12n
0434
(K12n
0434
)
A knot diagram
1
Linearized knot diagam
3 6 8 1 10 2 11 1 12 8 6 5
Solving Sequence
1,5 4,9
8 3 12 10 6 2 7 11
c
4
c
8
c
3
c
12
c
9
c
5
c
2
c
6
c
11
c
1
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h1.15244 × 10
89
u
53
− 2.36305 × 10
89
u
52
+ ··· + 1.14353 × 10
89
b + 6.98962 × 10
89
,
− 2.35956 × 10
90
u
53
+ 4.56370 × 10
90
u
52
+ ··· + 8.00468 × 10
89
a − 4.87445 × 10
90
, u
54
− 3u
53
+ ··· − 3u + 1i
I
u
2
= h13421u
13
+ 20820u
12
+ ··· + 17217b − 11948, 655u
13
+ 3102u
12
+ ··· + 5739a + 3767,
u
14
+ 2u
13
+ 4u
12
+ 3u
11
+ 6u
10
+ 6u
9
+ 14u
8
+ 14u
7
+ 19u
6
+ 14u
5
+ 10u
4
+ 2u
3
+ 3u
2
+ 1i
I
u
3
= hu
3
+ 2b − 3, u
3
+ 2a − 3, u
4
+ u
3
+ 2u
2
− u + 1i
I
u
4
= hu
2
+ b + 1, u
2
+ a + 1, u
4
+ u
3
+ 2u
2
+ 2u + 1i
* 4 irreducible components of dim
C
= 0, with total 76 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
= h1.15×10
89
u
53
−2.36×10
89
u
52
+· · ·+1.14×10
89
b+6.99×10
89
, −2.36×
10
90
u
53
+4.56×10
90
u
52
+· · ·+8.00×10
89
a−4.87×10
90
, u
54
−3u
53
+· · ·−3u+1i
(i) Arc colorings
a
1
=
0
u
a
5
=
1
0
a
4
=
1
−u
2
a
9
=
2.94773u
53
− 5.70129u
52
+ ··· − 14.5124u + 6.08949
−1.00780u
53
+ 2.06646u
52
+ ··· + 15.3054u − 6.11234
a
8
=
2.94773u
53
− 5.70129u
52
+ ··· − 14.5124u + 6.08949
−0.287284u
53
+ 0.699825u
52
+ ··· + 8.82747u − 2.97046
a
3
=
−1.97603u
53
+ 4.47321u
52
+ ··· + 27.0023u − 13.6868
0.915616u
53
− 1.04433u
52
+ ··· − 14.8536u + 3.07727
a
12
=
u
u
a
10
=
4.21790u
53
− 8.54770u
52
+ ··· − 22.8533u + 10.1883
0.262380u
53
− 0.779944u
52
+ ··· + 6.96448u − 2.01353
a
6
=
5.26626u
53
− 18.3261u
52
+ ··· + 62.9922u − 13.9709
0.751703u
53
− 1.91257u
52
+ ··· + 2.33641u − 1.75467
a
2
=
−11.3826u
53
+ 30.2001u
52
+ ··· + 7.41660u − 26.3662
0.520213u
53
− 0.0746840u
52
+ ··· − 27.1247u + 3.86789
a
7
=
−8.72344u
53
+ 33.9754u
52
+ ··· − 130.452u + 31.2985
3.58969u
53
− 10.8714u
52
+ ··· + 6.78177u + 2.52277
a
11
=
12.7906u
53
− 37.1295u
52
+ ··· + 18.7277u + 3.70834
1.17501u
53
− 4.52802u
52
+ ··· + 14.7445u − 5.03833
(ii) Obstruction class = −1
(iii) Cusp Shapes = 1.14333u
53
− 0.924812u
52
+ ··· − 6.63399u + 6.45142
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
54
+ 43u
53
+ ··· + 3692u + 441
c
2
, c
6
u
54
− u
53
+ ··· − 26u + 21
c
3
u
54
− 25u
52
+ ··· + 2432u + 1856
c
4
, c
12
u
54
− 3u
53
+ ··· − 3u + 1
c
5
u
54
+ 2u
53
+ ··· + 153u + 47
c
7
, c
10
u
54
+ u
53
+ ··· − 2486u + 121
c
8
u
54
+ 5u
53
+ ··· − 17089u + 1801
c
9
u
54
+ 9u
53
+ ··· + 3712u + 768
c
11
u
54
+ u
53
+ ··· + 1004850u + 134807
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
54
− 49y
53
+ ··· + 4263152y + 194481
c
2
, c
6
y
54
+ 43y
53
+ ··· + 3692y + 441
c
3
y
54
− 50y
53
+ ··· − 42856448y + 3444736
c
4
, c
12
y
54
+ 11y
53
+ ··· + 41y + 1
c
5
y
54
− 6y
53
+ ··· + 27633y + 2209
c
7
, c
10
y
54
+ 65y
53
+ ··· − 587818y + 14641
c
8
y
54
− 63y
53
+ ··· + 140310537y + 3243601
c
9
y
54
+ 31y
53
+ ··· − 9355264y + 589824
c
11
y
54
+ 75y
53
+ ··· − 92128132162y + 18172927249
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.037373 + 1.006010I
a = 1.030200 + 0.062419I
b = −0.490474 − 0.580472I
2.85970 + 0.80963I 6.77195 + 0.29503I
u = −0.037373 − 1.006010I
a = 1.030200 − 0.062419I
b = −0.490474 + 0.580472I
2.85970 − 0.80963I 6.77195 − 0.29503I
u = −0.543124 + 0.777830I
a = −0.471157 + 0.381929I
b = −0.50611 + 1.96562I
−7.74259 + 6.23460I −0.70370 − 6.97900I
u = −0.543124 − 0.777830I
a = −0.471157 − 0.381929I
b = −0.50611 − 1.96562I
−7.74259 − 6.23460I −0.70370 + 6.97900I
u = −0.431004 + 0.822553I
a = −1.029580 + 0.012079I
b = −0.807592 + 0.331900I
−0.65107 + 2.00888I 0.23679 − 4.07426I
u = −0.431004 − 0.822553I
a = −1.029580 − 0.012079I
b = −0.807592 − 0.331900I
−0.65107 − 2.00888I 0.23679 + 4.07426I
u = −0.795980 + 0.436234I
a = −0.277873 + 0.419648I
b = −0.318797 − 0.205145I
−1.27040 + 1.87667I −3.97787 − 4.44520I
u = −0.795980 − 0.436234I
a = −0.277873 − 0.419648I
b = −0.318797 + 0.205145I
−1.27040 − 1.87667I −3.97787 + 4.44520I
u = 0.527527 + 1.001810I
a = 1.149730 − 0.365464I
b = 1.53010 − 0.50566I
−2.71697 − 1.97809I 0. + 2.58049I
u = 0.527527 − 1.001810I
a = 1.149730 + 0.365464I
b = 1.53010 + 0.50566I
−2.71697 + 1.97809I 0. − 2.58049I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.918205 + 0.762698I
a = −1.118580 − 0.397034I
b = −1.122090 + 0.488407I
−2.04155 + 2.12181I 0
u = −0.918205 − 0.762698I
a = −1.118580 + 0.397034I
b = −1.122090 − 0.488407I
−2.04155 − 2.12181I 0
u = −0.364190 + 1.145600I
a = −0.442213 + 0.376301I
b = 0.400143 − 0.343043I
3.58333 + 4.89977I 0. − 7.27006I
u = −0.364190 − 1.145600I
a = −0.442213 − 0.376301I
b = 0.400143 + 0.343043I
3.58333 − 4.89977I 0. + 7.27006I
u = 0.960632 + 0.774462I
a = 1.13070 − 0.89501I
b = 1.59243 + 0.09416I
−7.46820 + 0.80208I 0
u = 0.960632 − 0.774462I
a = 1.13070 + 0.89501I
b = 1.59243 − 0.09416I
−7.46820 − 0.80208I 0
u = 0.600991 + 0.467590I
a = 0.158333 − 0.973691I
b = 0.100996 + 0.808006I
−3.72491 − 3.82211I 6.70276 + 1.18963I
u = 0.600991 − 0.467590I
a = 0.158333 + 0.973691I
b = 0.100996 − 0.808006I
−3.72491 + 3.82211I 6.70276 − 1.18963I
u = 0.979992 + 0.797814I
a = −1.43891 + 0.26324I
b = −1.97461 − 0.43491I
−15.3307 − 5.7207I 0
u = 0.979992 − 0.797814I
a = −1.43891 − 0.26324I
b = −1.97461 + 0.43491I
−15.3307 + 5.7207I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.187854 + 1.250900I
a = −0.186276 + 0.095635I
b = −0.859056 + 0.377021I
−0.658796 + 0.749765I 0
u = 0.187854 − 1.250900I
a = −0.186276 − 0.095635I
b = −0.859056 − 0.377021I
−0.658796 − 0.749765I 0
u = −0.247033 + 0.676299I
a = −0.301606 + 0.279111I
b = −0.365687 + 0.725077I
−0.05790 + 1.76249I 0.05580 − 5.36659I
u = −0.247033 − 0.676299I
a = −0.301606 − 0.279111I
b = −0.365687 − 0.725077I
−0.05790 − 1.76249I 0.05580 + 5.36659I
u = 1.098870 + 0.656535I
a = 1.55286 − 0.44234I
b = 1.158690 + 0.463793I
−4.13666 − 6.24317I 0
u = 1.098870 − 0.656535I
a = 1.55286 + 0.44234I
b = 1.158690 − 0.463793I
−4.13666 + 6.24317I 0
u = −0.697329 + 0.022686I
a = −1.38730 + 3.11746I
b = 0.181432 + 0.532548I
−9.05440 − 2.92567I −6.42699 + 0.09398I
u = −0.697329 − 0.022686I
a = −1.38730 − 3.11746I
b = 0.181432 − 0.532548I
−9.05440 + 2.92567I −6.42699 − 0.09398I
u = 1.026470 + 0.845684I
a = −1.40395 + 1.00681I
b = −1.220970 − 0.303738I
−4.13120 − 4.24024I 0
u = 1.026470 − 0.845684I
a = −1.40395 − 1.00681I
b = −1.220970 + 0.303738I
−4.13120 + 4.24024I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.837598 + 1.066200I
a = −1.124140 + 0.742986I
b = −1.77532 − 0.42316I
−6.55172 − 7.42273I 0
u = 0.837598 − 1.066200I
a = −1.124140 − 0.742986I
b = −1.77532 + 0.42316I
−6.55172 + 7.42273I 0
u = 0.815947 + 1.102350I
a = 0.53489 − 1.31244I
b = 1.53981 − 0.09220I
−14.3214 − 0.9597I 0
u = 0.815947 − 1.102350I
a = 0.53489 + 1.31244I
b = 1.53981 + 0.09220I
−14.3214 + 0.9597I 0
u = −1.131240 + 0.821749I
a = 1.105120 + 0.458003I
b = 1.61964 − 0.06450I
−10.58060 − 0.64727I 0
u = −1.131240 − 0.821749I
a = 1.105120 − 0.458003I
b = 1.61964 + 0.06450I
−10.58060 + 0.64727I 0
u = −0.090452 + 0.526330I
a = 1.120460 + 0.305656I
b = 0.74665 − 1.44801I
1.157250 − 0.155163I 7.37161 − 1.36723I
u = −0.090452 − 0.526330I
a = 1.120460 − 0.305656I
b = 0.74665 + 1.44801I
1.157250 + 0.155163I 7.37161 + 1.36723I
u = −0.93222 + 1.15582I
a = −0.936289 − 0.829653I
b = −1.54017 + 0.35175I
−9.48565 + 8.12595I 0
u = −0.93222 − 1.15582I
a = −0.936289 + 0.829653I
b = −1.54017 − 0.35175I
−9.48565 − 8.12595I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.94640 + 1.15434I
a = 0.757645 + 0.359126I
b = 0.951028 − 0.386906I
−0.63092 + 4.66377I 0
u = −0.94640 − 1.15434I
a = 0.757645 − 0.359126I
b = 0.951028 + 0.386906I
−0.63092 − 4.66377I 0
u = −0.055729 + 0.503312I
a = −1.96871 − 3.65912I
b = 0.886771 + 0.795520I
−8.54356 − 3.22703I 3.94778 − 2.72438I
u = −0.055729 − 0.503312I
a = −1.96871 + 3.65912I
b = 0.886771 − 0.795520I
−8.54356 + 3.22703I 3.94778 + 2.72438I
u = 0.99851 + 1.13262I
a = 1.34755 − 0.60244I
b = 1.70196 + 0.68361I
−14.2209 − 14.9873I 0
u = 0.99851 − 1.13262I
a = 1.34755 + 0.60244I
b = 1.70196 − 0.68361I
−14.2209 + 14.9873I 0
u = 1.19097 + 0.94277I
a = −0.950142 + 0.775950I
b = −1.54086 + 0.39585I
−14.9446 + 7.1061I 0
u = 1.19097 − 0.94277I
a = −0.950142 − 0.775950I
b = −1.54086 − 0.39585I
−14.9446 − 7.1061I 0
u = −0.79135 + 1.35810I
a = 0.524839 + 0.318013I
b = 0.921922 − 0.092922I
−0.47705 + 4.55318I 0
u = −0.79135 − 1.35810I
a = 0.524839 − 0.318013I
b = 0.921922 + 0.092922I
−0.47705 − 4.55318I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.124133 + 0.402569I
a = 0.92386 + 1.37352I
b = 0.575765 − 0.613700I
1.34934 − 0.45303I 8.18333 + 1.54346I
u = 0.124133 − 0.402569I
a = 0.92386 − 1.37352I
b = 0.575765 + 0.613700I
1.34934 + 0.45303I 8.18333 − 1.54346I
u = 0.132130 + 0.214010I
a = −4.29946 + 0.59400I
b = −1.385600 − 0.232769I
−0.15771 − 3.49876I 0.819601 − 0.411516I
u = 0.132130 − 0.214010I
a = −4.29946 − 0.59400I
b = −1.385600 + 0.232769I
−0.15771 + 3.49876I 0.819601 + 0.411516I
10
II. I
u
2
= h13421u
13
+ 20820u
12
+ · · · + 17217b − 11948, 655u
13
+ 3102u
12
+
· · · + 5739a + 3767, u
14
+ 2u
13
+ · · · + 3u
2
+ 1i
(i) Arc colorings
a
1
=
0
u
a
5
=
1
0
a
4
=
1
−u
2
a
9
=
−0.114131u
13
− 0.540512u
12
+ ··· − 4.39449u − 0.656386
−0.779520u
13
− 1.20927u
12
+ ··· − 0.757507u + 0.693965
a
8
=
−0.114131u
13
− 0.540512u
12
+ ··· − 4.39449u − 0.656386
−0.369518u
13
− 0.334727u
12
+ ··· − 0.871638u + 0.381716
a
3
=
1.42975u
13
+ 3.35738u
12
+ ··· + 4.06354u + 0.526514
0.404310u
13
+ 1.03537u
12
+ ··· + 0.381716u + 1.36952
a
12
=
u
u
a
10
=
0.448220u
13
+ 0.508974u
12
+ ··· − 3.72910u − 1.31841
−0.217169u
13
− 0.159784u
12
+ ··· − 0.0921183u + 0.0319452
a
6
=
1.04374u
13
+ 2.01934u
12
+ ··· − 1.69768u − 1.46297
0.349771u
13
+ 0.851891u
12
+ ··· + 0.693965u + 0.779520
a
2
=
2.37672u
13
+ 6.11082u
12
+ ··· + 6.79526u + 0.653598
−0.0935703u
13
+ 0.0622060u
12
+ ··· − 0.144799u + 1.79927
a
7
=
−1.98949u
13
− 3.59296u
12
+ ··· + 6.07400u + 5.76122
−0.589998u
13
− 1.12546u
12
+ ··· − 4.11413u − 0.312250
a
11
=
−1.79427u
13
− 4.66998u
12
+ ··· − 2.77847u + 1.07324
0.562351u
13
+ 1.04949u
12
+ ··· + 0.665389u − 0.662020
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
2746
5739
u
13
+
4976
1913
u
12
+ ··· +
19957
5739
u +
38557
5739
11
(iv) u-Polynomials at the component
12
Crossings u-Polynomials at each crossing
c
1
u
14
− 10u
13
+ ··· − 16u + 1
c
2
u
14
− 4u
13
+ ··· − 2u + 1
c
3
u
14
− u
12
+ u
11
− u
10
+ 5u
8
− 3u
7
− 5u
6
+ 3u
5
+ 4u
4
− u
3
− 3u
2
+ 1
c
4
u
14
+ 2u
13
+ ··· + 3u
2
+ 1
c
5
u
14
− 3u
12
+ u
11
+ 4u
10
− 3u
9
− 5u
8
+ 3u
7
+ 5u
6
− u
4
− u
3
− u
2
+ 1
c
6
u
14
+ 4u
13
+ ··· + 2u + 1
c
7
u
14
+ 6u
12
+ ··· − 2u + 1
c
8
u
14
+ 4u
13
+ ··· + 55u + 19
c
9
u
14
+ 2u
13
+ ··· + 1130u + 325
c
10
u
14
+ 6u
12
+ ··· + 2u + 1
c
11
u
14
− 3u
11
+ ··· − 121u + 19
c
12
u
14
− 2u
13
+ ··· + 3u
2
+ 1
13
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
14
− 2y
13
+ ··· − 36y + 1
c
2
, c
6
y
14
+ 10y
13
+ ··· + 16y + 1
c
3
y
14
− 2y
13
+ ··· − 6y + 1
c
4
, c
12
y
14
+ 4y
13
+ ··· + 6y + 1
c
5
y
14
− 6y
13
+ ··· − 2y + 1
c
7
, c
10
y
14
+ 12y
13
+ ··· + 10y + 1
c
8
y
14
− 16y
13
+ ··· + 1269y + 361
c
9
y
14
+ 6y
13
+ ··· − 62700y + 105625
c
11
y
14
− 24y
12
+ ··· − 5065y + 361
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.819607 + 0.515589I
a = −0.642113 − 0.758617I
b = −0.465178 + 0.621015I
−4.31778 + 3.99647I −6.54046 − 4.82744I
u = −0.819607 − 0.515589I
a = −0.642113 + 0.758617I
b = −0.465178 − 0.621015I
−4.31778 − 3.99647I −6.54046 + 4.82744I
u = 0.157391 + 1.079850I
a = 0.799329 + 0.677674I
b = −0.803174 + 0.138913I
1.96129 + 2.14587I 2.42560 − 2.43593I
u = 0.157391 − 1.079850I
a = 0.799329 − 0.677674I
b = −0.803174 − 0.138913I
1.96129 − 2.14587I 2.42560 + 2.43593I
u = −0.522544 + 1.221350I
a = −0.021609 + 0.753511I
b = 0.794322 − 0.068763I
2.62934 + 4.67740I −0.17980 − 4.29340I
u = −0.522544 − 1.221350I
a = −0.021609 − 0.753511I
b = 0.794322 + 0.068763I
2.62934 − 4.67740I −0.17980 + 4.29340I
u = −0.163995 + 0.636516I
a = 0.790950 − 0.043131I
b = −0.014726 − 1.396170I
1.00700 + 1.01107I 3.78201 − 5.56453I
u = −0.163995 − 0.636516I
a = 0.790950 + 0.043131I
b = −0.014726 + 1.396170I
1.00700 − 1.01107I 3.78201 + 5.56453I
u = 1.065560 + 0.835049I
a = −1.52550 + 0.63079I
b = −1.195830 − 0.385658I
−3.10509 − 6.09159I 2.11795 + 6.25265I
u = 1.065560 − 0.835049I
a = −1.52550 − 0.63079I
b = −1.195830 + 0.385658I
−3.10509 + 6.09159I 2.11795 − 6.25265I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.350432 + 0.386096I
a = 0.71355 − 4.60985I
b = 0.789643 + 0.752742I
−8.76271 − 3.69641I −2.70956 + 11.15415I
u = 0.350432 − 0.386096I
a = 0.71355 + 4.60985I
b = 0.789643 − 0.752742I
−8.76271 + 3.69641I −2.70956 − 11.15415I
u = −1.06723 + 1.10388I
a = 0.885391 + 0.210981I
b = 0.894938 − 0.522276I
−0.92659 + 4.05089I −1.39574 − 1.45833I
u = −1.06723 − 1.10388I
a = 0.885391 − 0.210981I
b = 0.894938 + 0.522276I
−0.92659 − 4.05089I −1.39574 + 1.45833I
17
III. I
u
3
= hu
3
+ 2b − 3, u
3
+ 2a − 3, u
4
+ u
3
+ 2u
2
− u + 1i
(i) Arc colorings
a
1
=
0
u
a
5
=
1
0
a
4
=
1
−u
2
a
9
=
−
1
2
u
3
+
3
2
−
1
2
u
3
+
3
2
a
8
=
−
1
2
u
3
+
3
2
−u
3
− u + 2
a
3
=
1
2
u
3
−
3
2
u
3
+ u − 3
a
12
=
u
u
a
10
=
−
1
2
u
3
+
3
2
−
1
2
u
3
+
3
2
a
6
=
1
2
u
3
−
3
2
1
2
u
3
−
5
2
a
2
=
−
1
2
u
3
− u
2
− 2u −
1
2
−
1
2
u
3
− 2u
2
− 2u −
3
2
a
7
=
0
−u
a
11
=
1
2
u
3
+ u
2
+ 2u +
1
2
1
2
u
3
+ u
2
+ 3u +
1
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 7u
3
+ 11u
2
+ 17u + 4
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
, c
8
c
10
(u
2
− u + 1)
2
c
2
, c
7
(u
2
+ u + 1)
2
c
3
, c
5
(u
2
− u − 1)
2
c
4
u
4
+ u
3
+ 2u
2
− u + 1
c
9
u
4
c
11
, c
12
u
4
− u
3
+ 2u
2
+ u + 1
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
7
, c
8
, c
10
(y
2
+ y + 1)
2
c
3
, c
5
(y
2
− 3y + 1)
2
c
4
, c
11
, c
12
y
4
+ 3y
3
+ 8y
2
+ 3y + 1
c
9
y
4
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.309017 + 0.535233I
a = 1.61803
b = 1.61803
− 4.05977I 5.50000 + 12.73768I
u = 0.309017 − 0.535233I
a = 1.61803
b = 1.61803
4.05977I 5.50000 − 12.73768I
u = −0.80902 + 1.40126I
a = −0.618034
b = −0.618034
4.05977I 5.50000 − 1.11873I
u = −0.80902 − 1.40126I
a = −0.618034
b = −0.618034
− 4.05977I 5.50000 + 1.11873I
21
IV. I
u
4
= hu
2
+ b + 1, u
2
+ a + 1, u
4
+ u
3
+ 2u
2
+ 2u + 1i
(i) Arc colorings
a
1
=
0
u
a
5
=
1
0
a
4
=
1
−u
2
a
9
=
−u
2
− 1
−u
2
− 1
a
8
=
−u
2
− 1
−u
3
− 2u
2
− 2u − 2
a
3
=
u
3
+ 2u + 1
−u
2
+ u − 1
a
12
=
u
u
a
10
=
−u
2
− 1
−u
2
− 1
a
6
=
u
3
+ 2u + 1
u
3
+ 2u
a
2
=
−u
2
− 1
−2u
3
− 2u
2
− 2u − 3
a
7
=
0
−u
a
11
=
u
3
+ 2u + 1
u
3
+ 3u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −3u
3
− 3u
2
− 3u − 2
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
, c
8
c
10
(u
2
− u + 1)
2
c
2
, c
7
(u
2
+ u + 1)
2
c
3
, c
5
u
4
+ u
3
− u
2
− u + 1
c
4
u
4
+ u
3
+ 2u
2
+ 2u + 1
c
9
u
4
c
11
, c
12
u
4
− u
3
+ 2u
2
− 2u + 1
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
7
, c
8
, c
10
(y
2
+ y + 1)
2
c
3
, c
5
y
4
− 3y
3
+ 5y
2
− 3y + 1
c
4
, c
11
, c
12
y
4
+ 3y
3
+ 2y
2
+ 1
c
9
y
4
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.621744 + 0.440597I
a = −1.192440 + 0.547877I
b = −1.192440 + 0.547877I
0 −1.07732 − 0.95444I
u = −0.621744 − 0.440597I
a = −1.192440 − 0.547877I
b = −1.192440 − 0.547877I
0 −1.07732 + 0.95444I
u = 0.121744 + 1.306620I
a = 0.692440 − 0.318148I
b = 0.692440 − 0.318148I
0 4.57732 + 1.64363I
u = 0.121744 − 1.306620I
a = 0.692440 + 0.318148I
b = 0.692440 + 0.318148I
0 4.57732 − 1.64363I
25
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
4
)(u
14
− 10u
13
+ ··· − 16u + 1)
· (u
54
+ 43u
53
+ ··· + 3692u + 441)
c
2
((u
2
+ u + 1)
4
)(u
14
− 4u
13
+ ··· − 2u + 1)(u
54
− u
53
+ ··· − 26u + 21)
c
3
(u
2
− u − 1)
2
(u
4
+ u
3
− u
2
− u + 1)
· (u
14
− u
12
+ u
11
− u
10
+ 5u
8
− 3u
7
− 5u
6
+ 3u
5
+ 4u
4
− u
3
− 3u
2
+ 1)
· (u
54
− 25u
52
+ ··· + 2432u + 1856)
c
4
(u
4
+ u
3
+ 2u
2
− u + 1)(u
4
+ u
3
+ 2u
2
+ 2u + 1)(u
14
+ 2u
13
+ ··· + 3u
2
+ 1)
· (u
54
− 3u
53
+ ··· − 3u + 1)
c
5
(u
2
− u − 1)
2
(u
4
+ u
3
− u
2
− u + 1)
· (u
14
− 3u
12
+ u
11
+ 4u
10
− 3u
9
− 5u
8
+ 3u
7
+ 5u
6
− u
4
− u
3
− u
2
+ 1)
· (u
54
+ 2u
53
+ ··· + 153u + 47)
c
6
((u
2
− u + 1)
4
)(u
14
+ 4u
13
+ ··· + 2u + 1)(u
54
− u
53
+ ··· − 26u + 21)
c
7
((u
2
+ u + 1)
4
)(u
14
+ 6u
12
+ ··· − 2u + 1)
· (u
54
+ u
53
+ ··· − 2486u + 121)
c
8
((u
2
− u + 1)
4
)(u
14
+ 4u
13
+ ··· + 55u + 19)
· (u
54
+ 5u
53
+ ··· − 17089u + 1801)
c
9
u
8
(u
14
+ 2u
13
+ ··· + 1130u + 325)(u
54
+ 9u
53
+ ··· + 3712u + 768)
c
10
((u
2
− u + 1)
4
)(u
14
+ 6u
12
+ ··· + 2u + 1)
· (u
54
+ u
53
+ ··· − 2486u + 121)
c
11
(u
4
− u
3
+ 2u
2
− 2u + 1)(u
4
− u
3
+ 2u
2
+ u + 1)
· (u
14
− 3u
11
+ ··· − 121u + 19)(u
54
+ u
53
+ ··· + 1004850u + 134807)
c
12
(u
4
− u
3
+ 2u
2
− 2u + 1)(u
4
− u
3
+ 2u
2
+ u + 1)(u
14
− 2u
13
+ ··· + 3u
2
+ 1)
· (u
54
− 3u
53
+ ··· − 3u + 1)
26
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
4
)(y
14
− 2y
13
+ ··· − 36y + 1)
· (y
54
− 49y
53
+ ··· + 4263152y + 194481)
c
2
, c
6
((y
2
+ y + 1)
4
)(y
14
+ 10y
13
+ ··· + 16y + 1)
· (y
54
+ 43y
53
+ ··· + 3692y + 441)
c
3
((y
2
− 3y + 1)
2
)(y
4
− 3y
3
+ ··· − 3y + 1)(y
14
− 2y
13
+ ··· − 6y + 1)
· (y
54
− 50y
53
+ ··· − 42856448y + 3444736)
c
4
, c
12
(y
4
+ 3y
3
+ 2y
2
+ 1)(y
4
+ 3y
3
+ ··· + 3y + 1)(y
14
+ 4y
13
+ ··· + 6y + 1)
· (y
54
+ 11y
53
+ ··· + 41y + 1)
c
5
((y
2
− 3y + 1)
2
)(y
4
− 3y
3
+ ··· − 3y + 1)(y
14
− 6y
13
+ ··· − 2y + 1)
· (y
54
− 6y
53
+ ··· + 27633y + 2209)
c
7
, c
10
((y
2
+ y + 1)
4
)(y
14
+ 12y
13
+ ··· + 10y + 1)
· (y
54
+ 65y
53
+ ··· − 587818y + 14641)
c
8
((y
2
+ y + 1)
4
)(y
14
− 16y
13
+ ··· + 1269y + 361)
· (y
54
− 63y
53
+ ··· + 140310537y + 3243601)
c
9
y
8
(y
14
+ 6y
13
+ ··· − 62700y + 105625)
· (y
54
+ 31y
53
+ ··· − 9355264y + 589824)
c
11
(y
4
+ 3y
3
+ 2y
2
+ 1)(y
4
+ 3y
3
+ 8y
2
+ 3y + 1)
· (y
14
− 24y
12
+ ··· − 5065y + 361)
· (y
54
+ 75y
53
+ ··· − 92128132162y + 18172927249)
27
