12a
1016
(K12a
1016
)
A knot diagram
1
Linearized knot diagam
4 6 1 10 9 11 12 2 5 3 8 7
Solving Sequence
4,10 2,5
1 3 11 9 6 7 8 12
c
4
c
1
c
3
c
10
c
9
c
5
c
6
c
8
c
12
c
2
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.43965 × 10
142
u
91
− 2.96374 × 10
142
u
90
+ ··· + 1.68305 × 10
144
b + 1.79998 × 10
144
,
3.24920 × 10
145
u
91
+ 5.02902 × 10
145
u
90
+ ··· + 2.86119 × 10
145
a − 3.31514 × 10
144
, u
92
+ 2u
91
+ ··· + 2u + 1i
I
u
2
= hb + 1, −u
3
− 11u
2
+ 17a − 9u − 5, u
4
+ u
3
+ u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 96 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−2.44 × 10
142
u
91
− 2.96 × 10
142
u
90
+ · · · + 1.68 × 10
144
b + 1.80 ×
10
144
, 3.25 × 10
145
u
91
+ 5.03 × 10
145
u
90
+ · · · + 2.86 × 10
145
a − 3.32 ×
10
144
, u
92
+ 2u
91
+ · · · + 2u + 1i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
2
=
−1.13561u
91
− 1.75767u
90
+ ··· − 7.01717u + 0.115866
0.0144954u
91
+ 0.0176093u
90
+ ··· + 0.109965u − 1.06947
a
5
=
1
u
2
a
1
=
−1.12112u
91
− 1.74006u
90
+ ··· − 6.90720u − 0.953605
0.0144954u
91
+ 0.0176093u
90
+ ··· + 0.109965u − 1.06947
a
3
=
−1.14289u
91
− 1.76597u
90
+ ··· − 7.02281u + 0.125248
0.0106639u
91
+ 0.00260308u
90
+ ··· + 0.0904560u − 1.08464
a
11
=
−1.31145u
91
− 3.32635u
90
+ ··· − 11.3186u − 5.95210
0.544767u
91
+ 1.07553u
90
+ ··· + 3.57377u + 1.08287
a
9
=
u
u
3
+ u
a
6
=
u
2
+ 1
u
4
+ 2u
2
a
7
=
0.104548u
91
+ 0.533416u
90
+ ··· − 1.42374u + 4.75175
−0.210757u
91
− 0.419015u
90
+ ··· − 0.811424u − 0.740713
a
8
=
−1.20284u
91
− 2.85259u
90
+ ··· − 5.65875u − 6.26189
0.602208u
91
+ 1.20272u
90
+ ··· + 4.08126u + 1.16263
a
12
=
−0.519155u
91
− 1.70050u
90
+ ··· − 11.2427u − 3.96239
0.285601u
91
+ 0.468224u
90
+ ··· + 1.92592u + 0.636332
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4.11119u
91
− 6.51477u
90
+ ··· − 21.5680u − 8.41021
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
92
− 5u
91
+ ··· − 2416u + 289
c
2
u
92
− 7u
91
+ ··· − 48824u + 4624
c
4
, c
5
, c
9
u
92
+ 2u
91
+ ··· + 2u + 1
c
6
u
92
+ 2u
91
+ ··· − 1508u + 740
c
7
, c
11
, c
12
u
92
− 2u
91
+ ··· − 4u + 1
c
8
17(17u
92
− 174u
91
+ ··· + 130298u + 44509)
c
10
17(17u
92
+ 140u
91
+ ··· + 7874u + 24302)
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
92
− 51y
91
+ ··· + 749832y + 83521
c
2
y
92
− 27y
91
+ ··· − 41819456y + 21381376
c
4
, c
5
, c
9
y
92
+ 86y
91
+ ··· − 2y + 1
c
6
y
92
− 6y
91
+ ··· + 4263096y + 547600
c
7
, c
11
, c
12
y
92
+ 82y
91
+ ··· − 2y + 1
c
8
289(289y
92
− 25210y
91
+ ··· + 2.82378 × 10
10
y + 1.98105 × 10
9
)
c
10
289(289y
92
− 13548y
91
+ ··· + 5.92033 × 10
9
y + 5.90587 × 10
8
)
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.723429 + 0.708922I
a = −0.068530 − 0.266178I
b = 1.030650 − 0.427212I
0.53754 + 3.89977I 0
u = 0.723429 − 0.708922I
a = −0.068530 + 0.266178I
b = 1.030650 + 0.427212I
0.53754 − 3.89977I 0
u = −0.755871 + 0.677347I
a = −0.116138 + 0.330806I
b = 1.146220 + 0.435160I
−5.05109 − 7.87160I 0
u = −0.755871 − 0.677347I
a = −0.116138 − 0.330806I
b = 1.146220 − 0.435160I
−5.05109 + 7.87160I 0
u = 0.917926 + 0.462287I
a = 0.472649 − 0.649934I
b = 1.170350 + 0.255984I
−9.61838 − 3.26653I 0
u = 0.917926 − 0.462287I
a = 0.472649 + 0.649934I
b = 1.170350 − 0.255984I
−9.61838 + 3.26653I 0
u = −0.818704 + 0.470594I
a = 0.620242 + 0.998337I
b = 1.287710 − 0.562306I
−5.6448 + 13.1488I 0
u = −0.818704 − 0.470594I
a = 0.620242 − 0.998337I
b = 1.287710 + 0.562306I
−5.6448 − 13.1488I 0
u = −0.837149 + 0.425208I
a = 0.708549 + 0.797862I
b = 1.112130 − 0.479118I
−1.89958 + 4.64735I 0
u = −0.837149 − 0.425208I
a = 0.708549 − 0.797862I
b = 1.112130 + 0.479118I
−1.89958 − 4.64735I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.679164 + 0.816347I
a = 0.058176 + 0.239150I
b = 0.885022 + 0.292304I
−0.801850 + 0.602505I 0
u = −0.679164 − 0.816347I
a = 0.058176 − 0.239150I
b = 0.885022 − 0.292304I
−0.801850 − 0.602505I 0
u = 0.820373 + 0.454211I
a = 0.675976 − 0.935007I
b = 1.211960 + 0.552100I
−0.20311 − 9.12601I 0
u = 0.820373 − 0.454211I
a = 0.675976 + 0.935007I
b = 1.211960 − 0.552100I
−0.20311 + 9.12601I 0
u = −0.780319 + 0.298193I
a = 1.014290 + 0.508885I
b = 0.759730 − 0.433721I
−0.79364 + 3.83441I 0
u = −0.780319 − 0.298193I
a = 1.014290 − 0.508885I
b = 0.759730 + 0.433721I
−0.79364 − 3.83441I 0
u = −0.508684 + 0.554434I
a = 0.009437 − 0.236074I
b = 0.378877 + 0.709246I
0.333433 + 0.235331I 2.44269 − 1.33984I
u = −0.508684 − 0.554434I
a = 0.009437 + 0.236074I
b = 0.378877 − 0.709246I
0.333433 − 0.235331I 2.44269 + 1.33984I
u = −0.036100 + 1.251740I
a = 1.326040 − 0.471491I
b = −1.73590 + 0.19170I
−4.09748 + 3.83030I 0
u = −0.036100 − 1.251740I
a = 1.326040 + 0.471491I
b = −1.73590 − 0.19170I
−4.09748 − 3.83030I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.027948 + 1.287430I
a = 0.807838 + 0.454026I
b = −1.53431 − 0.15728I
1.06309 − 1.30891I 0
u = 0.027948 − 1.287430I
a = 0.807838 − 0.454026I
b = −1.53431 + 0.15728I
1.06309 + 1.30891I 0
u = 0.531244 + 0.471938I
a = −0.084246 + 0.425593I
b = 0.177103 − 0.931948I
2.92557 − 3.81766I 4.57168 + 6.93434I
u = 0.531244 − 0.471938I
a = −0.084246 − 0.425593I
b = 0.177103 + 0.931948I
2.92557 + 3.81766I 4.57168 − 6.93434I
u = −0.549556 + 0.440216I
a = −0.146223 − 0.506320I
b = 0.080541 + 1.063430I
−1.93813 + 7.45601I −1.14672 − 8.36768I
u = −0.549556 − 0.440216I
a = −0.146223 + 0.506320I
b = 0.080541 − 1.063430I
−1.93813 − 7.45601I −1.14672 + 8.36768I
u = −0.112173 + 1.307740I
a = 0.99969 − 1.56602I
b = −1.43510 + 0.71195I
−3.18580 + 0.28744I 0
u = −0.112173 − 1.307740I
a = 0.99969 + 1.56602I
b = −1.43510 − 0.71195I
−3.18580 − 0.28744I 0
u = 0.639929 + 0.234530I
a = 1.306120 − 0.290351I
b = 0.419159 + 0.406209I
2.26085 + 0.24700I 4.77847 + 1.60729I
u = 0.639929 − 0.234530I
a = 1.306120 + 0.290351I
b = 0.419159 − 0.406209I
2.26085 − 0.24700I 4.77847 − 1.60729I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.872325 + 1.004060I
a = 0.101148 − 0.324936I
b = 0.959957 − 0.089915I
−8.36829 − 2.94551I 0
u = 0.872325 − 1.004060I
a = 0.101148 + 0.324936I
b = 0.959957 + 0.089915I
−8.36829 + 2.94551I 0
u = 0.097873 + 1.350170I
a = 0.63263 + 1.66426I
b = −1.103100 − 0.603007I
2.06203 − 1.91481I 0
u = 0.097873 − 1.350170I
a = 0.63263 − 1.66426I
b = −1.103100 + 0.603007I
2.06203 + 1.91481I 0
u = 0.151680 + 1.346250I
a = 0.76051 + 1.99171I
b = −1.13321 − 1.07861I
−1.87291 − 7.85148I 0
u = 0.151680 − 1.346250I
a = 0.76051 − 1.99171I
b = −1.13321 + 1.07861I
−1.87291 + 7.85148I 0
u = −0.138270 + 1.358800I
a = 0.66638 − 1.88607I
b = −1.009970 + 0.953371I
3.22510 + 4.72100I 0
u = −0.138270 − 1.358800I
a = 0.66638 + 1.88607I
b = −1.009970 − 0.953371I
3.22510 − 4.72100I 0
u = −0.540093 + 0.295440I
a = 1.60359 + 0.21389I
b = 0.155996 − 0.537063I
−2.23514 − 3.97057I −0.795717 + 0.624942I
u = −0.540093 − 0.295440I
a = 1.60359 − 0.21389I
b = 0.155996 + 0.537063I
−2.23514 + 3.97057I −0.795717 − 0.624942I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.054258 + 1.403060I
a = 1.05324 − 2.71332I
b = −0.840395 + 0.129390I
4.79962 + 0.34018I 0
u = −0.054258 − 1.403060I
a = 1.05324 + 2.71332I
b = −0.840395 − 0.129390I
4.79962 − 0.34018I 0
u = 0.034934 + 1.411120I
a = 1.55901 + 4.66262I
b = −0.922785 − 0.025140I
0.43080 + 2.76175I 0
u = 0.034934 − 1.411120I
a = 1.55901 − 4.66262I
b = −0.922785 + 0.025140I
0.43080 − 2.76175I 0
u = 0.07790 + 1.41886I
a = 1.13505 + 1.45161I
b = −0.501962 − 0.230422I
1.33300 − 3.10007I 0
u = 0.07790 − 1.41886I
a = 1.13505 − 1.45161I
b = −0.501962 + 0.230422I
1.33300 + 3.10007I 0
u = −0.30977 + 1.39567I
a = 0.437079 + 1.045170I
b = 0.777453 − 0.469099I
2.83351 − 0.71101I 0
u = −0.30977 − 1.39567I
a = 0.437079 − 1.045170I
b = 0.777453 + 0.469099I
2.83351 + 0.71101I 0
u = 0.475179 + 0.304749I
a = −0.034351 + 0.929835I
b = −0.578262 − 0.755556I
−4.66057 − 0.77078I −5.52980 + 5.29384I
u = 0.475179 − 0.304749I
a = −0.034351 − 0.929835I
b = −0.578262 + 0.755556I
−4.66057 + 0.77078I −5.52980 − 5.29384I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.14742 + 1.43063I
a = 0.16567 + 1.61582I
b = −0.278816 − 0.974072I
0.92558 − 2.99536I 0
u = 0.14742 − 1.43063I
a = 0.16567 − 1.61582I
b = −0.278816 + 0.974072I
0.92558 + 2.99536I 0
u = 0.517746 + 0.164875I
a = −0.437178 + 0.861152I
b = −1.27172 − 0.67226I
−6.59592 − 5.44870I −8.87418 + 7.66099I
u = 0.517746 − 0.164875I
a = −0.437178 − 0.861152I
b = −1.27172 + 0.67226I
−6.59592 + 5.44870I −8.87418 − 7.66099I
u = 0.31166 + 1.43603I
a = 0.288699 − 1.233570I
b = 0.897418 + 0.544087I
7.56798 − 3.49046I 0
u = 0.31166 − 1.43603I
a = 0.288699 + 1.233570I
b = 0.897418 − 0.544087I
7.56798 + 3.49046I 0
u = −0.279069 + 0.437448I
a = 0.540250 − 0.363433I
b = 0.014327 + 0.254945I
0.076878 + 0.928772I 1.77549 − 6.97869I
u = −0.279069 − 0.437448I
a = 0.540250 + 0.363433I
b = 0.014327 − 0.254945I
0.076878 − 0.928772I 1.77549 + 6.97869I
u = −0.19572 + 1.46899I
a = −0.58313 − 1.63411I
b = 0.272489 + 1.347670I
4.24474 + 10.19690I 0
u = −0.19572 − 1.46899I
a = −0.58313 + 1.63411I
b = 0.272489 − 1.347670I
4.24474 − 10.19690I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.506332 + 0.066712I
a = −0.747080 − 0.454115I
b = −1.49694 + 0.27867I
−7.35852 − 1.90033I −10.89986 + 0.67632I
u = −0.506332 − 0.066712I
a = −0.747080 + 0.454115I
b = −1.49694 − 0.27867I
−7.35852 + 1.90033I −10.89986 − 0.67632I
u = 0.18964 + 1.47755I
a = −0.57786 + 1.49123I
b = 0.328015 − 1.241050I
9.24369 − 6.48174I 0
u = 0.18964 − 1.47755I
a = −0.57786 − 1.49123I
b = 0.328015 + 1.241050I
9.24369 + 6.48174I 0
u = −0.477519 + 0.178866I
a = −0.473581 − 1.039140I
b = −1.109380 + 0.564891I
−1.60225 + 2.51291I −3.70004 − 8.45487I
u = −0.477519 − 0.178866I
a = −0.473581 + 1.039140I
b = −1.109380 − 0.564891I
−1.60225 − 2.51291I −3.70004 + 8.45487I
u = −0.31089 + 1.46801I
a = 0.098323 + 1.393730I
b = 1.033910 − 0.595051I
4.94388 + 7.87236I 0
u = −0.31089 − 1.46801I
a = 0.098323 − 1.393730I
b = 1.033910 + 0.595051I
4.94388 − 7.87236I 0
u = −0.17588 + 1.49414I
a = −0.530299 − 1.224910I
b = 0.405401 + 1.031980I
6.96522 + 2.75896I 0
u = −0.17588 − 1.49414I
a = −0.530299 + 1.224910I
b = 0.405401 − 1.031980I
6.96522 − 2.75896I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.15243 + 1.50603I
a = −0.366384 − 0.991531I
b = 0.389992 + 0.803857I
6.75562 + 2.72068I 0
u = −0.15243 − 1.50603I
a = −0.366384 + 0.991531I
b = 0.389992 − 0.803857I
6.75562 − 2.72068I 0
u = −0.30523 + 1.49802I
a = −0.16998 + 1.57415I
b = 1.218150 − 0.641250I
4.31942 + 8.78400I 0
u = −0.30523 − 1.49802I
a = −0.16998 − 1.57415I
b = 1.218150 + 0.641250I
4.31942 − 8.78400I 0
u = 0.306365 + 0.351401I
a = 2.37372 + 1.25949I
b = −0.676812 + 0.283730I
−4.21670 − 1.78372I −4.08948 + 6.84585I
u = 0.306365 − 0.351401I
a = 2.37372 − 1.25949I
b = −0.676812 − 0.283730I
−4.21670 + 1.78372I −4.08948 − 6.84585I
u = 0.29882 + 1.50626I
a = −0.25823 − 1.68961I
b = 1.29074 + 0.68762I
6.1406 − 13.1964I 0
u = 0.29882 − 1.50626I
a = −0.25823 + 1.68961I
b = 1.29074 − 0.68762I
6.1406 + 13.1964I 0
u = −0.29742 + 1.51179I
a = −0.33990 + 1.73044I
b = 1.34484 − 0.69377I
0.7723 + 17.2144I 0
u = −0.29742 − 1.51179I
a = −0.33990 − 1.73044I
b = 1.34484 + 0.69377I
0.7723 − 17.2144I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.32689 + 1.50963I
a = −0.325754 − 1.336240I
b = 1.255170 + 0.478109I
−3.27782 − 7.72836I 0
u = 0.32689 − 1.50963I
a = −0.325754 + 1.336240I
b = 1.255170 − 0.478109I
−3.27782 + 7.72836I 0
u = 0.14716 + 1.55671I
a = −0.496177 + 0.578156I
b = 0.643062 − 0.573865I
8.30821 + 0.96783I 0
u = 0.14716 − 1.55671I
a = −0.496177 − 0.578156I
b = 0.643062 + 0.573865I
8.30821 − 0.96783I 0
u = 0.417977 + 0.073002I
a = −1.40356 + 0.82916I
b = −1.214270 − 0.174607I
−2.41043 − 0.16113I −6.41199 − 3.08513I
u = 0.417977 − 0.073002I
a = −1.40356 − 0.82916I
b = −1.214270 + 0.174607I
−2.41043 + 0.16113I −6.41199 + 3.08513I
u = 0.112135 + 0.407702I
a = 4.76075 + 1.11963I
b = −1.125990 + 0.161420I
−5.17066 + 3.31019I 5.13185 + 5.07018I
u = 0.112135 − 0.407702I
a = 4.76075 − 1.11963I
b = −1.125990 − 0.161420I
−5.17066 − 3.31019I 5.13185 − 5.07018I
u = −0.15307 + 1.59919I
a = −0.570219 − 0.335579I
b = 0.795921 + 0.433246I
2.79603 − 4.53346I 0
u = −0.15307 − 1.59919I
a = −0.570219 + 0.335579I
b = 0.795921 − 0.433246I
2.79603 + 4.53346I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.172880 + 0.325783I
a = 4.14198 − 2.59757I
b = −0.973359 − 0.135697I
−0.571740 − 0.532703I 3.27414 − 13.20976I
u = −0.172880 − 0.325783I
a = 4.14198 + 2.59757I
b = −0.973359 + 0.135697I
−0.571740 + 0.532703I 3.27414 + 13.20976I
14
II. I
u
2
= hb + 1, −u
3
− 11u
2
+ 17a − 9u − 5, u
4
+ u
3
+ u
2
+ 1i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
2
=
0.0588235u
3
+ 0.647059u
2
+ 0.529412u + 0.294118
−1
a
5
=
1
u
2
a
1
=
0.0588235u
3
+ 0.647059u
2
+ 0.529412u − 0.705882
−1
a
3
=
0.0588235u
3
+ 0.647059u
2
+ 0.529412u + 0.294118
−1
a
11
=
−0.0103806u
3
+ 0.00346021u
2
+ 0.318339u + 0.242215
0.588235u
3
+ 0.470588u
2
+ 1.29412u − 0.0588235
a
9
=
u
u
3
+ u
a
6
=
u
2
+ 1
−u
3
+ u
2
− 1
a
7
=
0.0726644u
3
+ 0.975779u
2
− 0.228374u + 1.30450
−0.117647u
3
+ 1.70588u
2
− 0.0588235u + 0.411765
a
8
=
−0.283737u
3
− 0.238754u
2
+ 1.03460u + 0.287197
1.41176u
3
+ 0.529412u
2
+ 1.70588u + 0.0588235
a
12
=
1.26298u
3
+ 0.245675u
2
+ 0.602076u + 0.197232
1.76471u
3
+ 1.41176u
2
− 0.117647u + 0.823529
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
631
289
u
3
+
2715
289
u
2
+
84
289
u −
112
289
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
4
c
2
u
4
c
3
(u + 1)
4
c
4
, c
5
u
4
+ u
3
+ u
2
+ 1
c
6
u
4
− u
3
+ 5u
2
+ u + 2
c
7
u
4
+ u
3
+ 3u
2
+ 2u + 1
c
8
17(17u
4
− 3u
3
+ 11u
2
+ 1)
c
9
u
4
− u
3
+ u
2
+ 1
c
10
17(17u
4
+ 3u
3
− 4u
2
+ u + 2)
c
11
, c
12
u
4
− u
3
+ 3u
2
− 2u + 1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
(y −1)
4
c
2
y
4
c
4
, c
5
, c
9
y
4
+ y
3
+ 3y
2
+ 2y + 1
c
6
y
4
+ 9y
3
+ 31y
2
+ 19y + 4
c
7
, c
11
, c
12
y
4
+ 5y
3
+ 7y
2
+ 2y + 1
c
8
289(289y
4
+ 365y
3
+ 155y
2
+ 22y + 1)
c
10
289(289y
4
− 145y
3
+ 78y
2
− 17y + 4)
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.351808 + 0.720342I
a = 0.195047 + 0.703062I
b = −1.00000
−1.43393 − 1.41510I −2.89659 + 5.20302I
u = 0.351808 − 0.720342I
a = 0.195047 − 0.703062I
b = −1.00000
−1.43393 + 1.41510I −2.89659 − 5.20302I
u = −0.851808 + 0.911292I
a = −0.136224 − 0.449937I
b = −1.00000
−8.43568 + 3.16396I −4.9044 − 16.9987I
u = −0.851808 − 0.911292I
a = −0.136224 + 0.449937I
b = −1.00000
−8.43568 − 3.16396I −4.9044 + 16.9987I
18
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
4
)(u
92
− 5u
91
+ ··· − 2416u + 289)
c
2
u
4
(u
92
− 7u
91
+ ··· − 48824u + 4624)
c
3
((u + 1)
4
)(u
92
− 5u
91
+ ··· − 2416u + 289)
c
4
, c
5
(u
4
+ u
3
+ u
2
+ 1)(u
92
+ 2u
91
+ ··· + 2u + 1)
c
6
(u
4
− u
3
+ 5u
2
+ u + 2)(u
92
+ 2u
91
+ ··· − 1508u + 740)
c
7
(u
4
+ u
3
+ 3u
2
+ 2u + 1)(u
92
− 2u
91
+ ··· − 4u + 1)
c
8
289(17u
4
− 3u
3
+ 11u
2
+ 1)
· (17u
92
− 174u
91
+ ··· + 130298u + 44509)
c
9
(u
4
− u
3
+ u
2
+ 1)(u
92
+ 2u
91
+ ··· + 2u + 1)
c
10
289(17u
4
+ 3u
3
− 4u
2
+ u + 2)
· (17u
92
+ 140u
91
+ ··· + 7874u + 24302)
c
11
, c
12
(u
4
− u
3
+ 3u
2
− 2u + 1)(u
92
− 2u
91
+ ··· − 4u + 1)
19
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
3
((y −1)
4
)(y
92
− 51y
91
+ ··· + 749832y + 83521)
c
2
y
4
(y
92
− 27y
91
+ ··· − 4.18195 × 10
7
y + 2.13814 × 10
7
)
c
4
, c
5
, c
9
(y
4
+ y
3
+ 3y
2
+ 2y + 1)(y
92
+ 86y
91
+ ··· − 2y + 1)
c
6
(y
4
+ 9y
3
+ 31y
2
+ 19y + 4)(y
92
− 6y
91
+ ··· + 4263096y + 547600)
c
7
, c
11
, c
12
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)(y
92
+ 82y
91
+ ··· − 2y + 1)
c
8
83521(289y
4
+ 365y
3
+ 155y
2
+ 22y + 1)
· (289y
92
− 25210y
91
+ ··· + 28237789026y + 1981051081)
c
10
83521(289y
4
− 145y
3
+ 78y
2
− 17y + 4)
· (289y
92
− 13548y
91
+ ··· + 5920326256y + 590587204)
20
