12n
0449
(K12n
0449
)
A knot diagram
1
Linearized knot diagam
3 6 11 10 2 12 4 3 6 8 7 9
Solving Sequence
3,6
2 1
5,10
4 9 8 11 7 12
c
2
c
1
c
5
c
4
c
9
c
8
c
10
c
7
c
12
c
3
, c
6
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−4292389719u
17
+ 51152895286u
16
+ ··· + 4997872592b − 142666014976,
635549962u
17
− 7071211853u
16
+ ··· + 4997872592a + 18555030320,
u
18
− 14u
17
+ ··· − 32u − 64i
I
u
2
= h2861u
12
+ 19240u
11
+ ··· + 3447b − 26153, −10868u
12
− 66331u
11
+ ··· + 17235a + 57767,
u
13
+ 7u
12
+ 18u
11
+ 18u
10
− 5u
9
− 30u
8
− 29u
7
− 5u
6
+ 22u
5
+ 26u
4
− u
3
− 25u
2
− 19u − 5i
I
u
3
= h−48036a
5
u
2
− 192549a
4
u
2
+ ··· − 3719319a − 1942337, a
5
u
2
− 3a
4
u
2
+ ··· + 13a + 8, u
3
+ 2u
2
+ 1i
I
u
4
= hb
2
+ ba + a
2
, a
3
+ a
2
− 1, u − 1i
* 4 irreducible components of dim
C
= 0, with total 55 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−4.29 × 10
9
u
17
+ 5.12 × 10
10
u
16
+ · · · + 5.00 × 10
9
b − 1.43 × 10
11
, 6.36 ×
10
8
u
17
−7.07×10
9
u
16
+· · ·+5.00×10
9
a+1.86×10
10
, u
18
−14u
17
+· · ·−32u−64i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
−u
2
a
1
=
−u
2
+ 1
−u
2
a
5
=
u
−u
3
+ u
a
10
=
−0.127164u
17
+ 1.41484u
16
+ ··· + 2.40021u − 3.71259
0.858843u
17
− 10.2349u
16
+ ··· + 31.2801u + 28.5453
a
4
=
−0.0537381u
17
+ 0.686664u
16
+ ··· − 3.43651u − 1.95932
0.0261593u
17
− 0.244759u
16
+ ··· + 4.59772u + 1.60130
a
9
=
−0.127164u
17
+ 1.41484u
16
+ ··· + 2.40021u − 3.71259
−0.0465960u
17
+ 0.240296u
16
+ ··· + 11.4471u + 5.15636
a
8
=
−0.0805681u
17
+ 1.17455u
16
+ ··· − 9.04691u − 8.86894
−0.0465960u
17
+ 0.240296u
16
+ ··· + 11.4471u + 5.15636
a
11
=
0.161781u
17
− 1.96128u
16
+ ··· + 9.04249u + 3.48865
0.189746u
17
− 2.43818u
16
+ ··· + 14.8327u + 10.0529
a
7
=
0.119990u
17
− 1.53654u
16
+ ··· + 8.62391u + 4.68769
0.458477u
17
− 5.52095u
16
+ ··· + 15.8725u + 14.8725
a
12
=
0.0119305u
17
− 0.112150u
16
+ ··· − 0.757572u + 2.47991
0.0656686u
17
− 0.798814u
16
+ ··· + 3.67894u + 3.43924
(ii) Obstruction class = −1
(iii) Cusp Shapes =
336395251
1249468148
u
17
−
1919281435
624734074
u
16
+ ··· −
4336282305
312367037
u +
1452677222
312367037
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
18
+ 44u
17
+ ··· + 58880u + 4096
c
2
, c
5
u
18
+ 14u
17
+ ··· + 32u − 64
c
3
, c
7
u
18
+ u
17
+ ··· + u + 1
c
4
, c
8
u
18
+ 15u
16
+ ··· − 2u − 1
c
6
, c
11
u
18
− 8u
17
+ ··· + 66u
2
− 4
c
9
, c
12
u
18
+ u
17
+ ··· − 29u − 1
c
10
u
18
− 17u
17
+ ··· − 112u + 8
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
18
− 180y
17
+ ··· − 1103757312y + 16777216
c
2
, c
5
y
18
− 44y
17
+ ··· − 58880y + 4096
c
3
, c
7
y
18
− 9y
17
+ ··· + 3y + 1
c
4
, c
8
y
18
+ 30y
17
+ ··· − 20y + 1
c
6
, c
11
y
18
+ 12y
17
+ ··· − 528y + 16
c
9
, c
12
y
18
+ 43y
17
+ ··· − 425y + 1
c
10
y
18
− 11y
17
+ ··· − 1312y + 64
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.899219
a = −0.0543767
b = 0.529143
−1.46517 −7.81630
u = 1.054770 + 0.455060I
a = −0.286687 + 0.255744I
b = 0.697632 + 0.987067I
−2.44657 − 1.20776I −2.90617 + 2.14647I
u = 1.054770 − 0.455060I
a = −0.286687 − 0.255744I
b = 0.697632 − 0.987067I
−2.44657 + 1.20776I −2.90617 − 2.14647I
u = 1.182210 + 0.365563I
a = −0.196661 − 0.172033I
b = −0.688510 + 0.458421I
−4.86247 − 0.74221I −4.48012 − 1.53917I
u = 1.182210 − 0.365563I
a = −0.196661 + 0.172033I
b = −0.688510 − 0.458421I
−4.86247 + 0.74221I −4.48012 + 1.53917I
u = 0.011252 + 0.650614I
a = 0.249333 + 0.938849I
b = 0.628633 + 0.554074I
−1.41190 − 2.84945I 2.25914 + 3.12009I
u = 0.011252 − 0.650614I
a = 0.249333 − 0.938849I
b = 0.628633 − 0.554074I
−1.41190 + 2.84945I 2.25914 − 3.12009I
u = −1.56372
a = −1.20023
b = 2.20274
−1.13784 −8.76730
u = −1.57964 + 0.17770I
a = 1.028070 + 0.171267I
b = −1.99303 + 0.23309I
−5.95294 + 6.24667I −5.65069 − 4.46750I
u = −1.57964 − 0.17770I
a = 1.028070 − 0.171267I
b = −1.99303 − 0.23309I
−5.95294 − 6.24667I −5.65069 + 4.46750I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.337307 + 0.100488I
a = −1.45027 − 1.37394I
b = −0.205154 − 0.227150I
1.118560 + 0.696320I 7.37877 − 3.46588I
u = −0.337307 − 0.100488I
a = −1.45027 + 1.37394I
b = −0.205154 + 0.227150I
1.118560 − 0.696320I 7.37877 + 3.46588I
u = 2.31673 + 0.16616I
a = 0.176104 − 1.366420I
b = −1.81352 + 4.75613I
17.0902 − 12.5383I −5.56236 + 5.19794I
u = 2.31673 − 0.16616I
a = 0.176104 + 1.366420I
b = −1.81352 − 4.75613I
17.0902 + 12.5383I −5.56236 − 5.19794I
u = 2.30666 + 0.43513I
a = 0.124162 − 1.296380I
b = −3.32718 + 4.18498I
18.8942 + 0.4671I −7.70038 + 0.38231I
u = 2.30666 − 0.43513I
a = 0.124162 + 1.296380I
b = −3.32718 − 4.18498I
18.8942 − 0.4671I −7.70038 − 0.38231I
u = 2.37757 + 0.25374I
a = −0.141746 + 1.335690I
b = 2.33519 − 5.00160I
−17.0153 − 6.5912I −3.54637 + 4.05505I
u = 2.37757 − 0.25374I
a = −0.141746 − 1.335690I
b = 2.33519 + 5.00160I
−17.0153 + 6.5912I −3.54637 − 4.05505I
6
II. I
u
2
= h2861u
12
+ 19240u
11
+ · · · + 3447b − 26153, −10868u
12
−
66331u
11
+ · · · + 17235a + 57767, u
13
+ 7u
12
+ · · · − 19u − 5i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
−u
2
a
1
=
−u
2
+ 1
−u
2
a
5
=
u
−u
3
+ u
a
10
=
0.630577u
12
+ 3.84862u
11
+ ··· − 10.2507u − 3.35173
−0.829997u
12
− 5.58167u
11
+ ··· + 17.5666u + 7.58718
a
4
=
−0.00765883u
12
− 0.137163u
11
+ ··· + 1.89643u − 0.681288
0.0478677u
12
+ 0.190601u
11
+ ··· − 1.76936u − 0.908616
a
9
=
0.630577u
12
+ 3.84862u
11
+ ··· − 10.2507u − 3.35173
−0.321439u
12
− 2.49405u
11
+ ··· + 9.97650u + 4.76008
a
8
=
0.952016u
12
+ 6.34267u
11
+ ··· − 20.2272u − 8.11181
−0.321439u
12
− 2.49405u
11
+ ··· + 9.97650u + 4.76008
a
11
=
0.265390u
12
+ 1.06603u
11
+ ··· + 2.70496u + 4.37534
−1.05628u
12
− 6.69481u
11
+ ··· + 18.3551u + 5.76124
a
7
=
−0.526429u
12
− 2.96321u
11
+ ··· + 4.12620u − 0.318132
−0.0272701u
12
+ 0.319698u
11
+ ··· − 4.18190u − 1.79954
a
12
=
0.0912097u
12
+ 0.512272u
11
+ ··· − 0.0696258u + 1.71958
0.0835509u
12
+ 0.375109u
11
+ ··· + 0.826806u + 0.0382942
(ii) Obstruction class = 1
(iii) Cusp Shapes =
9460
3447
u
12
+
61031
3447
u
11
+ ··· −
23618
383
u −
94159
3447
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
13
− 13u
12
+ ··· + 111u − 25
c
2
u
13
+ 7u
12
+ ··· − 19u − 5
c
3
, c
7
u
13
− u
12
+ ··· + 2u + 1
c
4
, c
8
u
13
+ 9u
11
+ ··· + u + 1
c
5
u
13
− 7u
12
+ ··· − 19u + 5
c
6
u
13
− 3u
12
+ ··· − 10u + 4
c
9
, c
12
u
13
− u
12
+ ··· + 2u − 1
c
10
u
13
+ 8u
12
+ ··· − 99u − 27
c
11
u
13
+ 3u
12
+ ··· − 10u − 4
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
13
− 45y
12
+ ··· − 4029y −625
c
2
, c
5
y
13
− 13y
12
+ ··· + 111y −25
c
3
, c
7
y
13
− 5y
12
+ ··· + 16y −1
c
4
, c
8
y
13
+ 18y
12
+ ··· − 9y −1
c
6
, c
11
y
13
+ 9y
12
+ ··· − 20y −16
c
9
, c
12
y
13
+ 15y
12
+ ··· + 8y
2
− 1
c
10
y
13
− 8y
12
+ ··· + 3807y −729
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.856243 + 0.439666I
a = 0.053687 + 1.058490I
b = 0.666388 − 0.086808I
−5.33979 − 2.00841I −6.30003 + 4.09243I
u = 0.856243 − 0.439666I
a = 0.053687 − 1.058490I
b = 0.666388 + 0.086808I
−5.33979 + 2.00841I −6.30003 − 4.09243I
u = −0.056167 + 1.060590I
a = −0.794885 − 0.705726I
b = −0.85889 − 1.67983I
−3.27208 − 3.50308I −5.03802 + 3.23691I
u = −0.056167 − 1.060590I
a = −0.794885 + 0.705726I
b = −0.85889 + 1.67983I
−3.27208 + 3.50308I −5.03802 − 3.23691I
u = 1.10413
a = 0.938401
b = −0.651589
−0.224822 1.29960
u = −1.074570 + 0.503982I
a = −0.476495 − 0.014009I
b = −0.14184 − 1.44672I
−5.72718 + 8.88579I −3.64178 − 7.62615I
u = −1.074570 − 0.503982I
a = −0.476495 + 0.014009I
b = −0.14184 + 1.44672I
−5.72718 − 8.88579I −3.64178 + 7.62615I
u = −1.033670 + 0.730191I
a = 0.539770 + 0.500315I
b = −1.15414 + 1.81649I
−3.61034 + 0.42465I −7.93042 + 0.83468I
u = −1.033670 − 0.730191I
a = 0.539770 − 0.500315I
b = −1.15414 − 1.81649I
−3.61034 − 0.42465I −7.93042 − 0.83468I
u = −0.537801 + 0.322672I
a = 0.581072 − 0.696232I
b = 0.576934 + 1.237160I
−1.38260 + 4.11097I −0.96481 − 7.32347I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.537801 − 0.322672I
a = 0.581072 + 0.696232I
b = 0.576934 − 1.237160I
−1.38260 − 4.11097I −0.96481 + 7.32347I
u = −2.20610 + 0.12523I
a = 0.027651 − 1.287690I
b = 0.73733 + 3.92048I
−18.3891 − 1.5099I −4.27475 + 0.24744I
u = −2.20610 − 0.12523I
a = 0.027651 + 1.287690I
b = 0.73733 − 3.92048I
−18.3891 + 1.5099I −4.27475 − 0.24744I
11
III. I
u
3
= h−4.80 × 10
4
a
5
u
2
− 1.93 × 10
5
a
4
u
2
+ · · · − 3.72 × 10
6
a − 1.94 ×
10
6
, a
5
u
2
− 3a
4
u
2
+ · · · + 13a + 8, u
3
+ 2u
2
+ 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
−u
2
a
1
=
−u
2
+ 1
−u
2
a
5
=
u
2u
2
+ u + 1
a
10
=
a
0.0107216a
5
u
2
+ 0.0429770a
4
u
2
+ ··· + 0.830153a + 0.433530
a
4
=
−0.0276588a
5
u
2
+ 0.0409242a
4
u
2
+ ··· − 0.707287a + 0.0149656
0.0276588a
5
u
2
− 0.0409242a
4
u
2
+ ··· + 0.707287a + 0.985034
a
9
=
a
0.0107216a
5
u
2
+ 0.0429770a
4
u
2
+ ··· + 0.830153a + 0.433530
a
8
=
−0.0107216a
5
u
2
− 0.0429770a
4
u
2
+ ··· + 0.169847a − 0.433530
0.0107216a
5
u
2
+ 0.0429770a
4
u
2
+ ··· + 0.830153a + 0.433530
a
11
=
−0.114428a
5
u
2
+ 0.0317676a
4
u
2
+ ··· − 0.244681a + 1.20229
0.125150a
5
u
2
+ 0.0112093a
4
u
2
+ ··· + 1.07483a − 0.768759
a
7
=
−0.0212085a
5
u
2
+ 0.145939a
4
u
2
+ ··· − 1.19184a + 0.989840
0.379146a
5
u
2
+ 0.374514a
4
u
2
+ ··· + 0.519904a + 0.992191
a
12
=
−0.135637a
5
u
2
+ 0.177707a
4
u
2
+ ··· − 1.43652a + 2.19213
−0.164698a
5
u
2
+ 0.0554376a
4
u
2
+ ··· + 0.353544a − 1.34279
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
877944
2240141
a
5
u
2
−
2031720
2240141
a
4
u
2
+ ··· +
2110148
2240141
a −
15981979
2240141
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
3
+ 4u
2
− 4u + 1)
6
c
2
, c
5
(u
3
− 2u
2
− 1)
6
c
3
, c
7
u
18
+ 2u
17
+ ··· − 129u
2
+ 27
c
4
, c
8
u
18
+ 20u
16
+ ··· + 180u + 11
c
6
, c
11
(u
3
+ u
2
+ 2u + 1)
6
c
9
, c
12
u
18
− 3u
17
+ ··· + 4276u + 383
c
10
(u
3
+ u
2
− u − 2)
6
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
3
− 24y
2
+ 8y −1)
6
c
2
, c
5
(y
3
− 4y
2
− 4y −1)
6
c
3
, c
7
y
18
− 4y
17
+ ··· − 6966y + 729
c
4
, c
8
y
18
+ 40y
17
+ ··· − 15834y + 121
c
6
, c
11
(y
3
+ 3y
2
+ 2y −1)
6
c
9
, c
12
y
18
+ 49y
17
+ ··· − 7285948y + 146689
c
10
(y
3
− 3y
2
+ 5y −4)
6
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.102785 + 0.665457I
a = −0.271547 + 1.307830I
b = −0.22345 + 1.73716I
−1.13951 − 2.56897I −0.10440 + 2.13317I
u = 0.102785 + 0.665457I
a = −1.48693 − 0.70223I
b = −0.624969 − 0.126877I
−1.13951 − 2.56897I −0.10440 + 2.13317I
u = 0.102785 + 0.665457I
a = 1.56533 + 0.54666I
b = −0.121877 + 0.223759I
−5.27710 − 5.39709I −6.63367 + 5.11262I
u = 0.102785 + 0.665457I
a = −0.029119 + 0.292106I
b = 0.310540 − 1.045640I
−5.27710 + 0.25915I −6.63367 − 0.84628I
u = 0.102785 + 0.665457I
a = 2.67067 + 0.73911I
b = 2.26454 + 0.01108I
−5.27710 + 0.25915I −6.63367 − 0.84628I
u = 0.102785 + 0.665457I
a = −0.11892 − 2.98573I
b = −0.48087 − 2.93264I
−5.27710 − 5.39709I −6.63367 + 5.11262I
u = 0.102785 − 0.665457I
a = −0.271547 − 1.307830I
b = −0.22345 − 1.73716I
−1.13951 + 2.56897I −0.10440 − 2.13317I
u = 0.102785 − 0.665457I
a = −1.48693 + 0.70223I
b = −0.624969 + 0.126877I
−1.13951 + 2.56897I −0.10440 − 2.13317I
u = 0.102785 − 0.665457I
a = 1.56533 − 0.54666I
b = −0.121877 − 0.223759I
−5.27710 + 5.39709I −6.63367 − 5.11262I
u = 0.102785 − 0.665457I
a = −0.029119 − 0.292106I
b = 0.310540 + 1.045640I
−5.27710 − 0.25915I −6.63367 + 0.84628I
15
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.102785 − 0.665457I
a = 2.67067 − 0.73911I
b = 2.26454 − 0.01108I
−5.27710 − 0.25915I −6.63367 + 0.84628I
u = 0.102785 − 0.665457I
a = −0.11892 + 2.98573I
b = −0.48087 + 2.93264I
−5.27710 + 5.39709I −6.63367 − 5.11262I
u = −2.20557
a = −0.132067 + 1.061970I
b = 0.73082 − 2.94300I
19.5761 + 2.8281I −8.26193 − 2.97945I
u = −2.20557
a = −0.132067 − 1.061970I
b = 0.73082 + 2.94300I
19.5761 − 2.8281I −8.26193 + 2.97945I
u = −2.20557
a = 0.248720 + 1.254260I
b = −1.03878 − 3.80675I
−15.7648 −1.73266 + 0.I
u = −2.20557
a = 0.248720 − 1.254260I
b = −1.03878 + 3.80675I
−15.7648 −1.73266 + 0.I
u = −2.20557
a = −0.44614 + 1.55281I
b = 1.68404 − 4.99299I
19.5761 − 2.8281I −8.26193 + 2.97945I
u = −2.20557
a = −0.44614 − 1.55281I
b = 1.68404 + 4.99299I
19.5761 + 2.8281I −8.26193 − 2.97945I
16
IV. I
u
4
= hb
2
+ ba + a
2
, a
3
+ a
2
− 1, u − 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
1
a
2
=
1
−1
a
1
=
0
−1
a
5
=
1
0
a
10
=
a
b
a
4
=
ba + 1
−ba − a
2
a
9
=
a
b + a
a
8
=
−b
b + a
a
11
=
a
b
a
7
=
a
2
+ a − 1
−a
2
b + b + a
a
12
=
a
2
ba + a
2
− 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4a − 3
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
6
c
3
, c
4
, c
7
c
8
u
6
− u
5
+ u
4
− 2u
3
+ u
2
+ 1
c
5
(u + 1)
6
c
6
(u
3
+ u
2
+ 2u + 1)
2
c
9
, c
12
(u
3
+ u
2
− 1)
2
c
10
u
6
c
11
(u
3
− u
2
+ 2u − 1)
2
18
(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
7
c
8
y
6
+ y
5
− y
4
+ 3y
2
+ 2y + 1
c
6
, c
11
(y
3
+ 3y
2
+ 2y −1)
2
c
9
, c
12
(y
3
− y
2
+ 2y −1)
2
c
10
y
6
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −0.877439 + 0.744862I
b = 1.083790 + 0.387453I
−4.66906 − 2.82812I −6.50976 + 2.97945I
u = 1.00000
a = −0.877439 + 0.744862I
b = −0.206350 − 1.132320I
−4.66906 − 2.82812I −6.50976 + 2.97945I
u = 1.00000
a = −0.877439 − 0.744862I
b = 1.083790 − 0.387453I
−4.66906 + 2.82812I −6.50976 − 2.97945I
u = 1.00000
a = −0.877439 − 0.744862I
b = −0.206350 + 1.132320I
−4.66906 + 2.82812I −6.50976 − 2.97945I
u = 1.00000
a = 0.754878
b = −0.377439 + 0.653743I
−0.531480 0.0195110
u = 1.00000
a = 0.754878
b = −0.377439 − 0.653743I
−0.531480 0.0195110
20
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
6
)(u
3
+ 4u
2
− 4u + 1)
6
(u
13
− 13u
12
+ ··· + 111u − 25)
· (u
18
+ 44u
17
+ ··· + 58880u + 4096)
c
2
((u − 1)
6
)(u
3
− 2u
2
− 1)
6
(u
13
+ 7u
12
+ ··· − 19u − 5)
· (u
18
+ 14u
17
+ ··· + 32u − 64)
c
3
, c
7
(u
6
− u
5
+ u
4
− 2u
3
+ u
2
+ 1)(u
13
− u
12
+ ··· + 2u + 1)
· (u
18
+ u
17
+ ··· + u + 1)(u
18
+ 2u
17
+ ··· − 129u
2
+ 27)
c
4
, c
8
(u
6
− u
5
+ u
4
− 2u
3
+ u
2
+ 1)(u
13
+ 9u
11
+ ··· + u + 1)
· (u
18
+ 15u
16
+ ··· − 2u − 1)(u
18
+ 20u
16
+ ··· + 180u + 11)
c
5
((u + 1)
6
)(u
3
− 2u
2
− 1)
6
(u
13
− 7u
12
+ ··· − 19u + 5)
· (u
18
+ 14u
17
+ ··· + 32u − 64)
c
6
((u
3
+ u
2
+ 2u + 1)
8
)(u
13
− 3u
12
+ ··· − 10u + 4)
· (u
18
− 8u
17
+ ··· + 66u
2
− 4)
c
9
, c
12
((u
3
+ u
2
− 1)
2
)(u
13
− u
12
+ ··· + 2u − 1)
· (u
18
− 3u
17
+ ··· + 4276u + 383)(u
18
+ u
17
+ ··· − 29u − 1)
c
10
u
6
(u
3
+ u
2
− u − 2)
6
(u
13
+ 8u
12
+ ··· − 99u − 27)
· (u
18
− 17u
17
+ ··· − 112u + 8)
c
11
((u
3
− u
2
+ 2u − 1)
2
)(u
3
+ u
2
+ 2u + 1)
6
(u
13
+ 3u
12
+ ··· − 10u − 4)
· (u
18
− 8u
17
+ ··· + 66u
2
− 4)
21
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
6
)(y
3
− 24y
2
+ 8y −1)
6
(y
13
− 45y
12
+ ··· − 4029y −625)
· (y
18
− 180y
17
+ ··· − 1103757312y + 16777216)
c
2
, c
5
((y −1)
6
)(y
3
− 4y
2
− 4y −1)
6
(y
13
− 13y
12
+ ··· + 111y −25)
· (y
18
− 44y
17
+ ··· − 58880y + 4096)
c
3
, c
7
(y
6
+ y
5
− y
4
+ 3y
2
+ 2y + 1)(y
13
− 5y
12
+ ··· + 16y −1)
· (y
18
− 9y
17
+ ··· + 3y + 1)(y
18
− 4y
17
+ ··· − 6966y + 729)
c
4
, c
8
(y
6
+ y
5
− y
4
+ 3y
2
+ 2y + 1)(y
13
+ 18y
12
+ ··· − 9y −1)
· (y
18
+ 30y
17
+ ··· − 20y + 1)(y
18
+ 40y
17
+ ··· − 15834y + 121)
c
6
, c
11
((y
3
+ 3y
2
+ 2y −1)
8
)(y
13
+ 9y
12
+ ··· − 20y −16)
· (y
18
+ 12y
17
+ ··· − 528y + 16)
c
9
, c
12
((y
3
− y
2
+ 2y −1)
2
)(y
13
+ 15y
12
+ ··· + 8y
2
− 1)
· (y
18
+ 43y
17
+ ··· − 425y + 1)
· (y
18
+ 49y
17
+ ··· − 7285948y + 146689)
c
10
y
6
(y
3
− 3y
2
+ 5y −4)
6
(y
13
− 8y
12
+ ··· + 3807y −729)
· (y
18
− 11y
17
+ ··· − 1312y + 64)
22
