12a
0027
(K12a
0027
)
A knot diagram
1
Linearized knot diagam
3 5 6 9 2 11 12 10 4 1 8 7
Solving Sequence
7,12
8
1,3
2 11 6 4 5 10 9
c
7
c
12
c
1
c
11
c
6
c
3
c
5
c
10
c
9
c
2
, c
4
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h7u
98
− 14u
97
+ ··· + 2b − 3, −2u
98
+ 6u
97
+ ··· + 2a + 13, u
99
− 3u
98
+ ··· − 5u + 1i
I
u
2
= hu
2
a + b + a, −u
2
a + a
2
− au − a − u, u
3
+ u
2
+ 2u + 1i
* 2 irreducible components of dim
C
= 0, with total 105 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
=
h7u
98
−14u
97
+· · ·+2b−3, −2u
98
+6u
97
+· · ·+2a+13, u
99
−3u
98
+· · ·−5u+1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
8
=
1
−u
2
a
1
=
u
u
a
3
=
u
98
− 3u
97
+ ··· +
39
2
u −
13
2
−
7
2
u
98
+ 7u
97
+ ··· −
5
2
u +
3
2
a
2
=
1
2
u
96
− u
95
+ ··· +
7
2
u +
1
2
−
1
2
u
98
+ u
97
+ ··· −
3
2
u +
1
2
a
11
=
−u
u
3
+ u
a
6
=
−u
4
− u
2
+ 1
u
6
+ 2u
4
+ u
2
a
4
=
3
2
u
98
−
11
2
u
97
+ ··· +
59
2
u − 10
−5u
98
+
17
2
u
97
+ ··· −
1
2
u
2
+
5
2
u
a
5
=
−
3
2
u
98
+
5
2
u
97
+ ··· −
21
2
u + 5
2u
98
−
11
2
u
97
+ ··· +
17
2
u − 3
a
10
=
−u
5
− 2u
3
− u
−u
5
− u
3
+ u
a
9
=
u
12
+ 5u
10
+ 9u
8
+ 6u
6
− u
2
+ 1
u
12
+ 4u
10
+ 4u
8
− 2u
6
− 3u
4
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6u
98
+
31
2
u
97
+ ··· − 36u +
27
2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
99
+ 46u
98
+ ··· + 16u − 1
c
2
, c
5
u
99
+ 4u
98
+ ··· + 8u
2
− 1
c
3
u
99
− 4u
98
+ ··· + 2572u − 137
c
4
, c
9
u
99
+ u
98
+ ··· − 96u − 64
c
6
u
99
− 3u
98
+ ··· − 3u − 1
c
7
, c
11
, c
12
u
99
+ 3u
98
+ ··· − 5u − 1
c
8
u
99
+ 35u
98
+ ··· − 84992u − 4096
c
10
u
99
+ 23u
98
+ ··· − 57155u − 3971
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
99
+ 18y
98
+ ··· + 668y −1
c
2
, c
5
y
99
+ 46y
98
+ ··· + 16y −1
c
3
y
99
− 10y
98
+ ··· + 1215192y −18769
c
4
, c
9
y
99
+ 35y
98
+ ··· − 84992y −4096
c
6
y
99
− 3y
98
+ ··· + 11y −1
c
7
, c
11
, c
12
y
99
+ 89y
98
+ ··· + 11y −1
c
8
y
99
+ 47y
98
+ ··· + 571473920y −16777216
c
10
y
99
+ 17y
98
+ ··· − 195279369y −15768841
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.097244 + 0.981797I
a = 2.04862 − 0.31996I
b = 0.87684 − 1.15533I
0.35746 + 3.48895I 0
u = 0.097244 − 0.981797I
a = 2.04862 + 0.31996I
b = 0.87684 + 1.15533I
0.35746 − 3.48895I 0
u = −0.241159 + 1.003900I
a = 0.743897 + 0.599270I
b = 0.235254 + 1.068130I
1.45005 − 3.85058I 0
u = −0.241159 − 1.003900I
a = 0.743897 − 0.599270I
b = 0.235254 − 1.068130I
1.45005 + 3.85058I 0
u = −0.279788 + 1.028500I
a = −1.69573 − 0.23995I
b = −0.75934 − 1.30793I
−0.48248 − 8.85489I 0
u = −0.279788 − 1.028500I
a = −1.69573 + 0.23995I
b = −0.75934 + 1.30793I
−0.48248 + 8.85489I 0
u = −0.083304 + 0.867925I
a = −1.26249 + 0.65568I
b = −0.425485 + 0.825817I
1.85193 − 1.48646I 0
u = −0.083304 − 0.867925I
a = −1.26249 − 0.65568I
b = −0.425485 − 0.825817I
1.85193 + 1.48646I 0
u = −0.186497 + 1.138810I
a = 0.208803 + 0.976336I
b = −0.166068 + 0.234327I
−3.13347 − 2.11250I 0
u = −0.186497 − 1.138810I
a = 0.208803 − 0.976336I
b = −0.166068 − 0.234327I
−3.13347 + 2.11250I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.377785 + 0.732769I
a = −2.20424 − 0.02865I
b = −0.310300 − 0.261459I
−1.09710 − 9.01214I 3.30278 + 5.60818I
u = 0.377785 − 0.732769I
a = −2.20424 + 0.02865I
b = −0.310300 + 0.261459I
−1.09710 + 9.01214I 3.30278 − 5.60818I
u = 0.333700 + 0.724275I
a = 1.227330 + 0.309160I
b = 0.325047 + 0.485644I
1.02452 − 3.91155I 6.36380 + 1.73760I
u = 0.333700 − 0.724275I
a = 1.227330 − 0.309160I
b = 0.325047 − 0.485644I
1.02452 + 3.91155I 6.36380 − 1.73760I
u = 0.740677 + 0.279197I
a = −1.016830 − 0.007956I
b = −0.55702 − 1.98662I
0.49179 + 13.06500I 6.00000 − 10.29674I
u = 0.740677 − 0.279197I
a = −1.016830 + 0.007956I
b = −0.55702 + 1.98662I
0.49179 − 13.06500I 6.00000 + 10.29674I
u = 0.729685 + 0.269752I
a = 0.863425 + 0.159552I
b = 0.559986 + 1.127160I
2.65224 + 7.83389I 9.00346 − 6.47919I
u = 0.729685 − 0.269752I
a = 0.863425 − 0.159552I
b = 0.559986 − 1.127160I
2.65224 − 7.83389I 9.00346 + 6.47919I
u = 0.096314 + 0.766780I
a = −1.116870 + 0.545298I
b = −0.199635 + 0.904057I
1.83916 − 1.48668I 7.61074 + 2.57845I
u = 0.096314 − 0.766780I
a = −1.116870 − 0.545298I
b = −0.199635 − 0.904057I
1.83916 + 1.48668I 7.61074 − 2.57845I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.703876 + 0.291295I
a = −0.918311 − 0.507560I
b = 0.791968 − 0.717683I
−2.39425 + 5.38386I 2.41583 − 5.64244I
u = 0.703876 − 0.291295I
a = −0.918311 + 0.507560I
b = 0.791968 + 0.717683I
−2.39425 − 5.38386I 2.41583 + 5.64244I
u = −0.743542 + 0.146436I
a = 0.729914 − 0.278562I
b = −0.624512 + 1.086470I
2.20310 + 5.02116I 7.72280 − 4.85982I
u = −0.743542 − 0.146436I
a = 0.729914 + 0.278562I
b = −0.624512 − 1.086470I
2.20310 − 5.02116I 7.72280 + 4.85982I
u = −0.722428 + 0.166392I
a = −0.646892 + 0.246384I
b = −0.119774 − 0.503182I
3.98275 + 0.16547I 11.36045 + 0.28037I
u = −0.722428 − 0.166392I
a = −0.646892 − 0.246384I
b = −0.119774 + 0.503182I
3.98275 − 0.16547I 11.36045 − 0.28037I
u = −0.695963 + 0.253051I
a = 1.289800 − 0.066583I
b = 0.80561 − 2.01774I
1.95789 − 6.88040I 7.65412 + 7.00034I
u = −0.695963 − 0.253051I
a = 1.289800 + 0.066583I
b = 0.80561 + 2.01774I
1.95789 + 6.88040I 7.65412 − 7.00034I
u = −0.154249 + 1.251540I
a = 0.421251 + 1.095310I
b = 0.256625 + 0.781174I
−3.11910 − 1.98420I 0
u = −0.154249 − 1.251540I
a = 0.421251 − 1.095310I
b = 0.256625 − 0.781174I
−3.11910 + 1.98420I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.698720 + 0.234478I
a = 0.726419 + 0.362753I
b = 0.102288 − 0.667634I
3.72540 + 4.97999I 10.16129 − 7.32767I
u = 0.698720 − 0.234478I
a = 0.726419 − 0.362753I
b = 0.102288 + 0.667634I
3.72540 − 4.97999I 10.16129 + 7.32767I
u = −0.696507 + 0.225107I
a = −0.938874 + 0.165702I
b = −0.801377 + 1.084320I
3.84572 − 1.97170I 11.21068 + 2.11045I
u = −0.696507 − 0.225107I
a = −0.938874 − 0.165702I
b = −0.801377 − 1.084320I
3.84572 + 1.97170I 11.21068 − 2.11045I
u = 0.370896 + 0.620543I
a = −0.472196 + 1.229890I
b = −0.127332 − 0.459413I
−3.70912 − 1.56688I −0.638807 + 0.132287I
u = 0.370896 − 0.620543I
a = −0.472196 − 1.229890I
b = −0.127332 + 0.459413I
−3.70912 + 1.56688I −0.638807 − 0.132287I
u = 0.603417 + 0.395727I
a = −1.117180 + 0.736528I
b = −0.617446 − 1.243390I
−5.63536 + 5.78895I −0.23280 − 7.62647I
u = 0.603417 − 0.395727I
a = −1.117180 − 0.736528I
b = −0.617446 + 1.243390I
−5.63536 − 5.78895I −0.23280 + 7.62647I
u = 0.677801 + 0.214055I
a = −0.819154 − 0.329300I
b = 0.517625 + 1.103900I
2.51097 − 0.21528I 8.42557 − 2.66746I
u = 0.677801 − 0.214055I
a = −0.819154 + 0.329300I
b = 0.517625 − 1.103900I
2.51097 + 0.21528I 8.42557 + 2.66746I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.537902 + 0.452830I
a = −1.70799 − 0.61180I
b = 0.326702 − 0.635629I
−5.88927 − 2.00342I −1.337204 + 0.288944I
u = 0.537902 − 0.452830I
a = −1.70799 + 0.61180I
b = 0.326702 + 0.635629I
−5.88927 + 2.00342I −1.337204 − 0.288944I
u = −0.697168 + 0.060925I
a = 0.366847 + 0.115672I
b = −0.707313 − 0.805982I
0.120657 − 1.223660I 3.45904 + 0.32029I
u = −0.697168 − 0.060925I
a = 0.366847 − 0.115672I
b = −0.707313 + 0.805982I
0.120657 + 1.223660I 3.45904 − 0.32029I
u = −0.272806 + 1.279290I
a = −1.39980 − 0.25877I
b = −0.993381 − 0.971337I
−4.02944 − 4.74706I 0
u = −0.272806 − 1.279290I
a = −1.39980 + 0.25877I
b = −0.993381 + 0.971337I
−4.02944 + 4.74706I 0
u = 0.543711 + 0.378118I
a = 0.873451 + 0.129748I
b = 0.379726 + 0.601257I
−2.59306 + 1.73305I 3.09759 − 4.20577I
u = 0.543711 − 0.378118I
a = 0.873451 − 0.129748I
b = 0.379726 − 0.601257I
−2.59306 − 1.73305I 3.09759 + 4.20577I
u = −0.186173 + 0.633028I
a = 2.46650 − 0.07811I
b = 0.431819 − 0.672278I
0.31359 + 3.36493I 4.72638 − 1.84364I
u = −0.186173 − 0.633028I
a = 2.46650 + 0.07811I
b = 0.431819 + 0.672278I
0.31359 − 3.36493I 4.72638 + 1.84364I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.600800 + 0.238251I
a = 0.736053 − 1.089880I
b = −0.814916 − 0.941966I
−0.362748 − 0.270534I 4.74956 + 1.95395I
u = −0.600800 − 0.238251I
a = 0.736053 + 1.089880I
b = −0.814916 + 0.941966I
−0.362748 + 0.270534I 4.74956 − 1.95395I
u = −0.137414 + 1.347150I
a = −0.01027 + 1.77849I
b = 0.19722 + 1.87070I
−3.44253 − 2.00602I 0
u = −0.137414 − 1.347150I
a = −0.01027 − 1.77849I
b = 0.19722 − 1.87070I
−3.44253 + 2.00602I 0
u = 0.124884 + 1.363920I
a = −0.192051 + 1.282780I
b = 0.491862 + 1.299790I
−3.69339 − 0.74625I 0
u = 0.124884 − 1.363920I
a = −0.192051 − 1.282780I
b = 0.491862 − 1.299790I
−3.69339 + 0.74625I 0
u = −0.301279 + 1.339420I
a = 0.134474 + 1.089060I
b = −0.822673 + 0.717588I
−2.46672 + 1.24828I 0
u = −0.301279 − 1.339420I
a = 0.134474 − 1.089060I
b = −0.822673 − 0.717588I
−2.46672 − 1.24828I 0
u = 0.160449 + 1.365720I
a = 0.723959 − 0.721327I
b = −0.069135 − 1.091360I
−4.20605 + 4.29473I 0
u = 0.160449 − 1.365720I
a = 0.723959 + 0.721327I
b = −0.069135 + 1.091360I
−4.20605 − 4.29473I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.287523 + 1.355060I
a = −0.371002 + 0.062591I
b = 0.108011 + 0.097232I
−0.81787 − 3.48504I 0
u = −0.287523 − 1.355060I
a = −0.371002 − 0.062591I
b = 0.108011 − 0.097232I
−0.81787 + 3.48504I 0
u = −0.119628 + 1.394690I
a = −0.54723 − 2.79461I
b = −1.37495 − 3.36028I
−5.51850 + 2.16849I 0
u = −0.119628 − 1.394690I
a = −0.54723 + 2.79461I
b = −1.37495 + 3.36028I
−5.51850 − 2.16849I 0
u = −0.174124 + 1.397150I
a = 1.65518 − 2.73301I
b = 2.10071 − 3.49563I
−6.53817 − 4.72115I 0
u = −0.174124 − 1.397150I
a = 1.65518 + 2.73301I
b = 2.10071 + 3.49563I
−6.53817 + 4.72115I 0
u = 0.266526 + 1.384670I
a = −0.114547 + 1.130050I
b = 0.855633 + 0.916968I
−2.57686 + 3.21592I 0
u = 0.266526 − 1.384670I
a = −0.114547 − 1.130050I
b = 0.855633 − 0.916968I
−2.57686 − 3.21592I 0
u = −0.242918 + 1.392810I
a = −2.54960 − 1.04148I
b = −3.01247 − 1.70084I
−5.56827 − 3.38998I 0
u = −0.242918 − 1.392810I
a = −2.54960 + 1.04148I
b = −3.01247 + 1.70084I
−5.56827 + 3.38998I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.27531 + 1.38849I
a = 0.34632 + 2.48882I
b = 0.00132 + 2.80564I
−1.28675 − 5.50091I 0
u = −0.27531 − 1.38849I
a = 0.34632 − 2.48882I
b = 0.00132 − 2.80564I
−1.28675 + 5.50091I 0
u = 0.27646 + 1.39300I
a = 0.325279 − 0.173882I
b = −0.334850 − 0.166748I
−1.45487 + 8.52318I 0
u = 0.27646 − 1.39300I
a = 0.325279 + 0.173882I
b = −0.334850 + 0.166748I
−1.45487 − 8.52318I 0
u = −0.27521 + 1.40135I
a = −0.93845 − 3.79189I
b = −0.20033 − 4.55593I
−3.31550 − 10.41430I 0
u = −0.27521 − 1.40135I
a = −0.93845 + 3.79189I
b = −0.20033 + 4.55593I
−3.31550 + 10.41430I 0
u = 0.08531 + 1.42654I
a = −0.01422 + 1.63925I
b = −0.37744 + 1.95240I
−5.52758 − 2.77432I 0
u = 0.08531 − 1.42654I
a = −0.01422 − 1.63925I
b = −0.37744 − 1.95240I
−5.52758 + 2.77432I 0
u = 0.28948 + 1.41098I
a = −0.53762 + 2.28358I
b = −0.18360 + 2.72086I
−2.70723 + 11.53590I 0
u = 0.28948 − 1.41098I
a = −0.53762 − 2.28358I
b = −0.18360 − 2.72086I
−2.70723 − 11.53590I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.20680 + 1.42573I
a = −0.14956 + 1.91224I
b = −0.13645 + 2.29208I
−8.34001 + 4.49589I 0
u = 0.20680 − 1.42573I
a = −0.14956 − 1.91224I
b = −0.13645 − 2.29208I
−8.34001 − 4.49589I 0
u = 0.11642 + 1.43673I
a = −0.76418 − 1.79191I
b = −1.05886 − 2.68694I
−10.09890 + 0.04542I 0
u = 0.11642 − 1.43673I
a = −0.76418 + 1.79191I
b = −1.05886 + 2.68694I
−10.09890 − 0.04542I 0
u = 0.27647 + 1.41769I
a = 1.92512 − 0.85955I
b = 2.34279 − 1.70867I
−7.85233 + 8.95388I 0
u = 0.27647 − 1.41769I
a = 1.92512 + 0.85955I
b = 2.34279 + 1.70867I
−7.85233 − 8.95388I 0
u = 0.29374 + 1.41633I
a = 1.05302 − 3.29529I
b = 0.26354 − 4.09901I
−4.9177 + 16.8211I 0
u = 0.29374 − 1.41633I
a = 1.05302 + 3.29529I
b = 0.26354 + 4.09901I
−4.9177 − 16.8211I 0
u = 0.08060 + 1.44466I
a = 0.35894 − 1.96207I
b = 1.27517 − 2.56719I
−7.88042 − 7.77481I 0
u = 0.08060 − 1.44466I
a = 0.35894 + 1.96207I
b = 1.27517 + 2.56719I
−7.88042 + 7.77481I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.19100 + 1.44219I
a = 1.57052 − 1.82738I
b = 2.28952 − 2.55481I
−11.93240 + 0.63088I 0
u = 0.19100 − 1.44219I
a = 1.57052 + 1.82738I
b = 2.28952 + 2.55481I
−11.93240 − 0.63088I 0
u = 0.22075 + 1.43946I
a = −0.25799 − 3.07972I
b = −0.84724 − 3.95588I
−11.5132 + 8.7877I 0
u = 0.22075 − 1.43946I
a = −0.25799 + 3.07972I
b = −0.84724 + 3.95588I
−11.5132 − 8.7877I 0
u = −0.386679 + 0.320996I
a = 1.30987 + 1.84261I
b = 0.966745 − 0.337142I
−1.11901 − 2.51665I 2.75791 + 6.45556I
u = −0.386679 − 0.320996I
a = 1.30987 − 1.84261I
b = 0.966745 + 0.337142I
−1.11901 + 2.51665I 2.75791 − 6.45556I
u = −0.455711
a = −0.596026
b = −0.512055
0.788812 12.7430
u = 0.387705 + 0.081581I
a = −0.04372 + 1.66634I
b = 0.395896 − 0.874862I
0.53012 + 2.26283I −0.75033 − 6.11283I
u = 0.387705 − 0.081581I
a = −0.04372 − 1.66634I
b = 0.395896 + 0.874862I
0.53012 − 2.26283I −0.75033 + 6.11283I
14
II. I
u
2
= hu
2
a + b + a, −u
2
a + a
2
− au − a − u, u
3
+ u
2
+ 2u + 1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
8
=
1
−u
2
a
1
=
u
u
a
3
=
a
−u
2
a − a
a
2
=
−u
2
+ a − 1
−u
2
a − a + u + 1
a
11
=
−u
−u
2
− u − 1
a
6
=
−u
−u
a
4
=
u
2
a + au + 2a
au
a
5
=
u
2
a + au + 2a
au
a
10
=
1
−u
2
a
9
=
1
−u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
2
a + au + 5u
2
+ 3a + 5u + 12
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
(u
2
− u + 1)
3
c
2
(u
2
+ u + 1)
3
c
4
, c
8
, c
9
u
6
c
6
, c
10
(u
3
− u
2
+ 1)
2
c
7
(u
3
+ u
2
+ 2u + 1)
2
c
11
, c
12
(u
3
− u
2
+ 2u − 1)
2
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
5
(y
2
+ y + 1)
3
c
4
, c
8
, c
9
y
6
c
6
, c
10
(y
3
− y
2
+ 2y −1)
2
c
7
, c
11
, c
12
(y
3
+ 3y
2
+ 2y −1)
2
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.215080 + 1.307140I
a = 0.206350 + 1.132320I
b = −0.500000 + 0.866025I
−3.02413 − 4.85801I 6.43615 + 6.24253I
u = −0.215080 + 1.307140I
a = −1.083790 − 0.387453I
b = −0.500000 − 0.866025I
−3.02413 − 0.79824I 2.88198 − 0.84592I
u = −0.215080 − 1.307140I
a = 0.206350 − 1.132320I
b = −0.500000 − 0.866025I
−3.02413 + 4.85801I 6.43615 − 6.24253I
u = −0.215080 − 1.307140I
a = −1.083790 + 0.387453I
b = −0.500000 + 0.866025I
−3.02413 + 0.79824I 2.88198 + 0.84592I
u = −0.569840
a = 0.377439 + 0.653743I
b = −0.500000 − 0.866025I
1.11345 − 2.02988I 12.18187 + 2.43783I
u = −0.569840
a = 0.377439 − 0.653743I
b = −0.500000 + 0.866025I
1.11345 + 2.02988I 12.18187 − 2.43783I
18
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
3
)(u
99
+ 46u
98
+ ··· + 16u − 1)
c
2
((u
2
+ u + 1)
3
)(u
99
+ 4u
98
+ ··· + 8u
2
− 1)
c
3
((u
2
− u + 1)
3
)(u
99
− 4u
98
+ ··· + 2572u − 137)
c
4
, c
9
u
6
(u
99
+ u
98
+ ··· − 96u − 64)
c
5
((u
2
− u + 1)
3
)(u
99
+ 4u
98
+ ··· + 8u
2
− 1)
c
6
((u
3
− u
2
+ 1)
2
)(u
99
− 3u
98
+ ··· − 3u − 1)
c
7
((u
3
+ u
2
+ 2u + 1)
2
)(u
99
+ 3u
98
+ ··· − 5u − 1)
c
8
u
6
(u
99
+ 35u
98
+ ··· − 84992u − 4096)
c
10
((u
3
− u
2
+ 1)
2
)(u
99
+ 23u
98
+ ··· − 57155u − 3971)
c
11
, c
12
((u
3
− u
2
+ 2u − 1)
2
)(u
99
+ 3u
98
+ ··· − 5u − 1)
19
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
3
)(y
99
+ 18y
98
+ ··· + 668y −1)
c
2
, c
5
((y
2
+ y + 1)
3
)(y
99
+ 46y
98
+ ··· + 16y −1)
c
3
((y
2
+ y + 1)
3
)(y
99
− 10y
98
+ ··· + 1215192y −18769)
c
4
, c
9
y
6
(y
99
+ 35y
98
+ ··· − 84992y −4096)
c
6
((y
3
− y
2
+ 2y −1)
2
)(y
99
− 3y
98
+ ··· + 11y −1)
c
7
, c
11
, c
12
((y
3
+ 3y
2
+ 2y −1)
2
)(y
99
+ 89y
98
+ ··· + 11y −1)
c
8
y
6
(y
99
+ 47y
98
+ ··· + 5.71474 × 10
8
y −1.67772 × 10
7
)
c
10
((y
3
− y
2
+ 2y −1)
2
)(y
99
+ 17y
98
+ ··· − 1.95279 × 10
8
y −1.57688 × 10
7
)
20
