12n
0544
(K12n
0544
)
A knot diagram
1
Linearized knot diagam
3 6 11 7 2 9 4 1 7 8 3 8
Solving Sequence
4,11
3
8,12
1 2 7 5 10 9 6
c
3
c
11
c
12
c
1
c
7
c
4
c
10
c
9
c
6
c
2
, c
5
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= hb − u, −297940u
22
+ 1271608u
21
+ ··· + 35873a − 1822970, u
23
− u
22
+ ··· + 2u − 1i
I
u
2
= h−3.19561 × 10
118
u
57
+ 9.66229 × 10
118
u
56
+ ··· + 3.56639 × 10
118
b + 1.16120 × 10
121
,
− 5.59702 × 10
119
u
57
+ 1.70818 × 10
120
u
56
+ ··· + 1.13768 × 10
121
a − 1.17564 × 10
123
,
u
58
− 3u
57
+ ··· − 1554u + 319i
I
u
3
= hb + u, u
11
− 2u
10
+ 6u
9
− 9u
8
+ 14u
7
− 14u
6
+ 15u
5
− 10u
4
+ 8u
3
− 4u
2
+ a + 3u,
u
12
− u
11
+ 5u
10
− 4u
9
+ 10u
8
− 5u
7
+ 11u
6
− 2u
5
+ 8u
4
+ u
3
+ 4u
2
+ 2u + 1i
I
u
4
= h−u
9
− 6u
7
+ 2u
6
− 13u
5
+ 5u
4
− 13u
3
+ 2u
2
+ b − 6u, 2u
8
+ 11u
6
− 4u
5
+ 20u
4
− 8u
3
+ 14u
2
+ a + u + 3,
u
10
+ 6u
8
− 2u
7
+ 13u
6
− 5u
5
+ 13u
4
− 2u
3
+ 6u
2
+ 1i
* 4 irreducible components of dim
C
= 0, with total 103 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
= hb − u, −2.98 × 10
5
u
22
+ 1.27 × 10
6
u
21
+ · · · + 3.59 × 10
4
a − 1.82 ×
10
6
, u
23
− u
22
+ · · · + 2u − 1i
(i) Arc colorings
a
4
=
1
0
a
11
=
0
u
a
3
=
1
u
2
a
8
=
8.30541u
22
− 35.4475u
21
+ ··· − 119.158u + 50.8173
u
a
12
=
u
u
3
+ u
a
1
=
−6.42670u
22
+ 32.7476u
21
+ ··· + 118.160u − 51.7962
2.08212u
22
− 9.08254u
21
+ ··· − 29.5331u + 12.6710
a
2
=
−6.22329u
22
+ 26.3650u
21
+ ··· + 88.6247u − 38.1463
2.15839u
22
− 6.69484u
21
+ ··· − 16.9712u + 6.49179
a
7
=
8.30541u
22
− 35.4475u
21
+ ··· − 120.158u + 50.8173
u
a
5
=
27.1421u
22
− 24.0277u
21
+ ··· − 34.2065u − 7.30541
−u
2
a
10
=
−3.87484u
22
+ 24.8029u
21
+ ··· + 100.302u − 45.5822
3.11435u
22
− 17.5854u
21
+ ··· − 61.5896u + 27.1421
a
9
=
4.63399u
22
− 17.0272u
21
+ ··· − 47.3917u + 18.8850
1.03222u
22
− 8.50286u
21
+ ··· − 31.0564u + 14.4711
a
6
=
−0.909765u
22
+ 6.70869u
21
+ ··· + 19.6352u − 10.1222
2.15839u
22
− 6.69484u
21
+ ··· − 16.9712u + 6.49179
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
1000543
35873
u
22
−
712577
35873
u
21
+ ··· −
3006108
35873
u +
2311747
35873
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
23
+ 8u
22
+ ··· + 224u + 64
c
2
, c
5
u
23
+ 8u
22
+ ··· − 56u − 8
c
3
, c
4
, c
7
c
11
u
23
+ u
22
+ ··· + 2u + 1
c
6
, c
8
, c
9
c
12
u
23
+ u
22
+ ··· − u + 1
c
10
u
23
+ 19u
22
+ ··· + 1792u + 256
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
23
+ 4y
22
+ ··· − 46592y −4096
c
2
, c
5
y
23
− 8y
22
+ ··· + 224y −64
c
3
, c
4
, c
7
c
11
y
23
+ 9y
22
+ ··· − 14y −1
c
6
, c
8
, c
9
c
12
y
23
− 7y
22
+ ··· + 7y −1
c
10
y
23
+ 3y
22
+ ··· − 917504y −65536
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.595557 + 0.724305I
a = 0.588152 + 0.605726I
b = 0.595557 + 0.724305I
−3.26156 − 2.02161I −7.52324 + 1.29376I
u = 0.595557 − 0.724305I
a = 0.588152 − 0.605726I
b = 0.595557 − 0.724305I
−3.26156 + 2.02161I −7.52324 − 1.29376I
u = −0.076288 + 0.784165I
a = −1.76014 − 1.54801I
b = −0.076288 + 0.784165I
−4.83015 − 0.57289I −12.62080 + 1.94666I
u = −0.076288 − 0.784165I
a = −1.76014 + 1.54801I
b = −0.076288 − 0.784165I
−4.83015 + 0.57289I −12.62080 − 1.94666I
u = 0.034883 + 0.769214I
a = −2.73995 − 0.59974I
b = 0.034883 + 0.769214I
−3.21113 + 6.60809I −8.60360 − 5.54346I
u = 0.034883 − 0.769214I
a = −2.73995 + 0.59974I
b = 0.034883 − 0.769214I
−3.21113 − 6.60809I −8.60360 + 5.54346I
u = 0.892857 + 0.857700I
a = 0.995548 − 0.607995I
b = 0.892857 + 0.857700I
2.59080 − 3.50765I −2.16401 + 2.34355I
u = 0.892857 − 0.857700I
a = 0.995548 + 0.607995I
b = 0.892857 − 0.857700I
2.59080 + 3.50765I −2.16401 − 2.34355I
u = −0.954684 + 0.841112I
a = −0.696145 + 0.071332I
b = −0.954684 + 0.841112I
0.46179 − 3.67942I −15.1455 + 3.7839I
u = −0.954684 − 0.841112I
a = −0.696145 − 0.071332I
b = −0.954684 − 0.841112I
0.46179 + 3.67942I −15.1455 − 3.7839I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.030245 + 0.711475I
a = 1.98396 − 0.44610I
b = −0.030245 + 0.711475I
−1.04488 − 2.00499I −5.60935 + 2.44566I
u = −0.030245 − 0.711475I
a = 1.98396 + 0.44610I
b = −0.030245 − 0.711475I
−1.04488 + 2.00499I −5.60935 − 2.44566I
u = −0.820681 + 1.010850I
a = −0.875561 − 0.658608I
b = −0.820681 + 1.010850I
3.30522 − 2.73850I −1.61112 + 1.01002I
u = −0.820681 − 1.010850I
a = −0.875561 + 0.658608I
b = −0.820681 − 1.010850I
3.30522 + 2.73850I −1.61112 − 1.01002I
u = 0.771841 + 1.092470I
a = 1.131310 − 0.059859I
b = 0.771841 + 1.092470I
−5.97493 + 8.04810I −9.91244 − 7.34824I
u = 0.771841 − 1.092470I
a = 1.131310 + 0.059859I
b = 0.771841 − 1.092470I
−5.97493 − 8.04810I −9.91244 + 7.34824I
u = −0.134711 + 0.539165I
a = 0.665406 + 0.037719I
b = −0.134711 + 0.539165I
−0.392979 − 1.193410I −3.74262 + 6.17586I
u = −0.134711 − 0.539165I
a = 0.665406 − 0.037719I
b = −0.134711 − 0.539165I
−0.392979 + 1.193410I −3.74262 − 6.17586I
u = 0.518072
a = 2.27868
b = 0.518072
−2.81486 2.60140
u = −0.83900 + 1.23581I
a = −1.080680 − 0.355800I
b = −0.83900 + 1.23581I
1.69434 − 10.77260I −3.35458 + 6.38544I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.83900 − 1.23581I
a = −1.080680 + 0.355800I
b = −0.83900 − 1.23581I
1.69434 + 10.77260I −3.35458 − 6.38544I
u = 0.80144 + 1.27487I
a = 1.148760 − 0.417261I
b = 0.80144 + 1.27487I
−0.2661 + 17.0711I −5.51346 − 9.58728I
u = 0.80144 − 1.27487I
a = 1.148760 + 0.417261I
b = 0.80144 − 1.27487I
−0.2661 − 17.0711I −5.51346 + 9.58728I
7
II. I
u
2
= h−3.20 × 10
118
u
57
+ 9.66 × 10
118
u
56
+ · · · + 3.57 × 10
118
b + 1.16 ×
10
121
, −5.60 × 10
119
u
57
+ 1.71 × 10
120
u
56
+ · · · + 1.14 × 10
121
a − 1.18 ×
10
123
, u
58
− 3u
57
+ · · · − 1554u + 319i
(i) Arc colorings
a
4
=
1
0
a
11
=
0
u
a
3
=
1
u
2
a
8
=
0.0491969u
57
− 0.150146u
56
+ ··· − 319.134u + 103.337
0.896035u
57
− 2.70926u
56
+ ··· + 2187.69u − 325.595
a
12
=
u
u
3
+ u
a
1
=
0.697741u
57
− 2.72311u
56
+ ··· + 4242.50u − 894.659
0.446252u
57
− 0.981013u
56
+ ··· − 427.855u + 208.612
a
2
=
−0.128099u
57
− 0.508562u
56
+ ··· + 3468.94u − 902.338
0.631071u
57
− 1.40121u
56
+ ··· − 573.075u + 292.501
a
7
=
−0.846838u
57
+ 2.55911u
56
+ ··· − 2506.82u + 428.932
0.896035u
57
− 2.70926u
56
+ ··· + 2187.69u − 325.595
a
5
=
−0.624323u
57
+ 2.17283u
56
+ ··· − 2326.98u + 416.764
0.138074u
57
− 1.25210u
56
+ ··· + 3319.00u − 821.619
a
10
=
0.567460u
57
− 2.49194u
56
+ ··· + 4488.01u − 991.415
−0.538016u
57
+ 1.58442u
56
+ ··· − 1160.49u + 155.114
a
9
=
1.58726u
57
− 5.10882u
56
+ ··· + 5564.88u − 1026.14
−0.716147u
57
+ 1.76858u
56
+ ··· − 559.740u − 36.0934
a
6
=
−0.295318u
57
+ 0.123708u
56
+ ··· + 2668.23u − 756.863
0.248161u
57
− 0.642225u
56
+ ··· + 25.6544u + 48.6724
(ii) Obstruction class = −1
(iii) Cusp Shapes = 7.52804u
57
− 17.2152u
56
+ ··· − 2223.72u + 2324.01
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
29
+ 12u
28
+ ··· + 221u + 25)
2
c
2
, c
5
(u
29
− 2u
28
+ ··· + 9u − 5)
2
c
3
, c
4
, c
7
c
11
u
58
+ 3u
57
+ ··· + 1554u + 319
c
6
, c
8
, c
9
c
12
u
58
+ 2u
57
+ ··· − 174u + 71
c
10
(u
29
− 6u
28
+ ··· + 16u − 1)
2
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
29
+ 20y
28
+ ··· + 2541y −625)
2
c
2
, c
5
(y
29
− 12y
28
+ ··· + 221y −25)
2
c
3
, c
4
, c
7
c
11
y
58
+ 27y
57
+ ··· + 2796268y + 101761
c
6
, c
8
, c
9
c
12
y
58
− 22y
57
+ ··· − 163614y + 5041
c
10
(y
29
− 16y
28
+ ··· + 54y −1)
2
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.127047 + 0.952571I
a = 0.23783 − 1.58753I
b = −0.01551 + 1.47649I
−6.73564 − 2.26625I −7.53399 + 2.10986I
u = 0.127047 − 0.952571I
a = 0.23783 + 1.58753I
b = −0.01551 − 1.47649I
−6.73564 + 2.26625I −7.53399 − 2.10986I
u = 0.977889 + 0.395391I
a = −0.936601 + 0.438187I
b = −0.993488 + 0.566307I
4.63913 − 2.75586I 0
u = 0.977889 − 0.395391I
a = −0.936601 − 0.438187I
b = −0.993488 − 0.566307I
4.63913 + 2.75586I 0
u = −0.668662 + 0.632286I
a = 0.556317 + 0.387986I
b = 0.387221 + 0.812398I
−0.167430 − 0.855798I −5.76721 + 5.00765I
u = −0.668662 − 0.632286I
a = 0.556317 − 0.387986I
b = 0.387221 − 0.812398I
−0.167430 + 0.855798I −5.76721 − 5.00765I
u = 0.387221 + 0.812398I
a = −0.202528 + 0.663324I
b = −0.668662 + 0.632286I
−0.167430 − 0.855798I −5.76721 + 5.00765I
u = 0.387221 − 0.812398I
a = −0.202528 − 0.663324I
b = −0.668662 − 0.632286I
−0.167430 + 0.855798I −5.76721 − 5.00765I
u = −0.110836 + 0.876726I
a = 1.96629 + 0.41853I
b = 0.654584 − 0.910489I
−3.66053 − 6.90208I −9.96617 + 6.29904I
u = −0.110836 − 0.876726I
a = 1.96629 − 0.41853I
b = 0.654584 + 0.910489I
−3.66053 + 6.90208I −9.96617 − 6.29904I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.654584 + 0.910489I
a = −1.51908 − 0.44975I
b = −0.110836 − 0.876726I
−3.66053 + 6.90208I 0
u = 0.654584 − 0.910489I
a = −1.51908 + 0.44975I
b = −0.110836 + 0.876726I
−3.66053 − 6.90208I 0
u = 0.814690 + 0.780723I
a = −1.40132 + 0.34702I
b = −0.726543 − 1.203870I
2.61948 + 3.58008I 0
u = 0.814690 − 0.780723I
a = −1.40132 − 0.34702I
b = −0.726543 + 1.203870I
2.61948 − 3.58008I 0
u = −0.993488 + 0.566307I
a = 0.852627 + 0.427457I
b = 0.977889 + 0.395391I
4.63913 − 2.75586I 0
u = −0.993488 − 0.566307I
a = 0.852627 − 0.427457I
b = 0.977889 − 0.395391I
4.63913 + 2.75586I 0
u = 0.443209 + 1.072830I
a = −1.48211 + 0.72163I
b = −0.650204 − 1.000790I
−1.23755 + 4.31563I 0
u = 0.443209 − 1.072830I
a = −1.48211 − 0.72163I
b = −0.650204 + 1.000790I
−1.23755 − 4.31563I 0
u = −0.850210 + 0.803191I
a = −0.634473 − 0.269123I
b = −1.234730 − 0.504043I
3.93086 − 3.48812I 0
u = −0.850210 − 0.803191I
a = −0.634473 + 0.269123I
b = −1.234730 + 0.504043I
3.93086 + 3.48812I 0
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.650204 + 1.000790I
a = 1.54577 + 0.42567I
b = 0.443209 − 1.072830I
−1.23755 − 4.31563I 0
u = −0.650204 − 1.000790I
a = 1.54577 − 0.42567I
b = 0.443209 + 1.072830I
−1.23755 + 4.31563I 0
u = 0.961290 + 0.747797I
a = −0.214703 − 0.719788I
b = 0.293154 − 0.718460I
−4.70521 − 1.62785I 0
u = 0.961290 − 0.747797I
a = −0.214703 + 0.719788I
b = 0.293154 + 0.718460I
−4.70521 + 1.62785I 0
u = 0.293154 + 0.718460I
a = 1.178760 + 0.019061I
b = 0.961290 − 0.747797I
−4.70521 + 1.62785I −12.78119 − 2.62015I
u = 0.293154 − 0.718460I
a = 1.178760 − 0.019061I
b = 0.961290 + 0.747797I
−4.70521 − 1.62785I −12.78119 + 2.62015I
u = −0.750845 + 0.972729I
a = 0.891287 − 0.126207I
b = 0.138741 − 0.574265I
−0.54706 − 2.65768I 0
u = −0.750845 − 0.972729I
a = 0.891287 + 0.126207I
b = 0.138741 + 0.574265I
−0.54706 + 2.65768I 0
u = −0.835011 + 0.907349I
a = 1.36765 + 0.44806I
b = 0.65037 − 1.27337I
1.86996 − 8.79177I 0
u = −0.835011 − 0.907349I
a = 1.36765 − 0.44806I
b = 0.65037 + 1.27337I
1.86996 + 8.79177I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.879347 + 0.893897I
a = 0.311886 + 0.304169I
b = 0.794571 + 1.007140I
1.92974 + 2.45935I 0
u = −0.879347 − 0.893897I
a = 0.311886 − 0.304169I
b = 0.794571 − 1.007140I
1.92974 − 2.45935I 0
u = 0.831284 + 0.944870I
a = 0.644636 − 0.342540I
b = 1.246010 − 0.447063I
2.30912 + 9.86806I 0
u = 0.831284 − 0.944870I
a = 0.644636 + 0.342540I
b = 1.246010 + 0.447063I
2.30912 − 9.86806I 0
u = 0.794571 + 1.007140I
a = −0.256766 + 0.339709I
b = −0.879347 + 0.893897I
1.92974 + 2.45935I 0
u = 0.794571 − 1.007140I
a = −0.256766 − 0.339709I
b = −0.879347 − 0.893897I
1.92974 − 2.45935I 0
u = 0.188057 + 1.304610I
a = −0.034973 + 0.242616I
b = 0.188057 − 1.304610I
−11.0631 0
u = 0.188057 − 1.304610I
a = −0.034973 − 0.242616I
b = 0.188057 + 1.304610I
−11.0631 0
u = 1.246010 + 0.447063I
a = 0.528405 − 0.449901I
b = 0.831284 − 0.944870I
2.30912 − 9.86806I 0
u = 1.246010 − 0.447063I
a = 0.528405 + 0.449901I
b = 0.831284 + 0.944870I
2.30912 + 9.86806I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.234730 + 0.504043I
a = −0.444964 − 0.409054I
b = −0.850210 − 0.803191I
3.93086 + 3.48812I 0
u = −1.234730 − 0.504043I
a = −0.444964 + 0.409054I
b = −0.850210 + 0.803191I
3.93086 − 3.48812I 0
u = 0.191238 + 0.563226I
a = −0.019603 + 0.414508I
b = 0.33099 − 1.93554I
−5.12050 + 3.68484I −9.5195 − 25.5363I
u = 0.191238 − 0.563226I
a = −0.019603 − 0.414508I
b = 0.33099 + 1.93554I
−5.12050 − 3.68484I −9.5195 + 25.5363I
u = −0.726543 + 1.203870I
a = 1.013080 + 0.561957I
b = 0.814690 − 0.780723I
2.61948 − 3.58008I 0
u = −0.726543 − 1.203870I
a = 1.013080 − 0.561957I
b = 0.814690 + 0.780723I
2.61948 + 3.58008I 0
u = 0.138741 + 0.574265I
a = −1.79959 + 0.51679I
b = −0.750845 − 0.972729I
−0.54706 + 2.65768I −5.51240 − 3.43968I
u = 0.138741 − 0.574265I
a = −1.79959 − 0.51679I
b = −0.750845 + 0.972729I
−0.54706 − 2.65768I −5.51240 + 3.43968I
u = 0.65037 + 1.27337I
a = −1.032490 + 0.688756I
b = −0.835011 − 0.907349I
1.86996 + 8.79177I 0
u = 0.65037 − 1.27337I
a = −1.032490 − 0.688756I
b = −0.835011 + 0.907349I
1.86996 − 8.79177I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.03227 + 1.44258I
a = 0.078303 − 1.166600I
b = 0.152775 + 0.491791I
−7.68709 + 1.70661I 0
u = 0.03227 − 1.44258I
a = 0.078303 + 1.166600I
b = 0.152775 − 0.491791I
−7.68709 − 1.70661I 0
u = −0.01551 + 1.47649I
a = 0.005861 − 1.044740I
b = 0.127047 + 0.952571I
−6.73564 − 2.26625I 0
u = −0.01551 − 1.47649I
a = 0.005861 + 1.044740I
b = 0.127047 − 0.952571I
−6.73564 + 2.26625I 0
u = 0.152775 + 0.491791I
a = 1.11061 − 3.08212I
b = 0.03227 + 1.44258I
−7.68709 + 1.70661I −3.08074 − 5.87302I
u = 0.152775 − 0.491791I
a = 1.11061 + 3.08212I
b = 0.03227 − 1.44258I
−7.68709 − 1.70661I −3.08074 + 5.87302I
u = 0.33099 + 1.93554I
a = −0.0546110 + 0.1132170I
b = 0.191238 − 0.563226I
−5.12050 − 3.68484I 0
u = 0.33099 − 1.93554I
a = −0.0546110 − 0.1132170I
b = 0.191238 + 0.563226I
−5.12050 + 3.68484I 0
16
III. I
u
3
= hb + u, u
11
− 2u
10
+ · · · + a + 3u, u
12
− u
11
+ · · · + 2u + 1i
(i) Arc colorings
a
4
=
1
0
a
11
=
0
u
a
3
=
1
u
2
a
8
=
−u
11
+ 2u
10
+ ··· + 4u
2
− 3u
−u
a
12
=
u
u
3
+ u
a
1
=
u
11
− 2u
10
+ ··· + 3u − 1
−u
10
+ u
9
− 4u
8
+ 3u
7
− 6u
6
+ 2u
5
− 5u
4
+ u
3
− 3u
2
− 1
a
2
=
u
11
− u
10
+ 5u
9
− 5u
8
+ 11u
7
− 8u
6
+ 13u
5
− 5u
4
+ 8u
3
− u
2
+ 4u + 1
−2u
10
+ 2u
9
− 7u
8
+ 5u
7
− 10u
6
+ 3u
5
− 9u
4
+ u
3
− 5u
2
− 2u − 2
a
7
=
−u
11
+ 2u
10
+ ··· + 4u
2
− 2u
−u
a
5
=
u
11
− u
10
+ 5u
9
− 4u
8
+ 9u
7
− 4u
6
+ 8u
5
+ 5u
3
+ 2u
2
+ 2u + 2
−u
2
a
10
=
u
9
− 2u
8
+ 5u
7
− 8u
6
+ 10u
5
− 10u
4
+ 8u
3
− 5u
2
+ u − 2
−u
8
+ u
7
− 3u
6
+ 2u
5
− 3u
4
− 2u
2
− 1
a
9
=
−u
11
+ u
10
− 4u
9
+ 3u
8
− 6u
7
+ u
6
− 4u
5
− 3u
4
− u
3
− 3u
2
− 2u − 2
u
10
− u
9
+ 3u
8
− 2u
7
+ 3u
6
+ 2u
4
+ u
2
+ u
a
6
=
−u
10
+ u
9
− 3u
8
+ u
7
− 2u
6
− 3u
5
+ u
4
− 4u
3
+ u
2
− 3u
2u
10
− 2u
9
+ 7u
8
− 5u
7
+ 10u
6
− 3u
5
+ 9u
4
− u
3
+ 5u
2
+ 2u + 2
(ii) Obstruction class = 1
(iii) Cusp Shapes
= 2u
11
+ u
10
+ 4u
9
+ 5u
8
− u
7
+ 15u
6
− 6u
5
+ 15u
4
− 4u
3
+ 3u
2
+ 4u − 4
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
12
− 5u
11
+ ··· − 6u + 1
c
2
u
12
+ u
11
− 2u
10
− 3u
9
+ u
8
+ 2u
7
+ u
6
+ 2u
5
− 4u
3
− u
2
+ 2u + 1
c
3
, c
7
u
12
− u
11
+ ··· + 2u + 1
c
4
, c
11
u
12
+ u
11
+ ··· − 2u + 1
c
5
u
12
− u
11
− 2u
10
+ 3u
9
+ u
8
− 2u
7
+ u
6
− 2u
5
+ 4u
3
− u
2
− 2u + 1
c
6
, c
8
u
12
+ u
11
− 3u
10
+ u
9
+ 5u
8
− 7u
7
+ 7u
5
− 7u
4
+ u
3
+ 4u
2
− 3u + 1
c
9
, c
12
u
12
− u
11
− 3u
10
− u
9
+ 5u
8
+ 7u
7
− 7u
5
− 7u
4
− u
3
+ 4u
2
+ 3u + 1
c
10
u
12
− 6u
11
+ ··· − 4u + 1
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
12
− y
11
+ ··· − 2y + 1
c
2
, c
5
y
12
− 5y
11
+ ··· − 6y + 1
c
3
, c
4
, c
7
c
11
y
12
+ 9y
11
+ ··· + 4y + 1
c
6
, c
8
, c
9
c
12
y
12
− 7y
11
+ ··· − y + 1
c
10
y
12
+ 4y
11
+ ··· + 28y + 1
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.466084 + 0.809264I
a = 2.16254 − 0.39601I
b = 0.466084 − 0.809264I
−2.49985 − 7.76270I −3.72598 + 11.08235I
u = −0.466084 − 0.809264I
a = 2.16254 + 0.39601I
b = 0.466084 + 0.809264I
−2.49985 + 7.76270I −3.72598 − 11.08235I
u = 0.519595 + 0.992665I
a = −1.68774 + 0.62888I
b = −0.519595 − 0.992665I
−0.29532 + 4.35182I 0.13392 − 4.24607I
u = 0.519595 − 0.992665I
a = −1.68774 − 0.62888I
b = −0.519595 + 0.992665I
−0.29532 − 4.35182I 0.13392 + 4.24607I
u = 0.854627 + 0.760787I
a = −0.871446 − 0.113522I
b = −0.854627 − 0.760787I
0.91868 + 3.75006I 3.14617 − 6.86627I
u = 0.854627 − 0.760787I
a = −0.871446 + 0.113522I
b = −0.854627 + 0.760787I
0.91868 − 3.75006I 3.14617 + 6.86627I
u = −0.017122 + 1.272490I
a = −0.196657 + 0.030724I
b = 0.017122 − 1.272490I
−10.46040 − 1.58679I −9.53450 + 4.49112I
u = −0.017122 − 1.272490I
a = −0.196657 − 0.030724I
b = 0.017122 + 1.272490I
−10.46040 + 1.58679I −9.53450 − 4.49112I
u = −0.050049 + 1.373520I
a = −0.126746 + 0.670182I
b = 0.050049 − 1.373520I
−8.56258 + 2.71427I −11.98375 − 3.60830I
u = −0.050049 − 1.373520I
a = −0.126746 − 0.670182I
b = 0.050049 + 1.373520I
−8.56258 − 2.71427I −11.98375 + 3.60830I
20
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.340967 + 0.334336I
a = −0.27996 − 2.09817I
b = 0.340967 − 0.334336I
−3.77450 + 0.33015I −6.53587 + 0.59190I
u = −0.340967 − 0.334336I
a = −0.27996 + 2.09817I
b = 0.340967 + 0.334336I
−3.77450 − 0.33015I −6.53587 − 0.59190I
21
IV.
I
u
4
= h−u
9
−6u
7
+· · ·+b−6u, 2u
8
+11u
6
+· · ·+a+3, u
10
+6u
8
+· · ·+6u
2
+1i
(i) Arc colorings
a
4
=
1
0
a
11
=
0
u
a
3
=
1
u
2
a
8
=
−2u
8
− 11u
6
+ 4u
5
− 20u
4
+ 8u
3
− 14u
2
− u − 3
u
9
+ 6u
7
− 2u
6
+ 13u
5
− 5u
4
+ 13u
3
− 2u
2
+ 6u
a
12
=
u
u
3
+ u
a
1
=
5u
8
+ 27u
6
− 10u
5
+ 49u
4
− 19u
3
+ 36u
2
+ 2u + 8
−u
9
− u
8
− 6u
7
− 3u
6
− 11u
5
− 3u
4
− 9u
3
− 3u
2
− 6u − 1
a
2
=
u
9
+ 3u
8
+ 6u
7
+ 14u
6
+ 7u
5
+ 23u
4
+ 2u
3
+ 17u
2
+ 8u + 4
−u
9
− 6u
7
+ 2u
6
− 13u
5
+ 6u
4
− 13u
3
+ 5u
2
− 7u + 1
a
7
=
−u
9
− 2u
8
− 6u
7
− 9u
6
− 9u
5
− 15u
4
− 5u
3
− 12u
2
− 7u − 3
u
9
+ 6u
7
− 2u
6
+ 13u
5
− 5u
4
+ 13u
3
− 2u
2
+ 6u
a
5
=
3u
9
− u
8
+ 16u
7
− 12u
6
+ 30u
5
− 24u
4
+ 24u
3
− 11u
2
+ 6u − 6
u
8
+ 6u
6
− 2u
5
+ 13u
4
− 5u
3
+ 13u
2
− 2u + 6
a
10
=
u
9
+ 5u
8
+ 5u
7
+ 26u
6
− 2u
5
+ 50u
4
− 16u
3
+ 42u
2
+ u + 10
−2u
8
− 11u
6
+ 4u
5
− 20u
4
+ 8u
3
− 14u
2
− 3
a
9
=
u
9
+ 9u
8
+ 5u
7
+ 47u
6
− 10u
5
+ 87u
4
− 30u
3
+ 69u
2
+ 2u + 16
−3u
8
− 16u
6
+ 6u
5
− 28u
4
+ 11u
3
− 19u
2
− u − 4
a
6
=
2u
9
+ 7u
8
+ 10u
7
+ 35u
6
+ u
5
+ 68u
4
− 23u
3
+ 62u
2
− 3u + 15
u
9
− 3u
8
+ 6u
7
− 19u
6
+ 19u
5
− 38u
4
+ 26u
3
− 28u
2
+ 6u − 6
(ii) Obstruction class = 1
(iii) Cusp Shapes = 3u
9
+ 9u
8
+ 14u
7
+ 43u
6
− 3u
5
+ 85u
4
− 44u
3
+ 87u
2
− 16u + 11
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
5
− 3u
4
+ 7u
3
− 8u
2
+ 5u − 1)
2
c
2
(u
5
− u
4
− u
3
+ 2u
2
+ u − 1)
2
c
3
, c
7
u
10
+ 6u
8
− 2u
7
+ 13u
6
− 5u
5
+ 13u
4
− 2u
3
+ 6u
2
+ 1
c
4
, c
11
u
10
+ 6u
8
+ 2u
7
+ 13u
6
+ 5u
5
+ 13u
4
+ 2u
3
+ 6u
2
+ 1
c
5
(u
5
+ u
4
− u
3
− 2u
2
+ u + 1)
2
c
6
, c
8
u
10
− 5u
9
+ 6u
8
+ 6u
7
− 15u
6
+ 3u
5
+ 9u
4
− 6u
3
− u
2
+ 2u + 1
c
9
, c
12
u
10
+ 5u
9
+ 6u
8
− 6u
7
− 15u
6
− 3u
5
+ 9u
4
+ 6u
3
− u
2
− 2u + 1
c
10
(u
5
+ 4u
4
+ 4u
3
− u
2
− 2u − 1)
2
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
5
+ 5y
4
+ 11y
3
+ 9y −1)
2
c
2
, c
5
(y
5
− 3y
4
+ 7y
3
− 8y
2
+ 5y −1)
2
c
3
, c
4
, c
7
c
11
y
10
+ 12y
9
+ ··· + 12y + 1
c
6
, c
8
, c
9
c
12
y
10
− 13y
9
+ ··· − 6y + 1
c
10
(y
5
− 8y
4
+ 20y
3
− 9y
2
+ 2y −1)
2
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.581760 + 0.813360I
a = −0.429730 + 0.600807I
b = −0.581760 + 0.813360I
0.265516 −2.34553 + 0.I
u = 0.581760 − 0.813360I
a = −0.429730 − 0.600807I
b = −0.581760 − 0.813360I
0.265516 −2.34553 + 0.I
u = −0.021542 + 0.707790I
a = 0.42920 − 2.79487I
b = 0.042962 + 1.411540I
−8.15907 + 1.42206I −16.8796 + 1.7077I
u = −0.021542 − 0.707790I
a = 0.42920 + 2.79487I
b = 0.042962 − 1.411540I
−8.15907 − 1.42206I −16.8796 − 1.7077I
u = −0.042962 + 1.411540I
a = −0.30004 − 1.38575I
b = 0.021542 + 0.707790I
−8.15907 − 1.42206I −16.8796 − 1.7077I
u = −0.042962 − 1.411540I
a = −0.30004 + 1.38575I
b = 0.021542 − 0.707790I
−8.15907 + 1.42206I −16.8796 + 1.7077I
u = −0.122679 + 0.543931I
a = 0.578758 − 0.866663I
b = 0.39458 + 1.74948I
−5.13317 − 3.45949I −10.9476 − 9.1982I
u = −0.122679 − 0.543931I
a = 0.578758 + 0.866663I
b = 0.39458 − 1.74948I
−5.13317 + 3.45949I −10.9476 + 9.1982I
u = −0.39458 + 1.74948I
a = −0.278184 − 0.166129I
b = 0.122679 + 0.543931I
−5.13317 + 3.45949I −10.9476 + 9.1982I
u = −0.39458 − 1.74948I
a = −0.278184 + 0.166129I
b = 0.122679 − 0.543931I
−5.13317 − 3.45949I −10.9476 − 9.1982I
25
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
5
− 3u
4
+ 7u
3
− 8u
2
+ 5u − 1)
2
)(u
12
− 5u
11
+ ··· − 6u + 1)
· (u
23
+ 8u
22
+ ··· + 224u + 64)(u
29
+ 12u
28
+ ··· + 221u + 25)
2
c
2
(u
5
− u
4
− u
3
+ 2u
2
+ u − 1)
2
· (u
12
+ u
11
− 2u
10
− 3u
9
+ u
8
+ 2u
7
+ u
6
+ 2u
5
− 4u
3
− u
2
+ 2u + 1)
· (u
23
+ 8u
22
+ ··· − 56u − 8)(u
29
− 2u
28
+ ··· + 9u − 5)
2
c
3
, c
7
(u
10
+ 6u
8
− 2u
7
+ 13u
6
− 5u
5
+ 13u
4
− 2u
3
+ 6u
2
+ 1)
· (u
12
− u
11
+ ··· + 2u + 1)(u
23
+ u
22
+ ··· + 2u + 1)
· (u
58
+ 3u
57
+ ··· + 1554u + 319)
c
4
, c
11
(u
10
+ 6u
8
+ 2u
7
+ 13u
6
+ 5u
5
+ 13u
4
+ 2u
3
+ 6u
2
+ 1)
· (u
12
+ u
11
+ ··· − 2u + 1)(u
23
+ u
22
+ ··· + 2u + 1)
· (u
58
+ 3u
57
+ ··· + 1554u + 319)
c
5
(u
5
+ u
4
− u
3
− 2u
2
+ u + 1)
2
· (u
12
− u
11
− 2u
10
+ 3u
9
+ u
8
− 2u
7
+ u
6
− 2u
5
+ 4u
3
− u
2
− 2u + 1)
· (u
23
+ 8u
22
+ ··· − 56u − 8)(u
29
− 2u
28
+ ··· + 9u − 5)
2
c
6
, c
8
(u
10
− 5u
9
+ 6u
8
+ 6u
7
− 15u
6
+ 3u
5
+ 9u
4
− 6u
3
− u
2
+ 2u + 1)
· (u
12
+ u
11
− 3u
10
+ u
9
+ 5u
8
− 7u
7
+ 7u
5
− 7u
4
+ u
3
+ 4u
2
− 3u + 1)
· (u
23
+ u
22
+ ··· − u + 1)(u
58
+ 2u
57
+ ··· − 174u + 71)
c
9
, c
12
(u
10
+ 5u
9
+ 6u
8
− 6u
7
− 15u
6
− 3u
5
+ 9u
4
+ 6u
3
− u
2
− 2u + 1)
· (u
12
− u
11
− 3u
10
− u
9
+ 5u
8
+ 7u
7
− 7u
5
− 7u
4
− u
3
+ 4u
2
+ 3u + 1)
· (u
23
+ u
22
+ ··· − u + 1)(u
58
+ 2u
57
+ ··· − 174u + 71)
c
10
((u
5
+ 4u
4
+ 4u
3
− u
2
− 2u − 1)
2
)(u
12
− 6u
11
+ ··· − 4u + 1)
· (u
23
+ 19u
22
+ ··· + 1792u + 256)(u
29
− 6u
28
+ ··· + 16u − 1)
2
26
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
5
+ 5y
4
+ 11y
3
+ 9y −1)
2
)(y
12
− y
11
+ ··· − 2y + 1)
· (y
23
+ 4y
22
+ ··· − 46592y −4096)
· (y
29
+ 20y
28
+ ··· + 2541y −625)
2
c
2
, c
5
((y
5
− 3y
4
+ 7y
3
− 8y
2
+ 5y −1)
2
)(y
12
− 5y
11
+ ··· − 6y + 1)
· (y
23
− 8y
22
+ ··· + 224y −64)(y
29
− 12y
28
+ ··· + 221y −25)
2
c
3
, c
4
, c
7
c
11
(y
10
+ 12y
9
+ ··· + 12y + 1)(y
12
+ 9y
11
+ ··· + 4y + 1)
· (y
23
+ 9y
22
+ ··· − 14y −1)(y
58
+ 27y
57
+ ··· + 2796268y + 101761)
c
6
, c
8
, c
9
c
12
(y
10
− 13y
9
+ ··· − 6y + 1)(y
12
− 7y
11
+ ··· − y + 1)
· (y
23
− 7y
22
+ ··· + 7y −1)(y
58
− 22y
57
+ ··· − 163614y + 5041)
c
10
((y
5
− 8y
4
+ 20y
3
− 9y
2
+ 2y −1)
2
)(y
12
+ 4y
11
+ ··· + 28y + 1)
· (y
23
+ 3y
22
+ ··· − 917504y −65536)(y
29
− 16y
28
+ ··· + 54y −1)
2
27
