11a
160
(K11a
160
)
A knot diagram
1
Linearized knot diagam
5 1 10 8 2 9 4 11 3 7 6
Solving Sequence
2,5 6,9
7 1 3 10 11 8 4
c
5
c
6
c
1
c
2
c
9
c
11
c
8
c
4
c
3
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−5u
29
− 20u
28
+ ··· + 2b − 14, 3u
29
+ 16u
28
+ ··· + 4a − 9u, u
30
+ 6u
29
+ ··· + 26u + 4i
I
u
2
= h4584333581u
13
a
3
+ 6949760010u
13
a
2
+ ··· − 45118851a − 4067169136,
− 2u
13
a
3
− 2u
13
a
2
+ ··· + a − 4, u
14
− u
13
− 3u
12
+ 4u
11
+ 4u
10
− 7u
9
− u
8
+ 6u
7
− 2u
6
− 2u
5
+ 2u
4
− u + 1i
I
u
3
= hu
12
+ u
11
− 3u
10
− 2u
9
+ 5u
8
+ 2u
7
− 3u
6
+ u
5
+ 2u
4
− 2u
3
− 2u
2
+ b + u + 2,
− u
13
+ u
12
+ 5u
11
− 4u
10
− 9u
9
+ 8u
8
+ 8u
7
− 9u
6
+ 9u
4
− 4u
3
− 6u
2
+ a + 2u + 3,
u
14
− u
13
− 3u
12
+ 4u
11
+ 4u
10
− 7u
9
− u
8
+ 7u
7
− 3u
6
− 4u
5
+ 4u
4
+ 2u
3
− 2u
2
− u + 1i
* 3 irreducible components of dim
C
= 0, with total 100 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−5u
29
− 20u
28
+ · · · + 2b − 14, 3u
29
+ 16u
28
+ · · · + 4a − 9u, u
30
+
6u
29
+ · · · + 26u + 4i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
u
2
a
9
=
−
3
4
u
29
− 4u
28
+ ··· − 2u
2
+
9
4
u
5
2
u
29
+ 10u
28
+ ··· +
77
2
u + 7
a
7
=
−7u
29
−
69
2
u
28
+ ··· − 133u −
43
2
−
11
2
u
29
− 29u
28
+ ··· −
289
2
u − 26
a
1
=
u
u
a
3
=
−u
3
−u
3
+ u
a
10
=
17
4
u
29
+ 26u
28
+ ··· +
625
4
u + 28
1
2
u
29
+ 5u
28
+ ··· +
97
2
u + 9
a
11
=
u
3
u
5
− u
3
+ u
a
8
=
29
4
u
29
+ 34u
28
+ ··· +
497
4
u + 20
13
2
u
29
+ 32u
28
+ ··· +
281
2
u + 25
a
4
=
u
29
+
3
2
u
28
+ ··· − 29u −
11
2
11
2
u
29
+ 27u
28
+ ··· +
157
2
u + 12
a
4
=
u
29
+
3
2
u
28
+ ··· − 29u −
11
2
11
2
u
29
+ 27u
28
+ ··· +
157
2
u + 12
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 2u
29
+ 12u
28
+ 8u
27
−69u
26
−140u
25
+ 91u
24
+ 537u
23
+ 337u
22
−834u
21
−1449u
20
−
13u
19
+ 2090u
18
+ 1957u
17
−581u
16
−2559u
15
−1877u
14
+ 350u
13
+ 1886u
12
+ 1755u
11
+
441u
10
− 966u
9
− 1388u
8
− 688u
7
+ 298u
6
+ 655u
5
+ 378u
4
− 5u
3
− 123u
2
− 80u − 22
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
30
+ 6u
29
+ ··· + 26u + 4
c
2
u
30
+ 14u
29
+ ··· + 28u + 16
c
3
, c
4
, c
7
c
9
u
30
− u
29
+ ··· + u + 1
c
6
, c
8
u
30
+ u
29
+ ··· − 4u + 1
c
10
u
30
+ 27u
29
+ ··· + 237568u + 16384
c
11
u
30
+ 18u
29
+ ··· − 314u − 52
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
30
− 14y
29
+ ··· − 28y + 16
c
2
y
30
+ 2y
29
+ ··· + 272y + 256
c
3
, c
4
, c
7
c
9
y
30
− 21y
29
+ ··· − y + 1
c
6
, c
8
y
30
− 9y
29
+ ··· − 22y + 1
c
10
y
30
− y
29
+ ··· − 335544320y + 268435456
c
11
y
30
+ 10y
29
+ ··· − 170460y + 2704
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.439336 + 0.898767I
a = 0.0838685 − 0.0685218I
b = −1.000000 − 0.322600I
3.15371 − 2.25650I 2.07479 + 3.80636I
u = −0.439336 − 0.898767I
a = 0.0838685 + 0.0685218I
b = −1.000000 + 0.322600I
3.15371 + 2.25650I 2.07479 − 3.80636I
u = −0.722214 + 0.756555I
a = −0.439844 − 0.438388I
b = 0.272057 − 0.561915I
8.50027 + 8.77817I 5.31474 − 7.47276I
u = −0.722214 − 0.756555I
a = −0.439844 + 0.438388I
b = 0.272057 + 0.561915I
8.50027 − 8.77817I 5.31474 + 7.47276I
u = 0.926063
a = 1.84538
b = 0.400139
−2.97639 3.61540
u = −0.322085 + 0.845243I
a = −0.394213 + 0.321013I
b = 1.54730 + 1.17314I
6.21887 − 11.79360I 3.80243 + 6.19160I
u = −0.322085 − 0.845243I
a = −0.394213 − 0.321013I
b = 1.54730 − 1.17314I
6.21887 + 11.79360I 3.80243 − 6.19160I
u = 0.179468 + 0.841852I
a = −0.235984 + 0.259151I
b = 0.431156 − 0.249453I
1.38263 + 1.72204I −2.32664 + 0.60868I
u = 0.179468 − 0.841852I
a = −0.235984 − 0.259151I
b = 0.431156 + 0.249453I
1.38263 − 1.72204I −2.32664 − 0.60868I
u = 1.14537
a = 1.61718
b = 0.972133
−2.84813 −1.74440
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.902723 + 0.723773I
a = 0.684334 − 0.575975I
b = −0.0118221 − 0.1286980I
7.98240 − 3.24098I 5.21335 + 3.14058I
u = −0.902723 − 0.723773I
a = 0.684334 + 0.575975I
b = −0.0118221 + 0.1286980I
7.98240 + 3.24098I 5.21335 − 3.14058I
u = 1.103300 + 0.364983I
a = 1.55520 − 0.98449I
b = 1.25361 + 0.73971I
−5.00799 − 1.36896I −7.09046 + 4.51225I
u = 1.103300 − 0.364983I
a = 1.55520 + 0.98449I
b = 1.25361 − 0.73971I
−5.00799 + 1.36896I −7.09046 − 4.51225I
u = −1.107070 + 0.415384I
a = −1.078500 − 0.245150I
b = −1.062860 + 0.303827I
−2.31526 + 1.75344I −3.75152 − 0.07888I
u = −1.107070 − 0.415384I
a = −1.078500 + 0.245150I
b = −1.062860 − 0.303827I
−2.31526 − 1.75344I −3.75152 + 0.07888I
u = −1.114950 + 0.506217I
a = 2.03271 + 0.97995I
b = 2.09198 − 0.46050I
−4.02021 + 6.15111I −5.67724 − 4.92712I
u = −1.114950 − 0.506217I
a = 2.03271 − 0.97995I
b = 2.09198 + 0.46050I
−4.02021 − 6.15111I −5.67724 + 4.92712I
u = 1.212810 + 0.208647I
a = −1.46726 + 1.37249I
b = −1.63850 + 0.28323I
1.15159 + 8.63900I −1.81852 − 4.95805I
u = 1.212810 − 0.208647I
a = −1.46726 − 1.37249I
b = −1.63850 − 0.28323I
1.15159 − 8.63900I −1.81852 + 4.95805I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.199610 + 0.446464I
a = −0.854653 + 0.108182I
b = −0.517155 − 0.771435I
−1.92835 − 6.42721I −4.67944 + 7.09422I
u = 1.199610 − 0.446464I
a = −0.854653 − 0.108182I
b = −0.517155 + 0.771435I
−1.92835 + 6.42721I −4.67944 − 7.09422I
u = −1.157040 + 0.588836I
a = −2.39255 − 0.65462I
b = −2.02356 + 1.41500I
3.7202 + 17.0985I 0.80952 − 9.70777I
u = −1.157040 − 0.588836I
a = −2.39255 + 0.65462I
b = −2.02356 − 1.41500I
3.7202 − 17.0985I 0.80952 + 9.70777I
u = −0.594964 + 0.357254I
a = −0.390744 + 0.913670I
b = −0.074831 + 0.824062I
−0.55728 + 1.33045I −2.87243 − 5.52992I
u = −0.594964 − 0.357254I
a = −0.390744 − 0.913670I
b = −0.074831 − 0.824062I
−0.55728 − 1.33045I −2.87243 + 5.52992I
u = −1.141330 + 0.635650I
a = 1.17423 + 0.86253I
b = 1.282610 − 0.490541I
0.98575 + 7.90704I 0.97053 − 7.34135I
u = −1.141330 − 0.635650I
a = 1.17423 − 0.86253I
b = 1.282610 + 0.490541I
0.98575 − 7.90704I 0.97053 + 7.34135I
u = −0.229199 + 0.619350I
a = 0.242118 − 0.914072I
b = −1.236100 − 0.431601I
−1.54965 − 1.73951I −3.40461 + 1.10111I
u = −0.229199 − 0.619350I
a = 0.242118 + 0.914072I
b = −1.236100 + 0.431601I
−1.54965 + 1.73951I −3.40461 − 1.10111I
7
II. I
u
2
= h4.58 × 10
9
a
3
u
13
+ 6.95 × 10
9
a
2
u
13
+ · · · − 4.51 × 10
7
a − 4.07 ×
10
9
, −2u
13
a
3
− 2u
13
a
2
+ · · · + a − 4, u
14
− u
13
+ · · · − u + 1i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
u
2
a
9
=
a
−0.858220a
3
u
13
− 1.30104a
2
u
13
+ ··· + 0.00844657a + 0.761403
a
7
=
−0.285097a
3
u
13
− 0.713627a
2
u
13
+ ··· + 0.0914136a + 0.664261
−2.20874a
3
u
13
− 1.66317a
2
u
13
+ ··· − 0.0419375a + 1.39631
a
1
=
u
u
a
3
=
−u
3
−u
3
+ u
a
10
=
−0.100479a
3
u
13
+ 0.285033a
2
u
13
+ ··· + 0.856611a + 0.924305
−1.72044a
3
u
13
− 1.88475a
2
u
13
+ ··· + 0.0429787a + 1.64797
a
11
=
u
3
u
5
− u
3
+ u
a
8
=
−0.100479a
3
u
13
+ 0.285033a
2
u
13
+ ··· + 0.856611a + 0.924305
−0.344202a
3
u
13
− 1.03547a
2
u
13
+ ··· + 0.0994736a + 0.860482
a
4
=
−0.0876640a
3
u
13
+ 0.537440a
2
u
13
+ ··· − 0.230678a + 2.32540
−1.05501a
3
u
13
− 2.45763a
2
u
13
+ ··· + 0.114279a + 2.10614
a
4
=
−0.0876640a
3
u
13
+ 0.537440a
2
u
13
+ ··· − 0.230678a + 2.32540
−1.05501a
3
u
13
− 2.45763a
2
u
13
+ ··· + 0.114279a + 2.10614
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
783664904
254365539
u
13
a
3
−
12683216
84788513
u
13
a
2
+ ··· −
129411644
84788513
a +
810307330
254365539
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
(u
14
− u
13
+ ··· − u + 1)
4
c
2
(u
14
+ 7u
13
+ ··· + u + 1)
4
c
3
, c
4
, c
7
c
9
u
56
+ u
55
+ ··· + 362u + 259
c
6
, c
8
u
56
− 15u
55
+ ··· − 26u + 1
c
10
(u
2
− u + 1)
28
c
11
(u
14
− 3u
13
+ ··· − 7u + 3)
4
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
14
− 7y
13
+ ··· − y + 1)
4
c
2
(y
14
+ y
13
+ ··· + 7y + 1)
4
c
3
, c
4
, c
7
c
9
y
56
− 45y
55
+ ··· − 2168856y + 67081
c
6
, c
8
y
56
+ 11y
55
+ ··· − 92y + 1
c
10
(y
2
+ y + 1)
28
c
11
(y
14
+ 5y
13
+ ··· + 23y + 9)
4
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.989783 + 0.381937I
a = 0.657240 − 0.120571I
b = 0.714102 − 0.891128I
3.24009 − 3.43472I 0.49073 + 3.99358I
u = 0.989783 + 0.381937I
a = 1.32255 − 1.58704I
b = 2.39216 − 0.27199I
3.24009 + 0.62505I 0.49073 − 2.93462I
u = 0.989783 + 0.381937I
a = −2.56099 − 0.78225I
b = −1.063230 − 0.840351I
3.24009 + 0.62505I 0.49073 − 2.93462I
u = 0.989783 + 0.381937I
a = −2.08989 + 2.37774I
b = −2.34188 + 0.29641I
3.24009 − 3.43472I 0.49073 + 3.99358I
u = 0.989783 − 0.381937I
a = 0.657240 + 0.120571I
b = 0.714102 + 0.891128I
3.24009 + 3.43472I 0.49073 − 3.99358I
u = 0.989783 − 0.381937I
a = 1.32255 + 1.58704I
b = 2.39216 + 0.27199I
3.24009 − 0.62505I 0.49073 + 2.93462I
u = 0.989783 − 0.381937I
a = −2.56099 + 0.78225I
b = −1.063230 + 0.840351I
3.24009 − 0.62505I 0.49073 + 2.93462I
u = 0.989783 − 0.381937I
a = −2.08989 − 2.37774I
b = −2.34188 − 0.29641I
3.24009 + 3.43472I 0.49073 − 3.99358I
u = 0.728347 + 0.560551I
a = 0.597987 − 0.378073I
b = −0.012399 − 0.961994I
3.49442 − 4.22117I 3.23919 + 7.32128I
u = 0.728347 + 0.560551I
a = −1.358540 − 0.008569I
b = −0.321734 − 0.081885I
3.49442 − 0.16140I 3.23919 + 0.39308I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.728347 + 0.560551I
a = −0.34870 + 1.50038I
b = −0.741817 + 0.609882I
3.49442 − 4.22117I 3.23919 + 7.32128I
u = 0.728347 + 0.560551I
a = 0.261952 − 0.336693I
b = 1.003780 − 0.395230I
3.49442 − 0.16140I 3.23919 + 0.39308I
u = 0.728347 − 0.560551I
a = 0.597987 + 0.378073I
b = −0.012399 + 0.961994I
3.49442 + 4.22117I 3.23919 − 7.32128I
u = 0.728347 − 0.560551I
a = −1.358540 + 0.008569I
b = −0.321734 + 0.081885I
3.49442 + 0.16140I 3.23919 − 0.39308I
u = 0.728347 − 0.560551I
a = −0.34870 − 1.50038I
b = −0.741817 − 0.609882I
3.49442 + 4.22117I 3.23919 − 7.32128I
u = 0.728347 − 0.560551I
a = 0.261952 + 0.336693I
b = 1.003780 + 0.395230I
3.49442 + 0.16140I 3.23919 − 0.39308I
u = −1.068410 + 0.522447I
a = −0.525510 − 0.092447I
b = −0.806781 − 0.696072I
4.37100 + 3.04196I 3.67153 − 2.86716I
u = −1.068410 + 0.522447I
a = 2.37666 − 0.01914I
b = 1.64556 − 2.27656I
4.37100 + 7.10173I 3.67153 − 9.79536I
u = −1.068410 + 0.522447I
a = 0.63399 − 2.35193I
b = −0.844123 − 0.882615I
4.37100 + 7.10173I 3.67153 − 9.79536I
u = −1.068410 + 0.522447I
a = −3.03321 − 1.32932I
b = −2.32986 + 1.58159I
4.37100 + 3.04196I 3.67153 − 2.86716I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.068410 − 0.522447I
a = −0.525510 + 0.092447I
b = −0.806781 + 0.696072I
4.37100 − 3.04196I 3.67153 + 2.86716I
u = −1.068410 − 0.522447I
a = 2.37666 + 0.01914I
b = 1.64556 + 2.27656I
4.37100 − 7.10173I 3.67153 + 9.79536I
u = −1.068410 − 0.522447I
a = 0.63399 + 2.35193I
b = −0.844123 + 0.882615I
4.37100 − 7.10173I 3.67153 + 9.79536I
u = −1.068410 − 0.522447I
a = −3.03321 + 1.32932I
b = −2.32986 − 1.58159I
4.37100 − 3.04196I 3.67153 + 2.86716I
u = −1.157220 + 0.286866I
a = −1.227340 − 0.668393I
b = −1.119640 + 0.713558I
−2.89147 − 2.50043I −3.32829 + 3.28061I
u = −1.157220 + 0.286866I
a = −1.44410 − 0.25370I
b = −1.172660 + 0.475656I
−2.89147 + 1.55933I −3.32829 − 3.64759I
u = −1.157220 + 0.286866I
a = 0.312105 − 0.206190I
b = −0.216236 − 0.532280I
−2.89147 + 1.55933I −3.32829 − 3.64759I
u = −1.157220 + 0.286866I
a = 1.39506 + 1.87867I
b = 1.76504 + 0.51757I
−2.89147 − 2.50043I −3.32829 + 3.28061I
u = −1.157220 − 0.286866I
a = −1.227340 + 0.668393I
b = −1.119640 − 0.713558I
−2.89147 + 2.50043I −3.32829 − 3.28061I
u = −1.157220 − 0.286866I
a = −1.44410 + 0.25370I
b = −1.172660 − 0.475656I
−2.89147 − 1.55933I −3.32829 + 3.64759I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.157220 − 0.286866I
a = 0.312105 + 0.206190I
b = −0.216236 + 0.532280I
−2.89147 − 1.55933I −3.32829 + 3.64759I
u = −1.157220 − 0.286866I
a = 1.39506 − 1.87867I
b = 1.76504 − 0.51757I
−2.89147 + 2.50043I −3.32829 − 3.28061I
u = 0.268039 + 0.757899I
a = −0.449529 − 0.923610I
b = 1.32307 − 0.54117I
1.42232 + 5.65867I 2.33383 − 6.09636I
u = 0.268039 + 0.757899I
a = −0.501123 + 0.090881I
b = 0.680414 − 0.544761I
1.42232 + 1.59890I 2.33383 + 0.83184I
u = 0.268039 + 0.757899I
a = 0.443932 + 0.162321I
b = −1.46411 + 1.38595I
1.42232 + 5.65867I 2.33383 − 6.09636I
u = 0.268039 + 0.757899I
a = −0.155374 + 0.294611I
b = 0.121708 + 0.244509I
1.42232 + 1.59890I 2.33383 + 0.83184I
u = 0.268039 − 0.757899I
a = −0.449529 + 0.923610I
b = 1.32307 + 0.54117I
1.42232 − 5.65867I 2.33383 + 6.09636I
u = 0.268039 − 0.757899I
a = −0.501123 − 0.090881I
b = 0.680414 + 0.544761I
1.42232 − 1.59890I 2.33383 − 0.83184I
u = 0.268039 − 0.757899I
a = 0.443932 − 0.162321I
b = −1.46411 − 1.38595I
1.42232 − 5.65867I 2.33383 + 6.09636I
u = 0.268039 − 0.757899I
a = −0.155374 − 0.294611I
b = 0.121708 − 0.244509I
1.42232 − 1.59890I 2.33383 − 0.83184I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.142590 + 0.546762I
a = 0.638961 + 0.080893I
b = 0.450729 + 0.190702I
−1.12941 − 6.50135I −0.72348 + 2.71621I
u = 1.142590 + 0.546762I
a = −1.43117 + 0.49772I
b = −1.28962 − 0.92983I
−1.12941 − 6.50135I −0.72348 + 2.71621I
u = 1.142590 + 0.546762I
a = −1.89157 + 0.84278I
b = −2.19597 − 0.59687I
−1.12941 − 10.56110I −0.72348 + 9.64441I
u = 1.142590 + 0.546762I
a = 2.78876 − 0.44602I
b = 1.97531 + 1.69293I
−1.12941 − 10.56110I −0.72348 + 9.64441I
u = 1.142590 − 0.546762I
a = 0.638961 − 0.080893I
b = 0.450729 − 0.190702I
−1.12941 + 6.50135I −0.72348 − 2.71621I
u = 1.142590 − 0.546762I
a = −1.43117 − 0.49772I
b = −1.28962 + 0.92983I
−1.12941 + 6.50135I −0.72348 − 2.71621I
u = 1.142590 − 0.546762I
a = −1.89157 − 0.84278I
b = −2.19597 + 0.59687I
−1.12941 + 10.56110I −0.72348 − 9.64441I
u = 1.142590 − 0.546762I
a = 2.78876 + 0.44602I
b = 1.97531 − 1.69293I
−1.12941 + 10.56110I −0.72348 − 9.64441I
u = −0.403136 + 0.584808I
a = −0.960172 + 0.108584I
b = 1.76299 + 1.35127I
6.29745 + 1.40130I 8.31651 − 2.04159I
u = −0.403136 + 0.584808I
a = −0.658559 − 0.684835I
b = 1.06707 − 1.07964I
6.29745 − 2.65847I 8.31651 + 4.88661I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.403136 + 0.584808I
a = 1.20920 + 1.58112I
b = 0.319173 + 0.158025I
6.29745 + 1.40130I 8.31651 − 2.04159I
u = −0.403136 + 0.584808I
a = 1.99737 − 0.37568I
b = −0.80106 − 1.47821I
6.29745 − 2.65847I 8.31651 + 4.88661I
u = −0.403136 − 0.584808I
a = −0.960172 − 0.108584I
b = 1.76299 − 1.35127I
6.29745 − 1.40130I 8.31651 + 2.04159I
u = −0.403136 − 0.584808I
a = −0.658559 + 0.684835I
b = 1.06707 + 1.07964I
6.29745 + 2.65847I 8.31651 − 4.88661I
u = −0.403136 − 0.584808I
a = 1.20920 − 1.58112I
b = 0.319173 − 0.158025I
6.29745 − 1.40130I 8.31651 + 2.04159I
u = −0.403136 − 0.584808I
a = 1.99737 + 0.37568I
b = −0.80106 + 1.47821I
6.29745 + 2.65847I 8.31651 − 4.88661I
16
III.
I
u
3
= hu
12
+ u
11
+ · · · + b + 2, −u
13
+ u
12
+ · · · + a + 3, u
14
− u
13
+ · · · − u + 1i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
u
2
a
9
=
u
13
− u
12
+ ··· − 2u − 3
−u
12
− u
11
+ ··· − u − 2
a
7
=
−u
13
+ u
12
+ ··· − 5u
2
+ 2
−u
13
+ u
12
+ ··· − 2u
2
+ 1
a
1
=
u
u
a
3
=
−u
3
−u
3
+ u
a
10
=
−u
12
− u
11
+ 3u
10
+ 2u
9
− 5u
8
− 3u
7
+ 4u
6
− 4u
4
+ 3u
3
+ 3u
2
− 2u − 2
−u
12
+ 3u
10
− u
9
− 4u
8
+ 2u
7
+ u
6
− 2u
5
+ u
4
+ u
3
− 1
a
11
=
u
3
u
5
− u
3
+ u
a
8
=
u
13
− u
12
+ ··· − 2u − 2
−u
12
+ 3u
10
− u
9
− 4u
8
+ 2u
7
+ u
6
− 3u
5
+ u
4
+ 2u
3
− u − 1
a
4
=
−3u
13
+ 11u
11
+ ··· + u + 5
−2u
13
+ u
12
+ ··· − 4u
2
+ 3
a
4
=
−3u
13
+ 11u
11
+ ··· + u + 5
−2u
13
+ u
12
+ ··· − 4u
2
+ 3
(ii) Obstruction class = 1
(iii) Cusp Shapes
= 2u
13
+5u
12
−12u
11
−11u
10
+28u
9
+10u
8
−30u
7
+6u
6
+18u
5
−15u
4
−3u
3
+12u
2
+6u−1
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
14
+ u
13
+ ··· + u + 1
c
2
u
14
+ 7u
13
+ ··· + 5u + 1
c
3
, c
7
u
14
+ u
13
+ ··· + 3u + 1
c
4
, c
9
u
14
− u
13
+ ··· − 3u + 1
c
5
u
14
− u
13
+ ··· − u + 1
c
6
, c
8
u
14
+ u
13
+ u
12
− 3u
11
− u
10
− u
9
+ 5u
8
− 2u
7
− 4u
5
+ 4u
4
+ u
2
− 2u + 1
c
10
u
14
+ 2u
13
+ u
12
+ 4u
10
+ 4u
9
+ 2u
7
+ 5u
6
+ u
5
− u
4
+ 3u
3
+ u
2
− u + 1
c
11
u
14
+ 3u
13
+ ··· + 3u + 1
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
14
− 7y
13
+ ··· − 5y + 1
c
2
y
14
+ y
13
+ ··· + 7y + 1
c
3
, c
4
, c
7
c
9
y
14
− 15y
13
+ ··· − 9y + 1
c
6
, c
8
y
14
+ y
13
+ ··· − 2y + 1
c
10
y
14
− 2y
13
+ ··· + y + 1
c
11
y
14
+ 5y
13
+ ··· + y + 1
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.341418 + 0.896272I
a = −0.144947 − 0.094275I
b = 0.680620 − 0.402114I
1.48125 + 2.28994I −0.76956 − 11.07837I
u = 0.341418 − 0.896272I
a = −0.144947 + 0.094275I
b = 0.680620 + 0.402114I
1.48125 − 2.28994I −0.76956 + 11.07837I
u = −1.088540 + 0.205382I
a = −1.361470 − 0.363666I
b = −0.739933 + 0.366961I
−3.69709 + 0.34310I −7.64356 − 0.71321I
u = −1.088540 − 0.205382I
a = −1.361470 + 0.363666I
b = −0.739933 − 0.366961I
−3.69709 − 0.34310I −7.64356 + 0.71321I
u = 1.020860 + 0.434206I
a = 2.42462 − 0.94126I
b = 2.25373 + 0.19331I
3.52230 − 0.63660I 2.40553 + 3.12380I
u = 1.020860 − 0.434206I
a = 2.42462 + 0.94126I
b = 2.25373 − 0.19331I
3.52230 + 0.63660I 2.40553 − 3.12380I
u = −1.041720 + 0.508997I
a = 0.98641 + 1.35407I
b = 1.33024 − 0.77334I
4.08559 + 5.66390I 2.38420 − 4.61852I
u = −1.041720 − 0.508997I
a = 0.98641 − 1.35407I
b = 1.33024 + 0.77334I
4.08559 − 5.66390I 2.38420 + 4.61852I
u = −0.552395 + 0.530092I
a = 1.41370 − 0.38398I
b = −0.892127 − 0.192652I
5.63571 − 1.41240I 4.95246 − 0.76426I
u = −0.552395 − 0.530092I
a = 1.41370 + 0.38398I
b = −0.892127 + 0.192652I
5.63571 + 1.41240I 4.95246 + 0.76426I
20
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.658163 + 0.329875I
a = −1.54185 + 1.44828I
b = −1.51377 + 0.82770I
4.85404 − 2.75383I 6.20128 + 4.14732I
u = 0.658163 − 0.329875I
a = −1.54185 − 1.44828I
b = −1.51377 − 0.82770I
4.85404 + 2.75383I 6.20128 − 4.14732I
u = 1.162210 + 0.578741I
a = −1.276460 + 0.354911I
b = −1.118750 − 0.737948I
−1.07739 − 7.66495I −1.03033 + 9.99597I
u = 1.162210 − 0.578741I
a = −1.276460 − 0.354911I
b = −1.118750 + 0.737948I
−1.07739 + 7.66495I −1.03033 − 9.99597I
21
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
14
− u
13
+ ··· − u + 1)
4
)(u
14
+ u
13
+ ··· + u + 1)
· (u
30
+ 6u
29
+ ··· + 26u + 4)
c
2
((u
14
+ 7u
13
+ ··· + u + 1)
4
)(u
14
+ 7u
13
+ ··· + 5u + 1)
· (u
30
+ 14u
29
+ ··· + 28u + 16)
c
3
, c
7
(u
14
+ u
13
+ ··· + 3u + 1)(u
30
− u
29
+ ··· + u + 1)
· (u
56
+ u
55
+ ··· + 362u + 259)
c
4
, c
9
(u
14
− u
13
+ ··· − 3u + 1)(u
30
− u
29
+ ··· + u + 1)
· (u
56
+ u
55
+ ··· + 362u + 259)
c
5
((u
14
− u
13
+ ··· − u + 1)
4
)(u
14
− u
13
+ ··· − u + 1)
· (u
30
+ 6u
29
+ ··· + 26u + 4)
c
6
, c
8
(u
14
+ u
13
+ u
12
− 3u
11
− u
10
− u
9
+ 5u
8
− 2u
7
− 4u
5
+ 4u
4
+ u
2
− 2u + 1)
· (u
30
+ u
29
+ ··· − 4u + 1)(u
56
− 15u
55
+ ··· − 26u + 1)
c
10
(u
2
− u + 1)
28
· (u
14
+ 2u
13
+ u
12
+ 4u
10
+ 4u
9
+ 2u
7
+ 5u
6
+ u
5
− u
4
+ 3u
3
+ u
2
− u + 1)
· (u
30
+ 27u
29
+ ··· + 237568u + 16384)
c
11
((u
14
− 3u
13
+ ··· − 7u + 3)
4
)(u
14
+ 3u
13
+ ··· + 3u + 1)
· (u
30
+ 18u
29
+ ··· − 314u − 52)
22
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
14
− 7y
13
+ ··· − 5y + 1)(y
14
− 7y
13
+ ··· − y + 1)
4
· (y
30
− 14y
29
+ ··· − 28y + 16)
c
2
(y
14
+ y
13
+ ··· + 7y + 1)(y
14
+ y
13
+ ··· + 7y + 1)
4
· (y
30
+ 2y
29
+ ··· + 272y + 256)
c
3
, c
4
, c
7
c
9
(y
14
− 15y
13
+ ··· − 9y + 1)(y
30
− 21y
29
+ ··· − y + 1)
· (y
56
− 45y
55
+ ··· − 2168856y + 67081)
c
6
, c
8
(y
14
+ y
13
+ ··· − 2y + 1)(y
30
− 9y
29
+ ··· − 22y + 1)
· (y
56
+ 11y
55
+ ··· − 92y + 1)
c
10
((y
2
+ y + 1)
28
)(y
14
− 2y
13
+ ··· + y + 1)
· (y
30
− y
29
+ ··· − 335544320y + 268435456)
c
11
((y
14
+ 5y
13
+ ··· + 23y + 9)
4
)(y
14
+ 5y
13
+ ··· + y + 1)
· (y
30
+ 10y
29
+ ··· − 170460y + 2704)
23
