12n
0127
(K12n
0127
)
A knot diagram
1
Linearized knot diagam
3 5 7 2 8 3 10 12 6 5 9 11
Solving Sequence
8,10 3,7
4 6 5 11 2 1 9 12
c
7
c
3
c
6
c
5
c
10
c
2
c
1
c
9
c
11
c
4
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h5.41187 × 10
277
u
67
− 3.29717 × 10
278
u
66
+ ··· + 7.63032 × 10
279
b + 2.06591 × 10
280
,
1.99190 × 10
278
u
67
− 1.24347 × 10
279
u
66
+ ··· + 1.41959 × 10
279
a + 5.26734 × 10
280
,
u
68
− 6u
67
+ ··· + 992u + 64i
I
u
2
= hu
8
− 3u
6
+ u
5
+ 4u
4
− 2u
3
− u
2
+ b + 2u − 1, −u
8
+ 2u
7
+ 2u
6
− 5u
5
− u
4
+ 5u
3
− u
2
+ a,
u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1i
I
v
1
= ha, −186v
5
+ 1767v
4
− 16759v
3
+ 279v
2
+ 385b − 93v + 306, v
6
− 10v
5
+ 95v
4
− 48v
3
+ 15v
2
− 5v + 1i
* 3 irreducible components of dim
C
= 0, with total 83 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
= h5.41 × 10
277
u
67
− 3.30 × 10
278
u
66
+ · · · + 7.63 × 10
279
b + 2.07 ×
10
280
, 1.99 × 10
278
u
67
− 1.24 × 10
279
u
66
+ · · · + 1.42 × 10
279
a + 5.27 ×
10
280
, u
68
− 6u
67
+ · · · + 992u + 64i
(i) Arc colorings
a
8
=
1
0
a
10
=
0
u
a
3
=
−0.140315u
67
+ 0.875931u
66
+ ··· − 399.413u − 37.1045
−0.00709259u
67
+ 0.0432114u
66
+ ··· − 24.8919u − 2.70750
a
7
=
1
u
2
a
4
=
−0.140548u
67
+ 0.877681u
66
+ ··· − 399.309u − 36.5756
−0.00717314u
67
+ 0.0436428u
66
+ ··· − 25.2257u − 2.73000
a
6
=
−0.0867373u
67
+ 0.540807u
66
+ ··· − 250.013u − 21.8923
−0.00337015u
67
+ 0.0205084u
66
+ ··· − 14.4347u − 1.57057
a
5
=
−0.0833671u
67
+ 0.520298u
66
+ ··· − 235.578u − 20.3217
−0.00337015u
67
+ 0.0205084u
66
+ ··· − 14.4347u − 1.57057
a
11
=
−0.118608u
67
+ 0.755698u
66
+ ··· − 203.655u − 6.99277
−0.00539155u
67
+ 0.0336077u
66
+ ··· − 12.9981u − 0.898136
a
2
=
−0.0830107u
67
+ 0.517632u
66
+ ··· − 243.251u − 23.6948
−0.00363676u
67
+ 0.0222357u
66
+ ··· − 13.9337u − 1.53678
a
1
=
−0.0181153u
67
+ 0.110616u
66
+ ··· − 71.0211u − 7.16788
u
2
a
9
=
−0.128840u
67
+ 0.819695u
66
+ ··· − 230.862u − 8.73309
−0.00484013u
67
+ 0.0303889u
66
+ ··· − 12.2087u − 0.842183
a
12
=
0.126251u
67
− 0.763024u
66
+ ··· + 580.255u + 57.9332
0.000316220u
67
− 0.00143516u
66
+ ··· + 6.38612u + 0.783678
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.416483u
67
+ 2.60331u
66
+ ··· − 1160.89u − 97.1731
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
68
+ 72u
67
+ ··· − 116u + 1
c
2
, c
4
u
68
− 12u
67
+ ··· + 4u − 1
c
3
, c
6
u
68
+ 3u
67
+ ··· + 2048u + 512
c
5
u
68
+ 4u
67
+ ··· + 20u
2
− 1
c
7
u
68
+ 6u
67
+ ··· − 992u + 64
c
8
, c
11
u
68
+ 5u
67
+ ··· − 61u + 1
c
9
u
68
− 4u
67
+ ··· − 1569175u − 179693
c
10
u
68
− 8u
67
+ ··· − 679u + 1423
c
12
u
68
+ 33u
67
+ ··· − 4365u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
68
− 140y
67
+ ··· + 13088y + 1
c
2
, c
4
y
68
− 72y
67
+ ··· + 116y + 1
c
3
, c
6
y
68
− 51y
67
+ ··· − 1048576y + 262144
c
5
y
68
− 16y
67
+ ··· − 40y + 1
c
7
y
68
+ 30y
67
+ ··· − 332800y + 4096
c
8
, c
11
y
68
+ 33y
67
+ ··· − 4365y + 1
c
9
y
68
− 20y
67
+ ··· − 70781434415y + 32289574249
c
10
y
68
− 68y
67
+ ··· + 88237y + 2024929
c
12
y
68
+ 9y
67
+ ··· − 19115909y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.950113 + 0.315579I
a = 0.548757 − 0.167876I
b = 0.776522 − 0.767567I
1.45198 − 0.17538I 0
u = −0.950113 − 0.315579I
a = 0.548757 + 0.167876I
b = 0.776522 + 0.767567I
1.45198 + 0.17538I 0
u = −0.138014 + 0.941313I
a = −1.52735 − 0.38576I
b = −0.026016 + 0.803652I
−1.98118 − 0.16998I 0
u = −0.138014 − 0.941313I
a = −1.52735 + 0.38576I
b = −0.026016 − 0.803652I
−1.98118 + 0.16998I 0
u = −0.985804 + 0.387544I
a = 0.0078436 − 0.0769643I
b = −0.113466 − 0.711289I
3.23957 − 1.57241I 0
u = −0.985804 − 0.387544I
a = 0.0078436 + 0.0769643I
b = −0.113466 + 0.711289I
3.23957 + 1.57241I 0
u = 0.654795 + 0.664515I
a = −0.052917 − 0.398943I
b = 0.109744 + 0.545343I
−1.99133 + 1.66625I 0. − 3.30828I
u = 0.654795 − 0.664515I
a = −0.052917 + 0.398943I
b = 0.109744 − 0.545343I
−1.99133 − 1.66625I 0. + 3.30828I
u = 0.918521 + 0.022770I
a = −0.80746 − 3.11284I
b = −0.45158 − 1.99901I
−2.78363 − 2.76140I 0. + 6.78295I
u = 0.918521 − 0.022770I
a = −0.80746 + 3.11284I
b = −0.45158 + 1.99901I
−2.78363 + 2.76140I 0. − 6.78295I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.618022 + 0.678734I
a = 0.34805 + 1.72657I
b = −0.0123186 + 0.1252700I
−7.66872 + 1.43842I −12.36030 + 0.I
u = 0.618022 − 0.678734I
a = 0.34805 − 1.72657I
b = −0.0123186 − 0.1252700I
−7.66872 − 1.43842I −12.36030 + 0.I
u = −0.833182 + 0.382913I
a = −1.22956 − 1.32718I
b = 0.0823456 − 0.0914731I
−9.13954 + 3.03771I −6.42466 + 6.40081I
u = −0.833182 − 0.382913I
a = −1.22956 + 1.32718I
b = 0.0823456 + 0.0914731I
−9.13954 − 3.03771I −6.42466 − 6.40081I
u = −0.343117 + 1.102390I
a = 1.62260 + 0.06591I
b = −1.11538 − 1.08043I
1.02080 − 2.73193I 0
u = −0.343117 − 1.102390I
a = 1.62260 − 0.06591I
b = −1.11538 + 1.08043I
1.02080 + 2.73193I 0
u = −0.091668 + 1.182840I
a = −1.058340 + 0.288071I
b = 0.110946 − 0.754708I
−5.18749 − 3.49319I 0
u = −0.091668 − 1.182840I
a = −1.058340 − 0.288071I
b = 0.110946 + 0.754708I
−5.18749 + 3.49319I 0
u = 1.058570 + 0.536792I
a = −0.0374936 + 0.0394319I
b = −0.072006 + 0.563424I
2.39963 + 7.06465I 0
u = 1.058570 − 0.536792I
a = −0.0374936 − 0.0394319I
b = −0.072006 − 0.563424I
2.39963 − 7.06465I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.291235 + 0.741989I
a = 1.43685 − 0.21711I
b = −0.423071 + 0.457603I
0.59153 − 2.55241I 2.37006 + 1.53670I
u = 0.291235 − 0.741989I
a = 1.43685 + 0.21711I
b = −0.423071 − 0.457603I
0.59153 + 2.55241I 2.37006 − 1.53670I
u = 0.284392 + 1.184020I
a = −1.348990 + 0.014290I
b = 0.066230 − 0.901010I
−4.78405 + 4.34186I 0
u = 0.284392 − 1.184020I
a = −1.348990 − 0.014290I
b = 0.066230 + 0.901010I
−4.78405 − 4.34186I 0
u = −0.378527 + 1.199800I
a = −0.185821 − 0.027577I
b = 0.08329 + 1.60214I
−3.90942 − 3.06813I 0
u = −0.378527 − 1.199800I
a = −0.185821 + 0.027577I
b = 0.08329 − 1.60214I
−3.90942 + 3.06813I 0
u = 0.618286 + 1.143470I
a = 0.941109 + 0.552542I
b = −0.161234 + 0.197997I
−9.06891 + 3.72651I 0
u = 0.618286 − 1.143470I
a = 0.941109 − 0.552542I
b = −0.161234 − 0.197997I
−9.06891 − 3.72651I 0
u = 1.215690 + 0.466052I
a = 0.729712 + 0.700660I
b = 0.98247 + 1.78974I
−1.26231 − 4.39904I 0
u = 1.215690 − 0.466052I
a = 0.729712 − 0.700660I
b = 0.98247 − 1.78974I
−1.26231 + 4.39904I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.533248 + 0.422514I
a = −3.12926 + 0.99004I
b = −0.520884 + 1.056390I
−1.175210 − 0.433161I −4.73090 + 4.14534I
u = −0.533248 − 0.422514I
a = −3.12926 − 0.99004I
b = −0.520884 − 1.056390I
−1.175210 + 0.433161I −4.73090 − 4.14534I
u = −0.395435 + 1.259920I
a = 1.202320 − 0.400059I
b = −0.210830 − 0.120552I
−13.78770 − 0.65730I 0
u = −0.395435 − 1.259920I
a = 1.202320 + 0.400059I
b = −0.210830 + 0.120552I
−13.78770 + 0.65730I 0
u = 0.195281 + 1.367220I
a = 0.161197 + 0.187003I
b = −0.03055 − 1.73074I
−8.15277 − 0.56922I 0
u = 0.195281 − 1.367220I
a = 0.161197 − 0.187003I
b = −0.03055 + 1.73074I
−8.15277 + 0.56922I 0
u = 0.501266 + 1.311640I
a = −0.032263 − 0.145766I
b = −0.00664 − 1.54510I
−6.75213 + 7.96693I 0
u = 0.501266 − 1.311640I
a = −0.032263 + 0.145766I
b = −0.00664 + 1.54510I
−6.75213 − 7.96693I 0
u = −0.651697 + 1.252300I
a = 1.368070 − 0.194338I
b = −0.50799 − 1.66891I
−1.42714 − 5.94125I 0
u = −0.651697 − 1.252300I
a = 1.368070 + 0.194338I
b = −0.50799 + 1.66891I
−1.42714 + 5.94125I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.443948 + 0.381193I
a = 0.023452 − 0.289831I
b = −0.092531 − 1.256890I
3.20421 − 1.15270I 2.54366 + 10.12386I
u = −0.443948 − 0.381193I
a = 0.023452 + 0.289831I
b = −0.092531 + 1.256890I
3.20421 + 1.15270I 2.54366 − 10.12386I
u = −0.68544 + 1.24203I
a = 0.920678 − 0.419746I
b = −0.202383 − 0.229028I
−11.5445 − 8.9372I 0
u = −0.68544 − 1.24203I
a = 0.920678 + 0.419746I
b = −0.202383 + 0.229028I
−11.5445 + 8.9372I 0
u = −0.047717 + 0.545973I
a = −0.040233 + 0.322065I
b = −0.19956 + 1.40398I
2.67134 + 4.86258I −14.4423 − 3.8383I
u = −0.047717 − 0.545973I
a = −0.040233 − 0.322065I
b = −0.19956 − 1.40398I
2.67134 − 4.86258I −14.4423 + 3.8383I
u = 0.53438 + 1.35483I
a = 1.200600 + 0.014989I
b = −0.49203 + 1.82310I
−6.53057 + 2.65488I 0
u = 0.53438 − 1.35483I
a = 1.200600 − 0.014989I
b = −0.49203 − 1.82310I
−6.53057 − 2.65488I 0
u = 0.477410 + 0.194259I
a = 3.46449 − 0.24479I
b = 0.066672 + 0.494530I
−1.07758 + 1.62874I 1.55460 − 6.14952I
u = 0.477410 − 0.194259I
a = 3.46449 + 0.24479I
b = 0.066672 − 0.494530I
−1.07758 − 1.62874I 1.55460 + 6.14952I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.72857 + 1.29465I
a = 1.294820 + 0.292927I
b = −0.44191 + 1.67576I
−4.00028 + 11.30660I 0
u = 0.72857 − 1.29465I
a = 1.294820 − 0.292927I
b = −0.44191 − 1.67576I
−4.00028 − 11.30660I 0
u = −0.199150 + 0.463613I
a = −5.65825 + 2.26682I
b = 0.979716 + 0.919145I
−1.11507 − 2.15821I −17.5757 + 1.3433I
u = −0.199150 − 0.463613I
a = −5.65825 − 2.26682I
b = 0.979716 − 0.919145I
−1.11507 + 2.15821I −17.5757 − 1.3433I
u = −0.207672 + 0.089139I
a = 11.0630 + 18.1211I
b = 0.455149 + 0.270879I
−1.10951 − 2.08005I 43.7323 + 52.4587I
u = −0.207672 − 0.089139I
a = 11.0630 − 18.1211I
b = 0.455149 − 0.270879I
−1.10951 + 2.08005I 43.7323 − 52.4587I
u = 1.06862 + 1.46334I
a = −1.083940 − 0.489279I
b = 1.02549 − 2.05791I
−10.9823 + 16.7933I 0
u = 1.06862 − 1.46334I
a = −1.083940 + 0.489279I
b = 1.02549 + 2.05791I
−10.9823 − 16.7933I 0
u = −1.00127 + 1.57480I
a = −1.057930 + 0.383092I
b = 1.22819 + 2.06366I
−8.36607 − 10.64720I 0
u = −1.00127 − 1.57480I
a = −1.057930 − 0.383092I
b = 1.22819 − 2.06366I
−8.36607 + 10.64720I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.122992
a = −7.00758
b = −0.657961
−1.12640 −9.50710
u = 1.18225 + 1.81842I
a = −0.873443 − 0.339937I
b = 1.41202 − 2.62610I
−14.9486 + 6.6050I 0
u = 1.18225 − 1.81842I
a = −0.873443 + 0.339937I
b = 1.41202 + 2.62610I
−14.9486 − 6.6050I 0
u = 2.21003 + 0.87540I
a = −0.404299 − 0.141048I
b = −2.64545 − 2.40849I
−8.52431 − 6.48393I 0
u = 2.21003 − 0.87540I
a = −0.404299 + 0.141048I
b = −2.64545 + 2.40849I
−8.52431 + 6.48393I 0
u = −2.40291
a = −0.382796
b = −3.59332
−4.25382 0
u = −0.40837 + 2.39079I
a = −0.860811 + 0.059303I
b = 3.47268 + 1.22842I
−5.26056 − 3.80306I 0
u = −0.40837 − 2.39079I
a = −0.860811 − 0.059303I
b = 3.47268 − 1.22842I
−5.26056 + 3.80306I 0
11
II. I
u
2
= hu
8
− 3u
6
+ u
5
+ 4u
4
− 2u
3
− u
2
+ b + 2u − 1, −u
8
+ 2u
7
+ 2u
6
−
5u
5
− u
4
+ 5u
3
− u
2
+ a, u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1i
(i) Arc colorings
a
8
=
1
0
a
10
=
0
u
a
3
=
u
8
− 2u
7
− 2u
6
+ 5u
5
+ u
4
− 5u
3
+ u
2
−u
8
+ 3u
6
− u
5
− 4u
4
+ 2u
3
+ u
2
− 2u + 1
a
7
=
1
u
2
a
4
=
u
8
− 2u
7
− 2u
6
+ 5u
5
+ u
4
− 5u
3
+ u
2
−u
8
+ 3u
6
− u
5
− 4u
4
+ 2u
3
+ u
2
− 2u + 1
a
6
=
1
u
2
a
5
=
−u
2
+ 1
u
2
a
11
=
−u
5
+ 2u
3
− u
u
5
− u
3
+ u
a
2
=
u
8
− 2u
7
− 2u
6
+ 5u
5
+ u
4
− 5u
3
+ 2u
2
− 1
−u
8
+ 3u
6
− u
5
− 4u
4
+ 2u
3
− 2u + 1
a
1
=
u
2
− 1
−u
2
a
9
=
−u
−u
3
+ u
a
12
=
u
8
− 3u
6
+ 3u
4
− 1
−u
8
+ 2u
6
− 2u
4
(ii) Obstruction class = 1
(iii) Cusp Shapes = 5u
8
− 9u
7
− 7u
6
+ 22u
5
− 2u
4
− 23u
3
+ 13u
2
− u − 9
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
9
c
3
, c
6
u
9
c
4
(u + 1)
9
c
5
u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
2
+ u + 1
c
7
u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1
c
8
u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1
c
9
u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1
c
10
, c
12
u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1
c
11
u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
9
c
3
, c
6
y
9
c
5
y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1
c
7
, c
9
y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1
c
8
, c
11
y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1
c
10
, c
12
y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.772920 + 0.510351I
a = −0.939568 − 0.981640I
b = 0.457852 − 1.072010I
−3.42837 + 2.09337I −8.61953 − 2.85927I
u = 0.772920 − 0.510351I
a = −0.939568 + 0.981640I
b = 0.457852 + 1.072010I
−3.42837 − 2.09337I −8.61953 + 2.85927I
u = −0.825933
a = 2.14893
b = 1.46592
−0.446489 5.48680
u = −1.173910 + 0.391555I
a = 0.119081 + 0.409451I
b = 0.522253 + 0.392004I
2.72642 − 1.33617I −5.51122 − 2.15019I
u = −1.173910 − 0.391555I
a = 0.119081 − 0.409451I
b = 0.522253 − 0.392004I
2.72642 + 1.33617I −5.51122 + 2.15019I
u = 0.141484 + 0.739668I
a = 2.26219 + 2.13290I
b = −1.63880 − 0.65075I
−1.02799 − 2.45442I −5.09778 + 12.45976I
u = 0.141484 − 0.739668I
a = 2.26219 − 2.13290I
b = −1.63880 + 0.65075I
−1.02799 + 2.45442I −5.09778 − 12.45976I
u = 1.172470 + 0.500383I
a = −0.016164 − 0.378317I
b = 0.425734 − 0.444312I
1.95319 + 7.08493I −9.51486 − 6.49599I
u = 1.172470 − 0.500383I
a = −0.016164 + 0.378317I
b = 0.425734 + 0.444312I
1.95319 − 7.08493I −9.51486 + 6.49599I
15
III. I
v
1
=
ha, −186v
5
+1767v
4
+· · ·+385b+306, v
6
−10v
5
+95v
4
−48v
3
+15v
2
−5v +1i
(i) Arc colorings
a
8
=
1
0
a
10
=
v
0
a
3
=
0
0.483117v
5
− 4.58961v
4
+ ··· + 0.241558v −0.794805
a
7
=
1
0
a
4
=
−0.483117v
5
+ 4.58961v
4
+ ··· − 0.241558v + 0.794805
0.483117v
5
− 4.58961v
4
+ ··· + 0.241558v −0.794805
a
6
=
1
0.207792v
5
− 1.97403v
4
+ ··· + 0.103896v + 1.41299
a
5
=
−0.207792v
5
+ 1.97403v
4
+ ··· − 0.103896v −0.412987
0.207792v
5
− 1.97403v
4
+ ··· + 0.103896v + 1.41299
a
11
=
−0.241558v
5
+ 2.36623v
4
+ ··· − 1.62078v + 0.483117
0.345455v
5
− 3.38182v
4
+ ··· + 5.07273v −0.690909
a
2
=
−1
0.207792v
5
− 1.97403v
4
+ ··· + 0.103896v + 1.41299
a
1
=
−1
0
a
9
=
0.103896v
5
− 1.01558v
4
+ ··· + 3.45195v −0.207792
0.345455v
5
− 3.38182v
4
+ ··· + 5.07273v −0.690909
a
12
=
−0.101299v
5
+ 1.03377v
4
+ ··· − 1.55065v −0.483117
0.345455v
5
− 3.38182v
4
+ ··· + 5.07273v −1.69091
(ii) Obstruction class = 1
(iii) Cusp Shapes =
2033
385
v
5
−
4009
77
v
4
+
190301
385
v
3
−
71002
385
v
2
+
3599
77
v −
5364
385
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
(u
3
− u
2
+ 2u − 1)
2
c
2
(u
3
+ u
2
− 1)
2
c
4
(u
3
− u
2
+ 1)
2
c
5
(u
3
+ 3u
2
+ 2u − 1)
2
c
6
(u
3
+ u
2
+ 2u + 1)
2
c
7
u
6
c
8
, c
12
(u
2
+ u + 1)
3
c
9
, c
10
u
6
+ 2u
5
+ 7u
4
− 8u
3
+ 7u
2
− 3u + 1
c
11
(u
2
− u + 1)
3
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
6
(y
3
+ 3y
2
+ 2y −1)
2
c
2
, c
4
(y
3
− y
2
+ 2y −1)
2
c
5
(y
3
− 5y
2
+ 10y −1)
2
c
7
y
6
c
8
, c
11
, c
12
(y
2
+ y + 1)
3
c
9
, c
10
y
6
+ 10y
5
+ 95y
4
+ 48y
3
+ 15y
2
+ 5y + 1
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.299729 + 0.124916I
a = 0
b = −0.215080 + 1.307140I
3.02413 + 0.79824I −7.24138 + 7.14502I
v = 0.299729 − 0.124916I
a = 0
b = −0.215080 − 1.307140I
3.02413 − 0.79824I −7.24138 − 7.14502I
v = −0.041684 + 0.322031I
a = 0
b = −0.215080 − 1.307140I
3.02413 − 4.85801I 8.78307 + 4.05565I
v = −0.041684 − 0.322031I
a = 0
b = −0.215080 + 1.307140I
3.02413 + 4.85801I 8.78307 − 4.05565I
v = 4.74195 + 8.21331I
a = 0
b = −0.569840
−1.11345 − 2.02988I 37.9583 − 74.4205I
v = 4.74195 − 8.21331I
a = 0
b = −0.569840
−1.11345 + 2.02988I 37.9583 + 74.4205I
19
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
9
)(u
3
− u
2
+ 2u − 1)
2
(u
68
+ 72u
67
+ ··· − 116u + 1)
c
2
((u − 1)
9
)(u
3
+ u
2
− 1)
2
(u
68
− 12u
67
+ ··· + 4u − 1)
c
3
u
9
(u
3
− u
2
+ 2u − 1)
2
(u
68
+ 3u
67
+ ··· + 2048u + 512)
c
4
((u + 1)
9
)(u
3
− u
2
+ 1)
2
(u
68
− 12u
67
+ ··· + 4u − 1)
c
5
(u
3
+ 3u
2
+ 2u − 1)
2
· (u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
2
+ u + 1)
· (u
68
+ 4u
67
+ ··· + 20u
2
− 1)
c
6
u
9
(u
3
+ u
2
+ 2u + 1)
2
(u
68
+ 3u
67
+ ··· + 2048u + 512)
c
7
u
6
(u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1)
· (u
68
+ 6u
67
+ ··· − 992u + 64)
c
8
(u
2
+ u + 1)
3
(u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1)
· (u
68
+ 5u
67
+ ··· − 61u + 1)
c
9
(u
6
+ 2u
5
+ 7u
4
− 8u
3
+ 7u
2
− 3u + 1)
· (u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1)
· (u
68
− 4u
67
+ ··· − 1569175u − 179693)
c
10
(u
6
+ 2u
5
+ 7u
4
− 8u
3
+ 7u
2
− 3u + 1)
· (u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
· (u
68
− 8u
67
+ ··· − 679u + 1423)
c
11
(u
2
− u + 1)
3
(u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1)
· (u
68
+ 5u
67
+ ··· − 61u + 1)
c
12
(u
2
+ u + 1)
3
· (u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
· (u
68
+ 33u
67
+ ··· − 4365u + 1)
20
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
9
)(y
3
+ 3y
2
+ 2y −1)
2
(y
68
− 140y
67
+ ··· + 13088y + 1)
c
2
, c
4
((y −1)
9
)(y
3
− y
2
+ 2y −1)
2
(y
68
− 72y
67
+ ··· + 116y + 1)
c
3
, c
6
y
9
(y
3
+ 3y
2
+ 2y −1)
2
(y
68
− 51y
67
+ ··· − 1048576y + 262144)
c
5
(y
3
− 5y
2
+ 10y −1)
2
· (y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1)
· (y
68
− 16y
67
+ ··· − 40y + 1)
c
7
y
6
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1)
· (y
68
+ 30y
67
+ ··· − 332800y + 4096)
c
8
, c
11
(y
2
+ y + 1)
3
· (y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1)
· (y
68
+ 33y
67
+ ··· − 4365y + 1)
c
9
(y
6
+ 10y
5
+ 95y
4
+ 48y
3
+ 15y
2
+ 5y + 1)
· (y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1)
· (y
68
− 20y
67
+ ··· − 70781434415y + 32289574249)
c
10
(y
6
+ 10y
5
+ 95y
4
+ 48y
3
+ 15y
2
+ 5y + 1)
· (y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1)
· (y
68
− 68y
67
+ ··· + 88237y + 2024929)
c
12
((y
2
+ y + 1)
3
)(y
9
+ 7y
8
+ ··· + 13y −1)
· (y
68
+ 9y
67
+ ··· − 19115909y + 1)
21
