12n
0698
(K12n
0698
)
A knot diagram
1
Linearized knot diagam
4 5 9 11 10 3 11 12 6 2 8 9
Solving Sequence
9,12 1,4
2 3 8 11 5 7 6 10
c
12
c
1
c
3
c
8
c
11
c
4
c
7
c
6
c
10
c
2
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h4.82224 × 10
104
u
71
+ 2.70914 × 10
103
u
70
+ ··· + 1.50566 × 10
105
b + 5.07425 × 10
105
,
− 3.95098 × 10
106
u
71
− 5.31311 × 10
105
u
70
+ ··· + 1.95736 × 10
106
a − 4.15435 × 10
107
,
u
72
− u
71
+ ··· + 53u − 13i
I
u
2
= h55u
17
− 68u
16
+ ··· + b + 45,
u
16
− 9u
14
+ 32u
12
− 54u
10
+ u
9
+ 33u
8
− 5u
7
+ 23u
6
+ 8u
5
− 39u
4
− 4u
3
+ 10u
2
+ a + 1,
u
18
− 10u
16
+ 41u
14
− 86u
12
+ u
11
+ 87u
10
− 6u
9
− 10u
8
+ 13u
7
− 62u
6
− 12u
5
+ 49u
4
+ 4u
3
− 10u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 90 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
= h4.82 × 10
104
u
71
+ 2.71 × 10
103
u
70
+ · · · + 1.51 × 10
105
b + 5.07 ×
10
105
, −3.95 × 10
106
u
71
− 5.31 × 10
105
u
70
+ · · · + 1.96 × 10
106
a − 4.15 ×
10
107
, u
72
− u
71
+ · · · + 53u − 13i
(i) Arc colorings
a
9
=
0
u
a
12
=
1
0
a
1
=
1
−u
2
a
4
=
2.01852u
71
+ 0.271443u
70
+ ··· − 65.0023u + 21.2242
−0.320274u
71
− 0.0179930u
70
+ ··· + 10.2838u − 3.37011
a
2
=
1.34277u
71
+ 0.0225101u
70
+ ··· − 40.7482u + 15.2242
−1.75378u
71
− 0.432113u
70
+ ··· + 60.3842u − 19.0972
a
3
=
2.01852u
71
+ 0.271443u
70
+ ··· − 65.0023u + 21.2242
2.48267u
71
+ 0.427423u
70
+ ··· − 84.8436u + 26.3994
a
8
=
−u
u
a
11
=
−u
2
+ 1
u
2
a
5
=
0.787391u
71
+ 0.0299893u
70
+ ··· − 16.9800u + 6.61959
3.76108u
71
+ 0.707611u
70
+ ··· − 129.385u + 39.9767
a
7
=
u
3
− 2u
−u
3
+ u
a
6
=
−1.22082u
71
− 0.484053u
70
+ ··· + 44.6748u − 14.9450
0.413411u
71
+ 0.0302634u
70
+ ··· + 1.23588u + 0.424911
a
10
=
1.22688u
71
+ 0.0699200u
70
+ ··· − 40.1232u + 12.0753
−0.214089u
71
+ 0.417178u
70
+ ··· − 2.55754u − 0.600644
(ii) Obstruction class = −1
(iii) Cusp Shapes = −1.82373u
71
+ 0.228275u
70
+ ··· + 35.3694u − 11.5112
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
72
+ 6u
71
+ ··· − 38390u + 1825
c
2
u
72
+ 6u
71
+ ··· − 228u + 3
c
3
u
72
− u
71
+ ··· − 34023u − 7187
c
4
u
72
− 9u
70
+ ··· − 3368u + 431
c
5
, c
9
u
72
− 3u
71
+ ··· + 99u − 9
c
6
u
72
− 2u
71
+ ··· − 1062455u + 98953
c
7
, c
8
, c
11
c
12
u
72
− u
71
+ ··· + 53u − 13
c
10
u
72
− 6u
71
+ ··· − 1644u + 271
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
72
− 62y
71
+ ··· − 343686400y + 3330625
c
2
y
72
+ 14y
71
+ ··· − 66864y + 9
c
3
y
72
+ 61y
71
+ ··· + 1453616311y + 51652969
c
4
y
72
− 18y
71
+ ··· − 35272544y + 185761
c
5
, c
9
y
72
+ 53y
71
+ ··· − 5265y + 81
c
6
y
72
+ 44y
71
+ ··· − 139414609387y + 9791696209
c
7
, c
8
, c
11
c
12
y
72
− 59y
71
+ ··· + 2755y + 169
c
10
y
72
+ 14y
71
+ ··· + 1440312y + 73441
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.126859 + 0.988884I
a = 1.61742 − 0.09689I
b = 0.050276 − 0.299679I
−5.20735 + 5.44865I 0
u = 0.126859 − 0.988884I
a = 1.61742 + 0.09689I
b = 0.050276 + 0.299679I
−5.20735 − 5.44865I 0
u = −0.127845 + 1.002920I
a = 1.70641 + 0.18941I
b = −0.107709 + 0.230288I
−10.2342 − 11.1489I 0
u = −0.127845 − 1.002920I
a = 1.70641 − 0.18941I
b = −0.107709 − 0.230288I
−10.2342 + 11.1489I 0
u = −0.141541 + 0.954879I
a = 1.65626 − 0.08213I
b = 0.051271 + 0.607650I
−9.10926 + 1.32235I 0
u = −0.141541 − 0.954879I
a = 1.65626 + 0.08213I
b = 0.051271 − 0.607650I
−9.10926 − 1.32235I 0
u = −0.939877 + 0.013317I
a = −0.291635 − 1.080060I
b = 1.73084 + 0.47010I
−3.34758 + 0.14621I 5.65895 + 0.I
u = −0.939877 − 0.013317I
a = −0.291635 + 1.080060I
b = 1.73084 − 0.47010I
−3.34758 − 0.14621I 5.65895 + 0.I
u = 1.076150 + 0.148518I
a = −1.37015 + 0.85044I
b = 2.50989 − 0.59662I
2.74768 + 2.38827I 0
u = 1.076150 − 0.148518I
a = −1.37015 − 0.85044I
b = 2.50989 + 0.59662I
2.74768 − 2.38827I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.169948 + 1.080080I
a = −1.151840 − 0.173137I
b = 0.320494 − 0.089757I
−7.75026 + 1.40505I 0
u = 0.169948 − 1.080080I
a = −1.151840 + 0.173137I
b = 0.320494 + 0.089757I
−7.75026 − 1.40505I 0
u = −0.100523 + 0.879151I
a = −1.53673 + 0.45497I
b = 0.235088 − 0.021753I
−4.60409 + 0.28761I 6.69444 + 0.38443I
u = −0.100523 − 0.879151I
a = −1.53673 − 0.45497I
b = 0.235088 + 0.021753I
−4.60409 − 0.28761I 6.69444 − 0.38443I
u = −0.611340 + 0.627257I
a = −0.066441 + 0.364149I
b = −0.206420 + 0.446689I
−3.02185 − 3.31425I 3.79268 + 3.31898I
u = −0.611340 − 0.627257I
a = −0.066441 − 0.364149I
b = −0.206420 − 0.446689I
−3.02185 + 3.31425I 3.79268 − 3.31898I
u = 1.113140 + 0.172789I
a = −0.521124 − 0.520349I
b = 0.45809 − 1.47955I
0.00408 + 6.29362I 0
u = 1.113140 − 0.172789I
a = −0.521124 + 0.520349I
b = 0.45809 + 1.47955I
0.00408 − 6.29362I 0
u = 1.156820 + 0.028330I
a = 0.165309 + 1.262120I
b = 0.224082 − 0.645135I
3.70030 − 0.68226I 0
u = 1.156820 − 0.028330I
a = 0.165309 − 1.262120I
b = 0.224082 + 0.645135I
3.70030 + 0.68226I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.167160 + 0.206148I
a = −1.71705 − 0.04041I
b = 2.93225 − 0.19622I
0.36792 − 7.14775I 0
u = −1.167160 − 0.206148I
a = −1.71705 + 0.04041I
b = 2.93225 + 0.19622I
0.36792 + 7.14775I 0
u = 0.012163 + 0.813810I
a = −2.26681 − 0.64788I
b = 0.353647 + 0.193689I
−8.47599 − 2.01586I −1.74932 + 3.46594I
u = 0.012163 − 0.813810I
a = −2.26681 + 0.64788I
b = 0.353647 − 0.193689I
−8.47599 + 2.01586I −1.74932 − 3.46594I
u = −1.197050 + 0.139381I
a = −0.025309 + 0.409207I
b = −0.278101 + 0.921535I
4.25039 − 3.42640I 0
u = −1.197050 − 0.139381I
a = −0.025309 − 0.409207I
b = −0.278101 − 0.921535I
4.25039 + 3.42640I 0
u = −1.22306
a = 0.911163
b = −2.59828
5.53230 0
u = 1.257050 + 0.016904I
a = 0.864368 − 0.363359I
b = −2.47476 + 1.48717I
1.45015 − 3.58564I 0
u = 1.257050 − 0.016904I
a = 0.864368 + 0.363359I
b = −2.47476 − 1.48717I
1.45015 + 3.58564I 0
u = 1.126030 + 0.582449I
a = −0.511047 − 0.643523I
b = 1.44670 + 0.79597I
−4.85158 + 4.39466I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.126030 − 0.582449I
a = −0.511047 + 0.643523I
b = 1.44670 − 0.79597I
−4.85158 − 4.39466I 0
u = −1.209670 + 0.417858I
a = −0.856738 + 0.734668I
b = 1.90170 − 1.11652I
−1.19160 − 4.92957I 0
u = −1.209670 − 0.417858I
a = −0.856738 − 0.734668I
b = 1.90170 + 1.11652I
−1.19160 + 4.92957I 0
u = 1.272340 + 0.155410I
a = 0.812489 − 0.086231I
b = −1.47439 − 0.51290I
1.46025 + 2.68807I 0
u = 1.272340 − 0.155410I
a = 0.812489 + 0.086231I
b = −1.47439 + 0.51290I
1.46025 − 2.68807I 0
u = −1.185310 + 0.498510I
a = 0.82701 − 1.16892I
b = −0.71053 + 1.83597I
−5.90329 − 6.47727I 0
u = −1.185310 − 0.498510I
a = 0.82701 + 1.16892I
b = −0.71053 − 1.83597I
−5.90329 + 6.47727I 0
u = −1.306730 + 0.016350I
a = 0.763989 + 0.862315I
b = −0.989243 − 0.377234I
2.64593 − 3.47147I 0
u = −1.306730 − 0.016350I
a = 0.763989 − 0.862315I
b = −0.989243 + 0.377234I
2.64593 + 3.47147I 0
u = 1.185180 + 0.555323I
a = 0.648873 + 0.912240I
b = −0.71737 − 1.69599I
−1.96169 − 0.01375I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.185180 − 0.555323I
a = 0.648873 − 0.912240I
b = −0.71737 + 1.69599I
−1.96169 + 0.01375I 0
u = 1.267320 + 0.374432I
a = −1.10450 − 1.16691I
b = 2.31610 + 1.70281I
−4.57901 + 6.29919I 0
u = 1.267320 − 0.374432I
a = −1.10450 + 1.16691I
b = 2.31610 − 1.70281I
−4.57901 − 6.29919I 0
u = −1.294090 + 0.341511I
a = −0.290838 + 1.234360I
b = 1.16609 − 2.28504I
−4.40911 − 2.13637I 0
u = −1.294090 − 0.341511I
a = −0.290838 − 1.234360I
b = 1.16609 + 2.28504I
−4.40911 + 2.13637I 0
u = −1.204420 + 0.584547I
a = 0.437650 − 1.000750I
b = −0.55270 + 1.68415I
−6.94951 + 5.57839I 0
u = −1.204420 − 0.584547I
a = 0.437650 + 1.000750I
b = −0.55270 − 1.68415I
−6.94951 − 5.57839I 0
u = −0.365082 + 0.449645I
a = 0.724515 − 0.003907I
b = 0.590117 + 0.122833I
−3.33344 − 0.58612I 4.42329 + 3.18792I
u = −0.365082 − 0.449645I
a = 0.724515 + 0.003907I
b = 0.590117 − 0.122833I
−3.33344 + 0.58612I 4.42329 − 3.18792I
u = 1.36594 + 0.40578I
a = −0.422467 − 0.892800I
b = 1.05490 + 1.55127I
0.01877 + 4.33991I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.36594 − 0.40578I
a = −0.422467 + 0.892800I
b = 1.05490 − 1.55127I
0.01877 − 4.33991I 0
u = −1.38791 + 0.45935I
a = 0.810663 − 0.808801I
b = −1.89548 + 1.84655I
−0.45597 − 10.62370I 0
u = −1.38791 − 0.45935I
a = 0.810663 + 0.808801I
b = −1.89548 − 1.84655I
−0.45597 + 10.62370I 0
u = 1.39138 + 0.46126I
a = 0.849080 + 0.942667I
b = −2.01018 − 1.90844I
−5.4651 + 16.3720I 0
u = 1.39138 − 0.46126I
a = 0.849080 − 0.942667I
b = −2.01018 + 1.90844I
−5.4651 − 16.3720I 0
u = 1.41047 + 0.44601I
a = 0.610953 + 0.683746I
b = −1.76875 − 1.90527I
−4.21502 + 3.71603I 0
u = 1.41047 − 0.44601I
a = 0.610953 − 0.683746I
b = −1.76875 + 1.90527I
−4.21502 − 3.71603I 0
u = −1.39405 + 0.52910I
a = −0.526831 + 0.755276I
b = 1.12722 − 1.11980I
−2.92127 − 7.14791I 0
u = −1.39405 − 0.52910I
a = −0.526831 − 0.755276I
b = 1.12722 + 1.11980I
−2.92127 + 7.14791I 0
u = 0.365685 + 0.326725I
a = 1.41373 − 1.37865I
b = −0.564131 − 0.229982I
0.900933 − 0.329550I 6.04745 − 3.44320I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.365685 − 0.326725I
a = 1.41373 + 1.37865I
b = −0.564131 + 0.229982I
0.900933 + 0.329550I 6.04745 + 3.44320I
u = 0.483251
a = 0.865400
b = −0.374226
0.738726 12.8440
u = 0.271415 + 0.339694I
a = 1.14210 − 0.85589I
b = 0.475871 + 1.205610I
−2.32274 − 4.16974I 2.86926 + 0.82016I
u = 0.271415 − 0.339694I
a = 1.14210 + 0.85589I
b = 0.475871 − 1.205610I
−2.32274 + 4.16974I 2.86926 − 0.82016I
u = −1.58255 + 0.01145I
a = 0.252185 − 0.123258I
b = −1.217410 + 0.437776I
7.95850 + 0.06427I 0
u = −1.58255 − 0.01145I
a = 0.252185 + 0.123258I
b = −1.217410 − 0.437776I
7.95850 − 0.06427I 0
u = −0.110595 + 0.398425I
a = −0.50400 + 3.42521I
b = −0.525466 − 0.195616I
−2.69671 + 4.74873I 1.03045 − 3.19857I
u = −0.110595 − 0.398425I
a = −0.50400 − 3.42521I
b = −0.525466 + 0.195616I
−2.69671 − 4.74873I 1.03045 + 3.19857I
u = 1.58743 + 0.13147I
a = −0.036866 − 0.330156I
b = −0.272582 + 0.792813I
4.58019 + 6.01061I 0
u = 1.58743 − 0.13147I
a = −0.036866 + 0.330156I
b = −0.272582 − 0.792813I
4.58019 − 6.01061I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.040336 + 0.308718I
a = 1.162940 + 0.506483I
b = 0.306872 − 0.876204I
0.69881 + 1.66668I 4.53475 − 6.54101I
u = 0.040336 − 0.308718I
a = 1.162940 − 0.506483I
b = 0.306872 + 0.876204I
0.69881 − 1.66668I 4.53475 + 6.54101I
12
II. I
u
2
=
h55u
17
−68u
16
+· · ·+b+45, u
16
−9u
14
+· · ·+a+1, u
18
−10u
16
+· · ·−10u
2
+1i
(i) Arc colorings
a
9
=
0
u
a
12
=
1
0
a
1
=
1
−u
2
a
4
=
−u
16
+ 9u
14
+ ··· − 10u
2
− 1
−55u
17
+ 68u
16
+ ··· + 35u − 45
a
2
=
−59u
17
+ 70u
16
+ ··· + 44u − 48
119u
17
− 144u
16
+ ··· − 80u + 96
a
3
=
−u
16
+ 9u
14
+ ··· − 10u
2
− 1
−55u
17
+ 67u
16
+ ··· + 35u − 44
a
8
=
−u
u
a
11
=
−u
2
+ 1
u
2
a
5
=
13u
17
− 17u
16
+ ··· − 8u + 9
−96u
17
+ 116u
16
+ ··· + 63u − 77
a
7
=
u
3
− 2u
−u
3
+ u
a
6
=
−37u
17
+ 44u
16
+ ··· + 23u − 32
54u
17
− 67u
16
+ ··· − 32u + 44
a
10
=
−16u
17
+ 21u
16
+ ··· + 4u − 10
−19u
17
+ 22u
16
+ ··· + 15u − 16
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −230u
17
+ 282u
16
+ 1952u
15
− 2397u
14
− 6471u
13
+ 7965u
12
+ 9941u
11
− 12521u
10
−
4527u
9
+ 7084u
8
−6484u
7
+ 4905u
6
+ 8225u
5
−7445u
4
−2069u
3
+ 1737u
2
+ 144u − 174
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
18
− 11u
17
+ ··· − 39u + 5
c
2
u
18
+ 7u
17
+ ··· + 3u + 1
c
3
u
18
+ 2u
16
+ ··· − 6u
2
+ 1
c
4
u
18
− u
17
+ ··· − u + 1
c
5
u
18
− 2u
17
+ ··· − 8u + 5
c
6
u
18
+ 3u
17
+ ··· − 6u + 1
c
7
, c
8
u
18
− 10u
16
+ ··· − 10u
2
+ 1
c
9
u
18
+ 2u
17
+ ··· + 8u + 5
c
10
u
18
− u
17
+ ··· − u + 1
c
11
, c
12
u
18
− 10u
16
+ ··· − 10u
2
+ 1
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
18
− 3y
17
+ ··· + 169y + 25
c
2
y
18
+ y
17
+ ··· − 7y + 1
c
3
y
18
+ 4y
17
+ ··· − 12y + 1
c
4
y
18
+ y
17
+ ··· − 3y + 1
c
5
, c
9
y
18
+ 12y
17
+ ··· + 116y + 25
c
6
y
18
+ 11y
17
+ ··· − 10y + 1
c
7
, c
8
, c
11
c
12
y
18
− 20y
17
+ ··· − 20y + 1
c
10
y
18
− 3y
17
+ ··· + y + 1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.034780 + 0.909417I
a = −1.54704 − 0.01895I
b = 0.338766 − 0.248147I
−6.97448 + 1.13968I 4.89374 − 0.18325I
u = 0.034780 − 0.909417I
a = −1.54704 + 0.01895I
b = 0.338766 + 0.248147I
−6.97448 − 1.13968I 4.89374 + 0.18325I
u = 1.207980 + 0.098270I
a = 0.739289 − 0.918515I
b = −1.354920 + 0.330046I
4.03681 + 2.12143I 15.7293 − 1.9822I
u = 1.207980 − 0.098270I
a = 0.739289 + 0.918515I
b = −1.354920 − 0.330046I
4.03681 − 2.12143I 15.7293 + 1.9822I
u = −1.221290 + 0.000878I
a = 1.034340 + 0.008877I
b = −1.83950 − 1.59017I
1.08464 + 4.68616I 9.18075 − 6.62870I
u = −1.221290 − 0.000878I
a = 1.034340 − 0.008877I
b = −1.83950 + 1.59017I
1.08464 − 4.68616I 9.18075 + 6.62870I
u = −1.242500 + 0.470628I
a = −0.780988 + 0.794704I
b = 1.46588 − 0.99279I
−3.02478 − 6.13837I 6.43166 + 4.31912I
u = −1.242500 − 0.470628I
a = −0.780988 − 0.794704I
b = 1.46588 + 0.99279I
−3.02478 + 6.13837I 6.43166 − 4.31912I
u = 1.297070 + 0.392739I
a = −0.598955 − 0.773625I
b = 1.81748 + 1.61626I
−3.07920 + 3.40899I 8.53631 − 2.87922I
u = 1.297070 − 0.392739I
a = −0.598955 + 0.773625I
b = 1.81748 − 1.61626I
−3.07920 − 3.40899I 8.53631 + 2.87922I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.53345 + 0.10123I
a = −0.292336 − 0.163807I
b = 0.743032 − 0.190463I
5.16035 + 6.11216I 16.2770 − 5.8147I
u = 1.53345 − 0.10123I
a = −0.292336 + 0.163807I
b = 0.743032 + 0.190463I
5.16035 − 6.11216I 16.2770 + 5.8147I
u = −1.56582 + 0.04096I
a = −0.315755 + 0.060524I
b = 1.35534 − 0.49741I
8.11860 + 0.22024I 22.9414 − 14.5563I
u = −1.56582 − 0.04096I
a = −0.315755 − 0.060524I
b = 1.35534 + 0.49741I
8.11860 − 0.22024I 22.9414 + 14.5563I
u = −0.403896 + 0.125852I
a = −2.15630 + 0.13786I
b = 0.415201 + 0.902527I
−1.63695 − 4.97346I 9.65134 + 6.36185I
u = −0.403896 − 0.125852I
a = −2.15630 − 0.13786I
b = 0.415201 − 0.902527I
−1.63695 + 4.97346I 9.65134 − 6.36185I
u = 0.360211 + 0.184792I
a = −2.08226 − 0.15931I
b = 0.558708 + 0.874453I
1.24981 − 1.03640I 10.85847 + 2.38119I
u = 0.360211 − 0.184792I
a = −2.08226 + 0.15931I
b = 0.558708 − 0.874453I
1.24981 + 1.03640I 10.85847 − 2.38119I
17
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
18
− 11u
17
+ ··· − 39u + 5)(u
72
+ 6u
71
+ ··· − 38390u + 1825)
c
2
(u
18
+ 7u
17
+ ··· + 3u + 1)(u
72
+ 6u
71
+ ··· − 228u + 3)
c
3
(u
18
+ 2u
16
+ ··· − 6u
2
+ 1)(u
72
− u
71
+ ··· − 34023u − 7187)
c
4
(u
18
− u
17
+ ··· − u + 1)(u
72
− 9u
70
+ ··· − 3368u + 431)
c
5
(u
18
− 2u
17
+ ··· − 8u + 5)(u
72
− 3u
71
+ ··· + 99u − 9)
c
6
(u
18
+ 3u
17
+ ··· − 6u + 1)(u
72
− 2u
71
+ ··· − 1062455u + 98953)
c
7
, c
8
(u
18
− 10u
16
+ ··· − 10u
2
+ 1)(u
72
− u
71
+ ··· + 53u − 13)
c
9
(u
18
+ 2u
17
+ ··· + 8u + 5)(u
72
− 3u
71
+ ··· + 99u − 9)
c
10
(u
18
− u
17
+ ··· − u + 1)(u
72
− 6u
71
+ ··· − 1644u + 271)
c
11
, c
12
(u
18
− 10u
16
+ ··· − 10u
2
+ 1)(u
72
− u
71
+ ··· + 53u − 13)
18
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
18
− 3y
17
+ ··· + 169y + 25)
· (y
72
− 62y
71
+ ··· − 343686400y + 3330625)
c
2
(y
18
+ y
17
+ ··· − 7y + 1)(y
72
+ 14y
71
+ ··· − 66864y + 9)
c
3
(y
18
+ 4y
17
+ ··· − 12y + 1)
· (y
72
+ 61y
71
+ ··· + 1453616311y + 51652969)
c
4
(y
18
+ y
17
+ ··· − 3y + 1)(y
72
− 18y
71
+ ··· − 3.52725 × 10
7
y + 185761)
c
5
, c
9
(y
18
+ 12y
17
+ ··· + 116y + 25)(y
72
+ 53y
71
+ ··· − 5265y + 81)
c
6
(y
18
+ 11y
17
+ ··· − 10y + 1)
· (y
72
+ 44y
71
+ ··· − 139414609387y + 9791696209)
c
7
, c
8
, c
11
c
12
(y
18
− 20y
17
+ ··· − 20y + 1)(y
72
− 59y
71
+ ··· + 2755y + 169)
c
10
(y
18
− 3y
17
+ ··· + y + 1)(y
72
+ 14y
71
+ ··· + 1440312y + 73441)
19
