12a
0805
(K12a
0805
)
A knot diagram
1
Linearized knot diagam
4 5 6 9 10 11 12 1 2 3 7 8
Solving Sequence
7,11
12 8 1 9
3,6
4 10 5 2
c
11
c
7
c
12
c
8
c
6
c
3
c
10
c
5
c
2
c
1
, c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−437u
29
+ 1525u
28
+ ··· + 13b + 2231, 5117u
29
− 17060u
28
+ ··· + 143a − 29622,
u
30
− 5u
29
+ ··· − 38u + 11i
I
u
2
= h−269u
22
a + 526u
22
+ ··· − 286a − 712, 2u
22
a + 3u
22
+ ··· − 7a − 6, u
23
+ 2u
22
+ ··· − 2u + 1i
I
u
3
= hu
8
− u
7
− 5u
6
+ 5u
5
+ 7u
4
− 6u
3
− 4u
2
+ b + 2u, −u
2
+ a + 2,
u
9
− 2u
8
− 5u
7
+ 11u
6
+ 6u
5
− 17u
4
− u
3
+ 8u
2
− u + 1i
I
u
4
= hb + a − u − 1, a
2
− 3au − 2a + u + 2, u
2
+ u − 1i
I
v
1
= ha, b − 1, v + 1i
* 5 irreducible components of dim
C
= 0, with total 90 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−437u
29
+ 1525u
28
+ · · · + 13b + 2231, 5117u
29
− 17060u
28
+ · · · +
143a − 29622, u
30
− 5u
29
+ · · · − 38u + 11i
(i) Arc colorings
a
7
=
0
u
a
11
=
1
0
a
12
=
1
−u
2
a
8
=
u
−u
3
+ u
a
1
=
−u
2
+ 1
u
4
− 2u
2
a
9
=
−u
3
+ 2u
u
5
− 3u
3
+ u
a
3
=
−35.7832u
29
+ 119.301u
28
+ ··· − 569.783u + 207.147
33.6154u
29
− 117.308u
28
+ ··· + 442.615u − 171.615
a
6
=
−u
u
a
4
=
−21.4755u
29
+ 79.1469u
28
+ ··· − 257.476u + 109.839
19.3077u
29
− 77.1538u
28
+ ··· + 130.308u − 74.3077
a
10
=
−11.2448u
29
+ 33.5315u
28
+ ··· − 296.245u + 97.6084
21.6923u
29
− 63.8462u
28
+ ··· + 601.692u − 187.692
a
5
=
27.0629u
29
− 88.6224u
28
+ ··· + 448.063u − 156.699
−12.5385u
29
+ 34.7692u
28
+ ··· − 371.538u + 113.538
a
2
=
−28.1678u
29
+ 95.9930u
28
+ ··· − 426.168u + 161.531
33.4615u
29
− 116.231u
28
+ ··· + 484.462u − 183.462
(ii) Obstruction class = −1
(iii) Cusp Shapes =
697
13
u
29
−
2097
13
u
28
+ ··· +
18078
13
u −
5897
13
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
30
+ 4u
29
+ ··· + 5u − 1
c
2
u
30
+ 17u
29
+ ··· − 21u − 11
c
4
, c
10
u
30
− 6u
28
+ ··· − 3u − 1
c
5
, c
9
u
30
− u
29
+ ··· − 4u + 1
c
6
, c
7
, c
8
c
11
, c
12
u
30
+ 5u
29
+ ··· + 38u + 11
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
30
+ 28y
28
+ ··· − 93y + 1
c
2
y
30
− 3y
29
+ ··· − 1739y + 121
c
4
, c
10
y
30
− 12y
29
+ ··· − 33y + 1
c
5
, c
9
y
30
− 19y
29
+ ··· − 38y + 1
c
6
, c
7
, c
8
c
11
, c
12
y
30
− 43y
29
+ ··· − 1180y + 121
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.01658
a = 2.92862
b = −1.50043
1.74384 5.98900
u = −0.878022 + 0.002899I
a = 0.238285 + 0.304913I
b = −0.559876 − 0.690935I
1.314950 − 0.451834I 6.61404 + 1.58489I
u = −0.878022 − 0.002899I
a = 0.238285 − 0.304913I
b = −0.559876 + 0.690935I
1.314950 + 0.451834I 6.61404 − 1.58489I
u = −1.130260 + 0.186589I
a = −1.246950 − 0.354613I
b = 0.627496 − 0.880698I
3.04303 − 4.92292I 3.35262 + 6.51542I
u = −1.130260 − 0.186589I
a = −1.246950 + 0.354613I
b = 0.627496 + 0.880698I
3.04303 + 4.92292I 3.35262 − 6.51542I
u = 1.18652
a = −1.61412
b = 1.01453
6.25305 14.0800
u = 0.313981 + 0.719655I
a = −0.258210 − 0.371938I
b = −0.865351 + 0.635662I
0.07877 − 5.69968I 6.25097 + 7.15473I
u = 0.313981 − 0.719655I
a = −0.258210 + 0.371938I
b = −0.865351 − 0.635662I
0.07877 + 5.69968I 6.25097 − 7.15473I
u = 0.439811 + 0.644843I
a = −0.712132 + 0.794843I
b = 1.079900 + 0.783683I
0.48551 + 10.07530I 5.95949 − 9.67797I
u = 0.439811 − 0.644843I
a = −0.712132 − 0.794843I
b = 1.079900 − 0.783683I
0.48551 − 10.07530I 5.95949 + 9.67797I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.174900 + 0.352174I
a = 1.84786 + 0.33394I
b = −1.28819 + 0.84300I
5.5646 − 13.4956I 9.26736 + 8.87328I
u = −1.174900 − 0.352174I
a = 1.84786 − 0.33394I
b = −1.28819 − 0.84300I
5.5646 + 13.4956I 9.26736 − 8.87328I
u = −1.198660 + 0.506727I
a = −0.495699 − 0.735221I
b = 0.712841 + 0.295117I
4.63959 + 1.45693I 20.4781 − 6.0794I
u = −1.198660 − 0.506727I
a = −0.495699 + 0.735221I
b = 0.712841 − 0.295117I
4.63959 − 1.45693I 20.4781 + 6.0794I
u = −1.32795
a = −0.917911
b = 0.203761
3.16863 1.59560
u = 0.360310 + 0.392975I
a = 0.55572 − 1.55779I
b = −0.494454 − 0.710271I
−1.69300 + 2.96011I −0.46924 − 8.93785I
u = 0.360310 − 0.392975I
a = 0.55572 + 1.55779I
b = −0.494454 + 0.710271I
−1.69300 − 2.96011I −0.46924 + 8.93785I
u = −0.481507
a = 0.778558
b = −0.569296
0.855934 11.6870
u = 0.270687 + 0.323054I
a = 1.45188 − 0.61952I
b = 0.413056 − 0.459484I
−1.90583 − 0.45249I −1.79458 − 1.14821I
u = 0.270687 − 0.323054I
a = 1.45188 + 0.61952I
b = 0.413056 + 0.459484I
−1.90583 + 0.45249I −1.79458 + 1.14821I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.70982 + 0.01754I
a = −0.504443 − 0.628284I
b = 0.562401 + 1.059590I
10.64730 − 0.25494I 0
u = 1.70982 − 0.01754I
a = −0.504443 + 0.628284I
b = 0.562401 − 1.059590I
10.64730 + 0.25494I 0
u = −1.73772
a = −2.71628
b = 1.72980
11.7131 0
u = 1.76484 + 0.04602I
a = 1.241500 + 0.064835I
b = −0.701863 − 0.995930I
13.5460 + 5.9087I 0
u = 1.76484 − 0.04602I
a = 1.241500 − 0.064835I
b = −0.701863 + 0.995930I
13.5460 − 5.9087I 0
u = 1.77253 + 0.09377I
a = −2.08526 − 0.07253I
b = 1.43463 + 0.88148I
16.1500 + 15.4410I 0
u = 1.77253 − 0.09377I
a = −2.08526 + 0.07253I
b = 1.43463 − 0.88148I
16.1500 − 15.4410I 0
u = −1.77800
a = 1.81911
b = −1.19344
17.0939 0
u = 1.81090 + 0.09745I
a = 1.055730 − 0.361250I
b = −0.763050 − 0.096600I
15.7188 + 1.2036I 0
u = 1.81090 − 0.09745I
a = 1.055730 + 0.361250I
b = −0.763050 + 0.096600I
15.7188 − 1.2036I 0
7
II. I
u
2
= h−269u
22
a + 526u
22
+ · · · − 286a − 712, 2u
22
a + 3u
22
+ · · · − 7a −
6, u
23
+ 2u
22
+ · · · − 2u + 1i
(i) Arc colorings
a
7
=
0
u
a
11
=
1
0
a
12
=
1
−u
2
a
8
=
u
−u
3
+ u
a
1
=
−u
2
+ 1
u
4
− 2u
2
a
9
=
−u
3
+ 2u
u
5
− 3u
3
+ u
a
3
=
a
0.651332au
22
− 1.27361u
22
+ ··· + 0.692494a + 1.72397
a
6
=
−u
u
a
4
=
−2.45521au
22
+ 1.61501u
22
+ ··· − 0.707022a + 0.806295
3.10654au
22
− 2.88862u
22
+ ··· + 2.39952a + 0.917676
a
10
=
0.273608au
22
− 0.486683u
22
+ ··· − 1.72397a − 0.0750605
0.00726392au
22
+ 2.23487u
22
+ ··· − 0.222760a − 1.86925
a
5
=
−1.01453au
22
+ 1.53027u
22
+ ··· + 0.445521a + 1.73850
1.44068au
22
− 4.08475u
22
+ ··· + 1.15254a + 0.932203
a
2
=
0.806295au
22
− 3.92978u
22
+ ··· + 1.27361a − 2.48668
−0.806295au
22
+ 4.92978u
22
+ ··· − 1.27361a + 0.486683
(ii) Obstruction class = −1
(iii) Cusp Shapes = u
22
− 10u
21
− 25u
20
+ 139u
19
+ 224u
18
− 798u
17
− 1029u
16
+
2424u
15
+ 2796u
14
− 4094u
13
− 4866u
12
+ 3507u
11
+ 5634u
10
− 630u
9
− 4167u
8
−
1372u
7
+ 1603u
6
+ 1148u
5
− 81u
4
− 337u
3
− 100u
2
+ 12u + 27
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
46
− 5u
45
+ ··· + 602u − 47
c
2
(u
23
− 11u
22
+ ··· + 14u − 4)
2
c
4
, c
10
u
46
− 8u
44
+ ··· + 2009u + 851
c
5
, c
9
u
46
+ 2u
44
+ ··· − u − 1
c
6
, c
7
, c
8
c
11
, c
12
(u
23
− 2u
22
+ ··· − 2u − 1)
2
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
46
+ 23y
45
+ ··· − 6896y + 2209
c
2
(y
23
− 5y
22
+ ··· + 268y −16)
2
c
4
, c
10
y
46
− 16y
45
+ ··· − 19209411y + 724201
c
5
, c
9
y
46
+ 4y
45
+ ··· − 35y + 1
c
6
, c
7
, c
8
c
11
, c
12
(y
23
− 32y
22
+ ··· + 18y −1)
2
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.999683 + 0.186821I
a = −0.042700 − 1.410890I
b = −0.18371 + 1.64920I
2.50463 + 5.52558I 5.10396 − 8.15770I
u = 0.999683 + 0.186821I
a = 1.68330 − 1.01369I
b = −0.995212 − 0.632466I
2.50463 + 5.52558I 5.10396 − 8.15770I
u = 0.999683 − 0.186821I
a = −0.042700 + 1.410890I
b = −0.18371 − 1.64920I
2.50463 − 5.52558I 5.10396 + 8.15770I
u = 0.999683 − 0.186821I
a = 1.68330 + 1.01369I
b = −0.995212 + 0.632466I
2.50463 − 5.52558I 5.10396 + 8.15770I
u = −1.105860 + 0.055480I
a = −1.92578 + 0.18458I
b = 1.35825 − 1.09576I
5.84113 − 4.35667I 13.8335 + 5.4983I
u = −1.105860 + 0.055480I
a = 1.60049 − 1.41054I
b = −0.614170 − 0.043824I
5.84113 − 4.35667I 13.8335 + 5.4983I
u = −1.105860 − 0.055480I
a = −1.92578 − 0.18458I
b = 1.35825 + 1.09576I
5.84113 + 4.35667I 13.8335 − 5.4983I
u = −1.105860 − 0.055480I
a = 1.60049 + 1.41054I
b = −0.614170 + 0.043824I
5.84113 + 4.35667I 13.8335 − 5.4983I
u = 1.18981
a = −1.50802
b = 1.05229
6.25240 14.1390
u = 1.18981
a = −1.73509
b = 0.992937
6.25240 14.1390
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.140950 + 0.349828I
a = 0.851056 − 0.861201I
b = −0.901717 − 0.147878I
7.12094 + 5.39909I 13.5404 − 6.0968I
u = 1.140950 + 0.349828I
a = −1.70952 + 0.17931I
b = 1.30005 + 0.76522I
7.12094 + 5.39909I 13.5404 − 6.0968I
u = 1.140950 − 0.349828I
a = 0.851056 + 0.861201I
b = −0.901717 + 0.147878I
7.12094 − 5.39909I 13.5404 + 6.0968I
u = 1.140950 − 0.349828I
a = −1.70952 − 0.17931I
b = 1.30005 − 0.76522I
7.12094 − 5.39909I 13.5404 + 6.0968I
u = −0.377702 + 0.629512I
a = 0.209564 − 0.786199I
b = 0.780693 + 0.190315I
2.35417 − 2.04864I 12.02442 + 4.27551I
u = −0.377702 + 0.629512I
a = 0.341684 + 0.460205I
b = −0.932101 + 0.597740I
2.35417 − 2.04864I 12.02442 + 4.27551I
u = −0.377702 − 0.629512I
a = 0.209564 + 0.786199I
b = 0.780693 − 0.190315I
2.35417 + 2.04864I 12.02442 − 4.27551I
u = −0.377702 − 0.629512I
a = 0.341684 − 0.460205I
b = −0.932101 − 0.597740I
2.35417 + 2.04864I 12.02442 − 4.27551I
u = −0.580448 + 0.322591I
a = −0.345114 + 0.640960I
b = −0.861693 − 0.321506I
0.229739 + 0.719364I 7.70501 − 1.54064I
u = −0.580448 + 0.322591I
a = 2.10527 + 0.09680I
b = −0.966346 + 0.634688I
0.229739 + 0.719364I 7.70501 − 1.54064I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.580448 − 0.322591I
a = −0.345114 − 0.640960I
b = −0.861693 + 0.321506I
0.229739 − 0.719364I 7.70501 + 1.54064I
u = −0.580448 − 0.322591I
a = 2.10527 − 0.09680I
b = −0.966346 − 0.634688I
0.229739 − 0.719364I 7.70501 + 1.54064I
u = −0.157596 + 0.449298I
a = 0.51417 − 1.77331I
b = 0.893978 − 0.534579I
−1.03877 − 3.41304I −1.13516 + 7.69580I
u = −0.157596 + 0.449298I
a = −0.0565579 + 0.1078630I
b = 0.545955 + 1.142730I
−1.03877 − 3.41304I −1.13516 + 7.69580I
u = −0.157596 − 0.449298I
a = 0.51417 + 1.77331I
b = 0.893978 + 0.534579I
−1.03877 + 3.41304I −1.13516 − 7.69580I
u = −0.157596 − 0.449298I
a = −0.0565579 − 0.1078630I
b = 0.545955 − 1.142730I
−1.03877 + 3.41304I −1.13516 − 7.69580I
u = 1.59673
a = −0.0933260
b = 0.587557
7.42882 28.8540
u = 1.59673
a = −2.54753
b = 1.94206
7.42882 28.8540
u = 0.313095 + 0.086295I
a = 1.18015 − 2.03047I
b = −0.959828 − 0.907570I
1.29868 + 3.82978I 14.5236 − 8.4853I
u = 0.313095 + 0.086295I
a = −2.82861 − 3.70039I
b = 0.569721 + 0.399803I
1.29868 + 3.82978I 14.5236 − 8.4853I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.313095 − 0.086295I
a = 1.18015 + 2.03047I
b = −0.959828 + 0.907570I
1.29868 − 3.82978I 14.5236 + 8.4853I
u = 0.313095 − 0.086295I
a = −2.82861 + 3.70039I
b = 0.569721 − 0.399803I
1.29868 − 3.82978I 14.5236 + 8.4853I
u = −1.73349 + 0.04283I
a = −0.05422 − 1.72140I
b = 0.12177 + 1.99221I
12.35220 − 6.42236I 6.09016 + 6.34054I
u = −1.73349 + 0.04283I
a = −1.78344 − 0.36813I
b = 1.091730 − 0.703323I
12.35220 − 6.42236I 6.09016 + 6.34054I
u = −1.73349 − 0.04283I
a = −0.05422 + 1.72140I
b = 0.12177 − 1.99221I
12.35220 + 6.42236I 6.09016 − 6.34054I
u = −1.73349 − 0.04283I
a = −1.78344 + 0.36813I
b = 1.091730 + 0.703323I
12.35220 + 6.42236I 6.09016 − 6.34054I
u = 1.75724 + 0.01445I
a = −1.45201 − 0.83740I
b = 0.696220 − 0.251137I
16.2384 + 4.6560I 13.26850 − 4.63684I
u = 1.75724 + 0.01445I
a = 2.07313 + 0.57426I
b = −1.57300 − 1.18808I
16.2384 + 4.6560I 13.26850 − 4.63684I
u = 1.75724 − 0.01445I
a = −1.45201 + 0.83740I
b = 0.696220 + 0.251137I
16.2384 − 4.6560I 13.26850 + 4.63684I
u = 1.75724 − 0.01445I
a = 2.07313 − 0.57426I
b = −1.57300 + 1.18808I
16.2384 − 4.6560I 13.26850 + 4.63684I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.76372 + 0.09254I
a = −1.227110 − 0.467441I
b = 1.007300 − 0.351627I
17.5310 − 7.2981I 12.96470 + 5.26666I
u = −1.76372 + 0.09254I
a = 2.09962 − 0.18292I
b = −1.54996 + 0.81454I
17.5310 − 7.2981I 12.96470 + 5.26666I
u = −1.76372 − 0.09254I
a = −1.227110 + 0.467441I
b = 1.007300 + 0.351627I
17.5310 + 7.2981I 12.96470 − 5.26666I
u = −1.76372 − 0.09254I
a = 2.09962 + 0.18292I
b = −1.54996 − 0.81454I
17.5310 + 7.2981I 12.96470 − 5.26666I
u = −1.77086
a = 1.70862 + 0.14562I
b = −1.115350 + 0.221258I
17.0133 14.1690
u = −1.77086
a = 1.70862 − 0.14562I
b = −1.115350 − 0.221258I
17.0133 14.1690
15
III. I
u
3
= hu
8
− u
7
+ · · · + b + 2u, −u
2
+ a + 2, u
9
− 2u
8
+ · · · − u + 1i
(i) Arc colorings
a
7
=
0
u
a
11
=
1
0
a
12
=
1
−u
2
a
8
=
u
−u
3
+ u
a
1
=
−u
2
+ 1
u
4
− 2u
2
a
9
=
−u
3
+ 2u
u
5
− 3u
3
+ u
a
3
=
u
2
− 2
−u
8
+ u
7
+ 5u
6
− 5u
5
− 7u
4
+ 6u
3
+ 4u
2
− 2u
a
6
=
−u
u
a
4
=
2u
8
− u
7
− 10u
6
+ 5u
5
+ 13u
4
− 5u
3
− 4u
2
− 3
−3u
8
+ 2u
7
+ 15u
6
− 10u
5
− 20u
4
+ 11u
3
+ 9u
2
− 2u + 1
a
10
=
−u
7
+ 5u
5
− 7u
3
− u
2
+ 4u + 2
u
8
− 6u
6
+ u
5
+ 11u
4
− 4u
3
− 6u
2
+ 3u − 1
a
5
=
u
8
− u
7
− 5u
6
+ 5u
5
+ 6u
4
− 6u
3
+ u − 3
−u
8
+ u
7
+ 5u
6
− 5u
5
− 7u
4
+ 6u
3
+ 4u
2
− u
a
2
=
u
8
− u
7
− 5u
6
+ 6u
5
+ 7u
4
− 10u
3
− 4u
2
+ 6u
−u
8
+ 5u
6
− 7u
4
− u
3
+ 4u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −5u
8
+ 32u
6
− 6u
5
− 64u
4
+ 25u
3
+ 41u
2
− 21u + 8
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
9
− u
8
+ 5u
7
+ 6u
5
+ 6u
4
+ 4u
3
+ 5u
2
+ 2u + 1
c
2
u
9
+ 8u
8
+ ··· + 114u + 29
c
4
, c
10
u
9
+ u
8
+ u
7
+ 2u
5
+ 2u
4
− u
2
+ 1
c
5
, c
9
u
9
− u
7
+ 2u
5
− 2u
4
− u
2
+ u − 1
c
6
, c
7
, c
8
u
9
+ 2u
8
− 5u
7
− 11u
6
+ 6u
5
+ 17u
4
− u
3
− 8u
2
− u − 1
c
11
, c
12
u
9
− 2u
8
− 5u
7
+ 11u
6
+ 6u
5
− 17u
4
− u
3
+ 8u
2
− u + 1
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
9
+ 9y
8
+ 37y
7
+ 80y
6
+ 90y
5
+ 34y
4
− 20y
3
− 21y
2
− 6y −1
c
2
y
9
+ 2y
8
− 5y
7
− 25y
6
− 15y
5
− 19y
4
− 13y
3
− 214y
2
− 112y −841
c
4
, c
10
y
9
+ y
8
+ 5y
7
+ 6y
5
− 6y
4
+ 4y
3
− 5y
2
+ 2y −1
c
5
, c
9
y
9
− 2y
8
+ 5y
7
− 4y
6
+ 6y
5
− 6y
4
− 5y
2
− y −1
c
6
, c
7
, c
8
c
11
, c
12
y
9
− 14y
8
+ ··· − 15y −1
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.058740 + 0.157360I
a = −0.903839 − 0.333206I
b = 0.697506 − 0.952517I
4.19323 − 5.25554I 11.10227 + 7.96200I
u = −1.058740 − 0.157360I
a = −0.903839 + 0.333206I
b = 0.697506 + 0.952517I
4.19323 + 5.25554I 11.10227 − 7.96200I
u = 1.180180 + 0.330999I
a = −0.716747 + 0.781273I
b = 0.620761 − 0.367622I
4.16417 − 1.30911I 4.70320 + 1.63386I
u = 1.180180 − 0.330999I
a = −0.716747 − 0.781273I
b = 0.620761 + 0.367622I
4.16417 + 1.30911I 4.70320 − 1.63386I
u = 0.035682 + 0.320509I
a = −2.10145 + 0.02287I
b = −0.625202 − 0.718766I
0.54144 + 3.69294I 2.15237 − 6.28351I
u = 0.035682 − 0.320509I
a = −2.10145 − 0.02287I
b = −0.625202 + 0.718766I
0.54144 − 3.69294I 2.15237 + 6.28351I
u = 1.75217 + 0.04113I
a = 1.068410 + 0.144146I
b = −0.752703 − 1.076140I
14.3916 + 6.0909I 12.47244 − 6.62825I
u = 1.75217 − 0.04113I
a = 1.068410 − 0.144146I
b = −0.752703 + 1.076140I
14.3916 − 6.0909I 12.47244 + 6.62825I
u = −1.81858
a = 1.30725
b = −0.880724
15.9267 10.1390
19
IV. I
u
4
= hb + a − u − 1, a
2
− 3au − 2a + u + 2, u
2
+ u − 1i
(i) Arc colorings
a
7
=
0
u
a
11
=
1
0
a
12
=
1
u − 1
a
8
=
u
−u + 1
a
1
=
u
−u
a
9
=
1
0
a
3
=
a
−a + u + 1
a
6
=
−u
u
a
4
=
a − u
−a + 2u + 1
a
10
=
−2au − a + u + 3
au
a
5
=
u + 1
−a + 2u + 1
a
2
=
a
−a + u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 7u − 2
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
(u − 1)
4
c
2
u
4
c
4
, c
5
, c
9
c
10
u
4
− u
3
− 3u
2
+ u + 1
c
6
, c
7
, c
8
(u
2
− u − 1)
2
c
11
, c
12
(u
2
+ u − 1)
2
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
(y −1)
4
c
2
y
4
c
4
, c
5
, c
9
c
10
y
4
− 7y
3
+ 13y
2
− 7y + 1
c
6
, c
7
, c
8
c
11
, c
12
(y
2
− 3y + 1)
2
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.618034
a = 0.880394
b = 0.737640
−0.657974 2.32620
u = 0.618034
a = 2.97371
b = −1.35567
−0.657974 2.32620
u = −1.61803
a = −0.140774
b = −0.477260
7.23771 −13.3260
u = −1.61803
a = −2.71333
b = 2.09529
7.23771 −13.3260
23
V. I
v
1
= ha, b − 1, v + 1i
(i) Arc colorings
a
7
=
−1
0
a
11
=
1
0
a
12
=
1
0
a
8
=
−1
0
a
1
=
1
0
a
9
=
−1
0
a
3
=
0
1
a
6
=
−1
0
a
4
=
−1
1
a
10
=
1
1
a
5
=
0
1
a
2
=
0
1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
5
, c
9
, c
10
u + 1
c
2
, c
6
, c
7
c
8
, c
11
, c
12
u
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
5
, c
9
, c
10
y −1
c
2
, c
6
, c
7
c
8
, c
11
, c
12
y
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −1.00000
a = 0
b = 1.00000
−1.64493 −6.00000
27
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
3
(u − 1)
4
(u + 1)(u
9
− u
8
+ 5u
7
+ 6u
5
+ 6u
4
+ 4u
3
+ 5u
2
+ 2u + 1)
· (u
30
+ 4u
29
+ ··· + 5u − 1)(u
46
− 5u
45
+ ··· + 602u − 47)
c
2
u
5
(u
9
+ 8u
8
+ ··· + 114u + 29)(u
23
− 11u
22
+ ··· + 14u − 4)
2
· (u
30
+ 17u
29
+ ··· − 21u − 11)
c
4
, c
10
(u + 1)(u
4
− u
3
− 3u
2
+ u + 1)(u
9
+ u
8
+ u
7
+ 2u
5
+ 2u
4
− u
2
+ 1)
· (u
30
− 6u
28
+ ··· − 3u − 1)(u
46
− 8u
44
+ ··· + 2009u + 851)
c
5
, c
9
(u + 1)(u
4
− u
3
− 3u
2
+ u + 1)(u
9
− u
7
+ 2u
5
− 2u
4
− u
2
+ u − 1)
· (u
30
− u
29
+ ··· − 4u + 1)(u
46
+ 2u
44
+ ··· − u − 1)
c
6
, c
7
, c
8
u(u
2
− u − 1)
2
(u
9
+ 2u
8
+ ··· − u − 1)
· ((u
23
− 2u
22
+ ··· − 2u − 1)
2
)(u
30
+ 5u
29
+ ··· + 38u + 11)
c
11
, c
12
u(u
2
+ u − 1)
2
(u
9
− 2u
8
+ ··· − u + 1)
· ((u
23
− 2u
22
+ ··· − 2u − 1)
2
)(u
30
+ 5u
29
+ ··· + 38u + 11)
28
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
3
(y −1)
5
· (y
9
+ 9y
8
+ 37y
7
+ 80y
6
+ 90y
5
+ 34y
4
− 20y
3
− 21y
2
− 6y −1)
· (y
30
+ 28y
28
+ ··· − 93y + 1)(y
46
+ 23y
45
+ ··· − 6896y + 2209)
c
2
y
5
(y
9
+ 2y
8
+ ··· − 112y −841)
· ((y
23
− 5y
22
+ ··· + 268y −16)
2
)(y
30
− 3y
29
+ ··· − 1739y + 121)
c
4
, c
10
(y −1)(y
4
− 7y
3
+ 13y
2
− 7y + 1)
· (y
9
+ y
8
+ 5y
7
+ 6y
5
− 6y
4
+ 4y
3
− 5y
2
+ 2y −1)
· (y
30
− 12y
29
+ ··· − 33y + 1)
· (y
46
− 16y
45
+ ··· − 19209411y + 724201)
c
5
, c
9
(y −1)(y
4
− 7y
3
+ 13y
2
− 7y + 1)
· (y
9
− 2y
8
+ 5y
7
− 4y
6
+ 6y
5
− 6y
4
− 5y
2
− y −1)
· (y
30
− 19y
29
+ ··· − 38y + 1)(y
46
+ 4y
45
+ ··· − 35y + 1)
c
6
, c
7
, c
8
c
11
, c
12
y(y
2
− 3y + 1)
2
(y
9
− 14y
8
+ ··· − 15y −1)
· ((y
23
− 32y
22
+ ··· + 18y −1)
2
)(y
30
− 43y
29
+ ··· − 1180y + 121)
29
