12a
0372
(K12a
0372
)
A knot diagram
1
Linearized knot diagam
3 6 9 10 2 11 12 1 5 4 8 7
Solving Sequence
2,5
6 3
1,10
4 11 7 9 8 12
c
5
c
2
c
1
c
4
c
10
c
6
c
9
c
8
c
12
c
3
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−4.00775 × 10
87
u
85
− 2.48507 × 10
88
u
84
+ ··· + 1.44535 × 10
88
b + 2.76929 × 10
89
,
− 3.45221 × 10
89
u
85
− 1.15168 × 10
90
u
84
+ ··· + 4.91419 × 10
89
a + 4.17969 × 10
90
,
u
86
+ 4u
85
+ ··· − 20u − 17i
I
u
2
= h−194a
5
− 315a
4
− 5270a
3
− 4555a
2
+ 69650b − 64279a − 26651,
a
6
+ 2a
5
+ 25a
4
+ 30a
3
+ 206a
2
+ 176a + 593, u − 1i
I
u
3
= hb, a
3
+ a
2
− 1, u + 1i
* 3 irreducible components of dim
C
= 0, with total 95 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−4.01 × 10
87
u
85
− 2.49 × 10
88
u
84
+ · · · + 1.45 × 10
88
b + 2.77 ×
10
89
, −3.45 × 10
89
u
85
− 1.15 × 10
90
u
84
+ · · · + 4.91 × 10
89
a + 4.18 ×
10
90
, u
86
+ 4u
85
+ · · · − 20u − 17i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
u
2
a
3
=
−u
−u
3
+ u
a
1
=
u
3
u
5
− u
3
+ u
a
10
=
0.702499u
85
+ 2.34358u
84
+ ··· − 17.6252u − 8.50536
0.277286u
85
+ 1.71936u
84
+ ··· + 8.31636u − 19.1600
a
4
=
0.504301u
85
+ 1.30510u
84
+ ··· − 13.8214u − 5.82459
0.0137884u
85
+ 0.0233804u
84
+ ··· + 1.94469u − 3.22686
a
11
=
0.294534u
85
+ 1.15575u
84
+ ··· + 5.28585u − 19.1152
0.244106u
85
+ 0.263311u
84
+ ··· − 4.48711u + 4.51370
a
7
=
−1.36374u
85
− 4.50519u
84
+ ··· + 9.32384u + 28.0444
0.448009u
85
+ 1.37637u
84
+ ··· − 4.79587u − 5.94786
a
9
=
0.425213u
85
+ 0.624223u
84
+ ··· − 25.9416u + 10.6546
0.277286u
85
+ 1.71936u
84
+ ··· + 8.31636u − 19.1600
a
8
=
−0.00970161u
85
− 0.280717u
84
+ ··· − 21.0594u + 11.2096
0.0519514u
85
+ 0.807957u
84
+ ··· + 2.49003u − 10.0728
a
12
=
−1.53639u
85
− 4.66319u
84
+ ··· + 30.2188u + 12.1772
0.253558u
85
+ 0.199433u
84
+ ··· − 14.9224u + 12.1204
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.907710u
85
− 2.76373u
84
+ ··· + 58.7556u + 7.47521
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
86
+ 42u
85
+ ··· + 8016u + 289
c
2
, c
5
u
86
+ 4u
85
+ ··· − 20u − 17
c
3
u
86
− u
85
+ ··· − 8992u + 16424
c
4
, c
9
, c
10
u
86
+ u
85
+ ··· + 16u + 8
c
6
, c
8
u
86
+ 2u
85
+ ··· − 11367u − 2391
c
7
, c
11
, c
12
u
86
− 2u
85
+ ··· − 3u − 3
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
86
+ 14y
85
+ ··· − 19463568y + 83521
c
2
, c
5
y
86
− 42y
85
+ ··· − 8016y + 289
c
3
y
86
− 5y
85
+ ··· − 1234215040y + 269747776
c
4
, c
9
, c
10
y
86
+ 79y
85
+ ··· − 1280y + 64
c
6
, c
8
y
86
− 56y
85
+ ··· + 68087067y + 5716881
c
7
, c
11
, c
12
y
86
+ 72y
85
+ ··· + 51y + 9
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.509248 + 0.852642I
a = 0.322825 + 0.048607I
b = −0.789445 − 0.160402I
6.59236 + 1.97479I 0
u = 0.509248 − 0.852642I
a = 0.322825 − 0.048607I
b = −0.789445 + 0.160402I
6.59236 − 1.97479I 0
u = 0.584122 + 0.824498I
a = −0.334198 − 0.153374I
b = 0.790561 + 0.106022I
3.13486 − 2.30297I 0
u = 0.584122 − 0.824498I
a = −0.334198 + 0.153374I
b = 0.790561 − 0.106022I
3.13486 + 2.30297I 0
u = −0.329631 + 0.932362I
a = −0.451079 − 0.979419I
b = 0.32373 − 1.38168I
−2.75721 − 10.22800I 0
u = −0.329631 − 0.932362I
a = −0.451079 + 0.979419I
b = 0.32373 + 1.38168I
−2.75721 + 10.22800I 0
u = 0.896991 + 0.410818I
a = 0.53853 + 2.78692I
b = 0.06533 + 1.51526I
−4.54753 − 1.67750I 0
u = 0.896991 − 0.410818I
a = 0.53853 − 2.78692I
b = 0.06533 − 1.51526I
−4.54753 + 1.67750I 0
u = −0.371807 + 0.912630I
a = 0.399618 + 0.904183I
b = −0.326539 + 1.355580I
1.81661 − 5.99490I 0
u = −0.371807 − 0.912630I
a = 0.399618 − 0.904183I
b = −0.326539 − 1.355580I
1.81661 + 5.99490I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.447851 + 0.874871I
a = −0.312467 + 0.033097I
b = 0.787438 + 0.204817I
2.26451 + 6.21660I 0
u = 0.447851 − 0.874871I
a = −0.312467 − 0.033097I
b = 0.787438 − 0.204817I
2.26451 − 6.21660I 0
u = −0.608566 + 0.769255I
a = −0.650245 + 0.848054I
b = 0.384469 + 0.945216I
−0.04968 − 1.95533I 0
u = −0.608566 − 0.769255I
a = −0.650245 − 0.848054I
b = 0.384469 − 0.945216I
−0.04968 + 1.95533I 0
u = −0.428356 + 0.876203I
a = −0.326362 − 0.791803I
b = 0.324167 − 1.315440I
−1.30715 − 1.70626I 0
u = −0.428356 − 0.876203I
a = −0.326362 + 0.791803I
b = 0.324167 + 1.315440I
−1.30715 + 1.70626I 0
u = −0.686031 + 0.768487I
a = 0.752897 − 0.902852I
b = −0.373726 − 1.024720I
3.93150 + 2.25304I 0
u = −0.686031 − 0.768487I
a = 0.752897 + 0.902852I
b = −0.373726 + 1.024720I
3.93150 − 2.25304I 0
u = 0.924737 + 0.534530I
a = 0.575892 + 0.848478I
b = −0.665118 + 0.182466I
0.27137 − 3.73444I 0
u = 0.924737 − 0.534530I
a = 0.575892 − 0.848478I
b = −0.665118 − 0.182466I
0.27137 + 3.73444I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.966175 + 0.460720I
a = −0.52607 − 2.70537I
b = −0.09038 − 1.52749I
−8.90441 − 5.42664I 0
u = 0.966175 − 0.460720I
a = −0.52607 + 2.70537I
b = −0.09038 + 1.52749I
−8.90441 + 5.42664I 0
u = −0.756050 + 0.766739I
a = −0.861234 + 0.982031I
b = 0.371400 + 1.094440I
0.10136 + 6.51112I 0
u = −0.756050 − 0.766739I
a = −0.861234 − 0.982031I
b = 0.371400 − 1.094440I
0.10136 − 6.51112I 0
u = −0.986156 + 0.463423I
a = 2.45774 − 1.20507I
b = −0.189677 − 1.345070I
−8.83115 + 0.16688I 0
u = −0.986156 − 0.463423I
a = 2.45774 + 1.20507I
b = −0.189677 + 1.345070I
−8.83115 − 0.16688I 0
u = −0.871820 + 0.230790I
a = −0.264628 + 0.427871I
b = −0.187263 + 0.458115I
−1.46632 + 0.85886I 0. − 2.31420I
u = −0.871820 − 0.230790I
a = −0.264628 − 0.427871I
b = −0.187263 − 0.458115I
−1.46632 − 0.85886I 0. + 2.31420I
u = −0.879504 + 0.671225I
a = −0.360993 + 0.571062I
b = −0.418022 + 0.882634I
−0.283252 − 1.079100I 0
u = −0.879504 − 0.671225I
a = −0.360993 − 0.571062I
b = −0.418022 − 0.882634I
−0.283252 + 1.079100I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.100000 + 0.189928I
a = −0.23593 − 2.68382I
b = −0.089636 − 1.408420I
−7.23808 + 0.30916I 0
u = 1.100000 − 0.189928I
a = −0.23593 + 2.68382I
b = −0.089636 + 1.408420I
−7.23808 − 0.30916I 0
u = −0.981639 + 0.534063I
a = −2.00458 + 1.26234I
b = 0.229804 + 1.325390I
−3.48232 + 3.39964I 0
u = −0.981639 − 0.534063I
a = −2.00458 − 1.26234I
b = 0.229804 − 1.325390I
−3.48232 − 3.39964I 0
u = 0.742085 + 0.454046I
a = −0.864160 − 0.546861I
b = 0.587415 − 0.064260I
0.916106 − 0.421753I 10.41879 + 0.I
u = 0.742085 − 0.454046I
a = −0.864160 + 0.546861I
b = 0.587415 + 0.064260I
0.916106 + 0.421753I 10.41879 + 0.I
u = 0.830940 + 0.240284I
a = 1.41644 + 0.82559I
b = −0.448531 + 0.114261I
−4.18135 + 2.25158I 7.13926 + 2.78271I
u = 0.830940 − 0.240284I
a = 1.41644 − 0.82559I
b = −0.448531 − 0.114261I
−4.18135 − 2.25158I 7.13926 − 2.78271I
u = 1.047320 + 0.468070I
a = −0.536699 − 1.151690I
b = 0.631147 − 0.292577I
−5.75601 − 5.20754I 0
u = 1.047320 − 0.468070I
a = −0.536699 + 1.151690I
b = 0.631147 + 0.292577I
−5.75601 + 5.20754I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.095810 + 0.344023I
a = 0.450668 − 0.368225I
b = 0.464015 − 0.457806I
−6.48632 + 1.75628I 0
u = −1.095810 − 0.344023I
a = 0.450668 + 0.368225I
b = 0.464015 + 0.457806I
−6.48632 − 1.75628I 0
u = −0.958955 + 0.647599I
a = 0.414297 − 0.568075I
b = 0.474434 − 0.815046I
3.10357 + 3.09687I 0
u = −0.958955 − 0.647599I
a = 0.414297 + 0.568075I
b = 0.474434 + 0.815046I
3.10357 − 3.09687I 0
u = 0.753237 + 0.364190I
a = −0.64318 − 2.95965I
b = −0.02689 − 1.50940I
−8.07669 + 1.87059I 2.84516 + 0.42953I
u = 0.753237 − 0.364190I
a = −0.64318 + 2.95965I
b = −0.02689 + 1.50940I
−8.07669 − 1.87059I 2.84516 − 0.42953I
u = −1.016700 + 0.633935I
a = −0.451131 + 0.561079I
b = −0.518692 + 0.772841I
−1.29006 + 7.25611I 0
u = −1.016700 − 0.633935I
a = −0.451131 − 0.561079I
b = −0.518692 − 0.772841I
−1.29006 − 7.25611I 0
u = −1.054830 + 0.577809I
a = 1.81540 − 1.65430I
b = −0.271885 − 1.362200I
−4.61406 + 7.15880I 0
u = −1.054830 − 0.577809I
a = 1.81540 + 1.65430I
b = −0.271885 + 1.362200I
−4.61406 − 7.15880I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.426091 + 0.660797I
a = −0.467482 − 0.247485I
b = 0.196765 − 1.275150I
−2.83344 − 2.33982I 4.51071 + 3.69455I
u = −0.426091 − 0.660797I
a = −0.467482 + 0.247485I
b = 0.196765 + 1.275150I
−2.83344 + 2.33982I 4.51071 − 3.69455I
u = 1.171760 + 0.330721I
a = 0.36279 + 2.60051I
b = 0.15928 + 1.45009I
−12.60960 + 0.53188I 0
u = 1.171760 − 0.330721I
a = 0.36279 − 2.60051I
b = 0.15928 − 1.45009I
−12.60960 − 0.53188I 0
u = −0.561224 + 0.536687I
a = −0.130904 − 0.198541I
b = −0.091191 + 1.196000I
−2.28991 + 0.95503I 5.78427 − 4.47037I
u = −0.561224 − 0.536687I
a = −0.130904 + 0.198541I
b = −0.091191 − 1.196000I
−2.28991 − 0.95503I 5.78427 + 4.47037I
u = −1.23000
a = 0.487096
b = 0.526354
0.302978 0
u = 1.033160 + 0.672308I
a = 0.249124 + 0.871946I
b = −0.792360 + 0.236164I
1.77987 − 3.27789I 0
u = 1.033160 − 0.672308I
a = 0.249124 − 0.871946I
b = −0.792360 − 0.236164I
1.77987 + 3.27789I 0
u = −1.120250 + 0.532355I
a = −1.98299 + 2.00595I
b = 0.25455 + 1.40909I
−11.17690 + 8.47102I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.120250 − 0.532355I
a = −1.98299 − 2.00595I
b = 0.25455 − 1.40909I
−11.17690 − 8.47102I 0
u = −1.253150 + 0.085853I
a = −0.518095 + 0.091265I
b = −0.562417 + 0.108346I
−3.71512 − 3.61639I 0
u = −1.253150 − 0.085853I
a = −0.518095 − 0.091265I
b = −0.562417 − 0.108346I
−3.71512 + 3.61639I 0
u = 1.087850 + 0.663273I
a = −0.201529 − 0.952587I
b = 0.799806 − 0.280258I
4.84791 − 7.60111I 0
u = 1.087850 − 0.663273I
a = −0.201529 + 0.952587I
b = 0.799806 + 0.280258I
4.84791 + 7.60111I 0
u = −0.226176 + 0.670392I
a = 1.092930 + 0.581518I
b = −0.183977 + 1.375540I
−8.69537 − 3.85336I 0.06507 + 3.00079I
u = −0.226176 − 0.670392I
a = 1.092930 − 0.581518I
b = −0.183977 − 1.375540I
−8.69537 + 3.85336I 0.06507 − 3.00079I
u = 1.122620 + 0.650698I
a = 0.176872 + 1.009790I
b = −0.799739 + 0.310768I
0.23048 − 11.85200I 0
u = 1.122620 − 0.650698I
a = 0.176872 − 1.009790I
b = −0.799739 − 0.310768I
0.23048 + 11.85200I 0
u = −1.126730 + 0.643608I
a = 1.51181 − 1.91377I
b = −0.32382 − 1.39843I
−3.40709 + 7.31230I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.126730 − 0.643608I
a = 1.51181 + 1.91377I
b = −0.32382 + 1.39843I
−3.40709 − 7.31230I 0
u = 1.292600 + 0.117096I
a = −0.17327 − 2.45986I
b = −0.156978 − 1.269640I
−7.24729 − 1.14255I 0
u = 1.292600 − 0.117096I
a = −0.17327 + 2.45986I
b = −0.156978 + 1.269640I
−7.24729 + 1.14255I 0
u = −0.590405 + 0.374886I
a = 0.544712 + 1.162400I
b = 0.011567 − 1.267360I
−7.59821 + 3.51299I 1.50213 − 4.82756I
u = −0.590405 − 0.374886I
a = 0.544712 − 1.162400I
b = 0.011567 + 1.267360I
−7.59821 − 3.51299I 1.50213 + 4.82756I
u = 1.305650 + 0.179739I
a = 0.24358 + 2.46781I
b = 0.200042 + 1.317550I
−3.91048 + 2.62248I 0
u = 1.305650 − 0.179739I
a = 0.24358 − 2.46781I
b = 0.200042 − 1.317550I
−3.91048 − 2.62248I 0
u = −1.165480 + 0.637891I
a = −1.49482 + 2.05321I
b = 0.32450 + 1.42352I
−0.57989 + 11.67450I 0
u = −1.165480 − 0.637891I
a = −1.49482 − 2.05321I
b = 0.32450 − 1.42352I
−0.57989 − 11.67450I 0
u = 1.322240 + 0.219958I
a = −0.28506 − 2.46512I
b = −0.226534 − 1.344900I
−8.34294 + 6.52071I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.322240 − 0.219958I
a = −0.28506 + 2.46512I
b = −0.226534 + 1.344900I
−8.34294 − 6.52071I 0
u = −1.188080 + 0.627308I
a = 1.50177 − 2.14199I
b = −0.32023 − 1.43864I
−5.3572 + 15.9154I 0
u = −1.188080 − 0.627308I
a = 1.50177 + 2.14199I
b = −0.32023 + 1.43864I
−5.3572 − 15.9154I 0
u = 0.032159 + 0.548639I
a = 0.683294 − 0.535532I
b = −0.458589 − 0.358951I
−3.33000 + 1.53573I 4.91213 − 4.32886I
u = 0.032159 − 0.548639I
a = 0.683294 + 0.535532I
b = −0.458589 + 0.358951I
−3.33000 − 1.53573I 4.91213 + 4.32886I
u = 0.255360
a = −1.59057
b = 0.336114
0.640620 15.8240
13
II.
I
u
2
= h−194a
5
+69650b+· · ·−64279a−26651, a
6
+2a
5
+· · ·+176a+593, u−1i
(i) Arc colorings
a
2
=
0
1
a
5
=
1
0
a
6
=
1
1
a
3
=
−1
0
a
1
=
1
1
a
10
=
a
0.00278536a
5
+ 0.00452261a
4
+ ··· + 0.922886a + 0.382642
a
4
=
−0.00104810a
5
+ 0.00603015a
4
+ ··· − 0.107581a − 0.651716
−2
a
11
=
0.00278536a
5
+ 0.00452261a
4
+ ··· − 0.0771141a + 0.382642
−0.00278536a
5
− 0.00452261a
4
+ ··· − 0.922886a − 0.382642
a
7
=
0.00314429a
5
− 0.0180905a
4
+ ··· + 0.322742a + 1.95515
−0.00104810a
5
+ 0.00603015a
4
+ ··· − 0.107581a + 3.34828
a
9
=
−0.00278536a
5
− 0.00452261a
4
+ ··· + 0.0771141a − 0.382642
0.00278536a
5
+ 0.00452261a
4
+ ··· + 0.922886a + 0.382642
a
8
=
−0.00835607a
5
− 0.0135678a
4
+ ··· − 0.768658a − 1.14793
−0.00278536a
5
− 0.00452261a
4
+ ··· + 0.0771141a − 0.382642
a
12
=
−0.0197559a
5
+ 0.0246231a
4
+ ··· − 1.78810a + 2.72930
−0.0211342a
5
− 0.00854271a
4
+ ··· − 2.20355a − 0.429117
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
776
34825
a
5
−
36
995
a
4
−
4216
6965
a
3
−
3644
6965
a
2
−
117816
34825
a −
106604
34825
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
(u − 1)
6
c
2
(u + 1)
6
c
3
, c
4
, c
9
c
10
(u
2
+ 2)
3
c
6
, c
8
(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
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y −1)
6
c
3
, c
4
, c
9
c
10
(y + 2)
6
c
6
, c
8
(y
3
− y
2
+ 2y −1)
2
c
7
, c
11
, c
12
(y
3
+ 3y
2
+ 2y −1)
2
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −0.87744 + 2.08357I
b = 1.414210I
−9.60386 + 2.82812I −3.50976 − 2.97945I
u = 1.00000
a = −0.87744 − 2.08357I
b = − 1.414210I
−9.60386 − 2.82812I −3.50976 + 2.97945I
u = 1.00000
a = 0.75488 + 2.82843I
b = 1.414210I
−5.46628 3.01951 + 0.I
u = 1.00000
a = 0.75488 − 2.82843I
b = − 1.414210I
−5.46628 3.01951 + 0.I
u = 1.00000
a = −0.87744 + 3.57329I
b = 1.414210I
−9.60386 − 2.82812I −3.50976 + 2.97945I
u = 1.00000
a = −0.87744 − 3.57329I
b = − 1.414210I
−9.60386 + 2.82812I −3.50976 − 2.97945I
17
III. I
u
3
= hb, a
3
+ a
2
− 1, u + 1i
(i) Arc colorings
a
2
=
0
−1
a
5
=
1
0
a
6
=
1
1
a
3
=
1
0
a
1
=
−1
−1
a
10
=
a
0
a
4
=
1
0
a
11
=
a
0
a
7
=
a
2
+ 1
1
a
9
=
a
0
a
8
=
2a
a
a
12
=
2a
2
+ a − 2
a
2
− 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −2a
2
+ 2a + 2
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
3
c
3
, c
4
, c
9
c
10
u
3
c
5
(u + 1)
3
c
6
, c
8
u
3
− u
2
+ 1
c
7
u
3
+ u
2
+ 2u + 1
c
11
, c
12
u
3
− u
2
+ 2u − 1
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y −1)
3
c
3
, c
4
, c
9
c
10
y
3
c
6
, c
8
y
3
− y
2
+ 2y −1
c
7
, c
11
, c
12
y
3
+ 3y
2
+ 2y −1
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = −0.877439 + 0.744862I
b = 0
−4.66906 − 2.82812I −0.18504 + 4.10401I
u = −1.00000
a = −0.877439 − 0.744862I
b = 0
−4.66906 + 2.82812I −0.18504 − 4.10401I
u = −1.00000
a = 0.754878
b = 0
−0.531480 2.37010
21
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
9
)(u
86
+ 42u
85
+ ··· + 8016u + 289)
c
2
((u − 1)
3
)(u + 1)
6
(u
86
+ 4u
85
+ ··· − 20u − 17)
c
3
u
3
(u
2
+ 2)
3
(u
86
− u
85
+ ··· − 8992u + 16424)
c
4
, c
9
, c
10
u
3
(u
2
+ 2)
3
(u
86
+ u
85
+ ··· + 16u + 8)
c
5
((u − 1)
6
)(u + 1)
3
(u
86
+ 4u
85
+ ··· − 20u − 17)
c
6
, c
8
(u
3
− u
2
+ 1)(u
3
+ u
2
− 1)
2
(u
86
+ 2u
85
+ ··· − 11367u − 2391)
c
7
((u
3
− u
2
+ 2u − 1)
2
)(u
3
+ u
2
+ 2u + 1)(u
86
− 2u
85
+ ··· − 3u − 3)
c
11
, c
12
(u
3
− u
2
+ 2u − 1)(u
3
+ u
2
+ 2u + 1)
2
(u
86
− 2u
85
+ ··· − 3u − 3)
22
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
9
)(y
86
+ 14y
85
+ ··· − 1.94636 × 10
7
y + 83521)
c
2
, c
5
((y −1)
9
)(y
86
− 42y
85
+ ··· − 8016y + 289)
c
3
y
3
(y + 2)
6
(y
86
− 5y
85
+ ··· − 1.23422 × 10
9
y + 2.69748 × 10
8
)
c
4
, c
9
, c
10
y
3
(y + 2)
6
(y
86
+ 79y
85
+ ··· − 1280y + 64)
c
6
, c
8
((y
3
− y
2
+ 2y −1)
3
)(y
86
− 56y
85
+ ··· + 6.80871 × 10
7
y + 5716881)
c
7
, c
11
, c
12
((y
3
+ 3y
2
+ 2y −1)
3
)(y
86
+ 72y
85
+ ··· + 51y + 9)
23
