12n
0781
(K12n
0781
)
A knot diagram
1
Linearized knot diagam
4 6 9 12 8 3 11 2 12 7 5 9
Solving Sequence
3,9 4,6
7 2 1 8 5 12 10 11
c
3
c
6
c
2
c
1
c
8
c
5
c
12
c
9
c
11
c
4
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h155164409u
19
− 1173171752u
18
+ ··· + 19656063b + 4652516609,
3194027005u
19
− 23918980957u
18
+ ··· + 864866772a + 84007929151,
u
20
− 9u
19
+ ··· − 101u − 44i
I
u
2
= h1153398772571u
26
a − 27659986158013u
26
+ ··· + 47932282550416a + 517986614105786,
6.62034 × 10
14
au
26
+ 1.26437 × 10
15
u
26
+ ··· − 4.24307 × 10
15
a − 1.06993 × 10
16
, u
27
+ 4u
26
+ ··· − 16u + 1i
I
u
3
= hb + u − 2, 2u
3
− 12u
2
+ 5a + 19u − 7, u
4
− 6u
3
+ 12u
2
− 11u + 5i
I
u
4
= hu
10
a + 2u
11
+ ··· − a − 3, 2u
11
a + 4u
11
+ ··· − 3a + 10,
u
12
+ 3u
11
− 2u
10
− 14u
9
− 7u
8
+ 19u
7
+ 20u
6
− 4u
5
− 13u
4
− 7u
3
+ 4u + 1i
* 4 irreducible components of dim
C
= 0, with total 102 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
= h1.55×10
8
u
19
−1.17×10
9
u
18
+· · ·+ 1 .97×10
7
b+4.65×10
9
, 3.19×10
9
u
19
−
2.39 × 10
10
u
18
+ · · · + 8.65 × 10
8
a + 8.40 × 10
10
, u
20
− 9u
19
+ · · · − 101u − 44i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
6
=
−3.69309u
19
+ 27.6563u
18
+ ··· − 289.384u − 97.1340
−7.89397u
19
+ 59.6850u
18
+ ··· − 701.033u − 236.696
a
7
=
−11.5871u
19
+ 87.3412u
18
+ ··· − 990.417u − 333.830
−7.89397u
19
+ 59.6850u
18
+ ··· − 701.033u − 236.696
a
2
=
−0.729812u
19
+ 5.09498u
18
+ ··· − 10.5444u − 0.980246
−3.00124u
19
+ 23.1501u
18
+ ··· − 293.563u − 98.7110
a
1
=
−0.770109u
19
+ 6.89068u
18
+ ··· − 123.191u − 34.8650
1.39273u
19
− 6.70756u
18
+ ··· − 150.601u − 35.6579
a
8
=
1.32525u
19
− 10.3344u
18
+ ··· + 119.923u + 43.4460
−2.61701u
19
+ 19.7532u
18
+ ··· − 222.509u − 77.4331
a
5
=
−3.35278u
19
+ 25.4969u
18
+ ··· − 322.784u − 103.076
−4.67803u
19
+ 35.8313u
18
+ ··· − 442.706u − 147.522
a
12
=
−0.770109u
19
+ 6.89068u
18
+ ··· − 123.191u − 34.8650
−0.0402972u
19
+ 1.79570u
18
+ ··· − 112.646u − 33.8848
a
10
=
−7.78475u
19
+ 58.9253u
18
+ ··· − 701.929u − 238.453
−11.1375u
19
+ 84.4222u
18
+ ··· − 1023.71u − 342.529
a
11
=
−4.05370u
19
+ 30.6802u
18
+ ··· − 397.822u − 137.762
−8.13629u
19
+ 61.2722u
18
+ ··· − 730.150u − 243.818
(ii) Obstruction class = −1
(iii) Cusp Shapes =
1862218903
19656063
u
19
−
13770753601
19656063
u
18
+ ··· +
47665991273
6552021
u +
49632160054
19656063
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
, c
12
u
20
+ 3u
19
+ ··· + 7u + 1
c
2
, c
6
, c
7
c
10
u
20
− 3u
18
+ ··· − 2u − 1
c
3
u
20
− 9u
19
+ ··· − 101u − 44
c
4
, c
8
, c
11
u
20
− u
19
+ ··· + u − 1
c
5
u
20
+ 4u
19
+ ··· + 371u + 44
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
9
, c
12
y
20
− 31y
19
+ ··· − 53y + 1
c
2
, c
6
, c
7
c
10
y
20
− 6y
19
+ ··· − 2y + 1
c
3
y
20
− 29y
19
+ ··· − 23841y + 1936
c
4
, c
8
, c
11
y
20
+ 9y
19
+ ··· + 3y + 1
c
5
y
20
− 22y
19
+ ··· − 10041y + 1936
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.052670 + 0.214579I
a = 0.32175 − 1.92778I
b = −0.836827 − 0.543539I
6.83483 + 4.33332I 0.05876 − 7.63423I
u = −1.052670 − 0.214579I
a = 0.32175 + 1.92778I
b = −0.836827 + 0.543539I
6.83483 − 4.33332I 0.05876 + 7.63423I
u = 1.120110 + 0.346275I
a = −0.233306 − 0.424229I
b = −0.38707 − 1.48766I
−5.30551 − 1.26066I 2.12940 + 5.78685I
u = 1.120110 − 0.346275I
a = −0.233306 + 0.424229I
b = −0.38707 + 1.48766I
−5.30551 + 1.26066I 2.12940 − 5.78685I
u = −0.476182 + 0.251897I
a = 0.298266 + 0.199444I
b = 0.127716 − 0.483656I
−0.934143 + 0.731157I −6.62873 − 3.56102I
u = −0.476182 − 0.251897I
a = 0.298266 − 0.199444I
b = 0.127716 + 0.483656I
−0.934143 − 0.731157I −6.62873 + 3.56102I
u = 1.46200 + 0.11516I
a = −0.105955 + 0.364783I
b = 0.313911 + 0.848453I
−7.00266 + 1.06770I −8.57959 − 5.53529I
u = 1.46200 − 0.11516I
a = −0.105955 − 0.364783I
b = 0.313911 − 0.848453I
−7.00266 − 1.06770I −8.57959 + 5.53529I
u = −0.42309 + 1.47138I
a = −1.165830 + 0.209425I
b = 1.44769 + 0.49745I
7.84975 + 9.25606I 2.98645 − 8.19728I
u = −0.42309 − 1.47138I
a = −1.165830 − 0.209425I
b = 1.44769 − 0.49745I
7.84975 − 9.25606I 2.98645 + 8.19728I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.44287 + 0.52695I
a = 1.215020 + 0.143277I
b = −0.794041 − 0.102232I
2.39136 + 0.46763I 16.5681 − 6.4930I
u = 1.44287 − 0.52695I
a = 1.215020 − 0.143277I
b = −0.794041 + 0.102232I
2.39136 − 0.46763I 16.5681 + 6.4930I
u = −0.374420 + 0.266879I
a = −3.88796 + 1.78468I
b = 0.790015 − 0.335634I
9.03012 − 2.73757I 11.18044 + 1.41623I
u = −0.374420 − 0.266879I
a = −3.88796 − 1.78468I
b = 0.790015 + 0.335634I
9.03012 + 2.73757I 11.18044 − 1.41623I
u = 1.67183
a = 0.0164989
b = 0.556210
−7.42843 21.0830
u = 1.64455 + 0.32821I
a = −0.97484 − 1.07134I
b = 0.955066 − 0.584622I
−3.92374 − 8.34608I 0. + 8.57009I
u = 1.64455 − 0.32821I
a = −0.97484 + 1.07134I
b = 0.955066 + 0.584622I
−3.92374 + 8.34608I 0. − 8.57009I
u = 1.66385 + 0.49105I
a = 0.747318 + 0.938443I
b = −1.33112 + 0.78381I
1.0956 − 16.1913I 1.21980 + 7.93611I
u = 1.66385 − 0.49105I
a = 0.747318 − 0.938443I
b = −1.33112 − 0.78381I
1.0956 + 16.1913I 1.21980 − 7.93611I
u = −2.68586
a = 0.713636
b = −1.12689
3.80648 0
6
II. I
u
2
= h1.15 × 10
12
au
26
− 2.77 × 10
13
u
26
+ · · · + 4.79 × 10
13
a + 5.18 ×
10
14
, 6.62 × 10
14
au
26
+ 1.26 × 10
15
u
26
+ · · · − 4.24 × 10
15
a − 1.07 ×
10
16
, u
27
+ 4u
26
+ · · · − 16u + 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
6
=
a
−0.0242410au
26
+ 0.581330u
26
+ ··· − 1.00739a − 10.8865
a
7
=
−0.0242410au
26
+ 0.581330u
26
+ ··· − 0.00739376a − 10.8865
−0.0242410au
26
+ 0.581330u
26
+ ··· − 1.00739a − 10.8865
a
2
=
−1.08669au
26
+ 0.00739376u
26
+ ··· + 7.02849a + 7.42850
−0.0360384au
26
− 1.26454u
26
+ ··· − 0.689023a + 8.59574
a
1
=
−0.841478au
26
− u
26
+ ··· + 6.18701a + 16
0.337969au
26
− 1.00739u
26
+ ··· − 0.596266a + 8.57150
a
8
=
−1.50664au
26
− 2.66029u
26
+ ··· + 10.2782a + 26.5660
−0.242104au
26
− 1.76324u
26
+ ··· + 1.68247a + 6.29618
a
5
=
0.513982au
26
− 4.80755u
26
+ ··· − 2.50550a + 27.3198
0.513982au
26
+ 1.68297u
26
+ ··· − 2.50550a − 9.53524
a
12
=
−0.841478au
26
− u
26
+ ··· + 6.18701a + 16
0.245212au
26
− 1.00739u
26
+ ··· − 0.841478a + 8.57150
a
10
=
2.50550au
26
+ 4.15537u
26
+ ··· − 10.7922a − 38.4438
0.398816u
26
+ 2.23271u
25
+ ··· + 57.1829u − 5.41613
a
11
=
1.92417au
26
+ 3.36740u
26
+ ··· + 0.0943422a − 27.9026
−0.396547u
26
+ 0.153675u
25
+ ··· + 32.0090u − 1.30351
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
195093488669178
47580483876995
u
26
+
621166284588117
47580483876995
u
25
+ ··· +
10739526635696416
47580483876995
u −
1670488305527964
47580483876995
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
, c
12
u
54
− 9u
53
+ ··· − 817482u + 44911
c
2
, c
6
, c
7
c
10
u
54
− 2u
53
+ ··· − 7504u + 1667
c
3
(u
27
+ 4u
26
+ ··· − 16u + 1)
2
c
4
, c
8
, c
11
u
54
+ 3u
53
+ ··· − 7068u + 1763
c
5
(u
27
− 2u
26
+ ··· − 67u + 47)
2
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
9
, c
12
y
54
− 53y
53
+ ··· + 26272962362y + 2016997921
c
2
, c
6
, c
7
c
10
y
54
− 28y
53
+ ··· − 34895734y + 2778889
c
3
(y
27
− 30y
26
+ ··· + 108y −1)
2
c
4
, c
8
, c
11
y
54
+ 27y
53
+ ··· + 38637652y + 3108169
c
5
(y
27
− 20y
26
+ ··· + 14171y −2209)
2
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.158532 + 0.935582I
a = −1.50310 + 0.50723I
b = 1.316050 − 0.206467I
2.66520 − 3.11494I 4.06258 + 4.43870I
u = −0.158532 + 0.935582I
a = −0.232784 + 0.158230I
b = −0.125783 + 1.310910I
2.66520 − 3.11494I 4.06258 + 4.43870I
u = −0.158532 − 0.935582I
a = −1.50310 − 0.50723I
b = 1.316050 + 0.206467I
2.66520 + 3.11494I 4.06258 − 4.43870I
u = −0.158532 − 0.935582I
a = −0.232784 − 0.158230I
b = −0.125783 − 1.310910I
2.66520 + 3.11494I 4.06258 − 4.43870I
u = 1.07088
a = 0.20349 + 1.69086I
b = −1.039390 + 0.501438I
7.61014 2.10720
u = 1.07088
a = 0.20349 − 1.69086I
b = −1.039390 − 0.501438I
7.61014 2.10720
u = 0.221976 + 0.825159I
a = 0.865041 − 0.769539I
b = −0.188178 − 0.427579I
1.85443 + 1.12451I 2.23685 + 3.40792I
u = 0.221976 + 0.825159I
a = 1.56832 + 0.15522I
b = −1.056960 − 0.253260I
1.85443 + 1.12451I 2.23685 + 3.40792I
u = 0.221976 − 0.825159I
a = 0.865041 + 0.769539I
b = −0.188178 + 0.427579I
1.85443 − 1.12451I 2.23685 − 3.40792I
u = 0.221976 − 0.825159I
a = 1.56832 − 0.15522I
b = −1.056960 + 0.253260I
1.85443 − 1.12451I 2.23685 − 3.40792I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.772781 + 0.145831I
a = −0.955249 + 0.172273I
b = 0.942406 − 0.743444I
5.86045 + 0.50074I −0.026133 − 1.385067I
u = −0.772781 + 0.145831I
a = −0.03004 − 1.56141I
b = −0.956615 − 0.919647I
5.86045 + 0.50074I −0.026133 − 1.385067I
u = −0.772781 − 0.145831I
a = −0.955249 − 0.172273I
b = 0.942406 + 0.743444I
5.86045 − 0.50074I −0.026133 + 1.385067I
u = −0.772781 − 0.145831I
a = −0.03004 + 1.56141I
b = −0.956615 + 0.919647I
5.86045 − 0.50074I −0.026133 + 1.385067I
u = 0.732746 + 0.037797I
a = −0.197320 + 0.642818I
b = 1.097490 − 0.609563I
6.70782 − 6.19371I 1.04615 + 5.14040I
u = 0.732746 + 0.037797I
a = 0.39411 + 1.87802I
b = −1.136770 + 0.758571I
6.70782 − 6.19371I 1.04615 + 5.14040I
u = 0.732746 − 0.037797I
a = −0.197320 − 0.642818I
b = 1.097490 + 0.609563I
6.70782 + 6.19371I 1.04615 − 5.14040I
u = 0.732746 − 0.037797I
a = 0.39411 − 1.87802I
b = −1.136770 − 0.758571I
6.70782 + 6.19371I 1.04615 − 5.14040I
u = −1.41462 + 0.08838I
a = 0.262151 − 0.521305I
b = 0.744839 − 1.008240I
−3.85325 − 2.16315I 0.43125 + 2.34406I
u = −1.41462 + 0.08838I
a = 0.94161 + 1.25020I
b = −0.893423 + 0.347194I
−3.85325 − 2.16315I 0.43125 + 2.34406I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.41462 − 0.08838I
a = 0.262151 + 0.521305I
b = 0.744839 + 1.008240I
−3.85325 + 2.16315I 0.43125 − 2.34406I
u = −1.41462 − 0.08838I
a = 0.94161 − 1.25020I
b = −0.893423 − 0.347194I
−3.85325 + 2.16315I 0.43125 − 2.34406I
u = 0.96419 + 1.06250I
a = −0.777537 − 0.509617I
b = 1.49984 − 0.06654I
7.39896 − 3.81582I 3.19122 + 3.12687I
u = 0.96419 + 1.06250I
a = 0.996480 + 0.564354I
b = −1.52086 + 0.54966I
7.39896 − 3.81582I 3.19122 + 3.12687I
u = 0.96419 − 1.06250I
a = −0.777537 + 0.509617I
b = 1.49984 + 0.06654I
7.39896 + 3.81582I 3.19122 − 3.12687I
u = 0.96419 − 1.06250I
a = 0.996480 − 0.564354I
b = −1.52086 − 0.54966I
7.39896 + 3.81582I 3.19122 − 3.12687I
u = 1.46227 + 0.17089I
a = −0.70585 − 1.22803I
b = 1.080150 − 0.757376I
−2.64494 − 4.30028I 1.62045 + 0.54924I
u = 1.46227 + 0.17089I
a = 1.11356 − 1.22226I
b = −0.794850 − 0.366906I
−2.64494 − 4.30028I 1.62045 + 0.54924I
u = 1.46227 − 0.17089I
a = −0.70585 + 1.22803I
b = 1.080150 + 0.757376I
−2.64494 + 4.30028I 1.62045 − 0.54924I
u = 1.46227 − 0.17089I
a = 1.11356 + 1.22226I
b = −0.794850 + 0.366906I
−2.64494 + 4.30028I 1.62045 − 0.54924I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.53479
a = 0.414758 + 0.269711I
b = −1.024280 − 0.077414I
3.41879 6.41080
u = −1.53479
a = 0.414758 − 0.269711I
b = −1.024280 + 0.077414I
3.41879 6.41080
u = −1.46424 + 0.50584I
a = 0.865744 − 0.882179I
b = −1.37593 − 0.68985I
−1.70679 + 8.63753I 0.70129 − 5.57252I
u = −1.46424 + 0.50584I
a = −0.222321 + 0.420033I
b = −0.51373 + 1.37153I
−1.70679 + 8.63753I 0.70129 − 5.57252I
u = −1.46424 − 0.50584I
a = 0.865744 + 0.882179I
b = −1.37593 + 0.68985I
−1.70679 − 8.63753I 0.70129 + 5.57252I
u = −1.46424 − 0.50584I
a = −0.222321 − 0.420033I
b = −0.51373 − 1.37153I
−1.70679 − 8.63753I 0.70129 + 5.57252I
u = 1.60572 + 0.14635I
a = 0.143649 + 0.671229I
b = 0.676206 + 1.121340I
−3.96610 − 0.49039I 2.17660 + 0.87451I
u = 1.60572 + 0.14635I
a = −0.032560 + 0.591612I
b = −0.898818 + 0.272522I
−3.96610 − 0.49039I 2.17660 + 0.87451I
u = 1.60572 − 0.14635I
a = 0.143649 − 0.671229I
b = 0.676206 − 1.121340I
−3.96610 + 0.49039I 2.17660 − 0.87451I
u = 1.60572 − 0.14635I
a = −0.032560 − 0.591612I
b = −0.898818 − 0.272522I
−3.96610 + 0.49039I 2.17660 − 0.87451I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.61132 + 0.29006I
a = −0.953605 + 0.809181I
b = 1.074430 + 0.451641I
−4.62159 + 3.33366I 0. − 1.64502I
u = −1.61132 + 0.29006I
a = 0.079718 − 0.306892I
b = 0.745769 − 0.725411I
−4.62159 + 3.33366I 0. − 1.64502I
u = −1.61132 − 0.29006I
a = −0.953605 − 0.809181I
b = 1.074430 − 0.451641I
−4.62159 − 3.33366I 0. + 1.64502I
u = −1.61132 − 0.29006I
a = 0.079718 + 0.306892I
b = 0.745769 + 0.725411I
−4.62159 − 3.33366I 0. + 1.64502I
u = −1.64260 + 0.12656I
a = −0.539122 + 1.081180I
b = 1.193170 + 0.752557I
−2.09892 + 7.32302I 1.91859 − 5.85391I
u = −1.64260 + 0.12656I
a = −0.147988 − 0.383193I
b = −0.958048 − 0.349092I
−2.09892 + 7.32302I 1.91859 − 5.85391I
u = −1.64260 − 0.12656I
a = −0.539122 − 1.081180I
b = 1.193170 − 0.752557I
−2.09892 − 7.32302I 1.91859 + 5.85391I
u = −1.64260 − 0.12656I
a = −0.147988 + 0.383193I
b = −0.958048 + 0.349092I
−2.09892 − 7.32302I 1.91859 + 5.85391I
u = 0.341878
a = −0.80620 + 4.25915I
b = 1.024170 − 0.310510I
10.0079 6.39560
u = 0.341878
a = −0.80620 − 4.25915I
b = 1.024170 + 0.310510I
10.0079 6.39560
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.1382100 + 0.0296626I
a = −2.23980 − 1.90608I
b = −0.676102 + 0.783648I
1.15814 − 2.56837I −5.68616 + 5.09265I
u = 0.1382100 + 0.0296626I
a = −4.00516 − 10.10660I
b = 0.765217 − 0.171124I
1.15814 − 2.56837I −5.68616 + 5.09265I
u = 0.1382100 − 0.0296626I
a = −2.23980 + 1.90608I
b = −0.676102 − 0.783648I
1.15814 + 2.56837I −5.68616 − 5.09265I
u = 0.1382100 − 0.0296626I
a = −4.00516 + 10.10660I
b = 0.765217 + 0.171124I
1.15814 + 2.56837I −5.68616 − 5.09265I
15
III. I
u
3
= hb + u − 2, 2u
3
− 12u
2
+ 5a + 19u − 7, u
4
− 6u
3
+ 12u
2
− 11u + 5i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
6
=
−
2
5
u
3
+
12
5
u
2
−
19
5
u +
7
5
−u + 2
a
7
=
−
2
5
u
3
+
12
5
u
2
−
24
5
u +
17
5
−u + 2
a
2
=
−
4
5
u
3
+
19
5
u
2
−
23
5
u +
9
5
u
2
− 4u + 4
a
1
=
1
5
u
3
−
1
5
u
2
−
8
5
u +
4
5
3u
3
− 13u
2
+ 13u − 6
a
8
=
−
1
5
u
3
+
1
5
u
2
+
8
5
u −
4
5
−u
3
+ 5u
2
− 5u + 1
a
5
=
4
5
u
3
−
19
5
u
2
+
28
5
u −
19
5
u
3
− 3u
2
+ 4u − 4
a
12
=
1
5
u
3
−
1
5
u
2
−
8
5
u +
4
5
u
3
− 4u
2
+ 3u − 1
a
10
=
11
5
u
3
−
51
5
u
2
+
62
5
u −
31
5
3u
3
− 14u
2
+ 19u − 11
a
11
=
7
5
u
3
−
27
5
u
2
+
19
5
u −
7
5
3u
3
− 13u
2
+ 15u − 7
(ii) Obstruction class = 1
(iii) Cusp Shapes = −22u
2
+ 35u − 21
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
u
4
− u
3
− 2u
2
− 4u + 1
c
2
, c
7
u
4
− 2u
3
+ 3u − 1
c
3
u
4
− 6u
3
+ 12u
2
− 11u + 5
c
4
u
4
− u
3
− 2u + 1
c
5
u
4
− 5u
3
+ 6u
2
+ 2u − 5
c
6
, c
10
u
4
+ 2u
3
− 3u − 1
c
8
, c
11
u
4
+ u
3
+ 2u + 1
c
12
u
4
+ u
3
− 2u
2
+ 4u + 1
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
9
, c
12
y
4
− 5y
3
− 2y
2
− 20y + 1
c
2
, c
6
, c
7
c
10
y
4
− 4y
3
+ 10y
2
− 9y + 1
c
3
y
4
− 12y
3
+ 22y
2
− y + 25
c
4
, c
8
, c
11
y
4
− y
3
− 2y
2
− 4y + 1
c
5
y
4
− 13y
3
+ 46y
2
− 64y + 25
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.620433 + 0.769480I
a = −1.109540 − 0.805650I
b = 1.37957 − 0.76948I
8.50524 − 7.16341I 5.27273 + 5.92572I
u = 0.620433 − 0.769480I
a = −1.109540 + 0.805650I
b = 1.37957 + 0.76948I
8.50524 + 7.16341I 5.27273 − 5.92572I
u = 1.64145
a = −0.140116
b = 0.358555
−7.61222 −22.8250
u = 3.11769
a = 0.759190
b = −1.11769
3.76121 −125.720
19
IV. I
u
4
=
hu
10
a+2u
11
+· · ·−a−3, 2u
11
a+4u
11
+· · ·−3a+10, u
12
+3u
11
+· · ·+4u+1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
6
=
a
−u
10
a − 2u
11
+ ··· + a + 3
a
7
=
−u
10
a − 2u
11
+ ··· + 2a + 3
−u
10
a − 2u
11
+ ··· + a + 3
a
2
=
3u
11
a + 9u
10
a + ··· − 14u − 5
u
10
a + 2u
9
a + ··· − 2u − 1
a
1
=
3u
10
a + u
11
+ ··· − 8u − 4
−6u
11
a + 3u
11
+ ··· − 3a + 1
a
8
=
u
10
a + u
11
+ ··· + u + 4
u
10
a − u
11
+ ··· − a + 4
a
5
=
−u
10
a − u
11
+ ··· + a − 8
−u
10
a + 3u
10
+ ··· + a − 4
a
12
=
3u
10
a + u
11
+ ··· − 8u − 4
−3u
11
a + u
11
+ ··· + 6u + 1
a
10
=
−u
11
a − 3u
10
a + ··· − 7u − 9
−u
10
− u
9
+ 5u
8
+ 6u
7
− 7u
6
− 11u
5
+ u
4
+ 5u
3
+ 2u
2
+ 2u − 2
a
11
=
−3u
11
a − 10u
10
a + ··· + 3a − 1
−u
10
− 2u
9
+ 3u
8
+ 9u
7
+ u
6
− 11u
5
− 7u
4
+ u
3
+ 2u
2
+ 3u
(ii) Obstruction class = 1
(iii) Cusp Shapes
= 2u
11
+ 3u
10
− 11u
9
− 19u
8
+ 17u
7
+ 42u
6
+ 2u
5
− 34u
4
− 22u
3
− 2u
2
+ 11u + 10
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
u
24
− 6u
23
+ ··· + 10u + 1
c
2
, c
7
u
24
− u
23
+ ··· + u
2
+ 1
c
3
(u
12
+ 3u
11
+ ··· + 4u + 1)
2
c
4
u
24
+ 10u
22
+ ··· + 8u + 1
c
5
(u
12
+ 5u
11
+ ··· − u + 1)
2
c
6
, c
10
u
24
+ u
23
+ ··· + u
2
+ 1
c
8
, c
11
u
24
+ 10u
22
+ ··· − 8u + 1
c
12
u
24
+ 6u
23
+ ··· − 10u + 1
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
9
, c
12
y
24
− 12y
23
+ ··· − 22y + 1
c
2
, c
6
, c
7
c
10
y
24
− 7y
23
+ ··· + 2y + 1
c
3
(y
12
− 13y
11
+ ··· − 16y + 1)
2
c
4
, c
8
, c
11
y
24
+ 20y
23
+ ··· − 12y + 1
c
5
(y
12
− 11y
11
+ ··· − 15y + 1)
2
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.825594 + 0.098170I
a = −0.53917 − 2.00160I
b = −0.762732 − 0.663101I
7.88103 + 3.00613I 2.46057 − 2.77569I
u = 0.825594 + 0.098170I
a = −1.31555 − 1.91865I
b = 0.818361 + 0.141778I
7.88103 + 3.00613I 2.46057 − 2.77569I
u = 0.825594 − 0.098170I
a = −0.53917 + 2.00160I
b = −0.762732 + 0.663101I
7.88103 − 3.00613I 2.46057 + 2.77569I
u = 0.825594 − 0.098170I
a = −1.31555 + 1.91865I
b = 0.818361 − 0.141778I
7.88103 − 3.00613I 2.46057 + 2.77569I
u = 1.25362
a = 0.243567 + 0.537746I
b = 0.160883 + 1.179440I
−5.74068 −1.95790
u = 1.25362
a = 0.243567 − 0.537746I
b = 0.160883 − 1.179440I
−5.74068 −1.95790
u = −1.107540 + 0.627422I
a = 0.725858 − 1.187980I
b = −1.244680 − 0.659147I
9.51415 + 2.44072I 5.50124 − 2.26022I
u = −1.107540 + 0.627422I
a = −0.974699 + 0.995211I
b = 1.183370 + 0.002215I
9.51415 + 2.44072I 5.50124 − 2.26022I
u = −1.107540 − 0.627422I
a = 0.725858 + 1.187980I
b = −1.244680 + 0.659147I
9.51415 − 2.44072I 5.50124 + 2.26022I
u = −1.107540 − 0.627422I
a = −0.974699 − 0.995211I
b = 1.183370 − 0.002215I
9.51415 − 2.44072I 5.50124 + 2.26022I
23
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.197871 + 0.665613I
a = 0.544098 + 0.505503I
b = −0.506495 + 0.897042I
1.83491 − 2.17307I 2.44305 + 0.96656I
u = −0.197871 + 0.665613I
a = 2.11053 − 0.83148I
b = −1.074320 + 0.072465I
1.83491 − 2.17307I 2.44305 + 0.96656I
u = −0.197871 − 0.665613I
a = 0.544098 − 0.505503I
b = −0.506495 − 0.897042I
1.83491 + 2.17307I 2.44305 − 0.96656I
u = −0.197871 − 0.665613I
a = 2.11053 + 0.83148I
b = −1.074320 − 0.072465I
1.83491 + 2.17307I 2.44305 − 0.96656I
u = −1.47309
a = 0.960868 + 0.116818I
b = −0.725226 − 0.147080I
2.06794 −0.326150
u = −1.47309
a = 0.960868 − 0.116818I
b = −0.725226 + 0.147080I
2.06794 −0.326150
u = 1.53037
a = 0.142205 + 0.666213I
b = 0.518363 + 0.759712I
−5.45448 −3.70880
u = 1.53037
a = 0.142205 − 0.666213I
b = 0.518363 − 0.759712I
−5.45448 −3.70880
u = −1.54061 + 0.22982I
a = 0.308882 + 0.905973I
b = 0.028277 + 0.455528I
−3.33520 + 5.64987I −0.48217 − 4.54553I
u = −1.54061 + 0.22982I
a = −0.757657 + 1.082380I
b = 1.133770 + 0.656888I
−3.33520 + 5.64987I −0.48217 − 4.54553I
24
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.54061 − 0.22982I
a = 0.308882 − 0.905973I
b = 0.028277 − 0.455528I
−3.33520 − 5.64987I −0.48217 + 4.54553I
u = −1.54061 − 0.22982I
a = −0.757657 − 1.082380I
b = 1.133770 − 0.656888I
−3.33520 − 5.64987I −0.48217 + 4.54553I
u = −0.270030
a = 1.05107 + 3.12255I
b = 0.970434 + 0.909500I
6.94627 7.14740
u = −0.270030
a = 1.05107 − 3.12255I
b = 0.970434 − 0.909500I
6.94627 7.14740
25
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
9
(u
4
− u
3
− 2u
2
− 4u + 1)(u
20
+ 3u
19
+ ··· + 7u + 1)
· (u
24
− 6u
23
+ ··· + 10u + 1)(u
54
− 9u
53
+ ··· − 817482u + 44911)
c
2
, c
7
(u
4
− 2u
3
+ 3u − 1)(u
20
− 3u
18
+ ··· − 2u − 1)(u
24
− u
23
+ ··· + u
2
+ 1)
· (u
54
− 2u
53
+ ··· − 7504u + 1667)
c
3
(u
4
− 6u
3
+ 12u
2
− 11u + 5)(u
12
+ 3u
11
+ ··· + 4u + 1)
2
· (u
20
− 9u
19
+ ··· − 101u − 44)(u
27
+ 4u
26
+ ··· − 16u + 1)
2
c
4
(u
4
− u
3
− 2u + 1)(u
20
− u
19
+ ··· + u − 1)(u
24
+ 10u
22
+ ··· + 8u + 1)
· (u
54
+ 3u
53
+ ··· − 7068u + 1763)
c
5
(u
4
− 5u
3
+ 6u
2
+ 2u − 5)(u
12
+ 5u
11
+ ··· − u + 1)
2
· (u
20
+ 4u
19
+ ··· + 371u + 44)(u
27
− 2u
26
+ ··· − 67u + 47)
2
c
6
, c
10
(u
4
+ 2u
3
− 3u − 1)(u
20
− 3u
18
+ ··· − 2u − 1)(u
24
+ u
23
+ ··· + u
2
+ 1)
· (u
54
− 2u
53
+ ··· − 7504u + 1667)
c
8
, c
11
(u
4
+ u
3
+ 2u + 1)(u
20
− u
19
+ ··· + u − 1)(u
24
+ 10u
22
+ ··· − 8u + 1)
· (u
54
+ 3u
53
+ ··· − 7068u + 1763)
c
12
(u
4
+ u
3
− 2u
2
+ 4u + 1)(u
20
+ 3u
19
+ ··· + 7u + 1)
· (u
24
+ 6u
23
+ ··· − 10u + 1)(u
54
− 9u
53
+ ··· − 817482u + 44911)
26
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
9
, c
12
(y
4
− 5y
3
− 2y
2
− 20y + 1)(y
20
− 31y
19
+ ··· − 53y + 1)
· (y
24
− 12y
23
+ ··· − 22y + 1)
· (y
54
− 53y
53
+ ··· + 26272962362y + 2016997921)
c
2
, c
6
, c
7
c
10
(y
4
− 4y
3
+ 10y
2
− 9y + 1)(y
20
− 6y
19
+ ··· − 2y + 1)
· (y
24
− 7y
23
+ ··· + 2y + 1)
· (y
54
− 28y
53
+ ··· − 34895734y + 2778889)
c
3
(y
4
− 12y
3
+ 22y
2
− y + 25)(y
12
− 13y
11
+ ··· − 16y + 1)
2
· (y
20
− 29y
19
+ ··· − 23841y + 1936)(y
27
− 30y
26
+ ··· + 108y −1)
2
c
4
, c
8
, c
11
(y
4
− y
3
− 2y
2
− 4y + 1)(y
20
+ 9y
19
+ ··· + 3y + 1)
· (y
24
+ 20y
23
+ ··· − 12y + 1)
· (y
54
+ 27y
53
+ ··· + 38637652y + 3108169)
c
5
(y
4
− 13y
3
+ 46y
2
− 64y + 25)(y
12
− 11y
11
+ ··· − 15y + 1)
2
· (y
20
− 22y
19
+ ··· − 10041y + 1936)
· (y
27
− 20y
26
+ ··· + 14171y −2209)
2
27
