11a
297
(K11a
297
)
A knot diagram
1
Linearized knot diagam
7 10 1 8 2 9 11 3 6 5 4
Solving Sequence
6,9
7
2,10
3 1 5 11 8 4
c
6
c
9
c
2
c
1
c
5
c
10
c
8
c
4
c
3
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−u
14
− 5u
13
+ ··· + 2b − 4,
u
13
+ 5u
12
+ 17u
11
+ 38u
10
+ 66u
9
+ 91u
8
+ 106u
7
+ 108u
6
+ 96u
5
+ 76u
4
+ 53u
3
+ 33u
2
+ 2a + 14u + 1,
u
15
+ 5u
14
+ ··· + 18u + 4i
I
u
2
= h458u
21
+ 5062u
20
+ ··· + 989b + 22293, 16339u
21
+ 151170u
20
+ ··· + 12857a + 26538,
u
22
+ 10u
21
+ ··· + 121u + 13i
I
u
3
= h−1564u
11
a
3
− 1275u
11
a
2
+ ··· + 2263a + 139, 3u
11
a
3
− 3u
11
a
2
+ ··· − 17a + 30,
u
12
− 3u
11
+ 8u
10
− 13u
9
+ 18u
8
− 21u
7
+ 19u
6
− 17u
5
+ 10u
4
− 6u
3
+ 4u
2
+ 1i
I
u
4
= h−44u
15
+ 195u
14
+ ··· + 31b − 7, 139u
15
− 752u
14
+ ··· + 93a − 538, u
16
− 5u
15
+ ··· − 13u + 3i
I
u
5
= h17a
3
u
2
− 4a
3
u − 24a
2
u
2
+ 28a
3
+ 13a
2
u + 27u
2
a − 41a
2
− 24au − 19u
2
+ 25b + 68a + 3u − 46,
− 2a
3
u
2
+ a
4
+ a
3
u + 3a
2
u
2
− 2a
3
− a
2
u − 2u
2
a + 3a
2
+ 3au − 2u
2
− 5a + 3u + 1, u
3
− u
2
+ 2u − 1i
I
u
6
= hb − u + 1, a − u, u
2
− u + 1i
I
u
7
= hb + u − 2, a + 2, u
2
− u + 1i
I
u
8
= hb + u − 1, a + 1, u
2
− u + 1i
I
u
9
= hb, a − 1, u
2
− u + 1i
I
u
10
= hb + u, a − u, u
2
− u + 1i
* 10 irreducible components of dim
C
= 0, with total 123 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).
1
I.
I
u
1
= h−u
14
−5u
13
+· · ·+2b−4, u
13
+5u
12
+· · ·+2a+1, u
15
+5u
14
+· · ·+18u+4i
(i) Arc colorings
a
6
=
1
0
a
9
=
0
u
a
7
=
1
u
2
a
2
=
−
1
2
u
13
−
5
2
u
12
+ ··· − 7u −
1
2
1
2
u
14
+
5
2
u
13
+ ··· +
15
2
u + 2
a
10
=
−u
u
a
3
=
−
1
2
u
13
−
5
2
u
12
+ ··· −
9
2
u
2
+
3
2
1
2
u
14
+
5
2
u
13
+ ··· + 7u
2
+
1
2
u
a
1
=
−
1
2
u
14
− 3u
13
+ ··· −
11
2
u −
1
2
3
2
u
14
+
15
2
u
13
+ ··· +
19
2
u + 2
a
5
=
3
4
u
14
+
17
4
u
13
+ ··· +
53
4
u + 4
−
1
2
u
14
−
5
2
u
13
+ ··· +
1
2
u + 1
a
11
=
−u
14
−
9
2
u
13
+ ··· − 4u −
3
2
1
2
u
14
+
3
2
u
13
+ ··· −
25
2
u − 4
a
8
=
1
4
u
14
+
3
4
u
13
+ ··· −
15
2
u
2
−
13
4
u
1
2
u
14
+
5
2
u
13
+ ··· +
15
2
u + 1
a
4
=
1
2
u
14
+ u
13
+ ··· −
17
2
u −
1
2
1
2
u
14
+
9
2
u
13
+ ··· +
51
2
u + 6
a
4
=
1
2
u
14
+ u
13
+ ··· −
17
2
u −
1
2
1
2
u
14
+
9
2
u
13
+ ··· +
51
2
u + 6
(ii) Obstruction class = −1
(iii) Cusp Shapes = 2u
14
+ 10u
13
+ 32u
12
+ 70u
11
+ 120u
10
+ 168u
9
+ 200u
8
+
210u
7
+ 194u
6
+ 166u
5
+ 124u
4
+ 88u
3
+ 46u
2
+ 20u + 14
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
u
15
+ 5u
13
+ ··· + 4u − 4
c
2
, c
4
, c
5
c
7
u
15
− 3u
13
+ ··· + u − 1
c
3
, c
6
, c
9
c
11
u
15
− 5u
14
+ ··· + 18u − 4
c
10
u
15
− 11u
14
+ ··· + 176u − 32
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
15
+ 10y
14
+ ··· − 96y −16
c
2
, c
4
, c
5
c
7
y
15
− 6y
14
+ ··· + y −1
c
3
, c
6
, c
9
c
11
y
15
+ 9y
14
+ ··· + 12y −16
c
10
y
15
+ y
14
+ ··· + 768y −1024
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.098485 + 1.023240I
a = 2.08691 − 0.20313I
b = −1.16195 − 0.84340I
3.40393 + 1.50668I 7.87127 − 3.28737I
u = 0.098485 − 1.023240I
a = 2.08691 + 0.20313I
b = −1.16195 + 0.84340I
3.40393 − 1.50668I 7.87127 + 3.28737I
u = −1.047180 + 0.169551I
a = −0.083836 − 0.178717I
b = −0.766772 + 0.909869I
−4.75552 − 7.02459I −1.15185 + 6.50183I
u = −1.047180 − 0.169551I
a = −0.083836 + 0.178717I
b = −0.766772 − 0.909869I
−4.75552 + 7.02459I −1.15185 − 6.50183I
u = 0.512134 + 0.744784I
a = 0.671930 + 0.465248I
b = −0.192367 − 0.393774I
0.10584 − 1.99596I 0.94373 + 4.15257I
u = 0.512134 − 0.744784I
a = 0.671930 − 0.465248I
b = −0.192367 + 0.393774I
0.10584 + 1.99596I 0.94373 − 4.15257I
u = 0.169504 + 1.110950I
a = −1.315650 + 0.395534I
b = 0.893182 + 0.343990I
4.49181 − 2.74770I 10.33723 + 3.64679I
u = 0.169504 − 1.110950I
a = −1.315650 − 0.395534I
b = 0.893182 − 0.343990I
4.49181 + 2.74770I 10.33723 − 3.64679I
u = −0.779677 + 0.941659I
a = −0.230487 + 0.628566I
b = 0.809054 − 0.248430I
2.30094 + 0.81192I 14.02805 + 1.67822I
u = −0.779677 − 0.941659I
a = −0.230487 − 0.628566I
b = 0.809054 + 0.248430I
2.30094 − 0.81192I 14.02805 − 1.67822I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.64988 + 1.32515I
a = 1.108270 − 0.321240I
b = −1.128320 − 0.520392I
6.65899 + 10.66370I 9.06568 − 8.84200I
u = −0.64988 − 1.32515I
a = 1.108270 + 0.321240I
b = −1.128320 + 0.520392I
6.65899 − 10.66370I 9.06568 + 8.84200I
u = −0.57422 + 1.36194I
a = −1.61047 − 0.06346I
b = 1.23126 + 1.12739I
2.8705 + 18.8513I 5.24479 − 9.91686I
u = −0.57422 − 1.36194I
a = −1.61047 + 0.06346I
b = 1.23126 − 1.12739I
2.8705 − 18.8513I 5.24479 + 9.91686I
u = −0.458343
a = 0.746665
b = 0.631819
1.10086 9.32220
6
II. I
u
2
= h458u
21
+ 5062u
20
+ · · · + 989b + 22293, 16339u
21
+ 151170u
20
+
· · · + 12857a + 26538, u
22
+ 10u
21
+ · · · + 121u + 13i
(i) Arc colorings
a
6
=
1
0
a
9
=
0
u
a
7
=
1
u
2
a
2
=
−1.27083u
21
− 11.7578u
20
+ ··· − 38.7638u − 2.06409
−0.463094u
21
− 5.11830u
20
+ ··· − 185.199u − 22.5410
a
10
=
−u
u
a
3
=
−0.783464u
21
− 6.59400u
20
+ ··· − 72.2572u − 8.08431
−0.950455u
21
− 10.2821u
20
+ ··· − 151.706u − 16.5207
a
1
=
−0.0301781u
21
− 0.556584u
20
+ ··· + 47.9511u + 8.12095
−0.670374u
21
− 5.63195u
20
+ ··· − 55.4914u − 6.87260
a
5
=
0.407793u
21
+ 6.13961u
20
+ ··· + 99.4987u + 9.79093
−3.21941u
21
− 31.0364u
20
+ ··· − 312.446u − 36.5511
a
11
=
−5.46939u
21
− 50.2551u
20
+ ··· + 127.721u + 29.0951
4.94338u
21
+ 38.8938u
20
+ ··· − 396.051u − 48.6906
a
8
=
−1.50828u
21
− 13.8280u
20
+ ··· − 167.105u − 21.2748
0.758342u
21
+ 6.17189u
20
+ ··· − 85.3943u − 11.7867
a
4
=
−0.164424u
21
+ 1.44170u
20
+ ··· + 36.5840u + 0.859998
−2.96461u
21
− 29.0586u
20
+ ··· − 325.218u − 37.9434
a
4
=
−0.164424u
21
+ 1.44170u
20
+ ··· + 36.5840u + 0.859998
−2.96461u
21
− 29.0586u
20
+ ··· − 325.218u − 37.9434
(ii) Obstruction class = −1
(iii) Cusp Shapes =
26708
989
u
21
+
254306
989
u
20
+ ··· +
1482904
989
u +
166160
989
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
(u
11
− u
9
+ u
8
+ 2u
7
− 2u
6
− 5u
5
− 3u
4
− u
2
− 2u − 1)
2
c
2
, c
4
, c
5
c
7
u
22
− 2u
21
+ ··· + u + 1
c
3
, c
6
, c
9
c
11
u
22
− 10u
21
+ ··· − 121u + 13
c
10
(u
11
− 9u
10
+ ··· + 288u − 64)
2
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
(y
11
− 2y
10
+ ··· + 2y −1)
2
c
2
, c
4
, c
5
c
7
y
22
− 8y
21
+ ··· − 27y + 1
c
3
, c
6
, c
9
c
11
y
22
+ 18y
21
+ ··· + 335y + 169
c
10
(y
11
+ 7y
10
+ ··· − 3072y −4096)
2
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.115902 + 0.927291I
a = −1.75739 + 0.44731I
b = 1.063560 + 0.786366I
2.66286 + 2.55524I 8.64051 − 2.98354I
u = −0.115902 − 0.927291I
a = −1.75739 − 0.44731I
b = 1.063560 − 0.786366I
2.66286 − 2.55524I 8.64051 + 2.98354I
u = −1.176180 + 0.028069I
a = −0.095579 + 0.158176I
b = 0.764183 − 0.949488I
−1.29847 − 12.74380I 2.12242 + 8.78453I
u = −1.176180 − 0.028069I
a = −0.095579 − 0.158176I
b = 0.764183 + 0.949488I
−1.29847 + 12.74380I 2.12242 − 8.78453I
u = −0.406334 + 1.133600I
a = −1.85192 + 0.12875I
b = 1.26965 + 1.19997I
3.91310 + 5.97461I 23.9284 − 13.7192I
u = −0.406334 − 1.133600I
a = −1.85192 − 0.12875I
b = 1.26965 − 1.19997I
3.91310 − 5.97461I 23.9284 + 13.7192I
u = −1.131520 + 0.515293I
a = 0.212406 − 0.219355I
b = −0.710834 − 0.065637I
3.59155 − 3.95294I 13.25217 + 1.78901I
u = −1.131520 − 0.515293I
a = 0.212406 + 0.219355I
b = −0.710834 + 0.065637I
3.59155 + 3.95294I 13.25217 − 1.78901I
u = 0.120881 + 0.735421I
a = 1.04658 − 1.15332I
b = −0.865794 + 0.005763I
2.66286 − 2.55524I 8.64051 + 2.98354I
u = 0.120881 − 0.735421I
a = 1.04658 + 1.15332I
b = −0.865794 − 0.005763I
2.66286 + 2.55524I 8.64051 − 2.98354I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.516445 + 1.146110I
a = −1.291240 + 0.466206I
b = 1.233030 + 0.635865I
3.59155 + 3.95294I 13.25217 − 1.78901I
u = −0.516445 − 1.146110I
a = −1.291240 − 0.466206I
b = 1.233030 − 0.635865I
3.59155 − 3.95294I 13.25217 + 1.78901I
u = −0.294431 + 1.334600I
a = 1.358550 − 0.270993I
b = −1.096640 − 0.608492I
9.48854 11.69821 + 0.I
u = −0.294431 − 1.334600I
a = 1.358550 + 0.270993I
b = −1.096640 + 0.608492I
9.48854 11.69821 + 0.I
u = −0.014795 + 1.378240I
a = 0.518042 − 0.284615I
b = −0.476892 − 0.061840I
1.19109 − 2.38125I 9.20735 + 4.36639I
u = −0.014795 − 1.378240I
a = 0.518042 + 0.284615I
b = −0.476892 + 0.061840I
1.19109 + 2.38125I 9.20735 − 4.36639I
u = −0.566257 + 1.273700I
a = 1.60595 − 0.02258I
b = −1.23709 − 1.11266I
−1.29847 + 12.74380I 2.12242 − 8.78453I
u = −0.566257 − 1.273700I
a = 1.60595 + 0.02258I
b = −1.23709 + 1.11266I
−1.29847 − 12.74380I 2.12242 + 8.78453I
u = −0.438712 + 0.175989I
a = 1.317360 − 0.248972I
b = 0.692955 − 0.824926I
1.19109 − 2.38125I 9.20735 + 4.36639I
u = −0.438712 − 0.175989I
a = 1.317360 + 0.248972I
b = 0.692955 + 0.824926I
1.19109 + 2.38125I 9.20735 − 4.36639I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.46031 + 1.82644I
a = −0.255076 + 0.291430I
b = 0.363872 − 0.119625I
3.91310 − 5.97461I 0
u = −0.46031 − 1.82644I
a = −0.255076 − 0.291430I
b = 0.363872 + 0.119625I
3.91310 + 5.97461I 0
12
III. I
u
3
= h−1564u
11
a
3
− 1275u
11
a
2
+ · · · + 2263a + 139, 3u
11
a
3
− 3u
11
a
2
+
· · · − 17a + 30, u
12
− 3u
11
+ · · · + 4u
2
+ 1i
(i) Arc colorings
a
6
=
1
0
a
9
=
0
u
a
7
=
1
u
2
a
2
=
a
1.84652a
3
u
11
+ 1.50531a
2
u
11
+ ··· − 2.67178a − 0.164109
a
10
=
−u
u
a
3
=
3.56080a
3
u
11
+ 0.0767414a
2
u
11
+ ··· + 4.18536a − 0.592680
−1.71429a
3
u
11
+ 1.42857a
2
u
11
+ ··· − 5.85714a + 0.428571
a
1
=
−1.84652a
3
u
11
− 1.50531a
2
u
11
+ ··· + 3.67178a + 0.164109
−1.71429a
3
u
11
+ 1.42857a
2
u
11
+ ··· − 5.85714a + 0.428571
a
5
=
−0.923259a
3
u
11
+ 0.243211a
2
u
11
+ ··· − 1.16411a − 4.40142
0.219599a
3
u
11
− 0.0342385a
2
u
11
+ ··· + 1.40732a + 5.27981
a
11
=
−1.70366a
3
u
11
+ 2.20897a
2
u
11
+ ··· − 4.75679a − 5.12161
u
11
a
3
− 2u
11
a
2
+ ··· + 5a + 6
a
8
=
0.0979929a
3
u
11
− 3.20425a
2
u
11
+ ··· − 3.96340a + 0.531287
0.780401a
3
u
11
+ 0.0425030a
2
u
11
+ ··· + 3.59268a + 0.687131
a
4
=
0.587957a
3
u
11
+ 1.84888a
2
u
11
+ ··· − 1.78040a − 2.10980
−1.57143a
3
u
11
+ 1.14286a
2
u
11
+ ··· + 2.71429a + 3.14286
a
4
=
0.587957a
3
u
11
+ 1.84888a
2
u
11
+ ··· − 1.78040a − 2.10980
−1.57143a
3
u
11
+ 1.14286a
2
u
11
+ ··· + 2.71429a + 3.14286
(ii) Obstruction class = −1
(iii) Cusp Shapes =
1972
847
u
11
a
3
−
4616
847
u
11
a
2
+ ··· +
4696
847
a +
2734
847
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
(u
24
+ 5u
22
+ ··· − 10u + 1)
2
c
2
, c
4
, c
5
c
7
u
48
− 3u
47
+ ··· + 14u + 7
c
3
, c
6
, c
9
c
11
(u
12
+ 3u
11
+ ··· + 4u
2
+ 1)
4
c
10
(u
2
+ u + 1)
24
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
(y
24
+ 10y
23
+ ··· + 20y + 1)
2
c
2
, c
4
, c
5
c
7
y
48
+ 17y
47
+ ··· + 1428y + 49
c
3
, c
6
, c
9
c
11
(y
12
+ 7y
11
+ ··· + 8y + 1)
4
c
10
(y
2
+ y + 1)
24
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.234552 + 1.002020I
a = −0.597795 − 0.302093I
b = 0.22904 + 1.51797I
2.07792 + 4.93563I 4.02829 − 7.11030I
u = −0.234552 + 1.002020I
a = −1.25972 + 1.80552I
b = 1.41318 − 2.05306I
2.07792 + 8.99540I 4.0283 − 14.0385I
u = −0.234552 + 1.002020I
a = −2.51733 − 0.10179I
b = 1.131840 + 0.654685I
2.07792 + 4.93563I 4.02829 − 7.11030I
u = −0.234552 + 1.002020I
a = 2.46751 + 1.09420I
b = −0.212046 − 0.211827I
2.07792 + 8.99540I 4.0283 − 14.0385I
u = −0.234552 − 1.002020I
a = −0.597795 + 0.302093I
b = 0.22904 − 1.51797I
2.07792 − 4.93563I 4.02829 + 7.11030I
u = −0.234552 − 1.002020I
a = −1.25972 − 1.80552I
b = 1.41318 + 2.05306I
2.07792 − 8.99540I 4.0283 + 14.0385I
u = −0.234552 − 1.002020I
a = −2.51733 + 0.10179I
b = 1.131840 − 0.654685I
2.07792 − 4.93563I 4.02829 + 7.11030I
u = −0.234552 − 1.002020I
a = 2.46751 − 1.09420I
b = −0.212046 + 0.211827I
2.07792 − 8.99540I 4.0283 + 14.0385I
u = 1.090290 + 0.140460I
a = 0.538183 − 0.070205I
b = −0.746925 + 0.933267I
−2.70277 − 3.11251I −4.28153 + 9.09172I
u = 1.090290 + 0.140460I
a = −0.165125 − 0.441725I
b = 0.537490 + 1.055820I
−2.70277 + 0.94726I −4.28153 + 2.16352I
16
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.090290 + 0.140460I
a = −0.287918 − 0.168255I
b = −0.319731 − 0.721848I
−2.70277 + 0.94726I −4.28153 + 2.16352I
u = 1.090290 + 0.140460I
a = 0.216596 − 0.017151I
b = 0.348815 − 0.911669I
−2.70277 − 3.11251I −4.28153 + 9.09172I
u = 1.090290 − 0.140460I
a = 0.538183 + 0.070205I
b = −0.746925 − 0.933267I
−2.70277 + 3.11251I −4.28153 − 9.09172I
u = 1.090290 − 0.140460I
a = −0.165125 + 0.441725I
b = 0.537490 − 1.055820I
−2.70277 − 0.94726I −4.28153 − 2.16352I
u = 1.090290 − 0.140460I
a = −0.287918 + 0.168255I
b = −0.319731 + 0.721848I
−2.70277 − 0.94726I −4.28153 − 2.16352I
u = 1.090290 − 0.140460I
a = 0.216596 + 0.017151I
b = 0.348815 + 0.911669I
−2.70277 + 3.11251I −4.28153 − 9.09172I
u = −0.185688 + 0.817666I
a = 0.378746 − 1.189790I
b = −0.006229 − 0.983343I
−2.70277 − 0.94726I −4.28153 − 2.16352I
u = −0.185688 + 0.817666I
a = 0.35004 − 1.84034I
b = −0.69044 + 2.01862I
−2.70277 + 3.11251I −4.28153 − 9.09172I
u = −0.185688 + 0.817666I
a = −2.61261 − 0.58128I
b = 0.082567 + 0.311441I
−2.70277 + 3.11251I −4.28153 − 9.09172I
u = −0.185688 + 0.817666I
a = 2.84972 + 0.44116I
b = −1.70773 − 0.70812I
−2.70277 − 0.94726I −4.28153 − 2.16352I
17
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.185688 − 0.817666I
a = 0.378746 + 1.189790I
b = −0.006229 + 0.983343I
−2.70277 + 0.94726I −4.28153 + 2.16352I
u = −0.185688 − 0.817666I
a = 0.35004 + 1.84034I
b = −0.69044 − 2.01862I
−2.70277 − 3.11251I −4.28153 + 9.09172I
u = −0.185688 − 0.817666I
a = −2.61261 + 0.58128I
b = 0.082567 − 0.311441I
−2.70277 − 3.11251I −4.28153 + 9.09172I
u = −0.185688 − 0.817666I
a = 2.84972 − 0.44116I
b = −1.70773 + 0.70812I
−2.70277 + 0.94726I −4.28153 + 2.16352I
u = 0.529049 + 1.245360I
a = 0.882539 + 0.059263I
b = −0.550794 + 0.261194I
0.62485 − 2.52824I 0.25324 − 1.69361I
u = 0.529049 + 1.245360I
a = 1.195580 + 0.202913I
b = −0.816916 + 0.968854I
0.62485 − 6.58801I 0.25324 + 5.23459I
u = 0.529049 + 1.245360I
a = −1.68191 + 0.25584I
b = 1.25894 − 1.09149I
0.62485 − 6.58801I 0.25324 + 5.23459I
u = 0.529049 + 1.245360I
a = −0.242083 + 0.132540I
b = 0.223576 − 0.582679I
0.62485 − 2.52824I 0.25324 − 1.69361I
u = 0.529049 − 1.245360I
a = 0.882539 − 0.059263I
b = −0.550794 − 0.261194I
0.62485 + 2.52824I 0.25324 + 1.69361I
u = 0.529049 − 1.245360I
a = 1.195580 − 0.202913I
b = −0.816916 − 0.968854I
0.62485 + 6.58801I 0.25324 − 5.23459I
18
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.529049 − 1.245360I
a = −1.68191 − 0.25584I
b = 1.25894 + 1.09149I
0.62485 + 6.58801I 0.25324 − 5.23459I
u = 0.529049 − 1.245360I
a = −0.242083 − 0.132540I
b = 0.223576 + 0.582679I
0.62485 + 2.52824I 0.25324 + 1.69361I
u = −0.251512 + 0.449740I
a = 0.586879 + 0.230300I
b = 0.619548 − 0.991194I
0.62485 − 2.52824I 0.25324 − 1.69361I
u = −0.251512 + 0.449740I
a = 0.96589 + 1.86894I
b = −0.253152 + 0.971646I
0.62485 − 6.58801I 0.25324 + 5.23459I
u = −0.251512 + 0.449740I
a = 2.30449 + 0.84444I
b = −0.038774 − 0.733952I
0.62485 − 2.52824I 0.25324 − 1.69361I
u = −0.251512 + 0.449740I
a = −3.34233 + 0.09769I
b = 1.45679 + 0.39389I
0.62485 − 6.58801I 0.25324 + 5.23459I
u = −0.251512 − 0.449740I
a = 0.586879 − 0.230300I
b = 0.619548 + 0.991194I
0.62485 + 2.52824I 0.25324 + 1.69361I
u = −0.251512 − 0.449740I
a = 0.96589 − 1.86894I
b = −0.253152 − 0.971646I
0.62485 + 6.58801I 0.25324 − 5.23459I
u = −0.251512 − 0.449740I
a = 2.30449 − 0.84444I
b = −0.038774 + 0.733952I
0.62485 + 2.52824I 0.25324 + 1.69361I
u = −0.251512 − 0.449740I
a = −3.34233 − 0.09769I
b = 1.45679 − 0.39389I
0.62485 + 6.58801I 0.25324 − 5.23459I
19
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.55241 + 1.40748I
a = −1.117820 + 0.247439I
b = 0.85749 − 1.22119I
2.07792 − 8.99540I 4.0283 + 14.0385I
u = 0.55241 + 1.40748I
a = −0.816501 − 0.179135I
b = 0.437562 − 0.344284I
2.07792 − 4.93563I 4.02829 + 7.11030I
u = 0.55241 + 1.40748I
a = 0.633601 − 0.469916I
b = −0.527372 + 0.822492I
2.07792 − 4.93563I 4.02829 + 7.11030I
u = 0.55241 + 1.40748I
a = 1.77136 − 0.08131I
b = −1.22673 + 0.90431I
2.07792 − 8.99540I 4.0283 + 14.0385I
u = 0.55241 − 1.40748I
a = −1.117820 − 0.247439I
b = 0.85749 + 1.22119I
2.07792 + 8.99540I 4.0283 − 14.0385I
u = 0.55241 − 1.40748I
a = −0.816501 + 0.179135I
b = 0.437562 + 0.344284I
2.07792 + 4.93563I 4.02829 − 7.11030I
u = 0.55241 − 1.40748I
a = 0.633601 + 0.469916I
b = −0.527372 − 0.822492I
2.07792 + 4.93563I 4.02829 − 7.11030I
u = 0.55241 − 1.40748I
a = 1.77136 + 0.08131I
b = −1.22673 − 0.90431I
2.07792 + 8.99540I 4.0283 − 14.0385I
20
IV. I
u
4
= h−44u
15
+ 195u
14
+ · · · + 31b − 7, 139u
15
− 752u
14
+ · · · + 93a −
538, u
16
− 5u
15
+ · · · − 13u + 3i
(i) Arc colorings
a
6
=
1
0
a
9
=
0
u
a
7
=
1
u
2
a
2
=
−1.49462u
15
+ 8.08602u
14
+ ··· − 19.9355u + 5.78495
1.41935u
15
− 6.29032u
14
+ ··· + 5.03226u + 0.225806
a
10
=
−u
u
a
3
=
−0.688172u
15
+ 2.98925u
14
+ ··· − 1.25806u + 1.52688
0.612903u
15
− 1.19355u
14
+ ··· − 13.6452u + 4.48387
a
1
=
−1.04301u
15
+ 5.31183u
14
+ ··· − 12.5161u + 3.72043
0.580645u
15
− 2.70968u
14
+ ··· − 3.03226u + 1.77419
a
5
=
0.698925u
15
− 2.81720u
14
+ ··· + 4.38710u + 3.04301
0.516129u
15
− 2.74194u
14
+ ··· + 14.1935u − 3.64516
a
11
=
−0.559140u
15
+ 1.05376u
14
+ ··· + 32.2903u − 12.6344
−0.870968u
15
+ 5.06452u
14
+ ··· − 27.4516u + 5.83871
a
8
=
−0.344086u
15
+ 1.49462u
14
+ ··· − 2.12903u − 1.23656
−0.193548u
15
+ 0.903226u
14
+ ··· − 4.32258u + 0.741935
a
4
=
0.967742u
15
− 4.51613u
14
+ ··· + 18.6129u + 0.290323
0.258065u
15
− 0.870968u
14
+ ··· + 7.09677u − 2.32258
a
4
=
0.967742u
15
− 4.51613u
14
+ ··· + 18.6129u + 0.290323
0.258065u
15
− 0.870968u
14
+ ··· + 7.09677u − 2.32258
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
73
31
u
15
+
320
31
u
14
+ ··· −
3387
31
u +
936
31
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
u
16
+ u
14
+ 8u
12
− 4u
10
+ 9u
8
− 11u
6
+ 18u
4
− 2u
2
+ 7
c
2
, c
5
u
16
− u
15
+ ··· − u + 1
c
3
, c
9
u
16
+ 5u
15
+ ··· + 13u + 3
c
4
, c
7
u
16
+ u
15
+ ··· + u + 1
c
6
, c
11
u
16
− 5u
15
+ ··· − 13u + 3
c
10
u
16
+ 7u
14
+ 23u
12
+ 47u
10
+ 66u
8
+ 62u
6
+ 46u
4
+ 20u
2
+ 7
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
(y
8
+ y
7
+ 8y
6
− 4y
5
+ 9y
4
− 11y
3
+ 18y
2
− 2y + 7)
2
c
2
, c
4
, c
5
c
7
y
16
+ 5y
15
+ ··· + 11y + 1
c
3
, c
6
, c
9
c
11
y
16
+ 15y
15
+ ··· + 137y + 9
c
10
(y
8
+ 7y
7
+ 23y
6
+ 47y
5
+ 66y
4
+ 62y
3
+ 46y
2
+ 20y + 7)
2
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.156162 + 0.941024I
a = −2.01687 + 0.31543I
b = 0.833985 − 1.005380I
2.04808 + 7.98268I 4.81427 − 4.30375I
u = −0.156162 − 0.941024I
a = −2.01687 − 0.31543I
b = 0.833985 + 1.005380I
2.04808 − 7.98268I 4.81427 + 4.30375I
u = 1.147790 + 0.077838I
a = 0.110982 − 0.089673I
b = −0.448678 + 0.874321I
−2.40315 − 2.04689I −0.09415 + 3.67599I
u = 1.147790 − 0.077838I
a = 0.110982 + 0.089673I
b = −0.448678 − 0.874321I
−2.40315 + 2.04689I −0.09415 − 3.67599I
u = −0.011362 + 0.809876I
a = 2.02963 − 0.17201I
b = −0.723898 + 1.047530I
−2.40315 + 2.04689I −0.09415 − 3.67599I
u = −0.011362 − 0.809876I
a = 2.02963 + 0.17201I
b = −0.723898 − 1.047530I
−2.40315 − 2.04689I −0.09415 + 3.67599I
u = 0.369082 + 1.156850I
a = −1.77547 − 0.00971I
b = 1.13680 − 1.17673I
3.58132 − 5.91907I −0.02049 + 8.16668I
u = 0.369082 − 1.156850I
a = −1.77547 + 0.00971I
b = 1.13680 + 1.17673I
3.58132 + 5.91907I −0.02049 − 8.16668I
u = 0.55090 + 1.37318I
a = 1.41055 − 0.15096I
b = −1.00775 + 1.04644I
2.04808 − 7.98268I 4.81427 + 4.30375I
u = 0.55090 − 1.37318I
a = 1.41055 + 0.15096I
b = −1.00775 − 1.04644I
2.04808 + 7.98268I 4.81427 − 4.30375I
24
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.58869 + 1.45312I
a = −0.564595 − 0.008590I
b = 0.468248 − 0.352677I
0.88608 − 3.10886I 7.3004 + 13.1054I
u = 0.58869 − 1.45312I
a = −0.564595 + 0.008590I
b = 0.468248 + 0.352677I
0.88608 + 3.10886I 7.3004 − 13.1054I
u = 0.144483 + 0.400393I
a = 2.09451 − 1.01208I
b = 0.368009 + 0.981568I
0.88608 + 3.10886I 7.3004 − 13.1054I
u = 0.144483 − 0.400393I
a = 2.09451 + 1.01208I
b = 0.368009 − 0.981568I
0.88608 − 3.10886I 7.3004 + 13.1054I
u = −0.13341 + 1.61975I
a = 0.377922 − 0.341658I
b = −0.126722 + 0.399203I
3.58132 − 5.91907I −0.02049 + 8.16668I
u = −0.13341 − 1.61975I
a = 0.377922 + 0.341658I
b = −0.126722 − 0.399203I
3.58132 + 5.91907I −0.02049 − 8.16668I
25
V. I
u
5
=
h17a
3
u
2
−24a
2
u
2
+· · ·+68a−46, −2a
3
u
2
+3a
2
u
2
+· · ·−5a+1, u
3
−u
2
+2u−1i
(i) Arc colorings
a
6
=
1
0
a
9
=
0
u
a
7
=
1
u
2
a
2
=
a
−0.680000a
3
u
2
+ 0.960000a
2
u
2
+ ··· − 2.72000a + 1.84000
a
10
=
−u
u
a
3
=
−0.280000a
3
u
2
+ 0.160000a
2
u
2
+ ··· + 0.880000a + 0.640000
−
2
5
a
3
u
2
+
4
5
a
2
u
2
+ ··· −
13
5
a +
6
5
a
1
=
0.680000a
3
u
2
− 0.960000a
2
u
2
+ ··· + 3.72000a − 1.84000
−
2
5
a
3
u
2
+
4
5
a
2
u
2
+ ··· −
8
5
a +
6
5
a
5
=
−0.440000a
3
u
2
+ 1.28000a
2
u
2
+ ··· − 2.76000a + 3.12000
−0.240000a
3
u
2
− 0.320000a
2
u
2
+ ··· − 0.960000a + 0.720000
a
11
=
−0.880000a
3
u
2
+ 1.36000a
2
u
2
+ ··· − 4.52000a + 3.44000
1
5
a
3
u
2
−
2
5
a
2
u
2
+ ··· +
4
5
a −
8
5
a
8
=
3
5
a
3
u
2
−
2
5
a
2
u
2
+ ··· +
7
5
a −
8
5
−0.160000a
3
u
2
− 1.08000a
2
u
2
+ ··· + 1.36000a − 0.320000
a
4
=
−
4
5
a
3
u
2
+
3
5
a
2
u
2
+ ··· −
6
5
a +
7
5
1
5
a
3
u
2
+
3
5
a
2
u
2
+ ··· −
6
5
a +
7
5
a
4
=
−
4
5
a
3
u
2
+
3
5
a
2
u
2
+ ··· −
6
5
a +
7
5
1
5
a
3
u
2
+
3
5
a
2
u
2
+ ··· −
6
5
a +
7
5
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
52
25
a
3
u
2
−
24
25
a
3
u−
44
25
a
2
u
2
+
68
25
a
3
+
28
25
a
2
u+
112
25
u
2
a−
96
25
a
2
−
44
25
au−
264
25
u
2
+
208
25
a+
168
25
u−
226
25
26
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
u
12
+ 5u
11
+ ··· + 50u + 25
c
2
, c
4
, c
5
c
7
u
12
− u
11
− 5u
9
+ 12u
8
− 5u
7
− 5u
6
+ 9u
5
− 8u
3
+ 4u
2
+ 4u + 1
c
3
, c
6
, c
9
c
11
(u
3
+ u
2
+ 2u + 1)
4
c
10
(u
2
+ u + 1)
6
27
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
12
− 13y
11
+ ··· − 1400y + 625
c
2
, c
4
, c
5
c
7
y
12
− y
11
+ ··· − 8y + 1
c
3
, c
6
, c
9
c
11
(y
3
+ 3y
2
+ 2y −1)
4
c
10
(y
2
+ y + 1)
6
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.215080 + 1.307140I
a = 0.557957 + 0.898602I
b = −0.291045 + 0.197103I
6.04826 − 3.62636I 11.01951 + 2.49479I
u = 0.215080 + 1.307140I
a = −1.48598 + 0.34361I
b = 1.37483 − 0.58456I
6.04826 − 3.62636I 11.01951 + 2.49479I
u = 0.215080 + 1.307140I
a = 1.42930 − 0.86373I
b = −1.16740 + 1.64205I
6.04826 − 7.68613I 11.0195 + 9.4230I
u = 0.215080 + 1.307140I
a = −2.04108 − 0.56107I
b = 0.961053 − 0.509737I
6.04826 − 7.68613I 11.0195 + 9.4230I
u = 0.215080 − 1.307140I
a = 0.557957 − 0.898602I
b = −0.291045 − 0.197103I
6.04826 + 3.62636I 11.01951 − 2.49479I
u = 0.215080 − 1.307140I
a = −1.48598 − 0.34361I
b = 1.37483 + 0.58456I
6.04826 + 3.62636I 11.01951 − 2.49479I
u = 0.215080 − 1.307140I
a = 1.42930 + 0.86373I
b = −1.16740 − 1.64205I
6.04826 + 7.68613I 11.0195 − 9.4230I
u = 0.215080 − 1.307140I
a = −2.04108 + 0.56107I
b = 0.961053 + 0.509737I
6.04826 + 7.68613I 11.0195 − 9.4230I
u = 0.569840
a = 0.938451 + 0.394948I
b = 0.365745 − 0.996574I
−2.22691 − 2.02988I −2.03902 + 3.46410I
u = 0.569840
a = 0.938451 − 0.394948I
b = 0.365745 + 0.996574I
−2.22691 + 2.02988I −2.03902 − 3.46410I
29
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.569840
a = 0.101346 + 1.406030I
b = −0.743183 + 0.342830I
−2.22691 − 2.02988I −2.03902 + 3.46410I
u = 0.569840
a = 0.101346 − 1.406030I
b = −0.743183 − 0.342830I
−2.22691 + 2.02988I −2.03902 − 3.46410I
30
VI. I
u
6
= hb − u + 1, a − u, u
2
− u + 1i
(i) Arc colorings
a
6
=
1
0
a
9
=
0
u
a
7
=
1
u − 1
a
2
=
u
u − 1
a
10
=
−u
u
a
3
=
−1
2u
a
1
=
0
u
a
5
=
0
−u
a
11
=
−u
u − 1
a
8
=
−u
3u − 2
a
4
=
−1
u + 1
a
4
=
−1
u + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 12u − 6
31
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
u
2
− u + 1
c
2
, c
7
u
2
− 3u + 3
c
3
, c
4
, c
5
c
6
, c
9
, c
10
c
11
u
2
+ u + 1
32
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
5
, c
6
, c
8
c
9
, c
10
, c
11
y
2
+ y + 1
c
2
, c
7
y
2
− 3y + 9
33
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = 0.500000 + 0.866025I
b = −0.500000 + 0.866025I
− 6.08965I 0. + 10.39230I
u = 0.500000 − 0.866025I
a = 0.500000 − 0.866025I
b = −0.500000 − 0.866025I
6.08965I 0. − 10.39230I
34
VII. I
u
7
= hb + u − 2, a + 2, u
2
− u + 1i
(i) Arc colorings
a
6
=
1
0
a
9
=
0
u
a
7
=
1
u − 1
a
2
=
−2
−u + 2
a
10
=
−u
u
a
3
=
−1
−u + 1
a
1
=
−u − 2
−u + 3
a
5
=
2u − 3
−3u + 3
a
11
=
2u − 1
−2u
a
8
=
−u
u + 1
a
4
=
3u − 2
−3u
a
4
=
3u − 2
−3u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 12u − 6
35
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
u
2
− u + 1
c
2
, c
3
, c
6
c
7
, c
9
, c
10
c
11
u
2
+ u + 1
c
4
, c
5
u
2
− 3u + 3
36
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
6
, c
7
, c
8
c
9
, c
10
, c
11
y
2
+ y + 1
c
4
, c
5
y
2
− 3y + 9
37
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = −2.00000
b = 1.50000 − 0.86603I
− 6.08965I 0. + 10.39230I
u = 0.500000 − 0.866025I
a = −2.00000
b = 1.50000 + 0.86603I
6.08965I 0. − 10.39230I
38
VIII. I
u
8
= hb + u − 1, a + 1, u
2
− u + 1i
(i) Arc colorings
a
6
=
1
0
a
9
=
0
u
a
7
=
1
u − 1
a
2
=
−1
−u + 1
a
10
=
−u
u
a
3
=
0
−u
a
1
=
−1
−u + 1
a
5
=
u
−u
a
11
=
−u
u
a
8
=
0
u
a
4
=
u
−u − 1
a
4
=
u
−u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 8u − 4
39
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
, c
10
u
2
c
2
, c
5
, c
6
c
11
u
2
− u + 1
c
3
, c
4
, c
7
c
9
u
2
+ u + 1
40
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
, c
10
y
2
c
2
, c
3
, c
4
c
5
, c
6
, c
7
c
9
, c
11
y
2
+ y + 1
41
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
8
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = −1.00000
b = 0.500000 − 0.866025I
− 4.05977I 0. + 6.92820I
u = 0.500000 − 0.866025I
a = −1.00000
b = 0.500000 + 0.866025I
4.05977I 0. − 6.92820I
42
IX. I
u
9
= hb, a − 1, u
2
− u + 1i
(i) Arc colorings
a
6
=
1
0
a
9
=
0
u
a
7
=
1
u − 1
a
2
=
1
0
a
10
=
−u
u
a
3
=
u
−u + 1
a
1
=
u
−u
a
5
=
1
0
a
11
=
0
u
a
8
=
1
0
a
4
=
1
0
a
4
=
1
0
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u − 2
43
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
u
2
− u + 1
c
2
, c
3
, c
6
c
7
, c
9
, c
10
c
11
u
2
+ u + 1
c
4
, c
5
u
2
44
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
6
, c
7
, c
8
c
9
, c
10
, c
11
y
2
+ y + 1
c
4
, c
5
y
2
45
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
9
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = 1.00000
b = 0
− 2.02988I 0. + 3.46410I
u = 0.500000 − 0.866025I
a = 1.00000
b = 0
2.02988I 0. − 3.46410I
46
X. I
u
10
= hb + u, a − u, u
2
− u + 1i
(i) Arc colorings
a
6
=
1
0
a
9
=
0
u
a
7
=
1
u − 1
a
2
=
u
−u
a
10
=
−u
u
a
3
=
u
−u
a
1
=
2u − 1
−2u
a
5
=
−u + 2
u − 1
a
11
=
1
u − 1
a
8
=
1
u − 1
a
4
=
2
u − 2
a
4
=
2
u − 2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u − 2
47
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
u
2
− u + 1
c
2
, c
7
u
2
c
3
, c
4
, c
5
c
6
, c
9
, c
10
c
11
u
2
+ u + 1
48
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
5
, c
6
, c
8
c
9
, c
10
, c
11
y
2
+ y + 1
c
2
, c
7
y
2
49
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
10
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = 0.500000 + 0.866025I
b = −0.500000 − 0.866025I
− 2.02988I 0. + 3.46410I
u = 0.500000 − 0.866025I
a = 0.500000 − 0.866025I
b = −0.500000 + 0.866025I
2.02988I 0. − 3.46410I
50
XI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
8
u
2
(u
2
− u + 1)
4
(u
11
− u
9
+ u
8
+ 2u
7
− 2u
6
− 5u
5
− 3u
4
− u
2
− 2u − 1)
2
· (u
12
+ 5u
11
+ ··· + 50u + 25)(u
15
+ 5u
13
+ ··· + 4u − 4)
· (u
16
+ u
14
+ 8u
12
− 4u
10
+ 9u
8
− 11u
6
+ 18u
4
− 2u
2
+ 7)
· (u
24
+ 5u
22
+ ··· − 10u + 1)
2
c
2
, c
5
u
2
(u
2
− 3u + 3)(u
2
− u + 1)(u
2
+ u + 1)
2
· (u
12
− u
11
− 5u
9
+ 12u
8
− 5u
7
− 5u
6
+ 9u
5
− 8u
3
+ 4u
2
+ 4u + 1)
· (u
15
− 3u
13
+ ··· + u − 1)(u
16
− u
15
+ ··· − u + 1)
· (u
22
− 2u
21
+ ··· + u + 1)(u
48
− 3u
47
+ ··· + 14u + 7)
c
3
, c
9
((u
2
+ u + 1)
5
)(u
3
+ u
2
+ 2u + 1)
4
(u
12
+ 3u
11
+ ··· + 4u
2
+ 1)
4
· (u
15
− 5u
14
+ ··· + 18u − 4)(u
16
+ 5u
15
+ ··· + 13u + 3)
· (u
22
− 10u
21
+ ··· − 121u + 13)
c
4
, c
7
u
2
(u
2
− 3u + 3)(u
2
+ u + 1)
3
· (u
12
− u
11
− 5u
9
+ 12u
8
− 5u
7
− 5u
6
+ 9u
5
− 8u
3
+ 4u
2
+ 4u + 1)
· (u
15
− 3u
13
+ ··· + u − 1)(u
16
+ u
15
+ ··· + u + 1)
· (u
22
− 2u
21
+ ··· + u + 1)(u
48
− 3u
47
+ ··· + 14u + 7)
c
6
, c
11
(u
2
− u + 1)(u
2
+ u + 1)
4
(u
3
+ u
2
+ 2u + 1)
4
· ((u
12
+ 3u
11
+ ··· + 4u
2
+ 1)
4
)(u
15
− 5u
14
+ ··· + 18u − 4)
· (u
16
− 5u
15
+ ··· − 13u + 3)(u
22
− 10u
21
+ ··· − 121u + 13)
c
10
u
2
(u
2
+ u + 1)
34
(u
11
− 9u
10
+ ··· + 288u − 64)
2
· (u
15
− 11u
14
+ ··· + 176u − 32)
· (u
16
+ 7u
14
+ 23u
12
+ 47u
10
+ 66u
8
+ 62u
6
+ 46u
4
+ 20u
2
+ 7)
51
XII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
2
(y
2
+ y + 1)
4
(y
8
+ y
7
+ 8y
6
− 4y
5
+ 9y
4
− 11y
3
+ 18y
2
− 2y + 7)
2
· ((y
11
− 2y
10
+ ··· + 2y −1)
2
)(y
12
− 13y
11
+ ··· − 1400y + 625)
· (y
15
+ 10y
14
+ ··· − 96y −16)(y
24
+ 10y
23
+ ··· + 20y + 1)
2
c
2
, c
4
, c
5
c
7
y
2
(y
2
− 3y + 9)(y
2
+ y + 1)
3
(y
12
− y
11
+ ··· − 8y + 1)
· (y
15
− 6y
14
+ ··· + y −1)(y
16
+ 5y
15
+ ··· + 11y + 1)
· (y
22
− 8y
21
+ ··· − 27y + 1)(y
48
+ 17y
47
+ ··· + 1428y + 49)
c
3
, c
6
, c
9
c
11
((y
2
+ y + 1)
5
)(y
3
+ 3y
2
+ 2y −1)
4
(y
12
+ 7y
11
+ ··· + 8y + 1)
4
· (y
15
+ 9y
14
+ ··· + 12y −16)(y
16
+ 15y
15
+ ··· + 137y + 9)
· (y
22
+ 18y
21
+ ··· + 335y + 169)
c
10
y
2
(y
2
+ y + 1)
34
· (y
8
+ 7y
7
+ 23y
6
+ 47y
5
+ 66y
4
+ 62y
3
+ 46y
2
+ 20y + 7)
2
· ((y
11
+ 7y
10
+ ··· − 3072y −4096)
2
)(y
15
+ y
14
+ ··· + 768y −1024)
52
