10
113
(K10a
36
)
A knot diagram
1
Linearized knot diagam
4 7 6 8 1 10 9 5 2 3
Solving Sequence
3,10 1,7
2 6 4 5 9 8
c
10
c
2
c
6
c
3
c
5
c
9
c
8
c
1
, c
4
, c
7
Ideals for irreducible components
2
of X
par
I
u
1
= h1.09017 × 10
16
u
25
− 1.42680 × 10
17
u
24
+ ··· + 1.22316 × 10
16
b − 1.07995 × 10
16
,
1.10038 × 10
16
u
25
− 1.55970 × 10
17
u
24
+ ··· + 2.44631 × 10
16
a − 3.72028 × 10
16
, u
26
− 14u
25
+ ··· − 5u + 2i
I
u
2
= hu
18
a + u
18
+ ··· − 2a + 1, 2u
18
a + 3u
18
+ ··· − 18a − 13, u
19
+ 9u
18
+ ··· − u − 2i
I
u
3
= h−u
2
+ b − u − 1, u
3
+ 3a − u − 1, u
4
+ 3u
3
+ 5u
2
+ 5u + 3i
I
u
4
= hu
2
+ b + 2u + 2, −u
2
+ a − u − 2, u
3
+ 2u
2
+ 3u + 1i
I
v
1
= ha, b + v, v
2
− v + 1i
* 5 irreducible components of dim
C
= 0, with total 73 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
=
h1.09×10
16
u
25
−1.43×10
17
u
24
+· · ·+1.22×10
16
b−1.08×10
16
, 1.10×10
16
u
25
−
1.56 × 10
17
u
24
+ · · · + 2.45 × 10
16
a − 3.72 × 10
16
, u
26
− 14u
25
+ · · · − 5u + 2i
(i) Arc colorings
a
3
=
0
u
a
10
=
1
0
a
1
=
1
−u
2
a
7
=
−0.449813u
25
+ 6.37572u
24
+ ··· − 2.20872u + 1.52077
−0.891275u
25
+ 11.6649u
24
+ ··· − 2.84515u + 0.882924
a
2
=
0.129701u
25
− 2.02435u
24
+ ··· − 4.90429u + 1.76047
0.0404708u
25
− 0.734657u
24
+ ··· − 1.02816u + 0.178460
a
6
=
0.441462u
25
− 5.28919u
24
+ ··· + 0.636436u + 0.637845
−0.891275u
25
+ 11.6649u
24
+ ··· − 2.84515u + 0.882924
a
4
=
0.993712u
25
− 13.0075u
24
+ ··· + 1.68701u − 0.405418
−0.904482u
25
+ 11.7178u
24
+ ··· − 3.56314u + 1.98742
a
5
=
0.363122u
25
− 4.69350u
24
+ ··· + 1.36473u − 0.261781
−0.0933259u
25
+ 1.56850u
24
+ ··· − 0.496488u − 0.119215
a
9
=
−0.433618u
25
+ 6.06965u
24
+ ··· + 9.02432u − 0.696343
0.0726845u
25
− 0.832738u
24
+ ··· + 2.33024u − 0.595532
a
8
=
−0.101086u
25
+ 1.86335u
24
+ ··· + 7.57533u − 0.827238
−0.651226u
25
+ 8.60822u
24
+ ··· + 0.0145807u + 0.0950498
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
12238612154218315
12231573450758407
u
25
+
120808672137987925
12231573450758407
u
24
+···+
208460927880809
12231573450758407
u−
140870794716261400
12231573450758407
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
u
26
+ 4u
25
+ ··· − 2u + 1
c
2
, c
5
u
26
+ 3u
24
+ ··· − 2u + 1
c
3
, c
6
u
26
+ 2u
25
+ ··· + 2u + 1
c
4
, c
8
u
26
+ 6u
25
+ ··· + 25u + 4
c
7
u
26
+ 10u
25
+ ··· + 81u + 16
c
10
u
26
+ 14u
25
+ ··· + 5u + 2
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
9
y
26
− 10y
25
+ ··· − 18y + 1
c
2
, c
5
y
26
+ 6y
25
+ ··· + 6y + 1
c
3
, c
6
y
26
+ 14y
25
+ ··· + 30y + 1
c
4
, c
8
y
26
− 10y
25
+ ··· − 81y + 16
c
7
y
26
+ 10y
25
+ ··· + 9439y + 256
c
10
y
26
+ 8y
24
+ ··· − 21y + 4
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.056680 + 0.510753I
a = −0.215461 + 0.700629I
b = 1.09337 + 1.26772I
1.49747 + 5.09068I −3.0367 − 14.8892I
u = 1.056680 − 0.510753I
a = −0.215461 − 0.700629I
b = 1.09337 − 1.26772I
1.49747 − 5.09068I −3.0367 + 14.8892I
u = −1.197700 + 0.220817I
a = 0.079663 − 0.840370I
b = 0.005740 − 0.465412I
2.92221 − 2.66541I 1.40924 + 2.72285I
u = −1.197700 − 0.220817I
a = 0.079663 + 0.840370I
b = 0.005740 + 0.465412I
2.92221 + 2.66541I 1.40924 − 2.72285I
u = 1.306830 + 0.079067I
a = −0.107470 + 0.279551I
b = −0.215760 + 1.218550I
−0.13330 + 3.14853I −10.05225 − 4.78603I
u = 1.306830 − 0.079067I
a = −0.107470 − 0.279551I
b = −0.215760 − 1.218550I
−0.13330 − 3.14853I −10.05225 + 4.78603I
u = 0.493624 + 0.435869I
a = 0.905680 − 0.839887I
b = −0.941763 − 0.771472I
−2.18699 − 0.53885I −10.45014 + 2.98932I
u = 0.493624 − 0.435869I
a = 0.905680 + 0.839887I
b = −0.941763 + 0.771472I
−2.18699 + 0.53885I −10.45014 − 2.98932I
u = 1.022930 + 0.871070I
a = 0.149244 − 0.992194I
b = −0.98451 − 1.19337I
−4.53791 + 8.53907I −8.63796 − 7.50515I
u = 1.022930 − 0.871070I
a = 0.149244 + 0.992194I
b = −0.98451 + 1.19337I
−4.53791 − 8.53907I −8.63796 + 7.50515I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.129304 + 0.643314I
a = 0.984267 − 0.517979I
b = −0.031311 − 0.673436I
−0.924615 − 1.060120I −5.32469 + 4.59251I
u = 0.129304 − 0.643314I
a = 0.984267 + 0.517979I
b = −0.031311 + 0.673436I
−0.924615 + 1.060120I −5.32469 − 4.59251I
u = 0.967641 + 1.016650I
a = −0.486502 + 0.264040I
b = −0.211831 + 0.733834I
−4.93342 − 1.67636I −14.6461 + 4.2929I
u = 0.967641 − 1.016650I
a = −0.486502 − 0.264040I
b = −0.211831 − 0.733834I
−4.93342 + 1.67636I −14.6461 − 4.2929I
u = 1.26531 + 0.92939I
a = 0.020000 + 0.955891I
b = 0.97670 + 1.20748I
2.62082 + 10.45440I −1.93774 − 5.95159I
u = 1.26531 − 0.92939I
a = 0.020000 − 0.955891I
b = 0.97670 − 1.20748I
2.62082 − 10.45440I −1.93774 + 5.95159I
u = −0.014473 + 0.410285I
a = −2.05321 + 1.74511I
b = 0.284111 + 0.970184I
−1.92544 + 2.11547I −8.52748 − 4.72090I
u = −0.014473 − 0.410285I
a = −2.05321 − 1.74511I
b = 0.284111 − 0.970184I
−1.92544 − 2.11547I −8.52748 + 4.72090I
u = 0.34430 + 1.56008I
a = 0.493219 − 0.417449I
b = 0.152881 − 0.590554I
0.16560 − 2.24390I −7.60792 + 3.01225I
u = 0.34430 − 1.56008I
a = 0.493219 + 0.417449I
b = 0.152881 + 0.590554I
0.16560 + 2.24390I −7.60792 − 3.01225I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.26295 + 1.01918I
a = −0.042904 − 1.006760I
b = −0.97925 − 1.20625I
0.9109 + 16.4735I −4.00000 − 9.70500I
u = 1.26295 − 1.01918I
a = −0.042904 + 1.006760I
b = −0.97925 + 1.20625I
0.9109 − 16.4735I −4.00000 + 9.70500I
u = −0.281192 + 0.094635I
a = −1.01688 + 4.90932I
b = 0.054013 + 1.156590I
−1.56544 − 2.09555I −7.86102 + 3.20965I
u = −0.281192 − 0.094635I
a = −1.01688 − 4.90932I
b = 0.054013 − 1.156590I
−1.56544 + 2.09555I −7.86102 − 3.20965I
u = 0.64380 + 1.75632I
a = −0.459645 + 0.377201I
b = −0.202381 + 0.586735I
−0.95700 − 7.52275I 0
u = 0.64380 − 1.75632I
a = −0.459645 − 0.377201I
b = −0.202381 − 0.586735I
−0.95700 + 7.52275I 0
7
II. I
u
2
=
hu
18
a+u
18
+· · ·−2a+1, 2u
18
a+3u
18
+· · ·−18a−13, u
19
+9u
18
+· · ·−u−2i
(i) Arc colorings
a
3
=
0
u
a
10
=
1
0
a
1
=
1
−u
2
a
7
=
a
−u
18
a − u
18
+ ··· + 2a − 1
a
2
=
u
18
a +
1
2
u
18
+ ··· − a −
3
2
u
18
+ 8u
17
+ ··· − 2a − 1
a
6
=
u
18
a + u
18
+ ··· − a + 1
−u
18
a − u
18
+ ··· + 2a − 1
a
4
=
u
18
a −
1
2
u
18
+ ··· + a +
1
2
−1
a
5
=
u
18
a + 8u
17
a + ··· − a + 2
−u
18
a − 2u
18
+ ··· + 2a + 1
a
9
=
−
1
2
u
18
−
7
2
u
17
+ ··· − a +
1
2
−u
18
a + u
18
+ ··· + u − 3
a
8
=
u
17
a −
1
2
u
18
+ ··· + 2a +
1
2
−u
17
− 8u
16
+ ··· − 3u − 2
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −5u
18
− 43u
17
− 177u
16
− 432u
15
− 640u
14
− 457u
13
+ 209u
12
+ 824u
11
+ 687u
10
−
101u
9
− 627u
8
− 368u
7
+ 164u
6
+ 274u
5
+ 34u
4
− 104u
3
− 41u
2
+ 25u + 9
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
u
38
− 3u
37
+ ··· + 10u − 1
c
2
, c
5
u
38
+ 2u
37
+ ··· + 109u + 11
c
3
, c
6
u
38
+ 4u
37
+ ··· + 7u + 1
c
4
, c
8
(u
19
− 2u
18
+ ··· − 4u + 1)
2
c
7
(u
19
+ 8u
18
+ ··· + 4u + 1)
2
c
10
(u
19
− 9u
18
+ ··· − u + 2)
2
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
9
y
38
+ 13y
37
+ ··· + 2y + 1
c
2
, c
5
y
38
+ 4y
37
+ ··· − 13311y + 121
c
3
, c
6
y
38
− 8y
37
+ ··· + 5y + 1
c
4
, c
8
(y
19
− 8y
18
+ ··· + 4y −1)
2
c
7
(y
19
+ 8y
18
+ ··· − 16y −1)
2
c
10
(y
19
− 3y
18
+ ··· + 37y −4)
2
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.488744 + 1.038280I
a = −0.478820 + 0.914222I
b = −1.13156 + 1.02165I
−1.59095 − 7.59815I −9.53397 + 8.95368I
u = −0.488744 + 1.038280I
a = −1.01797 − 1.24322I
b = 0.207487 − 0.730234I
−1.59095 − 7.59815I −9.53397 + 8.95368I
u = −0.488744 − 1.038280I
a = −0.478820 − 0.914222I
b = −1.13156 − 1.02165I
−1.59095 + 7.59815I −9.53397 − 8.95368I
u = −0.488744 − 1.038280I
a = −1.01797 + 1.24322I
b = 0.207487 + 0.730234I
−1.59095 + 7.59815I −9.53397 − 8.95368I
u = −0.752606 + 0.874521I
a = 0.794589 + 0.607095I
b = −0.361281 + 0.577577I
0.10793 − 3.14909I −5.58222 + 3.79428I
u = −0.752606 + 0.874521I
a = 0.312041 − 0.899421I
b = 0.895728 − 0.988619I
0.10793 − 3.14909I −5.58222 + 3.79428I
u = −0.752606 − 0.874521I
a = 0.794589 − 0.607095I
b = −0.361281 − 0.577577I
0.10793 + 3.14909I −5.58222 − 3.79428I
u = −0.752606 − 0.874521I
a = 0.312041 + 0.899421I
b = 0.895728 + 0.988619I
0.10793 + 3.14909I −5.58222 − 3.79428I
u = −1.211130 + 0.137559I
a = 0.091441 − 0.907433I
b = 0.287046 − 0.731500I
2.95026 − 2.66622I 1.58619 + 3.20879I
u = −1.211130 + 0.137559I
a = 0.040607 − 0.755883I
b = −0.261106 − 0.186172I
2.95026 − 2.66622I 1.58619 + 3.20879I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.211130 − 0.137559I
a = 0.091441 + 0.907433I
b = 0.287046 + 0.731500I
2.95026 + 2.66622I 1.58619 − 3.20879I
u = −1.211130 − 0.137559I
a = 0.040607 + 0.755883I
b = −0.261106 + 0.186172I
2.95026 + 2.66622I 1.58619 − 3.20879I
u = 0.687103 + 0.235969I
a = −0.068144 + 1.145470I
b = −1.44986 + 0.74441I
2.42247 + 8.22022I −0.13214 − 8.57000I
u = 0.687103 + 0.235969I
a = 0.69993 − 2.21894I
b = −0.854742 − 0.601611I
2.42247 + 8.22022I −0.13214 − 8.57000I
u = 0.687103 − 0.235969I
a = −0.068144 − 1.145470I
b = −1.44986 − 0.74441I
2.42247 − 8.22022I −0.13214 + 8.57000I
u = 0.687103 − 0.235969I
a = 0.69993 + 2.21894I
b = −0.854742 + 0.601611I
2.42247 − 8.22022I −0.13214 + 8.57000I
u = 0.689008 + 0.139635I
a = −0.128846 − 1.148580I
b = 1.37561 − 0.64670I
4.26470 + 2.32942I 3.40004 − 3.00608I
u = 0.689008 + 0.139635I
a = −0.76853 + 1.84609I
b = 0.966499 + 0.555876I
4.26470 + 2.32942I 3.40004 − 3.00608I
u = 0.689008 − 0.139635I
a = −0.128846 + 1.148580I
b = 1.37561 + 0.64670I
4.26470 − 2.32942I 3.40004 + 3.00608I
u = 0.689008 − 0.139635I
a = −0.76853 − 1.84609I
b = 0.966499 − 0.555876I
4.26470 − 2.32942I 3.40004 + 3.00608I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.378245 + 0.567353I
a = −0.400712 + 1.127850I
b = −1.02428 + 1.44155I
−3.84277 − 0.76131I −13.4982 + 7.0538I
u = −0.378245 + 0.567353I
a = −2.53438 − 0.54959I
b = 0.057884 − 0.472439I
−3.84277 − 0.76131I −13.4982 + 7.0538I
u = −0.378245 − 0.567353I
a = −0.400712 − 1.127850I
b = −1.02428 − 1.44155I
−3.84277 + 0.76131I −13.4982 − 7.0538I
u = −0.378245 − 0.567353I
a = −2.53438 + 0.54959I
b = 0.057884 + 0.472439I
−3.84277 + 0.76131I −13.4982 − 7.0538I
u = −0.865146 + 1.042810I
a = 0.422088 + 0.852186I
b = −0.475702 + 0.708695I
0.09217 − 3.26203I −7.82857 + 4.58696I
u = −0.865146 + 1.042810I
a = 0.299650 − 0.748328I
b = 0.926354 − 0.812087I
0.09217 − 3.26203I −7.82857 + 4.58696I
u = −0.865146 − 1.042810I
a = 0.422088 − 0.852186I
b = −0.475702 − 0.708695I
0.09217 + 3.26203I −7.82857 − 4.58696I
u = −0.865146 − 1.042810I
a = 0.299650 + 0.748328I
b = 0.926354 + 0.812087I
0.09217 + 3.26203I −7.82857 − 4.58696I
u = 0.494703
a = 0.176592
b = −1.65217
−2.37666 7.11410
u = 0.494703
a = 2.43502
b = −0.904693
−2.37666 7.11410
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.23842 + 1.01885I
a = 0.079408 − 1.045930I
b = 0.651625 − 0.880608I
2.68628 − 1.90197I 1.62421 + 1.37993I
u = −1.23842 + 1.01885I
a = −0.214414 + 0.212371I
b = −0.877077 + 0.378271I
2.68628 − 1.90197I 1.62421 + 1.37993I
u = −1.23842 − 1.01885I
a = 0.079408 + 1.045930I
b = 0.651625 + 0.880608I
2.68628 + 1.90197I 1.62421 − 1.37993I
u = −1.23842 − 1.01885I
a = −0.214414 − 0.212371I
b = −0.877077 − 0.378271I
2.68628 + 1.90197I 1.62421 − 1.37993I
u = −1.18917 + 1.13858I
a = −0.003038 + 1.092820I
b = −0.617784 + 0.888572I
2.32292 − 6.77576I −0.09240 + 8.89089I
u = −1.18917 + 1.13858I
a = 0.319294 − 0.326713I
b = 0.963591 − 0.457047I
2.32292 − 6.77576I −0.09240 + 8.89089I
u = −1.18917 − 1.13858I
a = −0.003038 − 1.092820I
b = −0.617784 − 0.888572I
2.32292 + 6.77576I −0.09240 − 8.89089I
u = −1.18917 − 1.13858I
a = 0.319294 + 0.326713I
b = 0.963591 + 0.457047I
2.32292 + 6.77576I −0.09240 − 8.89089I
14
III. I
u
3
= h−u
2
+ b − u − 1, u
3
+ 3a − u − 1, u
4
+ 3u
3
+ 5u
2
+ 5u + 3i
(i) Arc colorings
a
3
=
0
u
a
10
=
1
0
a
1
=
1
−u
2
a
7
=
−
1
3
u
3
+
1
3
u +
1
3
u
2
+ u + 1
a
2
=
−
1
3
u
3
− u
2
−
5
3
u −
2
3
u + 1
a
6
=
−
1
3
u
3
− u
2
−
2
3
u −
2
3
u
2
+ u + 1
a
4
=
2
3
u
3
+ u
2
+
4
3
u +
1
3
−u
3
− 2u
2
− 2u − 2
a
5
=
2
3
u
3
+ u
2
+
4
3
u +
1
3
−u − 2
a
9
=
1
3
u
3
+ u
2
+
2
3
u +
2
3
−u
2
− 2u − 1
a
8
=
0
−u
3
− 2u
2
− 2u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 3u
3
+ 8u
2
+ 16u + 9
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
, c
9
u
4
− u
3
+ 2u
2
+ 1
c
2
, c
5
, c
8
u
4
− u
3
+ 1
c
3
, c
6
u
4
− u + 1
c
4
u
4
+ u
3
+ 1
c
10
u
4
+ 3u
3
+ 5u
2
+ 5u + 3
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
, c
9
y
4
+ 3y
3
+ 6y
2
+ 4y + 1
c
2
, c
4
, c
5
c
8
y
4
− y
3
+ 2y
2
+ 1
c
3
, c
6
y
4
+ 2y
2
− y + 1
c
10
y
4
+ y
3
+ y
2
+ 5y + 9
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.324902 + 1.227920I
a = −0.253420 + 0.896839I
b = −0.727136 + 0.430014I
0.20545 − 7.54387I −3.11022 + 8.87572I
u = −0.324902 − 1.227920I
a = −0.253420 − 0.896839I
b = −0.727136 − 0.430014I
0.20545 + 7.54387I −3.11022 − 8.87572I
u = −1.175100 + 0.691825I
a = −0.079913 − 0.614328I
b = 0.727136 − 0.934099I
1.43949 − 4.22398I −2.38978 + 5.66623I
u = −1.175100 − 0.691825I
a = −0.079913 + 0.614328I
b = 0.727136 + 0.934099I
1.43949 + 4.22398I −2.38978 − 5.66623I
18
IV. I
u
4
= hu
2
+ b + 2u + 2, −u
2
+ a − u − 2, u
3
+ 2u
2
+ 3u + 1i
(i) Arc colorings
a
3
=
0
u
a
10
=
1
0
a
1
=
1
−u
2
a
7
=
u
2
+ u + 2
−u
2
− 2u − 2
a
2
=
−u
2
− 2u − 2
u + 1
a
6
=
2u
2
+ 3u + 4
−u
2
− 2u − 2
a
4
=
−2u
2
− 3u − 5
u
2
+ 2u + 2
a
5
=
u
2
+ 2u + 3
−u
2
− 1
a
9
=
u
2
+ u + 2
−u
2
− 2u − 1
a
8
=
3u
2
+ 4u + 6
−u
2
− 3u − 3
(ii) Obstruction class = 1
(iii) Cusp Shapes = −11u
2
− 14u − 24
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
u
3
− u
2
+ 2u − 1
c
2
, c
5
u
3
+ u
2
− 1
c
3
, c
4
, c
6
u
3
− u − 1
c
7
u
3
− 2u
2
+ u − 1
c
8
u
3
− u + 1
c
10
u
3
+ 2u
2
+ 3u + 1
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
9
y
3
+ 3y
2
+ 2y −1
c
2
, c
5
y
3
− y
2
+ 2y −1
c
3
, c
4
, c
6
c
8
y
3
− 2y
2
+ y −1
c
7
y
3
− 2y
2
− 3y −1
c
10
y
3
+ 2y
2
+ 5y −1
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.78492 + 1.30714I
a = 0.122561 − 0.744862I
b = 0.662359 − 0.562280I
1.37919 − 2.82812I −0.99341 + 4.27206I
u = −0.78492 − 1.30714I
a = 0.122561 + 0.744862I
b = 0.662359 + 0.562280I
1.37919 + 2.82812I −0.99341 − 4.27206I
u = −0.430160
a = 1.75488
b = −1.32472
−2.75839 −20.0130
22
V. I
v
1
= ha, b + v, v
2
− v + 1i
(i) Arc colorings
a
3
=
v
0
a
10
=
1
0
a
1
=
1
0
a
7
=
0
−v
a
2
=
v
1
a
6
=
v
−v
a
4
=
v − 1
1
a
5
=
0
−v
a
9
=
−v + 1
−1
a
8
=
−v + 1
−v − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −9
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
7
c
9
(u − 1)
2
c
2
, c
3
, c
5
c
6
u
2
− u + 1
c
8
(u + 1)
2
c
10
u
2
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
7
c
8
, c
9
(y − 1)
2
c
2
, c
3
, c
5
c
6
y
2
+ y + 1
c
10
y
2
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.500000 + 0.866025I
a = 0
b = −0.500000 − 0.866025I
−3.28987 −9.00000
v = 0.500000 − 0.866025I
a = 0
b = −0.500000 + 0.866025I
−3.28987 −9.00000
26
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
9
((u − 1)
2
)(u
3
− u
2
+ 2u − 1)(u
4
− u
3
+ 2u
2
+ 1)(u
26
+ 4u
25
+ ··· − 2u + 1)
· (u
38
− 3u
37
+ ··· + 10u − 1)
c
2
, c
5
(u
2
− u + 1)(u
3
+ u
2
− 1)(u
4
− u
3
+ 1)(u
26
+ 3u
24
+ ··· − 2u + 1)
· (u
38
+ 2u
37
+ ··· + 109u + 11)
c
3
, c
6
(u
2
− u + 1)(u
3
− u − 1)(u
4
− u + 1)(u
26
+ 2u
25
+ ··· + 2u + 1)
· (u
38
+ 4u
37
+ ··· + 7u + 1)
c
4
((u − 1)
2
)(u
3
− u − 1)(u
4
+ u
3
+ 1)(u
19
− 2u
18
+ ··· − 4u + 1)
2
· (u
26
+ 6u
25
+ ··· + 25u + 4)
c
7
(u − 1)
2
(u
3
− 2u
2
+ u − 1)(u
4
− u
3
+ 2u
2
+ 1)
· ((u
19
+ 8u
18
+ ··· + 4u + 1)
2
)(u
26
+ 10u
25
+ ··· + 81u + 16)
c
8
((u + 1)
2
)(u
3
− u + 1)(u
4
− u
3
+ 1)(u
19
− 2u
18
+ ··· − 4u + 1)
2
· (u
26
+ 6u
25
+ ··· + 25u + 4)
c
10
u
2
(u
3
+ 2u
2
+ 3u + 1)(u
4
+ 3u
3
+ 5u
2
+ 5u + 3)
· ((u
19
− 9u
18
+ ··· − u + 2)
2
)(u
26
+ 14u
25
+ ··· + 5u + 2)
27
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
9
(y − 1)
2
(y
3
+ 3y
2
+ 2y − 1)(y
4
+ 3y
3
+ 6y
2
+ 4y + 1)
· (y
26
− 10y
25
+ ··· − 18y + 1)(y
38
+ 13y
37
+ ··· + 2y + 1)
c
2
, c
5
(y
2
+ y + 1)(y
3
− y
2
+ 2y − 1)(y
4
− y
3
+ 2y
2
+ 1)(y
26
+ 6y
25
+ ··· + 6y + 1)
· (y
38
+ 4y
37
+ ··· − 13311y + 121)
c
3
, c
6
(y
2
+ y + 1)(y
3
− 2y
2
+ y − 1)(y
4
+ 2y
2
− y + 1)
· (y
26
+ 14y
25
+ ··· + 30y + 1)(y
38
− 8y
37
+ ··· + 5y + 1)
c
4
, c
8
(y − 1)
2
(y
3
− 2y
2
+ y − 1)(y
4
− y
3
+ 2y
2
+ 1)
· ((y
19
− 8y
18
+ ··· + 4y − 1)
2
)(y
26
− 10y
25
+ ··· − 81y + 16)
c
7
(y − 1)
2
(y
3
− 2y
2
− 3y − 1)(y
4
+ 3y
3
+ 6y
2
+ 4y + 1)
· ((y
19
+ 8y
18
+ ··· − 16y − 1)
2
)(y
26
+ 10y
25
+ ··· + 9439y + 256)
c
10
y
2
(y
3
+ 2y
2
+ 5y − 1)(y
4
+ y
3
+ y
2
+ 5y + 9)
· ((y
19
− 3y
18
+ ··· + 37y − 4)
2
)(y
26
+ 8y
24
+ ··· − 21y + 4)
28
