12n
0741
(K12n
0741
)
A knot diagram
1
Linearized knot diagam
4 10 12 10 1 3 11 4 1 7 8 6
Solving Sequence
7,11
8
3,12
4 6 1 5 10 2 9
c
7
c
11
c
3
c
6
c
12
c
5
c
10
c
2
c
9
c
1
, c
4
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h−173u
29
− 1170u
28
+ ··· + 2b + 538, 777u
29
+ 5170u
28
+ ··· + 4a − 2260, u
30
+ 8u
29
+ ··· + 10u − 4i
I
u
2
= h−8171u
8
a
3
+ 29276u
8
a
2
+ ··· − 86275a − 355947, u
8
a
3
+ 2u
8
a
2
+ ··· − 6a
2
+ 20,
u
9
− u
8
− 4u
7
+ 3u
6
+ 5u
5
− u
4
− 2u
3
− 2u
2
+ u − 1i
I
u
3
= h−5u
18
+ 8u
17
+ ··· + b + 4, 12u
18
− 20u
17
+ ··· + a − 7, u
19
− 3u
18
+ ··· − 3u + 1i
* 3 irreducible components of dim
C
= 0, with total 85 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−173u
29
− 1170u
28
+ · · · + 2b + 538, 777u
29
+ 5170u
28
+ · · · + 4a −
2260, u
30
+ 8u
29
+ · · · + 10u − 4i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
8
=
1
−u
2
a
3
=
−
777
4
u
29
−
2585
2
u
28
+ ··· −
7275
4
u + 565
173
2
u
29
+ 585u
28
+ ··· +
1769
2
u − 269
a
12
=
u
−u
3
+ u
a
4
=
−
349
4
u
29
−
1127
2
u
28
+ ··· −
2739
4
u + 219
103
2
u
29
+ 321u
28
+ ··· +
641
2
u − 107
a
6
=
−62.5000u
29
− 410.500u
28
+ ··· − 545.500u + 172.500
73
2
u
29
+ 244u
28
+ ··· +
697
2
u − 108
a
1
=
−
73
4
u
29
−
287
2
u
28
+ ··· −
1355
4
u + 95
−
35
2
u
29
− 99u
28
+ ··· −
51
2
u + 17
a
5
=
557
4
u
29
+
1839
2
u
28
+ ··· +
5051
4
u − 393
−
207
2
u
29
− 677u
28
+ ··· −
1797
2
u + 281
a
10
=
−u
u
a
2
=
107
4
u
29
+
325
2
u
28
+ ··· +
629
4
u − 53
−
269
2
u
29
− 870u
28
+ ··· −
2183
2
u + 349
a
9
=
−36.5000u
29
− 249.500u
28
+ ··· − 394.500u + 120.500
71
2
u
29
+ 241u
28
+ ··· +
747
2
u − 114
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 144u
29
+ 932u
28
+ 1166u
27
− 3950u
26
− 8068u
25
+ 10520u
24
+ 22058u
23
− 31648u
22
−
41053u
21
+ 75734u
20
+ 35810u
19
− 138024u
18
+ 30849u
17
+ 178037u
16
− 127069u
15
−
106576u
14
+ 194708u
13
− 23158u
12
− 141581u
11
+ 93195u
10
+ 10441u
9
− 78959u
8
+
26181u
7
− 2885u
6
− 24227u
5
+ 9152u
4
− 1810u
3
− 3043u
2
+ 1148u − 374
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
30
− 20u
29
+ ··· + 4520u − 448
c
2
, c
8
u
30
+ u
29
+ ··· − 24u + 5
c
3
, c
6
u
30
− u
29
+ ··· + 12u − 1
c
4
, c
9
u
30
+ 20u
28
+ ··· − u + 1
c
5
, c
12
u
30
+ 20u
29
+ ··· − 6144u − 512
c
7
, c
10
, c
11
u
30
− 8u
29
+ ··· − 10u − 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
30
− 16y
29
+ ··· − 8229568y + 200704
c
2
, c
8
y
30
− 3y
29
+ ··· − 256y + 25
c
3
, c
6
y
30
+ 7y
29
+ ··· − 80y + 1
c
4
, c
9
y
30
+ 40y
29
+ ··· + 9y + 1
c
5
, c
12
y
30
+ 14y
29
+ ··· − 3407872y + 262144
c
7
, c
10
, c
11
y
30
− 28y
29
+ ··· + 100y + 16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.727622 + 0.705125I
a = −0.641027 + 0.115701I
b = 0.687397 + 1.021870I
−2.97556 − 6.23052I 3.26934 + 3.73627I
u = 0.727622 − 0.705125I
a = −0.641027 − 0.115701I
b = 0.687397 − 1.021870I
−2.97556 + 6.23052I 3.26934 − 3.73627I
u = 0.407170 + 0.935936I
a = −0.438010 − 0.324040I
b = −0.682979 + 0.645597I
−7.02127 + 3.79327I 0.05806 − 6.52210I
u = 0.407170 − 0.935936I
a = −0.438010 + 0.324040I
b = −0.682979 − 0.645597I
−7.02127 − 3.79327I 0.05806 + 6.52210I
u = 0.427689 + 0.823483I
a = 0.796629 + 0.599604I
b = 0.96991 − 1.17666I
−3.86787 + 11.40560I 1.94326 − 7.48134I
u = 0.427689 − 0.823483I
a = 0.796629 − 0.599604I
b = 0.96991 + 1.17666I
−3.86787 − 11.40560I 1.94326 + 7.48134I
u = 1.005300 + 0.779911I
a = 0.231346 + 0.022494I
b = −0.272840 − 0.574864I
−5.41208 + 2.17475I 9.73919 + 5.03605I
u = 1.005300 − 0.779911I
a = 0.231346 − 0.022494I
b = −0.272840 + 0.574864I
−5.41208 − 2.17475I 9.73919 − 5.03605I
u = 1.313940 + 0.059506I
a = 0.372373 − 0.163949I
b = −1.166230 + 0.417498I
5.91755 + 3.45804I 11.41104 − 3.47795I
u = 1.313940 − 0.059506I
a = 0.372373 + 0.163949I
b = −1.166230 − 0.417498I
5.91755 − 3.45804I 11.41104 + 3.47795I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.31986
a = −0.423063
b = 1.29538
2.18151 4.39970
u = −0.654747
a = −0.472043
b = −0.106707
0.896294 12.8060
u = 0.039034 + 0.641181I
a = 0.279594 − 0.811369I
b = −0.457242 − 0.493923I
2.19604 − 1.41771I 2.97939 + 4.71269I
u = 0.039034 − 0.641181I
a = 0.279594 + 0.811369I
b = −0.457242 + 0.493923I
2.19604 + 1.41771I 2.97939 − 4.71269I
u = −1.359280 + 0.360594I
a = 0.830579 − 0.466140I
b = −0.008753 + 0.681742I
6.54442 − 2.48074I 9.12565 + 0.I
u = −1.359280 − 0.360594I
a = 0.830579 + 0.466140I
b = −0.008753 − 0.681742I
6.54442 + 2.48074I 9.12565 + 0.I
u = −1.41614 + 0.09837I
a = −0.21812 − 1.68007I
b = 0.429262 + 0.934517I
4.01008 − 2.17507I 0
u = −1.41614 − 0.09837I
a = −0.21812 + 1.68007I
b = 0.429262 − 0.934517I
4.01008 + 2.17507I 0
u = −1.43489 + 0.15441I
a = 0.22751 + 2.33475I
b = −0.81061 − 1.33560I
9.21909 − 5.77084I 0
u = −1.43489 − 0.15441I
a = 0.22751 − 2.33475I
b = −0.81061 + 1.33560I
9.21909 + 5.77084I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.340842 + 0.386198I
a = −0.70853 − 1.64819I
b = −0.852307 + 0.967588I
3.46376 + 3.69110I −2.17441 − 2.03577I
u = 0.340842 − 0.386198I
a = −0.70853 + 1.64819I
b = −0.852307 − 0.967588I
3.46376 − 3.69110I −2.17441 + 2.03577I
u = −1.49409 + 0.30547I
a = 0.16084 − 1.98951I
b = 1.10456 + 1.38075I
2.3325 − 15.5061I 0
u = −1.49409 − 0.30547I
a = 0.16084 + 1.98951I
b = 1.10456 − 1.38075I
2.3325 + 15.5061I 0
u = −1.49706 + 0.34161I
a = −0.064520 + 1.358570I
b = −0.885003 − 0.896360I
−0.89522 − 8.36672I 0
u = −1.49706 − 0.34161I
a = −0.064520 − 1.358570I
b = −0.885003 + 0.896360I
−0.89522 + 8.36672I 0
u = −1.57559 + 0.10910I
a = −0.517743 + 1.206130I
b = 0.180303 − 1.201000I
5.04077 + 3.42733I 0
u = −1.57559 − 0.10910I
a = −0.517743 − 1.206130I
b = 0.180303 + 1.201000I
5.04077 − 3.42733I 0
u = 0.182909 + 0.333059I
a = 0.38663 + 1.56291I
b = 0.670201 − 0.340664I
−1.174400 + 0.676840I −4.63993 − 2.36566I
u = 0.182909 − 0.333059I
a = 0.38663 − 1.56291I
b = 0.670201 + 0.340664I
−1.174400 − 0.676840I −4.63993 + 2.36566I
7
II. I
u
2
= h−8171a
3
u
8
+ 2.93 × 10
4
a
2
u
8
+ · · · − 8.63 × 10
4
a − 3.56 ×
10
5
, u
8
a
3
+ 2u
8
a
2
+ · · · − 6a
2
+ 20, u
9
− u
8
+ · · · + u − 1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
8
=
1
−u
2
a
3
=
a
0.0368350a
3
u
8
− 0.131977a
2
u
8
+ ··· + 0.388929a + 1.60462
a
12
=
u
−u
3
+ u
a
4
=
−0.0970216a
3
u
8
− 0.329653a
2
u
8
+ ··· + 0.730934a − 0.927002
0.349200a
3
u
8
+ 0.466016a
2
u
8
+ ··· + 0.921213a + 2.65521
a
6
=
0.0154895a
3
u
8
+ 0.0725160a
2
u
8
+ ··· + 0.0316192a + 1.77573
−0.451609a
3
u
8
− 0.579330a
2
u
8
+ ··· − 0.740857a − 1.41865
a
1
=
0.182183a
3
u
8
+ 0.0979592a
2
u
8
+ ··· − 0.599584a + 1.10198
−0.416915a
3
u
8
− 0.0688284a
2
u
8
+ ··· − 2.38249a − 2.38081
a
5
=
0.261826a
3
u
8
+ 0.0418299a
2
u
8
+ ··· − 0.0522569a + 0.418560
−0.514004a
3
u
8
− 0.178193a
2
u
8
+ ··· − 1.59989a − 2.14677
a
10
=
−u
u
a
2
=
−0.0970216a
3
u
8
− 0.329653a
2
u
8
+ ··· + 0.730934a − 0.927002
0.133857a
3
u
8
+ 0.197677a
2
u
8
+ ··· + 0.657995a + 2.53162
a
9
=
0.235697a
3
u
8
− 0.0385841a
2
u
8
+ ··· − 0.288364a − 1.35213
−0.0885780a
3
u
8
+ 0.0969539a
2
u
8
+ ··· − 2.45381a + 2.63002
(ii) Obstruction class = −1
(iii) Cusp Shapes =
156832
221827
u
8
a
3
+
113420
221827
u
8
a
2
+ ··· +
193092
221827
a −
704302
221827
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
9
+ 7u
8
+ 16u
7
+ 7u
6
− 19u
5
− 11u
4
+ 20u
3
+ 6u
2
− 11u + 3)
4
c
2
, c
8
u
36
− u
35
+ ··· − 8292u + 619
c
3
, c
6
u
36
+ 7u
35
+ ··· + 244u + 193
c
4
, c
9
u
36
− u
35
+ ··· − 520u + 2089
c
5
, c
12
(u
2
− u + 1)
18
c
7
, c
10
, c
11
(u
9
+ u
8
− 4u
7
− 3u
6
+ 5u
5
+ u
4
− 2u
3
+ 2u
2
+ u + 1)
4
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
9
− 17y
8
+ ··· + 85y −9)
4
c
2
, c
8
y
36
+ 11y
35
+ ··· − 41360324y + 383161
c
3
, c
6
y
36
+ 11y
35
+ ··· − 118980y + 37249
c
4
, c
9
y
36
+ 35y
35
+ ··· + 136249928y + 4363921
c
5
, c
12
(y
2
+ y + 1)
18
c
7
, c
10
, c
11
(y
9
− 9y
8
+ 32y
7
− 55y
6
+ 45y
5
− 19y
4
+ 16y
3
− 10y
2
− 3y −1)
4
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.482242 + 0.666986I
a = −0.829276 − 0.258734I
b = 0.030585 − 0.881502I
2.12882 − 0.18400I 2.24115 − 0.41812I
u = −0.482242 + 0.666986I
a = −0.693533 + 0.971150I
b = −0.702014 − 0.777525I
2.12882 − 4.24376I 2.24115 + 6.51008I
u = −0.482242 + 0.666986I
a = 0.579089 − 0.313786I
b = 0.638098 + 1.236810I
2.12882 − 4.24376I 2.24115 + 6.51008I
u = −0.482242 + 0.666986I
a = 0.317204 − 0.169060I
b = −0.396381 + 0.596506I
2.12882 − 0.18400I 2.24115 − 0.41812I
u = −0.482242 − 0.666986I
a = −0.829276 + 0.258734I
b = 0.030585 + 0.881502I
2.12882 + 0.18400I 2.24115 + 0.41812I
u = −0.482242 − 0.666986I
a = −0.693533 − 0.971150I
b = −0.702014 + 0.777525I
2.12882 + 4.24376I 2.24115 − 6.51008I
u = −0.482242 − 0.666986I
a = 0.579089 + 0.313786I
b = 0.638098 − 1.236810I
2.12882 + 4.24376I 2.24115 − 6.51008I
u = −0.482242 − 0.666986I
a = 0.317204 + 0.169060I
b = −0.396381 − 0.596506I
2.12882 + 0.18400I 2.24115 + 0.41812I
u = 1.28056
a = 0.24822 + 2.48346I
b = 0.425790 − 0.000287I
−2.09801 + 2.02988I −0.33330 − 3.46410I
u = 1.28056
a = 0.24822 − 2.48346I
b = 0.425790 + 0.000287I
−2.09801 − 2.02988I −0.33330 + 3.46410I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.28056
a = −0.65036 + 3.17999I
b = 0.74862 − 2.03443I
−2.09801 − 2.02988I −0.33330 + 3.46410I
u = 1.28056
a = −0.65036 − 3.17999I
b = 0.74862 + 2.03443I
−2.09801 + 2.02988I −0.33330 − 3.46410I
u = −1.380230 + 0.162431I
a = −1.051670 + 0.187613I
b = −0.693072 − 0.293619I
0.22800 − 5.44061I 3.88238 + 7.86053I
u = −1.380230 + 0.162431I
a = 0.207018 − 1.238430I
b = 1.253150 + 0.213191I
0.227995 − 1.380850I 3.88238 + 0.93232I
u = −1.380230 + 0.162431I
a = 0.96217 − 1.48521I
b = −1.05706 + 1.47865I
0.227995 − 1.380850I 3.88238 + 0.93232I
u = −1.380230 + 0.162431I
a = −1.89166 + 0.16166I
b = 2.06020 − 0.72212I
0.22800 − 5.44061I 3.88238 + 7.86053I
u = −1.380230 − 0.162431I
a = −1.051670 − 0.187613I
b = −0.693072 + 0.293619I
0.22800 + 5.44061I 3.88238 − 7.86053I
u = −1.380230 − 0.162431I
a = 0.207018 + 1.238430I
b = 1.253150 − 0.213191I
0.227995 + 1.380850I 3.88238 − 0.93232I
u = −1.380230 − 0.162431I
a = 0.96217 + 1.48521I
b = −1.05706 − 1.47865I
0.227995 + 1.380850I 3.88238 − 0.93232I
u = −1.380230 − 0.162431I
a = −1.89166 − 0.16166I
b = 2.06020 + 0.72212I
0.22800 + 5.44061I 3.88238 − 7.86053I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.230908 + 0.456719I
a = −0.700916 + 0.499752I
b = −0.37028 − 1.40207I
−4.89942 − 0.92019I −1.44626 − 2.77537I
u = 0.230908 + 0.456719I
a = 0.730726 + 0.224850I
b = 1.44747 + 0.99796I
−4.89942 + 3.13958I −1.44626 − 9.70357I
u = 0.230908 + 0.456719I
a = 3.16147 + 0.79514I
b = 1.048700 − 0.338629I
−4.89942 − 0.92019I −1.44626 − 2.77537I
u = 0.230908 + 0.456719I
a = −3.08241 + 1.25861I
b = −0.279189 + 0.459914I
−4.89942 + 3.13958I −1.44626 − 9.70357I
u = 0.230908 − 0.456719I
a = −0.700916 − 0.499752I
b = −0.37028 + 1.40207I
−4.89942 + 0.92019I −1.44626 + 2.77537I
u = 0.230908 − 0.456719I
a = 0.730726 − 0.224850I
b = 1.44747 − 0.99796I
−4.89942 − 3.13958I −1.44626 + 9.70357I
u = 0.230908 − 0.456719I
a = 3.16147 − 0.79514I
b = 1.048700 + 0.338629I
−4.89942 + 0.92019I −1.44626 + 2.77537I
u = 0.230908 − 0.456719I
a = −3.08241 − 1.25861I
b = −0.279189 − 0.459914I
−4.89942 − 3.13958I −1.44626 + 9.70357I
u = 1.49128 + 0.23430I
a = 0.510760 + 1.162850I
b = −0.059502 − 0.853778I
8.52641 + 3.47060I 5.48937 + 0.49112I
u = 1.49128 + 0.23430I
a = −0.362517 − 1.301200I
b = −0.612207 + 1.221860I
8.52641 + 3.47060I 5.48937 + 0.49112I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.49128 + 0.23430I
a = −0.11348 − 1.82407I
b = −0.792237 + 0.983649I
8.52641 + 7.53037I 5.48937 − 6.43708I
u = 1.49128 + 0.23430I
a = 0.15917 + 2.02163I
b = 0.80933 − 1.74941I
8.52641 + 7.53037I 5.48937 − 6.43708I
u = 1.49128 − 0.23430I
a = 0.510760 − 1.162850I
b = −0.059502 + 0.853778I
8.52641 − 3.47060I 5.48937 − 0.49112I
u = 1.49128 − 0.23430I
a = −0.362517 + 1.301200I
b = −0.612207 − 1.221860I
8.52641 − 3.47060I 5.48937 − 0.49112I
u = 1.49128 − 0.23430I
a = −0.11348 + 1.82407I
b = −0.792237 − 0.983649I
8.52641 − 7.53037I 5.48937 + 6.43708I
u = 1.49128 − 0.23430I
a = 0.15917 − 2.02163I
b = 0.80933 + 1.74941I
8.52641 − 7.53037I 5.48937 + 6.43708I
14
III. I
u
3
=
h−5u
18
+8u
17
+· · ·+b+4, 12u
18
−20u
17
+· · ·+a−7, u
19
−3u
18
+· · ·−3u+1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
8
=
1
−u
2
a
3
=
−12u
18
+ 20u
17
+ ··· − 27u + 7
5u
18
− 8u
17
+ ··· + 7u − 4
a
12
=
u
−u
3
+ u
a
4
=
−5u
18
+ 8u
17
+ ··· − 16u + 2
u
17
− u
16
+ ··· − 7u
2
− 2u
a
6
=
−7u
18
+ 13u
17
+ ··· − 19u + 7
2u
18
− 3u
17
+ ··· + 2u − 1
a
1
=
10u
18
− 17u
17
+ ··· + 24u − 6
−5u
18
+ 8u
17
+ ··· − 6u + 4
a
5
=
−12u
18
+ 20u
17
+ ··· − 29u + 8
7u
18
− 11u
17
+ ··· + 11u − 6
a
10
=
−u
u
a
2
=
u
16
− u
15
+ ··· − 7u − 2
−7u
18
+ 12u
17
+ ··· − 13u + 5
a
9
=
u
18
+ u
17
+ ··· − 8u + 4
−u
18
+ 2u
17
+ ··· − 2u + 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = u
17
−3u
16
−3u
15
+ 15u
14
−2u
13
−23u
12
+ 12u
11
+ 6u
10
−5u
9
+
5u
8
− 3u
7
+ 7u
6
− 12u
5
− 2u
4
+ 19u
3
− 3u
2
− 5u
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
19
− 15u
18
+ ··· + 29u − 13
c
2
, c
8
u
19
− u
18
+ ··· + 18u − 5
c
3
, c
6
u
19
+ u
18
+ ··· + 6u + 1
c
4
, c
9
u
19
+ 8u
17
+ ··· + u + 1
c
5
u
19
− u
18
+ ··· − 4u + 5
c
7
u
19
− 3u
18
+ ··· − 3u + 1
c
10
, c
11
u
19
+ 3u
18
+ ··· − 3u − 1
c
12
u
19
+ u
18
+ ··· − 4u − 5
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
19
− 19y
18
+ ··· − 745y −169
c
2
, c
8
y
19
+ 9y
18
+ ··· + 744y −25
c
3
, c
6
y
19
+ 7y
18
+ ··· + 4y −1
c
4
, c
9
y
19
+ 16y
18
+ ··· + 7y −1
c
5
, c
12
y
19
+ 13y
18
+ ··· − 204y −25
c
7
, c
10
, c
11
y
19
− 19y
18
+ ··· + 5y −1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.845692 + 0.661557I
a = −0.153266 − 0.466031I
b = −0.300237 − 0.194675I
−5.74523 + 2.61792I 0.07093 − 6.33010I
u = 0.845692 − 0.661557I
a = −0.153266 + 0.466031I
b = −0.300237 + 0.194675I
−5.74523 − 2.61792I 0.07093 + 6.33010I
u = −0.395840 + 0.806578I
a = −0.545217 − 0.152245I
b = 0.166562 − 0.802834I
3.24781 − 0.29442I 10.76895 + 0.40021I
u = −0.395840 − 0.806578I
a = −0.545217 + 0.152245I
b = 0.166562 + 0.802834I
3.24781 + 0.29442I 10.76895 − 0.40021I
u = −0.835448
a = 0.437061
b = −0.670199
0.213591 −1.61190
u = −1.161770 + 0.148655I
a = −0.301539 − 0.268731I
b = 0.883412 + 0.519992I
4.96317 − 3.33168I 2.78254 + 2.68060I
u = −1.161770 − 0.148655I
a = −0.301539 + 0.268731I
b = 0.883412 − 0.519992I
4.96317 + 3.33168I 2.78254 − 2.68060I
u = −0.498260 + 0.534494I
a = 0.570176 − 0.933196I
b = 0.733079 + 1.038500I
4.15390 − 3.99094I 9.36572 + 6.29710I
u = −0.498260 − 0.534494I
a = 0.570176 + 0.933196I
b = 0.733079 − 1.038500I
4.15390 + 3.99094I 9.36572 − 6.29710I
u = 1.328220 + 0.037070I
a = 0.59090 − 2.97401I
b = −0.439409 + 1.256160I
−1.08200 − 1.51093I 7.95202 − 0.16487I
18
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.328220 − 0.037070I
a = 0.59090 + 2.97401I
b = −0.439409 − 1.256160I
−1.08200 + 1.51093I 7.95202 + 0.16487I
u = −1.406710 + 0.134721I
a = 0.358797 − 0.109163I
b = −1.152130 + 0.551928I
0.54391 − 3.84947I 6.11362 + 2.50531I
u = −1.406710 − 0.134721I
a = 0.358797 + 0.109163I
b = −1.152130 − 0.551928I
0.54391 + 3.84947I 6.11362 − 2.50531I
u = 1.48263 + 0.20775I
a = 0.05248 + 2.08255I
b = 0.81500 − 1.42175I
10.53760 + 6.80667I 10.97954 − 4.95231I
u = 1.48263 − 0.20775I
a = 0.05248 − 2.08255I
b = 0.81500 + 1.42175I
10.53760 − 6.80667I 10.97954 + 4.95231I
u = 1.50740 + 0.26923I
a = −0.551403 − 1.163060I
b = −0.249129 + 1.104390I
9.55521 + 4.20504I 12.20929 − 4.02195I
u = 1.50740 − 0.26923I
a = −0.551403 + 1.163060I
b = −0.249129 − 1.104390I
9.55521 − 4.20504I 12.20929 + 4.02195I
u = 0.216351 + 0.218987I
a = −3.73945 − 1.53970I
b = −0.622048 − 0.799440I
−4.89702 + 2.21165I −1.43665 − 0.97531I
u = 0.216351 − 0.218987I
a = −3.73945 + 1.53970I
b = −0.622048 + 0.799440I
−4.89702 − 2.21165I −1.43665 + 0.97531I
19
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
9
+ 7u
8
+ 16u
7
+ 7u
6
− 19u
5
− 11u
4
+ 20u
3
+ 6u
2
− 11u + 3)
4
· (u
19
− 15u
18
+ ··· + 29u − 13)(u
30
− 20u
29
+ ··· + 4520u − 448)
c
2
, c
8
(u
19
− u
18
+ ··· + 18u − 5)(u
30
+ u
29
+ ··· − 24u + 5)
· (u
36
− u
35
+ ··· − 8292u + 619)
c
3
, c
6
(u
19
+ u
18
+ ··· + 6u + 1)(u
30
− u
29
+ ··· + 12u − 1)
· (u
36
+ 7u
35
+ ··· + 244u + 193)
c
4
, c
9
(u
19
+ 8u
17
+ ··· + u + 1)(u
30
+ 20u
28
+ ··· − u + 1)
· (u
36
− u
35
+ ··· − 520u + 2089)
c
5
((u
2
− u + 1)
18
)(u
19
− u
18
+ ··· − 4u + 5)
· (u
30
+ 20u
29
+ ··· − 6144u − 512)
c
7
(u
9
+ u
8
− 4u
7
− 3u
6
+ 5u
5
+ u
4
− 2u
3
+ 2u
2
+ u + 1)
4
· (u
19
− 3u
18
+ ··· − 3u + 1)(u
30
− 8u
29
+ ··· − 10u − 4)
c
10
, c
11
(u
9
+ u
8
− 4u
7
− 3u
6
+ 5u
5
+ u
4
− 2u
3
+ 2u
2
+ u + 1)
4
· (u
19
+ 3u
18
+ ··· − 3u − 1)(u
30
− 8u
29
+ ··· − 10u − 4)
c
12
((u
2
− u + 1)
18
)(u
19
+ u
18
+ ··· − 4u − 5)
· (u
30
+ 20u
29
+ ··· − 6144u − 512)
20
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
9
− 17y
8
+ ··· + 85y −9)
4
)(y
19
− 19y
18
+ ··· − 745y −169)
· (y
30
− 16y
29
+ ··· − 8229568y + 200704)
c
2
, c
8
(y
19
+ 9y
18
+ ··· + 744y −25)(y
30
− 3y
29
+ ··· − 256y + 25)
· (y
36
+ 11y
35
+ ··· − 41360324y + 383161)
c
3
, c
6
(y
19
+ 7y
18
+ ··· + 4y −1)(y
30
+ 7y
29
+ ··· − 80y + 1)
· (y
36
+ 11y
35
+ ··· − 118980y + 37249)
c
4
, c
9
(y
19
+ 16y
18
+ ··· + 7y −1)(y
30
+ 40y
29
+ ··· + 9y + 1)
· (y
36
+ 35y
35
+ ··· + 136249928y + 4363921)
c
5
, c
12
((y
2
+ y + 1)
18
)(y
19
+ 13y
18
+ ··· − 204y −25)
· (y
30
+ 14y
29
+ ··· − 3407872y + 262144)
c
7
, c
10
, c
11
(y
9
− 9y
8
+ 32y
7
− 55y
6
+ 45y
5
− 19y
4
+ 16y
3
− 10y
2
− 3y −1)
4
· (y
19
− 19y
18
+ ··· + 5y −1)(y
30
− 28y
29
+ ··· + 100y + 16)
21
