11a
277
(K11a
277
)
A knot diagram
1
Linearized knot diagam
9 5 1 10 2 4 11 3 6 7 8
Solving Sequence
2,6
5
3,10
4 7 9 1 8 11
c
5
c
2
c
4
c
6
c
9
c
1
c
8
c
11
c
3
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.82122 × 10
22
u
34
+ 1.39965 × 10
23
u
33
+ ··· + 1.46127 × 10
23
b + 1.58974 × 10
23
,
− 3.04671 × 10
23
u
34
+ 2.69618 × 10
24
u
33
+ ··· + 1.16902 × 10
24
a − 1.80715 × 10
25
,
u
35
− 9u
34
+ ··· + 129u − 8i
I
u
2
= h−u
23
a − u
23
+ ··· − 3a − 1, 4u
23
a − u
23
+ ··· − 18a − 11, u
24
+ 7u
23
+ ··· + 15u + 3i
I
u
3
= h−u
11
− 6u
10
− 20u
9
− 46u
8
− 76u
7
− 94u
6
− 86u
5
− 57u
4
− 28u
3
− 11u
2
+ b − 5u − 1,
− u
10
− 6u
9
− 20u
8
− 45u
7
− 72u
6
− 85u
5
− 72u
4
− 43u
3
− 18u
2
+ a − 6u − 3,
u
12
+ 6u
11
+ 20u
10
+ 46u
9
+ 77u
8
+ 98u
7
+ 95u
6
+ 71u
5
+ 42u
4
+ 21u
3
+ 10u
2
+ 3u + 1i
I
u
4
= hau + 2b − a − u − 1, a
2
+ au − a − 3u − 2, u
2
+ 1i
* 4 irreducible components of dim
C
= 0, with total 99 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−1.82 × 10
22
u
34
+ 1.40 × 10
23
u
33
+ · · · + 1.46 × 10
23
b + 1.59 ×
10
23
, −3.05 × 10
23
u
34
+ 2.70 × 10
24
u
33
+ · · · + 1.17 × 10
24
a − 1.81 ×
10
25
, u
35
− 9u
34
+ · · · + 129u − 8i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
5
=
1
−u
2
a
3
=
−u
u
3
+ u
a
10
=
0.260621u
34
− 2.30636u
33
+ ··· − 109.860u + 15.4587
0.124632u
34
− 0.957827u
33
+ ··· + 0.995973u − 1.08791
a
4
=
0.0292774u
34
− 0.335350u
33
+ ··· + 46.0876u − 8.56756
0.255676u
34
− 2.11726u
33
+ ··· − 17.8267u + 1.81119
a
7
=
0.0652835u
34
− 0.480129u
33
+ ··· + 39.1684u − 5.24345
0.0574092u
34
− 0.366296u
33
+ ··· + 9.72748u − 0.148606
a
9
=
0.135989u
34
− 1.34853u
33
+ ··· − 110.856u + 16.5466
0.124632u
34
− 0.957827u
33
+ ··· + 0.995973u − 1.08791
a
1
=
0.0878378u
34
− 0.551320u
33
+ ··· + 70.1500u − 12.5898
−0.239219u
34
+ 2.22799u
33
+ ··· + 24.9209u − 0.702702
a
8
=
0.0523471u
34
− 0.798413u
33
+ ··· − 122.147u + 17.1988
0.207975u
34
− 1.87903u
33
+ ··· − 13.1866u − 0.118874
a
11
=
−0.115771u
34
+ 1.07918u
33
+ ··· − 32.8480u + 6.98223
−0.0743855u
34
+ 0.536396u
33
+ ··· − 12.8514u + 0.573324
a
11
=
−0.115771u
34
+ 1.07918u
33
+ ··· − 32.8480u + 6.98223
−0.0743855u
34
+ 0.536396u
33
+ ··· − 12.8514u + 0.573324
(ii) Obstruction class = −1
(iii) Cusp Shapes =
90490086581286093778343
146127200816312655174817
u
34
−
992059524318749332684051
146127200816312655174817
u
33
+ ··· −
24335687627182500119507765
146127200816312655174817
u +
1325772668265518534675334
146127200816312655174817
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
u
35
+ 2u
34
+ ··· − u − 1
c
2
, c
5
u
35
− 9u
34
+ ··· + 129u − 8
c
3
, c
6
u
35
− 2u
34
+ ··· − 7u − 2
c
4
, c
8
u
35
+ 5u
33
+ ··· − 10u − 4
c
7
, c
10
, c
11
u
35
+ 10u
34
+ ··· − 7u − 2
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
9
y
35
− 28y
34
+ ··· + 97y −1
c
2
, c
5
y
35
+ 17y
34
+ ··· + 5825y −64
c
3
, c
6
y
35
+ 4y
34
+ ··· − 35y −4
c
4
, c
8
y
35
+ 10y
34
+ ··· − 68y −16
c
7
, c
10
, c
11
y
35
− 38y
34
+ ··· − 63y −4
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.029467 + 1.005660I
a = 1.62337 + 0.62304I
b = 1.118990 − 0.474878I
3.33325 + 0.06783I 5.95235 + 0.12495I
u = −0.029467 − 1.005660I
a = 1.62337 − 0.62304I
b = 1.118990 + 0.474878I
3.33325 − 0.06783I 5.95235 − 0.12495I
u = −0.160155 + 0.940171I
a = −1.89608 − 0.73160I
b = −1.218050 + 0.448463I
−1.89744 + 0.70933I −2.29610 + 0.18489I
u = −0.160155 − 0.940171I
a = −1.89608 + 0.73160I
b = −1.218050 − 0.448463I
−1.89744 − 0.70933I −2.29610 − 0.18489I
u = 1.032060 + 0.216151I
a = 0.065858 − 0.238657I
b = −0.970266 − 0.697041I
−0.31706 + 7.01027I −3.82014 − 7.79890I
u = 1.032060 − 0.216151I
a = 0.065858 + 0.238657I
b = −0.970266 + 0.697041I
−0.31706 − 7.01027I −3.82014 + 7.79890I
u = 0.030627 + 1.114570I
a = −1.64670 − 0.23881I
b = −1.037110 + 0.708446I
−0.301669 − 0.553139I −3.58187 + 1.60443I
u = 0.030627 − 1.114570I
a = −1.64670 + 0.23881I
b = −1.037110 − 0.708446I
−0.301669 + 0.553139I −3.58187 − 1.60443I
u = −1.11586
a = −0.236593
b = −0.124774
−2.17258 −20.5000
u = 0.746671 + 0.829900I
a = −0.135819 − 1.208780I
b = −1.42250 − 0.65236I
−5.09357 − 3.39425I −14.2242 + 15.5417I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.746671 − 0.829900I
a = −0.135819 + 1.208780I
b = −1.42250 + 0.65236I
−5.09357 + 3.39425I −14.2242 − 15.5417I
u = 0.648498 + 0.961930I
a = −1.22988 − 0.79688I
b = −1.54855 + 0.59812I
−4.64663 − 2.02674I −10.39702 − 3.31188I
u = 0.648498 − 0.961930I
a = −1.22988 + 0.79688I
b = −1.54855 − 0.59812I
−4.64663 + 2.02674I −10.39702 + 3.31188I
u = −0.795787 + 0.881934I
a = 0.657988 − 0.155281I
b = 0.328568 − 0.230594I
−6.54898 + 2.97371I −10.02830 − 2.31900I
u = −0.795787 − 0.881934I
a = 0.657988 + 0.155281I
b = 0.328568 + 0.230594I
−6.54898 − 2.97371I −10.02830 + 2.31900I
u = 0.405669 + 1.141420I
a = 0.894751 + 0.750550I
b = 1.090950 − 0.135501I
4.39987 − 1.11837I 2.66422 + 2.51524I
u = 0.405669 − 1.141420I
a = 0.894751 − 0.750550I
b = 1.090950 + 0.135501I
4.39987 + 1.11837I 2.66422 − 2.51524I
u = 0.719504 + 0.276631I
a = −0.532660 + 0.260522I
b = 0.894361 + 0.739088I
0.64524 + 2.18197I −1.66363 − 5.31437I
u = 0.719504 − 0.276631I
a = −0.532660 − 0.260522I
b = 0.894361 − 0.739088I
0.64524 − 2.18197I −1.66363 + 5.31437I
u = 1.204480 + 0.248072I
a = 0.084193 + 0.300543I
b = 0.972158 + 0.693076I
−7.58044 + 10.41690I −6.58450 − 6.84896I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.204480 − 0.248072I
a = 0.084193 − 0.300543I
b = 0.972158 − 0.693076I
−7.58044 − 10.41690I −6.58450 + 6.84896I
u = 0.548826 + 1.162060I
a = 1.67262 + 0.38811I
b = 1.47723 − 0.97539I
3.22979 − 7.07568I −1.38313 + 9.02703I
u = 0.548826 − 1.162060I
a = 1.67262 − 0.38811I
b = 1.47723 + 0.97539I
3.22979 + 7.07568I −1.38313 − 9.02703I
u = −0.308052 + 0.545459I
a = −0.928218 + 0.582030I
b = −0.165653 + 0.455061I
−0.241930 + 1.296500I −3.54219 − 4.67694I
u = −0.308052 − 0.545459I
a = −0.928218 − 0.582030I
b = −0.165653 − 0.455061I
−0.241930 − 1.296500I −3.54219 + 4.67694I
u = 0.271698 + 1.365610I
a = −0.854456 − 0.533102I
b = −0.898585 + 0.116131I
5.18517 + 2.44630I 0. − 4.73123I
u = 0.271698 − 1.365610I
a = −0.854456 + 0.533102I
b = −0.898585 − 0.116131I
5.18517 − 2.44630I 0. + 4.73123I
u = 0.595757 + 1.264360I
a = −1.58942 − 0.26495I
b = −1.41489 + 0.93635I
2.94252 − 12.83480I 0. + 9.50250I
u = 0.595757 − 1.264360I
a = −1.58942 + 0.26495I
b = −1.41489 − 0.93635I
2.94252 + 12.83480I 0. − 9.50250I
u = −1.41303
a = 0.370029
b = 0.216683
−8.46698 −18.1290
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.64890 + 1.31702I
a = 1.53917 + 0.20834I
b = 1.39598 − 0.92217I
−4.1620 − 16.9207I 0
u = 0.64890 − 1.31702I
a = 1.53917 − 0.20834I
b = 1.39598 + 0.92217I
−4.1620 + 16.9207I 0
u = 0.15479 + 1.53945I
a = 0.793512 + 0.415691I
b = 0.783542 − 0.094287I
−0.87578 + 5.04274I 0
u = 0.15479 − 1.53945I
a = 0.793512 − 0.415691I
b = 0.783542 + 0.094287I
−0.87578 − 5.04274I 0
u = 0.100849
a = 7.70512
b = −0.864213
−3.33456 −1.41010
8
II. I
u
2
=
h−u
23
a−u
23
+· · ·−3a−1, 4u
23
a−u
23
+· · ·−18a−11, u
24
+7u
23
+· · ·+15u+3i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
5
=
1
−u
2
a
3
=
−u
u
3
+ u
a
10
=
a
1
2
u
23
a +
1
2
u
23
+ ··· +
3
2
a +
1
2
a
4
=
1
2
u
23
a +
1
6
u
23
+ ··· +
3
2
a −
3
2
−u
23
a − 6u
22
a + ··· + u − 1
a
7
=
1
2
u
23
a +
5
6
u
23
+ ··· +
1
2
a +
7
2
u
23
a + 7u
22
a + ··· + 3a − 1
a
9
=
−
1
2
u
23
a −
1
2
u
23
+ ··· −
1
2
a −
1
2
1
2
u
23
a +
1
2
u
23
+ ··· +
3
2
a +
1
2
a
1
=
1
2
u
23
a +
5
6
u
23
+ ··· +
1
2
a +
9
2
−1
a
8
=
u
23
+ 8u
22
+ ··· + a − 2
−
1
2
u
23
a +
1
2
u
23
+ ··· −
3
2
a +
1
2
a
11
=
1
2
u
23
a +
5
6
u
23
+ ··· +
3
2
a +
5
2
1
2
u
23
a +
1
2
u
23
+ ··· +
3
2
a −
1
2
a
11
=
1
2
u
23
a +
5
6
u
23
+ ··· +
3
2
a +
5
2
1
2
u
23
a +
1
2
u
23
+ ··· +
3
2
a −
1
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2u
23
− 10u
22
− 38u
21
− 96u
20
− 196u
19
− 310u
18
− 390u
17
−
364u
16
− 176u
15
+ 152u
14
+ 576u
13
+ 960u
12
+ 1228u
11
+ 1294u
10
+ 1190u
9
+ 956u
8
+
698u
7
+ 454u
6
+ 254u
5
+ 136u
4
+ 48u
3
+ 26u
2
+ 2u − 6
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
u
48
+ u
47
+ ··· + 16u
2
+ 2
c
2
, c
5
(u
24
+ 7u
23
+ ··· + 15u + 3)
2
c
3
, c
6
u
48
− 7u
47
+ ··· − 28u + 8
c
4
, c
8
u
48
+ u
47
+ ··· − 48u + 32
c
7
, c
10
, c
11
(u
24
− 3u
23
+ ··· + 3u − 1)
2
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
9
y
48
+ y
47
+ ··· + 64y + 4
c
2
, c
5
(y
24
+ 15y
23
+ ··· + 69y + 9)
2
c
3
, c
6
y
48
− 21y
47
+ ··· + 176y + 64
c
4
, c
8
y
48
+ 9y
47
+ ··· + 20736y + 1024
c
7
, c
10
, c
11
(y
24
− 25y
23
+ ··· − 15y + 1)
2
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.333614 + 0.958581I
a = 0.238717 + 0.952089I
b = 0.52014 + 1.77867I
−7.10793 − 8.02681I −5.10804 + 8.04729I
u = 0.333614 + 0.958581I
a = −2.52196 + 0.45351I
b = −0.698461 + 0.545528I
−7.10793 − 8.02681I −5.10804 + 8.04729I
u = 0.333614 − 0.958581I
a = 0.238717 − 0.952089I
b = 0.52014 − 1.77867I
−7.10793 + 8.02681I −5.10804 − 8.04729I
u = 0.333614 − 0.958581I
a = −2.52196 − 0.45351I
b = −0.698461 − 0.545528I
−7.10793 + 8.02681I −5.10804 − 8.04729I
u = −1.06754
a = −0.247659 + 0.014314I
b = −0.127875 + 0.226247I
−2.16765 −17.3620
u = −1.06754
a = −0.247659 − 0.014314I
b = −0.127875 − 0.226247I
−2.16765 −17.3620
u = −0.277461 + 1.036230I
a = 0.412312 − 1.328630I
b = 0.487830 + 0.447909I
1.42987 + 1.40919I −2.00295 − 5.17297I
u = −0.277461 + 1.036230I
a = −2.14757 + 0.13261I
b = −1.86186 − 0.41467I
1.42987 + 1.40919I −2.00295 − 5.17297I
u = −0.277461 − 1.036230I
a = 0.412312 + 1.328630I
b = 0.487830 − 0.447909I
1.42987 − 1.40919I −2.00295 + 5.17297I
u = −0.277461 − 1.036230I
a = −2.14757 − 0.13261I
b = −1.86186 + 0.41467I
1.42987 − 1.40919I −2.00295 + 5.17297I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.263524 + 0.887339I
a = 0.252966 − 0.916113I
b = −0.23360 − 1.73518I
−0.45153 − 3.90914I −4.05947 + 8.41437I
u = 0.263524 + 0.887339I
a = 2.46741 − 0.35585I
b = 0.598566 − 0.647596I
−0.45153 − 3.90914I −4.05947 + 8.41437I
u = 0.263524 − 0.887339I
a = 0.252966 + 0.916113I
b = −0.23360 + 1.73518I
−0.45153 + 3.90914I −4.05947 − 8.41437I
u = 0.263524 − 0.887339I
a = 2.46741 + 0.35585I
b = 0.598566 + 0.647596I
−0.45153 + 3.90914I −4.05947 − 8.41437I
u = −0.887982 + 0.619939I
a = 0.994897 − 0.465007I
b = 0.852325 + 0.186324I
−6.92221 + 3.07969I −9.61105 − 4.95105I
u = −0.887982 + 0.619939I
a = 0.269644 − 0.075164I
b = −0.277184 − 0.666756I
−6.92221 + 3.07969I −9.61105 − 4.95105I
u = −0.887982 − 0.619939I
a = 0.994897 + 0.465007I
b = 0.852325 − 0.186324I
−6.92221 − 3.07969I −9.61105 + 4.95105I
u = −0.887982 − 0.619939I
a = 0.269644 + 0.075164I
b = −0.277184 + 0.666756I
−6.92221 − 3.07969I −9.61105 + 4.95105I
u = 0.237103 + 0.737994I
a = −0.590664 − 0.004510I
b = 0.198307 + 1.243170I
−0.89648 + 1.35600I −6.20233 + 1.19503I
u = 0.237103 + 0.737994I
a = −2.33888 + 0.63109I
b = −0.733711 + 0.878083I
−0.89648 + 1.35600I −6.20233 + 1.19503I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.237103 − 0.737994I
a = −0.590664 + 0.004510I
b = 0.198307 − 1.243170I
−0.89648 − 1.35600I −6.20233 − 1.19503I
u = 0.237103 − 0.737994I
a = −2.33888 − 0.63109I
b = −0.733711 − 0.878083I
−0.89648 − 1.35600I −6.20233 − 1.19503I
u = −1.24600
a = 0.424934 + 0.086154I
b = 0.235738 + 0.436377I
−8.40649 −13.8590
u = −1.24600
a = 0.424934 − 0.086154I
b = 0.235738 − 0.436377I
−8.40649 −13.8590
u = 0.387072 + 0.629729I
a = −0.214970 + 0.319082I
b = −0.514411 − 1.214470I
−8.06651 + 4.88076I −7.61294 − 0.00229I
u = 0.387072 + 0.629729I
a = 2.61397 − 0.51468I
b = 0.849819 − 0.782163I
−8.06651 + 4.88076I −7.61294 − 0.00229I
u = 0.387072 − 0.629729I
a = −0.214970 − 0.319082I
b = −0.514411 + 1.214470I
−8.06651 − 4.88076I −7.61294 + 0.00229I
u = 0.387072 − 0.629729I
a = 2.61397 + 0.51468I
b = 0.849819 + 0.782163I
−8.06651 − 4.88076I −7.61294 + 0.00229I
u = −0.334204 + 1.242180I
a = −1.064980 + 0.825666I
b = −0.715953 − 0.434854I
4.15748 + 4.71846I 5.79042 − 6.26335I
u = −0.334204 + 1.242180I
a = 1.63098 + 0.22953I
b = 1.44914 + 0.85482I
4.15748 + 4.71846I 5.79042 − 6.26335I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.334204 − 1.242180I
a = −1.064980 − 0.825666I
b = −0.715953 + 0.434854I
4.15748 − 4.71846I 5.79042 + 6.26335I
u = −0.334204 − 1.242180I
a = 1.63098 − 0.22953I
b = 1.44914 − 0.85482I
4.15748 − 4.71846I 5.79042 + 6.26335I
u = −0.510133 + 0.304616I
a = −0.939645 + 0.262682I
b = 0.433520 + 0.540630I
−0.17657 + 1.63085I −4.99918 − 5.43978I
u = −0.510133 + 0.304616I
a = −0.62521 + 1.43179I
b = −0.785164 + 0.276497I
−0.17657 + 1.63085I −4.99918 − 5.43978I
u = −0.510133 − 0.304616I
a = −0.939645 − 0.262682I
b = 0.433520 − 0.540630I
−0.17657 − 1.63085I −4.99918 + 5.43978I
u = −0.510133 − 0.304616I
a = −0.62521 − 1.43179I
b = −0.785164 − 0.276497I
−0.17657 − 1.63085I −4.99918 + 5.43978I
u = −0.54684 + 1.32589I
a = 0.913096 − 0.034885I
b = 0.839736 + 0.802838I
1.92307 + 5.70686I −7.16158 − 11.30466I
u = −0.54684 + 1.32589I
a = −1.364860 + 0.199330I
b = −1.070610 − 0.555366I
1.92307 + 5.70686I −7.16158 − 11.30466I
u = −0.54684 − 1.32589I
a = 0.913096 + 0.034885I
b = 0.839736 − 0.802838I
1.92307 − 5.70686I −7.16158 + 11.30466I
u = −0.54684 − 1.32589I
a = −1.364860 − 0.199330I
b = −1.070610 + 0.555366I
1.92307 − 5.70686I −7.16158 + 11.30466I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.34545 + 1.40335I
a = −1.311200 − 0.410770I
b = −1.20101 − 1.06820I
−0.65429 + 7.12209I 0.24406 − 7.53717I
u = −0.34545 + 1.40335I
a = 1.40359 − 0.60184I
b = 0.884534 + 0.381753I
−0.65429 + 7.12209I 0.24406 − 7.53717I
u = −0.34545 − 1.40335I
a = −1.311200 + 0.410770I
b = −1.20101 + 1.06820I
−0.65429 − 7.12209I 0.24406 + 7.53717I
u = −0.34545 − 1.40335I
a = 1.40359 + 0.60184I
b = 0.884534 − 0.381753I
−0.65429 − 7.12209I 0.24406 + 7.53717I
u = −0.66247 + 1.36339I
a = −0.691207 − 0.146838I
b = −0.720461 − 0.932573I
−4.26677 + 6.65894I −7.66647 − 7.55605I
u = −0.66247 + 1.36339I
a = 1.43628 − 0.21574I
b = 1.090640 + 0.480643I
−4.26677 + 6.65894I −7.66647 − 7.55605I
u = −0.66247 − 1.36339I
a = −0.691207 + 0.146838I
b = −0.720461 + 0.932573I
−4.26677 − 6.65894I −7.66647 + 7.55605I
u = −0.66247 − 1.36339I
a = 1.43628 + 0.21574I
b = 1.090640 − 0.480643I
−4.26677 − 6.65894I −7.66647 + 7.55605I
16
III.
I
u
3
= h−u
11
−6u
10
+· · ·+b−1, −u
10
−6u
9
+· · ·+a−3, u
12
+6u
11
+· · ·+3u+1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
5
=
1
−u
2
a
3
=
−u
u
3
+ u
a
10
=
u
10
+ 6u
9
+ ··· + 6u + 3
u
11
+ 6u
10
+ ··· + 5u + 1
a
4
=
u
11
+ 6u
10
+ ··· + 9u + 2
−u
2
− u − 1
a
7
=
−u
11
− 6u
10
+ ··· − 19u
2
− 7u
u
4
+ 2u
3
+ 3u
2
+ 2u + 1
a
9
=
−u
11
− 5u
10
+ ··· + u + 2
u
11
+ 6u
10
+ ··· + 5u + 1
a
1
=
−u
11
− 7u
10
+ ··· − 13u − 4
−u
11
− 5u
10
+ ··· − 3u
2
+ 1
a
8
=
−u
11
− 4u
10
+ ··· + 4u + 3
2u
11
+ 11u
10
+ ··· + 5u + 1
a
11
=
−u
11
− 6u
10
+ ··· − 8u − 1
u
8
+ 3u
7
+ 6u
6
+ 8u
5
+ 7u
4
+ 6u
3
+ 4u
2
+ 3u + 1
a
11
=
−u
11
− 6u
10
+ ··· − 8u − 1
u
8
+ 3u
7
+ 6u
6
+ 8u
5
+ 7u
4
+ 6u
3
+ 4u
2
+ 3u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes
= 9u
11
+51u
10
+164u
9
+360u
8
+570u
7
+678u
6
+597u
5
+401u
4
+209u
3
+104u
2
+47u+6
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
u
12
+ 2u
11
+ ··· − u − 1
c
2
u
12
− 6u
11
+ ··· − 3u + 1
c
3
, c
6
u
12
+ 2u
11
+ ··· + 2u + 1
c
4
, c
8
u
12
− u
10
+ u
9
+ 2u
8
− 4u
7
+ 2u
6
− u
5
+ 3u
4
− u
3
− u
2
− u − 1
c
5
u
12
+ 6u
11
+ ··· + 3u + 1
c
7
u
12
+ 3u
11
+ ··· + u − 1
c
10
, c
11
u
12
− 3u
11
+ ··· − u − 1
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
9
y
12
− 2y
10
+ ··· − 7y + 1
c
2
, c
5
y
12
+ 4y
11
+ ··· + 11y + 1
c
3
, c
6
y
12
− 12y
11
+ ··· − 10y
2
+ 1
c
4
, c
8
y
12
− 2y
11
+ ··· + y + 1
c
7
, c
10
, c
11
y
12
− 15y
11
+ ··· + y + 1
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.803624 + 0.881445I
a = 0.419174 − 0.885576I
b = 1.275410 − 0.219262I
−4.98090 + 3.00358I −6.27510 + 2.27848I
u = −0.803624 − 0.881445I
a = 0.419174 + 0.885576I
b = 1.275410 + 0.219262I
−4.98090 − 3.00358I −6.27510 − 2.27848I
u = −1.25207
a = −0.0881246
b = −0.437723
−1.97860 21.2940
u = −0.454285 + 1.279880I
a = −1.272580 + 0.120711I
b = −0.993655 − 0.754655I
2.68926 + 5.20905I 1.24389 − 5.17860I
u = −0.454285 − 1.279880I
a = −1.272580 − 0.120711I
b = −0.993655 + 0.754655I
2.68926 − 5.20905I 1.24389 + 5.17860I
u = 0.224527 + 0.491967I
a = −1.91527 − 1.61039I
b = −0.113628 − 1.019110I
−7.67039 − 6.40068I −6.43797 + 4.87755I
u = 0.224527 − 0.491967I
a = −1.91527 + 1.61039I
b = −0.113628 + 1.019110I
−7.67039 + 6.40068I −6.43797 − 4.87755I
u = −0.160845 + 0.502812I
a = 2.12350 + 0.53316I
b = −0.018632 + 1.181350I
−0.92209 − 2.24636I −7.11132 + 8.83230I
u = −0.160845 − 0.502812I
a = 2.12350 − 0.53316I
b = −0.018632 − 1.181350I
−0.92209 + 2.24636I −7.11132 − 8.83230I
u = −0.38777 + 1.48567I
a = 1.087720 + 0.062274I
b = 0.793975 + 0.673367I
−2.15077 + 6.80393I −5.48461 − 6.50411I
20
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.38777 − 1.48567I
a = 1.087720 − 0.062274I
b = 0.793975 − 0.673367I
−2.15077 − 6.80393I −5.48461 + 6.50411I
u = −1.58393
a = 0.203050
b = 0.550778
−8.14019 6.83590
21
IV. I
u
4
= hau + 2b − a − u − 1, a
2
+ au − a − 3u − 2, u
2
+ 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
5
=
1
1
a
3
=
−u
0
a
10
=
a
−
1
2
au +
1
2
a +
1
2
u +
1
2
a
4
=
1
2
au −
1
2
a −
5
2
u +
3
2
−u
a
7
=
1
2
au +
1
2
a −
3
2
u −
3
2
−1
a
9
=
1
2
au +
1
2
a −
1
2
u −
1
2
−
1
2
au +
1
2
a +
1
2
u +
1
2
a
1
=
−
1
2
au −
1
2
a +
3
2
u +
3
2
1
a
8
=
a
−
1
2
au +
1
2
a +
1
2
u +
1
2
a
11
=
−
1
2
au +
1
2
a +
3
2
u +
3
2
−
1
2
au +
1
2
a +
1
2
u +
3
2
a
11
=
−
1
2
au +
1
2
a +
3
2
u +
3
2
−
1
2
au +
1
2
a +
1
2
u +
3
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
u
4
+ 2u
3
− u
2
− 2u + 2
c
2
, c
3
, c
5
c
6
(u
2
+ 1)
2
c
4
, c
8
u
4
+ 3u
2
+ 2u + 2
c
7
(u − 1)
4
c
10
, c
11
(u + 1)
4
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
9
y
4
− 6y
3
+ 13y
2
− 8y + 4
c
2
, c
3
, c
5
c
6
(y + 1)
4
c
4
, c
8
y
4
+ 6y
3
+ 13y
2
+ 8y + 4
c
7
, c
10
, c
11
(y −1)
4
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = −1.11269 − 1.27510I
b = −0.693897 + 0.418797I
1.64493 0
u = 1.000000I
a = 2.11269 + 0.27510I
b = 1.69390 − 0.41880I
1.64493 0
u = − 1.000000I
a = −1.11269 + 1.27510I
b = −0.693897 − 0.418797I
1.64493 0
u = − 1.000000I
a = 2.11269 − 0.27510I
b = 1.69390 + 0.41880I
1.64493 0
25
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
9
(u
4
+ 2u
3
− u
2
− 2u + 2)(u
12
+ 2u
11
+ ··· − u − 1)
· (u
35
+ 2u
34
+ ··· − u − 1)(u
48
+ u
47
+ ··· + 16u
2
+ 2)
c
2
((u
2
+ 1)
2
)(u
12
− 6u
11
+ ··· − 3u + 1)(u
24
+ 7u
23
+ ··· + 15u + 3)
2
· (u
35
− 9u
34
+ ··· + 129u − 8)
c
3
, c
6
((u
2
+ 1)
2
)(u
12
+ 2u
11
+ ··· + 2u + 1)(u
35
− 2u
34
+ ··· − 7u − 2)
· (u
48
− 7u
47
+ ··· − 28u + 8)
c
4
, c
8
(u
4
+ 3u
2
+ 2u + 2)
· (u
12
− u
10
+ u
9
+ 2u
8
− 4u
7
+ 2u
6
− u
5
+ 3u
4
− u
3
− u
2
− u − 1)
· (u
35
+ 5u
33
+ ··· − 10u − 4)(u
48
+ u
47
+ ··· − 48u + 32)
c
5
((u
2
+ 1)
2
)(u
12
+ 6u
11
+ ··· + 3u + 1)(u
24
+ 7u
23
+ ··· + 15u + 3)
2
· (u
35
− 9u
34
+ ··· + 129u − 8)
c
7
((u − 1)
4
)(u
12
+ 3u
11
+ ··· + u − 1)(u
24
− 3u
23
+ ··· + 3u − 1)
2
· (u
35
+ 10u
34
+ ··· − 7u − 2)
c
10
, c
11
((u + 1)
4
)(u
12
− 3u
11
+ ··· − u − 1)(u
24
− 3u
23
+ ··· + 3u − 1)
2
· (u
35
+ 10u
34
+ ··· − 7u − 2)
26
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
9
(y
4
− 6y
3
+ 13y
2
− 8y + 4)(y
12
− 2y
10
+ ··· − 7y + 1)
· (y
35
− 28y
34
+ ··· + 97y −1)(y
48
+ y
47
+ ··· + 64y + 4)
c
2
, c
5
((y + 1)
4
)(y
12
+ 4y
11
+ ··· + 11y + 1)(y
24
+ 15y
23
+ ··· + 69y + 9)
2
· (y
35
+ 17y
34
+ ··· + 5825y −64)
c
3
, c
6
((y + 1)
4
)(y
12
− 12y
11
+ ··· − 10y
2
+ 1)(y
35
+ 4y
34
+ ··· − 35y −4)
· (y
48
− 21y
47
+ ··· + 176y + 64)
c
4
, c
8
(y
4
+ 6y
3
+ 13y
2
+ 8y + 4)(y
12
− 2y
11
+ ··· + y + 1)
· (y
35
+ 10y
34
+ ··· − 68y −16)(y
48
+ 9y
47
+ ··· + 20736y + 1024)
c
7
, c
10
, c
11
((y −1)
4
)(y
12
− 15y
11
+ ··· + y + 1)(y
24
− 25y
23
+ ··· − 15y + 1)
2
· (y
35
− 38y
34
+ ··· − 63y −4)
27
