12n
0211
(K12n
0211
)
A knot diagram
1
Linearized knot diagam
3 5 7 2 9 11 3 10 5 12 6 8
Solving Sequence
6,9
5
3,10
2 1 4 8 7 12 11
c
5
c
9
c
2
c
1
c
4
c
8
c
7
c
12
c
11
c
3
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h13u
16
+ 9u
15
+ ··· + 32b + 15, 21u
16
− 15u
15
+ ··· + 32a − 41,
u
17
+ 3u
15
+ 2u
14
+ 9u
13
+ 4u
12
+ 15u
11
+ 9u
10
+ 23u
9
+ 6u
8
+ 23u
7
+ 5u
6
+ 19u
5
− 3u
4
+ 11u
3
+ 1i
I
u
2
= h−u
3
+ u
2
+ 2b + 1, −u
3
− u
2
+ 2a − 1, u
4
+ u
2
− u + 1i
I
u
3
= h−33675480u
21
+ 230853871u
20
+ ··· + 427516113b + 1988747145,
− 330664297u
21
+ 1163900912u
20
+ ··· + 1282548339a + 9330160065,
u
22
− 2u
21
+ ··· − 12u + 9i
I
u
4
= hu
5
+ u
4
+ u
3
+ 2u
2
+ b + u + 1, u
5
+ u
4
+ u
3
+ u
2
+ a + u, u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1i
I
u
5
= hau + 5b − 3a + u − 3, a
2
+ au + 5u − 4, u
2
+ 1i
* 5 irreducible components of dim
C
= 0, with total 53 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
= h13u
16
+ 9u
15
+ · · · + 32b + 15, 21u
16
− 15u
15
+ · · · + 32a − 41, u
17
+
3u
15
+ · · · + 11u
3
+ 1i
(i) Arc colorings
a
6
=
1
0
a
9
=
0
u
a
5
=
1
−u
2
a
3
=
−0.656250u
16
+ 0.468750u
15
+ ··· + 2.90625u + 1.28125
−0.406250u
16
− 0.281250u
15
+ ··· − 0.343750u − 0.468750
a
10
=
−u
u
3
+ u
a
2
=
−0.468750u
16
+ 0.406250u
15
+ ··· + 3.21875u + 0.343750
−0.0937500u
16
− 0.218750u
15
+ ··· − 0.156250u − 0.531250
a
1
=
1
2
u
16
+ u
14
+ ··· −
5
2
u
3
+
5
2
u
1
4
u
16
+
1
2
u
14
+ ··· −
9
4
u
3
−
3
4
u
a
4
=
−0.281250u
16
+ 0.0937500u
15
+ ··· + 2.53125u + 0.156250
−0.531250u
16
+ 0.0937500u
15
+ ··· + 0.281250u + 0.156250
a
8
=
−u
3
u
5
+ u
3
+ u
a
7
=
1
4
u
15
+
1
2
u
13
+ ··· −
5
4
u
2
+
5
4
u
2
a
12
=
1
4
u
16
+
1
2
u
14
+ ··· −
9
4
u
3
+
9
4
u
−u
a
11
=
1
4
u
16
+
1
2
u
14
+ ··· −
9
4
u
3
+
5
4
u
−u
(ii) Obstruction class = −1
(iii) Cusp Shapes =
25
64
u
16
+
61
64
u
15
+ ··· +
639
64
u −
133
64
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
17
+ 25u
16
+ ··· − 31u + 16
c
2
, c
4
u
17
− 5u
16
+ ··· − u + 4
c
3
, c
7
u
17
− 3u
16
+ ··· + 176u + 64
c
5
, c
6
, c
9
c
11
u
17
+ 3u
15
+ ··· + 11u
3
− 1
c
8
, c
10
u
17
− 6u
16
+ ··· − 6u
2
+ 1
c
12
u
17
+ 19u
15
+ ··· − 5u
2
+ 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
17
− 61y
16
+ ··· − 15103y −256
c
2
, c
4
y
17
− 25y
16
+ ··· − 31y −16
c
3
, c
7
y
17
+ 27y
16
+ ··· + 4352y −4096
c
5
, c
6
, c
9
c
11
y
17
+ 6y
16
+ ··· + 6y
2
− 1
c
8
, c
10
y
17
+ 18y
16
+ ··· + 12y −1
c
12
y
17
+ 38y
16
+ ··· + 40y −16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.609453 + 0.805159I
a = 0.854862 − 0.986654I
b = −0.766890 − 0.457544I
−0.52072 − 2.33309I −2.02167 + 3.26936I
u = 0.609453 − 0.805159I
a = 0.854862 + 0.986654I
b = −0.766890 + 0.457544I
−0.52072 + 2.33309I −2.02167 − 3.26936I
u = 0.230202 + 0.870288I
a = −2.22993 − 0.26645I
b = −0.119488 + 0.657240I
−6.16563 − 1.02177I −6.84477 + 7.08191I
u = 0.230202 − 0.870288I
a = −2.22993 + 0.26645I
b = −0.119488 − 0.657240I
−6.16563 + 1.02177I −6.84477 − 7.08191I
u = −0.773626 + 0.937847I
a = 0.606886 − 0.071826I
b = −1.190660 + 0.370945I
−4.38989 + 4.09446I −5.30008 − 4.36784I
u = −0.773626 − 0.937847I
a = 0.606886 + 0.071826I
b = −1.190660 − 0.370945I
−4.38989 − 4.09446I −5.30008 + 4.36784I
u = −1.050610 + 0.636095I
a = −0.407370 + 0.267779I
b = 1.93722 − 0.60149I
−17.5984 − 0.0758I −7.31042 − 1.57550I
u = −1.050610 − 0.636095I
a = −0.407370 − 0.267779I
b = 1.93722 + 0.60149I
−17.5984 + 0.0758I −7.31042 + 1.57550I
u = −0.576669 + 1.098490I
a = −0.263264 − 0.069567I
b = 0.341659 − 0.129445I
1.86747 + 7.21175I 3.72852 − 5.27936I
u = −0.576669 − 1.098490I
a = −0.263264 + 0.069567I
b = 0.341659 + 0.129445I
1.86747 − 7.21175I 3.72852 + 5.27936I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.743234 + 1.053510I
a = −0.04444 + 2.04366I
b = 2.07902 + 0.33370I
−3.55752 − 7.80542I −4.29962 + 6.17985I
u = 0.743234 − 1.053510I
a = −0.04444 − 2.04366I
b = 2.07902 − 0.33370I
−3.55752 + 7.80542I −4.29962 − 6.17985I
u = 0.71574 + 1.23305I
a = −0.99869 − 1.97392I
b = −2.63254 + 0.11082I
−13.5091 − 13.2681I −3.78464 + 6.49717I
u = 0.71574 − 1.23305I
a = −0.99869 + 1.97392I
b = −2.63254 − 0.11082I
−13.5091 + 13.2681I −3.78464 − 6.49717I
u = 0.302591 + 0.411010I
a = 0.856584 + 0.998116I
b = 0.086217 − 0.461654I
−0.250655 − 1.078620I −3.32954 + 6.69723I
u = 0.302591 − 0.411010I
a = 0.856584 − 0.998116I
b = 0.086217 + 0.461654I
−0.250655 + 1.078620I −3.32954 − 6.69723I
u = −0.400636
a = −1.24927
b = −0.969091
−2.22247 −4.42560
6
II. I
u
2
= h−u
3
+ u
2
+ 2b + 1, −u
3
− u
2
+ 2a − 1, u
4
+ u
2
− u + 1i
(i) Arc colorings
a
6
=
1
0
a
9
=
0
u
a
5
=
1
−u
2
a
3
=
1
2
u
3
+
1
2
u
2
+
1
2
1
2
u
3
−
1
2
u
2
−
1
2
a
10
=
−u
u
3
+ u
a
2
=
1
2
u
3
+
1
2
u
2
−
1
2
1
2
u
3
+
1
2
u
2
−
1
2
a
1
=
−1
u
2
a
4
=
1
2
u
3
+
1
2
u
2
+
1
2
1
2
u
3
−
1
2
u
2
−
1
2
a
8
=
−u
3
u
2
a
7
=
−u
3
u
2
a
12
=
u
3
− u
2
− 1
u
a
11
=
u
3
− u
2
+ u − 1
u
(ii) Obstruction class = 1
(iii) Cusp Shapes =
11
4
u
3
+
21
4
u
2
−
1
2
u −
17
4
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
4
c
3
, c
7
u
4
c
4
(u + 1)
4
c
5
, c
6
u
4
+ u
2
− u + 1
c
8
, c
10
u
4
+ 2u
3
+ 3u
2
+ u + 1
c
9
, c
11
u
4
+ u
2
+ u + 1
c
12
u
4
+ 3u
3
+ 4u
2
+ 3u + 2
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
4
c
3
, c
7
y
4
c
5
, c
6
, c
9
c
11
y
4
+ 2y
3
+ 3y
2
+ y + 1
c
8
, c
10
y
4
+ 2y
3
+ 7y
2
+ 5y + 1
c
12
y
4
− y
3
+ 2y
2
+ 7y + 4
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.547424 + 0.585652I
a = 0.278726 + 0.483420I
b = −0.677958 − 0.157780I
−2.62503 − 1.39709I −5.84901 + 3.96898I
u = 0.547424 − 0.585652I
a = 0.278726 − 0.483420I
b = −0.677958 + 0.157780I
−2.62503 + 1.39709I −5.84901 − 3.96898I
u = −0.547424 + 1.120870I
a = 0.971274 − 0.813859I
b = 0.927958 + 0.413327I
0.98010 + 7.64338I −3.77599 − 8.10462I
u = −0.547424 − 1.120870I
a = 0.971274 + 0.813859I
b = 0.927958 − 0.413327I
0.98010 − 7.64338I −3.77599 + 8.10462I
10
III.
I
u
3
= h−3.37 × 10
7
u
21
+ 2.31 × 10
8
u
20
+ · · · + 4.28 × 10
8
b + 1.99 × 10
9
, −3.31 ×
10
8
u
21
+1.16×10
9
u
20
+· · ·+1.28×10
9
a+9.33×10
9
, u
22
−2u
21
+· · ·−12u+9i
(i) Arc colorings
a
6
=
1
0
a
9
=
0
u
a
5
=
1
−u
2
a
3
=
0.257818u
21
− 0.907491u
20
+ ··· + 8.27519u − 7.27470
0.0787701u
21
− 0.539989u
20
+ ··· + 5.17053u − 4.65186
a
10
=
−u
u
3
+ u
a
2
=
0.0569753u
21
− 0.732717u
20
+ ··· + 6.42310u − 8.39988
0.147735u
21
− 0.732052u
20
+ ··· + 6.08589u − 6.69407
a
1
=
−0.113449u
21
− 0.132459u
20
+ ··· + 2.54918u − 1.84329
0.183373u
21
− 0.457606u
20
+ ··· + 4.47394u − 2.89558
a
4
=
−0.325326u
21
+ 0.184523u
20
+ ··· + 0.502711u − 2.87359
−0.383495u
21
+ 0.177086u
20
+ ··· − 0.310468u − 2.63640
a
8
=
−u
3
u
5
+ u
3
+ u
a
7
=
−0.264604u
21
+ 0.445061u
20
+ ··· − 3.11735u − 0.705220
−0.121794u
21
+ 0.190645u
20
+ ··· − 0.910828u − 1.28085
a
12
=
1
9
u
21
−
2
9
u
20
+ ··· +
32
9
u −
4
3
0.0312057u
21
− 0.184205u
20
+ ··· + 2.13810u − 1.28530
a
11
=
0.142317u
21
− 0.406427u
20
+ ··· + 5.69365u − 2.61863
0.0312057u
21
− 0.184205u
20
+ ··· + 2.13810u − 1.28530
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
51496451
142505371
u
21
+
36892662
142505371
u
20
+ ··· +
723246262
142505371
u −
1135221198
142505371
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
11
+ 18u
10
+ ··· + 31u + 1)
2
c
2
, c
4
(u
11
− 4u
10
− u
9
+ 17u
8
+ u
7
− 40u
6
+ 3u
5
+ 37u
4
− 3u
3
− 9u
2
+ 7u − 1)
2
c
3
, c
7
(u
11
+ u
10
+ ··· − 4u + 8)
2
c
5
, c
6
, c
9
c
11
u
22
+ 2u
21
+ ··· + 12u + 9
c
8
, c
10
u
22
− 10u
21
+ ··· − 432u + 81
c
12
(u
11
+ 12u
9
+ 36u
7
+ 2u
6
+ 2u
5
+ 13u
4
+ 13u
3
+ u
2
+ 1)
2
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
11
− 46y
10
+ ··· + 863y −1)
2
c
2
, c
4
(y
11
− 18y
10
+ ··· + 31y −1)
2
c
3
, c
7
(y
11
+ 21y
10
+ ··· + 336y −64)
2
c
5
, c
6
, c
9
c
11
y
22
+ 10y
21
+ ··· + 432y + 81
c
8
, c
10
y
22
+ 2y
21
+ ··· + 12312y + 6561
c
12
(y
11
+ 24y
10
+ ··· − 2y −1)
2
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.545296 + 0.923005I
a = 0.012822 + 0.329575I
b = 0.622069 − 0.196649I
−0.14517 − 2.25109I −0.29632 + 2.34373I
u = 0.545296 − 0.923005I
a = 0.012822 − 0.329575I
b = 0.622069 + 0.196649I
−0.14517 + 2.25109I −0.29632 − 2.34373I
u = 0.858271 + 0.670516I
a = 0.369906 − 0.478944I
b = −1.92512 + 0.39933I
−4.72798 + 1.82060I −6.54374 − 1.21714I
u = 0.858271 − 0.670516I
a = 0.369906 + 0.478944I
b = −1.92512 − 0.39933I
−4.72798 − 1.82060I −6.54374 + 1.21714I
u = −0.240009 + 1.082970I
a = 0.454525 + 0.334757I
b = 0.515438 + 0.609605I
4.11473 8.33208 + 0.I
u = −0.240009 − 1.082970I
a = 0.454525 − 0.334757I
b = 0.515438 − 0.609605I
4.11473 8.33208 + 0.I
u = 0.705045 + 0.879700I
a = 0.12429 − 1.54454I
b = −0.016245 − 0.493238I
−9.06867 − 2.70718I −3.52709 + 2.44627I
u = 0.705045 − 0.879700I
a = 0.12429 + 1.54454I
b = −0.016245 + 0.493238I
−9.06867 + 2.70718I −3.52709 − 2.44627I
u = −0.800202 + 0.827914I
a = −0.14364 − 1.64878I
b = 0.910452 + 0.422891I
−4.72798 + 1.82060I −6.54374 − 1.21714I
u = −0.800202 − 0.827914I
a = −0.14364 + 1.64878I
b = 0.910452 − 0.422891I
−4.72798 − 1.82060I −6.54374 + 1.21714I
14
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.047914 + 1.160270I
a = 2.24792 − 1.55926I
b = 1.93663 − 2.04614I
1.59514 + 0.83621I −6.12521 − 2.51411I
u = 0.047914 − 1.160270I
a = 2.24792 + 1.55926I
b = 1.93663 + 2.04614I
1.59514 − 0.83621I −6.12521 + 2.51411I
u = 1.089810 + 0.428144I
a = −0.395831 + 0.234267I
b = 2.55516 − 0.12719I
−16.0296 + 6.7782I −6.17368 − 2.81310I
u = 1.089810 − 0.428144I
a = −0.395831 − 0.234267I
b = 2.55516 + 0.12719I
−16.0296 − 6.7782I −6.17368 + 2.81310I
u = −0.703030 + 0.415587I
a = 0.495039 + 0.546851I
b = −0.195521 − 0.253083I
−0.14517 − 2.25109I −0.29632 + 2.34373I
u = −0.703030 − 0.415587I
a = 0.495039 − 0.546851I
b = −0.195521 + 0.253083I
−0.14517 + 2.25109I −0.29632 − 2.34373I
u = 0.190193 + 0.774835I
a = −2.15826 + 2.04536I
b = −1.52590 + 1.49076I
1.59514 − 0.83621I −6.12521 + 2.51411I
u = 0.190193 − 0.774835I
a = −2.15826 − 2.04536I
b = −1.52590 − 1.49076I
1.59514 + 0.83621I −6.12521 − 2.51411I
u = −0.804264 + 1.135210I
a = −0.80264 + 1.70705I
b = −1.69330 − 0.63124I
−16.0296 + 6.7782I −6.17368 − 2.81310I
u = −0.804264 − 1.135210I
a = −0.80264 − 1.70705I
b = −1.69330 + 0.63124I
−16.0296 − 6.7782I −6.17368 + 2.81310I
15
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.11097 + 1.44346I
a = −2.20412 + 0.05114I
b = −2.68367 + 0.72362I
−9.06867 + 2.70718I −3.52709 − 2.44627I
u = 0.11097 − 1.44346I
a = −2.20412 − 0.05114I
b = −2.68367 − 0.72362I
−9.06867 − 2.70718I −3.52709 + 2.44627I
16
IV. I
u
4
= hu
5
+ u
4
+ u
3
+ 2u
2
+ b + u + 1, u
5
+ u
4
+ u
3
+ u
2
+ a + u, u
6
+
u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1i
(i) Arc colorings
a
6
=
1
0
a
9
=
0
u
a
5
=
1
−u
2
a
3
=
−u
5
− u
4
− u
3
− u
2
− u
−u
5
− u
4
− u
3
− 2u
2
− u − 1
a
10
=
−u
u
3
+ u
a
2
=
−u
5
− u
4
− u
3
− u
2
− u − 1
−u
5
− u
4
− u
3
− u
2
− u − 1
a
1
=
−1
u
2
a
4
=
−u
5
− u
4
− u
3
− u
2
− u
−u
5
− u
4
− u
3
− 2u
2
− u − 1
a
8
=
−u
3
u
5
+ u
3
+ u
a
7
=
−u
3
u
5
+ u
3
+ u
a
12
=
−u
5
− u
4
− 2u
3
− 2u
2
− 2u − 2
u
5
+ 2u
3
+ u
2
+ u + 1
a
11
=
−u
4
− u
2
− u − 1
u
5
+ 2u
3
+ u
2
+ u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = u
5
+ 5u
3
+ u
2
+ 5u − 2
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
6
c
3
, c
7
u
6
c
4
(u + 1)
6
c
5
, c
6
u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1
c
8
, c
10
u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1
c
9
, c
11
u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1
c
12
(u
3
− u
2
+ 1)
2
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
6
c
3
, c
7
y
6
c
5
, c
6
, c
9
c
11
y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1
c
8
, c
10
y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1
c
12
(y
3
− y
2
+ 2y −1)
2
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.498832 + 1.001300I
a = 0.767394 + 0.943705I
b = 0.521167 − 0.055259I
−1.37919 − 2.82812I −5.84740 + 3.54173I
u = 0.498832 − 1.001300I
a = 0.767394 − 0.943705I
b = 0.521167 + 0.055259I
−1.37919 + 2.82812I −5.84740 − 3.54173I
u = −0.284920 + 1.115140I
a = 1.37744 − 1.47725I
b = 1.53980 − 0.84179I
2.75839 −6 − 1.305207 + 0.10I
u = −0.284920 − 1.115140I
a = 1.37744 + 1.47725I
b = 1.53980 + 0.84179I
2.75839 −6 − 1.305207 + 0.10I
u = −0.713912 + 0.305839I
a = 0.355167 − 0.198843I
b = −1.060970 + 0.237841I
−1.37919 − 2.82812I −5.84740 + 3.54173I
u = −0.713912 − 0.305839I
a = 0.355167 + 0.198843I
b = −1.060970 − 0.237841I
−1.37919 + 2.82812I −5.84740 − 3.54173I
20
V. I
u
5
= hau + 5b − 3a + u − 3, a
2
+ au + 5u − 4, u
2
+ 1i
(i) Arc colorings
a
6
=
1
0
a
9
=
0
u
a
5
=
1
1
a
3
=
a
−
1
5
au +
3
5
a −
1
5
u +
3
5
a
10
=
−u
0
a
2
=
−
1
5
au +
3
5
a −
1
5
u +
3
5
−
2
5
au +
1
5
a −
2
5
u +
6
5
a
1
=
−
2
5
au −
4
5
a −
7
5
u +
16
5
−
1
5
au −
2
5
a −
6
5
u +
8
5
a
4
=
−u + 2
1
5
au +
2
5
a −
4
5
u +
2
5
a
8
=
u
u
a
7
=
2
5
au −
1
5
a −
8
5
u −
6
5
−1
a
12
=
−
1
5
au −
2
5
a −
6
5
u +
8
5
−u
a
11
=
−
1
5
au −
2
5
a −
11
5
u +
8
5
−u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
2
− 3u + 1)
2
c
2
(u
2
+ u − 1)
2
c
3
, c
7
u
4
+ 3u
2
+ 1
c
4
(u
2
− u − 1)
2
c
5
, c
6
, c
9
c
11
(u
2
+ 1)
2
c
8
, c
10
(u + 1)
4
c
12
u
4
+ 7u
2
+ 1
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
2
− 7y + 1)
2
c
2
, c
4
(y
2
− 3y + 1)
2
c
3
, c
7
(y
2
+ 3y + 1)
2
c
5
, c
6
, c
9
c
11
(y + 1)
4
c
8
, c
10
(y −1)
4
c
12
(y
2
+ 7y + 1)
2
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = −2.23607 + 0.61803I
b = −0.618034 + 0.618034I
−5.59278 0
u = 1.000000I
a = 2.23607 − 1.61803I
b = 1.61803 − 1.61803I
2.30291 0
u = − 1.000000I
a = −2.23607 − 0.61803I
b = −0.618034 − 0.618034I
−5.59278 0
u = − 1.000000I
a = 2.23607 + 1.61803I
b = 1.61803 + 1.61803I
2.30291 0
24
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
10
)(u
2
− 3u + 1)
2
(u
11
+ 18u
10
+ ··· + 31u + 1)
2
· (u
17
+ 25u
16
+ ··· − 31u + 16)
c
2
(u − 1)
10
(u
2
+ u − 1)
2
· (u
11
− 4u
10
− u
9
+ 17u
8
+ u
7
− 40u
6
+ 3u
5
+ 37u
4
− 3u
3
− 9u
2
+ 7u − 1)
2
· (u
17
− 5u
16
+ ··· − u + 4)
c
3
, c
7
u
10
(u
4
+ 3u
2
+ 1)(u
11
+ u
10
+ ··· − 4u + 8)
2
· (u
17
− 3u
16
+ ··· + 176u + 64)
c
4
(u + 1)
10
(u
2
− u − 1)
2
· (u
11
− 4u
10
− u
9
+ 17u
8
+ u
7
− 40u
6
+ 3u
5
+ 37u
4
− 3u
3
− 9u
2
+ 7u − 1)
2
· (u
17
− 5u
16
+ ··· − u + 4)
c
5
, c
6
(u
2
+ 1)
2
(u
4
+ u
2
− u + 1)(u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)
· (u
17
+ 3u
15
+ ··· + 11u
3
− 1)(u
22
+ 2u
21
+ ··· + 12u + 9)
c
8
, c
10
(u + 1)
4
(u
4
+ 2u
3
+ 3u
2
+ u + 1)(u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1)
· (u
17
− 6u
16
+ ··· − 6u
2
+ 1)(u
22
− 10u
21
+ ··· − 432u + 81)
c
9
, c
11
(u
2
+ 1)
2
(u
4
+ u
2
+ u + 1)(u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
· (u
17
+ 3u
15
+ ··· + 11u
3
− 1)(u
22
+ 2u
21
+ ··· + 12u + 9)
c
12
(u
3
− u
2
+ 1)
2
(u
4
+ 7u
2
+ 1)(u
4
+ 3u
3
+ 4u
2
+ 3u + 2)
· (u
11
+ 12u
9
+ 36u
7
+ 2u
6
+ 2u
5
+ 13u
4
+ 13u
3
+ u
2
+ 1)
2
· (u
17
+ 19u
15
+ ··· − 5u
2
+ 4)
25
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
10
)(y
2
− 7y + 1)
2
(y
11
− 46y
10
+ ··· + 863y −1)
2
· (y
17
− 61y
16
+ ··· − 15103y −256)
c
2
, c
4
((y −1)
10
)(y
2
− 3y + 1)
2
(y
11
− 18y
10
+ ··· + 31y −1)
2
· (y
17
− 25y
16
+ ··· − 31y −16)
c
3
, c
7
y
10
(y
2
+ 3y + 1)
2
(y
11
+ 21y
10
+ ··· + 336y −64)
2
· (y
17
+ 27y
16
+ ··· + 4352y −4096)
c
5
, c
6
, c
9
c
11
(y + 1)
4
(y
4
+ 2y
3
+ 3y
2
+ y + 1)(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
· (y
17
+ 6y
16
+ ··· + 6y
2
− 1)(y
22
+ 10y
21
+ ··· + 432y + 81)
c
8
, c
10
(y −1)
4
(y
4
+ 2y
3
+ 7y
2
+ 5y + 1)(y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1)
· (y
17
+ 18y
16
+ ··· + 12y −1)(y
22
+ 2y
21
+ ··· + 12312y + 6561)
c
12
(y
2
+ 7y + 1)
2
(y
3
− y
2
+ 2y −1)
2
(y
4
− y
3
+ 2y
2
+ 7y + 4)
· ((y
11
+ 24y
10
+ ··· − 2y −1)
2
)(y
17
+ 38y
16
+ ··· + 40y −16)
26
