11a
171
(K11a
171
)
A knot diagram
1
Linearized knot diagam
5 1 7 8 2 9 10 11 3 4 6
Solving Sequence
2,5 6,9
7 1 3 10 11 8 4
c
5
c
6
c
1
c
2
c
9
c
11
c
8
c
4
c
3
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h519990u
45
+ 1958497u
44
+ ··· + 69383b + 409894,
430369u
45
+ 1395316u
44
+ ··· + 69383a + 63169, u
46
+ 5u
45
+ ··· + 5u + 1i
I
u
2
= h−29u
30
a + 623u
30
+ ··· + 2a − 1427, 2u
29
a − 2u
30
+ ··· + 2a + 2, u
31
− 2u
30
+ ··· − 2u + 1i
I
u
3
= h2u
14
− u
13
− 7u
12
+ 6u
11
+ 12u
10
− 13u
9
− 10u
8
+ 15u
7
+ 4u
6
− 9u
5
+ 2u
4
+ 2u
3
− 3u
2
+ b − u + 2,
− u
15
+ 3u
14
+ ··· + a + 3,
u
16
− 2u
15
− 2u
14
+ 8u
13
− u
12
− 14u
11
+ 10u
10
+ 11u
9
− 15u
8
− u
7
+ 11u
6
− 6u
5
− 2u
4
+ 4u
3
− 2u + 1i
I
u
4
= hb − a − 1, a
2
+ 3a + 1, u + 1i
I
v
1
= ha, b − 1, v −1i
* 5 irreducible components of dim
C
= 0, with total 127 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
= h5.20 × 10
5
u
45
+ 1 .96 × 10
6
u
44
+ · · · + 6.94 × 10
4
b + 4.10 × 10
5
, 4.30 ×
10
5
u
45
+1.40×10
6
u
44
+· · ·+6.94×10
4
a+6.32×10
4
, u
46
+5u
45
+· · ·+5u +1i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
u
2
a
9
=
−6.20280u
45
− 20.1103u
44
+ ··· − 3.24905u − 0.910439
−7.49449u
45
− 28.2273u
44
+ ··· − 26.5100u − 5.90770
a
7
=
−8.99833u
45
− 31.6872u
44
+ ··· − 10.4069u − 1.60077
−5.46625u
45
− 23.1524u
44
+ ··· − 24.6669u − 5.54479
a
1
=
u
u
a
3
=
−u
3
−u
3
+ u
a
10
=
−6.82680u
45
− 25.1173u
44
+ ··· − 11.4935u − 3.08978
−5.46625u
45
− 22.1524u
44
+ ··· − 23.6669u − 5.54479
a
11
=
u
3
u
5
− u
3
+ u
a
8
=
−4.24914u
45
− 18.3303u
44
+ ··· − 13.4790u − 4.32022
−2.54225u
45
− 10.0590u
44
+ ··· − 8.86675u − 1.62373
a
4
=
−6.16768u
45
− 23.6777u
44
+ ··· − 9.23804u − 2.10931
−6.74815u
45
− 29.0939u
44
+ ··· − 27.8357u − 6.23964
a
4
=
−6.16768u
45
− 23.6777u
44
+ ··· − 9.23804u − 2.10931
−6.74815u
45
− 29.0939u
44
+ ··· − 27.8357u − 6.23964
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
130759
69383
u
45
+
81491
69383
u
44
+ ··· −
583416
69383
u −
777173
69383
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
46
+ 5u
45
+ ··· + 5u + 1
c
2
u
46
+ 23u
45
+ ··· − 11u + 1
c
3
, c
10
u
46
− u
45
+ ··· + 2u + 1
c
4
, c
9
u
46
− 2u
45
+ ··· + u + 1
c
6
, c
8
u
46
+ 6u
45
+ ··· − 9u + 1
c
7
u
46
+ 26u
45
+ ··· + u + 1
c
11
u
46
+ 15u
45
+ ··· + 1885u + 149
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
46
− 23y
45
+ ··· + 11y + 1
c
2
y
46
+ 5y
45
+ ··· − 73y + 1
c
3
, c
10
y
46
− 19y
45
+ ··· − 52y + 1
c
4
, c
9
y
46
− 2y
45
+ ··· + 27y + 1
c
6
, c
8
y
46
− 30y
45
+ ··· − 121y + 1
c
7
y
46
+ 38y
44
+ ··· + 49y + 1
c
11
y
46
+ 13y
45
+ ··· + 238229y + 22201
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.933486 + 0.444661I
a = 1.39390 − 0.39376I
b = 0.917537 − 0.675621I
−1.098380 + 0.644192I −5.70718 − 0.44366I
u = −0.933486 − 0.444661I
a = 1.39390 + 0.39376I
b = 0.917537 + 0.675621I
−1.098380 − 0.644192I −5.70718 + 0.44366I
u = −0.751399 + 0.721194I
a = 0.377914 + 0.652284I
b = −0.232701 + 0.476942I
1.87378 + 10.77040I −1.30875 − 9.40079I
u = −0.751399 − 0.721194I
a = 0.377914 − 0.652284I
b = −0.232701 − 0.476942I
1.87378 − 10.77040I −1.30875 + 9.40079I
u = −0.856947 + 0.701617I
a = −0.552390 + 0.650998I
b = −0.148213 + 0.105841I
1.57181 − 5.40355I −1.95277 + 5.01520I
u = −0.856947 − 0.701617I
a = −0.552390 − 0.650998I
b = −0.148213 − 0.105841I
1.57181 + 5.40355I −1.95277 − 5.01520I
u = −0.291347 + 0.840599I
a = 0.415288 − 0.440575I
b = −1.79617 − 0.89753I
−0.71987 − 13.43220I −2.36696 + 7.45298I
u = −0.291347 − 0.840599I
a = 0.415288 + 0.440575I
b = −1.79617 + 0.89753I
−0.71987 + 13.43220I −2.36696 − 7.45298I
u = −0.132938 + 0.848595I
a = 0.159620 − 0.433157I
b = −0.956107 + 0.290168I
−2.72587 + 3.54069I −7.48667 − 4.84167I
u = −0.132938 − 0.848595I
a = 0.159620 + 0.433157I
b = −0.956107 − 0.290168I
−2.72587 − 3.54069I −7.48667 + 4.84167I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.660174 + 0.548978I
a = 0.018944 − 1.119640I
b = −0.023291 − 1.106980I
−0.36479 + 3.45703I −5.70781 − 7.10352I
u = −0.660174 − 0.548978I
a = 0.018944 + 1.119640I
b = −0.023291 + 1.106980I
−0.36479 − 3.45703I −5.70781 + 7.10352I
u = 1.112300 + 0.261314I
a = −1.89980 − 0.01447I
b = −0.856736 − 0.971479I
−5.91551 − 1.58146I −13.59206 + 3.66934I
u = 1.112300 − 0.261314I
a = −1.89980 + 0.01447I
b = −0.856736 + 0.971479I
−5.91551 + 1.58146I −13.59206 − 3.66934I
u = 1.135200 + 0.294115I
a = −1.85511 + 1.41022I
b = −1.71754 − 0.41559I
−6.20814 + 1.80497I −14.2464 − 4.3963I
u = 1.135200 − 0.294115I
a = −1.85511 − 1.41022I
b = −1.71754 + 0.41559I
−6.20814 − 1.80497I −14.2464 + 4.3963I
u = −0.375652 + 0.726957I
a = 0.249990 + 0.342484I
b = 1.203890 − 0.206841I
−1.60276 − 0.98411I −7.53408 + 0.28472I
u = −0.375652 − 0.726957I
a = 0.249990 − 0.342484I
b = 1.203890 + 0.206841I
−1.60276 + 0.98411I −7.53408 − 0.28472I
u = 0.881986 + 0.787307I
a = 0.191650 − 0.055578I
b = −0.053824 + 0.253337I
3.98279 − 2.95487I 23.7349 − 13.5735I
u = 0.881986 − 0.787307I
a = 0.191650 + 0.055578I
b = −0.053824 − 0.253337I
3.98279 + 2.95487I 23.7349 + 13.5735I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.099790 + 0.438913I
a = −1.83196 − 1.36948I
b = −2.21067 − 0.24014I
−4.28647 + 3.53114I −10.17349 − 4.71484I
u = −1.099790 − 0.438913I
a = −1.83196 + 1.36948I
b = −2.21067 + 0.24014I
−4.28647 − 3.53114I −10.17349 + 4.71484I
u = 1.059210 + 0.534264I
a = 0.541434 − 0.766541I
b = 0.805091 + 0.458424I
0.17597 − 5.33365I −1.16724 + 4.83689I
u = 1.059210 − 0.534264I
a = 0.541434 + 0.766541I
b = 0.805091 − 0.458424I
0.17597 + 5.33365I −1.16724 − 4.83689I
u = 1.099340 + 0.465407I
a = −1.63134 + 0.89715I
b = −1.21983 − 1.23467I
−4.10186 − 3.81474I −9.79702 + 3.58298I
u = 1.099340 − 0.465407I
a = −1.63134 − 0.89715I
b = −1.21983 + 1.23467I
−4.10186 + 3.81474I −9.79702 − 3.58298I
u = −0.278150 + 0.732712I
a = −0.376095 + 0.785335I
b = 1.76661 + 0.88827I
−2.03242 − 4.83583I −8.60020 + 6.83106I
u = −0.278150 − 0.732712I
a = −0.376095 − 0.785335I
b = 1.76661 − 0.88827I
−2.03242 + 4.83583I −8.60020 − 6.83106I
u = −0.761418 + 0.115983I
a = 0.858924 − 0.607457I
b = 0.637850 − 0.558762I
−1.37145 + 0.34774I −7.35312 − 1.68014I
u = −0.761418 − 0.115983I
a = 0.858924 + 0.607457I
b = 0.637850 + 0.558762I
−1.37145 − 0.34774I −7.35312 + 1.68014I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.215530 + 0.243371I
a = 1.75500 − 1.20403I
b = 1.83289 + 0.11458I
−5.60396 + 10.10350I −8.00817 − 5.63549I
u = 1.215530 − 0.243371I
a = 1.75500 + 1.20403I
b = 1.83289 − 0.11458I
−5.60396 − 10.10350I −8.00817 + 5.63549I
u = 0.431319 + 0.618019I
a = 0.744120 − 0.125502I
b = −0.551257 + 0.192009I
2.00312 + 0.77598I 3.08048 − 0.37837I
u = 0.431319 − 0.618019I
a = 0.744120 + 0.125502I
b = −0.551257 − 0.192009I
2.00312 − 0.77598I 3.08048 + 0.37837I
u = −1.115390 + 0.573899I
a = −1.01263 − 1.47969I
b = −1.60084 − 0.24549I
−3.77845 + 5.97580I −9.62613 − 4.25022I
u = −1.115390 − 0.573899I
a = −1.01263 + 1.47969I
b = −1.60084 + 0.24549I
−3.77845 − 5.97580I −9.62613 + 4.25022I
u = −1.133410 + 0.543345I
a = −2.66832 − 1.09843I
b = −2.59106 + 0.99651I
−4.51494 + 9.66961I −12.1786 − 10.5958I
u = −1.133410 − 0.543345I
a = −2.66832 + 1.09843I
b = −2.59106 − 0.99651I
−4.51494 − 9.66961I −12.1786 + 10.5958I
u = 1.225340 + 0.349011I
a = 1.355770 − 0.047043I
b = 0.889349 + 1.016990I
−6.99619 − 7.57481I −10.39877 + 7.23305I
u = 1.225340 − 0.349011I
a = 1.355770 + 0.047043I
b = 0.889349 − 1.016990I
−6.99619 + 7.57481I −10.39877 − 7.23305I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.197320 + 0.502148I
a = 1.031320 + 0.860349I
b = 1.50432 − 0.00862I
−5.94279 + 1.33870I 0
u = −1.197320 − 0.502148I
a = 1.031320 − 0.860349I
b = 1.50432 + 0.00862I
−5.94279 − 1.33870I 0
u = −1.165270 + 0.576600I
a = 2.37516 + 1.00046I
b = 2.36478 − 1.14677I
−3.3293 + 18.6712I 0
u = −1.165270 − 0.576600I
a = 2.37516 − 1.00046I
b = 2.36478 + 1.14677I
−3.3293 − 18.6712I 0
u = 0.092447 + 0.293184I
a = −1.64140 + 2.88752I
b = 1.035920 − 0.158140I
−1.65225 + 0.00944I −6.31613 + 0.26061I
u = 0.092447 − 0.293184I
a = −1.64140 − 2.88752I
b = 1.035920 + 0.158140I
−1.65225 − 0.00944I −6.31613 − 0.26061I
9
II. I
u
2
= h−29u
30
a + 623u
30
+ · · · + 2a − 1427, 2u
29
a − 2u
30
+ · · · + 2a +
2, u
31
− 2u
30
+ · · · − 2u + 1i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
u
2
a
9
=
a
0.0368488au
30
− 0.791614u
30
+ ··· − 0.00254130a + 1.81321
a
7
=
1.79161au
30
− 1.31639u
30
+ ··· − 0.813215a + 1.22872
0.416773au
30
+ 2.63278u
30
+ ··· − 0.373571a − 3.45743
a
1
=
u
u
a
3
=
−u
3
−u
3
+ u
a
10
=
0.0368488au
30
+ 2.20839u
30
+ ··· + 0.997459a − 2.18679
0.108005au
30
− 0.561626u
30
+ ··· − 0.0419314a + 1.41804
a
11
=
u
3
u
5
− u
3
+ u
a
8
=
0.0368488au
30
+ 2.20839u
30
+ ··· + 0.997459a − 2.18679
−0.0368488au
30
+ 0.791614u
30
+ ··· + 0.00254130a + 0.186785
a
4
=
−1.14485au
30
+ 0.353240u
30
+ ··· + 0.0444727a − 0.231258
−0.0635324au
30
+ 2.33037u
30
+ ··· + 0.142313a − 3.54003
a
4
=
−1.14485au
30
+ 0.353240u
30
+ ··· + 0.0444727a − 0.231258
−0.0635324au
30
+ 2.33037u
30
+ ··· + 0.142313a − 3.54003
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 11u
30
− 17u
29
− 77u
28
+ 156u
27
+ 228u
26
− 647u
25
− 267u
24
+ 1574u
23
− 282u
22
−
2362u
21
+1582u
20
+2004u
19
−2748u
18
−365u
17
+2591u
16
−1168u
15
−1234u
14
+1358u
13
+
106u
12
−640u
11
+ 136u
10
+ 174u
9
−30u
8
−92u
7
+ 60u
6
+ 44u
5
−44u
4
+ 16u
3
+ 11u −11
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
(u
31
− 2u
30
+ ··· − 2u + 1)
2
c
2
(u
31
+ 16u
30
+ ··· + 2u + 1)
2
c
3
, c
10
u
62
+ 2u
61
+ ··· + u − 1
c
4
, c
9
u
62
+ 2u
61
+ ··· − 211u + 31
c
6
, c
8
u
62
− 3u
61
+ ··· + 378u − 49
c
7
(u
31
− 15u
30
+ ··· + 3u − 2)
2
c
11
(u
31
− 9u
30
+ ··· + 73u − 8)
2
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
31
− 16y
30
+ ··· + 2y −1)
2
c
2
(y
31
+ 28y
29
+ ··· − 14y −1)
2
c
3
, c
10
y
62
+ 12y
61
+ ··· + 29y + 1
c
4
, c
9
y
62
+ 58y
60
+ ··· − 104599y + 961
c
6
, c
8
y
62
+ 13y
61
+ ··· + 17738y + 2401
c
7
(y
31
− 3y
30
+ ··· + 69y −4)
2
c
11
(y
31
+ 13y
30
+ ··· + 833y −64)
2
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.790665 + 0.695036I
a = 0.669170 − 0.332267I
b = 0.0656518 + 0.0523021I
3.79486 − 2.62922I 6.53544 + 4.19495I
u = 0.790665 + 0.695036I
a = −0.207742 + 0.086773I
b = −0.126798 + 0.478191I
3.79486 − 2.62922I 6.53544 + 4.19495I
u = 0.790665 − 0.695036I
a = 0.669170 + 0.332267I
b = 0.0656518 − 0.0523021I
3.79486 + 2.62922I 6.53544 − 4.19495I
u = 0.790665 − 0.695036I
a = −0.207742 − 0.086773I
b = −0.126798 − 0.478191I
3.79486 + 2.62922I 6.53544 − 4.19495I
u = 0.271790 + 0.844936I
a = 0.569593 + 0.287323I
b = −1.48334 + 0.65965I
0.86287 + 5.06730I 2.75638 − 8.05298I
u = 0.271790 + 0.844936I
a = −0.119874 − 0.268542I
b = 0.884101 − 0.757543I
0.86287 + 5.06730I 2.75638 − 8.05298I
u = 0.271790 − 0.844936I
a = 0.569593 − 0.287323I
b = −1.48334 − 0.65965I
0.86287 − 5.06730I 2.75638 + 8.05298I
u = 0.271790 − 0.844936I
a = −0.119874 + 0.268542I
b = 0.884101 + 0.757543I
0.86287 − 5.06730I 2.75638 + 8.05298I
u = −1.11799
a = −0.284257
b = 0.391788
−2.94773 9.04290
u = −1.11799
a = 2.15022
b = 1.72304
−2.94773 9.04290
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.057020 + 0.392863I
a = 1.81595 + 1.58347I
b = 0.457743 + 1.080970I
−1.41458 + 1.86246I −6.47152 − 4.51832I
u = 1.057020 + 0.392863I
a = −1.94507 + 1.62723I
b = −2.78630 − 0.37900I
−1.41458 + 1.86246I −6.47152 − 4.51832I
u = 1.057020 − 0.392863I
a = 1.81595 − 1.58347I
b = 0.457743 − 1.080970I
−1.41458 − 1.86246I −6.47152 + 4.51832I
u = 1.057020 − 0.392863I
a = −1.94507 − 1.62723I
b = −2.78630 + 0.37900I
−1.41458 − 1.86246I −6.47152 + 4.51832I
u = −1.037230 + 0.490832I
a = 0.871323 − 0.069012I
b = 1.081080 + 0.215998I
0.442167 + 0.494118I −0.11941 − 1.82079I
u = −1.037230 + 0.490832I
a = 2.98544 + 0.56960I
b = 1.86765 − 1.56472I
0.442167 + 0.494118I −0.11941 − 1.82079I
u = −1.037230 − 0.490832I
a = 0.871323 + 0.069012I
b = 1.081080 − 0.215998I
0.442167 − 0.494118I −0.11941 + 1.82079I
u = −1.037230 − 0.490832I
a = 2.98544 − 0.56960I
b = 1.86765 + 1.56472I
0.442167 − 0.494118I −0.11941 + 1.82079I
u = 1.026550 + 0.519350I
a = −0.1270640 + 0.0109867I
b = −0.047205 + 0.721888I
0.44756 − 5.41860I −0.32653 + 5.88711I
u = 1.026550 + 0.519350I
a = 1.29914 − 1.65916I
b = 1.61693 + 0.26044I
0.44756 − 5.41860I −0.32653 + 5.88711I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.026550 − 0.519350I
a = −0.1270640 − 0.0109867I
b = −0.047205 − 0.721888I
0.44756 + 5.41860I −0.32653 − 5.88711I
u = 1.026550 − 0.519350I
a = 1.29914 + 1.65916I
b = 1.61693 − 0.26044I
0.44756 + 5.41860I −0.32653 − 5.88711I
u = 0.753184 + 0.319413I
a = −0.788685 + 0.289104I
b = 0.022444 + 1.150080I
−0.12340 − 4.63553I −7.19066 + 8.64807I
u = 0.753184 + 0.319413I
a = −0.30112 − 2.73557I
b = 0.95069 − 1.18509I
−0.12340 − 4.63553I −7.19066 + 8.64807I
u = 0.753184 − 0.319413I
a = −0.788685 − 0.289104I
b = 0.022444 − 1.150080I
−0.12340 + 4.63553I −7.19066 − 8.64807I
u = 0.753184 − 0.319413I
a = −0.30112 + 2.73557I
b = 0.95069 + 1.18509I
−0.12340 + 4.63553I −7.19066 − 8.64807I
u = −1.094170 + 0.506739I
a = −1.49471 + 1.74452I
b = 0.001444 + 1.236820I
−0.54438 + 8.91512I −2.96887 − 11.01596I
u = −1.094170 + 0.506739I
a = −2.77988 − 0.45386I
b = −2.38927 + 2.05281I
−0.54438 + 8.91512I −2.96887 − 11.01596I
u = −1.094170 − 0.506739I
a = −1.49471 − 1.74452I
b = 0.001444 − 1.236820I
−0.54438 − 8.91512I −2.96887 + 11.01596I
u = −1.094170 − 0.506739I
a = −2.77988 + 0.45386I
b = −2.38927 − 2.05281I
−0.54438 − 8.91512I −2.96887 + 11.01596I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.483181 + 0.627527I
a = 1.053820 − 0.244238I
b = 0.024721 + 0.257856I
2.01990 + 0.90453I 3.65108 − 0.79331I
u = 0.483181 + 0.627527I
a = 0.475298 + 0.027991I
b = −1.131290 + 0.256367I
2.01990 + 0.90453I 3.65108 − 0.79331I
u = 0.483181 − 0.627527I
a = 1.053820 + 0.244238I
b = 0.024721 − 0.257856I
2.01990 − 0.90453I 3.65108 + 0.79331I
u = 0.483181 − 0.627527I
a = 0.475298 − 0.027991I
b = −1.131290 − 0.256367I
2.01990 − 0.90453I 3.65108 + 0.79331I
u = −1.178190 + 0.355689I
a = 1.48280 + 0.00076I
b = 1.02174 − 1.55077I
−6.17761 − 0.88062I −14.6380 + 2.9072I
u = −1.178190 + 0.355689I
a = −1.38943 − 1.77723I
b = −1.80498 − 0.32855I
−6.17761 − 0.88062I −14.6380 + 2.9072I
u = −1.178190 − 0.355689I
a = 1.48280 − 0.00076I
b = 1.02174 + 1.55077I
−6.17761 + 0.88062I −14.6380 − 2.9072I
u = −1.178190 − 0.355689I
a = −1.38943 + 1.77723I
b = −1.80498 + 0.32855I
−6.17761 + 0.88062I −14.6380 − 2.9072I
u = 0.168042 + 0.738886I
a = 0.608505 + 1.197800I
b = −1.277980 − 0.170746I
−2.24573 + 4.52331I −8.41907 − 6.24640I
u = 0.168042 + 0.738886I
a = −0.382111 − 0.116834I
b = 1.53489 − 1.07053I
−2.24573 + 4.52331I −8.41907 − 6.24640I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.168042 − 0.738886I
a = 0.608505 − 1.197800I
b = −1.277980 + 0.170746I
−2.24573 − 4.52331I −8.41907 + 6.24640I
u = 0.168042 − 0.738886I
a = −0.382111 + 0.116834I
b = 1.53489 + 1.07053I
−2.24573 − 4.52331I −8.41907 + 6.24640I
u = −1.229730 + 0.258953I
a = −0.737514 − 0.824427I
b = −0.763646 − 0.121799I
−3.97519 − 1.59170I −1.35198 + 10.14097I
u = −1.229730 + 0.258953I
a = 1.60333 + 0.66052I
b = 1.73249 − 0.42359I
−3.97519 − 1.59170I −1.35198 + 10.14097I
u = −1.229730 − 0.258953I
a = −0.737514 + 0.824427I
b = −0.763646 + 0.121799I
−3.97519 + 1.59170I −1.35198 − 10.14097I
u = −1.229730 − 0.258953I
a = 1.60333 − 0.66052I
b = 1.73249 + 0.42359I
−3.97519 + 1.59170I −1.35198 − 10.14097I
u = 1.157760 + 0.512519I
a = 1.42443 − 1.28295I
b = 2.40547 − 0.13583I
−5.08886 − 9.19357I −11.4929 + 8.9901I
u = 1.157760 + 0.512519I
a = −2.67908 + 0.57634I
b = −2.05828 − 1.41962I
−5.08886 − 9.19357I −11.4929 + 8.9901I
u = 1.157760 − 0.512519I
a = 1.42443 + 1.28295I
b = 2.40547 + 0.13583I
−5.08886 + 9.19357I −11.4929 − 8.9901I
u = 1.157760 − 0.512519I
a = −2.67908 − 0.57634I
b = −2.05828 + 1.41962I
−5.08886 + 9.19357I −11.4929 − 8.9901I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.171540 + 0.571368I
a = −1.63048 + 0.31699I
b = −1.32040 − 0.86495I
−1.82208 − 10.29010I −1.64284 + 11.44923I
u = 1.171540 + 0.571368I
a = 1.92634 − 0.84777I
b = 2.04018 + 1.07427I
−1.82208 − 10.29010I −1.64284 + 11.44923I
u = 1.171540 − 0.571368I
a = −1.63048 − 0.31699I
b = −1.32040 + 0.86495I
−1.82208 + 10.29010I −1.64284 − 11.44923I
u = 1.171540 − 0.571368I
a = 1.92634 + 0.84777I
b = 2.04018 − 1.07427I
−1.82208 + 10.29010I −1.64284 − 11.44923I
u = −0.467072 + 0.505817I
a = 0.794897 − 0.380963I
b = −1.10555 − 1.62360I
2.11162 + 3.64112I 4.51546 − 4.55522I
u = −0.467072 + 0.505817I
a = −0.89772 − 1.89421I
b = −0.377102 − 0.526421I
2.11162 + 3.64112I 4.51546 − 4.55522I
u = −0.467072 − 0.505817I
a = 0.794897 + 0.380963I
b = −1.10555 + 1.62360I
2.11162 − 3.64112I 4.51546 + 4.55522I
u = −0.467072 − 0.505817I
a = −0.89772 + 1.89421I
b = −0.377102 + 0.526421I
2.11162 − 3.64112I 4.51546 + 4.55522I
u = −0.314340 + 0.572965I
a = 0.384701 + 0.785838I
b = −0.35569 + 1.42340I
1.67219 − 4.56405I 2.14197 + 7.53125I
u = −0.314340 + 0.572965I
a = −1.91723 + 0.69975I
b = 1.26319 + 1.26380I
1.67219 − 4.56405I 2.14197 + 7.53125I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.314340 − 0.572965I
a = 0.384701 − 0.785838I
b = −0.35569 − 1.42340I
1.67219 + 4.56405I 2.14197 − 7.53125I
u = −0.314340 − 0.572965I
a = −1.91723 − 0.69975I
b = 1.26319 − 1.26380I
1.67219 + 4.56405I 2.14197 − 7.53125I
19
III.
I
u
3
= h2u
14
−u
13
+· · ·+b+2, −u
15
+3u
14
+· · ·+a+3, u
16
−2u
15
+· · ·−2u+1i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
u
2
a
9
=
u
15
− 3u
14
+ ··· + 2u − 3
−2u
14
+ u
13
+ ··· + u − 2
a
7
=
u
15
− 3u
14
+ ··· − u − 2
−u
15
+ 3u
13
+ ··· − 2u − 1
a
1
=
u
u
a
3
=
−u
3
−u
3
+ u
a
10
=
−u
14
+ 4u
12
+ ··· + u − 2
−u
14
+ u
13
+ ··· + u − 1
a
11
=
u
3
u
5
− u
3
+ u
a
8
=
u
15
− 2u
14
+ ··· + 2u − 2
−u
14
+ u
13
+ ··· + u
2
− 1
a
4
=
−3u
15
+ 3u
14
+ ··· − 5u + 3
−3u
15
+ 4u
14
+ ··· − 4u + 3
a
4
=
−3u
15
+ 3u
14
+ ··· − 5u + 3
−3u
15
+ 4u
14
+ ··· − 4u + 3
(ii) Obstruction class = 1
(iii) Cusp Shapes = 20u
15
− 25u
14
− 65u
13
+ 116u
12
+ 83u
11
− 235u
10
+ 247u
8
−
98u
7
− 123u
6
+ 118u
5
− 7u
4
− 52u
3
+ 27u
2
+ 26u − 20
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
16
+ 2u
15
+ ··· + 2u + 1
c
2
u
16
+ 8u
15
+ ··· + 4u + 1
c
3
, c
10
u
16
+ 4u
14
+ ··· + u + 1
c
4
, c
9
u
16
− u
15
+ ··· + 4u
2
+ 1
c
5
u
16
− 2u
15
+ ··· − 2u + 1
c
6
, c
8
u
16
− 5u
15
+ ··· − 8u + 1
c
7
u
16
+ 11u
15
+ ··· + 38u + 5
c
11
u
16
+ 6u
15
+ ··· + 14u + 5
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
16
− 8y
15
+ ··· − 4y + 1
c
2
y
16
+ 4y
15
+ ··· + 8y + 1
c
3
, c
10
y
16
+ 8y
15
+ ··· + 5y + 1
c
4
, c
9
y
16
+ 5y
15
+ ··· + 8y + 1
c
6
, c
8
y
16
+ 9y
15
+ ··· − 8y + 1
c
7
y
16
+ 3y
15
+ ··· + 126y + 25
c
11
y
16
− 6y
14
+ ··· − 106y + 25
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.024370 + 0.459927I
a = 2.44332 + 0.20318I
b = 1.74413 + 1.13632I
−0.384219 + 0.628959I −3.48364 − 2.80361I
u = 1.024370 − 0.459927I
a = 2.44332 − 0.20318I
b = 1.74413 − 1.13632I
−0.384219 − 0.628959I −3.48364 + 2.80361I
u = −1.020340 + 0.486012I
a = 0.18997 + 1.48209I
b = 1.270210 − 0.038066I
−0.21632 + 6.81045I −4.49677 − 10.12296I
u = −1.020340 − 0.486012I
a = 0.18997 − 1.48209I
b = 1.270210 + 0.038066I
−0.21632 − 6.81045I −4.49677 + 10.12296I
u = 0.877768 + 0.808431I
a = −0.118784 + 0.214301I
b = 0.0389492 − 0.0700930I
3.87749 − 3.01517I −33.6443 + 18.9911I
u = 0.877768 − 0.808431I
a = −0.118784 − 0.214301I
b = 0.0389492 + 0.0700930I
3.87749 + 3.01517I −33.6443 − 18.9911I
u = 0.197391 + 0.752145I
a = −0.554414 − 0.452739I
b = 1.16852 − 0.80502I
−0.60305 + 4.58234I −2.40249 − 6.00817I
u = 0.197391 − 0.752145I
a = −0.554414 + 0.452739I
b = 1.16852 + 0.80502I
−0.60305 − 4.58234I −2.40249 + 6.00817I
u = −0.632624 + 0.437790I
a = 0.757123 − 1.153610I
b = −0.657889 + 0.179663I
1.10121 − 2.89037I −1.29781 + 2.83273I
u = −0.632624 − 0.437790I
a = 0.757123 + 1.153610I
b = −0.657889 − 0.179663I
1.10121 + 2.89037I −1.29781 − 2.83273I
23
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.189300 + 0.317097I
a = −1.20436 − 0.91552I
b = −1.309860 + 0.285883I
−4.77806 − 1.04547I −8.97927 + 2.31364I
u = −1.189300 − 0.317097I
a = −1.20436 + 0.91552I
b = −1.309860 − 0.285883I
−4.77806 + 1.04547I −8.97927 − 2.31364I
u = 1.151850 + 0.528952I
a = −2.18614 + 0.52851I
b = −1.99390 − 1.08782I
−3.34287 − 9.35884I −5.15004 + 8.71081I
u = 1.151850 − 0.528952I
a = −2.18614 − 0.52851I
b = −1.99390 + 1.08782I
−3.34287 + 9.35884I −5.15004 − 8.71081I
u = 0.590891 + 0.389110I
a = −0.32671 + 1.81658I
b = −0.76016 + 1.40762I
1.05595 − 4.33077I −0.04563 + 8.60569I
u = 0.590891 − 0.389110I
a = −0.32671 − 1.81658I
b = −0.76016 − 1.40762I
1.05595 + 4.33077I −0.04563 − 8.60569I
24
IV. I
u
4
= hb − a − 1, a
2
+ 3a + 1, u + 1i
(i) Arc colorings
a
2
=
0
−1
a
5
=
1
0
a
6
=
1
1
a
9
=
a
a + 1
a
7
=
a + 1
a + 2
a
1
=
−1
−1
a
3
=
1
0
a
10
=
2a + 1
a + 1
a
11
=
−1
−1
a
8
=
a + 1
a + 2
a
4
=
2
a + 3
a
4
=
2
a + 3
(ii) Obstruction class = 1
(iii) Cusp Shapes = −17
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
, c
8
(u − 1)
2
c
2
, c
5
(u + 1)
2
c
3
, c
4
, c
9
c
10
u
2
− u − 1
c
7
, c
11
u
2
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
8
(y −1)
2
c
3
, c
4
, c
9
c
10
y
2
− 3y + 1
c
7
, c
11
y
2
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = −0.381966
b = 0.618034
−3.28987 −17.0000
u = −1.00000
a = −2.61803
b = −1.61803
−3.28987 −17.0000
28
V. I
v
1
= ha, b − 1, v − 1i
(i) Arc colorings
a
2
=
1
0
a
5
=
1
0
a
6
=
1
0
a
9
=
0
1
a
7
=
1
1
a
1
=
1
0
a
3
=
1
0
a
10
=
1
1
a
11
=
1
0
a
8
=
1
1
a
4
=
2
1
a
4
=
2
1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6
29
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
c
7
, c
11
u
c
3
, c
4
, c
6
c
8
, c
9
, c
10
u + 1
30
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
7
, c
11
y
c
3
, c
4
, c
6
c
8
, c
9
, c
10
y −1
31
(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
32
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u(u − 1)
2
(u
16
+ 2u
15
+ ··· + 2u + 1)(u
31
− 2u
30
+ ··· − 2u + 1)
2
· (u
46
+ 5u
45
+ ··· + 5u + 1)
c
2
u(u + 1)
2
(u
16
+ 8u
15
+ ··· + 4u + 1)(u
31
+ 16u
30
+ ··· + 2u + 1)
2
· (u
46
+ 23u
45
+ ··· − 11u + 1)
c
3
, c
10
(u + 1)(u
2
− u − 1)(u
16
+ 4u
14
+ ··· + u + 1)(u
46
− u
45
+ ··· + 2u + 1)
· (u
62
+ 2u
61
+ ··· + u − 1)
c
4
, c
9
(u + 1)(u
2
− u − 1)(u
16
− u
15
+ ··· + 4u
2
+ 1)(u
46
− 2u
45
+ ··· + u + 1)
· (u
62
+ 2u
61
+ ··· − 211u + 31)
c
5
u(u + 1)
2
(u
16
− 2u
15
+ ··· − 2u + 1)(u
31
− 2u
30
+ ··· − 2u + 1)
2
· (u
46
+ 5u
45
+ ··· + 5u + 1)
c
6
, c
8
((u − 1)
2
)(u + 1)(u
16
− 5u
15
+ ··· − 8u + 1)(u
46
+ 6u
45
+ ··· − 9u + 1)
· (u
62
− 3u
61
+ ··· + 378u − 49)
c
7
u
3
(u
16
+ 11u
15
+ ··· + 38u + 5)(u
31
− 15u
30
+ ··· + 3u − 2)
2
· (u
46
+ 26u
45
+ ··· + u + 1)
c
11
u
3
(u
16
+ 6u
15
+ ··· + 14u + 5)(u
31
− 9u
30
+ ··· + 73u − 8)
2
· (u
46
+ 15u
45
+ ··· + 1885u + 149)
33
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
y(y −1)
2
(y
16
− 8y
15
+ ··· − 4y + 1)(y
31
− 16y
30
+ ··· + 2y −1)
2
· (y
46
− 23y
45
+ ··· + 11y + 1)
c
2
y(y −1)
2
(y
16
+ 4y
15
+ ··· + 8y + 1)(y
31
+ 28y
29
+ ··· − 14y −1)
2
· (y
46
+ 5y
45
+ ··· − 73y + 1)
c
3
, c
10
(y −1)(y
2
− 3y + 1)(y
16
+ 8y
15
+ ··· + 5y + 1)
· (y
46
− 19y
45
+ ··· − 52y + 1)(y
62
+ 12y
61
+ ··· + 29y + 1)
c
4
, c
9
(y −1)(y
2
− 3y + 1)(y
16
+ 5y
15
+ ··· + 8y + 1)(y
46
− 2y
45
+ ··· + 27y + 1)
· (y
62
+ 58y
60
+ ··· − 104599y + 961)
c
6
, c
8
((y −1)
3
)(y
16
+ 9y
15
+ ··· − 8y + 1)(y
46
− 30y
45
+ ··· − 121y + 1)
· (y
62
+ 13y
61
+ ··· + 17738y + 2401)
c
7
y
3
(y
16
+ 3y
15
+ ··· + 126y + 25)(y
31
− 3y
30
+ ··· + 69y −4)
2
· (y
46
+ 38y
44
+ ··· + 49y + 1)
c
11
y
3
(y
16
− 6y
14
+ ··· − 106y + 25)(y
31
+ 13y
30
+ ··· + 833y −64)
2
· (y
46
+ 13y
45
+ ··· + 238229y + 22201)
34
