12n
0742
(K12n
0742
)
A knot diagram
1
Linearized knot diagam
4 6 7 8 12 10 1 2 6 7 3 5
Solving Sequence
6,10 3,7
4 11 12 2 1 5 9 8
c
6
c
3
c
10
c
11
c
2
c
1
c
5
c
9
c
8
c
4
, c
7
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h54417405u
24
+ 534792001u
23
+ ··· + 33311573b + 3681796776,
32555757366u
24
+ 426906642534u
23
+ ··· + 2831483705a + 4024705159097,
u
25
+ 14u
24
+ ··· + 802u + 85i
I
u
2
= h26555u
18
− 198357u
17
+ ··· + 36185b − 144112,
163099u
18
− 1122706u
17
+ ··· + 36185a − 527630, u
19
− 7u
18
+ ··· − 7u + 1i
I
u
3
= h1445734u
6
a
5
− 1807249u
6
a
4
+ ··· − 3844804a + 2844990, u
6
a
5
− 2u
6
a
4
+ ··· − 37a + 3,
u
7
− 2u
6
+ 2u
5
+ u
4
− 2u
3
+ 3u
2
− 2u + 1i
I
u
4
= ha
5
− 5a
4
+ 5a
3
+ 5a
2
+ 7b − 10a − 2, a
6
− a
5
− a
4
+ 4a
3
+ 3a
2
− 1, u + 1i
I
v
1
= ha, b
3
+ b
2
− 1, v −1i
* 5 irreducible components of dim
C
= 0, with total 95 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
=
h5.44 × 10
7
u
24
+ 5.35 × 10
8
u
23
+ · · · + 3.33 × 10
7
b + 3.68 × 10
9
, 3.26 × 10
10
u
24
+
4.27 × 10
11
u
23
+ · · · + 2.83 × 10
9
a + 4.02 × 10
12
, u
25
+ 14u
24
+ · · · + 802u + 85i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
3
=
−11.4978u
24
− 150.771u
23
+ ··· − 10908.2u − 1421.41
−1.63359u
24
− 16.0542u
23
+ ··· − 598.744u − 110.526
a
7
=
1
−u
2
a
4
=
−1.30031u
24
− 16.5707u
23
+ ··· − 3108.43u − 444.101
−3.38147u
24
− 53.3166u
23
+ ··· − 6600.19u − 838.456
a
11
=
u
−u
3
+ u
a
12
=
6.05270u
24
+ 79.5081u
23
+ ··· + 5244.89u + 673.380
2.36945u
24
+ 27.1163u
23
+ ··· + 502.162u + 69.9568
a
2
=
−9.86418u
24
− 134.717u
23
+ ··· − 10309.5u − 1310.89
−1.63359u
24
− 16.0542u
23
+ ··· − 598.744u − 110.526
a
1
=
−4.83382u
24
− 68.1991u
23
+ ··· − 7333.97u − 961.507
−3.85589u
24
− 51.6884u
23
+ ··· − 3026.16u − 368.196
a
5
=
−3.32745u
24
− 47.7352u
23
+ ··· − 3929.81u − 486.742
−3.53542u
24
− 41.2464u
23
+ ··· − 561.643u − 67.3117
a
9
=
−u
u
a
8
=
4.06599u
24
+ 56.5411u
23
+ ··· + 7053.62u + 949.032
5.22968u
24
+ 70.3553u
23
+ ··· + 4181.88u + 514.479
(ii) Obstruction class = −1
(iii) Cusp Shapes =
989445234
33311573
u
24
+
12906576392
33311573
u
23
+ ··· +
940441773198
33311573
u +
123998150314
33311573
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
25
− 24u
24
+ ··· − 1246u + 85
c
2
, c
11
u
25
+ 18u
23
+ ··· + 10u + 1
c
3
, c
8
u
25
− 15u
23
+ ··· − u − 1
c
4
, c
7
u
25
− u
24
+ ··· + u − 1
c
5
, c
12
u
25
− 15u
24
+ ··· − 768u + 64
c
6
, c
9
, c
10
u
25
− 14u
24
+ ··· + 802u − 85
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
25
− 12y
24
+ ··· − 5534y −7225
c
2
, c
11
y
25
+ 36y
24
+ ··· + 36y −1
c
3
, c
8
y
25
− 30y
24
+ ··· + 15y −1
c
4
, c
7
y
25
+ 9y
24
+ ··· + 3y −1
c
5
, c
12
y
25
+ 13y
24
+ ··· + 30720y −4096
c
6
, c
9
, c
10
y
25
− 8y
24
+ ··· + 28824y −7225
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.150840 + 0.071771I
a = −0.388264 + 0.151015I
b = 0.994844 − 0.281020I
3.73403 + 0.45497I 9.6713 − 10.3747I
u = 1.150840 − 0.071771I
a = −0.388264 − 0.151015I
b = 0.994844 + 0.281020I
3.73403 − 0.45497I 9.6713 + 10.3747I
u = −0.485653 + 0.637254I
a = 0.238682 − 1.222900I
b = 0.134188 − 0.806451I
0.04540 − 2.20353I 6.08023 + 5.72200I
u = −0.485653 − 0.637254I
a = 0.238682 + 1.222900I
b = 0.134188 + 0.806451I
0.04540 + 2.20353I 6.08023 − 5.72200I
u = −1.170090 + 0.293084I
a = −0.088746 + 0.564255I
b = −0.211593 − 0.098690I
0.536147 − 0.634353I 11.05095 − 0.92711I
u = −1.170090 − 0.293084I
a = −0.088746 − 0.564255I
b = −0.211593 + 0.098690I
0.536147 + 0.634353I 11.05095 + 0.92711I
u = −1.30739
a = 0.650104
b = −0.261258
2.40793 2.92560
u = 1.275970 + 0.445097I
a = 0.185309 − 0.188647I
b = −0.799684 + 0.217507I
0.48601 + 6.98392I 7.58735 − 2.98209I
u = 1.275970 − 0.445097I
a = 0.185309 + 0.188647I
b = −0.799684 − 0.217507I
0.48601 − 6.98392I 7.58735 + 2.98209I
u = 0.022372 + 0.589385I
a = −0.859515 − 0.602687I
b = −0.650024 + 0.333678I
−2.78859 − 2.82391I 3.91126 + 3.02621I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.022372 − 0.589385I
a = −0.859515 + 0.602687I
b = −0.650024 − 0.333678I
−2.78859 + 2.82391I 3.91126 − 3.02621I
u = −0.547968 + 0.005640I
a = 0.882270 − 1.038890I
b = 0.219128 − 0.256889I
1.078030 − 0.317833I 10.34199 + 2.86675I
u = −0.547968 − 0.005640I
a = 0.882270 + 1.038890I
b = 0.219128 + 0.256889I
1.078030 + 0.317833I 10.34199 − 2.86675I
u = −0.90468 + 1.23994I
a = 0.366520 + 0.971389I
b = −0.37973 + 1.94506I
−12.68230 − 6.03173I 0
u = −0.90468 − 1.23994I
a = 0.366520 − 0.971389I
b = −0.37973 − 1.94506I
−12.68230 + 6.03173I 0
u = −1.10702 + 1.09764I
a = −0.598281 − 1.082670I
b = 0.79280 − 1.97341I
−13.8057 − 16.2441I 0
u = −1.10702 − 1.09764I
a = −0.598281 + 1.082670I
b = 0.79280 + 1.97341I
−13.8057 + 16.2441I 0
u = −1.07816 + 1.16839I
a = 0.771238 + 0.692967I
b = 0.05163 + 1.92956I
−13.9765 + 8.0107I 0
u = −1.07816 − 1.16839I
a = 0.771238 − 0.692967I
b = 0.05163 − 1.92956I
−13.9765 − 8.0107I 0
u = −1.16562 + 1.12611I
a = 0.578628 + 0.852161I
b = −0.65543 + 1.78358I
−8.04349 − 10.14930I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.16562 − 1.12611I
a = 0.578628 − 0.852161I
b = −0.65543 − 1.78358I
−8.04349 + 10.14930I 0
u = −1.05000 + 1.24515I
a = −0.549717 − 0.744389I
b = 0.19613 − 1.86795I
−8.47813 + 1.61102I 0
u = −1.05000 − 1.24515I
a = −0.549717 + 0.744389I
b = 0.19613 + 1.86795I
−8.47813 − 1.61102I 0
u = −1.28631 + 1.03268I
a = −0.739647 − 0.587900I
b = 0.43837 − 1.61163I
−11.46130 − 2.25746I 0
u = −1.28631 − 1.03268I
a = −0.739647 + 0.587900I
b = 0.43837 + 1.61163I
−11.46130 + 2.25746I 0
7
II. I
u
2
= h26555u
18
− 198357u
17
+ · · · + 36185b − 144112, 1.63 × 10
5
u
18
−
1.12 × 10
6
u
17
+ · · · + 3.62 × 10
4
a − 5.28 × 10
5
, u
19
− 7u
18
+ · · · − 7u + 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
3
=
−4.50736u
18
+ 31.0268u
17
+ ··· − 73.3920u + 14.5815
−0.733868u
18
+ 5.48175u
17
+ ··· − 17.8044u + 3.98264
a
7
=
1
−u
2
a
4
=
−3.98264u
18
+ 27.1446u
17
+ ··· − 56.4219u + 10.0741
−0.869393u
18
+ 5.81719u
17
+ ··· − 15.8157u + 3.77350
a
11
=
u
−u
3
+ u
a
12
=
−5.19580u
18
+ 34.7581u
17
+ ··· − 69.3087u + 9.04523
−1.23542u
18
+ 8.41895u
17
+ ··· − 20.2338u + 3.58332
a
2
=
−3.77350u
18
+ 25.5451u
17
+ ··· − 55.5876u + 10.5988
−0.733868u
18
+ 5.48175u
17
+ ··· − 17.8044u + 3.98264
a
1
=
1.43106u
18
− 8.75258u
17
+ ··· − 3.21879u + 5.32624
1.34440u
18
− 8.49272u
17
+ ··· + 13.2778u − 1.56476
a
5
=
3.37262u
18
− 24.2115u
17
+ ··· + 81.5293u − 19.2865
−0.115700u
18
+ 0.302081u
17
+ ··· + 6.21904u − 2.96929
a
9
=
−u
u
a
8
=
−6.03238u
18
+ 40.1547u
17
+ ··· − 80.8073u + 11.4943
−1.61249u
18
+ 10.9103u
17
+ ··· − 26.3254u + 5.19580
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
175307
36185
u
18
+
1123384
36185
u
17
+ ··· −
2188741
36185
u +
386871
36185
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
19
− 11u
18
+ ··· − 575u + 125
c
2
, c
11
u
19
+ u
18
+ ··· + 3u + 1
c
3
, c
8
u
19
+ u
18
+ ··· + 2u + 1
c
4
, c
7
u
19
+ 4u
17
+ ··· + 4u + 1
c
5
u
19
+ 3u
18
+ ··· − 30u − 7
c
6
u
19
− 7u
18
+ ··· − 7u + 1
c
9
, c
10
u
19
+ 7u
18
+ ··· − 7u − 1
c
12
u
19
− 3u
18
+ ··· − 30u + 7
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
19
− 9y
18
+ ··· + 103125y −15625
c
2
, c
11
y
19
+ 15y
18
+ ··· + 7y −1
c
3
, c
8
y
19
− 19y
18
+ ··· − 6y −1
c
4
, c
7
y
19
+ 8y
18
+ ··· + 22y −1
c
5
, c
12
y
19
+ 13y
18
+ ··· − 206y −49
c
6
, c
9
, c
10
y
19
− 9y
18
+ ··· − y −1
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.030941 + 1.036600I
a = −0.057572 − 0.720594I
b = 0.733161 − 0.814685I
−4.91601 − 3.49525I −0.97939 + 3.44758I
u = −0.030941 − 1.036600I
a = −0.057572 + 0.720594I
b = 0.733161 + 0.814685I
−4.91601 + 3.49525I −0.97939 − 3.44758I
u = −1.11948
a = −0.394977
b = 0.937170
3.52860 4.95410
u = 0.404942 + 0.627084I
a = 0.12194 + 1.73383I
b = −0.129374 + 1.114130I
−1.79745 + 4.35854I −0.0010 − 6.03173I
u = 0.404942 − 0.627084I
a = 0.12194 − 1.73383I
b = −0.129374 − 1.114130I
−1.79745 − 4.35854I −0.0010 + 6.03173I
u = −1.297110 + 0.232714I
a = 0.062267 − 0.224578I
b = 0.005685 + 0.709074I
−0.109284 − 0.792626I −1.36200 + 1.44719I
u = −1.297110 − 0.232714I
a = 0.062267 + 0.224578I
b = 0.005685 − 0.709074I
−0.109284 + 0.792626I −1.36200 − 1.44719I
u = 1.360490 + 0.283318I
a = −0.530378 + 0.419990I
b = 0.422327 + 0.086336I
0.10891 + 7.90490I 4.83691 − 9.16857I
u = 1.360490 − 0.283318I
a = −0.530378 − 0.419990I
b = 0.422327 − 0.086336I
0.10891 − 7.90490I 4.83691 + 9.16857I
u = −0.191568 + 0.560311I
a = 1.06731 + 1.40164I
b = −0.994805 + 0.947251I
−5.82927 − 1.11371I −3.17634 + 1.02276I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.191568 − 0.560311I
a = 1.06731 − 1.40164I
b = −0.994805 − 0.947251I
−5.82927 + 1.11371I −3.17634 − 1.02276I
u = 1.42423 + 0.16239I
a = 0.746131 + 0.085376I
b = −0.405505 − 0.273306I
2.38680 − 1.23386I 2.53593 + 6.06239I
u = 1.42423 − 0.16239I
a = 0.746131 − 0.085376I
b = −0.405505 + 0.273306I
2.38680 + 1.23386I 2.53593 − 6.06239I
u = 0.97747 + 1.08905I
a = 0.509235 − 1.105650I
b = −0.53468 − 1.86527I
−10.59590 + 5.86698I 3.20212 − 2.48946I
u = 0.97747 − 1.08905I
a = 0.509235 + 1.105650I
b = −0.53468 + 1.86527I
−10.59590 − 5.86698I 3.20212 + 2.48946I
u = 1.14236 + 1.02230I
a = −0.807801 + 0.694310I
b = 0.19902 + 1.67365I
−10.09310 + 1.89591I 3.41811 − 1.70053I
u = 1.14236 − 1.02230I
a = −0.807801 − 0.694310I
b = 0.19902 − 1.67365I
−10.09310 − 1.89591I 3.41811 + 1.70053I
u = 0.269868 + 0.223025I
a = 1.08636 − 4.55418I
b = 0.735580 − 1.012370I
−5.46263 + 6.62471I −0.45143 − 4.04109I
u = 0.269868 − 0.223025I
a = 1.08636 + 4.55418I
b = 0.735580 + 1.012370I
−5.46263 − 6.62471I −0.45143 + 4.04109I
12
III. I
u
3
= h1.45 × 10
6
a
5
u
6
− 1.81 × 10
6
a
4
u
6
+ · · · − 3.84 × 10
6
a + 2.84 ×
10
6
, u
6
a
5
− 2u
6
a
4
+ · · · − 37a + 3, u
7
− 2u
6
+ 2u
5
+ u
4
− 2u
3
+ 3u
2
− 2u + 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
3
=
a
−0.209331a
5
u
6
+ 0.261676a
4
u
6
+ ··· + 0.556698a − 0.411933
a
7
=
1
−u
2
a
4
=
0.209331a
5
u
6
− 0.261676a
4
u
6
+ ··· + 0.443302a + 0.411933
0.0993729a
5
u
6
− 0.219734a
4
u
6
+ ··· + 0.219607a + 0.321828
a
11
=
u
−u
3
+ u
a
12
=
−0.0322938a
5
u
6
+ 0.0201516a
4
u
6
+ ··· − 1.50291a − 0.470480
−0.0322938a
5
u
6
+ 0.0201516a
4
u
6
+ ··· − 1.50291a + 0.529520
a
2
=
0.209331a
5
u
6
− 0.261676a
4
u
6
+ ··· + 0.443302a + 0.411933
−0.209331a
5
u
6
+ 0.261676a
4
u
6
+ ··· + 0.556698a − 0.411933
a
1
=
−0.00106654a
5
u
6
− 0.272359a
4
u
6
+ ··· + 1.67095a − 1.26789
−0.00910831a
5
u
6
+ 0.0943514a
4
u
6
+ ··· − 2.00070a + 2.42464
a
5
=
0.0637385a
5
u
6
+ 0.118112a
4
u
6
+ ··· − 0.00769021a + 1.73068
−0.0231855a
5
u
6
− 0.0741997a
4
u
6
+ ··· + 0.497788a − 2.89512
a
9
=
−u
u
a
8
=
−0.0322938a
5
u
6
+ 0.0201516a
4
u
6
+ ··· − 1.50291a − 0.470480
0.0322938a
5
u
6
− 0.0201516a
4
u
6
+ ··· + 1.50291a + 0.470480
(ii) Obstruction class = −1
(iii) Cusp Shapes =
251624
6906439
u
6
a
5
−
2606528
6906439
u
6
a
4
+ ··· +
55270856
6906439
a +
8988269
6906439
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
7
+ 3u
6
+ 3u
5
− 2u
4
− 6u
3
− 3u
2
+ 3u + 2)
6
c
2
, c
11
u
42
− 3u
41
+ ··· + 3904u − 211
c
3
, c
8
u
42
− 24u
40
+ ··· − 18828u + 2079
c
4
, c
7
u
42
+ 6u
40
+ ··· − 824u + 37
c
5
, c
12
(u
3
+ u
2
+ 2u + 1)
14
c
6
, c
9
, c
10
(u
7
+ 2u
6
+ 2u
5
− u
4
− 2u
3
− 3u
2
− 2u − 1)
6
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
7
− 3y
6
+ 9y
5
− 16y
4
+ 30y
3
− 37y
2
+ 21y −4)
6
c
2
, c
11
y
42
+ 49y
41
+ ··· + 2545240y + 44521
c
3
, c
8
y
42
− 48y
41
+ ··· − 47845242y + 4322241
c
4
, c
7
y
42
+ 12y
41
+ ··· − 687930y + 1369
c
5
, c
12
(y
3
+ 3y
2
+ 2y −1)
14
c
6
, c
9
, c
10
(y
7
+ 4y
5
− y
4
− 6y
3
− 3y
2
− 2y −1)
6
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.17019
a = 0.868891
b = −0.539106
2.29929 1.30030
u = −1.17019
a = −0.528273 + 0.353145I
b = −0.596628 + 0.748519I
−1.83829 − 2.82812I −5.22897 + 2.97945I
u = −1.17019
a = −0.528273 − 0.353145I
b = −0.596628 − 0.748519I
−1.83829 + 2.82812I −5.22897 − 2.97945I
u = −1.17019
a = 0.556064
b = 0.255326
2.29929 1.30030
u = −1.17019
a = −1.12804 + 1.05290I
b = 0.926482 − 1.028530I
−1.83829 − 2.82812I −5.22897 + 2.97945I
u = −1.17019
a = −1.12804 − 1.05290I
b = 0.926482 + 1.028530I
−1.83829 + 2.82812I −5.22897 − 2.97945I
u = −0.011299 + 0.825523I
a = 0.714686 − 0.336755I
b = 2.48991 − 0.29670I
−6.79883 − 5.36696I −4.37320 + 4.79030I
u = −0.011299 + 0.825523I
a = −0.31540 + 1.38661I
b = −0.43610 + 2.25720I
−6.79883 + 0.28928I −4.37320 − 1.16859I
u = −0.011299 + 0.825523I
a = 0.28834 − 1.57933I
b = 0.376827 − 1.210580I
−2.66125 − 2.53884I 2.15607 + 1.81085I
u = −0.011299 + 0.825523I
a = −1.59987 − 0.21472I
b = 0.0550300 + 0.0998932I
−6.79883 + 0.28928I −4.37320 − 1.16859I
16
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.011299 + 0.825523I
a = 0.171890 + 0.180445I
b = −1.186770 − 0.129718I
−2.66125 − 2.53884I 2.15607 + 1.81085I
u = −0.011299 + 0.825523I
a = 0.13070 + 2.41689I
b = −0.225961 + 1.055410I
−6.79883 − 5.36696I −4.37320 + 4.79030I
u = −0.011299 − 0.825523I
a = 0.714686 + 0.336755I
b = 2.48991 + 0.29670I
−6.79883 + 5.36696I −4.37320 − 4.79030I
u = −0.011299 − 0.825523I
a = −0.31540 − 1.38661I
b = −0.43610 − 2.25720I
−6.79883 − 0.28928I −4.37320 + 1.16859I
u = −0.011299 − 0.825523I
a = 0.28834 + 1.57933I
b = 0.376827 + 1.210580I
−2.66125 + 2.53884I 2.15607 − 1.81085I
u = −0.011299 − 0.825523I
a = −1.59987 + 0.21472I
b = 0.0550300 − 0.0998932I
−6.79883 − 0.28928I −4.37320 + 1.16859I
u = −0.011299 − 0.825523I
a = 0.171890 − 0.180445I
b = −1.186770 + 0.129718I
−2.66125 + 2.53884I 2.15607 − 1.81085I
u = −0.011299 − 0.825523I
a = 0.13070 − 2.41689I
b = −0.225961 − 1.055410I
−6.79883 + 5.36696I −4.37320 − 4.79030I
u = 0.542568 + 0.510771I
a = 0.001593 + 0.449134I
b = −1.304380 − 0.124427I
−5.00506 + 1.89516I 3.50931 − 6.19343I
u = 0.542568 + 0.510771I
a = −0.61501 + 1.50358I
b = 0.26483 + 1.53096I
−0.86748 + 4.72329I 10.03858 − 9.17288I
17
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.542568 + 0.510771I
a = 0.60283 − 1.61972I
b = 0.36969 − 2.21523I
−5.00506 + 7.55141I 3.50931 − 12.15232I
u = 0.542568 + 0.510771I
a = −0.56538 − 1.75401I
b = 0.148437 − 0.129555I
−0.86748 + 4.72329I 10.03858 − 9.17288I
u = 0.542568 + 0.510771I
a = 1.61755 − 1.32277I
b = −0.558791 − 1.096730I
−5.00506 + 1.89516I 3.50931 − 6.19343I
u = 0.542568 + 0.510771I
a = 0.52210 + 3.07554I
b = 0.532763 + 0.178517I
−5.00506 + 7.55141I 3.50931 − 12.15232I
u = 0.542568 − 0.510771I
a = 0.001593 − 0.449134I
b = −1.304380 + 0.124427I
−5.00506 − 1.89516I 3.50931 + 6.19343I
u = 0.542568 − 0.510771I
a = −0.61501 − 1.50358I
b = 0.26483 − 1.53096I
−0.86748 − 4.72329I 10.03858 + 9.17288I
u = 0.542568 − 0.510771I
a = 0.60283 + 1.61972I
b = 0.36969 + 2.21523I
−5.00506 − 7.55141I 3.50931 + 12.15232I
u = 0.542568 − 0.510771I
a = −0.56538 + 1.75401I
b = 0.148437 + 0.129555I
−0.86748 − 4.72329I 10.03858 + 9.17288I
u = 0.542568 − 0.510771I
a = 1.61755 + 1.32277I
b = −0.558791 + 1.096730I
−5.00506 − 1.89516I 3.50931 + 6.19343I
u = 0.542568 − 0.510771I
a = 0.52210 − 3.07554I
b = 0.532763 − 0.178517I
−5.00506 − 7.55141I 3.50931 + 12.15232I
18
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.05382 + 1.07114I
a = −0.636651 + 0.799114I
b = 0.05712 + 1.80415I
−7.70577 + 3.91715I 4.22349 − 3.00324I
u = 1.05382 + 1.07114I
a = 0.483361 − 1.033770I
b = −0.29586 − 1.71294I
−11.84340 + 6.74527I −2.30577 − 5.98269I
u = 1.05382 + 1.07114I
a = 0.949402 − 0.634817I
b = 0.33592 − 2.21885I
−11.84340 + 1.08902I −2.30577 − 0.02379I
u = 1.05382 + 1.07114I
a = −0.784649 + 0.847003I
b = 0.20283 + 1.45463I
−11.84340 + 1.08902I −2.30577 − 0.02379I
u = 1.05382 + 1.07114I
a = 0.644337 − 0.975137I
b = −0.65087 − 1.65072I
−7.70577 + 3.91715I 4.22349 − 3.00324I
u = 1.05382 + 1.07114I
a = −0.665982 + 1.230780I
b = 1.13741 + 2.12047I
−11.84340 + 6.74527I −2.30577 − 5.98269I
u = 1.05382 − 1.07114I
a = −0.636651 − 0.799114I
b = 0.05712 − 1.80415I
−7.70577 − 3.91715I 4.22349 + 3.00324I
u = 1.05382 − 1.07114I
a = 0.483361 + 1.033770I
b = −0.29586 + 1.71294I
−11.84340 − 6.74527I −2.30577 + 5.98269I
u = 1.05382 − 1.07114I
a = 0.949402 + 0.634817I
b = 0.33592 + 2.21885I
−11.84340 − 1.08902I −2.30577 + 0.02379I
u = 1.05382 − 1.07114I
a = −0.784649 − 0.847003I
b = 0.20283 − 1.45463I
−11.84340 − 1.08902I −2.30577 + 0.02379I
19
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.05382 − 1.07114I
a = 0.644337 + 0.975137I
b = −0.65087 + 1.65072I
−7.70577 − 3.91715I 4.22349 + 3.00324I
u = 1.05382 − 1.07114I
a = −0.665982 − 1.230780I
b = 1.13741 − 2.12047I
−11.84340 − 6.74527I −2.30577 + 5.98269I
20
IV.
I
u
4
= ha
5
− 5a
4
+ 5a
3
+ 5a
2
+ 7b − 10a − 2, a
6
− a
5
− a
4
+ 4a
3
+ 3a
2
− 1, u + 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
−1
a
3
=
a
−
1
7
a
5
+
5
7
a
4
+ ··· +
10
7
a +
2
7
a
7
=
1
−1
a
4
=
1
7
a
5
−
5
7
a
4
+ ··· −
10
7
a −
2
7
−
2
7
a
5
+
10
7
a
4
+ ··· +
27
7
a +
4
7
a
11
=
−1
0
a
12
=
4
7
a
5
−
6
7
a
4
+ ··· +
2
7
a −
8
7
4
7
a
5
−
6
7
a
4
+ ··· +
2
7
a −
1
7
a
2
=
1
7
a
5
−
5
7
a
4
+ ··· −
3
7
a −
2
7
−
1
7
a
5
+
5
7
a
4
+ ··· +
10
7
a +
2
7
a
1
=
1
7
a
5
−
5
7
a
4
+ ··· −
3
7
a −
2
7
−
1
7
a
5
+
5
7
a
4
+ ··· +
10
7
a +
2
7
a
5
=
−
2
7
a
5
+
3
7
a
4
+ ··· +
6
7
a +
4
7
3
7
a
5
−
1
7
a
4
+ ··· +
12
7
a −
6
7
a
9
=
1
−1
a
8
=
4
7
a
5
−
6
7
a
4
+ ··· +
2
7
a +
6
7
−
4
7
a
5
+
6
7
a
4
+ ··· −
2
7
a −
6
7
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
4
7
a
5
+
20
7
a
4
−
20
7
a
3
−
20
7
a
2
+
40
7
a +
127
7
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
6
c
2
, c
11
(u
3
− u
2
+ 1)
2
c
3
, c
4
, c
7
c
8
u
6
− u
5
− u
4
+ 4u
3
+ 3u
2
− 1
c
5
(u
3
− u
2
+ 2u − 1)
2
c
6
(u + 1)
6
c
9
, c
10
(u − 1)
6
c
12
(u
3
+ u
2
+ 2u + 1)
2
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
6
c
2
, c
11
(y
3
− y
2
+ 2y −1)
2
c
3
, c
4
, c
7
c
8
y
6
− 3y
5
+ 15y
4
− 24y
3
+ 11y
2
− 6y + 1
c
5
, c
12
(y
3
+ 3y
2
+ 2y −1)
2
c
6
, c
9
, c
10
(y −1)
6
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = −1.22142
b = 0.754878
2.75839 20.0200
u = −1.00000
a = −0.542287 + 0.460350I
b = −0.877439 + 0.744862I
−1.37919 − 2.82812I 13.49024 + 2.97945I
u = −1.00000
a = −0.542287 − 0.460350I
b = −0.877439 − 0.744862I
−1.37919 + 2.82812I 13.49024 − 2.97945I
u = −1.00000
a = 0.466540
b = 0.754878
2.75839 20.0200
u = −1.00000
a = 1.41973 + 1.20521I
b = −0.877439 − 0.744862I
−1.37919 + 2.82812I 13.49024 − 2.97945I
u = −1.00000
a = 1.41973 − 1.20521I
b = −0.877439 + 0.744862I
−1.37919 − 2.82812I 13.49024 + 2.97945I
24
V. I
v
1
= ha, b
3
+ b
2
− 1, v − 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
1
0
a
3
=
0
b
a
7
=
1
0
a
4
=
−b
b
a
11
=
1
0
a
12
=
1
−b
2
a
2
=
−b
b
a
1
=
−b
b
a
5
=
−b
2
+ 1
b
2
+ b − 1
a
9
=
1
0
a
8
=
b
2
+ 1
−b
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4b + 6
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
, c
9
c
10
u
3
c
2
, c
3
, c
4
c
7
, c
8
, c
11
u
3
+ u
2
− 1
c
5
, c
12
u
3
− u
2
+ 2u − 1
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
, c
9
c
10
y
3
c
2
, c
3
, c
4
c
7
, c
8
, c
11
y
3
− y
2
+ 2y − 1
c
5
, c
12
y
3
+ 3y
2
+ 2y − 1
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 1.00000
a = 0
b = −0.877439 + 0.744862I
−3.02413 − 2.82812I 2.49024 + 2.97945I
v = 1.00000
a = 0
b = −0.877439 − 0.744862I
−3.02413 + 2.82812I 2.49024 − 2.97945I
v = 1.00000
a = 0
b = 0.754878
1.11345 9.01950
28
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
9
(u
7
+ 3u
6
+ 3u
5
− 2u
4
− 6u
3
− 3u
2
+ 3u + 2)
6
· (u
19
− 11u
18
+ ··· − 575u + 125)(u
25
− 24u
24
+ ··· − 1246u + 85)
c
2
, c
11
((u
3
− u
2
+ 1)
2
)(u
3
+ u
2
− 1)(u
19
+ u
18
+ ··· + 3u + 1)
· (u
25
+ 18u
23
+ ··· + 10u + 1)(u
42
− 3u
41
+ ··· + 3904u − 211)
c
3
, c
8
(u
3
+ u
2
− 1)(u
6
− u
5
+ ··· + 3u
2
− 1)(u
19
+ u
18
+ ··· + 2u + 1)
· (u
25
− 15u
23
+ ··· − u − 1)(u
42
− 24u
40
+ ··· − 18828u + 2079)
c
4
, c
7
(u
3
+ u
2
− 1)(u
6
− u
5
+ ··· + 3u
2
− 1)(u
19
+ 4u
17
+ ··· + 4u + 1)
· (u
25
− u
24
+ ··· + u − 1)(u
42
+ 6u
40
+ ··· − 824u + 37)
c
5
((u
3
− u
2
+ 2u − 1)
3
)(u
3
+ u
2
+ 2u + 1)
14
(u
19
+ 3u
18
+ ··· − 30u − 7)
· (u
25
− 15u
24
+ ··· − 768u + 64)
c
6
u
3
(u + 1)
6
(u
7
+ 2u
6
+ 2u
5
− u
4
− 2u
3
− 3u
2
− 2u − 1)
6
· (u
19
− 7u
18
+ ··· − 7u + 1)(u
25
− 14u
24
+ ··· + 802u − 85)
c
9
, c
10
u
3
(u − 1)
6
(u
7
+ 2u
6
+ 2u
5
− u
4
− 2u
3
− 3u
2
− 2u − 1)
6
· (u
19
+ 7u
18
+ ··· − 7u − 1)(u
25
− 14u
24
+ ··· + 802u − 85)
c
12
(u
3
− u
2
+ 2u − 1)(u
3
+ u
2
+ 2u + 1)
16
(u
19
− 3u
18
+ ··· − 30u + 7)
· (u
25
− 15u
24
+ ··· − 768u + 64)
29
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
9
(y
7
− 3y
6
+ 9y
5
− 16y
4
+ 30y
3
− 37y
2
+ 21y − 4)
6
· (y
19
− 9y
18
+ ··· + 103125y − 15625)
· (y
25
− 12y
24
+ ··· − 5534y − 7225)
c
2
, c
11
((y
3
− y
2
+ 2y − 1)
3
)(y
19
+ 15y
18
+ ··· + 7y − 1)
· (y
25
+ 36y
24
+ ··· + 36y − 1)(y
42
+ 49y
41
+ ··· + 2545240y + 44521)
c
3
, c
8
(y
3
− y
2
+ 2y − 1)(y
6
− 3y
5
+ 15y
4
− 24y
3
+ 11y
2
− 6y + 1)
· (y
19
− 19y
18
+ ··· − 6y − 1)(y
25
− 30y
24
+ ··· + 15y − 1)
· (y
42
− 48y
41
+ ··· − 47845242y + 4322241)
c
4
, c
7
(y
3
− y
2
+ 2y − 1)(y
6
− 3y
5
+ 15y
4
− 24y
3
+ 11y
2
− 6y + 1)
· (y
19
+ 8y
18
+ ··· + 22y − 1)(y
25
+ 9y
24
+ ··· + 3y − 1)
· (y
42
+ 12y
41
+ ··· − 687930y + 1369)
c
5
, c
12
((y
3
+ 3y
2
+ 2y − 1)
17
)(y
19
+ 13y
18
+ ··· − 206y − 49)
· (y
25
+ 13y
24
+ ··· + 30720y − 4096)
c
6
, c
9
, c
10
y
3
(y − 1)
6
(y
7
+ 4y
5
− y
4
− 6y
3
− 3y
2
− 2y − 1)
6
· (y
19
− 9y
18
+ ··· − y − 1)(y
25
− 8y
24
+ ··· + 28824y − 7225)
30
