12n
0365
(K12n
0365
)
A knot diagram
1
Linearized knot diagam
3 6 8 9 12 2 10 11 7 4 6 11
Solving Sequence
6,11
12 1
5,9
4 8 3 2 10 7
c
11
c
12
c
5
c
4
c
8
c
3
c
2
c
10
c
7
c
1
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h2.02561 × 10
72
u
49
+ 2.96495 × 10
72
u
48
+ ··· + 1.21339 × 10
74
b − 2.39856 × 10
74
,
− 7.63466 × 10
75
u
49
− 1.40414 × 10
76
u
48
+ ··· + 3.30041 × 10
76
a − 7.69213 × 10
76
,
u
50
+ 2u
49
+ ··· + 152u + 17i
I
u
2
= h−13362a
5
u + 25075a
4
u + ··· − 39143a − 74777,
a
6
− 5a
5
u − 5a
5
+ 14a
4
u + 2a
3
u + 9a
3
− 14a
2
u + 10a
2
− 5au − 13a + 3u, u
2
+ 1i
I
u
3
= h6u
12
+ 24u
10
− 3u
9
+ 36u
8
− 9u
7
+ 62u
6
− 9u
5
+ 82u
4
− 42u
3
+ 38u
2
+ 29b − 39u + 4,
− 4u
13
+ 22u
12
+ ··· + 29a + 92,
u
15
+ 5u
13
+ u
12
+ 10u
11
+ 4u
10
+ 18u
9
+ 6u
8
+ 29u
7
+ 7u
6
+ 25u
5
+ 7u
4
+ 11u
3
+ 3u
2
+ 3u + 1i
I
u
4
= hb, 5u
3
+ 6u
2
+ 4a + 3u − 5, u
4
+ u
3
+ u
2
+ 1i
* 4 irreducible components of dim
C
= 0, with total 81 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
= h2.03 × 10
72
u
49
+ 2.96 × 10
72
u
48
+ · · · + 1.21 × 10
74
b − 2.40 ×
10
74
, −7.63 × 10
75
u
49
− 1.40 × 10
76
u
48
+ · · · + 3.30 × 10
76
a − 7.69 ×
10
76
, u
50
+ 2u
49
+ · · · + 152u + 17i
(i) Arc colorings
a
6
=
0
u
a
11
=
1
0
a
12
=
1
u
2
a
1
=
u
2
+ 1
u
2
a
5
=
u
u
3
+ u
a
9
=
0.231325u
49
+ 0.425444u
48
+ ··· − 33.6337u + 2.33066
−0.0166939u
49
− 0.0244354u
48
+ ··· + 14.1364u + 1.97675
a
4
=
0.0189248u
49
+ 0.0297277u
48
+ ··· + 16.3779u − 0.398814
0.0435990u
49
+ 0.0673620u
48
+ ··· − 25.3529u − 1.26192
a
8
=
0.214631u
49
+ 0.401008u
48
+ ··· − 19.4973u + 4.30741
−0.0166939u
49
− 0.0244354u
48
+ ··· + 14.1364u + 1.97675
a
3
=
0.0365406u
49
+ 0.122206u
48
+ ··· + 121.471u + 14.8982
0.0672711u
49
+ 0.136915u
48
+ ··· − 14.6720u − 0.629900
a
2
=
0.0365406u
49
+ 0.122206u
48
+ ··· + 121.471u + 14.8982
0.0957047u
49
+ 0.192077u
48
+ ··· − 22.7602u − 1.46502
a
10
=
0.000887389u
49
+ 0.0626165u
48
+ ··· + 29.6760u − 5.39473
−0.0484569u
49
− 0.138861u
48
+ ··· − 24.3562u − 1.00579
a
7
=
0.00969873u
49
− 0.00903617u
48
+ ··· + 8.95010u + 9.56237
0.0484569u
49
+ 0.138861u
48
+ ··· + 24.3562u + 1.00579
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.0855761u
49
+ 0.331954u
48
+ ··· + 149.998u + 4.43588
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
50
+ 14u
49
+ ··· + 5136u + 289
c
2
, c
6
u
50
− 2u
49
+ ··· − 44u + 17
c
3
2(2u
50
+ 3u
49
+ ··· + 2699u + 3982)
c
4
2(2u
50
− 5u
49
+ ··· − 2584919u + 1407026)
c
5
, c
11
u
50
− 2u
49
+ ··· − 152u + 17
c
7
, c
9
u
50
+ 4u
49
+ ··· − 127u + 16
c
8
u
50
− 8u
49
+ ··· + 2976u + 256
c
10
u
50
+ 7u
49
+ ··· + 8u + 4
c
12
u
50
− 62u
49
+ ··· + 11952u + 289
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
50
+ 58y
49
+ ··· + 8224052y + 83521
c
2
, c
6
y
50
+ 14y
49
+ ··· + 5136y + 289
c
3
4(4y
50
+ 275y
49
+ ··· + 6.39567 × 10
8
y + 1.58563 × 10
7
)
c
4
4(4y
50
+ 115y
49
+ ··· + 2.59259 × 10
12
y + 1.97972 × 10
12
)
c
5
, c
11
y
50
+ 62y
49
+ ··· − 11952y + 289
c
7
, c
9
y
50
− 40y
49
+ ··· + 17759y + 256
c
8
y
50
+ 12y
49
+ ··· − 1020928y + 65536
c
10
y
50
+ y
49
+ ··· + 152y + 16
c
12
y
50
− 134y
49
+ ··· − 132056732y + 83521
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.737879 + 0.542454I
a = 0.847801 + 0.207388I
b = 0.83688 − 1.30980I
−0.03524 + 5.80828I 1.80389 − 9.34928I
u = −0.737879 − 0.542454I
a = 0.847801 − 0.207388I
b = 0.83688 + 1.30980I
−0.03524 − 5.80828I 1.80389 + 9.34928I
u = −0.564218 + 0.713559I
a = −0.596450 − 0.497655I
b = −1.25745 − 0.91387I
3.72647 + 3.16916I 9.86538 − 6.96751I
u = −0.564218 − 0.713559I
a = −0.596450 + 0.497655I
b = −1.25745 + 0.91387I
3.72647 − 3.16916I 9.86538 + 6.96751I
u = −0.322007 + 0.809098I
a = −1.58082 − 1.08895I
b = −0.855653 + 0.987594I
3.45702 − 0.25001I 11.35059 + 0.24450I
u = −0.322007 − 0.809098I
a = −1.58082 + 1.08895I
b = −0.855653 − 0.987594I
3.45702 + 0.25001I 11.35059 − 0.24450I
u = 0.092893 + 1.142970I
a = −0.576109 + 0.096453I
b = 1.149680 + 0.120400I
−0.168989 − 0.748778I 0
u = 0.092893 − 1.142970I
a = −0.576109 − 0.096453I
b = 1.149680 − 0.120400I
−0.168989 + 0.748778I 0
u = −0.015230 + 1.167690I
a = 0.345425 + 0.285302I
b = −1.194380 − 0.508201I
1.33404 − 5.95631I 0
u = −0.015230 − 1.167690I
a = 0.345425 − 0.285302I
b = −1.194380 + 0.508201I
1.33404 + 5.95631I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.058630 + 0.564153I
a = −0.684944 − 0.418407I
b = −0.89846 + 1.26634I
5.33295 + 11.18530I 0
u = −1.058630 − 0.564153I
a = −0.684944 + 0.418407I
b = −0.89846 − 1.26634I
5.33295 − 11.18530I 0
u = −0.810193 + 0.953463I
a = −0.207250 + 0.038953I
b = 0.336796 + 0.195309I
−5.21341 + 3.02399I 0
u = −0.810193 − 0.953463I
a = −0.207250 − 0.038953I
b = 0.336796 − 0.195309I
−5.21341 − 3.02399I 0
u = 0.572505 + 0.477849I
a = −1.106810 + 0.202089I
b = −0.158097 − 0.480865I
−0.01643 − 1.94498I 0.87974 + 3.02972I
u = 0.572505 − 0.477849I
a = −1.106810 − 0.202089I
b = −0.158097 + 0.480865I
−0.01643 + 1.94498I 0.87974 − 3.02972I
u = 1.151410 + 0.518515I
a = 0.369015 − 0.029245I
b = 0.089569 + 1.060610I
4.77019 − 2.61015I 0
u = 1.151410 − 0.518515I
a = 0.369015 + 0.029245I
b = 0.089569 − 1.060610I
4.77019 + 2.61015I 0
u = 0.226062 + 0.681121I
a = −0.697975 − 0.069523I
b = 0.239643 + 0.306301I
0.235392 − 1.266680I 2.17934 + 5.51042I
u = 0.226062 − 0.681121I
a = −0.697975 + 0.069523I
b = 0.239643 − 0.306301I
0.235392 + 1.266680I 2.17934 − 5.51042I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.409078 + 0.579666I
a = 5.55951 + 0.41408I
b = 0.290024 − 0.026703I
1.64557 − 1.46182I −49.4938 − 3.8392I
u = 0.409078 − 0.579666I
a = 5.55951 − 0.41408I
b = 0.290024 + 0.026703I
1.64557 + 1.46182I −49.4938 + 3.8392I
u = 0.20565 + 1.55151I
a = −0.362040 + 1.161030I
b = −0.507417 − 0.813843I
6.75526 − 4.85770I 0
u = 0.20565 − 1.55151I
a = −0.362040 − 1.161030I
b = −0.507417 + 0.813843I
6.75526 + 4.85770I 0
u = 0.01105 + 1.56936I
a = −0.251681 − 1.361360I
b = −0.187772 + 0.921101I
7.51460 − 1.56660I 0
u = 0.01105 − 1.56936I
a = −0.251681 + 1.361360I
b = −0.187772 − 0.921101I
7.51460 + 1.56660I 0
u = 0.175122 + 0.353457I
a = 1.98065 − 0.03015I
b = −0.960838 + 0.591042I
−1.43606 + 5.46886I −3.64987 − 5.42308I
u = 0.175122 − 0.353457I
a = 1.98065 + 0.03015I
b = −0.960838 − 0.591042I
−1.43606 − 5.46886I −3.64987 + 5.42308I
u = 0.146248 + 0.365089I
a = −2.47915 + 0.61555I
b = −0.095714 + 0.666726I
0.522597 − 1.281740I 1.45542 + 3.17634I
u = 0.146248 − 0.365089I
a = −2.47915 − 0.61555I
b = −0.095714 − 0.666726I
0.522597 + 1.281740I 1.45542 − 3.17634I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.11367 + 1.60575I
a = 0.943103 + 0.333746I
b = 0.806454 − 0.159713I
9.24524 − 3.37020I 0
u = 0.11367 − 1.60575I
a = 0.943103 − 0.333746I
b = 0.806454 + 0.159713I
9.24524 + 3.37020I 0
u = −0.25701 + 1.59600I
a = −0.06456 + 1.72172I
b = 1.33521 − 1.66319I
7.12550 + 9.55838I 0
u = −0.25701 − 1.59600I
a = −0.06456 − 1.72172I
b = 1.33521 + 1.66319I
7.12550 − 9.55838I 0
u = 0.05105 + 1.62454I
a = −0.41171 − 1.62511I
b = 0.91099 + 1.89793I
8.27324 − 2.71933I 0
u = 0.05105 − 1.62454I
a = −0.41171 + 1.62511I
b = 0.91099 − 1.89793I
8.27324 + 2.71933I 0
u = −0.39919 + 1.61362I
a = −0.21831 − 1.56417I
b = −1.22043 + 1.35112I
12.3391 + 16.5813I 0
u = −0.39919 − 1.61362I
a = −0.21831 + 1.56417I
b = −1.22043 − 1.35112I
12.3391 − 16.5813I 0
u = −0.16465 + 1.65456I
a = 0.967449 + 1.029180I
b = −1.61238 − 1.73076I
11.93760 + 5.99162I 0
u = −0.16465 − 1.65456I
a = 0.967449 − 1.029180I
b = −1.61238 + 1.73076I
11.93760 − 5.99162I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.06703 + 1.66709I
a = 0.677409 − 1.225970I
b = −1.96655 + 1.31397I
12.29170 + 1.16111I 0
u = −0.06703 − 1.66709I
a = 0.677409 + 1.225970I
b = −1.96655 − 1.31397I
12.29170 − 1.16111I 0
u = 0.43153 + 1.63520I
a = 0.267401 − 1.041780I
b = 0.639430 + 1.133170I
11.7068 − 8.4623I 0
u = 0.43153 − 1.63520I
a = 0.267401 + 1.041780I
b = 0.639430 − 1.133170I
11.7068 + 8.4623I 0
u = 0.26322 + 1.72469I
a = 0.021610 + 1.410470I
b = −0.98522 − 1.50703I
14.6583 − 9.1791I 0
u = 0.26322 − 1.72469I
a = 0.021610 − 1.410470I
b = −0.98522 + 1.50703I
14.6583 + 9.1791I 0
u = −0.30773 + 1.74544I
a = 0.296716 + 1.004440I
b = 0.262227 − 1.380400I
14.2488 + 0.8615I 0
u = −0.30773 − 1.74544I
a = 0.296716 − 1.004440I
b = 0.262227 + 1.380400I
14.2488 − 0.8615I 0
u = −0.145721 + 0.042290I
a = 1.42495 + 6.29903I
b = 1.003440 − 0.398879I
−3.59031 + 0.96879I −7.50173 − 1.09095I
u = −0.145721 − 0.042290I
a = 1.42495 − 6.29903I
b = 1.003440 + 0.398879I
−3.59031 − 0.96879I −7.50173 + 1.09095I
9
II. I
u
2
= h−1.34 × 10
4
a
5
u + 2.51 × 10
4
a
4
u + · · · − 3.91 × 10
4
a − 7.48 ×
10
4
, −5a
5
u + 14a
4
u + · · · + 10a
2
− 13a, u
2
+ 1i
(i) Arc colorings
a
6
=
0
u
a
11
=
1
0
a
12
=
1
−1
a
1
=
0
−1
a
5
=
u
0
a
9
=
a
0.500206a
5
u − 0.938682a
4
u + ··· + 1.46532a + 2.79927
a
4
=
−0.306255a
5
u + 1.70067a
4
u + ··· − 3.13716a − 0.883390
0.158387a
5
u − 0.374836a
4
u + ··· + 0.955303a + 1.85951
a
8
=
0.500206a
5
u − 0.938682a
4
u + ··· + 2.46532a + 2.79927
0.500206a
5
u − 0.938682a
4
u + ··· + 1.46532a + 2.79927
a
3
=
1
0.527009a
5
u − 2.31977a
4
u + ··· + 5.04107a + 2.85019
a
2
=
1
0.527009a
5
u − 2.31977a
4
u + ··· + 5.04107a + 1.85019
a
10
=
−0.144312a
5
u − 0.160484a
4
u + ··· − 0.144574a − 1.21825
0.00812339a
5
u + 2.51020a
4
u + ··· − 5.64115a + 2.53498
a
7
=
u
0.00812339a
5
u + 2.51020a
4
u + ··· − 5.64115a + 2.53498
(ii) Obstruction class = 1
(iii) Cusp Shapes =
45304
26713
a
5
u −
242984
26713
a
4
u + ··· +
450232
26713
a +
98588
26713
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
12
(u − 1)
12
c
2
, c
5
, c
6
c
11
(u
2
+ 1)
6
c
3
, c
10
u
12
− u
10
+ 5u
8
+ 6u
4
− 3u
2
+ 1
c
4
u
12
+ 3u
10
+ 5u
8
+ 4u
6
+ 2u
4
+ u
2
+ 1
c
7
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)
2
c
8
, c
9
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
2
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
12
(y − 1)
12
c
2
, c
5
, c
6
c
11
(y + 1)
12
c
3
, c
10
(y
6
− y
5
+ 5y
4
+ 6y
2
− 3y + 1)
2
c
4
(y
6
+ 3y
5
+ 5y
4
+ 4y
3
+ 2y
2
+ y + 1)
2
c
7
, c
8
, c
9
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = −0.973865 − 0.455201I
b = 1.073950 + 0.558752I
− 5.69302I 2.00000 + 5.51057I
u = 1.000000I
a = −0.008563 + 0.670038I
b = −1.002190 + 0.295542I
−1.89061 + 0.92430I −1.71672 − 0.79423I
u = 1.000000I
a = 1.320500 + 0.473476I
b = −1.002190 − 0.295542I
−1.89061 − 0.92430I −1.71672 + 0.79423I
u = 1.000000I
a = 0.143638 + 0.307302I
b = 1.073950 − 0.558752I
5.69302I 2.00000 − 5.51057I
u = 1.000000I
a = 1.96360 + 0.56994I
b = 0.428243 + 0.664531I
1.89061 + 0.92430I 5.71672 − 0.79423I
u = 1.000000I
a = 2.55469 + 3.43444I
b = 0.428243 − 0.664531I
1.89061 − 0.92430I 5.71672 + 0.79423I
u = − 1.000000I
a = −0.973865 + 0.455201I
b = 1.073950 − 0.558752I
5.69302I 2.00000 − 5.51057I
u = − 1.000000I
a = −0.008563 − 0.670038I
b = −1.002190 − 0.295542I
−1.89061 − 0.92430I −1.71672 + 0.79423I
u = − 1.000000I
a = 1.320500 − 0.473476I
b = −1.002190 + 0.295542I
−1.89061 + 0.92430I −1.71672 − 0.79423I
u = − 1.000000I
a = 0.143638 − 0.307302I
b = 1.073950 + 0.558752I
− 5.69302I 2.00000 + 5.51057I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = − 1.000000I
a = 1.96360 − 0.56994I
b = 0.428243 − 0.664531I
1.89061 − 0.92430I 5.71672 + 0.79423I
u = − 1.000000I
a = 2.55469 − 3.43444I
b = 0.428243 + 0.664531I
1.89061 + 0.92430I 5.71672 − 0.79423I
14
III. I
u
3
= h6u
12
+ 24u
10
+ · · · + 29b + 4, −4u
13
+ 22u
12
+ · · · + 29a +
92, u
15
+ 5u
13
+ · · · + 3u + 1i
(i) Arc colorings
a
6
=
0
u
a
11
=
1
0
a
12
=
1
u
2
a
1
=
u
2
+ 1
u
2
a
5
=
u
u
3
+ u
a
9
=
0.137931u
13
− 0.758621u
12
+ ··· + 0.689655u − 3.17241
−0.206897u
12
− 0.827586u
10
+ ··· + 1.34483u − 0.137931
a
4
=
−0.586207u
13
+ 0.965517u
12
+ ··· − u + 3.31034
0.379310u
12
+ 1.51724u
10
+ ··· + 1.03448u + 0.586207
a
8
=
0.137931u
13
− 0.965517u
12
+ ··· + 2.03448u − 3.31034
−0.206897u
12
− 0.827586u
10
+ ··· + 1.34483u − 0.137931
a
3
=
1
0
a
2
=
1
u
2
a
10
=
0.758621u
12
+ 3.03448u
10
+ ··· + 0.0689655u + 3.17241
−u
3
− u
a
7
=
u
u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
28
29
u
12
+
112
29
u
10
+
44
29
u
9
+
168
29
u
8
+
132
29
u
7
+
328
29
u
6
+
132
29
u
5
+
460
29
u
4
+
268
29
u
3
+
216
29
u
2
+
224
29
u+
154
29
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
15
+ 10u
14
+ ··· + 3u − 1
c
2
, c
5
, c
6
c
11
u
15
+ 5u
13
+ ··· + 3u − 1
c
3
, c
8
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
3
c
4
, c
7
, c
9
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
3
c
10
(u
5
− 3u
4
+ 4u
3
− u
2
− u + 1)
3
c
12
u
15
− 10u
14
+ ··· + 3u + 1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
12
y
15
− 10y
14
+ ··· + 95y − 1
c
2
, c
5
, c
6
c
11
y
15
+ 10y
14
+ ··· + 3y − 1
c
3
, c
8
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y − 1)
3
c
4
, c
7
, c
9
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y − 1)
3
c
10
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y − 1)
3
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.157313 + 1.036460I
a = −3.17294 + 2.29859I
b = −0.766826
2.40108 3.48114 + 0.I
u = 0.157313 − 1.036460I
a = −3.17294 − 2.29859I
b = −0.766826
2.40108 3.48114 + 0.I
u = 0.001127 + 1.228660I
a = −1.55554 + 2.09943I
b = 0.339110 − 0.822375I
0.32910 + 1.53058I 2.51511 − 4.43065I
u = 0.001127 − 1.228660I
a = −1.55554 − 2.09943I
b = 0.339110 + 0.822375I
0.32910 − 1.53058I 2.51511 + 4.43065I
u = −1.021430 + 0.758717I
a = 0.403745 − 0.032528I
b = −0.455697 − 1.200150I
5.87256 − 4.40083I 6.74431 + 3.49859I
u = −1.021430 − 0.758717I
a = 0.403745 + 0.032528I
b = −0.455697 + 1.200150I
5.87256 + 4.40083I 6.74431 − 3.49859I
u = 0.363053 + 0.617188I
a = −0.0663988 + 0.1194530I
b = 0.339110 + 0.822375I
0.32910 − 1.53058I 2.51511 + 4.43065I
u = 0.363053 − 0.617188I
a = −0.0663988 − 0.1194530I
b = 0.339110 − 0.822375I
0.32910 + 1.53058I 2.51511 − 4.43065I
u = −0.364180 + 0.611475I
a = −1.022160 + 0.511883I
b = 0.339110 + 0.822375I
0.32910 − 1.53058I 2.51511 + 4.43065I
u = −0.364180 − 0.611475I
a = −1.022160 − 0.511883I
b = 0.339110 − 0.822375I
0.32910 + 1.53058I 2.51511 − 4.43065I
18
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.975116 + 0.872207I
a = −0.457247 + 0.357517I
b = −0.455697 − 1.200150I
5.87256 − 4.40083I 6.74431 + 3.49859I
u = 0.975116 − 0.872207I
a = −0.457247 − 0.357517I
b = −0.455697 + 1.200150I
5.87256 + 4.40083I 6.74431 − 3.49859I
u = 0.04631 + 1.63092I
a = 0.480320 − 1.202230I
b = −0.455697 + 1.200150I
5.87256 + 4.40083I 6.74431 − 3.49859I
u = 0.04631 − 1.63092I
a = 0.480320 + 1.202230I
b = −0.455697 − 1.200150I
5.87256 − 4.40083I 6.74431 + 3.49859I
u = −0.314625
a = −4.21957
b = −0.766826
2.40108 3.48110
19
IV. I
u
4
= hb, 5u
3
+ 6u
2
+ 4a + 3u − 5, u
4
+ u
3
+ u
2
+ 1i
(i) Arc colorings
a
6
=
0
u
a
11
=
1
0
a
12
=
1
u
2
a
1
=
u
2
+ 1
u
2
a
5
=
u
u
3
+ u
a
9
=
−
5
4
u
3
−
3
2
u
2
−
3
4
u +
5
4
0
a
4
=
−
1
8
u
3
−
7
4
u
2
−
15
8
u −
19
8
u
3
+ u
a
8
=
−
5
4
u
3
−
3
2
u
2
−
3
4
u +
5
4
0
a
3
=
u
u
3
+ u
a
2
=
u
2u
3
+ u
a
10
=
−
9
4
u
3
−
3
2
u
2
−
3
4
u +
5
4
−u
3
− 2u
2
+ u − 2
a
7
=
u
3
u
3
+ 2u
2
− u + 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
71
16
u
3
+
71
8
u
2
−
113
16
u +
211
16
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
4
− 5u
3
+ 7u
2
− 2u + 1
c
2
u
4
+ u
3
+ 3u
2
+ 2u + 1
c
3
, c
4
2(2u
4
+ u
3
+ 5u
2
− u + 1)
c
5
u
4
− u
3
+ u
2
+ 1
c
6
, c
12
u
4
− u
3
+ 3u
2
− 2u + 1
c
7
(u + 1)
4
c
8
u
4
c
9
(u − 1)
4
c
10
u
4
− u
3
+ 5u
2
+ u + 2
c
11
u
4
+ u
3
+ u
2
+ 1
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
4
− 11y
3
+ 31y
2
+ 10y + 1
c
2
, c
6
, c
12
y
4
+ 5y
3
+ 7y
2
+ 2y + 1
c
3
, c
4
4(4y
4
+ 19y
3
+ 31y
2
+ 9y + 1)
c
5
, c
11
y
4
+ y
3
+ 3y
2
+ 2y + 1
c
7
, c
9
(y − 1)
4
c
8
y
4
c
10
y
4
+ 9y
3
+ 31y
2
+ 19y + 4
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.351808 + 0.720342I
a = 2.20896 − 1.16763I
b = 0
1.85594 − 1.41510I 9.43312 − 0.11741I
u = 0.351808 − 0.720342I
a = 2.20896 + 1.16763I
b = 0
1.85594 + 1.41510I 9.43312 + 0.11741I
u = −0.851808 + 0.911292I
a = 0.166035 + 0.111704I
b = 0
−5.14581 + 3.16396I 11.5981 − 25.6585I
u = −0.851808 − 0.911292I
a = 0.166035 − 0.111704I
b = 0
−5.14581 − 3.16396I 11.5981 + 25.6585I
23
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
12
)(u
4
− 5u
3
+ ··· − 2u + 1)(u
15
+ 10u
14
+ ··· + 3u − 1)
· (u
50
+ 14u
49
+ ··· + 5136u + 289)
c
2
((u
2
+ 1)
6
)(u
4
+ u
3
+ 3u
2
+ 2u + 1)(u
15
+ 5u
13
+ ··· + 3u − 1)
· (u
50
− 2u
49
+ ··· − 44u + 17)
c
3
4(2u
4
+ u
3
+ 5u
2
− u + 1)(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
3
· (u
12
− u
10
+ 5u
8
+ 6u
4
− 3u
2
+ 1)(2u
50
+ 3u
49
+ ··· + 2699u + 3982)
c
4
4(2u
4
+ u
3
+ 5u
2
− u + 1)(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
3
· (u
12
+ 3u
10
+ 5u
8
+ 4u
6
+ 2u
4
+ u
2
+ 1)
· (2u
50
− 5u
49
+ ··· − 2584919u + 1407026)
c
5
((u
2
+ 1)
6
)(u
4
− u
3
+ u
2
+ 1)(u
15
+ 5u
13
+ ··· + 3u − 1)
· (u
50
− 2u
49
+ ··· − 152u + 17)
c
6
((u
2
+ 1)
6
)(u
4
− u
3
+ 3u
2
− 2u + 1)(u
15
+ 5u
13
+ ··· + 3u − 1)
· (u
50
− 2u
49
+ ··· − 44u + 17)
c
7
(u + 1)
4
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
3
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)
2
· (u
50
+ 4u
49
+ ··· − 127u + 16)
c
8
u
4
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
3
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
2
· (u
50
− 8u
49
+ ··· + 2976u + 256)
c
9
(u − 1)
4
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
3
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
2
· (u
50
+ 4u
49
+ ··· − 127u + 16)
c
10
(u
4
− u
3
+ 5u
2
+ u + 2)(u
5
− 3u
4
+ 4u
3
− u
2
− u + 1)
3
· (u
12
− u
10
+ 5u
8
+ 6u
4
− 3u
2
+ 1)(u
50
+ 7u
49
+ ··· + 8u + 4)
c
11
((u
2
+ 1)
6
)(u
4
+ u
3
+ u
2
+ 1)(u
15
+ 5u
13
+ ··· + 3u − 1)
· (u
50
− 2u
49
+ ··· − 152u + 17)
c
12
((u − 1)
12
)(u
4
− u
3
+ 3u
2
− 2u + 1)(u
15
− 10u
14
+ ··· + 3u + 1)
· (u
50
− 62u
49
+ ··· + 11952u + 289)
24
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y − 1)
12
)(y
4
− 11y
3
+ ··· + 10y + 1)(y
15
− 10y
14
+ ··· + 95y − 1)
· (y
50
+ 58y
49
+ ··· + 8224052y + 83521)
c
2
, c
6
((y + 1)
12
)(y
4
+ 5y
3
+ ··· + 2y + 1)(y
15
+ 10y
14
+ ··· + 3y − 1)
· (y
50
+ 14y
49
+ ··· + 5136y + 289)
c
3
16(4y
4
+ 19y
3
+ 31y
2
+ 9y + 1)(y
5
+ 3y
4
+ 4y
3
+ y
2
− y − 1)
3
· (y
6
− y
5
+ 5y
4
+ 6y
2
− 3y + 1)
2
· (4y
50
+ 275y
49
+ ··· + 639567407y + 15856324)
c
4
16(4y
4
+ 19y
3
+ 31y
2
+ 9y + 1)(y
5
− 5y
4
+ 8y
3
− 3y
2
− y − 1)
3
· (y
6
+ 3y
5
+ 5y
4
+ 4y
3
+ 2y
2
+ y + 1)
2
· (4y
50
+ 115y
49
+ ··· + 2592594386231y + 1979722164676)
c
5
, c
11
((y + 1)
12
)(y
4
+ y
3
+ 3y
2
+ 2y + 1)(y
15
+ 10y
14
+ ··· + 3y − 1)
· (y
50
+ 62y
49
+ ··· − 11952y + 289)
c
7
, c
9
(y − 1)
4
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y − 1)
3
· (y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
· (y
50
− 40y
49
+ ··· + 17759y + 256)
c
8
y
4
(y
5
+ 3y
4
+ ··· − y − 1)
3
(y
6
− 3y
5
+ ··· − y + 1)
2
· (y
50
+ 12y
49
+ ··· − 1020928y + 65536)
c
10
(y
4
+ 9y
3
+ 31y
2
+ 19y + 4)(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y − 1)
3
· ((y
6
− y
5
+ 5y
4
+ 6y
2
− 3y + 1)
2
)(y
50
+ y
49
+ ··· + 152y + 16)
c
12
((y − 1)
12
)(y
4
+ 5y
3
+ ··· + 2y + 1)(y
15
− 10y
14
+ ··· + 95y − 1)
· (y
50
− 134y
49
+ ··· − 132056732y + 83521)
25
