12n
0686
(K12n
0686
)
A knot diagram
1
Linearized knot diagam
4 5 7 8 9 10 12 2 6 3 8 7
Solving Sequence
7,12 4,8
5 1 2 9 3 11 10 6
c
7
c
4
c
12
c
1
c
8
c
3
c
11
c
10
c
6
c
2
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.69505 × 10
130
u
65
+ 2.15148 × 10
129
u
64
+ ··· + 2.43963 × 10
130
b − 1.45063 × 10
131
,
− 8.57548 × 10
130
u
65
+ 3.16614 × 10
129
u
64
+ ··· + 2.43963 × 10
130
a − 6.80613 × 10
131
,
u
66
+ 8u
64
+ ··· + 14u + 1i
I
u
2
= h−u
17
− u
16
+ ··· + b − 7u, 244u
17
+ 447u
16
+ ··· + 19a + 657, u
18
+ u
17
+ ··· + 8u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 84 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
= h−2.70 × 10
130
u
65
+ 2.15 × 10
129
u
64
+ · · · + 2.44 × 10
130
b − 1.45 ×
10
131
, −8.58 × 10
130
u
65
+ 3.17 × 10
129
u
64
+ · · · + 2.44 × 10
130
a − 6.81 ×
10
131
, u
66
+ 8u
64
+ · · · + 14u + 1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
4
=
3.51508u
65
− 0.129779u
64
+ ··· + 210.106u + 27.8982
1.10470u
65
− 0.0881890u
64
+ ··· + 55.7119u + 5.94611
a
8
=
1
u
2
a
5
=
4.56038u
65
− 0.0374882u
64
+ ··· + 267.516u + 33.7146
1.04992u
65
− 0.150384u
64
+ ··· + 53.3745u + 5.85382
a
1
=
−u
u
a
2
=
7.93049u
65
− 1.14259u
64
+ ··· + 401.649u + 50.8636
1.21958u
65
− 0.156828u
64
+ ··· + 62.7169u + 7.17179
a
9
=
11.2952u
65
− 2.21571u
64
+ ··· + 527.820u + 67.7880
0.727751u
65
− 0.0696228u
64
+ ··· + 51.3476u + 6.91232
a
3
=
4.61977u
65
− 0.217968u
64
+ ··· + 265.817u + 33.8443
1.10470u
65
− 0.0881890u
64
+ ··· + 55.7119u + 5.94611
a
11
=
u
u
3
+ u
a
10
=
8.15717u
65
− 1.17920u
64
+ ··· + 412.691u + 52.1630
1.24237u
65
− 0.0782801u
64
+ ··· + 63.4671u + 7.14796
a
6
=
−13.9731u
65
+ 2.50512u
64
+ ··· − 652.317u − 80.5461
−1.33472u
65
+ 0.329465u
64
+ ··· − 50.4358u − 6.86127
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.613469u
65
+ 0.240964u
64
+ ··· + 17.8117u − 7.54006
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
66
+ 6u
65
+ ··· + 5840u + 651
c
2
u
66
+ 8u
65
+ ··· + 244u − 37
c
3
u
66
− 34u
64
+ ··· − 1660u − 803
c
4
u
66
+ 8u
64
+ ··· + 2550u − 731
c
5
, c
6
, c
9
u
66
+ u
65
+ ··· + 14u − 3
c
7
, c
11
, c
12
u
66
+ 8u
64
+ ··· + 14u + 1
c
8
u
66
+ u
65
+ ··· − 979u − 167
c
10
u
66
+ 27u
64
+ ··· − 2100877u + 215861
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
66
− 70y
65
+ ··· − 19635172y + 423801
c
2
y
66
+ 18y
65
+ ··· − 28826y + 1369
c
3
y
66
− 68y
65
+ ··· + 49426552y + 644809
c
4
y
66
+ 16y
65
+ ··· + 19981630y + 534361
c
5
, c
6
, c
9
y
66
− 71y
65
+ ··· − 304y + 9
c
7
, c
11
, c
12
y
66
+ 16y
65
+ ··· − 28y + 1
c
8
y
66
− 17y
65
+ ··· − 794781y + 27889
c
10
y
66
+ 54y
65
+ ··· − 373655164727y + 46595971321
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.381480 + 0.902641I
a = −0.495217 − 0.818731I
b = 0.252778 + 0.945202I
−4.89349 − 2.13130I −7.50430 + 3.71654I
u = 0.381480 − 0.902641I
a = −0.495217 + 0.818731I
b = 0.252778 − 0.945202I
−4.89349 + 2.13130I −7.50430 − 3.71654I
u = −0.038908 + 0.939745I
a = −0.275001 − 0.321868I
b = −0.871697 + 0.971052I
−3.77402 − 3.72825I −5.26113 + 2.10644I
u = −0.038908 − 0.939745I
a = −0.275001 + 0.321868I
b = −0.871697 − 0.971052I
−3.77402 + 3.72825I −5.26113 − 2.10644I
u = 0.905831 + 0.018069I
a = −0.533383 + 0.894315I
b = 0.0381606 − 0.1308590I
−7.85798 + 1.54242I −13.03025 − 0.57872I
u = 0.905831 − 0.018069I
a = −0.533383 − 0.894315I
b = 0.0381606 + 0.1308590I
−7.85798 − 1.54242I −13.03025 + 0.57872I
u = −0.265939 + 0.798350I
a = 0.838512 − 0.776076I
b = 0.057693 + 0.475963I
1.00311 + 2.04923I −3.92564 − 3.61296I
u = −0.265939 − 0.798350I
a = 0.838512 + 0.776076I
b = 0.057693 − 0.475963I
1.00311 − 2.04923I −3.92564 + 3.61296I
u = −0.755298 + 0.895200I
a = −1.00097 + 1.25369I
b = 1.87437 + 0.23139I
−11.19350 + 0.70321I 0
u = −0.755298 − 0.895200I
a = −1.00097 − 1.25369I
b = 1.87437 − 0.23139I
−11.19350 − 0.70321I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.496215 + 0.652094I
a = 0.27441 + 1.70971I
b = 0.62615 − 1.80443I
−5.71011 + 7.01316I −9.56711 − 9.06601I
u = −0.496215 − 0.652094I
a = 0.27441 − 1.70971I
b = 0.62615 + 1.80443I
−5.71011 − 7.01316I −9.56711 + 9.06601I
u = 0.830499 + 0.849156I
a = 0.256829 + 1.321510I
b = −1.65652 − 0.66579I
−4.73481 − 4.19817I 0
u = 0.830499 − 0.849156I
a = 0.256829 − 1.321510I
b = −1.65652 + 0.66579I
−4.73481 + 4.19817I 0
u = −0.792820 + 0.887815I
a = −0.33108 + 1.50593I
b = 2.02793 − 0.81025I
−11.23670 + 5.15790I 0
u = −0.792820 − 0.887815I
a = −0.33108 − 1.50593I
b = 2.02793 + 0.81025I
−11.23670 − 5.15790I 0
u = −0.185557 + 1.202860I
a = 0.628073 − 1.140700I
b = −0.424674 + 0.578911I
2.05717 + 2.26630I 0
u = −0.185557 − 1.202860I
a = 0.628073 + 1.140700I
b = −0.424674 − 0.578911I
2.05717 − 2.26630I 0
u = −0.166375 + 0.760046I
a = −2.11546 − 1.78936I
b = 0.611150 + 1.095880I
−5.12370 − 4.24500I −6.05961 − 1.11595I
u = −0.166375 − 0.760046I
a = −2.11546 + 1.78936I
b = 0.611150 − 1.095880I
−5.12370 + 4.24500I −6.05961 + 1.11595I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.017260 + 0.775267I
a = 0.72199 − 1.86824I
b = −0.239640 + 0.901747I
1.81981 + 1.76274I −0.73012 − 3.27359I
u = 0.017260 − 0.775267I
a = 0.72199 + 1.86824I
b = −0.239640 − 0.901747I
1.81981 − 1.76274I −0.73012 + 3.27359I
u = 0.779311 + 0.979842I
a = 0.771946 + 0.959390I
b = −1.60829 + 0.02335I
−4.32456 − 1.86631I 0
u = 0.779311 − 0.979842I
a = 0.771946 − 0.959390I
b = −1.60829 − 0.02335I
−4.32456 + 1.86631I 0
u = −1.020010 + 0.782197I
a = −0.059578 + 1.004880I
b = 1.247920 − 0.361242I
−4.77746 + 2.77204I 0
u = −1.020010 − 0.782197I
a = −0.059578 − 1.004880I
b = 1.247920 + 0.361242I
−4.77746 − 2.77204I 0
u = 1.005160 + 0.805635I
a = −0.761996 − 0.469288I
b = 1.85270 + 0.11551I
−12.76450 − 5.71162I 0
u = 1.005160 − 0.805635I
a = −0.761996 + 0.469288I
b = 1.85270 − 0.11551I
−12.76450 + 5.71162I 0
u = 0.021107 + 0.705377I
a = 0.578182 + 0.067715I
b = 0.834319 + 0.472388I
1.57907 + 2.38485I −0.324197 − 0.690209I
u = 0.021107 − 0.705377I
a = 0.578182 − 0.067715I
b = 0.834319 − 0.472388I
1.57907 − 2.38485I −0.324197 + 0.690209I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.490966 + 0.475053I
a = −0.55254 + 1.62553I
b = −0.09615 − 1.50670I
0.16917 − 3.95160I −7.93720 + 9.53197I
u = 0.490966 − 0.475053I
a = −0.55254 − 1.62553I
b = −0.09615 + 1.50670I
0.16917 + 3.95160I −7.93720 − 9.53197I
u = 0.379973 + 0.551049I
a = −1.78771 − 0.92141I
b = −0.300972 − 0.209570I
0.75753 − 4.12116I −7.35035 + 12.02767I
u = 0.379973 − 0.551049I
a = −1.78771 + 0.92141I
b = −0.300972 + 0.209570I
0.75753 + 4.12116I −7.35035 − 12.02767I
u = −1.064810 + 0.801331I
a = 0.792009 − 0.579040I
b = −1.72587 + 0.09376I
−5.93827 + 1.09172I 0
u = −1.064810 − 0.801331I
a = 0.792009 + 0.579040I
b = −1.72587 − 0.09376I
−5.93827 − 1.09172I 0
u = −0.143019 + 1.344970I
a = −0.473522 − 0.509487I
b = 0.417362 + 0.247824I
3.24630 + 2.81207I 0
u = −0.143019 − 1.344970I
a = −0.473522 + 0.509487I
b = 0.417362 − 0.247824I
3.24630 − 2.81207I 0
u = 1.089300 + 0.810624I
a = −0.721178 − 0.626134I
b = 1.64027 − 0.04042I
−6.51348 + 4.48861I 0
u = 1.089300 − 0.810624I
a = −0.721178 + 0.626134I
b = 1.64027 + 0.04042I
−6.51348 − 4.48861I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.474413 + 0.430132I
a = 2.22892 − 1.47522I
b = 0.398954 − 0.549454I
−5.98479 + 5.90839I −10.77299 − 9.08116I
u = −0.474413 − 0.430132I
a = 2.22892 + 1.47522I
b = 0.398954 + 0.549454I
−5.98479 − 5.90839I −10.77299 + 9.08116I
u = −1.117140 + 0.824420I
a = 0.676641 − 0.619494I
b = −1.66630 − 0.17442I
−13.8794 − 8.3029I 0
u = −1.117140 − 0.824420I
a = 0.676641 + 0.619494I
b = −1.66630 + 0.17442I
−13.8794 + 8.3029I 0
u = 0.868320 + 1.114680I
a = −0.75239 − 1.40142I
b = 1.42271 + 0.41666I
−11.78330 − 1.19681I 0
u = 0.868320 − 1.114680I
a = −0.75239 + 1.40142I
b = 1.42271 − 0.41666I
−11.78330 + 1.19681I 0
u = 1.20197 + 0.75106I
a = −0.035347 + 0.853586I
b = −1.196160 − 0.140651I
−11.31340 − 2.25996I 0
u = 1.20197 − 0.75106I
a = −0.035347 − 0.853586I
b = −1.196160 + 0.140651I
−11.31340 + 2.25996I 0
u = −0.91284 + 1.08691I
a = −0.446199 + 0.740868I
b = 1.41565 − 0.16249I
−3.84346 + 4.28579I 0
u = −0.91284 − 1.08691I
a = −0.446199 − 0.740868I
b = 1.41565 + 0.16249I
−3.84346 − 4.28579I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.91205 + 1.11570I
a = −0.63727 − 1.31272I
b = 1.67828 + 0.62567I
−5.52111 − 11.73990I 0
u = 0.91205 − 1.11570I
a = −0.63727 + 1.31272I
b = 1.67828 − 0.62567I
−5.52111 + 11.73990I 0
u = −0.91053 + 1.11720I
a = 0.70943 − 1.31981I
b = −1.55420 + 0.57473I
−4.93579 + 6.09434I 0
u = −0.91053 − 1.11720I
a = 0.70943 + 1.31981I
b = −1.55420 − 0.57473I
−4.93579 − 6.09434I 0
u = −0.91964 + 1.12282I
a = 0.59423 − 1.33466I
b = −1.79214 + 0.62953I
−12.8813 + 15.6604I 0
u = −0.91964 − 1.12282I
a = 0.59423 + 1.33466I
b = −1.79214 − 0.62953I
−12.8813 − 15.6604I 0
u = −0.514106 + 0.183956I
a = 0.91070 + 1.13917I
b = −0.429112 − 0.679047I
−0.992824 + 0.084224I −11.71855 + 1.75099I
u = −0.514106 − 0.183956I
a = 0.91070 − 1.13917I
b = −0.429112 + 0.679047I
−0.992824 − 0.084224I −11.71855 − 1.75099I
u = 0.32591 + 1.42708I
a = 0.480076 − 0.162455I
b = −0.612916 − 0.001301I
−2.95398 − 6.38488I 0
u = 0.32591 − 1.42708I
a = 0.480076 + 0.162455I
b = −0.612916 + 0.001301I
−2.95398 + 6.38488I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.04603 + 1.17919I
a = 0.290516 + 0.627195I
b = −1.387930 − 0.223326I
−10.02500 − 5.74966I 0
u = 1.04603 − 1.17919I
a = 0.290516 − 0.627195I
b = −1.387930 + 0.223326I
−10.02500 + 5.74966I 0
u = −0.228442 + 0.312802I
a = 0.53438 + 1.55461I
b = −1.109960 − 0.068072I
−0.710026 + 0.001156I −6.94437 − 0.21585I
u = −0.228442 − 0.312802I
a = 0.53438 − 1.55461I
b = −1.109960 + 0.068072I
−0.710026 − 0.001156I −6.94437 + 0.21585I
u = −0.332795
a = 1.34321
b = −0.576763
−0.861436 −11.4550
u = −0.165446
a = 9.04077
b = 1.12903
−8.63556 −9.01670
11
II. I
u
2
= h−u
17
− u
16
+ · · · + b − 7u, 244u
17
+ 447u
16
+ · · · + 19a +
657, u
18
+ u
17
+ · · · + 8u
2
+ 1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
4
=
−12.8421u
17
− 23.5263u
16
+ ··· − 27.7895u − 34.5789
u
17
+ u
16
+ ··· + 27u
3
+ 7u
a
8
=
1
u
2
a
5
=
−17.4737u
17
− 31.4211u
16
+ ··· − 33.6316u − 45.2632
3.47368u
17
+ 4.42105u
16
+ ··· + 11.6316u + 3.26316
a
1
=
−u
u
a
2
=
−4.89474u
17
+ 8.31579u
16
+ ··· − 35.5263u + 38.9474
−6.21053u
17
− 13.6316u
16
+ ··· − 7.94737u − 23.8947
a
9
=
4.68421u
17
− 11.9474u
16
+ ··· + 27.5789u − 48.8421
8.10526u
17
+ 9.31579u
16
+ ··· + 22.4737u + 7.94737
a
3
=
−11.8421u
17
− 22.5263u
16
+ ··· − 20.7895u − 34.5789
u
17
+ u
16
+ ··· + 27u
3
+ 7u
a
11
=
u
u
3
+ u
a
10
=
−2.31579u
17
+ 9.05263u
16
+ ··· − 22.4211u + 33.1579
−4.05263u
17
− 9.15789u
16
+ ··· − 7.73684u − 16.4737
a
6
=
−8.36842u
17
+ 3.89474u
16
+ ··· − 37.1579u + 36.6842
−9.52632u
17
− 13.5789u
16
+ ··· − 21.3684u − 15.7368
(ii) Obstruction class = 1
(iii) Cusp Shapes
= 49u
17
+ 9u
16
+ 240u
15
+ 9u
14
+ 621u
13
− 98u
12
+ 1237u
11
− 361u
10
+ 1867u
9
−
760u
8
+ 1897u
7
− 1242u
6
+ 1412u
5
− 1233u
4
+ 809u
3
− 508u
2
+ 170u − 89
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
18
− 13u
17
+ ··· − 88u + 11
c
2
u
18
+ 5u
17
+ ··· + 2u + 1
c
3
u
18
+ u
17
+ ··· + 6u
2
+ 1
c
4
u
18
− u
17
+ ··· + u
2
+ 1
c
5
, c
6
u
18
− 10u
16
+ ··· − 2u + 1
c
7
u
18
+ u
17
+ ··· + 8u
2
+ 1
c
8
u
18
+ u
16
+ ··· + u + 1
c
9
u
18
− 10u
16
+ ··· + 2u + 1
c
10
u
18
+ 3u
17
+ ··· − 3u + 1
c
11
, c
12
u
18
− u
17
+ ··· + 8u
2
+ 1
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
18
− 7y
17
+ ··· + 968y + 121
c
2
y
18
+ y
17
+ ··· + 2y + 1
c
3
y
18
− 9y
17
+ ··· + 12y + 1
c
4
y
18
− 5y
17
+ ··· + 2y + 1
c
5
, c
6
, c
9
y
18
− 20y
17
+ ··· + 16y + 1
c
7
, c
11
, c
12
y
18
+ 11y
17
+ ··· + 16y + 1
c
8
y
18
+ 2y
17
+ ··· − 5y + 1
c
10
y
18
+ 13y
17
+ ··· − 7y + 1
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.804642 + 0.868057I
a = −0.36882 + 1.48135I
b = 1.378990 − 0.248447I
−9.83536 + 1.64758I −9.43619 − 2.86445I
u = −0.804642 − 0.868057I
a = −0.36882 − 1.48135I
b = 1.378990 + 0.248447I
−9.83536 − 1.64758I −9.43619 + 2.86445I
u = 0.044577 + 1.238730I
a = −0.408391 + 0.683987I
b = −0.073590 − 0.432493I
3.80104 − 3.17945I 1.80104 + 7.13521I
u = 0.044577 − 1.238730I
a = −0.408391 − 0.683987I
b = −0.073590 + 0.432493I
3.80104 + 3.17945I 1.80104 − 7.13521I
u = 0.264515 + 1.248310I
a = 0.649266 + 1.187430I
b = −0.426970 − 0.481643I
1.90679 − 1.92588I −11.44215 − 7.89971I
u = 0.264515 − 1.248310I
a = 0.649266 − 1.187430I
b = −0.426970 + 0.481643I
1.90679 + 1.92588I −11.44215 + 7.89971I
u = 0.925026 + 0.906908I
a = 0.360696 + 1.026960I
b = −1.47624 − 0.36649I
−4.24577 − 3.38226I −8.45773 + 3.28670I
u = 0.925026 − 0.906908I
a = 0.360696 − 1.026960I
b = −1.47624 + 0.36649I
−4.24577 + 3.38226I −8.45773 − 3.28670I
u = −0.238208 + 1.279130I
a = 0.256462 + 0.472498I
b = 0.378917 − 0.523548I
−2.11329 + 6.53754I −2.93657 − 5.70476I
u = −0.238208 − 1.279130I
a = 0.256462 − 0.472498I
b = 0.378917 + 0.523548I
−2.11329 − 6.53754I −2.93657 + 5.70476I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.943992 + 0.928790I
a = −0.161234 + 0.776586I
b = 1.48226 − 0.39919I
−9.59239 + 4.85624I −9.87202 − 2.24813I
u = −0.943992 − 0.928790I
a = −0.161234 − 0.776586I
b = 1.48226 + 0.39919I
−9.59239 − 4.85624I −9.87202 + 2.24813I
u = 0.382414 + 0.542277I
a = 0.290004 − 0.853492I
b = −1.25094 + 0.68932I
−0.681831 − 0.856086I −6.33441 + 8.31733I
u = 0.382414 − 0.542277I
a = 0.290004 + 0.853492I
b = −1.25094 − 0.68932I
−0.681831 + 0.856086I −6.33441 − 8.31733I
u = −0.071184 + 0.625824I
a = 1.41490 − 1.09388I
b = 0.250613 + 0.951659I
1.25984 + 3.18601I −2.50556 − 8.38071I
u = −0.071184 − 0.625824I
a = 1.41490 + 1.09388I
b = 0.250613 − 0.951659I
1.25984 − 3.18601I −2.50556 + 8.38071I
u = −0.058505 + 0.569575I
a = −3.03288 − 1.16293I
b = 0.236963 + 1.167790I
−5.17305 − 5.14099I −6.31641 + 6.34700I
u = −0.058505 − 0.569575I
a = −3.03288 + 1.16293I
b = 0.236963 − 1.167790I
−5.17305 + 5.14099I −6.31641 − 6.34700I
16
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
18
− 13u
17
+ ··· − 88u + 11)(u
66
+ 6u
65
+ ··· + 5840u + 651)
c
2
(u
18
+ 5u
17
+ ··· + 2u + 1)(u
66
+ 8u
65
+ ··· + 244u − 37)
c
3
(u
18
+ u
17
+ ··· + 6u
2
+ 1)(u
66
− 34u
64
+ ··· − 1660u − 803)
c
4
(u
18
− u
17
+ ··· + u
2
+ 1)(u
66
+ 8u
64
+ ··· + 2550u − 731)
c
5
, c
6
(u
18
− 10u
16
+ ··· − 2u + 1)(u
66
+ u
65
+ ··· + 14u − 3)
c
7
(u
18
+ u
17
+ ··· + 8u
2
+ 1)(u
66
+ 8u
64
+ ··· + 14u + 1)
c
8
(u
18
+ u
16
+ ··· + u + 1)(u
66
+ u
65
+ ··· − 979u − 167)
c
9
(u
18
− 10u
16
+ ··· + 2u + 1)(u
66
+ u
65
+ ··· + 14u − 3)
c
10
(u
18
+ 3u
17
+ ··· − 3u + 1)(u
66
+ 27u
64
+ ··· − 2100877u + 215861)
c
11
, c
12
(u
18
− u
17
+ ··· + 8u
2
+ 1)(u
66
+ 8u
64
+ ··· + 14u + 1)
17
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
18
− 7y
17
+ ··· + 968y + 121)
· (y
66
− 70y
65
+ ··· − 19635172y + 423801)
c
2
(y
18
+ y
17
+ ··· + 2y + 1)(y
66
+ 18y
65
+ ··· − 28826y + 1369)
c
3
(y
18
− 9y
17
+ ··· + 12y + 1)
· (y
66
− 68y
65
+ ··· + 49426552y + 644809)
c
4
(y
18
− 5y
17
+ ··· + 2y + 1)(y
66
+ 16y
65
+ ··· + 1.99816 × 10
7
y + 534361)
c
5
, c
6
, c
9
(y
18
− 20y
17
+ ··· + 16y + 1)(y
66
− 71y
65
+ ··· − 304y + 9)
c
7
, c
11
, c
12
(y
18
+ 11y
17
+ ··· + 16y + 1)(y
66
+ 16y
65
+ ··· − 28y + 1)
c
8
(y
18
+ 2y
17
+ ··· − 5y + 1)(y
66
− 17y
65
+ ··· − 794781y + 27889)
c
10
(y
18
+ 13y
17
+ ··· − 7y + 1)
· (y
66
+ 54y
65
+ ··· − 373655164727y + 46595971321)
18
