12n
0806
(K12n
0806
)
A knot diagram
1
Linearized knot diagam
4 7 12 7 10 3 10 1 6 1 4 9
Solving Sequence
3,7
2
6,10
5 4 1 11 9 8 12
c
2
c
6
c
5
c
4
c
1
c
10
c
9
c
8
c
12
c
3
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= hu
5
− u
4
+ 2u
3
+ b + 4u − 2, u
5
− u
4
+ 2u
3
+ a + 4u − 1, u
6
− 2u
5
+ 3u
4
− 2u
3
+ 4u
2
− 4u + 1i
I
u
2
= h−u
5
a − u
4
a − 2u
3
a − au − u
2
+ b − u − 1, −u
5
a − 2u
4
a − 4u
3
a − 3u
2
a + a
2
− 3au + u
2
+ 1,
u
6
+ u
5
+ 3u
4
+ u
3
+ 3u
2
− u + 1i
I
u
3
= h734u
11
− 3080u
10
+ ··· + 7763b − 15155, 1450u
11
− 7683u
10
+ ··· + 7763a − 6462,
u
12
− 5u
11
+ 13u
10
− 25u
9
+ 45u
8
− 72u
7
+ 93u
6
− 97u
5
+ 87u
4
− 68u
3
+ 39u
2
− 17u + 7i
I
u
4
= h−u
7
− 2u
4
− u
3
+ u
2
+ b + 1, u
9
+ 2u
6
+ u
5
− 2u
4
+ a − u, u
10
+ u
9
+ u
7
+ 2u
6
− u
5
− 3u
4
− 2u
3
+ u + 1i
I
u
5
= h−u
9
− u
7
− u
6
− u
5
+ u
3
+ 2u
2
+ b − 1, −u
9
− u
7
− u
6
− u
5
+ u
3
+ 2u
2
+ a,
u
10
+ u
9
+ u
7
+ 2u
6
− u
5
− 3u
4
− 2u
3
+ u + 1i
I
u
6
= hu
2
+ b, u
2
+ a + 1, u
3
− u
2
+ 2u − 1i
I
u
7
= h−u
7
+ 5u
6
− 12u
5
+ 19u
4
− 20u
3
+ 14u
2
+ b − 8u + 3,
− 3u
7
+ 12u
6
− 25u
5
+ 34u
4
− 29u
3
+ 17u
2
+ 2a − 9u + 2,
u
8
− 4u
7
+ 9u
6
− 14u
5
+ 15u
4
− 13u
3
+ 9u
2
− 4u + 2i
I
u
8
= hau + u
2
+ b − a + u + 1, −u
3
a − 2u
2
a − u
3
+ a
2
− au − u
2
− u, u
4
+ u
3
+ u
2
+ 1i
I
u
9
= hb + 1, −u
4
− u
2
+ 2a, u
6
− u
5
+ u
4
+ u
3
+ 2i
I
u
10
= hb − a − 1, a
2
− a − 4, u + 1i
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
u
11
= h−u
2
+ b − u, −u
3
− 3u
2
+ a − 3u − 2, u
4
+ 2u
3
+ 2u
2
+ u − 1i
I
u
12
= h2u
3
+ 4u
2
+ b + 5u + 2, 2u
3
+ 4u
2
+ a + 5u + 3, u
4
+ 2u
3
+ 2u
2
+ u − 1i
* 12 irreducible components of dim
C
= 0, with total 85 representations.
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
2
I. I
u
1
= hu
5
− u
4
+ 2u
3
+ b + 4u − 2, u
5
− u
4
+ 2u
3
+ a + 4u − 1, u
6
− 2u
5
+
3u
4
− 2u
3
+ 4u
2
− 4u + 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
2
=
1
−u
2
a
6
=
u
u
a
10
=
−u
5
+ u
4
− 2u
3
− 4u + 1
−u
5
+ u
4
− 2u
3
− 4u + 2
a
5
=
u
5
− u
4
+ 2u
3
+ 4u − 1
u
5
− u
4
+ 2u
3
+ 3u − 1
a
4
=
u
5
− u
4
+ 2u
3
+ 4u − 1
u
2
a
1
=
−3u
5
+ 4u
4
− 6u
3
+ 2u
2
− 11u + 5
−u
5
+ u
4
− u
3
− 3u + 1
a
11
=
3u
5
− 4u
4
+ 7u
3
− 2u
2
+ 11u − 5
u
3
+ u
a
9
=
−u
5
+ u
4
− 2u
3
+ u
2
− 4u + 1
−u
5
+ u
4
− 2u
3
+ u
2
− 4u + 2
a
8
=
−3u
5
+ 4u
4
− 6u
3
+ 2u
2
− 11u + 4
−2u
5
+ 3u
4
− 4u
3
+ 2u
2
− 7u + 3
a
12
=
−2u
5
+ 3u
4
− 5u
3
+ 2u
2
− 8u + 4
−u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
5
− 8u
4
+ 12u
3
− 4u
2
+ 12u − 20
3
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
7
c
10
u
6
− 2u
5
− 3u
4
+ 6u
3
+ 4u + 1
c
2
, c
3
, c
5
c
6
, c
8
, c
9
c
11
, c
12
u
6
+ 2u
5
+ 3u
4
+ 2u
3
+ 4u
2
+ 4u + 1
4
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
7
c
10
y
6
− 10y
5
+ 33y
4
− 18y
3
− 54y
2
− 16y + 1
c
2
, c
3
, c
5
c
6
, c
8
, c
9
c
11
, c
12
y
6
+ 2y
5
+ 9y
4
+ 6y
3
+ 6y
2
− 8y + 1
5
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.565321 + 1.037410I
a = 0.556120 − 0.294180I
b = 1.55612 − 0.29418I
5.73543 + 5.68242I −3.14521 − 5.86849I
u = −0.565321 − 1.037410I
a = 0.556120 + 0.294180I
b = 1.55612 + 0.29418I
5.73543 − 5.68242I −3.14521 + 5.86849I
u = 0.716429
a = −2.52645
b = −1.52645
−9.00346 −10.3960
u = 0.378183
a = −0.608191
b = 0.391809
−0.650275 −15.5180
u = 1.01802 + 1.26802I
a = 1.011200 − 0.788474I
b = 2.01120 − 0.78847I
−8.3108 − 15.2657I −11.89809 + 7.17299I
u = 1.01802 − 1.26802I
a = 1.011200 + 0.788474I
b = 2.01120 + 0.78847I
−8.3108 + 15.2657I −11.89809 − 7.17299I
6
II. I
u
2
= h−u
5
a − u
4
a − 2u
3
a − au − u
2
+ b − u − 1, −u
5
a − 2u
4
a + · · · +
a
2
+ 1, u
6
+ u
5
+ 3u
4
+ u
3
+ 3u
2
− u + 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
2
=
1
−u
2
a
6
=
u
u
a
10
=
a
u
5
a + u
4
a + 2u
3
a + au + u
2
+ u + 1
a
5
=
−a
−u
5
− u
4
− 2u
3
+ au − u + 1
a
4
=
−a
−u
5
− u
4
+ u
2
a − 2u
3
+ au − u + 1
a
1
=
−u
3
− u + 1
−u
4
a + u
5
− u
3
a + u
4
− 2u
2
a + 2u
3
+ u
2
− a + u − 1
a
11
=
u
4
a + u
5
+ u
4
+ u
2
a + 2u
3
− au + a + 2u − 1
u
5
a + 2u
4
a − u
5
+ 2u
3
a − u
4
+ 2u
2
a − 3u
3
+ au − u
2
+ a − u + 2
a
9
=
−u
5
a − u
4
a − 2u
3
a + u
4
+ u
3
− au + u
2
+ a
u
4
+ u
3
+ 2u
2
+ u + 1
a
8
=
−u
5
a − u
4
a − 2u
3
a + u
3
− au + a + u
−u
5
a − u
4
a − 2u
3
a + u
3
− au + u
a
12
=
−u
4
a − u
5
− u
3
a − u
4
− 2u
2
a − 2u
3
− a − u + 1
−u
4
a − u
3
a − 2u
2
a − a − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −3u
4
− 7u
3
− 10u
2
− 9u − 16
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
7
c
10
u
12
− u
11
+ ··· − 11u + 1
c
2
, c
6
, c
8
c
12
(u
6
− u
5
+ 3u
4
− u
3
+ 3u
2
+ u + 1)
2
c
3
, c
5
, c
9
c
11
u
12
+ 5u
11
+ ··· + 17u + 7
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
7
c
10
y
12
− 19y
11
+ ··· − 37y + 1
c
2
, c
6
, c
8
c
12
(y
6
+ 5y
5
+ 13y
4
+ 21y
3
+ 17y
2
+ 5y + 1)
2
c
3
, c
5
, c
9
c
11
y
12
+ y
11
+ ··· + 257y + 49
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.028955 + 1.263070I
a = 0.565560 − 0.864727I
b = 1.113440 − 0.846070I
4.88968 − 2.84039I −6.95695 + 2.68362I
u = 0.028955 + 1.263070I
a = −0.374177 − 0.442775I
b = −1.46946 + 0.08347I
4.88968 − 2.84039I −6.95695 + 2.68362I
u = 0.028955 − 1.263070I
a = 0.565560 + 0.864727I
b = 1.113440 + 0.846070I
4.88968 + 2.84039I −6.95695 − 2.68362I
u = 0.028955 − 1.263070I
a = −0.374177 + 0.442775I
b = −1.46946 − 0.08347I
4.88968 + 2.84039I −6.95695 − 2.68362I
u = −0.80039 + 1.17645I
a = −1.035600 − 0.905749I
b = −1.97804 − 1.00830I
−9.60039 + 6.66133I −12.05452 − 4.58491I
u = −0.80039 + 1.17645I
a = 0.760760 + 1.153110I
b = 0.764071 − 0.032173I
−9.60039 + 6.66133I −12.05452 − 4.58491I
u = −0.80039 − 1.17645I
a = −1.035600 + 0.905749I
b = −1.97804 + 1.00830I
−9.60039 − 6.66133I −12.05452 + 4.58491I
u = −0.80039 − 1.17645I
a = 0.760760 − 1.153110I
b = 0.764071 + 0.032173I
−9.60039 − 6.66133I −12.05452 + 4.58491I
u = 0.271430 + 0.485552I
a = 0.041323 − 0.362162I
b = 1.22951 + 0.79439I
−1.04656 + 1.35140I −15.4885 − 6.6994I
u = 0.271430 + 0.485552I
a = −0.45786 + 2.36589I
b = 0.340472 + 0.389317I
−1.04656 + 1.35140I −15.4885 − 6.6994I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.271430 − 0.485552I
a = 0.041323 + 0.362162I
b = 1.22951 − 0.79439I
−1.04656 − 1.35140I −15.4885 + 6.6994I
u = 0.271430 − 0.485552I
a = −0.45786 − 2.36589I
b = 0.340472 − 0.389317I
−1.04656 − 1.35140I −15.4885 + 6.6994I
11
III. I
u
3
= h734u
11
− 3080u
10
+ · · · + 7763b − 15155, 1450u
11
− 7683u
10
+
· · · + 7763a − 6462, u
12
− 5u
11
+ · · · − 17u + 7i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
2
=
1
−u
2
a
6
=
u
u
a
10
=
−0.186783u
11
+ 0.989695u
10
+ ··· − 4.53265u + 0.832410
−0.0945511u
11
+ 0.396754u
10
+ ··· − 3.56421u + 1.95221
a
5
=
−0.147108u
11
+ 0.473657u
10
+ ··· + 4.45537u − 2.03465
−0.261883u
11
+ 1.26240u
10
+ ··· − 4.53549u + 1.02976
a
4
=
−0.147108u
11
+ 0.473657u
10
+ ··· + 4.45537u − 2.03465
−0.214865u
11
+ 0.915239u
10
+ ··· − 1.11323u − 0.803427
a
1
=
−0.267809u
11
+ 0.983254u
10
+ ··· + 2.83086u − 1.89733
−0.107948u
11
+ 0.660054u
10
+ ··· − 3.27631u − 0.615870
a
11
=
−0.0769033u
11
+ 0.516939u
10
+ ··· − 1.73606u + 0.269226
−0.154322u
11
+ 0.879170u
10
+ ··· − 5.04895u + 2.11001
a
9
=
−0.448023u
11
+ 2.12405u
10
+ ··· − 7.41852u + 1.75486
−0.355790u
11
+ 1.53111u
10
+ ··· − 6.45008u + 2.87466
a
8
=
0.0617029u
11
− 0.295118u
10
+ ··· + 1.00502u − 0.336854
−0.0854051u
11
+ 0.178539u
10
+ ··· + 5.46039u − 2.37151
a
12
=
−0.278887u
11
+ 1.29988u
10
+ ··· − 5.42831u + 1.17686
0.131779u
11
− 0.397656u
10
+ ··· − 2.68775u + 0.645627
(ii) Obstruction class = −1
(iii) Cusp Shapes =
21796
7763
u
11
−
13936
1109
u
10
+
237890
7763
u
9
−
434843
7763
u
8
+
110031
1109
u
7
−
1172937
7763
u
6
+
1426749
7763
u
5
−
1359518
7763
u
4
+
1096584
7763
u
3
−
724103
7763
u
2
+
299834
7763
u −
28345
1109
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
7
c
10
u
12
− u
11
+ ··· − 11u + 1
c
2
, c
6
, c
8
c
12
u
12
+ 5u
11
+ ··· + 17u + 7
c
3
, c
5
, c
9
c
11
(u
6
− u
5
+ 3u
4
− u
3
+ 3u
2
+ u + 1)
2
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
7
c
10
y
12
− 19y
11
+ ··· − 37y + 1
c
2
, c
6
, c
8
c
12
y
12
+ y
11
+ ··· + 257y + 49
c
3
, c
5
, c
9
c
11
(y
6
+ 5y
5
+ 13y
4
+ 21y
3
+ 17y
2
+ 5y + 1)
2
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.239056 + 0.890852I
a = 0.79735 + 1.21505I
b = 1.22951 + 0.79439I
−1.04656 + 1.35140I −15.4885 − 6.6994I
u = −0.239056 − 0.890852I
a = 0.79735 − 1.21505I
b = 1.22951 − 0.79439I
−1.04656 − 1.35140I −15.4885 + 6.6994I
u = 1.176420 + 0.148869I
a = 0.164789 + 0.045651I
b = 0.340472 − 0.389317I
−1.04656 − 1.35140I −15.4885 + 6.6994I
u = 1.176420 − 0.148869I
a = 0.164789 − 0.045651I
b = 0.340472 + 0.389317I
−1.04656 + 1.35140I −15.4885 − 6.6994I
u = −0.007700 + 0.692554I
a = −0.709646 − 0.783990I
b = 1.113440 − 0.846070I
4.88968 − 2.84039I −6.95695 + 2.68362I
u = −0.007700 − 0.692554I
a = −0.709646 + 0.783990I
b = 1.113440 + 0.846070I
4.88968 + 2.84039I −6.95695 − 2.68362I
u = 0.874959 + 1.026640I
a = −0.92937 + 1.12242I
b = −1.97804 + 1.00830I
−9.60039 − 6.66133I −12.05452 + 4.58491I
u = 0.874959 − 1.026640I
a = −0.92937 − 1.12242I
b = −1.97804 − 1.00830I
−9.60039 + 6.66133I −12.05452 − 4.58491I
u = −0.69640 + 1.36818I
a = −0.727697 − 0.439865I
b = −1.46946 − 0.08347I
4.88968 + 2.84039I −6.95695 − 2.68362I
u = −0.69640 − 1.36818I
a = −0.727697 + 0.439865I
b = −1.46946 + 0.08347I
4.88968 − 2.84039I −6.95695 + 2.68362I
15
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.39178 + 0.95258I
a = 0.761714 − 0.875845I
b = 0.764071 − 0.032173I
−9.60039 + 6.66133I −12.05452 − 4.58491I
u = 1.39178 − 0.95258I
a = 0.761714 + 0.875845I
b = 0.764071 + 0.032173I
−9.60039 − 6.66133I −12.05452 + 4.58491I
16
IV. I
u
4
= h−u
7
− 2u
4
− u
3
+ u
2
+ b + 1, u
9
+ 2u
6
+ u
5
− 2u
4
+ a − u, u
10
+
u
9
+ u
7
+ 2u
6
− u
5
− 3u
4
− 2u
3
+ u + 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
2
=
1
−u
2
a
6
=
u
u
a
10
=
−u
9
− 2u
6
− u
5
+ 2u
4
+ u
u
7
+ 2u
4
+ u
3
− u
2
− 1
a
5
=
−u
9
− u
7
− u
6
− u
5
+ u
3
+ 2u
2
−2u
9
− 3u
6
− u
5
+ 3u
4
+ 2u
3
+ 2u
2
− 1
a
4
=
−u
9
− u
7
− u
6
− u
5
+ u
3
+ 2u
2
u
2
a
1
=
u
8
+ u
6
+ u
5
+ u
4
− u
2
− u
2u
9
+ u
8
− u
7
+ 3u
6
+ 2u
5
− 4u
4
− 4u
3
− 2u
2
+ 2
a
11
=
2u
9
− u
8
+ u
6
− 4u
4
− 3u
3
− u
2
+ 3u + 2
u
3
+ u
a
9
=
u
9
+ u
8
+ u
6
+ 2u
5
− 3u
3
− 2u
2
+ u + 1
2u
9
+ u
8
+ u
7
+ 3u
6
+ 3u
5
− 2u
3
− 3u
2
a
8
=
2u
9
+ u
8
+ 2u
6
+ 3u
5
− 2u
4
− 4u
3
− 3u
2
+ u + 2
u
9
+ u
8
− u
7
+ u
6
+ 2u
5
− 2u
4
− 3u
3
− u
2
+ u + 2
a
12
=
−u
9
− u
5
+ 2u
4
+ 3u
3
+ u
2
− 2u − 1
−u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −13u
9
−9u
8
−2u
7
−20u
6
−24u
5
+ 8u
4
+ 21u
3
+ 16u
2
+ 2u − 18
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
10
− 2u
9
− 2u
8
+ 12u
6
+ 9u
5
− 43u
4
+ 11u
3
+ 37u
2
− 29u + 7
c
2
, c
3
, c
5
c
6
, c
8
, c
9
c
11
, c
12
u
10
− u
9
− u
7
+ 2u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1
c
4
, c
10
(u
5
+ 2u
4
− 2u
3
− 2u
2
+ u + 1)
2
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
10
− 8y
9
+ ··· − 323y + 49
c
2
, c
3
, c
5
c
6
, c
8
, c
9
c
11
, c
12
y
10
− y
9
+ 2y
8
− 5y
7
+ 10y
6
− 9y
5
+ 3y
4
+ 2y
3
− 2y
2
− y + 1
c
4
, c
10
(y
5
− 8y
4
+ 14y
3
− 12y
2
+ 5y − 1)
2
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.833438 + 0.554152I
a = −0.812076 − 0.979588I
b = −2.03262 − 0.35101I
1.24137 + 6.64784I −13.9589 − 7.4975I
u = −0.833438 − 0.554152I
a = −0.812076 + 0.979588I
b = −2.03262 + 0.35101I
1.24137 − 6.64784I −13.9589 + 7.4975I
u = −1.016860 + 0.408978I
a = −1.31220 − 0.69239I
b = −0.590675
−11.5552 −19.8669 + 0.I
u = −1.016860 − 0.408978I
a = −1.31220 + 0.69239I
b = −0.590675
−11.5552 −19.8669 + 0.I
u = 0.868230 + 0.062281I
a = 0.481330 − 0.323224I
b = 0.327959 + 0.538837I
−1.22103 + 1.14013I −11.60766 − 5.93486I
u = 0.868230 − 0.062281I
a = 0.481330 + 0.323224I
b = 0.327959 − 0.538837I
−1.22103 − 1.14013I −11.60766 + 5.93486I
u = −0.186852 + 0.738915I
a = 0.52801 + 1.66326I
b = 0.327959 + 0.538837I
−1.22103 + 1.14013I −11.60766 − 5.93486I
u = −0.186852 − 0.738915I
a = 0.52801 − 1.66326I
b = 0.327959 − 0.538837I
−1.22103 − 1.14013I −11.60766 + 5.93486I
u = 0.668920 + 1.200250I
a = −1.385060 + 0.017518I
b = −2.03262 + 0.35101I
1.24137 − 6.64784I −13.9589 + 7.4975I
u = 0.668920 − 1.200250I
a = −1.385060 − 0.017518I
b = −2.03262 − 0.35101I
1.24137 + 6.64784I −13.9589 − 7.4975I
20
V. I
u
5
= h−u
9
− u
7
− u
6
− u
5
+ u
3
+ 2u
2
+ b − 1, −u
9
− u
7
− u
6
− u
5
+ u
3
+
2u
2
+ a, u
10
+ u
9
+ u
7
+ 2u
6
− u
5
− 3u
4
− 2u
3
+ u + 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
2
=
1
−u
2
a
6
=
u
u
a
10
=
u
9
+ u
7
+ u
6
+ u
5
− u
3
− 2u
2
u
9
+ u
7
+ u
6
+ u
5
− u
3
− 2u
2
+ 1
a
5
=
u
9
− u
8
+ u
6
− u
5
− 2u
4
+ 2u + 1
u
9
− u
8
+ u
6
− u
5
− 2u
4
+ u + 1
a
4
=
u
9
− u
8
+ u
6
− u
5
− 2u
4
+ 2u + 1
−u
9
− u
8
+ u
7
− 2u
6
− 2u
5
+ 2u
4
+ 2u
3
− 1
a
1
=
u
8
+ u
6
+ u
5
+ u
4
− u
2
− u
−u
9
− u
6
− u
5
+ 2u
4
+ u
3
− 1
a
11
=
u
9
+ u
8
+ 2u
6
+ 2u
5
− 2u
3
− 2u
2
−u
9
+ u
7
− u
6
− u
5
+ 4u
4
+ 2u
3
− u
2
− u − 1
a
9
=
u
9
+ u
7
+ u
6
+ u
5
− u
3
− u
2
u
9
+ u
7
+ u
6
+ u
5
− u
3
− u
2
+ 1
a
8
=
2u
9
+ u
7
+ 2u
6
+ 2u
5
− 2u
4
− 2u
3
− 2u
2
+ 1
3u
9
− u
8
+ u
7
+ 3u
6
+ u
5
− 4u
4
− 2u
3
− 2u
2
+ 2u + 2
a
12
=
u
9
+ u
8
+ 2u
6
+ 2u
5
− u
4
− u
3
− u
2
− u + 1
u
9
− u
8
− u
7
+ u
6
− u
5
− 4u
4
− u
3
+ u
2
+ 2u + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −13u
9
−9u
8
−2u
7
−20u
6
−24u
5
+ 8u
4
+ 21u
3
+ 16u
2
+ 2u − 18
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
(u
5
+ 2u
4
− 2u
3
− 2u
2
+ u + 1)
2
c
2
, c
3
, c
5
c
6
, c
8
, c
9
c
11
, c
12
u
10
− u
9
− u
7
+ 2u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1
c
4
, c
10
u
10
− 2u
9
− 2u
8
+ 12u
6
+ 9u
5
− 43u
4
+ 11u
3
+ 37u
2
− 29u + 7
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
(y
5
− 8y
4
+ 14y
3
− 12y
2
+ 5y − 1)
2
c
2
, c
3
, c
5
c
6
, c
8
, c
9
c
11
, c
12
y
10
− y
9
+ 2y
8
− 5y
7
+ 10y
6
− 9y
5
+ 3y
4
+ 2y
3
− 2y
2
− y + 1
c
4
, c
10
y
10
− 8y
9
+ ··· − 323y + 49
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.833438 + 0.554152I
a = −0.885525 − 0.234725I
b = 0.114475 − 0.234725I
1.24137 + 6.64784I −13.9589 − 7.4975I
u = −0.833438 − 0.554152I
a = −0.885525 + 0.234725I
b = 0.114475 + 0.234725I
1.24137 − 6.64784I −13.9589 + 7.4975I
u = −1.016860 + 0.408978I
a = 2.06801 + 0.83175I
b = 3.06801 + 0.83175I
−11.5552 −19.8669 + 0.I
u = −1.016860 − 0.408978I
a = 2.06801 − 0.83175I
b = 3.06801 − 0.83175I
−11.5552 −19.8669 + 0.I
u = 0.868230 + 0.062281I
a = −0.719333 + 0.353776I
b = 0.280667 + 0.353776I
−1.22103 + 1.14013I −11.60766 − 5.93486I
u = 0.868230 − 0.062281I
a = −0.719333 − 0.353776I
b = 0.280667 − 0.353776I
−1.22103 − 1.14013I −11.60766 + 5.93486I
u = −0.186852 + 0.738915I
a = 0.541694 + 0.738059I
b = 1.54169 + 0.73806I
−1.22103 + 1.14013I −11.60766 − 5.93486I
u = −0.186852 − 0.738915I
a = 0.541694 − 0.738059I
b = 1.54169 − 0.73806I
−1.22103 − 1.14013I −11.60766 + 5.93486I
u = 0.668920 + 1.200250I
a = 0.495151 − 0.447313I
b = 1.49515 − 0.44731I
1.24137 − 6.64784I −13.9589 + 7.4975I
u = 0.668920 − 1.200250I
a = 0.495151 + 0.447313I
b = 1.49515 + 0.44731I
1.24137 + 6.64784I −13.9589 − 7.4975I
24
VI. I
u
6
= hu
2
+ b, u
2
+ a + 1, u
3
− u
2
+ 2u − 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
2
=
1
−u
2
a
6
=
u
u
a
10
=
−u
2
− 1
−u
2
a
5
=
u
2
+ 1
u
2
− u + 1
a
4
=
u
2
+ 1
u
2
a
1
=
0
−u
a
11
=
−u
2
− 1
−u
2
+ u − 1
a
9
=
−1
0
a
8
=
−1
u
2
a
12
=
−u
−u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8u
2
+ 8u − 20
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
7
c
10
u
3
+ u
2
− 1
c
2
, c
5
, c
8
c
11
u
3
− u
2
+ 2u − 1
c
3
, c
6
, c
9
c
12
u
3
+ u
2
+ 2u + 1
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
7
c
10
y
3
− y
2
+ 2y − 1
c
2
, c
3
, c
5
c
6
, c
8
, c
9
c
11
, c
12
y
3
+ 3y
2
+ 2y − 1
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 0.215080 + 1.307140I
a = 0.662359 − 0.562280I
b = 1.66236 − 0.56228I
6.04826 − 5.65624I −4.98049 + 5.95889I
u = 0.215080 − 1.307140I
a = 0.662359 + 0.562280I
b = 1.66236 + 0.56228I
6.04826 + 5.65624I −4.98049 − 5.95889I
u = 0.569840
a = −1.32472
b = −0.324718
−2.22691 −18.0390
28
VII.
I
u
7
= h−u
7
+5u
6
+· · ·+b+3, −3u
7
+12u
6
+· · ·+2a+2, u
8
−4u
7
+· · ·−4u+2i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
2
=
1
−u
2
a
6
=
u
u
a
10
=
3
2
u
7
− 6u
6
+ ··· +
9
2
u − 1
u
7
− 5u
6
+ 12u
5
− 19u
4
+ 20u
3
− 14u
2
+ 8u − 3
a
5
=
−
1
2
u
7
+ 2u
6
+ ··· −
7
2
u + 1
u
2
− u + 1
a
4
=
−
1
2
u
7
+ 2u
6
+ ··· −
7
2
u + 1
−u
3
+ 2u
2
− 2u + 1
a
1
=
1
2
u
7
− 2u
6
+ ··· +
3
2
u + 1
u
5
− 3u
4
+ 5u
3
− 6u
2
+ 3u − 1
a
11
=
u
7
− 2u
6
+ u
5
+ 3u
4
− 9u
3
+ 9u
2
− 5u + 3
u
7
− 3u
6
+ 5u
5
− 5u
4
+ u
3
+ 2u
2
− 2u + 2
a
9
=
3
2
u
7
− 6u
6
+ ··· +
3
2
u + 1
u
7
− 5u
6
+ 11u
5
− 16u
4
+ 15u
3
− 9u
2
+ 5u − 1
a
8
=
1
2
u
7
− 3u
6
+ ··· +
15
2
u − 4
−u
6
+ 3u
5
− 5u
4
+ 6u
3
− 4u
2
+ 4u − 3
a
12
=
3
2
u
7
− 5u
6
+ ··· −
1
2
u + 2
u
7
− 4u
6
+ 9u
5
− 13u
4
+ 12u
3
− 8u
2
+ 4u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
7
+ 17u
6
− 40u
5
+ 60u
4
− 64u
3
+ 52u
2
− 32u + 8
29
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
7
c
10
u
8
− 2u
7
+ 3u
5
− 3u
4
+ 3u
2
− u + 1
c
2
, c
8
u
8
− 4u
7
+ 9u
6
− 14u
5
+ 15u
4
− 13u
3
+ 9u
2
− 4u + 2
c
3
, c
9
(u
4
− u
3
+ u
2
+ 1)
2
c
5
, c
11
(u
4
+ u
3
+ u
2
+ 1)
2
c
6
, c
12
u
8
+ 4u
7
+ 9u
6
+ 14u
5
+ 15u
4
+ 13u
3
+ 9u
2
+ 4u + 2
30
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
7
c
10
y
8
− 4y
7
+ 6y
6
− 3y
5
+ 7y
4
− 12y
3
+ 3y
2
+ 5y + 1
c
2
, c
6
, c
8
c
12
y
8
+ 2y
7
− y
6
− 12y
5
− 5y
4
+ 25y
3
+ 37y
2
+ 20y + 4
c
3
, c
5
, c
9
c
11
(y
4
+ y
3
+ 3y
2
+ 2y + 1)
2
31
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = 0.192965 + 0.870342I
a = −0.81301 + 1.44822I
b = −1.51646 + 0.88804I
−0.732875 − 0.991478I −4.06428 − 5.52190I
u = 0.192965 − 0.870342I
a = −0.81301 − 1.44822I
b = −1.51646 − 0.88804I
−0.732875 + 0.991478I −4.06428 + 5.52190I
u = −0.138557 + 0.767522I
a = 0.066843 − 1.409780I
b = 1.41071 − 0.54257I
3.20028 + 5.62938I −9.43572 − 5.34414I
u = −0.138557 − 0.767522I
a = 0.066843 + 1.409780I
b = 1.41071 + 0.54257I
3.20028 − 5.62938I −9.43572 + 5.34414I
u = 1.354460 + 0.250532I
a = 0.008624 + 0.392991I
b = 0.164655 − 0.167700I
−0.732875 − 0.991478I −4.06428 − 5.52190I
u = 1.354460 − 0.250532I
a = 0.008624 − 0.392991I
b = 0.164655 + 0.167700I
−0.732875 + 0.991478I −4.06428 + 5.52190I
u = 0.59113 + 1.35317I
a = −0.762459 + 0.087166I
b = −1.55891 + 0.36873I
3.20028 − 5.62938I −9.43572 + 5.34414I
u = 0.59113 − 1.35317I
a = −0.762459 − 0.087166I
b = −1.55891 − 0.36873I
3.20028 + 5.62938I −9.43572 − 5.34414I
32
VIII.
I
u
8
= hau+u
2
+b−a+u+1, −u
3
a−2u
2
a−u
3
+a
2
−au−u
2
−u, u
4
+u
3
+u
2
+1i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
2
=
1
−u
2
a
6
=
u
u
a
10
=
a
−au − u
2
+ a − u − 1
a
5
=
−a
−u
3
+ au + 1
a
4
=
−a
u
2
a − u
3
+ au + 1
a
1
=
0
−u
3
a − u
2
a + u
3
− au + u
2
− a − 1
a
11
=
a
−u
2
a + 2u
3
− 2au + u
2
− 2
a
9
=
−u
3
a + a + 1
−u
3
a − au − u
2
+ a − u
a
8
=
−u
3
a + a + 1
−u
3
a + 1
a
12
=
u
3
a + u
2
a + au + a + u
−u
2
a − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −u
3
+ 5u
2
+ 4u − 4
33
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
7
c
10
u
8
− 2u
7
+ 3u
5
− 3u
4
+ 3u
2
− u + 1
c
2
, c
8
(u
4
+ u
3
+ u
2
+ 1)
2
c
3
, c
9
u
8
+ 4u
7
+ 9u
6
+ 14u
5
+ 15u
4
+ 13u
3
+ 9u
2
+ 4u + 2
c
5
, c
11
u
8
− 4u
7
+ 9u
6
− 14u
5
+ 15u
4
− 13u
3
+ 9u
2
− 4u + 2
c
6
, c
12
(u
4
− u
3
+ u
2
+ 1)
2
34
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
7
c
10
y
8
− 4y
7
+ 6y
6
− 3y
5
+ 7y
4
− 12y
3
+ 3y
2
+ 5y + 1
c
2
, c
6
, c
8
c
12
(y
4
+ y
3
+ 3y
2
+ 2y + 1)
2
c
3
, c
5
, c
9
c
11
y
8
+ 2y
7
− y
6
− 12y
5
− 5y
4
+ 25y
3
+ 37y
2
+ 20y + 4
35
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
8
√
−1(vol +
√
−1CS) Cusp shape
u = 0.351808 + 0.720342I
a = −0.646554 − 0.195306I
b = −1.51646 − 0.88804I
−0.732875 + 0.991478I −4.06428 + 5.52190I
u = 0.351808 + 0.720342I
a = −0.29599 + 1.82302I
b = 0.164655 + 0.167700I
−0.732875 + 0.991478I −4.06428 + 5.52190I
u = 0.351808 − 0.720342I
a = −0.646554 + 0.195306I
b = −1.51646 + 0.88804I
−0.732875 − 0.991478I −4.06428 − 5.52190I
u = 0.351808 − 0.720342I
a = −0.29599 − 1.82302I
b = 0.164655 − 0.167700I
−0.732875 − 0.991478I −4.06428 − 5.52190I
u = −0.851808 + 0.911292I
a = 0.885365 − 0.203552I
b = 1.41071 − 0.54257I
3.20028 + 5.62938I −9.43572 − 5.34414I
u = −0.851808 + 0.911292I
a = −0.442818 − 0.763288I
b = −1.55891 − 0.36873I
3.20028 + 5.62938I −9.43572 − 5.34414I
u = −0.851808 − 0.911292I
a = 0.885365 + 0.203552I
b = 1.41071 + 0.54257I
3.20028 − 5.62938I −9.43572 + 5.34414I
u = −0.851808 − 0.911292I
a = −0.442818 + 0.763288I
b = −1.55891 + 0.36873I
3.20028 − 5.62938I −9.43572 + 5.34414I
36
IX. I
u
9
= hb + 1, −u
4
− u
2
+ 2a, u
6
− u
5
+ u
4
+ u
3
+ 2i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
2
=
1
−u
2
a
6
=
u
u
a
10
=
1
2
u
4
+
1
2
u
2
−1
a
5
=
−
1
2
u
4
−
1
2
u
2
−
1
2
u
5
−
1
2
u
3
a
4
=
−
1
2
u
4
−
1
2
u
2
−u
3
− 1
a
1
=
1
2
u
5
+
1
2
u
4
+ ··· + u + 1
u
4
+ u + 1
a
11
=
−
1
2
u
5
−
1
2
u
3
− u
2
− u
−
1
2
u
5
−
1
2
u
3
− u
2
− u − 1
a
9
=
−
1
2
u
5
+
1
2
u
4
+ ··· −
1
2
u
2
+ 1
−
1
2
u
5
+
1
2
u
3
− u
2
a
8
=
1
2
u
5
+
1
2
u
4
+
1
2
u
3
+
1
2
u
2
+ u
1
2
u
5
+
1
2
u
3
+ u
a
12
=
1
2
u
5
−
1
2
u
4
+
1
2
u
3
+
1
2
u
2
1
2
u
5
+
1
2
u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = u
5
− u
3
+ 2u
2
− 12
37
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
7
c
10
(u
3
+ u
2
− u + 1)
2
c
2
, c
3
, c
5
c
6
, c
8
, c
9
c
11
, c
12
u
6
+ u
5
+ u
4
− u
3
+ 2
38
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
7
c
10
(y
3
− 3y
2
− y − 1)
2
c
2
, c
3
, c
5
c
6
, c
8
, c
9
c
11
, c
12
y
6
+ y
5
+ 3y
4
+ 3y
3
+ 4y
2
+ 4
39
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
9
√
−1(vol +
√
−1CS) Cusp shape
u = −0.822087 + 0.503636I
a = −0.042641 − 0.763625I
b = −1.00000
2.61340 + 3.17729I −10.45631 − 2.23029I
u = −0.822087 − 0.503636I
a = −0.042641 + 0.763625I
b = −1.00000
2.61340 − 3.17729I −10.45631 + 2.23029I
u = 0.402444 + 1.109930I
a = −0.361615 − 0.509199I
b = −1.00000
2.61340 − 3.17729I −10.45631 + 2.23029I
u = 0.402444 − 1.109930I
a = −0.361615 + 0.509199I
b = −1.00000
2.61340 + 3.17729I −10.45631 − 2.23029I
u = 0.919643 + 0.835431I
a = −1.09574 + 0.99541I
b = −1.00000
−10.1616 −13.08738 + 0.I
u = 0.919643 − 0.835431I
a = −1.09574 − 0.99541I
b = −1.00000
−10.1616 −13.08738 + 0.I
40
X. I
u
10
= hb − a − 1, a
2
− a − 4, u + 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
−1
a
2
=
1
−1
a
6
=
−1
−1
a
10
=
a
a + 1
a
5
=
a − 1
a
a
4
=
a − 1
1
a
1
=
−3
−a − 1
a
11
=
−2a + 3
−2
a
9
=
a + 1
a + 2
a
8
=
a + 4
2a + 3
a
12
=
a − 2
1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −26
41
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
7
c
10
u
2
+ u − 4
c
2
, c
3
, c
5
c
6
, c
8
, c
9
c
11
, c
12
(u − 1)
2
42
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
7
c
10
y
2
− 9y + 16
c
2
, c
3
, c
5
c
6
, c
8
, c
9
c
11
, c
12
(y − 1)
2
43
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
10
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = −1.56155
b = −0.561553
−11.5145 −26.0000
u = −1.00000
a = 2.56155
b = 3.56155
−11.5145 −26.0000
44
XI. I
u
11
= h−u
2
+ b − u, −u
3
− 3u
2
+ a − 3u − 2, u
4
+ 2u
3
+ 2u
2
+ u − 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
2
=
1
−u
2
a
6
=
u
u
a
10
=
u
3
+ 3u
2
+ 3u + 2
u
2
+ u
a
5
=
2u
3
+ 4u
2
+ 5u + 3
u
3
+ 2u
2
+ 2u
a
4
=
2u
3
+ 4u
2
+ 5u + 3
u
2
a
1
=
−u
3
− 4u
2
− 5u − 4
−u
a
11
=
−2u
3
− 7u
2
− 9u − 9
−u
3
− u
a
9
=
u
3
+ 2u
2
+ 2u + 2
0
a
8
=
−2u
3
− 5u
2
− 6u − 3
−u
2
− u
a
12
=
−2u
3
− 6u
2
− 8u − 7
−u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 5u
2
+ 5u − 1
45
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
4
+ 3u
3
+ u
2
− 5u − 5
c
2
, c
5
, c
8
c
11
u
4
+ 2u
3
+ 2u
2
+ u − 1
c
3
, c
6
, c
9
c
12
u
4
− 2u
3
+ 2u
2
− u − 1
c
4
, c
10
(u
2
− 3u + 1)
2
46
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
4
− 7y
3
+ 21y
2
− 35y + 25
c
2
, c
3
, c
5
c
6
, c
8
, c
9
c
11
, c
12
y
4
− 2y
2
− 5y + 1
c
4
, c
10
(y
2
− 7y + 1)
2
47
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
11
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 1.169630I
a = −0.927051 − 0.722871I
b = −1.61803
4.60582 −9.09017 + 0.I
u = −0.500000 − 1.169630I
a = −0.927051 + 0.722871I
b = −1.61803
4.60582 −9.09017 + 0.I
u = −1.43168
a = 0.919556
b = 0.618034
−11.1856 2.09020
u = 0.431683
a = 3.93455
b = 0.618034
−11.1856 2.09020
48
XII.
I
u
12
= h2u
3
+ 4u
2
+ b + 5u + 2, 2u
3
+ 4u
2
+ a + 5u + 3, u
4
+ 2u
3
+ 2u
2
+ u − 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
2
=
1
−u
2
a
6
=
u
u
a
10
=
−2u
3
− 4u
2
− 5u − 3
−2u
3
− 4u
2
− 5u − 2
a
5
=
u
2
+ 2u + 2
u
2
+ u + 2
a
4
=
u
2
+ 2u + 2
u
2
+ 2u + 1
a
1
=
−u
3
− 4u
2
− 5u − 4
−u
3
− 4u
2
− 4u − 3
a
11
=
u
3
+ 3u
2
+ 5u + 3
u
3
+ 3u
2
+ 4u + 2
a
9
=
−2u
3
− 3u
2
− 5u − 3
−2u
3
− 3u
2
− 5u − 2
a
8
=
−5u
3
− 10u
2
− 13u − 8
−5u
3
− 9u
2
− 11u − 6
a
12
=
u + 1
u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 5u
2
+ 5u − 1
49
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
(u
2
− 3u + 1)
2
c
2
, c
5
, c
8
c
11
u
4
+ 2u
3
+ 2u
2
+ u − 1
c
3
, c
6
, c
9
c
12
u
4
− 2u
3
+ 2u
2
− u − 1
c
4
, c
10
u
4
+ 3u
3
+ u
2
− 5u − 5
50
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
(y
2
− 7y + 1)
2
c
2
, c
3
, c
5
c
6
, c
8
, c
9
c
11
, c
12
y
4
− 2y
2
− 5y + 1
c
4
, c
10
y
4
− 7y
3
+ 21y
2
− 35y + 25
51
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
12
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 1.169630I
a = 0.118034 + 0.276112I
b = 1.118030 + 0.276112I
4.60582 −9.09017 + 0.I
u = −0.500000 − 1.169630I
a = 0.118034 − 0.276112I
b = 1.118030 − 0.276112I
4.60582 −9.09017 + 0.I
u = −1.43168
a = 1.82864
b = 2.82864
−11.1856 2.09020
u = 0.431683
a = −6.06471
b = −5.06471
−11.1856 2.09020
52
XIII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
7
c
10
(u
2
− 3u + 1)
2
(u
2
+ u − 4)(u
3
+ u
2
− 1)(u
3
+ u
2
− u + 1)
2
· (u
4
+ 3u
3
+ u
2
− 5u − 5)(u
5
+ 2u
4
− 2u
3
− 2u
2
+ u + 1)
2
· (u
6
− 2u
5
− 3u
4
+ 6u
3
+ 4u + 1)(u
8
− 2u
7
+ 3u
5
− 3u
4
+ 3u
2
− u + 1)
2
· (u
10
− 2u
9
− 2u
8
+ 12u
6
+ 9u
5
− 43u
4
+ 11u
3
+ 37u
2
− 29u + 7)
· (u
12
− u
11
+ ··· − 11u + 1)
2
c
2
, c
5
, c
8
c
11
((u − 1)
2
)(u
3
− u
2
+ 2u − 1)(u
4
+ u
3
+ u
2
+ 1)
2
(u
4
+ 2u
3
+ ··· + u − 1)
2
· (u
6
− u
5
+ 3u
4
− u
3
+ 3u
2
+ u + 1)
2
(u
6
+ u
5
+ u
4
− u
3
+ 2)
· (u
6
+ 2u
5
+ 3u
4
+ 2u
3
+ 4u
2
+ 4u + 1)
· (u
8
− 4u
7
+ 9u
6
− 14u
5
+ 15u
4
− 13u
3
+ 9u
2
− 4u + 2)
· (u
10
− u
9
− u
7
+ 2u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1)
2
· (u
12
+ 5u
11
+ ··· + 17u + 7)
c
3
, c
6
, c
9
c
12
((u − 1)
2
)(u
3
+ u
2
+ 2u + 1)(u
4
− 2u
3
+ ··· − u − 1)
2
(u
4
− u
3
+ u
2
+ 1)
2
· (u
6
− u
5
+ 3u
4
− u
3
+ 3u
2
+ u + 1)
2
(u
6
+ u
5
+ u
4
− u
3
+ 2)
· (u
6
+ 2u
5
+ 3u
4
+ 2u
3
+ 4u
2
+ 4u + 1)
· (u
8
+ 4u
7
+ 9u
6
+ 14u
5
+ 15u
4
+ 13u
3
+ 9u
2
+ 4u + 2)
· (u
10
− u
9
− u
7
+ 2u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1)
2
· (u
12
+ 5u
11
+ ··· + 17u + 7)
53
XIV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
7
c
10
(y
2
− 9y + 16)(y
2
− 7y + 1)
2
(y
3
− 3y
2
− y − 1)
2
(y
3
− y
2
+ 2y − 1)
· (y
4
− 7y
3
+ 21y
2
− 35y + 25)(y
5
− 8y
4
+ 14y
3
− 12y
2
+ 5y − 1)
2
· (y
6
− 10y
5
+ 33y
4
− 18y
3
− 54y
2
− 16y + 1)
· (y
8
− 4y
7
+ 6y
6
− 3y
5
+ 7y
4
− 12y
3
+ 3y
2
+ 5y + 1)
2
· (y
10
− 8y
9
+ ··· − 323y + 49)(y
12
− 19y
11
+ ··· − 37y + 1)
2
c
2
, c
3
, c
5
c
6
, c
8
, c
9
c
11
, c
12
(y − 1)
2
(y
3
+ 3y
2
+ 2y − 1)(y
4
− 2y
2
− 5y + 1)
2
· (y
4
+ y
3
+ 3y
2
+ 2y + 1)
2
(y
6
+ y
5
+ 3y
4
+ 3y
3
+ 4y
2
+ 4)
· (y
6
+ 2y
5
+ 9y
4
+ 6y
3
+ 6y
2
− 8y + 1)
· (y
6
+ 5y
5
+ 13y
4
+ 21y
3
+ 17y
2
+ 5y + 1)
2
· (y
8
+ 2y
7
− y
6
− 12y
5
− 5y
4
+ 25y
3
+ 37y
2
+ 20y + 4)
· (y
10
− y
9
+ 2y
8
− 5y
7
+ 10y
6
− 9y
5
+ 3y
4
+ 2y
3
− 2y
2
− y + 1)
2
· (y
12
+ y
11
+ ··· + 257y + 49)
54
