11a
302
(K11a
302
)
A knot diagram
1
Linearized knot diagam
10 6 1 8 2 9 4 11 3 5 7
Solving Sequence
4,7
8
5,11
9 1 3 6 2 10
c
7
c
4
c
8
c
11
c
3
c
6
c
2
c
10
c
1
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h86810u
20
− 51179u
19
+ ··· + 203617b − 498356,
548161u
20
− 27309u
19
+ ··· + 203617a + 1419959, u
21
− 7u
19
+ ··· + 5u + 1i
I
u
2
= h1.93742 × 10
205
u
83
− 1.36676 × 10
204
u
82
+ ··· + 2.85391 × 10
204
b + 1.87510 × 10
205
,
− 8.01634 × 10
204
u
83
− 1.47295 × 10
204
u
82
+ ··· + 2.85391 × 10
204
a − 2.38032 × 10
205
,
u
84
+ u
83
+ ··· + 13u + 1i
I
u
3
= h330474083u
21
+ 170598791u
20
+ ··· + 332950103b − 35950927,
− 211438488u
21
+ 97373739u
20
+ ··· + 332950103a + 43876857, u
22
− 6u
20
+ ··· − u + 1i
I
u
4
= hb + u, u
2
+ a, u
3
− u + 1i
* 4 irreducible components of dim
C
= 0, with total 130 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
= h86810u
20
− 51179u
19
+ · · · + 203617b − 498356, 5.48 × 10
5
u
20
−
2.73 × 10
4
u
19
+ · · · + 2.04 × 10
5
a + 1.42 × 10
6
, u
21
− 7u
19
+ · · · + 5u + 1i
(i) Arc colorings
a
4
=
0
u
a
7
=
1
0
a
8
=
1
−u
2
a
5
=
u
−u
3
+ u
a
11
=
−2.69212u
20
+ 0.134119u
19
+ ··· − 28.2075u − 6.97368
−0.426340u
20
+ 0.251349u
19
+ ··· + 7.71376u + 2.44752
a
9
=
−1.85734u
20
+ 0.844581u
19
+ ··· − 20.6981u − 4.31433
0.385469u
20
+ 0.103538u
19
+ ··· + 11.0661u + 3.11846
a
1
=
−3.11846u
20
+ 0.385469u
19
+ ··· − 20.4938u − 4.52616
−0.426340u
20
+ 0.251349u
19
+ ··· + 7.71376u + 2.44752
a
3
=
−0.482258u
20
− 0.0237357u
19
+ ··· − 5.29877u − 0.756499
−0.287854u
20
+ 0.284623u
19
+ ··· − 5.89970u − 1.78023
a
6
=
0.979437u
20
+ 0.0931160u
19
+ ··· − 4.09981u − 0.575374
0.0237357u
20
+ 0.194404u
19
+ ··· − 1.65479u − 0.482258
a
2
=
−0.575374u
20
− 0.979437u
19
+ ··· + 0.173792u + 0.222938
−0.482258u
20
− 0.0237357u
19
+ ··· − 5.29877u − 1.75650
a
10
=
−3.91939u
20
+ 0.521779u
19
+ ··· − 30.2187u − 6.71970
−1.01138u
20
+ 0.674192u
19
+ ··· + 6.41358u + 3.08915
a
10
=
−3.91939u
20
+ 0.521779u
19
+ ··· − 30.2187u − 6.71970
−1.01138u
20
+ 0.674192u
19
+ ··· + 6.41358u + 3.08915
(ii) Obstruction class = −1
(iii) Cusp Shapes =
338440
203617
u
20
+
515137
203617
u
19
+ ··· +
12952739
203617
u +
6217185
203617
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
u
21
− 2u
20
+ ··· + u + 1
c
2
, c
4
, c
5
c
7
u
21
− 7u
19
+ ··· + 5u − 1
c
3
, c
6
u
21
− u
20
+ ··· + 8u − 4
c
9
, c
11
u
21
− 7u
19
+ ··· − 3u − 1
c
10
u
21
− 7u
20
+ ··· + 256u − 64
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
21
+ 32y
19
+ ··· + 25y −1
c
2
, c
4
, c
5
c
7
y
21
− 14y
20
+ ··· + 7y −1
c
3
, c
6
y
21
+ 17y
20
+ ··· − 192y −16
c
9
, c
11
y
21
− 14y
20
+ ··· + 7y −1
c
10
y
21
+ 9y
20
+ ··· − 32768y −4096
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.928185 + 0.189936I
a = 0.674396 − 0.216214I
b = −0.735536 − 1.073720I
3.43423 + 3.77228I 11.55133 − 4.69984I
u = 0.928185 − 0.189936I
a = 0.674396 + 0.216214I
b = −0.735536 + 1.073720I
3.43423 − 3.77228I 11.55133 + 4.69984I
u = −0.827440 + 0.723293I
a = 0.126743 − 0.809716I
b = 0.567919 − 0.288839I
2.18487 − 3.00976I 10.87376 − 0.69402I
u = −0.827440 − 0.723293I
a = 0.126743 + 0.809716I
b = 0.567919 + 0.288839I
2.18487 + 3.00976I 10.87376 + 0.69402I
u = −0.067511 + 1.157490I
a = 0.0502069 − 0.0817577I
b = 0.997381 − 0.629444I
1.79260 − 6.58426I 8.00865 + 7.58329I
u = −0.067511 − 1.157490I
a = 0.0502069 + 0.0817577I
b = 0.997381 + 0.629444I
1.79260 + 6.58426I 8.00865 − 7.58329I
u = 1.111710 + 0.428960I
a = −1.95911 + 0.31173I
b = 1.78476 + 0.65605I
4.95885 + 9.25397I 8.29327 − 10.96531I
u = 1.111710 − 0.428960I
a = −1.95911 − 0.31173I
b = 1.78476 − 0.65605I
4.95885 − 9.25397I 8.29327 + 10.96531I
u = −1.205890 + 0.106741I
a = −1.92936 + 0.40120I
b = 1.207310 + 0.326297I
8.49324 − 2.76851I 15.4777 + 0.9885I
u = −1.205890 − 0.106741I
a = −1.92936 − 0.40120I
b = 1.207310 − 0.326297I
8.49324 + 2.76851I 15.4777 − 0.9885I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.789234
a = 1.20750
b = −0.556308
1.38786 6.70340
u = 1.188640 + 0.329356I
a = −1.011510 − 0.120494I
b = 0.284184 − 0.245258I
5.15265 + 4.73162I 8.09798 − 4.44428I
u = 1.188640 − 0.329356I
a = −1.011510 + 0.120494I
b = 0.284184 + 0.245258I
5.15265 − 4.73162I 8.09798 + 4.44428I
u = −0.372563 + 0.410285I
a = −0.39105 + 1.43567I
b = −0.909633 − 0.829475I
0.48724 + 1.81194I 3.30153 − 2.05952I
u = −0.372563 − 0.410285I
a = −0.39105 − 1.43567I
b = −0.909633 + 0.829475I
0.48724 − 1.81194I 3.30153 + 2.05952I
u = 1.36146 + 0.57065I
a = 0.843025 − 0.608835I
b = −1.304890 + 0.034538I
10.21620 + 5.64989I 15.0241 − 3.8611I
u = 1.36146 − 0.57065I
a = 0.843025 + 0.608835I
b = −1.304890 − 0.034538I
10.21620 − 5.64989I 15.0241 + 3.8611I
u = −1.41669 + 0.52365I
a = 1.55271 + 0.10596I
b = −1.38942 + 1.03688I
11.2036 − 18.3943I 11.0076 + 9.0976I
u = −1.41669 − 0.52365I
a = 1.55271 − 0.10596I
b = −1.38942 − 1.03688I
11.2036 + 18.3943I 11.0076 − 9.0976I
u = −0.305278 + 0.294373I
a = 0.94021 − 1.42121I
b = −0.223914 + 0.503703I
0.730644 − 1.059890I 8.01231 + 6.34216I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.305278 − 0.294373I
a = 0.94021 + 1.42121I
b = −0.223914 − 0.503703I
0.730644 + 1.059890I 8.01231 − 6.34216I
7
II. I
u
2
= h1.94 × 10
205
u
83
− 1.37 × 10
204
u
82
+ · · · + 2.85 × 10
204
b + 1.88 ×
10
205
, −8.02 × 10
204
u
83
− 1.47 × 10
204
u
82
+ · · · + 2.85 × 10
204
a − 2.38 ×
10
205
, u
84
+ u
83
+ · · · + 13u + 1i
(i) Arc colorings
a
4
=
0
u
a
7
=
1
0
a
8
=
1
−u
2
a
5
=
u
−u
3
+ u
a
11
=
2.80890u
83
+ 0.516116u
82
+ ··· + 106.773u + 8.34055
−6.78864u
83
+ 0.478907u
82
+ ··· − 76.5519u − 6.57029
a
9
=
−3.38419u
83
− 0.362972u
82
+ ··· − 77.5673u + 7.17563
−2.53005u
83
+ 0.224618u
82
+ ··· − 43.3946u − 3.81230
a
1
=
−3.97974u
83
+ 0.995023u
82
+ ··· + 30.2214u + 1.77026
−6.78864u
83
+ 0.478907u
82
+ ··· − 76.5519u − 6.57029
a
3
=
−5.43747u
83
+ 0.177775u
82
+ ··· − 43.6461u + 4.25595
−1.66531u
83
+ 0.0104175u
82
+ ··· − 30.8069u − 1.97472
a
6
=
2.24631u
83
+ 0.604610u
82
+ ··· + 192.633u + 22.6033
2.43802u
83
− 0.303260u
82
+ ··· + 7.34022u + 1.81171
a
2
=
−2.47215u
83
− 0.763880u
82
+ ··· − 175.607u − 18.2174
−2.61767u
83
+ 0.377913u
82
+ ··· − 16.3564u − 2.21693
a
10
=
−4.55591u
83
+ 1.15513u
82
+ ··· + 27.0524u + 1.66528
−5.34136u
83
+ 0.404432u
82
+ ··· − 59.5879u − 5.24176
a
10
=
−4.55591u
83
+ 1.15513u
82
+ ··· + 27.0524u + 1.66528
−5.34136u
83
+ 0.404432u
82
+ ··· − 59.5879u − 5.24176
(ii) Obstruction class = −1
(iii) Cusp Shapes = −1.51665u
83
− 0.0478998u
82
+ ··· + 23.8004u + 16.1335
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
u
84
− 2u
83
+ ··· + 184899u + 14113
c
2
, c
4
, c
5
c
7
u
84
− u
83
+ ··· − 13u + 1
c
3
, c
6
u
84
− 8u
83
+ ··· − 1444332u + 360028
c
9
, c
11
u
84
− 9u
82
+ ··· − 7203u + 9091
c
10
(u
42
+ 3u
41
+ ··· − 803u + 865)
2
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
84
− 42y
83
+ ··· − 25475290137y + 199176769
c
2
, c
4
, c
5
c
7
y
84
− 59y
83
+ ··· + 111y + 1
c
3
, c
6
y
84
+ 30y
83
+ ··· + 3877148205504y + 129620160784
c
9
, c
11
y
84
− 18y
83
+ ··· − 1277331827y + 82646281
c
10
(y
42
+ 27y
41
+ ··· + 7816621y + 748225)
2
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.962597 + 0.318394I
a = 1.377300 − 0.139751I
b = −0.664367 + 0.492109I
1.17898 0
u = −0.962597 − 0.318394I
a = 1.377300 + 0.139751I
b = −0.664367 − 0.492109I
1.17898 0
u = 0.985326 + 0.021789I
a = −1.93810 − 1.17823I
b = 0.947964 + 0.368637I
4.13302 + 3.67085I 0
u = 0.985326 − 0.021789I
a = −1.93810 + 1.17823I
b = 0.947964 − 0.368637I
4.13302 − 3.67085I 0
u = 0.787842 + 0.559097I
a = 1.18409 − 1.21681I
b = 0.073486 − 1.072000I
−0.36053 + 2.27504I 0
u = 0.787842 − 0.559097I
a = 1.18409 + 1.21681I
b = 0.073486 + 1.072000I
−0.36053 − 2.27504I 0
u = 0.069362 + 1.055510I
a = 0.006053 + 0.302515I
b = 1.042160 + 0.610320I
6.25983 + 0.22821I 0
u = 0.069362 − 1.055510I
a = 0.006053 − 0.302515I
b = 1.042160 − 0.610320I
6.25983 − 0.22821I 0
u = −0.906187 + 0.158270I
a = −1.40959 − 1.04548I
b = 0.422407 + 0.578901I
1.30396 − 0.89340I 5.00000 + 0.I
u = −0.906187 − 0.158270I
a = −1.40959 + 1.04548I
b = 0.422407 − 0.578901I
1.30396 + 0.89340I 5.00000 + 0.I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.396919 + 0.818374I
a = 0.150512 − 0.842112I
b = −1.076570 + 0.628616I
2.66616 − 4.59027I 9.89989 + 8.77883I
u = 0.396919 − 0.818374I
a = 0.150512 + 0.842112I
b = −1.076570 − 0.628616I
2.66616 + 4.59027I 9.89989 − 8.77883I
u = −0.254789 + 0.872661I
a = −0.065466 − 0.179749I
b = −0.655792 + 0.532899I
0.89781 − 2.28879I 5.00000 + 0.I
u = −0.254789 − 0.872661I
a = −0.065466 + 0.179749I
b = −0.655792 − 0.532899I
0.89781 + 2.28879I 5.00000 + 0.I
u = −1.092250 + 0.002765I
a = −0.733789 + 0.407597I
b = 0.29106 − 1.51046I
2.41193 − 0.49575I 0
u = −1.092250 − 0.002765I
a = −0.733789 − 0.407597I
b = 0.29106 + 1.51046I
2.41193 + 0.49575I 0
u = 1.095190 + 0.136546I
a = 0.596121 − 0.839742I
b = −0.528751 − 0.778109I
3.31027 + 4.01412I 0
u = 1.095190 − 0.136546I
a = 0.596121 + 0.839742I
b = −0.528751 + 0.778109I
3.31027 − 4.01412I 0
u = 0.478559 + 0.748201I
a = 0.876962 + 0.549123I
b = −0.017116 − 0.689696I
2.41193 + 0.49575I 6.97126 + 0.I
u = 0.478559 − 0.748201I
a = 0.876962 − 0.549123I
b = −0.017116 + 0.689696I
2.41193 − 0.49575I 6.97126 + 0.I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.069760 + 0.315438I
a = 2.47968 + 0.26967I
b = −0.463529 + 0.567527I
6.34003 − 8.91423I 0
u = −1.069760 − 0.315438I
a = 2.47968 − 0.26967I
b = −0.463529 − 0.567527I
6.34003 + 8.91423I 0
u = −1.107920 + 0.242581I
a = −2.35624 + 0.11814I
b = 2.03515 − 1.07118I
2.66616 − 4.59027I 0
u = −1.107920 − 0.242581I
a = −2.35624 − 0.11814I
b = 2.03515 + 1.07118I
2.66616 + 4.59027I 0
u = −0.415622 + 0.740224I
a = −0.0020036 − 0.1082310I
b = 0.069817 + 0.926327I
−0.53461 − 4.05993I 2.13658 + 6.95533I
u = −0.415622 − 0.740224I
a = −0.0020036 + 0.1082310I
b = 0.069817 − 0.926327I
−0.53461 + 4.05993I 2.13658 − 6.95533I
u = 1.092540 + 0.366898I
a = 1.60708 − 0.10147I
b = −0.711297 − 0.697297I
−0.53461 + 4.05993I 0
u = 1.092540 − 0.366898I
a = 1.60708 + 0.10147I
b = −0.711297 + 0.697297I
−0.53461 − 4.05993I 0
u = −0.058275 + 1.155740I
a = 0.235480 + 0.247651I
b = −0.956335 − 0.271666I
5.14021 + 2.16348I 0
u = −0.058275 − 1.155740I
a = 0.235480 − 0.247651I
b = −0.956335 + 0.271666I
5.14021 − 2.16348I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.096511 + 1.182560I
a = −0.0394892 − 0.0002488I
b = 0.993395 + 0.687665I
6.42748 + 12.43880I 0
u = 0.096511 − 1.182560I
a = −0.0394892 + 0.0002488I
b = 0.993395 − 0.687665I
6.42748 − 12.43880I 0
u = −0.152546 + 0.783755I
a = 0.804335 − 0.372548I
b = 0.249934 + 0.532891I
1.30396 − 0.89340I 6.53370 + 0.64889I
u = −0.152546 − 0.783755I
a = 0.804335 + 0.372548I
b = 0.249934 − 0.532891I
1.30396 + 0.89340I 6.53370 − 0.64889I
u = −1.124540 + 0.428916I
a = 1.038230 + 0.027685I
b = −1.012970 + 0.956168I
4.13302 − 3.67085I 0
u = −1.124540 − 0.428916I
a = 1.038230 − 0.027685I
b = −1.012970 − 0.956168I
4.13302 + 3.67085I 0
u = −1.208240 + 0.063695I
a = 1.52740 + 1.46381I
b = −0.649430 + 0.363725I
9.40902 − 7.37920I 0
u = −1.208240 − 0.063695I
a = 1.52740 − 1.46381I
b = −0.649430 − 0.363725I
9.40902 + 7.37920I 0
u = 1.209410 + 0.050801I
a = −1.57865 − 0.62605I
b = 0.856376 − 0.171706I
5.14325 + 1.81373I 0
u = 1.209410 − 0.050801I
a = −1.57865 + 0.62605I
b = 0.856376 + 0.171706I
5.14325 − 1.81373I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.334826 + 0.714497I
a = 0.113127 − 0.180207I
b = 0.313370 − 0.821251I
−2.88354 −3.04446 + 0.I
u = 0.334826 − 0.714497I
a = 0.113127 + 0.180207I
b = 0.313370 + 0.821251I
−2.88354 −3.04446 + 0.I
u = 1.208860 + 0.113613I
a = 1.24948 − 1.29597I
b = −1.42986 + 2.01391I
9.41934 + 8.23155I 0
u = 1.208860 − 0.113613I
a = 1.24948 + 1.29597I
b = −1.42986 − 2.01391I
9.41934 − 8.23155I 0
u = −1.230690 + 0.043766I
a = 1.50014 + 1.11883I
b = −1.73790 − 1.78298I
5.14021 − 2.16348I 0
u = −1.230690 − 0.043766I
a = 1.50014 − 1.11883I
b = −1.73790 + 1.78298I
5.14021 + 2.16348I 0
u = 1.248010 + 0.079685I
a = −1.85795 − 0.34215I
b = 1.41535 + 1.16871I
9.16439 + 2.30003I 0
u = 1.248010 − 0.079685I
a = −1.85795 + 0.34215I
b = 1.41535 − 1.16871I
9.16439 − 2.30003I 0
u = 0.529370 + 0.527660I
a = 0.217817 − 0.094410I
b = −0.713712 − 0.939195I
3.31027 + 4.01412I 10.91907 − 8.56399I
u = 0.529370 − 0.527660I
a = 0.217817 + 0.094410I
b = −0.713712 + 0.939195I
3.31027 − 4.01412I 10.91907 + 8.56399I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.358302 + 0.602891I
a = −0.280820 + 1.307900I
b = 0.512934 + 0.986421I
4.28784 + 5.30125I 7.89549 − 5.60852I
u = −0.358302 − 0.602891I
a = −0.280820 − 1.307900I
b = 0.512934 − 0.986421I
4.28784 − 5.30125I 7.89549 + 5.60852I
u = 1.331970 + 0.037459I
a = 1.18314 − 0.83290I
b = −1.35866 + 1.43338I
9.93256 − 3.56952I 0
u = 1.331970 − 0.037459I
a = 1.18314 + 0.83290I
b = −1.35866 − 1.43338I
9.93256 + 3.56952I 0
u = −1.357030 + 0.020794I
a = −1.26007 − 0.76022I
b = 0.725277 − 0.025979I
9.16439 + 2.30003I 0
u = −1.357030 − 0.020794I
a = −1.26007 + 0.76022I
b = 0.725277 + 0.025979I
9.16439 − 2.30003I 0
u = 1.38593 + 0.43780I
a = −1.47248 − 0.00386I
b = 1.32846 + 0.78944I
5.90536 + 7.10956I 0
u = 1.38593 − 0.43780I
a = −1.47248 + 0.00386I
b = 1.32846 − 0.78944I
5.90536 − 7.10956I 0
u = −1.36930 + 0.49505I
a = 1.51004 + 0.26261I
b = −1.25954 + 1.06934I
10.75840 − 5.70483I 0
u = −1.36930 − 0.49505I
a = 1.51004 − 0.26261I
b = −1.25954 − 1.06934I
10.75840 + 5.70483I 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.44638 + 0.30530I
a = −1.57740 + 0.38063I
b = 1.35856 − 1.09530I
9.40902 − 7.37920I 0
u = −1.44638 − 0.30530I
a = −1.57740 − 0.38063I
b = 1.35856 + 1.09530I
9.40902 + 7.37920I 0
u = 1.39980 + 0.47856I
a = −1.021700 + 0.576699I
b = 0.927889 + 0.295498I
9.93256 + 3.56952I 0
u = 1.39980 − 0.47856I
a = −1.021700 − 0.576699I
b = 0.927889 − 0.295498I
9.93256 − 3.56952I 0
u = 1.39804 + 0.51884I
a = 1.50066 − 0.14841I
b = −1.36732 − 1.06245I
6.42748 + 12.43880I 0
u = 1.39804 − 0.51884I
a = 1.50066 + 0.14841I
b = −1.36732 + 1.06245I
6.42748 − 12.43880I 0
u = −1.38900 + 0.54948I
a = −1.44142 − 0.29334I
b = 1.34989 − 0.51349I
9.41934 − 8.23155I 0
u = −1.38900 − 0.54948I
a = −1.44142 + 0.29334I
b = 1.34989 + 0.51349I
9.41934 + 8.23155I 0
u = −1.46634 + 0.53685I
a = 0.736389 + 0.411433I
b = −1.112130 + 0.159293I
6.25983 + 0.22821I 0
u = −1.46634 − 0.53685I
a = 0.736389 − 0.411433I
b = −1.112130 − 0.159293I
6.25983 − 0.22821I 0
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.48689 + 0.57208I
a = −0.816525 − 0.119314I
b = 0.809610 − 0.627801I
4.28784 − 5.30125I 0
u = −1.48689 − 0.57208I
a = −0.816525 + 0.119314I
b = 0.809610 + 0.627801I
4.28784 + 5.30125I 0
u = 1.55256 + 0.46316I
a = −0.960208 − 0.267593I
b = 0.878289 + 0.947608I
6.34003 + 8.91423I 0
u = 1.55256 − 0.46316I
a = −0.960208 + 0.267593I
b = 0.878289 − 0.947608I
6.34003 − 8.91423I 0
u = −0.30112 + 1.60051I
a = −0.0041748 − 0.0290256I
b = −0.460657 + 0.107893I
−0.36053 − 2.27504I 0
u = −0.30112 − 1.60051I
a = −0.0041748 + 0.0290256I
b = −0.460657 − 0.107893I
−0.36053 + 2.27504I 0
u = 1.52347 + 0.60928I
a = 0.567285 − 0.456782I
b = −0.938984 − 0.052647I
10.75840 − 5.70483I 0
u = 1.52347 − 0.60928I
a = 0.567285 + 0.456782I
b = −0.938984 + 0.052647I
10.75840 + 5.70483I 0
u = 0.210295 + 0.240685I
a = 3.56655 + 0.84064I
b = 0.665854 + 0.321804I
0.89781 − 2.28879I 4.75450 + 2.28484I
u = 0.210295 − 0.240685I
a = 3.56655 − 0.84064I
b = 0.665854 − 0.321804I
0.89781 + 2.28879I 4.75450 − 2.28484I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.0011085 + 0.1043920I
a = −11.28360 + 8.01560I
b = 0.866225 + 0.595290I
5.90536 − 7.10956I 7.76610 + 3.18386I
u = 0.0011085 − 0.1043920I
a = −11.28360 − 8.01560I
b = 0.866225 − 0.595290I
5.90536 + 7.10956I 7.76610 − 3.18386I
u = −0.0781250 + 0.0575559I
a = 6.07183 − 5.26345I
b = −1.018550 − 0.454621I
5.14325 + 1.81373I 18.0633 − 2.4655I
u = −0.0781250 − 0.0575559I
a = 6.07183 + 5.26345I
b = −1.018550 + 0.454621I
5.14325 − 1.81373I 18.0633 + 2.4655I
19
III.
I
u
3
= h3.30 × 10
8
u
21
+ 1.71 × 10
8
u
20
+ · · · + 3.33 × 10
8
b − 3.60 × 10
7
, −2.11 ×
10
8
u
21
+ 9.74 × 10
7
u
20
+ · · · + 3.33 × 10
8
a + 4.39 × 10
7
, u
22
− 6u
20
+ · · · − u + 1i
(i) Arc colorings
a
4
=
0
u
a
7
=
1
0
a
8
=
1
−u
2
a
5
=
u
−u
3
+ u
a
11
=
0.635046u
21
− 0.292457u
20
+ ··· + 1.34171u − 0.131782
−0.992563u
21
− 0.512385u
20
+ ··· − 1.17373u + 0.107977
a
9
=
−0.889535u
21
+ 0.0966271u
20
+ ··· + 0.989738u − 0.475909
−0.0212194u
21
− 0.0240420u
20
+ ··· − 2.18136u + 0.983265
a
1
=
−0.357518u
21
− 0.804843u
20
+ ··· + 0.167975u − 0.0238052
−0.992563u
21
− 0.512385u
20
+ ··· − 1.17373u + 0.107977
a
3
=
0.0573463u
21
+ 0.336094u
20
+ ··· + 3.47754u − 0.657519
0.0219546u
21
− 0.762143u
20
+ ··· + 1.34055u + 0.187482
a
6
=
0.386153u
21
− 0.405453u
20
+ ··· − 1.41651u + 1.50722
0.493967u
21
+ 0.175818u
20
+ ··· + 2.18607u + 0.167488
a
2
=
0.652627u
21
− 0.172652u
20
+ ··· + 2.19868u − 1.11453
−0.670297u
21
− 0.330174u
20
+ ··· − 0.834144u + 0.0125608
a
10
=
−0.336298u
21
− 0.780801u
20
+ ··· + 2.34934u − 0.00706984
−0.863842u
21
− 0.316590u
20
+ ··· − 0.649099u − 0.255654
a
10
=
−0.336298u
21
− 0.780801u
20
+ ··· + 2.34934u − 0.00706984
−0.863842u
21
− 0.316590u
20
+ ··· − 0.649099u − 0.255654
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
50225472
332950103
u
21
−
1070367108
332950103
u
20
+ ··· −
3170922714
332950103
u +
2708776809
332950103
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
22
− 9u
21
+ ··· − 11u + 1
c
2
, c
4
u
22
− 6u
20
+ ··· + u + 1
c
3
u
22
+ u
21
+ ··· − 8u + 4
c
5
, c
7
u
22
− 6u
20
+ ··· − u + 1
c
6
u
22
− u
21
+ ··· + 8u + 4
c
8
u
22
+ 9u
21
+ ··· + 11u + 1
c
9
u
22
− u
21
+ ··· − 5u + 1
c
10
u
22
+ 7u
20
+ ··· + 84u
2
+ 23
c
11
u
22
+ u
21
+ ··· + 5u + 1
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
22
− 9y
21
+ ··· − 17y + 1
c
2
, c
4
, c
5
c
7
y
22
− 12y
21
+ ··· + 5y + 1
c
3
, c
6
y
22
+ 3y
21
+ ··· + 256y + 16
c
9
, c
11
y
22
− 3y
21
+ ··· − 21y + 1
c
10
(y
11
+ 7y
10
+ ··· + 84y + 23)
2
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.831103 + 0.513463I
a = −1.27286 − 1.19665I
b = 0.024234 − 1.029540I
−0.50092 − 2.11174I −5.15528 − 11.05035I
u = −0.831103 − 0.513463I
a = −1.27286 + 1.19665I
b = 0.024234 + 1.029540I
−0.50092 + 2.11174I −5.15528 + 11.05035I
u = 0.996853 + 0.278091I
a = 1.329730 − 0.474336I
b = −1.116110 − 0.772027I
2.14439 + 3.53044I 4.95647 − 3.30554I
u = 0.996853 − 0.278091I
a = 1.329730 + 0.474336I
b = −1.116110 + 0.772027I
2.14439 − 3.53044I 4.95647 + 3.30554I
u = −0.934195 + 0.222884I
a = 1.98665 + 1.58078I
b = −0.879814 − 0.359757I
7.04578 − 7.81545I 13.0279 + 5.9552I
u = −0.934195 − 0.222884I
a = 1.98665 − 1.58078I
b = −0.879814 + 0.359757I
7.04578 + 7.81545I 13.0279 − 5.9552I
u = 1.220700 + 0.018399I
a = −1.075790 + 0.004794I
b = 1.047590 − 0.787761I
4.05165 + 2.03043I 8.21995 − 2.84126I
u = 1.220700 − 0.018399I
a = −1.075790 − 0.004794I
b = 1.047590 + 0.787761I
4.05165 − 2.03043I 8.21995 + 2.84126I
u = 0.041486 + 0.760088I
a = 0.332109 − 0.176049I
b = −0.856724 + 0.482949I
4.05165 − 2.03043I 8.21995 + 2.84126I
u = 0.041486 − 0.760088I
a = 0.332109 + 0.176049I
b = −0.856724 − 0.482949I
4.05165 + 2.03043I 8.21995 − 2.84126I
23
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.274880 + 0.054997I
a = 0.257710 − 0.116488I
b = 0.216019 − 0.842080I
8.58189 + 6.24482I 12.19966 − 3.97801I
u = −1.274880 − 0.054997I
a = 0.257710 + 0.116488I
b = 0.216019 + 0.842080I
8.58189 − 6.24482I 12.19966 + 3.97801I
u = 0.456280 + 0.389882I
a = 1.22510 + 1.37492I
b = 0.063660 − 0.989377I
0.122720 1.50261 + 0.I
u = 0.456280 − 0.389882I
a = 1.22510 − 1.37492I
b = 0.063660 + 0.989377I
0.122720 1.50261 + 0.I
u = 1.36566 + 0.38329I
a = −1.60654 − 0.00056I
b = 1.19451 + 0.76861I
8.58189 + 6.24482I 12.19966 − 3.97801I
u = 1.36566 − 0.38329I
a = −1.60654 + 0.00056I
b = 1.19451 − 0.76861I
8.58189 − 6.24482I 12.19966 + 3.97801I
u = −1.42191 + 0.45186I
a = −1.333420 + 0.069874I
b = 1.29904 − 0.80185I
7.04578 − 7.81545I 13.0279 + 5.9552I
u = −1.42191 − 0.45186I
a = −1.333420 − 0.069874I
b = 1.29904 + 0.80185I
7.04578 + 7.81545I 13.0279 − 5.9552I
u = 0.40576 + 1.50605I
a = 0.181803 + 0.126321I
b = 0.277976 − 0.054179I
−0.50092 + 2.11174I −5.15528 + 11.05035I
u = 0.40576 − 1.50605I
a = 0.181803 − 0.126321I
b = 0.277976 + 0.054179I
−0.50092 − 2.11174I −5.15528 − 11.05035I
24
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.024657 + 0.437672I
a = −1.02449 + 1.22474I
b = −0.770375 − 0.789792I
2.14439 + 3.53044I 4.95647 − 3.30554I
u = −0.024657 − 0.437672I
a = −1.02449 − 1.22474I
b = −0.770375 + 0.789792I
2.14439 − 3.53044I 4.95647 + 3.30554I
25
IV. I
u
4
= hb + u, u
2
+ a, u
3
− u + 1i
(i) Arc colorings
a
4
=
0
u
a
7
=
1
0
a
8
=
1
−u
2
a
5
=
u
1
a
11
=
−u
2
−u
a
9
=
−u
2
+ u + 1
−u
2
− u + 1
a
1
=
−u
2
− u
−u
a
3
=
u
2
− 2
u
2
+ u − 1
a
6
=
2u
2
+ u
u + 1
a
2
=
−2u
−1
a
10
=
−u
2
−u
a
10
=
−u
2
−u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
2
− 9u + 12
26
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
3
− 2u
2
+ u − 1
c
2
, c
4
, c
9
u
3
− u − 1
c
3
u
3
+ u
2
+ 2u + 1
c
5
, c
7
, c
11
u
3
− u + 1
c
6
u
3
− u
2
+ 2u − 1
c
8
u
3
+ 2u
2
+ u + 1
c
10
u
3
27
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
3
− 2y
2
− 3y −1
c
2
, c
4
, c
5
c
7
, c
9
, c
11
y
3
− 2y
2
+ y −1
c
3
, c
6
y
3
+ 3y
2
+ 2y −1
c
10
y
3
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.662359 + 0.562280I
a = −0.122561 − 0.744862I
b = −0.662359 − 0.562280I
1.83893 + 3.77083I 5.54852 − 8.03996I
u = 0.662359 − 0.562280I
a = −0.122561 + 0.744862I
b = −0.662359 + 0.562280I
1.83893 − 3.77083I 5.54852 + 8.03996I
u = −1.32472
a = −1.75488
b = 1.32472
9.48162 16.9030
29
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
3
− 2u
2
+ u − 1)(u
21
− 2u
20
+ ··· + u + 1)(u
22
− 9u
21
+ ··· − 11u + 1)
· (u
84
− 2u
83
+ ··· + 184899u + 14113)
c
2
, c
4
(u
3
− u − 1)(u
21
− 7u
19
+ ··· + 5u − 1)(u
22
− 6u
20
+ ··· + u + 1)
· (u
84
− u
83
+ ··· − 13u + 1)
c
3
(u
3
+ u
2
+ 2u + 1)(u
21
− u
20
+ ··· + 8u − 4)(u
22
+ u
21
+ ··· − 8u + 4)
· (u
84
− 8u
83
+ ··· − 1444332u + 360028)
c
5
, c
7
(u
3
− u + 1)(u
21
− 7u
19
+ ··· + 5u − 1)(u
22
− 6u
20
+ ··· − u + 1)
· (u
84
− u
83
+ ··· − 13u + 1)
c
6
(u
3
− u
2
+ 2u − 1)(u
21
− u
20
+ ··· + 8u − 4)(u
22
− u
21
+ ··· + 8u + 4)
· (u
84
− 8u
83
+ ··· − 1444332u + 360028)
c
8
(u
3
+ 2u
2
+ u + 1)(u
21
− 2u
20
+ ··· + u + 1)(u
22
+ 9u
21
+ ··· + 11u + 1)
· (u
84
− 2u
83
+ ··· + 184899u + 14113)
c
9
(u
3
− u − 1)(u
21
− 7u
19
+ ··· − 3u − 1)(u
22
− u
21
+ ··· − 5u + 1)
· (u
84
− 9u
82
+ ··· − 7203u + 9091)
c
10
u
3
(u
21
− 7u
20
+ ··· + 256u − 64)(u
22
+ 7u
20
+ ··· + 84u
2
+ 23)
· (u
42
+ 3u
41
+ ··· − 803u + 865)
2
c
11
(u
3
− u + 1)(u
21
− 7u
19
+ ··· − 3u − 1)(u
22
+ u
21
+ ··· + 5u + 1)
· (u
84
− 9u
82
+ ··· − 7203u + 9091)
30
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
8
(y
3
− 2y
2
− 3y −1)(y
21
+ 32y
19
+ ··· + 25y −1)
· (y
22
− 9y
21
+ ··· − 17y + 1)
· (y
84
− 42y
83
+ ··· − 25475290137y + 199176769)
c
2
, c
4
, c
5
c
7
(y
3
− 2y
2
+ y −1)(y
21
− 14y
20
+ ··· + 7y −1)
· (y
22
− 12y
21
+ ··· + 5y + 1)(y
84
− 59y
83
+ ··· + 111y + 1)
c
3
, c
6
(y
3
+ 3y
2
+ 2y −1)(y
21
+ 17y
20
+ ··· − 192y −16)
· (y
22
+ 3y
21
+ ··· + 256y + 16)
· (y
84
+ 30y
83
+ ··· + 3877148205504y + 129620160784)
c
9
, c
11
(y
3
− 2y
2
+ y −1)(y
21
− 14y
20
+ ··· + 7y −1)
· (y
22
− 3y
21
+ ··· − 21y + 1)
· (y
84
− 18y
83
+ ··· − 1277331827y + 82646281)
c
10
y
3
(y
11
+ 7y
10
+ ··· + 84y + 23)
2
(y
21
+ 9y
20
+ ··· − 32768y −4096)
· (y
42
+ 27y
41
+ ··· + 7816621y + 748225)
2
31
