12n
0412
(K12n
0412
)
A knot diagram
1
Linearized knot diagam
3 6 11 7 2 10 3 12 6 4 8 9
Solving Sequence
3,11 4,6
2 1 5 10 7 8 9 12
c
3
c
2
c
1
c
5
c
10
c
6
c
7
c
9
c
12
c
4
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.84897 × 10
24
u
44
− 2.54096 × 10
24
u
43
+ ··· + 3.58820 × 10
24
b + 5.26379 × 10
24
,
1.76545 × 10
23
u
44
+ 3.27410 × 10
23
u
43
+ ··· + 4.32313 × 10
22
a + 2.31306 × 10
23
, u
45
+ 2u
44
+ ··· + 8u − 1i
I
u
2
= h−u
12
+ u
11
− 6u
10
+ 5u
9
− 12u
8
+ 9u
7
− 6u
6
+ 6u
5
+ 6u
4
+ 3u
2
+ b − u − 1,
2u
12
− u
11
+ 11u
10
− 4u
9
+ 20u
8
− 6u
7
+ 7u
6
− 6u
5
− 14u
4
− 7u
3
− 10u
2
+ a − 4u − 2,
u
13
− u
12
+ 7u
11
− 6u
10
+ 18u
9
− 14u
8
+ 18u
7
− 15u
6
− 6u
4
− 9u
3
+ u
2
− 2u + 1i
I
u
3
= h−u
2
+ b, a − 1, u
4
− u
3
+ 2u
2
− 2u + 1i
I
u
4
= hb − 1, a − 1, u + 1i
* 4 irreducible components of dim
C
= 0, with total 63 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−1.85×10
24
u
44
−2.54×10
24
u
43
+· · ·+3.59×10
24
b+5.26×10
24
, 1.77×
10
23
u
44
+3.27×10
23
u
43
+· · ·+4.32×10
22
a+2.31×10
23
, u
45
+2u
44
+· · ·+8u−1i
(i) Arc colorings
a
3
=
1
0
a
11
=
0
u
a
4
=
1
u
2
a
6
=
−4.08374u
44
− 7.57346u
43
+ ··· − 218.809u − 5.35044
0.515292u
44
+ 0.708144u
43
+ ··· + 6.15932u − 1.46697
a
2
=
2.87916u
44
+ 5.44800u
43
+ ··· + 83.3782u − 24.3626
−1.12930u
44
− 2.18153u
43
+ ··· − 42.3482u + 3.36146
a
1
=
1.74987u
44
+ 3.26646u
43
+ ··· + 41.0300u − 21.0011
−1.12930u
44
− 2.18153u
43
+ ··· − 42.3482u + 3.36146
a
5
=
2.61866u
44
+ 4.36589u
43
+ ··· + 46.2417u − 15.9362
−2.70869u
44
− 4.60335u
43
+ ··· − 87.4930u + 7.47428
a
10
=
u
u
3
+ u
a
7
=
−3.56455u
44
− 6.80670u
43
+ ··· − 206.802u − 6.30618
1.00518u
44
+ 1.76026u
43
+ ··· + 20.8578u − 2.69432
a
8
=
−2.55937u
44
− 5.04644u
43
+ ··· − 185.944u − 9.00050
1.00518u
44
+ 1.76026u
43
+ ··· + 20.8578u − 2.69432
a
9
=
−1.96341u
44
− 3.93259u
43
+ ··· − 196.681u − 18.9609
−1.50697u
44
− 2.36388u
43
+ ··· − 62.6688u + 4.32930
a
12
=
4.25404u
44
+ 7.98425u
43
+ ··· + 282.601u + 14.5444
−0.0622841u
44
− 1.08570u
43
+ ··· + 10.5596u + 0.527328
(ii) Obstruction class = −1
(iii) Cusp Shapes =
20998050926369734752976211
3588196003166548679987327
u
44
+
37483540873690423560378912
3588196003166548679987327
u
43
+
··· +
1213475306781566067904042936
3588196003166548679987327
u −
19958410998607784963592834
3588196003166548679987327
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
45
+ 48u
44
+ ··· + 584u + 1
c
2
, c
5
u
45
+ 4u
44
+ ··· − 42u + 1
c
3
, c
10
u
45
+ 2u
44
+ ··· + 8u − 1
c
4
u
45
+ 9u
44
+ ··· + 1549u + 311
c
6
, c
9
u
45
− 4u
44
+ ··· − 15u − 1
c
7
u
45
+ 3u
44
+ ··· − 8958u + 563
c
8
, c
11
, c
12
u
45
+ 4u
44
+ ··· + 58u + 28
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
45
− 96y
44
+ ··· + 113992y −1
c
2
, c
5
y
45
− 48y
44
+ ··· + 584y −1
c
3
, c
10
y
45
+ 42y
44
+ ··· + 252y −1
c
4
y
45
+ 9y
44
+ ··· − 3165011y −96721
c
6
, c
9
y
45
− 12y
44
+ ··· + 105y −1
c
7
y
45
− y
44
+ ··· + 19794202y −316969
c
8
, c
11
, c
12
y
45
− 36y
44
+ ··· − 1060y −784
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.969825
a = 0.229176
b = 0.627201
2.96038 −2.69630
u = −0.927844 + 0.271505I
a = −1.041520 − 0.768905I
b = −1.52557 + 0.45145I
−4.45709 + 9.42399I 1.94019 − 6.31293I
u = −0.927844 − 0.271505I
a = −1.041520 + 0.768905I
b = −1.52557 − 0.45145I
−4.45709 − 9.42399I 1.94019 + 6.31293I
u = 0.845626 + 0.121557I
a = −1.42589 + 0.88397I
b = −1.59489 − 0.20003I
−8.64870 − 3.87589I −1.85841 + 2.88964I
u = 0.845626 − 0.121557I
a = −1.42589 − 0.88397I
b = −1.59489 + 0.20003I
−8.64870 + 3.87589I −1.85841 − 2.88964I
u = −0.164418 + 1.159280I
a = 0.703495 − 0.012931I
b = −0.763782 − 0.015983I
1.53495 + 1.91036I 0
u = −0.164418 − 1.159280I
a = 0.703495 + 0.012931I
b = −0.763782 + 0.015983I
1.53495 − 1.91036I 0
u = −0.669119 + 1.011720I
a = −0.065566 + 0.383511I
b = 1.37234 + 0.41380I
−2.27065 − 3.93661I 0
u = −0.669119 − 1.011720I
a = −0.065566 − 0.383511I
b = 1.37234 − 0.41380I
−2.27065 + 3.93661I 0
u = 0.433424 + 1.140140I
a = 0.033142 − 0.457634I
b = 1.53847 − 0.16157I
−5.53838 − 0.69987I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.433424 − 1.140140I
a = 0.033142 + 0.457634I
b = 1.53847 + 0.16157I
−5.53838 + 0.69987I 0
u = 0.664310 + 0.362711I
a = 0.328543 − 0.232382I
b = 0.261717 + 1.042650I
1.25167 − 3.95167I 3.83579 + 7.35409I
u = 0.664310 − 0.362711I
a = 0.328543 + 0.232382I
b = 0.261717 − 1.042650I
1.25167 + 3.95167I 3.83579 − 7.35409I
u = 0.186812 + 1.238700I
a = −0.67404 + 1.33349I
b = −0.0820505 − 0.0136120I
4.44974 − 2.14104I 0
u = 0.186812 − 1.238700I
a = −0.67404 − 1.33349I
b = −0.0820505 + 0.0136120I
4.44974 + 2.14104I 0
u = −0.277987 + 1.263490I
a = −0.29175 + 2.28733I
b = 1.44630 + 0.06917I
−0.68250 + 1.70775I 0
u = −0.277987 − 1.263490I
a = −0.29175 − 2.28733I
b = 1.44630 − 0.06917I
−0.68250 − 1.70775I 0
u = −0.042319 + 1.295400I
a = 1.92633 − 1.12849I
b = −1.43287 + 0.42714I
1.71514 + 2.64308I 0
u = −0.042319 − 1.295400I
a = 1.92633 + 1.12849I
b = −1.43287 − 0.42714I
1.71514 − 2.64308I 0
u = −0.698216 + 0.025057I
a = −2.07891 + 1.01497I
b = −1.51929 + 0.08671I
−4.51834 + 1.81580I −0.317984 − 1.183332I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.698216 − 0.025057I
a = −2.07891 − 1.01497I
b = −1.51929 − 0.08671I
−4.51834 − 1.81580I −0.317984 + 1.183332I
u = 0.022131 + 1.309670I
a = −0.56784 − 1.95572I
b = 0.735072 + 0.094789I
11.93010 − 0.31866I 0
u = 0.022131 − 1.309670I
a = −0.56784 + 1.95572I
b = 0.735072 − 0.094789I
11.93010 + 0.31866I 0
u = −0.283028 + 1.297280I
a = 0.178492 + 0.638649I
b = 1.58589 − 0.07568I
−0.37999 + 5.35975I 0
u = −0.283028 − 1.297280I
a = 0.178492 − 0.638649I
b = 1.58589 + 0.07568I
−0.37999 − 5.35975I 0
u = −0.597996 + 0.198058I
a = 0.565513 + 0.398750I
b = 0.610778 − 0.503827I
−1.21115 + 0.91442I −3.60220 − 2.86568I
u = −0.597996 − 0.198058I
a = 0.565513 − 0.398750I
b = 0.610778 + 0.503827I
−1.21115 − 0.91442I −3.60220 + 2.86568I
u = 0.373344 + 1.342530I
a = 0.355758 − 0.038695I
b = −0.554848 + 0.011852I
7.39338 − 4.75135I 0
u = 0.373344 − 1.342530I
a = 0.355758 + 0.038695I
b = −0.554848 − 0.011852I
7.39338 + 4.75135I 0
u = 0.364735 + 1.347540I
a = −0.11146 − 1.99685I
b = 1.62752 + 0.23183I
−4.02855 − 8.22129I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.364735 − 1.347540I
a = −0.11146 + 1.99685I
b = 1.62752 − 0.23183I
−4.02855 + 8.22129I 0
u = −0.224203 + 1.388850I
a = −0.14008 − 1.68654I
b = −0.683694 + 1.023800I
3.89960 + 3.89681I 0
u = −0.224203 − 1.388850I
a = −0.14008 + 1.68654I
b = −0.683694 − 1.023800I
3.89960 − 3.89681I 0
u = −0.42343 + 1.35553I
a = −0.257759 − 1.007550I
b = −0.974975 + 0.080869I
6.02639 + 5.09405I 0
u = −0.42343 − 1.35553I
a = −0.257759 + 1.007550I
b = −0.974975 − 0.080869I
6.02639 − 5.09405I 0
u = 0.26016 + 1.44165I
a = −0.50945 + 1.62773I
b = −0.22976 − 1.42824I
7.03160 − 7.34948I 0
u = 0.26016 − 1.44165I
a = −0.50945 − 1.62773I
b = −0.22976 + 1.42824I
7.03160 + 7.34948I 0
u = −0.38297 + 1.43752I
a = −0.11849 + 1.78135I
b = 1.60904 − 0.50615I
0.9685 + 14.1285I 0
u = −0.38297 − 1.43752I
a = −0.11849 − 1.78135I
b = 1.60904 + 0.50615I
0.9685 − 14.1285I 0
u = 0.15138 + 1.55206I
a = 0.159781 + 1.093010I
b = −0.865603 − 0.853905I
8.49461 − 3.13739I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.15138 − 1.55206I
a = 0.159781 − 1.093010I
b = −0.865603 + 0.853905I
8.49461 + 3.13739I 0
u = 0.331161
a = 1.93794
b = −0.0592996
0.981240 11.9230
u = −0.294649 + 0.018682I
a = 1.26352 + 2.17214I
b = 1.52527 − 0.31408I
−2.46259 + 1.58513I −5.29016 − 4.20356I
u = −0.294649 − 0.018682I
a = 1.26352 − 2.17214I
b = 1.52527 + 0.31408I
−2.46259 − 1.58513I −5.29016 + 4.20356I
u = 0.0675368
a = −22.6308
b = −0.738031
7.70079 22.1050
9
II.
I
u
2
= h−u
12
+u
11
+· · · +b − 1, 2u
12
−u
11
+· · · +a − 2, u
13
−u
12
+· · · −2u + 1i
(i) Arc colorings
a
3
=
1
0
a
11
=
0
u
a
4
=
1
u
2
a
6
=
−2u
12
+ u
11
+ ··· + 4u + 2
u
12
− u
11
+ 6u
10
− 5u
9
+ 12u
8
− 9u
7
+ 6u
6
− 6u
5
− 6u
4
− 3u
2
+ u + 1
a
2
=
−2u
12
+ 2u
11
+ ··· − 6u − 1
u
12
− u
11
+ 5u
10
− 4u
9
+ 7u
8
− 5u
7
− u
6
− u
5
− 5u
4
+ u
3
+ 2u
2
− 1
a
1
=
−u
12
+ u
11
+ ··· − 6u − 2
u
12
− u
11
+ 5u
10
− 4u
9
+ 7u
8
− 5u
7
− u
6
− u
5
− 5u
4
+ u
3
+ 2u
2
− 1
a
5
=
3u
12
− 2u
11
+ ··· − u + 3
−3u
12
+ 3u
11
+ ··· + 8u
2
− 3u
a
10
=
u
u
3
+ u
a
7
=
−2u
12
+ 2u
11
+ ··· + 3u + 2
u
12
− 2u
11
+ ··· − 4u
2
+ 2u
a
8
=
−u
12
− 5u
10
− u
9
− 8u
8
− 3u
7
− u
6
+ 8u
4
+ 7u
3
+ 6u
2
+ 5u + 2
u
12
− 2u
11
+ ··· − 4u
2
+ 2u
a
9
=
2u
12
− 2u
11
+ ··· − u − 5
u
12
− u
11
+ ··· + 2u − 1
a
12
=
−2u
12
+ 2u
11
+ ··· + 2u + 4
u
12
− 2u
11
+ ··· + 4u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes
= 4u
12
− 7u
11
+ 29u
10
− 36u
9
+ 73u
8
− 64u
7
+ 69u
6
− 36u
5
− 4u
4
+ 5u
3
− 37u
2
− 5
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
13
− 13u
12
+ ··· + 10u − 1
c
2
u
13
+ 3u
12
+ ··· + 5u
2
− 1
c
3
u
13
− u
12
+ ··· − 2u + 1
c
4
u
13
− 4u
11
+ ··· + 9u + 1
c
5
u
13
− 3u
12
+ ··· − 5u
2
+ 1
c
6
u
13
− 3u
12
+ 5u
10
− u
8
− 5u
7
− 2u
6
+ 6u
5
− u
3
− u
2
− u + 1
c
7
u
13
− 7u
11
+ ··· + 2u + 1
c
8
u
13
− 8u
11
+ ··· + 6u
2
− 1
c
9
u
13
+ 3u
12
− 5u
10
+ u
8
− 5u
7
+ 2u
6
+ 6u
5
− u
3
+ u
2
− u − 1
c
10
u
13
+ u
12
+ ··· − 2u − 1
c
11
, c
12
u
13
− 8u
11
+ ··· − 6u
2
+ 1
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
13
− 21y
12
+ ··· + 18y −1
c
2
, c
5
y
13
− 13y
12
+ ··· + 10y −1
c
3
, c
10
y
13
+ 13y
12
+ ··· + 2y −1
c
4
y
13
− 8y
12
+ ··· + 31y −1
c
6
, c
9
y
13
− 9y
12
+ ··· + 3y −1
c
7
y
13
− 14y
12
+ ··· + 44y −1
c
8
, c
11
, c
12
y
13
− 16y
12
+ ··· + 12y −1
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.07246
a = 0.492294
b = 0.465079
3.43265 15.5060
u = −0.034598 + 1.249270I
a = 1.56218 − 1.13850I
b = −1.74571 + 0.26973I
0.86628 + 1.87846I 2.04855 − 1.94061I
u = −0.034598 − 1.249270I
a = 1.56218 + 1.13850I
b = −1.74571 − 0.26973I
0.86628 − 1.87846I 2.04855 + 1.94061I
u = −0.686240
a = 1.32157
b = 0.679844
0.244931 −2.02350
u = 0.131294 + 1.356980I
a = 0.02881 + 1.98048I
b = −1.022270 − 0.441982I
11.95140 − 1.70968I 8.67976 + 4.17356I
u = 0.131294 − 1.356980I
a = 0.02881 − 1.98048I
b = −1.022270 + 0.441982I
11.95140 + 1.70968I 8.67976 − 4.17356I
u = −0.250597 + 1.356050I
a = −0.34025 − 1.50111I
b = −0.729247 + 0.638631I
4.69917 + 3.36697I 7.60609 − 2.02916I
u = −0.250597 − 1.356050I
a = −0.34025 + 1.50111I
b = −0.729247 − 0.638631I
4.69917 − 3.36697I 7.60609 + 2.02916I
u = −0.103530 + 0.564621I
a = 0.205252 + 1.185250I
b = 1.40513 + 0.23742I
−1.72775 − 1.40884I 6.28546 + 0.80673I
u = −0.103530 − 0.564621I
a = 0.205252 − 1.185250I
b = 1.40513 − 0.23742I
−1.72775 + 1.40884I 6.28546 − 0.80673I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.39553 + 1.43394I
a = −0.341272 + 0.786047I
b = −0.429218 − 0.541128I
8.26062 − 5.29255I 11.21555 + 5.90616I
u = 0.39553 − 1.43394I
a = −0.341272 − 0.786047I
b = −0.429218 + 0.541128I
8.26062 + 5.29255I 11.21555 − 5.90616I
u = 0.337585
a = 4.95670
b = 0.897695
7.44054 −9.15310
14
III. I
u
3
= h−u
2
+ b, a − 1, u
4
− u
3
+ 2u
2
− 2u + 1i
(i) Arc colorings
a
3
=
1
0
a
11
=
0
u
a
4
=
1
u
2
a
6
=
1
u
2
a
2
=
−u
2
+ 1
−u
3
+ 2u
2
− 2u + 1
a
1
=
−u
3
+ u
2
− 2u + 2
−u
3
+ 2u
2
− 2u + 1
a
5
=
−u
3
+ 3u
2
− 2u + 2
u
3
− 2u
2
+ 3u − 1
a
10
=
u
u
3
+ u
a
7
=
−u
2
+ 1
−u
3
+ 2u
2
− 2u + 1
a
8
=
−u
3
+ u
2
− 2u + 2
−u
3
+ 2u
2
− 2u + 1
a
9
=
0
u
a
12
=
−u
3
+ u
2
− 2u + 2
−u
3
+ 2u
2
− u + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 6
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
4
+ 5u
3
+ 6u
2
− 4u + 1
c
2
, c
5
u
4
− 3u
3
+ 2u
2
+ 1
c
3
, c
6
, c
9
c
10
u
4
− u
3
+ 2u
2
− 2u + 1
c
4
u
4
+ 3u
3
+ 2u
2
+ 1
c
7
u
4
− 5u
3
+ 6u
2
+ 4u + 1
c
8
, c
11
, c
12
(u − 1)
4
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
4
− 13y
3
+ 78y
2
− 4y + 1
c
2
, c
4
, c
5
y
4
− 5y
3
+ 6y
2
+ 4y + 1
c
3
, c
6
, c
9
c
10
y
4
+ 3y
3
+ 2y
2
+ 1
c
8
, c
11
, c
12
(y −1)
4
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.621744 + 0.440597I
a = 1.00000
b = 0.192440 + 0.547877I
1.64493 6.00000
u = 0.621744 − 0.440597I
a = 1.00000
b = 0.192440 − 0.547877I
1.64493 6.00000
u = −0.121744 + 1.306620I
a = 1.00000
b = −1.69244 − 0.31815I
1.64493 6.00000
u = −0.121744 − 1.306620I
a = 1.00000
b = −1.69244 + 0.31815I
1.64493 6.00000
18
IV. I
u
4
= hb − 1, a − 1, u + 1i
(i) Arc colorings
a
3
=
1
0
a
11
=
0
−1
a
4
=
1
1
a
6
=
1
1
a
2
=
0
−1
a
1
=
−1
−1
a
5
=
1
0
a
10
=
−1
−2
a
7
=
0
−1
a
8
=
−1
−1
a
9
=
0
−1
a
12
=
−1
−2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 6
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
5
, c
6
, c
9
c
10
u + 1
c
4
, c
7
, c
8
c
11
, c
12
u − 1
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
7
, c
8
, c
9
c
10
, c
11
, c
12
y −1
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 1.00000
b = 1.00000
1.64493 6.00000
22
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u + 1)(u
4
+ 5u
3
+ ··· − 4u + 1)(u
13
− 13u
12
+ ··· + 10u − 1)
· (u
45
+ 48u
44
+ ··· + 584u + 1)
c
2
(u + 1)(u
4
− 3u
3
+ 2u
2
+ 1)(u
13
+ 3u
12
+ ··· + 5u
2
− 1)
· (u
45
+ 4u
44
+ ··· − 42u + 1)
c
3
(u + 1)(u
4
− u
3
+ 2u
2
− 2u + 1)(u
13
− u
12
+ ··· − 2u + 1)
· (u
45
+ 2u
44
+ ··· + 8u − 1)
c
4
(u − 1)(u
4
+ 3u
3
+ 2u
2
+ 1)(u
13
− 4u
11
+ ··· + 9u + 1)
· (u
45
+ 9u
44
+ ··· + 1549u + 311)
c
5
(u + 1)(u
4
− 3u
3
+ 2u
2
+ 1)(u
13
− 3u
12
+ ··· − 5u
2
+ 1)
· (u
45
+ 4u
44
+ ··· − 42u + 1)
c
6
(u + 1)(u
4
− u
3
+ 2u
2
− 2u + 1)
· (u
13
− 3u
12
+ 5u
10
− u
8
− 5u
7
− 2u
6
+ 6u
5
− u
3
− u
2
− u + 1)
· (u
45
− 4u
44
+ ··· − 15u − 1)
c
7
(u − 1)(u
4
− 5u
3
+ ··· + 4u + 1)(u
13
− 7u
11
+ ··· + 2u + 1)
· (u
45
+ 3u
44
+ ··· − 8958u + 563)
c
8
((u − 1)
5
)(u
13
− 8u
11
+ ··· + 6u
2
− 1)(u
45
+ 4u
44
+ ··· + 58u + 28)
c
9
(u + 1)(u
4
− u
3
+ 2u
2
− 2u + 1)
· (u
13
+ 3u
12
− 5u
10
+ u
8
− 5u
7
+ 2u
6
+ 6u
5
− u
3
+ u
2
− u − 1)
· (u
45
− 4u
44
+ ··· − 15u − 1)
c
10
(u + 1)(u
4
− u
3
+ 2u
2
− 2u + 1)(u
13
+ u
12
+ ··· − 2u − 1)
· (u
45
+ 2u
44
+ ··· + 8u − 1)
c
11
, c
12
((u − 1)
5
)(u
13
− 8u
11
+ ··· − 6u
2
+ 1)(u
45
+ 4u
44
+ ··· + 58u + 28)
23
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y −1)(y
4
− 13y
3
+ ··· − 4y + 1)(y
13
− 21y
12
+ ··· + 18y −1)
· (y
45
− 96y
44
+ ··· + 113992y −1)
c
2
, c
5
(y −1)(y
4
− 5y
3
+ ··· + 4y + 1)(y
13
− 13y
12
+ ··· + 10y −1)
· (y
45
− 48y
44
+ ··· + 584y −1)
c
3
, c
10
(y −1)(y
4
+ 3y
3
+ 2y
2
+ 1)(y
13
+ 13y
12
+ ··· + 2y −1)
· (y
45
+ 42y
44
+ ··· + 252y −1)
c
4
(y −1)(y
4
− 5y
3
+ ··· + 4y + 1)(y
13
− 8y
12
+ ··· + 31y −1)
· (y
45
+ 9y
44
+ ··· − 3165011y −96721)
c
6
, c
9
(y −1)(y
4
+ 3y
3
+ 2y
2
+ 1)(y
13
− 9y
12
+ ··· + 3y −1)
· (y
45
− 12y
44
+ ··· + 105y −1)
c
7
(y −1)(y
4
− 13y
3
+ ··· − 4y + 1)(y
13
− 14y
12
+ ··· + 44y −1)
· (y
45
− y
44
+ ··· + 19794202y −316969)
c
8
, c
11
, c
12
((y −1)
5
)(y
13
− 16y
12
+ ··· + 12y −1)
· (y
45
− 36y
44
+ ··· − 1060y −784)
24
