12n
0668
(K12n
0668
)
A knot diagram
1
Linearized knot diagam
4 5 6 8 9 12 11 2 3 8 6 7
Solving Sequence
6,11
12 7 8
1,4
2 3 10 9 5
c
11
c
6
c
7
c
12
c
1
c
3
c
10
c
9
c
5
c
2
, c
4
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h−70612u
32
− 259819u
31
+ ··· + 11551b + 473521,
70736u
32
+ 311623u
31
+ ··· + 103959a − 759123, u
33
+ 5u
32
+ ··· − 27u − 9i
I
u
2
= h−u
15
+ u
14
+ 6u
13
− 5u
12
− 14u
11
+ 8u
10
+ 15u
9
− 2u
8
− 7u
7
− 5u
6
+ 2u
5
+ u
4
+ 2u
2
+ b − 3u + 1,
u
15
− u
14
− 6u
13
+ 5u
12
+ 13u
11
− 7u
10
− 10u
9
− u
8
− 3u
7
+ 5u
6
+ 6u
5
+ 6u
4
+ u
3
− 6u
2
+ a − u − 4,
u
16
− 2u
15
− 6u
14
+ 12u
13
+ 15u
12
− 26u
11
− 22u
10
+ 20u
9
+ 23u
8
+ 6u
7
− 14u
6
− 13u
5
− 4u
4
+ u
3
+ 9u
2
+ 1i
I
u
3
= h−u
17
a − 7u
17
+ ··· + a + 7, −u
17
a + u
17
+ ··· − a + 3, u
18
− 2u
17
+ ··· − 2u + 1i
I
u
4
= hb
2
+ b − 1, a + 1, u + 1i
I
v
1
= ha, b + 1, v −1i
* 5 irreducible components of dim
C
= 0, with total 88 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−7.06 × 10
4
u
32
− 2.60 × 10
5
u
31
+ · · · + 1.16 × 10
4
b + 4.74 × 10
5
, 7.07 ×
10
4
u
32
+3.12×10
5
u
31
+· · ·+1.04×10
5
a−7.59×10
5
, u
33
+5u
32
+· · ·−27u−9i
(i) Arc colorings
a
6
=
0
u
a
11
=
1
0
a
12
=
1
u
2
a
7
=
−u
−u
3
+ u
a
8
=
u
3
− 2u
−u
3
+ u
a
1
=
−u
2
+ 1
−u
4
+ 2u
2
a
4
=
−0.680422u
32
− 2.99756u
31
+ ··· + 13.8497u + 7.30214
6.11306u
32
+ 22.4932u
31
+ ··· − 91.7728u − 40.9939
a
2
=
−11.9768u
32
− 41.2941u
31
+ ··· + 157.358u + 64.2446
−3.85404u
32
− 19.2469u
31
+ ··· + 90.4188u + 47.0737
a
3
=
−0.680422u
32
− 2.99756u
31
+ ··· + 13.8497u + 7.30214
5.63986u
32
+ 22.1549u
31
+ ··· − 96.5720u − 44.6349
a
10
=
u
6
− 3u
4
+ 2u
2
+ 1
−u
6
+ 2u
4
− u
2
a
9
=
0.537664u
32
+ 2.96977u
31
+ ··· − 21.8762u − 9.12449
−4.55935u
32
− 18.5188u
31
+ ··· + 82.5148u + 36.1951
a
5
=
4.30313u
32
+ 14.8725u
31
+ ··· − 56.2462u − 22.2317
0.236603u
32
+ 3.16916u
31
+ ··· − 20.1004u − 12.6795
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
924167
11551
u
32
−
3254604
11551
u
31
+ ··· +
13356036
11551
u +
5544210
11551
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
33
+ 2u
32
+ ··· + 7u − 1
c
2
u
33
+ 22u
32
+ ··· + 90u + 9
c
4
, c
9
u
33
− 2u
32
+ ··· − 37u + 7
c
5
, c
8
u
33
− u
32
+ ··· + 2u + 1
c
6
, c
11
, c
12
u
33
+ 5u
32
+ ··· − 27u − 9
c
7
, c
10
u
33
− 15u
32
+ ··· − 621u + 1341
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
33
− 50y
32
+ ··· + 37y −1
c
2
y
33
+ 58y
31
+ ··· − 540y −81
c
4
, c
9
y
33
+ 18y
32
+ ··· + 1173y −49
c
5
, c
8
y
33
− 13y
32
+ ··· + 30y −1
c
6
, c
11
, c
12
y
33
− 33y
32
+ ··· + 351y −81
c
7
, c
10
y
33
− 13y
32
+ ··· + 28562733y −1798281
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.615295 + 0.690025I
a = −0.98614 + 1.55343I
b = −0.40560 − 1.50849I
−6.37902 + 7.26772I −8.48178 − 3.05803I
u = 0.615295 − 0.690025I
a = −0.98614 − 1.55343I
b = −0.40560 + 1.50849I
−6.37902 − 7.26772I −8.48178 + 3.05803I
u = 0.457629 + 0.777634I
a = −1.51279 + 1.36228I
b = 0.72143 − 1.81895I
−5.86299 − 12.19570I −7.30193 + 8.04387I
u = 0.457629 − 0.777634I
a = −1.51279 − 1.36228I
b = 0.72143 + 1.81895I
−5.86299 + 12.19570I −7.30193 − 8.04387I
u = −0.087307 + 0.812187I
a = −0.141714 + 0.501526I
b = 0.491481 − 0.424666I
2.71643 + 3.62722I −8.53869 − 2.13399I
u = −0.087307 − 0.812187I
a = −0.141714 − 0.501526I
b = 0.491481 + 0.424666I
2.71643 − 3.62722I −8.53869 + 2.13399I
u = −1.161150 + 0.326234I
a = 0.206831 − 0.059375I
b = −0.393012 − 0.608436I
−0.540380 + 0.517517I −9.25187 − 4.14256I
u = −1.161150 − 0.326234I
a = 0.206831 + 0.059375I
b = −0.393012 + 0.608436I
−0.540380 − 0.517517I −9.25187 + 4.14256I
u = 0.430358 + 0.659643I
a = 0.91402 − 1.98819I
b = −0.01529 + 1.61480I
−4.97909 − 0.59659I −11.69644 − 1.11532I
u = 0.430358 − 0.659643I
a = 0.91402 + 1.98819I
b = −0.01529 − 1.61480I
−4.97909 + 0.59659I −11.69644 + 1.11532I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.478485 + 0.624833I
a = 1.95619 − 1.29179I
b = −0.69033 + 1.45431I
−5.15410 − 3.61074I −12.7241 + 8.1859I
u = 0.478485 − 0.624833I
a = 1.95619 + 1.29179I
b = −0.69033 − 1.45431I
−5.15410 + 3.61074I −12.7241 − 8.1859I
u = −1.23864
a = 0.294761
b = −1.07773
−2.25658 −4.76340
u = 1.26064
a = 0.775692
b = 0.800176
−5.61796 −16.2880
u = 1.347420 + 0.163931I
a = 0.321296 + 0.675196I
b = 0.111312 + 0.951165I
−4.31416 − 4.24029I 0. + 5.24975I
u = 1.347420 − 0.163931I
a = 0.321296 − 0.675196I
b = 0.111312 − 0.951165I
−4.31416 + 4.24029I 0. − 5.24975I
u = 1.307390 + 0.370979I
a = −0.395726 + 0.191298I
b = −0.565963 − 0.166815I
−1.64117 − 7.89167I 0
u = 1.307390 − 0.370979I
a = −0.395726 − 0.191298I
b = −0.565963 + 0.166815I
−1.64117 + 7.89167I 0
u = −1.39825
a = −1.11011
b = 1.72724
−6.43514 −13.8800
u = −0.161042 + 0.523048I
a = −0.958016 + 0.069367I
b = 0.421774 + 0.647047I
0.41915 + 1.76265I −3.15254 − 5.56900I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.161042 − 0.523048I
a = −0.958016 − 0.069367I
b = 0.421774 − 0.647047I
0.41915 − 1.76265I −3.15254 + 5.56900I
u = 1.46232 + 0.04987I
a = 0.207692 − 0.644243I
b = 0.408897 − 0.964739I
−7.32359 + 0.12289I 0
u = 1.46232 − 0.04987I
a = 0.207692 + 0.644243I
b = 0.408897 + 0.964739I
−7.32359 − 0.12289I 0
u = −1.47199 + 0.24653I
a = −1.246970 − 0.231738I
b = 0.32685 + 2.11863I
−11.11090 + 3.92371I 0
u = −1.47199 − 0.24653I
a = −1.246970 + 0.231738I
b = 0.32685 − 2.11863I
−11.11090 − 3.92371I 0
u = −0.494115 + 0.101505I
a = −0.444814 + 0.225779I
b = −0.395720 + 0.470268I
−1.070850 + 0.384320I −10.13714 − 2.26166I
u = −0.494115 − 0.101505I
a = −0.444814 − 0.225779I
b = −0.395720 − 0.470268I
−1.070850 − 0.384320I −10.13714 + 2.26166I
u = −1.48426 + 0.22127I
a = −1.39684 + 0.31844I
b = 1.23193 + 1.83135I
−11.50660 + 6.70613I 0
u = −1.48426 − 0.22127I
a = −1.39684 − 0.31844I
b = 1.23193 − 1.83135I
−11.50660 − 6.70613I 0
u = −1.50332 + 0.28479I
a = 1.319620 − 0.230307I
b = −0.82368 − 2.17854I
−12.2142 + 16.0764I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.50332 − 0.28479I
a = 1.319620 + 0.230307I
b = −0.82368 + 2.17854I
−12.2142 − 16.0764I 0
u = −1.54758 + 0.20289I
a = 1.177190 + 0.120725I
b = −0.14892 − 1.47002I
−13.53260 − 4.04812I 0
u = −1.54758 − 0.20289I
a = 1.177190 − 0.120725I
b = −0.14892 + 1.47002I
−13.53260 + 4.04812I 0
8
II.
I
u
2
= h−u
15
+u
14
+· · ·+b +1, u
15
−u
14
+· · ·+a −4, u
16
−2u
15
+· · ·+9u
2
+1i
(i) Arc colorings
a
6
=
0
u
a
11
=
1
0
a
12
=
1
u
2
a
7
=
−u
−u
3
+ u
a
8
=
u
3
− 2u
−u
3
+ u
a
1
=
−u
2
+ 1
−u
4
+ 2u
2
a
4
=
−u
15
+ u
14
+ ··· + u + 4
u
15
− u
14
+ ··· + 3u − 1
a
2
=
2u
15
− 3u
14
+ ··· − 4u
2
+ 10u
−3u
15
+ 2u
14
+ ··· − u + 1
a
3
=
−u
15
+ u
14
+ ··· + u + 4
3u
15
− 2u
14
+ ··· + 2u − 2
a
10
=
u
6
− 3u
4
+ 2u
2
+ 1
−u
6
+ 2u
4
− u
2
a
9
=
−u
14
+ u
13
+ ··· + 7u − 1
3u
15
− 2u
14
+ ··· − 5u − 3
a
5
=
−2u
15
+ 2u
14
+ ··· + 11u
2
+ 4
3u
15
− 2u
14
+ ··· + 3u − 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −6u
15
+ u
14
+ 40u
13
+ 7u
12
− 101u
11
− 62u
10
+ 95u
9
+ 144u
8
+
34u
7
− 109u
6
− 111u
5
− 33u
4
+ 29u
3
+ 52u
2
+ 22u + 5
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
16
− 7u
15
+ ··· − 4u + 1
c
2
u
16
+ 9u
15
+ ··· + 11u + 5
c
4
, c
9
u
16
− u
15
+ ··· + 2u
2
+ 1
c
5
, c
8
u
16
+ 2u
14
+ ··· + u + 1
c
6
u
16
+ 2u
15
+ ··· + 9u
2
+ 1
c
7
u
16
− 6u
15
+ ··· − 12u + 5
c
10
u
16
+ 6u
15
+ ··· + 12u + 5
c
11
, c
12
u
16
− 2u
15
+ ··· + 9u
2
+ 1
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
16
− y
15
+ ··· + 16y + 1
c
2
y
16
− 3y
15
+ ··· − 191y + 25
c
4
, c
9
y
16
+ 7y
15
+ ··· + 4y + 1
c
5
, c
8
y
16
+ 4y
15
+ ··· + 7y + 1
c
6
, c
11
, c
12
y
16
− 16y
15
+ ··· + 18y + 1
c
7
, c
10
y
16
+ 18y
14
+ ··· + 396y + 25
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.513943 + 0.697356I
a = −1.22872 − 1.28747I
b = 0.23245 + 1.44429I
−4.25844 + 2.34152I −8.19461 − 3.09667I
u = −0.513943 − 0.697356I
a = −1.22872 + 1.28747I
b = 0.23245 − 1.44429I
−4.25844 − 2.34152I −8.19461 + 3.09667I
u = −0.041928 + 0.737611I
a = −0.828729 − 0.160875I
b = 0.811180 − 0.178567I
3.49750 + 3.94912I 1.82875 − 5.70898I
u = −0.041928 − 0.737611I
a = −0.828729 + 0.160875I
b = 0.811180 + 0.178567I
3.49750 − 3.94912I 1.82875 + 5.70898I
u = −1.239030 + 0.314632I
a = −0.137190 − 0.504551I
b = −0.482263 − 0.342547I
−0.197771 − 0.146116I −3.97287 + 4.66079I
u = −1.239030 − 0.314632I
a = −0.137190 + 0.504551I
b = −0.482263 + 0.342547I
−0.197771 + 0.146116I −3.97287 − 4.66079I
u = 1.331470 + 0.116092I
a = −0.300310 − 0.649478I
b = 1.39100 + 0.87664I
−3.21145 + 2.06263I −9.83386 − 3.81751I
u = 1.331470 − 0.116092I
a = −0.300310 + 0.649478I
b = 1.39100 − 0.87664I
−3.21145 − 2.06263I −9.83386 + 3.81751I
u = 1.306250 + 0.303862I
a = 0.116790 + 0.407149I
b = −1.108390 − 0.136579I
−0.72717 − 7.70203I −3.85260 + 5.91558I
u = 1.306250 − 0.303862I
a = 0.116790 − 0.407149I
b = −1.108390 + 0.136579I
−0.72717 + 7.70203I −3.85260 − 5.91558I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.363160 + 0.105294I
a = −0.139846 + 1.028760I
b = 0.098436 + 1.343460I
−3.45321 + 5.20308I −7.91234 − 8.27064I
u = −1.363160 − 0.105294I
a = −0.139846 − 1.028760I
b = 0.098436 − 1.343460I
−3.45321 − 5.20308I −7.91234 + 8.27064I
u = 1.50649 + 0.23461I
a = 1.206110 + 0.124568I
b = −0.67768 + 1.70952I
−10.83930 − 5.72011I −10.87989 + 2.94641I
u = 1.50649 − 0.23461I
a = 1.206110 − 0.124568I
b = −0.67768 − 1.70952I
−10.83930 + 5.72011I −10.87989 − 2.94641I
u = 0.013846 + 0.326826I
a = 3.31189 + 0.40322I
b = −0.764739 + 0.955045I
1.09551 − 3.67765I −0.68259 + 6.26202I
u = 0.013846 − 0.326826I
a = 3.31189 − 0.40322I
b = −0.764739 − 0.955045I
1.09551 + 3.67765I −0.68259 − 6.26202I
13
III.
I
u
3
= h−u
17
a−7u
17
+· · ·+a+7, −u
17
a+u
17
+· · ·−a+3, u
18
−2u
17
+· · ·−2u+1i
(i) Arc colorings
a
6
=
0
u
a
11
=
1
0
a
12
=
1
u
2
a
7
=
−u
−u
3
+ u
a
8
=
u
3
− 2u
−u
3
+ u
a
1
=
−u
2
+ 1
−u
4
+ 2u
2
a
4
=
a
1
2
u
17
a +
7
2
u
17
+ ··· −
1
2
a −
7
2
a
2
=
−u
17
+ 2u
16
+ ··· − 5u + 2
9
2
u
17
a +
7
2
u
17
+ ··· −
7
2
a −
9
2
a
3
=
a
1
2
u
17
a +
7
2
u
17
+ ··· −
1
2
a −
7
2
a
10
=
u
6
− 3u
4
+ 2u
2
+ 1
−u
6
+ 2u
4
− u
2
a
9
=
−
1
2
u
17
a −
1
2
u
17
+ ··· +
1
2
a +
7
2
−
3
2
u
17
a −
7
2
u
17
+ ··· +
3
2
a +
1
2
a
5
=
1
2
u
17
a −
1
2
u
17
+ ··· +
1
2
a +
3
2
1
2
u
17
a +
11
2
u
17
+ ··· −
1
2
a −
11
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 11u
17
− 9u
16
− 88u
15
+ 43u
14
+ 295u
13
− 13u
12
− 526u
11
−
254u
10
+ 489u
9
+ 529u
8
− 136u
7
− 370u
6
− 102u
5
+ 70u
4
+ 28u
3
− 12u
2
+ 27u − 11
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
36
+ 3u
35
+ ··· + 7002u + 1463
c
2
(u
18
− 7u
17
+ ··· − 3u + 2)
2
c
4
, c
9
u
36
+ 2u
35
+ ··· − 3995u + 2209
c
5
, c
8
u
36
+ 2u
35
+ ··· − 11u + 7
c
6
, c
11
, c
12
(u
18
− 2u
17
+ ··· − 2u + 1)
2
c
7
, c
10
(u
18
+ 9u
17
+ ··· − 9u + 8)
2
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
36
− 23y
35
+ ··· − 22808118y + 2140369
c
2
(y
18
+ 3y
17
+ ··· + 27y + 4)
2
c
4
, c
9
y
36
+ 16y
35
+ ··· + 14457905y + 4879681
c
5
, c
8
y
36
+ 4y
35
+ ··· − 527y + 49
c
6
, c
11
, c
12
(y
18
− 18y
17
+ ··· + 6y + 1)
2
c
7
, c
10
(y
18
− 13y
17
+ ··· − 65y + 64)
2
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.623735 + 0.676903I
a = 1.09092 + 0.90516I
b = −0.388747 − 1.126670I
−5.00931 + 1.37809I −15.9129 + 1.4125I
u = −0.623735 + 0.676903I
a = −1.20346 − 1.43263I
b = −0.60225 + 1.58175I
−5.00931 + 1.37809I −15.9129 + 1.4125I
u = −0.623735 − 0.676903I
a = 1.09092 − 0.90516I
b = −0.388747 + 1.126670I
−5.00931 − 1.37809I −15.9129 − 1.4125I
u = −0.623735 − 0.676903I
a = −1.20346 + 1.43263I
b = −0.60225 − 1.58175I
−5.00931 − 1.37809I −15.9129 − 1.4125I
u = −0.459508 + 0.785840I
a = 0.82807 + 1.29522I
b = −0.149366 − 1.191720I
−4.44669 + 3.56504I −11.6079 − 9.8797I
u = −0.459508 + 0.785840I
a = −1.35269 − 1.24838I
b = 0.64977 + 1.98575I
−4.44669 + 3.56504I −11.6079 − 9.8797I
u = −0.459508 − 0.785840I
a = 0.82807 − 1.29522I
b = −0.149366 + 1.191720I
−4.44669 − 3.56504I −11.6079 + 9.8797I
u = −0.459508 − 0.785840I
a = −1.35269 + 1.24838I
b = 0.64977 − 1.98575I
−4.44669 − 3.56504I −11.6079 + 9.8797I
u = −1.217420 + 0.149232I
a = 0.758661 + 0.017633I
b = −0.639849 + 0.209705I
−2.54082 − 0.26760I −6.08660 + 2.02101I
u = −1.217420 + 0.149232I
a = −0.324598 − 0.531544I
b = −1.80724 + 0.07151I
−2.54082 − 0.26760I −6.08660 + 2.02101I
17
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.217420 − 0.149232I
a = 0.758661 − 0.017633I
b = −0.639849 − 0.209705I
−2.54082 + 0.26760I −6.08660 − 2.02101I
u = −1.217420 − 0.149232I
a = −0.324598 + 0.531544I
b = −1.80724 − 0.07151I
−2.54082 + 0.26760I −6.08660 − 2.02101I
u = 1.321350 + 0.051743I
a = 0.448951 + 0.755907I
b = −1.46818 + 1.80716I
−2.27934 − 4.22577I −4.79351 + 4.92260I
u = 1.321350 + 0.051743I
a = −0.695523 + 1.089510I
b = 0.944109 + 0.327725I
−2.27934 − 4.22577I −4.79351 + 4.92260I
u = 1.321350 − 0.051743I
a = 0.448951 − 0.755907I
b = −1.46818 − 1.80716I
−2.27934 + 4.22577I −4.79351 − 4.92260I
u = 1.321350 − 0.051743I
a = −0.695523 − 1.089510I
b = 0.944109 − 0.327725I
−2.27934 + 4.22577I −4.79351 − 4.92260I
u = −1.42431 + 0.11756I
a = −0.52531 + 1.44263I
b = 1.084790 + 0.698218I
−5.01391 + 6.10285I −11.9670 − 7.7853I
u = −1.42431 + 0.11756I
a = −0.210685 − 0.092418I
b = 1.05013 − 1.59041I
−5.01391 + 6.10285I −11.9670 − 7.7853I
u = −1.42431 − 0.11756I
a = −0.52531 − 1.44263I
b = 1.084790 − 0.698218I
−5.01391 − 6.10285I −11.9670 + 7.7853I
u = −1.42431 − 0.11756I
a = −0.210685 + 0.092418I
b = 1.05013 + 1.59041I
−5.01391 − 6.10285I −11.9670 + 7.7853I
18
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.070160 + 0.483617I
a = −1.35137 + 1.38836I
b = 0.0469130 + 0.1026370I
1.40266 + 2.67585I −0.517536 + 0.048745I
u = 0.070160 + 0.483617I
a = −2.01365 − 1.09287I
b = 1.56099 + 0.71516I
1.40266 + 2.67585I −0.517536 + 0.048745I
u = 0.070160 − 0.483617I
a = −1.35137 − 1.38836I
b = 0.0469130 − 0.1026370I
1.40266 − 2.67585I −0.517536 − 0.048745I
u = 0.070160 − 0.483617I
a = −2.01365 + 1.09287I
b = 1.56099 − 0.71516I
1.40266 − 2.67585I −0.517536 − 0.048745I
u = 1.50796 + 0.28469I
a = −1.038930 + 0.071518I
b = 0.51644 − 1.48081I
−10.83170 − 7.47357I −12.4267 + 8.5659I
u = 1.50796 + 0.28469I
a = 1.193430 + 0.323516I
b = −0.59284 + 2.23330I
−10.83170 − 7.47357I −12.4267 + 8.5659I
u = 1.50796 − 0.28469I
a = −1.038930 − 0.071518I
b = 0.51644 + 1.48081I
−10.83170 + 7.47357I −12.4267 − 8.5659I
u = 1.50796 − 0.28469I
a = 1.193430 − 0.323516I
b = −0.59284 − 2.23330I
−10.83170 + 7.47357I −12.4267 − 8.5659I
u = 1.53783 + 0.20210I
a = −0.916476 − 0.183325I
b = 0.90960 − 1.50238I
−12.11830 − 4.51784I −16.4492 + 1.0407I
u = 1.53783 + 0.20210I
a = 1.401570 − 0.085363I
b = 0.081288 + 1.327820I
−12.11830 − 4.51784I −16.4492 + 1.0407I
19
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.53783 − 0.20210I
a = −0.916476 + 0.183325I
b = 0.90960 + 1.50238I
−12.11830 + 4.51784I −16.4492 − 1.0407I
u = 1.53783 − 0.20210I
a = 1.401570 + 0.085363I
b = 0.081288 − 1.327820I
−12.11830 + 4.51784I −16.4492 − 1.0407I
u = 0.287680 + 0.336405I
a = 0.912787 + 0.372724I
b = −0.103332 − 1.226040I
0.53649 − 4.39821I −7.7387 + 12.1185I
u = 0.287680 + 0.336405I
a = 2.99830 + 2.04992I
b = −1.092230 + 0.505133I
0.53649 − 4.39821I −7.7387 + 12.1185I
u = 0.287680 − 0.336405I
a = 0.912787 − 0.372724I
b = −0.103332 + 1.226040I
0.53649 + 4.39821I −7.7387 − 12.1185I
u = 0.287680 − 0.336405I
a = 2.99830 − 2.04992I
b = −1.092230 − 0.505133I
0.53649 + 4.39821I −7.7387 − 12.1185I
20
IV. I
u
4
= hb
2
+ b − 1, a + 1, u + 1i
(i) Arc colorings
a
6
=
0
−1
a
11
=
1
0
a
12
=
1
1
a
7
=
1
0
a
8
=
1
0
a
1
=
0
1
a
4
=
−1
b
a
2
=
−1
b + 1
a
3
=
−1
b + 1
a
10
=
1
0
a
9
=
−b
b + 2
a
5
=
b − 1
b
(ii) Obstruction class = 1
(iii) Cusp Shapes = −17
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
6
(u − 1)
2
c
2
, c
7
, c
10
u
2
c
4
, c
5
, c
8
c
9
u
2
− u − 1
c
11
, c
12
(u + 1)
2
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
6
c
11
, c
12
(y −1)
2
c
2
, c
7
, c
10
y
2
c
4
, c
5
, c
8
c
9
y
2
− 3y + 1
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = −1.00000
b = 0.618034
−3.28987 −17.0000
u = −1.00000
a = −1.00000
b = −1.61803
−3.28987 −17.0000
24
V. I
v
1
= ha, b + 1, v − 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
1
0
a
12
=
1
0
a
7
=
1
0
a
8
=
1
0
a
1
=
1
0
a
4
=
0
−1
a
2
=
1
1
a
3
=
−1
−1
a
10
=
1
0
a
9
=
2
1
a
5
=
−1
−1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
5
, c
8
, c
9
u + 1
c
2
, c
6
, c
7
c
10
, c
11
, c
12
u
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
5
, c
8
, c
9
y −1
c
2
, c
6
, c
7
c
10
, c
11
, c
12
y
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 1.00000
a = 0
b = −1.00000
−1.64493 −6.00000
28
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
3
((u − 1)
2
)(u + 1)(u
16
− 7u
15
+ ··· − 4u + 1)(u
33
+ 2u
32
+ ··· + 7u − 1)
· (u
36
+ 3u
35
+ ··· + 7002u + 1463)
c
2
u
3
(u
16
+ 9u
15
+ ··· + 11u + 5)(u
18
− 7u
17
+ ··· − 3u + 2)
2
· (u
33
+ 22u
32
+ ··· + 90u + 9)
c
4
, c
9
(u + 1)(u
2
− u − 1)(u
16
− u
15
+ ··· + 2u
2
+ 1)(u
33
− 2u
32
+ ··· − 37u + 7)
· (u
36
+ 2u
35
+ ··· − 3995u + 2209)
c
5
, c
8
(u + 1)(u
2
− u − 1)(u
16
+ 2u
14
+ ··· + u + 1)(u
33
− u
32
+ ··· + 2u + 1)
· (u
36
+ 2u
35
+ ··· − 11u + 7)
c
6
u(u − 1)
2
(u
16
+ 2u
15
+ ··· + 9u
2
+ 1)(u
18
− 2u
17
+ ··· − 2u + 1)
2
· (u
33
+ 5u
32
+ ··· − 27u − 9)
c
7
u
3
(u
16
− 6u
15
+ ··· − 12u + 5)(u
18
+ 9u
17
+ ··· − 9u + 8)
2
· (u
33
− 15u
32
+ ··· − 621u + 1341)
c
10
u
3
(u
16
+ 6u
15
+ ··· + 12u + 5)(u
18
+ 9u
17
+ ··· − 9u + 8)
2
· (u
33
− 15u
32
+ ··· − 621u + 1341)
c
11
, c
12
u(u + 1)
2
(u
16
− 2u
15
+ ··· + 9u
2
+ 1)(u
18
− 2u
17
+ ··· − 2u + 1)
2
· (u
33
+ 5u
32
+ ··· − 27u − 9)
29
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
3
((y −1)
3
)(y
16
− y
15
+ ··· + 16y + 1)(y
33
− 50y
32
+ ··· + 37y −1)
· (y
36
− 23y
35
+ ··· − 22808118y + 2140369)
c
2
y
3
(y
16
− 3y
15
+ ··· − 191y + 25)(y
18
+ 3y
17
+ ··· + 27y + 4)
2
· (y
33
+ 58y
31
+ ··· − 540y −81)
c
4
, c
9
(y −1)(y
2
− 3y + 1)(y
16
+ 7y
15
+ ··· + 4y + 1)
· (y
33
+ 18y
32
+ ··· + 1173y −49)
· (y
36
+ 16y
35
+ ··· + 14457905y + 4879681)
c
5
, c
8
(y −1)(y
2
− 3y + 1)(y
16
+ 4y
15
+ ··· + 7y + 1)
· (y
33
− 13y
32
+ ··· + 30y −1)(y
36
+ 4y
35
+ ··· − 527y + 49)
c
6
, c
11
, c
12
y(y −1)
2
(y
16
− 16y
15
+ ··· + 18y + 1)(y
18
− 18y
17
+ ··· + 6y + 1)
2
· (y
33
− 33y
32
+ ··· + 351y −81)
c
7
, c
10
y
3
(y
16
+ 18y
14
+ ··· + 396y + 25)(y
18
− 13y
17
+ ··· − 65y + 64)
2
· (y
33
− 13y
32
+ ··· + 28562733y −1798281)
30
