12n
0364
(K12n
0364
)
A knot diagram
1
Linearized knot diagam
3 5 10 12 2 9 3 4 7 8 5 11
Solving Sequence
5,11
12 1
4,8
10 3 2 6 7 9
c
11
c
12
c
4
c
10
c
3
c
2
c
5
c
7
c
9
c
1
, c
6
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h1.65018 × 10
76
u
49
− 3.54268 × 10
76
u
48
+ ··· + 4.05963 × 10
77
b − 6.66248 × 10
77
,
− 6.81584 × 10
77
u
49
+ 7.40970 × 10
76
u
48
+ ··· + 1.10422 × 10
80
a − 9.55385 × 10
79
,
u
50
− 2u
49
+ ··· − 44u + 17i
I
u
2
= h−6839a
5
u − 100530a
4
u + ··· − 679911a + 101996,
a
6
− 5a
5
u − 6a
5
+ 20a
4
u + 2a
4
− 16a
3
u + 22a
3
− 6a
2
u − 29a
2
+ 8au + 7a − u, 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, −3u
3
− 2u
2
+ 4a − 7u − 7, u
4
− u
3
+ 3u
2
− 2u + 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
= h1.65 × 10
76
u
49
− 3.54 × 10
76
u
48
+ · · · + 4.06 × 10
77
b − 6.66 ×
10
77
, −6.82 × 10
77
u
49
+ 7.41 × 10
76
u
48
+ · · · + 1.10 × 10
80
a − 9.55 ×
10
79
, u
50
− 2u
49
+ · · · − 44u + 17i
(i) Arc colorings
a
5
=
0
u
a
11
=
1
0
a
12
=
1
u
2
a
1
=
u
2
+ 1
u
2
a
4
=
u
u
3
+ u
a
8
=
0.00617254u
49
− 0.000671034u
48
+ ··· − 2.01092u + 0.865212
−0.0406485u
49
+ 0.0872659u
48
+ ··· − 5.79426u + 1.64115
a
10
=
−0.0282098u
49
+ 0.0868361u
48
+ ··· − 8.88364u + 0.883519
−0.0345582u
49
+ 0.0421933u
48
+ ··· + 0.600393u − 0.0303720
a
3
=
0.0506811u
49
− 0.0563455u
48
+ ··· + 2.97171u − 2.07332
0.0131686u
49
− 0.0624266u
48
+ ··· + 4.05011u − 1.14409
a
2
=
0.0506811u
49
− 0.0563455u
48
+ ··· + 2.97171u − 2.07332
0.0188729u
49
− 0.0895465u
48
+ ··· + 5.16927u − 1.90937
a
6
=
0.0138068u
49
− 0.0333179u
48
+ ··· + 11.0786u − 1.72666
0.0968175u
49
− 0.183692u
48
+ ··· + 0.235614u − 0.540740
a
7
=
−0.0145850u
49
+ 0.0659148u
48
+ ··· − 7.07269u + 2.34119
−0.00275585u
49
− 0.0265966u
48
+ ··· + 6.09637u − 1.52987
a
9
=
0.0367912u
49
− 0.0525595u
48
+ ··· − 2.24087u + 0.402118
−0.0284670u
49
+ 0.0549091u
48
+ ··· − 6.13338u + 1.01913
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.692160u
49
− 1.33300u
48
+ ··· + 22.8194u − 11.6257
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
50
+ 62u
49
+ ··· − 11952u + 289
c
2
, c
5
u
50
+ 2u
49
+ ··· + 152u + 17
c
3
u
50
− 7u
49
+ ··· − 8u + 4
c
4
, c
11
u
50
+ 2u
49
+ ··· + 44u + 17
c
6
, c
9
u
50
− 4u
49
+ ··· + 127u + 16
c
7
2(2u
50
− 3u
49
+ ··· − 2699u + 3982)
c
8
2(2u
50
+ 5u
49
+ ··· + 2584919u + 1407026)
c
10
u
50
+ 8u
49
+ ··· − 2976u + 256
c
12
u
50
− 14u
49
+ ··· − 5136u + 289
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
50
− 134y
49
+ ··· − 132056732y + 83521
c
2
, c
5
y
50
+ 62y
49
+ ··· − 11952y + 289
c
3
y
50
+ y
49
+ ··· + 152y + 16
c
4
, c
11
y
50
+ 14y
49
+ ··· + 5136y + 289
c
6
, c
9
y
50
− 40y
49
+ ··· + 17759y + 256
c
7
4(4y
50
+ 275y
49
+ ··· + 6.39567 × 10
8
y + 1.58563 × 10
7
)
c
8
4(4y
50
+ 115y
49
+ ··· + 2.59259 × 10
12
y + 1.97972 × 10
12
)
c
10
y
50
+ 12y
49
+ ··· − 1020928y + 65536
c
12
y
50
+ 58y
49
+ ··· + 8224052y + 83521
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.068272 + 1.028420I
a = −0.309956 + 0.515004I
b = 1.003440 − 0.398879I
3.59031 − 0.96879I 7.50173 + 1.09095I
u = −0.068272 − 1.028420I
a = −0.309956 − 0.515004I
b = 1.003440 + 0.398879I
3.59031 + 0.96879I 7.50173 − 1.09095I
u = 0.480788 + 0.815784I
a = 1.12478 + 0.91870I
b = −0.158097 + 0.480865I
0.01643 − 1.94498I −0.87974 + 3.02972I
u = 0.480788 − 0.815784I
a = 1.12478 − 0.91870I
b = −0.158097 − 0.480865I
0.01643 + 1.94498I −0.87974 − 3.02972I
u = −0.636460 + 0.850925I
a = −0.41580 + 1.74505I
b = 0.83688 + 1.30980I
0.03524 + 5.80828I −1.80389 − 9.34928I
u = −0.636460 − 0.850925I
a = −0.41580 − 1.74505I
b = 0.83688 − 1.30980I
0.03524 − 5.80828I −1.80389 + 9.34928I
u = 0.039464 + 1.141930I
a = 0.518130 − 0.112235I
b = −0.960838 + 0.591042I
1.43606 − 5.46886I 3.64987 + 5.42308I
u = 0.039464 − 1.141930I
a = 0.518130 + 0.112235I
b = −0.960838 − 0.591042I
1.43606 + 5.46886I 3.64987 − 5.42308I
u = −0.591483 + 0.619229I
a = −0.901275 + 0.820990I
b = −1.25745 + 0.91387I
−3.72647 + 3.16916I −9.86538 − 6.96751I
u = −0.591483 − 0.619229I
a = −0.901275 − 0.820990I
b = −1.25745 − 0.91387I
−3.72647 − 3.16916I −9.86538 + 6.96751I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.914944 + 0.798812I
a = −0.044773 + 0.967248I
b = −0.187772 + 0.921101I
−7.51460 + 1.56660I 0. − 4.59872I
u = −0.914944 − 0.798812I
a = −0.044773 − 0.967248I
b = −0.187772 − 0.921101I
−7.51460 − 1.56660I 0. + 4.59872I
u = 0.114923 + 0.775485I
a = 1.67601 − 1.41606I
b = −0.095714 − 0.666726I
−0.522597 − 1.281740I −1.45542 + 3.17634I
u = 0.114923 − 0.775485I
a = 1.67601 + 1.41606I
b = −0.095714 + 0.666726I
−0.522597 + 1.281740I −1.45542 − 3.17634I
u = 0.391145 + 0.663226I
a = −5.02638 + 0.41948I
b = 0.290024 + 0.026703I
−1.64557 − 1.46182I 49.4938 − 3.8392I
u = 0.391145 − 0.663226I
a = −5.02638 − 0.41948I
b = 0.290024 − 0.026703I
−1.64557 + 1.46182I 49.4938 + 3.8392I
u = 1.016150 + 0.749484I
a = 0.920704 + 0.734457I
b = 0.91099 + 1.89793I
−8.27324 + 2.71933I 0
u = 1.016150 − 0.749484I
a = 0.920704 − 0.734457I
b = 0.91099 − 1.89793I
−8.27324 − 2.71933I 0
u = −0.914753 + 0.943767I
a = −1.186270 − 0.030672I
b = 0.806454 − 0.159713I
−9.24524 + 3.37020I 0
u = −0.914753 − 0.943767I
a = −1.186270 + 0.030672I
b = 0.806454 + 0.159713I
−9.24524 − 3.37020I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.814625 + 1.036590I
a = 0.774534 − 0.946809I
b = −0.507417 − 0.813843I
−6.75526 + 4.85770I 0
u = −0.814625 − 1.036590I
a = 0.774534 + 0.946809I
b = −0.507417 + 0.813843I
−6.75526 − 4.85770I 0
u = −0.870996 + 1.028870I
a = 0.45821 − 1.35144I
b = −0.89846 − 1.26634I
−5.33295 + 11.18530I 0
u = −0.870996 − 1.028870I
a = 0.45821 + 1.35144I
b = −0.89846 + 1.26634I
−5.33295 − 11.18530I 0
u = 1.009310 + 0.913920I
a = 0.34174 + 1.43865I
b = −1.96655 + 1.31397I
−12.29170 − 1.16111I 0
u = 1.009310 − 0.913920I
a = 0.34174 − 1.43865I
b = −1.96655 − 1.31397I
−12.29170 + 1.16111I 0
u = 1.258650 + 0.560245I
a = −0.518042 − 0.849518I
b = −0.98522 − 1.50703I
−14.6583 + 9.1791I 0
u = 1.258650 − 0.560245I
a = −0.518042 + 0.849518I
b = −0.98522 + 1.50703I
−14.6583 − 9.1791I 0
u = 0.952955 + 1.024640I
a = −0.865928 − 0.017593I
b = −1.61238 − 1.73076I
−11.93760 − 5.99162I 0
u = 0.952955 − 1.024640I
a = −0.865928 + 0.017593I
b = −1.61238 + 1.73076I
−11.93760 + 5.99162I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.851045 + 1.112060I
a = −0.80295 − 1.35413I
b = 1.33521 − 1.66319I
−7.12550 − 9.55838I 0
u = 0.851045 − 1.112060I
a = −0.80295 + 1.35413I
b = 1.33521 + 1.66319I
−7.12550 + 9.55838I 0
u = −1.309460 + 0.524121I
a = 0.222301 − 0.788694I
b = 0.262227 − 1.380400I
−14.2488 − 0.8615I 0
u = −1.309460 − 0.524121I
a = 0.222301 + 0.788694I
b = 0.262227 + 1.380400I
−14.2488 + 0.8615I 0
u = −0.404137 + 0.399130I
a = −0.80482 − 2.22372I
b = −0.855653 − 0.987594I
−3.45702 − 0.25001I −11.35059 + 0.24450I
u = −0.404137 − 0.399130I
a = −0.80482 + 2.22372I
b = −0.855653 + 0.987594I
−3.45702 + 0.25001I −11.35059 − 0.24450I
u = 0.90070 + 1.11853I
a = −0.589704 − 0.573106I
b = 0.089569 − 1.060610I
−4.77019 − 2.61015I 0
u = 0.90070 − 1.11853I
a = −0.589704 + 0.573106I
b = 0.089569 + 1.060610I
−4.77019 + 2.61015I 0
u = 0.250161 + 0.501573I
a = 1.39564 − 0.73889I
b = 0.239643 − 0.306301I
−0.235392 − 1.266680I −2.17934 + 5.51042I
u = 0.250161 − 0.501573I
a = 1.39564 + 0.73889I
b = 0.239643 + 0.306301I
−0.235392 + 1.266680I −2.17934 − 5.51042I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.176902 + 0.505057I
a = 1.72876 − 0.17664I
b = −1.194380 − 0.508201I
−1.33404 + 5.95631I −8.20112 − 6.23089I
u = −0.176902 − 0.505057I
a = 1.72876 + 0.17664I
b = −1.194380 + 0.508201I
−1.33404 − 5.95631I −8.20112 + 6.23089I
u = 0.82735 + 1.27724I
a = 0.84861 + 1.21665I
b = −1.22043 + 1.35112I
−12.3391 − 16.5813I 0
u = 0.82735 − 1.27724I
a = 0.84861 − 1.21665I
b = −1.22043 − 1.35112I
−12.3391 + 16.5813I 0
u = 0.14425 + 1.53138I
a = 0.0056819 − 0.0217967I
b = 0.336796 + 0.195309I
5.21341 − 3.02399I 0
u = 0.14425 − 1.53138I
a = 0.0056819 + 0.0217967I
b = 0.336796 − 0.195309I
5.21341 + 3.02399I 0
u = −0.84092 + 1.31844I
a = −0.628284 + 0.707391I
b = 0.639430 + 1.133170I
−11.7068 + 8.4623I 0
u = −0.84092 − 1.31844I
a = −0.628284 − 0.707391I
b = 0.639430 − 1.133170I
−11.7068 − 8.4623I 0
u = 0.306063 + 0.264763I
a = −0.67826 − 2.24848I
b = 1.149680 + 0.120400I
0.168989 + 0.748778I −4.44695 + 0.25975I
u = 0.306063 − 0.264763I
a = −0.67826 + 2.24848I
b = 1.149680 − 0.120400I
0.168989 − 0.748778I −4.44695 − 0.25975I
9
II. I
u
2
= h−6839a
5
u − 1.01 × 10
5
a
4
u + · · · − 6.80 × 10
5
a + 1.02 ×
10
5
, −5a
5
u + 20a
4
u + · · · − 29a
2
+ 7a, u
2
+ 1i
(i) Arc colorings
a
5
=
0
u
a
11
=
1
0
a
12
=
1
−1
a
1
=
0
−1
a
4
=
u
0
a
8
=
a
0.163327a
5
u + 2.40083a
4
u + ··· + 16.2375a − 2.43584
a
10
=
−0.0197263a
5
u + 0.856399a
4
u + ··· + 3.63150a + 0.836673
0.0806247a
5
u − 0.463927a
4
u + ··· − 1.15007a + 0.616698
a
3
=
1
0.320947a
5
u − 3.11277a
4
u + ··· − 7.63413a + 2.20818
a
2
=
1
0.320947a
5
u − 3.11277a
4
u + ··· − 7.63413a + 1.20818
a
6
=
u
0.283094a
5
u − 0.227306a
4
u + ··· + 5.61761a − 1.94421
a
7
=
0.0650539a
5
u − 2.95016a
4
u + ··· − 12.4434a + 2.11490
0.186540a
5
u − 2.61663a
4
u + ··· − 7.68727a + 0.569914
a
9
=
0.163327a
5
u + 2.40083a
4
u + ··· + 17.2375a − 2.43584
0.163327a
5
u + 2.40083a
4
u + ··· + 16.2375a − 2.43584
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
6556
41873
a
5
u +
362488
41873
a
4
u + ··· +
1586112
41873
a −
146544
41873
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
12
(u − 1)
12
c
2
, c
4
, c
5
c
11
(u
2
+ 1)
6
c
3
, c
7
u
12
− u
10
+ 5u
8
+ 6u
4
− 3u
2
+ 1
c
6
, c
10
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
2
c
8
u
12
+ 3u
10
+ 5u
8
+ 4u
6
+ 2u
4
+ u
2
+ 1
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
4
, c
5
c
11
(y + 1)
12
c
3
, c
7
(y
6
− y
5
+ 5y
4
+ 6y
2
− 3y + 1)
2
c
6
, c
9
, c
10
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
c
8
(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 = 1.217590 − 0.251449I
b = −1.073950 + 0.558752I
− 5.69302I −2.00000 + 5.51057I
u = 1.000000I
a = −1.010760 + 0.965580I
b = 1.002190 − 0.295542I
1.89061 − 0.92430I 1.71672 + 0.79423I
u = 1.000000I
a = 0.318306 + 0.177934I
b = 1.002190 + 0.295542I
1.89061 + 0.92430I 1.71672 − 0.79423I
u = 1.000000I
a = 0.100084 + 0.103550I
b = −1.073950 − 0.558752I
5.69302I −2.00000 − 5.51057I
u = 1.000000I
a = 2.39185 + 1.23447I
b = −0.428243 − 0.664531I
−1.89061 − 0.92430I −5.71672 + 0.79423I
u = 1.000000I
a = 2.98293 + 2.76991I
b = −0.428243 + 0.664531I
−1.89061 + 0.92430I −5.71672 − 0.79423I
u = − 1.000000I
a = 1.217590 + 0.251449I
b = −1.073950 − 0.558752I
5.69302I −2.00000 − 5.51057I
u = − 1.000000I
a = −1.010760 − 0.965580I
b = 1.002190 + 0.295542I
1.89061 + 0.92430I 1.71672 − 0.79423I
u = − 1.000000I
a = 0.318306 − 0.177934I
b = 1.002190 − 0.295542I
1.89061 − 0.92430I 1.71672 + 0.79423I
u = − 1.000000I
a = 0.100084 − 0.103550I
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 = 2.39185 − 1.23447I
b = −0.428243 + 0.664531I
−1.89061 + 0.92430I −5.71672 − 0.79423I
u = − 1.000000I
a = 2.98293 − 2.76991I
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
5
=
0
u
a
11
=
1
0
a
12
=
1
u
2
a
1
=
u
2
+ 1
u
2
a
4
=
u
u
3
+ u
a
8
=
−0.137931u
13
+ 0.758621u
12
+ ··· − 2.82759u + 3.17241
−0.206897u
12
− 0.827586u
10
+ ··· − 1.34483u − 0.137931
a
10
=
0.586207u
13
− 0.586207u
12
+ ··· − 0.586207u − 0.724138
0.379310u
12
+ 1.51724u
10
+ ··· − 1.03448u + 0.586207
a
3
=
1
0
a
2
=
1
u
2
a
6
=
u
u
3
+ u
a
7
=
−0.137931u
13
+ 0.965517u
12
+ ··· − 1.48276u + 3.31034
−0.206897u
12
− 0.827586u
10
+ ··· − 1.34483u − 0.137931
a
9
=
0.758621u
12
+ 3.03448u
10
+ ··· − 2.06897u + 3.17241
−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
4
, c
5
c
11
u
15
+ 5u
13
+ ··· + 3u + 1
c
3
(u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1)
3
c
6
, c
8
, c
9
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
3
c
7
, c
10
(u
5
+ u
4
+ 2u
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
4
, c
5
c
11
y
15
+ 10y
14
+ ··· + 3y − 1
c
3
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y − 1)
3
c
6
, c
8
, c
9
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y − 1)
3
c
7
, c
10
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y − 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 = 3.87069 − 2.29859I
b = −0.766826
−2.40108 −3.48114 + 0.I
u = −0.157313 − 1.036460I
a = 3.87069 + 2.29859I
b = −0.766826
−2.40108 −3.48114 + 0.I
u = −0.001127 + 1.228660I
a = 0.207187 − 1.120700I
b = 0.339110 + 0.822375I
−0.32910 + 1.53058I −2.51511 − 4.43065I
u = −0.001127 − 1.228660I
a = 0.207187 + 1.120700I
b = 0.339110 − 0.822375I
−0.32910 − 1.53058I −2.51511 + 4.43065I
u = 1.021430 + 0.758717I
a = 0.119200 + 1.050670I
b = −0.455697 + 1.200150I
−5.87256 − 4.40083I −6.74431 + 3.49859I
u = 1.021430 − 0.758717I
a = 0.119200 − 1.050670I
b = −0.455697 − 1.200150I
−5.87256 + 4.40083I −6.74431 − 3.49859I
u = −0.363053 + 0.617188I
a = 1.69633 − 1.09818I
b = 0.339110 − 0.822375I
−0.32910 − 1.53058I −2.51511 + 4.43065I
u = −0.363053 − 0.617188I
a = 1.69633 + 1.09818I
b = 0.339110 + 0.822375I
−0.32910 + 1.53058I −2.51511 − 4.43065I
u = 0.364180 + 0.611475I
a = 0.74058 − 1.49061I
b = 0.339110 − 0.822375I
−0.32910 − 1.53058I −2.51511 + 4.43065I
u = 0.364180 − 0.611475I
a = 0.74058 + 1.49061I
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 = −0.741792 + 0.660626I
b = −0.455697 + 1.200150I
−5.87256 − 4.40083I −6.74431 + 3.49859I
u = −0.975116 − 0.872207I
a = −0.741792 − 0.660626I
b = −0.455697 − 1.200150I
−5.87256 + 4.40083I −6.74431 − 3.49859I
u = −0.04631 + 1.63092I
a = 0.195775 + 0.184082I
b = −0.455697 − 1.200150I
−5.87256 + 4.40083I −6.74431 − 3.49859I
u = −0.04631 − 1.63092I
a = 0.195775 − 0.184082I
b = −0.455697 + 1.200150I
−5.87256 − 4.40083I −6.74431 + 3.49859I
u = 0.314625
a = 2.82406
b = −0.766826
−2.40108 −3.48110
19
IV. I
u
4
= hb, −3u
3
− 2u
2
+ 4a − 7u − 7, u
4
− u
3
+ 3u
2
− 2u + 1i
(i) Arc colorings
a
5
=
0
u
a
11
=
1
0
a
12
=
1
u
2
a
1
=
u
2
+ 1
u
2
a
4
=
u
u
3
+ u
a
8
=
3
4
u
3
+
1
2
u
2
+
7
4
u +
7
4
0
a
10
=
1
0
a
3
=
u
3
+ 2u
u
3
+ u
a
2
=
u
3
+ 2u
u
3
− u
2
+ 2u − 1
a
6
=
−1
0
a
7
=
5
4
u
3
−
1
2
u
2
+
13
4
u −
3
4
−1
a
9
=
5
4
u
3
−
1
2
u
2
+
13
4
u +
1
4
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
113
16
u
3
+
21
8
u
2
−
13
16
u −
169
16
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
u
4
− u
3
+ 3u
2
− 2u + 1
c
2
u
4
− u
3
+ u
2
+ 1
c
3
u
4
− u
3
+ 5u
2
+ u + 2
c
4
u
4
+ u
3
+ 3u
2
+ 2u + 1
c
5
u
4
+ u
3
+ u
2
+ 1
c
6
(u − 1)
4
c
7
, c
8
2(2u
4
+ u
3
+ 5u
2
− u + 1)
c
9
(u + 1)
4
c
10
u
4
c
12
u
4
− 5u
3
+ 7u
2
− 2u + 1
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
11
y
4
+ 5y
3
+ 7y
2
+ 2y + 1
c
2
, c
5
y
4
+ y
3
+ 3y
2
+ 2y + 1
c
3
y
4
+ 9y
3
+ 31y
2
+ 19y + 4
c
6
, c
9
(y − 1)
4
c
7
, c
8
4(4y
4
+ 19y
3
+ 31y
2
+ 9y + 1)
c
10
y
4
c
12
y
4
− 11y
3
+ 31y
2
+ 10y + 1
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.395123 + 0.506844I
a = 2.20896 + 1.16763I
b = 0
−1.85594 − 1.41510I −9.43312 − 0.11741I
u = 0.395123 − 0.506844I
a = 2.20896 − 1.16763I
b = 0
−1.85594 + 1.41510I −9.43312 + 0.11741I
u = 0.10488 + 1.55249I
a = 0.166035 + 0.111704I
b = 0
5.14581 − 3.16396I −11.5981 + 25.6585I
u = 0.10488 − 1.55249I
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
− u
3
+ 3u
2
− 2u + 1)(u
15
+ 10u
14
+ ··· + 3u − 1)
· (u
50
+ 62u
49
+ ··· − 11952u + 289)
c
2
((u
2
+ 1)
6
)(u
4
− u
3
+ u
2
+ 1)(u
15
+ 5u
13
+ ··· + 3u + 1)
· (u
50
+ 2u
49
+ ··· + 152u + 17)
c
3
(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
4
((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
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 − 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
7
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
8
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
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
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
11
((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
12
((u − 1)
12
)(u
4
− 5u
3
+ ··· − 2u + 1)(u
15
− 10u
14
+ ··· + 3u + 1)
· (u
50
− 14u
49
+ ··· − 5136u + 289)
24
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y − 1)
12
)(y
4
+ 5y
3
+ ··· + 2y + 1)(y
15
− 10y
14
+ ··· + 95y − 1)
· (y
50
− 134y
49
+ ··· − 132056732y + 83521)
c
2
, c
5
((y + 1)
12
)(y
4
+ y
3
+ 3y
2
+ 2y + 1)(y
15
+ 10y
14
+ ··· + 3y − 1)
· (y
50
+ 62y
49
+ ··· − 11952y + 289)
c
3
(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
4
, c
11
((y + 1)
12
)(y
4
+ 5y
3
+ ··· + 2y + 1)(y
15
+ 10y
14
+ ··· + 3y − 1)
· (y
50
+ 14y
49
+ ··· + 5136y + 289)
c
6
, 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
7
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
8
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
10
y
4
(y
5
+ 3y
4
+ ··· − y − 1)
3
(y
6
− 3y
5
+ ··· − y + 1)
2
· (y
50
+ 12y
49
+ ··· − 1020928y + 65536)
c
12
((y − 1)
12
)(y
4
− 11y
3
+ ··· + 10y + 1)(y
15
− 10y
14
+ ··· + 95y − 1)
· (y
50
+ 58y
49
+ ··· + 8224052y + 83521)
25
