11a
163
(K11a
163
)
A knot diagram
1
Linearized knot diagam
6 1 11 8 2 10 4 5 3 7 9
Solving Sequence
2,5
6 1
3,9
10 8 4 7 11
c
5
c
1
c
2
c
9
c
8
c
4
c
7
c
11
c
3
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h3.66420 × 10
64
u
71
− 1.34364 × 10
65
u
70
+ ··· + 5.98806 × 10
65
b + 5.69300 × 10
65
,
− 1.86215 × 10
65
u
71
+ 7.77862 × 10
65
u
70
+ ··· + 5.98806 × 10
65
a − 1.33999 × 10
65
, u
72
+ 17u
70
+ ··· + u + 1i
I
u
2
= h2u
12
+ u
11
+ 6u
10
+ 3u
9
+ 11u
8
+ 7u
7
+ 7u
6
+ 10u
5
+ 8u
3
− 3u
2
+ b + 2u,
u
12
+ u
11
+ 3u
10
+ 2u
9
+ 4u
8
+ 2u
7
− 4u
4
− 2u
3
− 3u
2
+ a,
u
13
+ u
12
+ 4u
11
+ 3u
10
+ 8u
9
+ 6u
8
+ 8u
7
+ 7u
6
+ 3u
5
+ 6u
4
− u
3
+ 3u
2
− u + 1i
* 2 irreducible components of dim
C
= 0, with total 85 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
= h3.66×10
64
u
71
−1.34×10
65
u
70
+· · ·+5.99×10
65
b+5.69×10
65
, −1.86×
10
65
u
71
+7.78×10
65
u
70
+· · ·+5.99×10
65
a−1.34×10
65
, u
72
+17u
70
+· · ·+u+1i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
−u
2
a
1
=
−u
u
3
+ u
a
3
=
−u
3
u
5
+ u
3
+ u
a
9
=
0.310978u
71
− 1.29902u
70
+ ··· − 3.70836u + 0.223776
−0.0611917u
71
+ 0.224387u
70
+ ··· + 1.02932u − 0.950725
a
10
=
0.0969772u
71
− 1.15579u
70
+ ··· − 3.31741u + 0.426345
−0.254667u
71
− 0.194746u
70
+ ··· + 0.186158u − 1.47703
a
8
=
0.249786u
71
− 1.07463u
70
+ ··· − 2.67904u − 0.726949
−0.0611917u
71
+ 0.224387u
70
+ ··· + 1.02932u − 0.950725
a
4
=
−2.35209u
71
− 2.74506u
70
+ ··· − 5.81147u + 0.452584
−0.873645u
71
− 0.690474u
70
+ ··· + 0.140283u − 2.05357
a
7
=
0.518603u
71
+ 1.42755u
70
+ ··· + 7.61883u + 0.135936
0.614017u
71
− 0.318119u
70
+ ··· − 1.29823u + 1.23094
a
11
=
−1.75192u
71
− 0.223371u
70
+ ··· − 10.3144u + 0.548362
−1.06712u
71
+ 0.982309u
70
+ ··· + 4.11161u + 1.60445
a
11
=
−1.75192u
71
− 0.223371u
70
+ ··· − 10.3144u + 0.548362
−1.06712u
71
+ 0.982309u
70
+ ··· + 4.11161u + 1.60445
(ii) Obstruction class = −1
(iii) Cusp Shapes = 1.46166u
71
− 1.65225u
70
+ ··· − 4.80947u − 8.48974
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
72
+ 17u
70
+ ··· + u + 1
c
2
u
72
+ 34u
71
+ ··· + 11u + 1
c
3
u
72
+ 6u
71
+ ··· + 50529u + 18761
c
4
, c
7
, c
8
u
72
+ 2u
71
+ ··· + 17u − 1
c
6
, c
10
u
72
− u
71
+ ··· + 704u + 121
c
9
u
72
− 2u
71
+ ··· − 25u − 1
c
11
u
72
+ 12u
71
+ ··· − 916u − 88
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
72
+ 34y
71
+ ··· + 11y + 1
c
2
y
72
+ 14y
71
+ ··· + 87y + 1
c
3
y
72
+ 28y
71
+ ··· + 9764167099y + 351975121
c
4
, c
7
, c
8
y
72
− 76y
71
+ ··· − 13y + 1
c
6
, c
10
y
72
− 59y
71
+ ··· − 471900y + 14641
c
9
y
72
+ 4y
71
+ ··· − 33y + 1
c
11
y
72
+ 8y
71
+ ··· + 92336y + 7744
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.840708 + 0.557697I
a = −0.880577 − 0.427963I
b = 1.343390 − 0.024122I
−2.78766 − 0.58394I −2.05211 + 2.44149I
u = −0.840708 − 0.557697I
a = −0.880577 + 0.427963I
b = 1.343390 + 0.024122I
−2.78766 + 0.58394I −2.05211 − 2.44149I
u = 0.950154 + 0.340310I
a = 0.730739 + 0.652349I
b = −1.54739 − 0.27859I
−7.89489 − 10.18180I −4.39970 + 5.17085I
u = 0.950154 − 0.340310I
a = 0.730739 − 0.652349I
b = −1.54739 + 0.27859I
−7.89489 + 10.18180I −4.39970 − 5.17085I
u = −0.341711 + 0.959879I
a = −0.96938 + 2.00953I
b = −0.220351 + 0.064200I
−4.43635 − 1.24068I −13.95090 + 0.I
u = −0.341711 − 0.959879I
a = −0.96938 − 2.00953I
b = −0.220351 − 0.064200I
−4.43635 + 1.24068I −13.95090 + 0.I
u = 0.314455 + 0.987227I
a = −1.18996 − 1.25711I
b = −0.240890 + 1.025020I
−4.69737 + 1.04071I −11.41192 + 0.I
u = 0.314455 − 0.987227I
a = −1.18996 + 1.25711I
b = −0.240890 − 1.025020I
−4.69737 − 1.04071I −11.41192 + 0.I
u = 0.775035 + 0.705599I
a = 0.106869 + 0.795488I
b = 0.140516 − 0.628949I
0.45501 + 2.74412I 0. − 6.58454I
u = 0.775035 − 0.705599I
a = 0.106869 − 0.795488I
b = 0.140516 + 0.628949I
0.45501 − 2.74412I 0. + 6.58454I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.05938
a = 0.181417
b = −1.41763
−3.29623 −2.05430
u = 0.474907 + 0.952227I
a = −0.633361 − 0.443998I
b = 0.748919 + 0.467243I
−0.15843 + 2.64508I 0
u = 0.474907 − 0.952227I
a = −0.633361 + 0.443998I
b = 0.748919 − 0.467243I
−0.15843 − 2.64508I 0
u = 0.541899 + 0.922731I
a = 0.420914 + 0.880805I
b = 0.174435 − 0.624288I
0.03676 + 2.24980I 0
u = 0.541899 − 0.922731I
a = 0.420914 − 0.880805I
b = 0.174435 + 0.624288I
0.03676 − 2.24980I 0
u = −0.834732 + 0.404612I
a = −0.539302 + 1.118290I
b = 0.549489 − 0.813801I
−1.04725 + 6.18742I −1.76655 − 5.50914I
u = −0.834732 − 0.404612I
a = −0.539302 − 1.118290I
b = 0.549489 + 0.813801I
−1.04725 − 6.18742I −1.76655 + 5.50914I
u = 0.794162 + 0.453233I
a = −1.084850 − 0.732074I
b = 1.44309 + 0.14451I
−3.22516 − 3.95142I −2.96229 + 3.51289I
u = 0.794162 − 0.453233I
a = −1.084850 + 0.732074I
b = 1.44309 − 0.14451I
−3.22516 + 3.95142I −2.96229 − 3.51289I
u = −0.005532 + 1.088180I
a = −1.073720 + 0.449198I
b = −1.53636 − 0.04905I
−8.67044 − 2.20266I −8.24814 + 0.I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.005532 − 1.088180I
a = −1.073720 − 0.449198I
b = −1.53636 + 0.04905I
−8.67044 + 2.20266I −8.24814 + 0.I
u = 0.426028 + 1.029620I
a = 2.09550 + 0.82862I
b = 1.56968 − 0.04690I
−10.60600 + 5.33661I 0
u = 0.426028 − 1.029620I
a = 2.09550 − 0.82862I
b = 1.56968 + 0.04690I
−10.60600 − 5.33661I 0
u = −0.880421
a = −0.281963
b = 1.12632
−1.79480 −8.89990
u = −0.421636 + 1.054610I
a = 0.447812 − 0.783280I
b = 1.69289 − 0.25084I
−11.08040 − 0.40194I 0
u = −0.421636 − 1.054610I
a = 0.447812 + 0.783280I
b = 1.69289 + 0.25084I
−11.08040 + 0.40194I 0
u = 0.470200 + 1.042550I
a = 0.79513 + 2.99296I
b = 1.47270 − 0.0001I
−10.28460 + 1.13066I 0
u = 0.470200 − 1.042550I
a = 0.79513 − 2.99296I
b = 1.47270 + 0.0001I
−10.28460 − 1.13066I 0
u = −0.533946 + 1.013710I
a = −0.879687 + 0.301042I
b = −0.662168 − 0.098832I
−3.06053 − 4.69031I 0
u = −0.533946 − 1.013710I
a = −0.879687 − 0.301042I
b = −0.662168 + 0.098832I
−3.06053 + 4.69031I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.208920 + 0.825464I
a = 0.353262 + 0.439079I
b = 0.594004 − 0.357212I
−1.46471 + 0.85730I −6.08976 − 4.46736I
u = −0.208920 − 0.825464I
a = 0.353262 − 0.439079I
b = 0.594004 + 0.357212I
−1.46471 − 0.85730I −6.08976 + 4.46736I
u = 0.442925 + 0.726814I
a = −0.30006 − 2.18686I
b = −0.947495 + 0.274305I
0.609165 + 1.192600I −2.86974 − 6.15662I
u = 0.442925 − 0.726814I
a = −0.30006 + 2.18686I
b = −0.947495 − 0.274305I
0.609165 − 1.192600I −2.86974 + 6.15662I
u = −0.462289 + 1.065050I
a = 0.35283 − 2.29105I
b = 1.57534 + 0.38822I
−10.78700 − 6.40801I 0
u = −0.462289 − 1.065050I
a = 0.35283 + 2.29105I
b = 1.57534 − 0.38822I
−10.78700 + 6.40801I 0
u = −0.651335 + 0.521113I
a = 0.60688 − 1.32770I
b = −0.286712 + 0.512099I
2.41607 + 1.66211I 3.86075 − 3.01699I
u = −0.651335 − 0.521113I
a = 0.60688 + 1.32770I
b = −0.286712 − 0.512099I
2.41607 − 1.66211I 3.86075 + 3.01699I
u = −0.575499 + 1.031320I
a = 0.47397 − 1.46431I
b = 0.371678 + 0.605414I
0.91167 − 6.46667I 0
u = −0.575499 − 1.031320I
a = 0.47397 + 1.46431I
b = 0.371678 − 0.605414I
0.91167 + 6.46667I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.550811 + 1.056740I
a = 0.747495 + 0.338296I
b = −0.639979 − 1.016950I
−2.99967 + 5.33296I 0
u = 0.550811 − 1.056740I
a = 0.747495 − 0.338296I
b = −0.639979 + 1.016950I
−2.99967 − 5.33296I 0
u = −0.086155 + 1.193610I
a = −0.013978 + 0.141660I
b = −0.653821 + 0.551694I
−6.57891 + 3.67515I 0
u = −0.086155 − 1.193610I
a = −0.013978 − 0.141660I
b = −0.653821 − 0.551694I
−6.57891 − 3.67515I 0
u = 0.614768 + 0.453497I
a = 0.21295 + 1.65927I
b = 0.649805 − 0.820980I
−1.24059 − 0.70092I −3.96458 + 1.25636I
u = 0.614768 − 0.453497I
a = 0.21295 − 1.65927I
b = 0.649805 + 0.820980I
−1.24059 + 0.70092I −3.96458 − 1.25636I
u = 0.613054 + 1.092110I
a = −0.09290 − 2.30276I
b = −1.47613 + 0.18050I
−5.13451 + 9.23572I 0
u = 0.613054 − 1.092110I
a = −0.09290 + 2.30276I
b = −1.47613 − 0.18050I
−5.13451 − 9.23572I 0
u = −0.614621 + 1.121980I
a = −0.68974 + 1.30969I
b = −0.638676 − 0.884132I
−3.19452 − 11.57250I 0
u = −0.614621 − 1.121980I
a = −0.68974 − 1.30969I
b = −0.638676 + 0.884132I
−3.19452 + 11.57250I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.681999 + 0.181568I
a = 0.673913 − 0.420450I
b = −0.081091 + 0.148188I
1.48009 + 0.06732I 8.50693 + 1.19475I
u = 0.681999 − 0.181568I
a = 0.673913 + 0.420450I
b = −0.081091 − 0.148188I
1.48009 − 0.06732I 8.50693 − 1.19475I
u = −0.838953 + 0.988789I
a = 0.222398 + 0.901799I
b = −1.346560 − 0.145983I
−4.06336 − 5.47241I 0
u = −0.838953 − 0.988789I
a = 0.222398 − 0.901799I
b = −1.346560 + 0.145983I
−4.06336 + 5.47241I 0
u = 0.079295 + 0.696769I
a = −1.44779 + 1.05434I
b = −1.58629 − 0.11135I
−8.96742 − 2.37559I −5.52309 + 3.97031I
u = 0.079295 − 0.696769I
a = −1.44779 − 1.05434I
b = −1.58629 + 0.11135I
−8.96742 + 2.37559I −5.52309 − 3.97031I
u = −0.609332 + 1.155210I
a = −0.38230 + 1.37330I
b = −1.360490 − 0.234606I
−4.80243 − 5.41014I 0
u = −0.609332 − 1.155210I
a = −0.38230 − 1.37330I
b = −1.360490 + 0.234606I
−4.80243 + 5.41014I 0
u = 0.600309 + 1.184400I
a = −0.265300 − 0.552477I
b = −0.248151 + 0.167852I
−1.42281 + 5.04884I 0
u = 0.600309 − 1.184400I
a = −0.265300 + 0.552477I
b = −0.248151 − 0.167852I
−1.42281 − 5.04884I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.630641 + 1.185250I
a = 0.45048 + 1.91943I
b = 1.58800 − 0.29668I
−10.4703 + 15.9193I 0
u = 0.630641 − 1.185250I
a = 0.45048 − 1.91943I
b = 1.58800 + 0.29668I
−10.4703 − 15.9193I 0
u = 0.157141 + 1.357400I
a = 0.921605 + 0.073306I
b = 1.55044 + 0.19302I
−13.8147 − 6.4968I 0
u = 0.157141 − 1.357400I
a = 0.921605 − 0.073306I
b = 1.55044 − 0.19302I
−13.8147 + 6.4968I 0
u = −0.482865 + 0.381048I
a = 0.522791 + 0.286679I
b = 0.647093 − 0.330038I
−1.50033 + 0.49934I −4.97310 − 1.55605I
u = −0.482865 − 0.381048I
a = 0.522791 − 0.286679I
b = 0.647093 + 0.330038I
−1.50033 − 0.49934I −4.97310 + 1.55605I
u = −0.59705 + 1.31039I
a = 0.650728 − 1.145870I
b = 1.46461 + 0.05246I
−7.22620 − 5.83293I 0
u = −0.59705 − 1.31039I
a = 0.650728 + 1.145870I
b = 1.46461 − 0.05246I
−7.22620 + 5.83293I 0
u = 0.293343 + 0.413513I
a = 2.10950 + 1.82789I
b = −1.44649 + 0.12482I
−8.45650 + 2.58799I −6.38429 − 2.67811I
u = 0.293343 − 0.413513I
a = 2.10950 − 1.82789I
b = −1.44649 − 0.12482I
−8.45650 − 2.58799I −6.38429 + 2.67811I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.335948 + 0.212346I
a = 3.09741 − 1.06498I
b = −1.51139 + 0.23154I
−8.60610 + 2.68144I −5.49009 − 1.95050I
u = −0.335948 − 0.212346I
a = 3.09741 + 1.06498I
b = −1.51139 − 0.23154I
−8.60610 − 2.68144I −5.49009 + 1.95050I
12
II.
I
u
2
= h2u
12
+u
11
+· · · +b+2u, u
12
+u
11
+· · · −3u
2
+a, u
13
+u
12
+· · · −u+1i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
−u
2
a
1
=
−u
u
3
+ u
a
3
=
−u
3
u
5
+ u
3
+ u
a
9
=
−u
12
− u
11
− 3u
10
− 2u
9
− 4u
8
− 2u
7
+ 4u
4
+ 2u
3
+ 3u
2
−2u
12
− u
11
− 6u
10
− 3u
9
− 11u
8
− 7u
7
− 7u
6
− 10u
5
− 8u
3
+ 3u
2
− 2u
a
10
=
−u
12
− u
11
− 3u
10
− 3u
9
− 5u
8
− 5u
7
− 2u
6
− 4u
5
+ u
4
+ u
3
+ u
2
+ u − 1
−2u
12
− u
11
− 6u
10
− 3u
9
− 11u
8
− 7u
7
− 7u
6
− 10u
5
− 7u
3
+ 3u
2
− u
a
8
=
−3u
12
− 2u
11
+ ··· + 6u
2
− 2u
−2u
12
− u
11
− 6u
10
− 3u
9
− 11u
8
− 7u
7
− 7u
6
− 10u
5
− 8u
3
+ 3u
2
− 2u
a
4
=
u
12
+ u
11
+ 2u
10
+ 2u
9
+ 2u
8
+ 3u
7
− 2u
6
+ u
5
− 2u
4
− 3u
3
+ u
2
− 2u + 1
−u
12
− u
11
− 3u
10
− 2u
9
− 5u
8
− 4u
7
− 3u
6
− 3u
5
− 3u
3
+ u
2
− 1
a
7
=
2u
12
+ 4u
10
− u
9
+ 6u
8
− u
6
+ 4u
5
− 4u
4
+ 6u
3
− 3u
2
+ 2u
3u
12
+ 2u
11
+ ··· + 2u + 1
a
11
=
3u
12
+ 2u
11
+ ··· − 3u
2
+ 4u
u
12
+ u
11
+ 3u
10
+ 3u
9
+ 5u
8
+ 6u
7
+ 3u
6
+ 6u
5
+ u
4
+ 3u
3
+ 2u
2
− u + 2
a
11
=
3u
12
+ 2u
11
+ ··· − 3u
2
+ 4u
u
12
+ u
11
+ 3u
10
+ 3u
9
+ 5u
8
+ 6u
7
+ 3u
6
+ 6u
5
+ u
4
+ 3u
3
+ 2u
2
− u + 2
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −6u
12
−6u
11
−20u
10
−13u
9
−33u
8
−24u
7
−21u
6
−22u
5
+ 6u
4
−20u
3
+ 10u
2
−5u −3
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
13
− u
12
+ ··· − u − 1
c
2
u
13
+ 7u
12
+ ··· − 5u − 1
c
3
u
13
+ u
12
− u
11
− 5u
10
− 2u
9
+ u
8
+ u
7
− u
6
+ 3u
5
+ 3u
4
+ u
3
− u
2
− u − 1
c
4
u
13
+ u
12
+ ··· − u − 1
c
5
u
13
+ u
12
+ ··· − u + 1
c
6
u
13
+ 2u
12
+ ··· − 7u
2
+ 1
c
7
, c
8
u
13
− u
12
+ ··· − u + 1
c
9
u
13
− u
12
+ u
11
+ u
10
− 3u
9
+ 3u
8
+ u
7
+ u
6
− u
5
− 2u
4
+ 5u
3
− u
2
− u + 1
c
10
u
13
− 2u
12
+ ··· + 7u
2
− 1
c
11
u
13
+ u
12
+ ··· + 3u − 1
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
13
+ 7y
12
+ ··· − 5y −1
c
2
y
13
+ 3y
12
+ ··· − 13y −1
c
3
y
13
− 3y
12
+ ··· − y −1
c
4
, c
7
, c
8
y
13
− 15y
12
+ ··· + 3y −1
c
6
, c
10
y
13
− 14y
12
+ ··· + 14y −1
c
9
y
13
+ y
12
+ ··· + 3y −1
c
11
y
13
+ y
12
+ ··· + 3y −1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.349870 + 0.909420I
a = −1.41921 − 1.69350I
b = −0.074648 + 0.625560I
−3.76256 + 1.44897I −0.77634 − 5.07895I
u = 0.349870 − 0.909420I
a = −1.41921 + 1.69350I
b = −0.074648 − 0.625560I
−3.76256 − 1.44897I −0.77634 + 5.07895I
u = −1.08055
a = −0.243893
b = 1.22413
−1.28306 7.99490
u = −0.345453 + 1.027120I
a = 1.76185 − 1.53952I
b = 1.57855 + 0.11169I
−10.26050 − 4.15031I −8.69293 + 2.72489I
u = −0.345453 − 1.027120I
a = 1.76185 + 1.53952I
b = 1.57855 − 0.11169I
−10.26050 + 4.15031I −8.69293 − 2.72489I
u = −0.272707 + 0.834669I
a = 0.072435 − 0.706115I
b = −1.55282 + 0.17586I
−9.45221 + 1.59908I −10.36413 + 2.46917I
u = −0.272707 − 0.834669I
a = 0.072435 + 0.706115I
b = −1.55282 − 0.17586I
−9.45221 − 1.59908I −10.36413 − 2.46917I
u = 0.564862 + 1.080820I
a = 0.247391 + 0.117235I
b = −0.462098 − 0.376436I
−1.43963 + 4.27361I −3.28652 − 1.94242I
u = 0.564862 − 1.080820I
a = 0.247391 − 0.117235I
b = −0.462098 + 0.376436I
−1.43963 − 4.27361I −3.28652 + 1.94242I
u = 0.443976 + 0.410014I
a = −0.83249 + 1.56580I
b = 0.717243 − 0.152288I
0.639447 + 0.198383I −2.33125 + 0.81736I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.443976 − 0.410014I
a = −0.83249 − 1.56580I
b = 0.717243 + 0.152288I
0.639447 − 0.198383I −2.33125 − 0.81736I
u = −0.700273 + 1.221280I
a = −0.208029 + 1.117420I
b = −1.318300 − 0.155459I
−4.69184 − 6.21694I −5.54626 + 10.85275I
u = −0.700273 − 1.221280I
a = −0.208029 − 1.117420I
b = −1.318300 + 0.155459I
−4.69184 + 6.21694I −5.54626 − 10.85275I
17
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
13
− u
12
+ ··· − u − 1)(u
72
+ 17u
70
+ ··· + u + 1)
c
2
(u
13
+ 7u
12
+ ··· − 5u − 1)(u
72
+ 34u
71
+ ··· + 11u + 1)
c
3
(u
13
+ u
12
− u
11
− 5u
10
− 2u
9
+ u
8
+ u
7
− u
6
+ 3u
5
+ 3u
4
+ u
3
− u
2
− u − 1)
· (u
72
+ 6u
71
+ ··· + 50529u + 18761)
c
4
(u
13
+ u
12
+ ··· − u − 1)(u
72
+ 2u
71
+ ··· + 17u − 1)
c
5
(u
13
+ u
12
+ ··· − u + 1)(u
72
+ 17u
70
+ ··· + u + 1)
c
6
(u
13
+ 2u
12
+ ··· − 7u
2
+ 1)(u
72
− u
71
+ ··· + 704u + 121)
c
7
, c
8
(u
13
− u
12
+ ··· − u + 1)(u
72
+ 2u
71
+ ··· + 17u − 1)
c
9
(u
13
− u
12
+ u
11
+ u
10
− 3u
9
+ 3u
8
+ u
7
+ u
6
− u
5
− 2u
4
+ 5u
3
− u
2
− u + 1)
· (u
72
− 2u
71
+ ··· − 25u − 1)
c
10
(u
13
− 2u
12
+ ··· + 7u
2
− 1)(u
72
− u
71
+ ··· + 704u + 121)
c
11
(u
13
+ u
12
+ ··· + 3u − 1)(u
72
+ 12u
71
+ ··· − 916u − 88)
18
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
13
+ 7y
12
+ ··· − 5y −1)(y
72
+ 34y
71
+ ··· + 11y + 1)
c
2
(y
13
+ 3y
12
+ ··· − 13y −1)(y
72
+ 14y
71
+ ··· + 87y + 1)
c
3
(y
13
− 3y
12
+ ··· − y −1)
· (y
72
+ 28y
71
+ ··· + 9764167099y + 351975121)
c
4
, c
7
, c
8
(y
13
− 15y
12
+ ··· + 3y −1)(y
72
− 76y
71
+ ··· − 13y + 1)
c
6
, c
10
(y
13
− 14y
12
+ ··· + 14y −1)(y
72
− 59y
71
+ ··· − 471900y + 14641)
c
9
(y
13
+ y
12
+ ··· + 3y −1)(y
72
+ 4y
71
+ ··· − 33y + 1)
c
11
(y
13
+ y
12
+ ··· + 3y −1)(y
72
+ 8y
71
+ ··· + 92336y + 7744)
19
