)
· (y
30
+ 64y
29
+ ··· − 1263195y + 73441)
c
6
, c
9
((y
3
+ 3y
2
+ 2y −1)
3
)(y
11
+ 6y
10
+ ··· − 6y −1)
· ((y
15
− 3y
14
+ ··· + 36y −1)
2
)(y
22
+ 6y
21
+ ··· − 672y + 256)
c
7
y
6
(y
3
+ 2y
2
+ 5y −1)(y
11
+ 7y
10
+ ··· + 59y −1)
· (y
22
+ 13y
21
+ ··· + 368y + 64)(y
30
+ 17y
29
+ ··· + 280176y + 7744)
c
11
((y −1)
3
)(y
3
− 2y
2
+ y −1)
2
(y
11
+ y
10
+ ··· − 2y −1)
· ((y
15
+ 28y
13
+ ··· − 9y −1)
2
)(y
22
− y
21
+ ··· − 460y + 16)
c
12
y
3
(y
3
+ 3y
2
+ 2y −1)
2
(y
11
− 17y
10
+ ··· − 7y −1)
· (y
22
− 60y
21
+ ··· − 67175y + 6889)
· (y
30
− 22y
29
+ ··· − 9540868384y + 1043031616)
32
