12n
0630
(K12n
0630
)
A knot diagram
1
Linearized knot diagam
3 7 9 12 3 12 2 5 6 7 5 10
Solving Sequence
6,12 3,7
2 1 5 4 11 10 9 8
c
6
c
2
c
1
c
5
c
4
c
11
c
10
c
9
c
8
c
3
, c
7
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−397668u
11
− 278148u
10
+ ··· + 7297577b + 2368848,
− 1957869u
11
+ 467354u
10
+ ··· + 36487885a − 28305373,
u
12
− u
11
− 6u
10
+ 13u
9
+ 18u
8
− 60u
7
+ 13u
6
+ 62u
5
− 29u
4
− 23u
3
+ 7u
2
+ 2u + 5i
I
u
2
= h−3.02231 × 10
15
u
19
+ 1.19819 × 10
15
u
18
+ ··· + 5.91941 × 10
15
b + 5.59657 × 10
14
,
9227751817881066u
19
+ 3660231888309292u
18
+ ··· + 5919405752257771a + 5607818622219472,
u
20
+ 4u
18
+ ··· + 3u + 1i
I
u
3
= h−2.64152 × 10
16
u
15
− 7.92608 × 10
15
u
14
+ ··· + 8.40192 × 10
18
b + 2.48982 × 10
18
,
− 2.01301 × 10
18
u
15
+ 1.13113 × 10
19
u
14
+ ··· + 5.96536 × 10
20
a + 4.26142 × 10
21
,
u
16
− u
15
+ ··· + 163u + 71i
I
u
4
= hu
2
+ b − 1, u
2
+ a + u, u
3
− u + 1i
I
u
5
= hb − u − 1, a − u, u
2
+ u + 1i
* 5 irreducible components of dim
C
= 0, with total 53 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−3.98 × 10
5
u
11
− 2.78 × 10
5
u
10
+ · · · + 7.30 × 10
6
b + 2.37 × 10
6
, −1.96 ×
10
6
u
11
+ 4.67× 10
5
u
10
+ · · · + 3.65 × 10
7
a −2.83 × 10
7
, u
12
− u
11
+ · · · + 2u + 5i
(i) Arc colorings
a
6
=
1
0
a
12
=
0
u
a
3
=
0.0536581u
11
− 0.0128085u
10
+ ··· + 0.801672u + 0.775747
0.0544932u
11
+ 0.0381151u
10
+ ··· + 0.115543u − 0.324607
a
7
=
1
u
2
a
2
=
0.109535u
11
− 0.0184761u
10
+ ··· + 0.336139u + 0.896107
0.268311u
11
+ 0.00905821u
10
+ ··· − 0.264263u − 0.575656
a
1
=
0.0908787u
11
+ 0.0231775u
10
+ ··· + 0.150881u + 0.429910
0.255543u
11
− 0.178786u
10
+ ··· − 0.0241484u + 0.207817
a
5
=
−0.0776514u
11
− 0.0522672u
10
+ ··· + 1.20161u + 1.87973
0.114056u
11
+ 0.0999037u
10
+ ··· + 0.248152u − 0.454394
a
4
=
−0.0776514u
11
− 0.0522672u
10
+ ··· + 1.20161u + 1.87973
0.131309u
11
+ 0.0394587u
10
+ ··· − 0.399942u − 1.10399
a
11
=
−0.313406u
11
+ 0.172062u
10
+ ··· + 2.31775u + 0.230813
0.0700486u
11
+ 0.0126635u
10
+ ··· + 0.664609u + 0.230518
a
10
=
−0.0649215u
11
+ 0.0104283u
10
+ ··· + 1.13264u − 0.245386
0.155876u
11
− 0.0790595u
10
+ ··· − 0.751512u − 0.203733
a
9
=
−0.220797u
11
+ 0.0894879u
10
+ ··· + 1.88416u − 0.0416525
0.155876u
11
− 0.0790595u
10
+ ··· − 0.751512u − 0.203733
a
8
=
0.131232u
11
− 0.216101u
10
+ ··· + 0.285872u + 0.275328
0.0893665u
11
+ 0.00788878u
10
+ ··· − 0.146247u − 0.586750
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
5487178
7297577
u
11
+
4986967
7297577
u
10
+ ··· −
3943475
384083
u −
53169632
7297577
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
12
+ 22u
11
+ ··· + 2624u + 256
c
2
, c
7
u
12
− 4u
11
+ ··· − 24u + 16
c
3
, c
6
u
12
− u
11
+ ··· + 2u + 5
c
4
, c
11
u
12
− 15u
10
+ ··· + 425u + 152
c
5
, c
12
u
12
+ 2u
11
+ ··· − 9u + 7
c
8
, c
10
u
12
− u
11
+ ··· + 1494u + 607
c
9
u
12
− 5u
11
+ ··· + 31u + 14
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
12
+ 6y
11
+ ··· − 471040y + 65536
c
2
, c
7
y
12
+ 22y
11
+ ··· + 2624y + 256
c
3
, c
6
y
12
− 13y
11
+ ··· + 66y + 25
c
4
, c
11
y
12
− 30y
11
+ ··· + 13631y + 23104
c
5
, c
12
y
12
+ 14y
11
+ ··· + 591y + 49
c
8
, c
10
y
12
− 21y
11
+ ··· + 947430y + 368449
c
9
y
12
− 7y
11
+ ··· + 3519y + 196
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.073080 + 0.247830I
a = −0.205686 + 0.226684I
b = −0.644126 − 0.709985I
−5.72012 + 1.08206I −7.15082 − 4.03183I
u = 1.073080 − 0.247830I
a = −0.205686 − 0.226684I
b = −0.644126 + 0.709985I
−5.72012 − 1.08206I −7.15082 + 4.03183I
u = 1.009660 + 0.511160I
a = −0.494615 − 1.267450I
b = 1.039140 − 0.687591I
0.57034 − 4.05390I −4.38416 + 4.91735I
u = 1.009660 − 0.511160I
a = −0.494615 + 1.267450I
b = 1.039140 + 0.687591I
0.57034 + 4.05390I −4.38416 − 4.91735I
u = −0.830480 + 0.173166I
a = −0.551557 + 0.852128I
b = −0.062030 − 1.028400I
−14.8564 + 1.0416I −8.90880 − 6.97569I
u = −0.830480 − 0.173166I
a = −0.551557 − 0.852128I
b = −0.062030 + 1.028400I
−14.8564 − 1.0416I −8.90880 + 6.97569I
u = −0.137010 + 0.433413I
a = 0.896797 + 0.679594I
b = 0.142411 + 0.345315I
−0.227997 + 0.989058I −3.44966 − 7.41497I
u = −0.137010 − 0.433413I
a = 0.896797 − 0.679594I
b = 0.142411 − 0.345315I
−0.227997 − 0.989058I −3.44966 + 7.41497I
u = 1.50435 + 1.39749I
a = 0.844739 + 0.586786I
b = −1.60755 + 1.62037I
19.5110 − 12.6758I −3.44721 + 4.54307I
u = 1.50435 − 1.39749I
a = 0.844739 − 0.586786I
b = −1.60755 − 1.62037I
19.5110 + 12.6758I −3.44721 − 4.54307I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −2.11959 + 0.80100I
a = 0.410323 − 0.816861I
b = 0.13215 − 2.51818I
−8.32399 + 2.80123I −4.65935 − 1.22361I
u = −2.11959 − 0.80100I
a = 0.410323 + 0.816861I
b = 0.13215 + 2.51818I
−8.32399 − 2.80123I −4.65935 + 1.22361I
6
II.
I
u
2
= h−3.02×10
15
u
19
+1.20×10
15
u
18
+· · ·+5.92×10
15
b+5.60×10
14
, 9.23×
10
15
u
19
+3.66×10
15
u
18
+· · ·+5.92×10
15
a+5.61×10
15
, u
20
+4u
18
+· · ·+3u+1i
(i) Arc colorings
a
6
=
1
0
a
12
=
0
u
a
3
=
−1.55890u
19
− 0.618344u
18
+ ··· − 13.8199u − 0.947362
0.510577u
19
− 0.202418u
18
+ ··· + 2.63545u − 0.0945461
a
7
=
1
u
2
a
2
=
−1.70332u
19
− 0.312792u
18
+ ··· − 13.0414u − 0.234471
0.440100u
19
− 0.230469u
18
+ ··· + 1.86321u − 0.400099
a
1
=
−1.07358u
19
− 0.813886u
18
+ ··· − 33.9072u − 8.78031
−0.504783u
19
+ 0.295424u
18
+ ··· − 2.61547u − 0.255554
a
5
=
0.879796u
19
− 0.232552u
18
+ ··· + 4.44267u − 1.81413
−0.380687u
19
− 0.0331509u
18
+ ··· − 0.811015u − 1.69737
a
4
=
0.879796u
19
− 0.232552u
18
+ ··· + 4.44267u − 1.81413
−0.330693u
19
+ 0.000465385u
18
+ ··· − 0.628875u − 1.92992
a
11
=
0.719586u
19
+ 0.369219u
18
+ ··· + 13.5809u + 3.96598
0.431366u
19
− 0.236260u
18
+ ··· + 3.50101u + 0.447132
a
10
=
1.18109u
19
+ 0.216905u
18
+ ··· + 18.9092u + 4.78233
0.518834u
19
− 0.220231u
18
+ ··· + 3.49645u + 0.599447
a
9
=
0.662252u
19
+ 0.437136u
18
+ ··· + 15.4127u + 4.18288
0.518834u
19
− 0.220231u
18
+ ··· + 3.49645u + 0.599447
a
8
=
0.743184u
19
+ 1.10142u
18
+ ··· + 21.8615u + 6.70129
0.418161u
19
+ 0.0155632u
18
+ ··· + 1.62432u + 2.08223
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −
39814249508127817
5919405752257771
u
19
−
6706137336893893
5919405752257771
u
18
+···−
334591284011249395
5919405752257771
u−
66498336645743408
5919405752257771
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
10
− 13u
9
+ ··· − 343u + 67)
2
c
2
, c
7
u
20
+ 13u
18
+ ··· + 343u
2
+ 67
c
3
, c
6
u
20
+ 4u
18
+ ··· + 3u + 1
c
4
(u
10
− u
9
− 2u
8
+ u
7
− 4u
6
+ 5u
5
+ 7u
4
− 4u
3
+ 2u
2
− 5u − 1)
2
c
5
, c
12
u
20
− 5u
19
+ ··· − 4u + 1
c
8
, c
10
u
20
− 3u
19
+ ··· − 313u + 391
c
9
(u
10
+ u
9
+ 2u
8
− 8u
7
− 15u
6
− 41u
5
− 44u
4
− 57u
3
− 3u
2
+ 6u + 1)
2
c
11
(u
10
+ u
9
− 2u
8
− u
7
− 4u
6
− 5u
5
+ 7u
4
+ 4u
3
+ 2u
2
+ 5u − 1)
2
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
10
− 19y
9
+ ··· − 5223y + 4489)
2
c
2
, c
7
(y
10
+ 13y
9
+ ··· + 343y + 67)
2
c
3
, c
6
y
20
+ 8y
19
+ ··· + 13y + 1
c
4
, c
11
(y
10
− 5y
9
+ ··· − 29y + 1)
2
c
5
, c
12
y
20
− 9y
19
+ ··· − 6y + 1
c
8
, c
10
y
20
− y
19
+ ··· + 705145y + 152881
c
9
(y
10
+ 3y
9
+ ··· − 42y + 1)
2
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.169912 + 1.033690I
a = −1.027740 + 0.367867I
b = 0.939266 + 0.170399I
1.81830 − 61.381650 + 0.10I
u = 0.169912 − 1.033690I
a = −1.027740 − 0.367867I
b = 0.939266 − 0.170399I
1.81830 − 61.381650 + 0.10I
u = −1.058270 + 0.332331I
a = 0.776808 − 0.003579I
b = 0.266712 + 0.446040I
−2.63705 + 1.91138I −5.85314 − 2.19256I
u = −1.058270 − 0.332331I
a = 0.776808 + 0.003579I
b = 0.266712 − 0.446040I
−2.63705 − 1.91138I −5.85314 + 2.19256I
u = 0.749999 + 0.461306I
a = 0.626786 + 0.928745I
b = −0.423468 − 1.053800I
−14.3530 −2.56768 + 0.I
u = 0.749999 − 0.461306I
a = 0.626786 − 0.928745I
b = −0.423468 + 1.053800I
−14.3530 −2.56768 + 0.I
u = 0.021655 + 1.184100I
a = 1.077240 − 0.017516I
b = −0.99403 + 1.07585I
−2.63705 − 1.91138I −5.85314 + 2.19256I
u = 0.021655 − 1.184100I
a = 1.077240 + 0.017516I
b = −0.99403 − 1.07585I
−2.63705 + 1.91138I −5.85314 − 2.19256I
u = −0.674532 + 1.047120I
a = 1.368660 − 0.287017I
b = −0.948711 − 0.785310I
−2.51892 + 5.10495I −2.50119 − 5.27179I
u = −0.674532 − 1.047120I
a = 1.368660 + 0.287017I
b = −0.948711 + 0.785310I
−2.51892 − 5.10495I −2.50119 + 5.27179I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.966161 + 1.030760I
a = −0.970102 + 0.568270I
b = 1.231870 + 0.292979I
−4.58274 + 3.70357I −6.31936 − 0.16987I
u = −0.966161 − 1.030760I
a = −0.970102 − 0.568270I
b = 1.231870 − 0.292979I
−4.58274 − 3.70357I −6.31936 + 0.16987I
u = 1.36430 + 0.42550I
a = −0.055504 − 0.690748I
b = 0.374039 − 0.261089I
−2.51892 − 5.10495I −2.50119 + 5.27179I
u = 1.36430 − 0.42550I
a = −0.055504 + 0.690748I
b = 0.374039 + 0.261089I
−2.51892 + 5.10495I −2.50119 − 5.27179I
u = 0.028356 + 0.409589I
a = 7.65404 − 3.49906I
b = −0.456837 − 0.233907I
6.13648 − 2.74090I 17.7667 − 11.6717I
u = 0.028356 − 0.409589I
a = 7.65404 + 3.49906I
b = −0.456837 + 0.233907I
6.13648 + 2.74090I 17.7667 + 11.6717I
u = −0.263839 + 0.272160I
a = 0.75729 + 1.74372I
b = 0.27219 + 1.44939I
−4.58274 + 3.70357I −6.31936 − 0.16987I
u = −0.263839 − 0.272160I
a = 0.75729 − 1.74372I
b = 0.27219 − 1.44939I
−4.58274 − 3.70357I −6.31936 + 0.16987I
u = 0.62858 + 2.01281I
a = −0.707467 − 0.154937I
b = 2.23897 − 0.22781I
6.13648 − 2.74090I 17.7667 − 11.6717I
u = 0.62858 − 2.01281I
a = −0.707467 + 0.154937I
b = 2.23897 + 0.22781I
6.13648 + 2.74090I 17.7667 + 11.6717I
11
III. I
u
3
= h−2.64 × 10
16
u
15
− 7.93 × 10
15
u
14
+ · · · + 8.40 × 10
18
b + 2.49 ×
10
18
, −2.01 × 10
18
u
15
+ 1.13 × 10
19
u
14
+ · · · + 5.97 × 10
20
a + 4.26 ×
10
21
, u
16
− u
15
+ · · · + 163u + 71i
(i) Arc colorings
a
6
=
1
0
a
12
=
0
u
a
3
=
0.00337450u
15
− 0.0189617u
14
+ ··· + 1.89959u − 7.14361
0.00314395u
15
+ 0.000943365u
14
+ ··· + 0.0449932u − 0.296340
a
7
=
1
u
2
a
2
=
0.0107975u
15
− 0.0252968u
14
+ ··· + 4.15572u − 5.74058
0.00250302u
15
+ 0.00276345u
14
+ ··· − 0.659364u − 0.373579
a
1
=
−0.0655553u
15
+ 0.0741115u
14
+ ··· − 27.0806u − 10.9764
0.00312829u
15
+ 0.00290945u
14
+ ··· − 1.59008u − 0.820416
a
5
=
−0.0104767u
15
+ 0.0209012u
14
+ ··· − 5.81764u + 1.25426
0.00216927u
15
+ 0.00594923u
14
+ ··· − 1.37136u − 0.417612
a
4
=
−0.0104767u
15
+ 0.0209012u
14
+ ··· − 5.81764u + 1.25426
0.00117374u
15
+ 0.00575176u
14
+ ··· − 0.416019u + 0.322528
a
11
=
0.0252415u
15
− 0.0178660u
14
+ ··· + 7.88004u + 4.68578
0.00657981u
15
− 0.00108658u
14
+ ··· − 0.0698176u − 0.177735
a
10
=
0.0337177u
15
− 0.0306569u
14
+ ··· + 10.8046u + 5.03170
0.00820697u
15
− 0.00225643u
14
+ ··· + 0.0316438u + 0.128600
a
9
=
0.0255108u
15
− 0.0284004u
14
+ ··· + 10.7729u + 4.90310
0.00820697u
15
− 0.00225643u
14
+ ··· + 0.0316438u + 0.128600
a
8
=
0.0387732u
15
− 0.0335190u
14
+ ··· + 13.0924u + 8.52027
0.00517636u
15
− 0.00187196u
14
+ ··· + 0.247599u + 0.297704
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
942004923634454628
8401916491839065525
u
15
+
81627954125616557
763810590167187775
u
14
+ ··· −
310716039596242128796
8401916491839065525
u −
169186114798085193871
8401916491839065525
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
8
+ 15u
7
+ 78u
6
+ 153u
5
+ 154u
4
+ 76u
3
− 159u
2
− 174u + 121)
2
c
2
, c
7
(u
8
+ u
7
+ 8u
6
+ u
5
+ 8u
4
− 12u
3
+ u
2
− 14u + 11)
2
c
3
, c
6
u
16
− u
15
+ ··· + 163u + 71
c
4
, c
11
(u
8
− 7u
7
+ 14u
6
− 10u
5
+ 16u
4
+ 2u
3
+ 5u
2
− 18u + 28)
2
c
5
, c
12
u
16
+ 2u
15
+ ··· + 516u + 113
c
8
, c
10
u
16
− 30u
14
+ ··· − 305u + 25
c
9
(u
8
+ u
7
+ 4u
6
+ u
5
+ 10u
4
+ 9u
2
− 2u + 1)
2
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
8
− 69y
7
+ ··· − 68754y + 14641)
2
c
2
, c
7
(y
8
+ 15y
7
+ 78y
6
+ 153y
5
+ 154y
4
+ 76y
3
− 159y
2
− 174y + 121)
2
c
3
, c
6
y
16
+ y
15
+ ··· + 18445y + 5041
c
4
, c
11
(y
8
− 21y
7
+ 88y
6
+ 386y
5
+ 240y
4
+ 580y
3
+ 993y
2
− 44y + 784)
2
c
5
, c
12
y
16
− 2y
15
+ ··· + 42912y + 12769
c
8
, c
10
y
16
− 60y
15
+ ··· − 30675y + 625
c
9
(y
8
+ 7y
7
+ 34y
6
+ 97y
5
+ 178y
4
+ 192y
3
+ 101y
2
+ 14y + 1)
2
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.930105 + 0.642390I
a = −0.0256301 + 0.0507802I
b = −0.046860 + 1.356980I
−4.46347 + 4.82161I −6.01453 − 6.61722I
u = −0.930105 − 0.642390I
a = −0.0256301 − 0.0507802I
b = −0.046860 − 1.356980I
−4.46347 − 4.82161I −6.01453 + 6.61722I
u = 0.837926 + 0.838459I
a = 1.37082 + 0.68579I
b = −1.060800 + 0.622192I
−4.46347 − 4.82161I −6.01453 + 6.61722I
u = 0.837926 − 0.838459I
a = 1.37082 − 0.68579I
b = −1.060800 − 0.622192I
−4.46347 + 4.82161I −6.01453 − 6.61722I
u = 1.200940 + 0.035935I
a = 0.089945 + 0.500990I
b = 0.875246 + 0.803241I
−0.47591 + 2.83833I −2.49972 − 2.93638I
u = 1.200940 − 0.035935I
a = 0.089945 − 0.500990I
b = 0.875246 − 0.803241I
−0.47591 − 2.83833I −2.49972 + 2.93638I
u = −0.668009 + 1.003610I
a = 1.019600 − 0.478974I
b = −0.425332 − 1.024850I
−0.47591 + 2.83833I −2.49972 − 2.93638I
u = −0.668009 − 1.003610I
a = 1.019600 + 0.478974I
b = −0.425332 + 1.024850I
−0.47591 − 2.83833I −2.49972 + 2.93638I
u = −0.219451 + 0.356043I
a = −7.73951 − 0.17352I
b = −0.222770 + 0.248407I
5.99986 + 2.87814I −11.5340 − 17.1252I
u = −0.219451 − 0.356043I
a = −7.73951 + 0.17352I
b = −0.222770 − 0.248407I
5.99986 − 2.87814I −11.5340 + 17.1252I
15
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.90749 + 0.26315I
a = −0.237198 + 1.251610I
b = 0.02100 + 2.20047I
−19.1547 + 0.7815I −4.45172 − 0.30321I
u = −1.90749 − 0.26315I
a = −0.237198 − 1.251610I
b = 0.02100 − 2.20047I
−19.1547 − 0.7815I −4.45172 + 0.30321I
u = 0.62790 + 2.02093I
a = −0.709426 − 0.166954I
b = 2.23737 − 0.20974I
5.99986 − 2.87814I −11.5340 + 17.1252I
u = 0.62790 − 2.02093I
a = −0.709426 + 0.166954I
b = 2.23737 + 0.20974I
5.99986 + 2.87814I −11.5340 − 17.1252I
u = 1.55829 + 2.01508I
a = 0.196181 + 0.265717I
b = −2.37786 − 1.70668I
−19.1547 + 0.7815I −4.45172 − 0.30321I
u = 1.55829 − 2.01508I
a = 0.196181 − 0.265717I
b = −2.37786 + 1.70668I
−19.1547 − 0.7815I −4.45172 + 0.30321I
16
IV. I
u
4
= hu
2
+ b − 1, u
2
+ a + u, u
3
− u + 1i
(i) Arc colorings
a
6
=
1
0
a
12
=
0
u
a
3
=
−u
2
− u
−u
2
+ 1
a
7
=
1
u
2
a
2
=
−u
2
− u
−u
2
+ 1
a
1
=
−u
2
− u
−u
2
+ 1
a
5
=
−u
−u
2
− u + 1
a
4
=
−u
−u
2
a
11
=
u − 1
u − 1
a
10
=
u
2
+ u − 1
u
2
− 1
a
9
=
u
u
2
− 1
a
8
=
1
u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 7u
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
u
3
c
3
, c
6
u
3
− u + 1
c
4
, c
8
, c
10
u
3
+ 2u
2
+ u + 1
c
5
, c
9
, c
12
u
3
− u
2
+ 1
c
11
u
3
− 2u
2
+ u − 1
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
7
y
3
c
3
, c
6
y
3
− 2y
2
+ y −1
c
4
, c
8
, c
10
c
11
y
3
− 2y
2
− 3y −1
c
5
, c
9
, c
12
y
3
− y
2
+ 2y −1
19
(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 = 0.877439 − 0.744862I
1.45094 − 3.77083I 4.63651 + 3.93596I
u = 0.662359 − 0.562280I
a = −0.78492 + 1.30714I
b = 0.877439 + 0.744862I
1.45094 + 3.77083I 4.63651 − 3.93596I
u = −1.32472
a = −0.430160
b = −0.754878
−6.19175 −9.27300
20
V. I
u
5
= hb − u − 1, a − u, u
2
+ u + 1i
(i) Arc colorings
a
6
=
1
0
a
12
=
0
u
a
3
=
u
u + 1
a
7
=
1
−u − 1
a
2
=
0
u
a
1
=
1
0
a
5
=
0
u
a
4
=
0
u
a
11
=
0
u
a
10
=
u
u + 1
a
9
=
−1
u + 1
a
8
=
−1
0
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u − 2
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
6
, c
7
, c
8
c
10
u
2
+ u + 1
c
4
, c
11
u
2
c
5
, c
9
, c
12
u
2
− u + 1
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
5
, c
6
, c
7
c
8
, c
9
, c
10
c
12
y
2
+ y + 1
c
4
, c
11
y
2
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = −0.500000 + 0.866025I
b = 0.500000 + 0.866025I
2.02988I 0. − 3.46410I
u = −0.500000 − 0.866025I
a = −0.500000 − 0.866025I
b = 0.500000 − 0.866025I
− 2.02988I 0. + 3.46410I
24
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
3
(u
2
+ u + 1)
· (u
8
+ 15u
7
+ 78u
6
+ 153u
5
+ 154u
4
+ 76u
3
− 159u
2
− 174u + 121)
2
· ((u
10
− 13u
9
+ ··· − 343u + 67)
2
)(u
12
+ 22u
11
+ ··· + 2624u + 256)
c
2
, c
7
u
3
(u
2
+ u + 1)(u
8
+ u
7
+ 8u
6
+ u
5
+ 8u
4
− 12u
3
+ u
2
− 14u + 11)
2
· (u
12
− 4u
11
+ ··· − 24u + 16)(u
20
+ 13u
18
+ ··· + 343u
2
+ 67)
c
3
, c
6
(u
2
+ u + 1)(u
3
− u + 1)(u
12
− u
11
+ ··· + 2u + 5)
· (u
16
− u
15
+ ··· + 163u + 71)(u
20
+ 4u
18
+ ··· + 3u + 1)
c
4
u
2
(u
3
+ 2u
2
+ u + 1)
· (u
8
− 7u
7
+ 14u
6
− 10u
5
+ 16u
4
+ 2u
3
+ 5u
2
− 18u + 28)
2
· (u
10
− u
9
− 2u
8
+ u
7
− 4u
6
+ 5u
5
+ 7u
4
− 4u
3
+ 2u
2
− 5u − 1)
2
· (u
12
− 15u
10
+ ··· + 425u + 152)
c
5
, c
12
(u
2
− u + 1)(u
3
− u
2
+ 1)(u
12
+ 2u
11
+ ··· − 9u + 7)
· (u
16
+ 2u
15
+ ··· + 516u + 113)(u
20
− 5u
19
+ ··· − 4u + 1)
c
8
, c
10
(u
2
+ u + 1)(u
3
+ 2u
2
+ u + 1)(u
12
− u
11
+ ··· + 1494u + 607)
· (u
16
− 30u
14
+ ··· − 305u + 25)(u
20
− 3u
19
+ ··· − 313u + 391)
c
9
(u
2
− u + 1)(u
3
− u
2
+ 1)(u
8
+ u
7
+ ··· − 2u + 1)
2
· (u
10
+ u
9
+ 2u
8
− 8u
7
− 15u
6
− 41u
5
− 44u
4
− 57u
3
− 3u
2
+ 6u + 1)
2
· (u
12
− 5u
11
+ ··· + 31u + 14)
c
11
u
2
(u
3
− 2u
2
+ u − 1)
· (u
8
− 7u
7
+ 14u
6
− 10u
5
+ 16u
4
+ 2u
3
+ 5u
2
− 18u + 28)
2
· (u
10
+ u
9
− 2u
8
− u
7
− 4u
6
− 5u
5
+ 7u
4
+ 4u
3
+ 2u
2
+ 5u − 1)
2
· (u
12
− 15u
10
+ ··· + 425u + 152)
25
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
3
(y
2
+ y + 1)(y
8
− 69y
7
+ ··· − 68754y + 14641)
2
· (y
10
− 19y
9
+ ··· − 5223y + 4489)
2
· (y
12
+ 6y
11
+ ··· − 471040y + 65536)
c
2
, c
7
y
3
(y
2
+ y + 1)
· (y
8
+ 15y
7
+ 78y
6
+ 153y
5
+ 154y
4
+ 76y
3
− 159y
2
− 174y + 121)
2
· ((y
10
+ 13y
9
+ ··· + 343y + 67)
2
)(y
12
+ 22y
11
+ ··· + 2624y + 256)
c
3
, c
6
(y
2
+ y + 1)(y
3
− 2y
2
+ y −1)(y
12
− 13y
11
+ ··· + 66y + 25)
· (y
16
+ y
15
+ ··· + 18445y + 5041)(y
20
+ 8y
19
+ ··· + 13y + 1)
c
4
, c
11
y
2
(y
3
− 2y
2
− 3y −1)
· (y
8
− 21y
7
+ 88y
6
+ 386y
5
+ 240y
4
+ 580y
3
+ 993y
2
− 44y + 784)
2
· ((y
10
− 5y
9
+ ··· − 29y + 1)
2
)(y
12
− 30y
11
+ ··· + 13631y + 23104)
c
5
, c
12
(y
2
+ y + 1)(y
3
− y
2
+ 2y −1)(y
12
+ 14y
11
+ ··· + 591y + 49)
· (y
16
− 2y
15
+ ··· + 42912y + 12769)(y
20
− 9y
19
+ ··· − 6y + 1)
c
8
, c
10
(y
2
+ y + 1)(y
3
− 2y
2
− 3y −1)(y
12
− 21y
11
+ ··· + 947430y + 368449)
· (y
16
− 60y
15
+ ··· − 30675y + 625)
· (y
20
− y
19
+ ··· + 705145y + 152881)
c
9
(y
2
+ y + 1)(y
3
− y
2
+ 2y −1)
· (y
8
+ 7y
7
+ 34y
6
+ 97y
5
+ 178y
4
+ 192y
3
+ 101y
2
+ 14y + 1)
2
· ((y
10
+ 3y
9
+ ··· − 42y + 1)
2
)(y
12
− 7y
11
+ ··· + 3519y + 196)
26
