12n
0600
(K12n
0600
)
A knot diagram
1
Linearized knot diagam
3 7 9 11 10 2 12 4 3 5 7 8
Solving Sequence
4,8 9,12
1 3 10 7 2 6 11 5
c
8
c
12
c
3
c
9
c
7
c
2
c
6
c
11
c
4
c
1
, c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= hu
7
− u
6
+ 5u
5
− 8u
4
+ 12u
3
− 15u
2
+ 8b + 16u − 6, u
6
+ 3u
4
− u
3
+ u
2
+ 4a − 4u − 2,
u
8
+ 4u
6
− 3u
5
+ 4u
4
− 11u
3
+ u
2
− 6u + 2i
I
u
2
= h−u
2
a − u
3
+ b − a − u − 1, 2u
3
a − 2u
2
a − u
3
+ 2a
2
+ 2au + u
2
+ 2a − 1, u
4
+ u
2
+ u + 1i
I
u
3
= h−211u
9
− 520u
8
− 1473u
7
− 2621u
6
− 4433u
5
− 6682u
4
− 6460u
3
− 6461u
2
+ 893b − 3449u − 911,
− 3011u
9
− 6938u
8
+ ··· + 8930a − 4451,
u
10
+ 3u
9
+ 8u
8
+ 16u
7
+ 27u
6
+ 43u
5
+ 49u
4
+ 48u
3
+ 38u
2
+ 16u + 5i
I
u
4
= h−u
5
+ u
4
− u
2
a − 2u
3
+ 2u
2
+ b − a − 2u + 2, 2u
5
a + 2u
3
a + u
4
− 2u
2
a − u
3
+ a
2
+ au + u
2
− 2a − 2u + 2,
u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1i
I
u
5
= hb − 1, 6a − u − 3, u
2
+ 3i
I
u
6
= hb + u, 2a − u + 1, u
2
+ 1i
I
v
1
= ha, b − 1, v + 1i
* 7 irreducible components of dim
C
= 0, with total 43 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
= hu
7
− u
6
+ · · · + 8b − 6, u
6
+ 3u
4
− u
3
+ u
2
+ 4a − 4u − 2, u
8
+ 4u
6
−
3u
5
+ 4u
4
− 11u
3
+ u
2
− 6u + 2i
(i) Arc colorings
a
4
=
0
u
a
8
=
1
0
a
9
=
1
u
2
a
12
=
−
1
4
u
6
−
3
4
u
4
+ ··· + u +
1
2
−
1
8
u
7
+
1
8
u
6
+ ··· − 2u +
3
4
a
1
=
1
8
u
7
−
3
8
u
6
+ ··· + 3u −
1
4
−
1
8
u
7
+
1
8
u
6
+ ··· − 2u +
3
4
a
3
=
u
u
3
+ u
a
10
=
u
2
+ 1
u
4
+ 2u
2
a
7
=
−
1
4
u
6
−
3
4
u
4
+ ··· + u +
1
2
3
8
u
7
+
1
8
u
6
+ ··· − 2u +
3
4
a
2
=
1
4
u
6
+
3
4
u
4
+ ··· +
1
4
u
2
+
1
2
−
3
8
u
7
+
3
8
u
6
+ ··· − u +
1
4
a
6
=
u
3
+ 2u
1
2
u
7
+
1
2
u
6
+ ··· − 3u + 1
a
11
=
1
−
1
2
u
7
+
1
2
u
6
+ ··· − 4u + 1
a
5
=
−u
−
1
2
u
7
−
1
2
u
6
+ ··· + 3u − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes =
1
2
u
7
+
1
2
u
6
+
5
2
u
5
+ u
4
+ u
3
−
9
2
u
2
− 10u − 17
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
8
+ 5u
7
+ 4u
6
− 21u
5
− 39u
4
+ 31u
3
+ 86u
2
+ 57u + 4
c
2
, c
6
, c
7
c
11
, c
12
u
8
− 3u
7
+ 2u
6
+ u
5
− 3u
4
+ 5u
3
+ 2u
2
− 7u − 2
c
3
, c
4
, c
5
c
8
, c
9
, c
10
u
8
+ 4u
6
+ 3u
5
+ 4u
4
+ 11u
3
+ u
2
+ 6u + 2
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
8
− 17y
7
+ ··· − 2561y + 16
c
2
, c
6
, c
7
c
11
, c
12
y
8
− 5y
7
+ 4y
6
+ 21y
5
− 39y
4
− 31y
3
+ 86y
2
− 57y + 4
c
3
, c
4
, c
5
c
8
, c
9
, c
10
y
8
+ 8y
7
+ 24y
6
+ 25y
5
− 38y
4
− 133y
3
− 115y
2
− 32y + 4
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.220679 + 0.854461I
a = 0.332670 + 0.556447I
b = −0.208499 − 1.323920I
4.23170 + 1.04444I −12.01624 − 6.62288I
u = −0.220679 − 0.854461I
a = 0.332670 − 0.556447I
b = −0.208499 + 1.323920I
4.23170 − 1.04444I −12.01624 + 6.62288I
u = 1.30710
a = −1.49781
b = −1.66764
−14.6274 −17.3150
u = −0.66283 + 1.38843I
a = −0.983264 − 0.973100I
b = −1.51379 + 0.50848I
−6.1134 + 13.7627I −12.22207 − 6.91669I
u = −0.66283 − 1.38843I
a = −0.983264 + 0.973100I
b = −1.51379 − 0.50848I
−6.1134 − 13.7627I −12.22207 + 6.91669I
u = 0.07864 + 1.65422I
a = 0.509409 + 0.080495I
b = 0.915236 − 0.302637I
10.25980 + 1.08243I −6.90626 − 6.60767I
u = 0.07864 − 1.65422I
a = 0.509409 − 0.080495I
b = 0.915236 + 0.302637I
10.25980 − 1.08243I −6.90626 + 6.60767I
u = 0.302631
a = 0.780180
b = 0.281755
−0.483877 −20.3950
5
II. I
u
2
= h−u
2
a − u
3
+ b − a − u − 1, 2u
3
a − 2u
2
a − u
3
+ 2a
2
+ 2au + u
2
+
2a − 1, u
4
+ u
2
+ u + 1i
(i) Arc colorings
a
4
=
0
u
a
8
=
1
0
a
9
=
1
u
2
a
12
=
a
u
2
a + u
3
+ a + u + 1
a
1
=
−u
2
a − u
3
− u − 1
u
2
a + u
3
+ a + u + 1
a
3
=
u
u
3
+ u
a
10
=
u
2
+ 1
u
2
− u − 1
a
7
=
a
−u
3
a + u
2
a − u
3
− u − 1
a
2
=
u
3
a + au + a + u − 1
u
3
a + u
2
a + 3u
3
− au − u
2
+ a + 2u + 1
a
6
=
u
3
+ 2u
3u
3
+ 1
a
11
=
1
−u
3
+ 2u
2
+ 1
a
5
=
−u
−2u
3
− u
2
− u − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
3
+ 4u
2
− 14
6
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
8
+ 7u
7
+ 19u
6
+ 11u
5
− 48u
4
− 98u
3
+ u
2
+ 170u + 169
c
2
, c
6
, c
7
c
11
, c
12
u
8
− 3u
7
+ u
6
+ 3u
5
− u
2
− 12u + 13
c
3
, c
4
, c
5
c
8
, c
9
, c
10
(u
4
+ u
2
− u + 1)
2
7
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
8
− 11y
7
+ ··· − 28562y + 28561
c
2
, c
6
, c
7
c
11
, c
12
y
8
− 7y
7
+ 19y
6
− 11y
5
− 48y
4
+ 98y
3
+ y
2
− 170y + 169
c
3
, c
4
, c
5
c
8
, c
9
, c
10
(y
4
+ 2y
3
+ 3y
2
+ y + 1)
2
8
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.547424 + 0.585652I
a = 0.429852 − 0.104809I
b = 1.195840 + 0.535402I
−4.26996 + 1.39709I −15.7702 − 3.8674I
u = −0.547424 + 0.585652I
a = −1.32498 − 1.44768I
b = −1.344030 + 0.375890I
−4.26996 + 1.39709I −15.7702 − 3.8674I
u = −0.547424 − 0.585652I
a = 0.429852 + 0.104809I
b = 1.195840 − 0.535402I
−4.26996 − 1.39709I −15.7702 + 3.8674I
u = −0.547424 − 0.585652I
a = −1.32498 + 1.44768I
b = −1.344030 − 0.375890I
−4.26996 − 1.39709I −15.7702 + 3.8674I
u = 0.547424 + 1.120870I
a = −1.018240 + 0.928993I
b = −1.53596 − 0.48899I
−0.66484 − 7.64338I −10.22981 + 6.51087I
u = 0.547424 + 1.120870I
a = 0.413361 − 0.422149I
b = 0.184153 + 1.209330I
−0.66484 − 7.64338I −10.22981 + 6.51087I
u = 0.547424 − 1.120870I
a = −1.018240 − 0.928993I
b = −1.53596 + 0.48899I
−0.66484 + 7.64338I −10.22981 − 6.51087I
u = 0.547424 − 1.120870I
a = 0.413361 + 0.422149I
b = 0.184153 − 1.209330I
−0.66484 + 7.64338I −10.22981 − 6.51087I
9
III. I
u
3
= h−211u
9
− 520u
8
+ · · · + 893b − 911, −3011u
9
− 6938u
8
+ · · · +
8930a − 4451, u
10
+ 3u
9
+ · · · + 16u + 5i
(i) Arc colorings
a
4
=
0
u
a
8
=
1
0
a
9
=
1
u
2
a
12
=
0.337178u
9
+ 0.776932u
8
+ ··· + 5.47738u + 0.498432
0.236282u
9
+ 0.582307u
8
+ ··· + 3.86226u + 1.02016
a
1
=
0.100896u
9
+ 0.194625u
8
+ ··· + 1.61512u − 0.521725
0.236282u
9
+ 0.582307u
8
+ ··· + 3.86226u + 1.02016
a
3
=
u
u
3
+ u
a
10
=
u
2
+ 1
u
4
+ 2u
2
a
7
=
−0.0959686u
9
− 0.0241881u
8
+ ··· + 1.61803u + 1.10224
−0.265398u
9
− 0.407615u
8
+ ··· − 1.60358u − 0.814110
a
2
=
−0.287682u
9
− 0.473908u
8
+ ··· − 1.81713u − 1.84871
−0.627100u
9
− 1.23740u
8
+ ··· − 5.58231u − 2.79283
a
6
=
0.717357u
9
+ 1.49586u
8
+ ··· + 12.0804u + 5.15409
1.26876u
9
+ 2.38746u
8
+ ··· + 13.5353u + 5.48264
a
11
=
0.0494961u
9
+ 0.303024u
8
+ ··· + 2.66025u − 1.35028
−0.390817u
9
− 0.655095u
8
+ ··· − 2.72004u − 1.77268
a
5
=
−0.0454647u
9
− 0.527212u
8
+ ··· − 8.74222u − 3.44748
0.671892u
9
+ 0.968645u
8
+ ··· + 5.33819u + 1.70661
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
714
893
u
9
−
2860
893
u
8
−
6762
893
u
7
−
14862
893
u
6
−
23042
893
u
5
−
37644
893
u
4
−
2246
47
u
3
−
35982
893
u
2
−
26560
893
u−
15280
893
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
5
+ 7u
4
+ 17u
3
+ 14u
2
+ 1)
2
c
2
, c
6
, c
7
c
11
, c
12
(u
5
+ u
4
− 3u
3
− 2u
2
+ 2u − 1)
2
c
3
, c
4
, c
5
c
8
, c
9
, c
10
u
10
− 3u
9
+ ··· − 16u + 5
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
5
− 15y
4
+ 93y
3
− 210y
2
− 28y −1)
2
c
2
, c
6
, c
7
c
11
, c
12
(y
5
− 7y
4
+ 17y
3
− 14y
2
− 1)
2
c
3
, c
4
, c
5
c
8
, c
9
, c
10
y
10
+ 7y
9
+ ··· + 124y + 25
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.030539 + 1.180900I
a = −0.203705 + 0.519644I
b = −0.331409 − 0.386277I
2.91669 − 1.13882I −8.71808 + 6.05450I
u = 0.030539 − 1.180900I
a = −0.203705 − 0.519644I
b = −0.331409 + 0.386277I
2.91669 + 1.13882I −8.71808 − 6.05450I
u = −1.280020 + 0.074043I
a = 1.49558 + 0.07831I
b = 1.58033 + 0.28256I
−10.17380 − 6.99719I −15.1390 + 3.5468I
u = −1.280020 − 0.074043I
a = 1.49558 − 0.07831I
b = 1.58033 − 0.28256I
−10.17380 + 6.99719I −15.1390 − 3.5468I
u = −0.255771 + 0.477985I
a = −1.33342 + 0.89783I
b = −0.331409 + 0.386277I
2.91669 + 1.13882I −8.71808 − 6.05450I
u = −0.255771 − 0.477985I
a = −1.33342 − 0.89783I
b = −0.331409 − 0.386277I
2.91669 − 1.13882I −8.71808 + 6.05450I
u = 0.68764 + 1.45529I
a = 0.803516 − 0.827954I
b = 1.58033 + 0.28256I
−10.17380 − 6.99719I −15.1390 + 3.5468I
u = 0.68764 − 1.45529I
a = 0.803516 + 0.827954I
b = 1.58033 − 0.28256I
−10.17380 + 6.99719I −15.1390 − 3.5468I
u = −0.68239 + 1.54821I
a = −0.661966 − 0.593569I
b = −1.49784
−5.22495 −14.2858 + 0.I
u = −0.68239 − 1.54821I
a = −0.661966 + 0.593569I
b = −1.49784
−5.22495 −14.2858 + 0.I
13
IV. I
u
4
= h−u
5
+ u
4
− u
2
a − 2u
3
+ 2u
2
+ b − a − 2u + 2, 2u
5
a + u
4
+ · · · −
2a + 2, u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1i
(i) Arc colorings
a
4
=
0
u
a
8
=
1
0
a
9
=
1
u
2
a
12
=
a
u
5
− u
4
+ u
2
a + 2u
3
− 2u
2
+ a + 2u − 2
a
1
=
−u
5
+ u
4
− u
2
a − 2u
3
+ 2u
2
− 2u + 2
u
5
− u
4
+ u
2
a + 2u
3
− 2u
2
+ a + 2u − 2
a
3
=
u
u
3
+ u
a
10
=
u
2
+ 1
u
4
+ 2u
2
a
7
=
u
5
a − u
4
a + u
3
a − 2u
2
a − u
3
+ au + u
2
− 2a + 2
−u
5
a + u
5
− 2u
3
a + 2u
3
− au + 2u − 1
a
2
=
−u
5
a − u
5
− 2u
3
a + u
4
− u
3
− 2au + 2u
2
+ a + 2
−2u
5
a + 2u
5
+ ··· + 3a − 2
a
6
=
2u
5
− 2u
4
+ 3u
3
− 3u
2
+ 2u − 3
−u
5
− 3u
3
+ u
2
− 3u
a
11
=
u
5
+ 2u
3
+ u − 1
u
5
+ u
3
− u
2
+ u − 2
a
5
=
u
4
+ u
2
+ 1
2u
5
− u
4
+ 4u
3
− 2u
2
+ 4u − 2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
3
− 4u − 10
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
6
+ 5u
5
+ 8u
4
+ 6u
3
+ 8u
2
+ 8u + 1)
2
c
2
, c
6
, c
7
c
11
, c
12
(u
6
+ u
5
− 2u
4
+ 2u
2
− 2u − 1)
2
c
3
, c
4
, c
5
c
8
, c
9
, c
10
(u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)
2
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
6
− 9y
5
+ 20y
4
+ 14y
3
− 16y
2
− 48y + 1)
2
c
2
, c
6
, c
7
c
11
, c
12
(y
6
− 5y
5
+ 8y
4
− 6y
3
+ 8y
2
− 8y + 1)
2
c
3
, c
4
, c
5
c
8
, c
9
, c
10
(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
2
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.498832 + 1.001300I
a = −0.275405 − 0.924742I
b = −0.592989 + 0.847544I
−3.02413 + 2.82812I −13.50976 − 2.97945I
u = −0.498832 + 1.001300I
a = 1.101290 + 0.801486I
b = 1.47043 − 0.10268I
−3.02413 + 2.82812I −13.50976 − 2.97945I
u = −0.498832 − 1.001300I
a = −0.275405 + 0.924742I
b = −0.592989 − 0.847544I
−3.02413 − 2.82812I −13.50976 + 2.97945I
u = −0.498832 − 1.001300I
a = 1.101290 − 0.801486I
b = 1.47043 + 0.10268I
−3.02413 − 2.82812I −13.50976 + 2.97945I
u = 0.284920 + 1.115140I
a = −1.46787 − 0.56029I
b = 0.379278
1.11345 −6.98049 + 0.I
u = 0.284920 + 1.115140I
a = −0.89664 + 1.67543I
b = −1.13416
1.11345 −6.98049 + 0.I
u = 0.284920 − 1.115140I
a = −1.46787 + 0.56029I
b = 0.379278
1.11345 −6.98049 + 0.I
u = 0.284920 − 1.115140I
a = −0.89664 − 1.67543I
b = −1.13416
1.11345 −6.98049 + 0.I
u = 0.713912 + 0.305839I
a = 0.448508 + 0.102156I
b = −0.592989 + 0.847544I
−3.02413 + 2.82812I −13.50976 − 2.97945I
u = 0.713912 + 0.305839I
a = 1.59012 − 0.92088I
b = 1.47043 − 0.10268I
−3.02413 + 2.82812I −13.50976 − 2.97945I
17
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.713912 − 0.305839I
a = 0.448508 − 0.102156I
b = −0.592989 − 0.847544I
−3.02413 − 2.82812I −13.50976 + 2.97945I
u = 0.713912 − 0.305839I
a = 1.59012 + 0.92088I
b = 1.47043 + 0.10268I
−3.02413 − 2.82812I −13.50976 + 2.97945I
18
V. I
u
5
= hb − 1, 6a − u − 3, u
2
+ 3i
(i) Arc colorings
a
4
=
0
u
a
8
=
1
0
a
9
=
1
−3
a
12
=
1
6
u +
1
2
1
a
1
=
1
6
u −
1
2
1
a
3
=
u
−2u
a
10
=
−2
3
a
7
=
−
1
6
u +
1
2
−1
a
2
=
7
6
u −
1
2
−2u + 1
a
6
=
u
−2u
a
11
=
1
0
a
5
=
−u
u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
(u − 1)
2
c
3
, c
4
, c
5
c
8
, c
9
, c
10
u
2
+ 3
c
6
, c
11
, c
12
(u + 1)
2
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
7
, c
11
, c
12
(y − 1)
2
c
3
, c
4
, c
5
c
8
, c
9
, c
10
(y + 3)
2
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 1.73205I
a = 0.500000 + 0.288675I
b = 1.00000
9.86960 −12.0000
u = − 1.73205I
a = 0.500000 − 0.288675I
b = 1.00000
9.86960 −12.0000
22
VI. I
u
6
= hb + u, 2a − u + 1, u
2
+ 1i
(i) Arc colorings
a
4
=
0
u
a
8
=
1
0
a
9
=
1
−1
a
12
=
1
2
u −
1
2
−u
a
1
=
3
2
u −
1
2
−u
a
3
=
u
0
a
10
=
0
−1
a
7
=
−
1
2
u +
1
2
1
a
2
=
1
2
u −
1
2
−u
a
6
=
−u
2
a
11
=
−1
−2u
a
5
=
−u
u + 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u + 1)
2
c
2
, c
3
, c
4
c
5
, c
6
, c
7
c
8
, c
9
, c
10
c
11
, c
12
u
2
+ 1
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y − 1)
2
c
2
, c
3
, c
4
c
5
, c
6
, c
7
c
8
, c
9
, c
10
c
11
, c
12
(y + 1)
2
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = −0.500000 + 0.500000I
b = − 1.000000I
4.93480 −4.00000
u = − 1.000000I
a = −0.500000 − 0.500000I
b = 1.000000I
4.93480 −4.00000
26
VII. I
v
1
= ha, b − 1, v + 1i
(i) Arc colorings
a
4
=
−1
0
a
8
=
1
0
a
9
=
1
0
a
12
=
0
1
a
1
=
−1
1
a
3
=
−1
0
a
10
=
1
0
a
7
=
1
−1
a
2
=
−2
1
a
6
=
−1
0
a
11
=
1
0
a
5
=
−1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
27
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
u − 1
c
3
, c
4
, c
5
c
8
, c
9
, c
10
u
c
6
, c
11
, c
12
u + 1
28
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
7
, c
11
, c
12
y − 1
c
3
, c
4
, c
5
c
8
, c
9
, c
10
y
29
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −1.00000
a = 0
b = 1.00000
−3.28987 −12.0000
30
VIII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)
3
(u + 1)
2
(u
5
+ 7u
4
+ 17u
3
+ 14u
2
+ 1)
2
· (u
6
+ 5u
5
+ 8u
4
+ 6u
3
+ 8u
2
+ 8u + 1)
2
· (u
8
+ 5u
7
+ 4u
6
− 21u
5
− 39u
4
+ 31u
3
+ 86u
2
+ 57u + 4)
· (u
8
+ 7u
7
+ 19u
6
+ 11u
5
− 48u
4
− 98u
3
+ u
2
+ 170u + 169)
c
2
, c
7
(u − 1)
3
(u
2
+ 1)(u
5
+ u
4
− 3u
3
− 2u
2
+ 2u − 1)
2
· ((u
6
+ u
5
− 2u
4
+ 2u
2
− 2u − 1)
2
)(u
8
− 3u
7
+ ··· − 12u + 13)
· (u
8
− 3u
7
+ 2u
6
+ u
5
− 3u
4
+ 5u
3
+ 2u
2
− 7u − 2)
c
3
, c
4
, c
5
c
8
, c
9
, c
10
u(u
2
+ 1)(u
2
+ 3)(u
4
+ u
2
− u + 1)
2
(u
6
+ u
5
+ ··· + 2u + 1)
2
· (u
8
+ 4u
6
+ ··· + 6u + 2)(u
10
− 3u
9
+ ··· − 16u + 5)
c
6
, c
11
, c
12
(u + 1)
3
(u
2
+ 1)(u
5
+ u
4
− 3u
3
− 2u
2
+ 2u − 1)
2
· ((u
6
+ u
5
− 2u
4
+ 2u
2
− 2u − 1)
2
)(u
8
− 3u
7
+ ··· − 12u + 13)
· (u
8
− 3u
7
+ 2u
6
+ u
5
− 3u
4
+ 5u
3
+ 2u
2
− 7u − 2)
31
IX. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y − 1)
5
(y
5
− 15y
4
+ 93y
3
− 210y
2
− 28y − 1)
2
· (y
6
− 9y
5
+ 20y
4
+ 14y
3
− 16y
2
− 48y + 1)
2
· (y
8
− 17y
7
+ ··· − 2561y + 16)(y
8
− 11y
7
+ ··· − 28562y + 28561)
c
2
, c
6
, c
7
c
11
, c
12
(y − 1)
3
(y + 1)
2
(y
5
− 7y
4
+ 17y
3
− 14y
2
− 1)
2
· (y
6
− 5y
5
+ 8y
4
− 6y
3
+ 8y
2
− 8y + 1)
2
· (y
8
− 7y
7
+ 19y
6
− 11y
5
− 48y
4
+ 98y
3
+ y
2
− 170y + 169)
· (y
8
− 5y
7
+ 4y
6
+ 21y
5
− 39y
4
− 31y
3
+ 86y
2
− 57y + 4)
c
3
, c
4
, c
5
c
8
, c
9
, c
10
y(y + 1)
2
(y + 3)
2
(y
4
+ 2y
3
+ 3y
2
+ y + 1)
2
· (y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
2
· (y
8
+ 8y
7
+ 24y
6
+ 25y
5
− 38y
4
− 133y
3
− 115y
2
− 32y + 4)
· (y
10
+ 7y
9
+ ··· + 124y + 25)
32
