12n
0747
(K12n
0747
)
A knot diagram
1
Linearized knot diagam
4 5 7 10 3 12 4 12 1 5 6 9
Solving Sequence
9,12 1,4
2 10 5 8 7 3 6 11
c
12
c
1
c
9
c
4
c
8
c
7
c
3
c
6
c
11
c
2
, c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.18510 × 10
87
u
63
+ 3.43048 × 10
87
u
62
+ ··· + 1.06222 × 10
86
b + 4.40024 × 10
87
,
1.30342 × 10
88
u
63
− 1.96828 × 10
88
u
62
+ ··· + 1.06222 × 10
86
a − 2.56911 × 10
88
, u
64
− 2u
63
+ ··· − 23u + 1i
I
u
2
= hu
5
− u
4
− 3u
3
+ u
2
+ b + 2u + 1, 2u
9
− 2u
8
− 12u
7
+ 9u
6
+ 24u
5
− 11u
4
− 17u
3
+ a + 2u + 6,
u
10
− u
9
− 6u
8
+ 4u
7
+ 13u
6
− 4u
5
− 11u
4
− 2u
3
+ 2u
2
+ 4u + 1i
I
u
3
= hb + a + u + 1, a
2
+ au + 3a + u + 1, u
2
+ u − 1i
* 3 irreducible components of dim
C
= 0, with total 78 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−2.19 × 10
87
u
63
+ 3.43 × 10
87
u
62
+ · · · + 1.06 × 10
86
b + 4.40 ×
10
87
, 1.30 × 10
88
u
63
− 1.97 × 10
88
u
62
+ · · · + 1.06 × 10
86
a − 2.57 ×
10
88
, u
64
− 2u
63
+ · · · − 23u + 1i
(i) Arc colorings
a
9
=
0
u
a
12
=
1
0
a
1
=
1
−u
2
a
4
=
−122.708u
63
+ 185.299u
62
+ ··· − 5249.53u + 241.862
20.5711u
63
− 32.2954u
62
+ ··· + 884.457u − 41.4249
a
2
=
80.9216u
63
− 120.495u
62
+ ··· + 3818.05u − 185.936
−10.4054u
63
+ 15.9135u
62
+ ··· − 498.812u + 22.3121
a
10
=
u
−u
3
+ u
a
5
=
−97.7534u
63
+ 145.797u
62
+ ··· − 4117.81u + 187.718
42.6309u
63
− 64.8314u
62
+ ··· + 1801.77u − 85.1621
a
8
=
−u
u
a
7
=
−44.4529u
63
+ 65.0075u
62
+ ··· − 1944.92u + 88.7000
−21.8652u
63
+ 33.1776u
62
+ ··· − 951.044u + 46.6180
a
3
=
148.216u
63
− 219.442u
62
+ ··· + 6319.96u − 310.655
−26.4978u
63
+ 40.7839u
62
+ ··· − 1214.82u + 58.2926
a
6
=
−66.3181u
63
+ 98.1851u
62
+ ··· − 2895.96u + 135.318
−21.8652u
63
+ 33.1776u
62
+ ··· − 951.044u + 46.6180
a
11
=
−17.7302u
63
+ 25.0723u
62
+ ··· − 616.299u + 35.7654
51.1592u
63
− 77.8247u
62
+ ··· + 2236.56u − 107.971
(ii) Obstruction class = −1
(iii) Cusp Shapes = 812.905u
63
− 1227.04u
62
+ ··· + 34392.6u − 1624.68
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
64
− 6u
63
+ ··· + 392u + 49
c
2
, c
5
u
64
− 2u
63
+ ··· + 14u + 1
c
3
, c
7
u
64
− u
63
+ ··· − 30u + 7
c
4
, c
10
u
64
− 2u
63
+ ··· − 649u − 23
c
6
, c
11
u
64
− u
63
+ ··· + 16u + 1
c
8
, c
9
, c
12
u
64
− 2u
63
+ ··· − 23u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
64
− 10y
63
+ ··· − 254506y + 2401
c
2
, c
5
y
64
− 18y
63
+ ··· − 60y + 1
c
3
, c
7
y
64
− 21y
63
+ ··· − 3056y + 49
c
4
, c
10
y
64
− 28y
63
+ ··· − 464395y + 529
c
6
, c
11
y
64
− 51y
63
+ ··· − 312y + 1
c
8
, c
9
, c
12
y
64
− 58y
63
+ ··· + 39y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.145672 + 0.968068I
a = 0.158850 − 0.010710I
b = −0.509053 + 0.675145I
1.07637 + 4.19054I 0
u = 0.145672 − 0.968068I
a = 0.158850 + 0.010710I
b = −0.509053 − 0.675145I
1.07637 − 4.19054I 0
u = −0.317235 + 1.010710I
a = −0.0311390 + 0.0511144I
b = −1.146370 − 0.672425I
−4.56279 − 10.69090I 0
u = −0.317235 − 1.010710I
a = −0.0311390 − 0.0511144I
b = −1.146370 + 0.672425I
−4.56279 + 10.69090I 0
u = −0.317994 + 0.869749I
a = 0.0728894 + 0.0793513I
b = 1.254910 + 0.487312I
−6.15152 − 3.00155I 0
u = −0.317994 − 0.869749I
a = 0.0728894 − 0.0793513I
b = 1.254910 − 0.487312I
−6.15152 + 3.00155I 0
u = −0.950390 + 0.519722I
a = 0.594935 + 1.039960I
b = −0.623717 + 0.052076I
−4.21641 − 1.93351I 0
u = −0.950390 − 0.519722I
a = 0.594935 − 1.039960I
b = −0.623717 − 0.052076I
−4.21641 + 1.93351I 0
u = −0.017192 + 0.901588I
a = 0.068027 + 0.657514I
b = −1.070960 + 0.469701I
−5.87061 + 3.95242I 0
u = −0.017192 − 0.901588I
a = 0.068027 − 0.657514I
b = −1.070960 − 0.469701I
−5.87061 − 3.95242I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.076120 + 0.259760I
a = 0.82530 + 1.41539I
b = −0.22338 − 1.44415I
2.60826 + 0.73468I 0
u = 1.076120 − 0.259760I
a = 0.82530 − 1.41539I
b = −0.22338 + 1.44415I
2.60826 − 0.73468I 0
u = 0.045996 + 0.875054I
a = 0.201918 − 0.847332I
b = 1.087860 − 0.197488I
−4.71214 − 3.22971I 0
u = 0.045996 − 0.875054I
a = 0.201918 + 0.847332I
b = 1.087860 + 0.197488I
−4.71214 + 3.22971I 0
u = 1.149260 + 0.077977I
a = −0.74710 + 1.82542I
b = 1.69518 − 1.61779I
3.76038 + 0.86686I 0
u = 1.149260 − 0.077977I
a = −0.74710 − 1.82542I
b = 1.69518 + 1.61779I
3.76038 − 0.86686I 0
u = 1.16929
a = −0.910966
b = −0.966261
8.52254 0
u = −0.936704 + 0.797768I
a = −0.469421 − 0.560340I
b = 0.560431 − 0.288250I
−2.68573 + 4.64400I 0
u = −0.936704 − 0.797768I
a = −0.469421 + 0.560340I
b = 0.560431 + 0.288250I
−2.68573 − 4.64400I 0
u = 1.222740 + 0.203951I
a = 0.695120 − 0.912173I
b = −1.110160 + 0.648732I
1.76600 + 0.88415I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.222740 − 0.203951I
a = 0.695120 + 0.912173I
b = −1.110160 − 0.648732I
1.76600 − 0.88415I 0
u = −1.246660 + 0.059464I
a = −0.55090 − 1.49771I
b = −0.171764 + 0.903029I
5.22128 + 0.20023I 0
u = −1.246660 − 0.059464I
a = −0.55090 + 1.49771I
b = −0.171764 − 0.903029I
5.22128 − 0.20023I 0
u = 1.272690 + 0.032209I
a = 0.15479 − 2.26835I
b = −0.88983 + 1.50685I
3.53094 + 4.77456I 0
u = 1.272690 − 0.032209I
a = 0.15479 + 2.26835I
b = −0.88983 − 1.50685I
3.53094 − 4.77456I 0
u = 0.088214 + 0.702646I
a = 0.445527 + 0.157220I
b = 0.698844 − 0.817971I
−0.19370 + 2.61233I 7.84382 − 3.48904I
u = 0.088214 − 0.702646I
a = 0.445527 − 0.157220I
b = 0.698844 + 0.817971I
−0.19370 − 2.61233I 7.84382 + 3.48904I
u = 1.240250 + 0.395827I
a = 0.50755 − 1.33041I
b = −0.398132 + 0.148486I
−1.02699 + 7.77383I 0
u = 1.240250 − 0.395827I
a = 0.50755 + 1.33041I
b = −0.398132 − 0.148486I
−1.02699 − 7.77383I 0
u = −1.300310 + 0.106200I
a = 0.10878 + 2.07536I
b = 0.21246 − 1.86082I
4.03767 − 5.60876I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.300310 − 0.106200I
a = 0.10878 − 2.07536I
b = 0.21246 + 1.86082I
4.03767 + 5.60876I 0
u = 0.127283 + 0.672520I
a = −0.046765 + 0.488251I
b = 1.054710 − 0.369106I
−1.43385 + 2.27144I 1.22544 − 3.26874I
u = 0.127283 − 0.672520I
a = −0.046765 − 0.488251I
b = 1.054710 + 0.369106I
−1.43385 − 2.27144I 1.22544 + 3.26874I
u = −1.266290 + 0.418664I
a = −0.46184 − 1.34292I
b = 1.53300 + 1.08160I
−1.99825 − 8.66191I 0
u = −1.266290 − 0.418664I
a = −0.46184 + 1.34292I
b = 1.53300 − 1.08160I
−1.99825 + 8.66191I 0
u = 1.261270 + 0.461738I
a = −0.471642 − 0.784639I
b = −0.246549 + 0.646298I
4.61034 + 1.14842I 0
u = 1.261270 − 0.461738I
a = −0.471642 + 0.784639I
b = −0.246549 − 0.646298I
4.61034 − 1.14842I 0
u = −1.323370 + 0.315223I
a = −0.00992 + 1.87693I
b = −0.84124 − 1.24795I
4.22712 − 6.35841I 0
u = −1.323370 − 0.315223I
a = −0.00992 − 1.87693I
b = −0.84124 + 1.24795I
4.22712 + 6.35841I 0
u = 1.290860 + 0.454754I
a = −0.544269 + 0.810497I
b = 0.318363 + 0.015687I
−1.80259 + 0.89192I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.290860 − 0.454754I
a = −0.544269 − 0.810497I
b = 0.318363 − 0.015687I
−1.80259 − 0.89192I 0
u = −1.37057
a = −0.961744
b = −0.218443
8.24072 0
u = −1.306900 + 0.427782I
a = 0.534404 + 0.813965I
b = −1.58618 − 0.60287I
−0.48910 − 1.44438I 0
u = −1.306900 − 0.427782I
a = 0.534404 − 0.813965I
b = −1.58618 + 0.60287I
−0.48910 + 1.44438I 0
u = −1.366280 + 0.266791I
a = 0.53978 + 1.75105I
b = −0.88158 − 1.25458I
3.30380 − 5.68458I 0
u = −1.366280 − 0.266791I
a = 0.53978 − 1.75105I
b = −0.88158 + 1.25458I
3.30380 + 5.68458I 0
u = −1.38190 + 0.42110I
a = −0.02647 − 1.49795I
b = 0.78691 + 1.35385I
5.89179 − 9.11420I 0
u = −1.38190 − 0.42110I
a = −0.02647 + 1.49795I
b = 0.78691 − 1.35385I
5.89179 + 9.11420I 0
u = 0.553755
a = 1.04389
b = −0.735717
1.07870 9.45760
u = −0.517206
a = −1.23311
b = −0.969631
2.29968 −3.88090
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.493387
a = −3.44102
b = 0.0313711
6.36082 23.1340
u = 0.490027
a = 3.42978
b = −1.25784
2.53719 −23.9910
u = 1.49141 + 0.35489I
a = 0.78851 − 1.38211I
b = −1.63953 + 1.04123I
−0.31770 + 7.46862I 0
u = 1.49141 − 0.35489I
a = 0.78851 + 1.38211I
b = −1.63953 − 1.04123I
−0.31770 − 7.46862I 0
u = 1.47502 + 0.42826I
a = −0.46070 + 1.53329I
b = 1.42814 − 1.18260I
1.1028 + 15.8670I 0
u = 1.47502 − 0.42826I
a = −0.46070 − 1.53329I
b = 1.42814 + 1.18260I
1.1028 − 15.8670I 0
u = −1.54760
a = −0.228222
b = 1.16480
13.5060 0
u = 1.62930
a = −1.54611
b = 2.23107
10.1076 0
u = −1.64577
a = −1.16219
b = 1.38735
9.05367 0
u = 0.175687 + 0.165118I
a = 2.69632 − 1.12663I
b = −0.541818 − 0.646762I
1.211640 + 0.322145I 9.95422 − 2.34487I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.175687 − 0.165118I
a = 2.69632 + 1.12663I
b = −0.541818 + 0.646762I
1.211640 − 0.322145I 9.95422 + 2.34487I
u = 0.0579910 + 0.0764411I
a = −8.09290 + 2.32584I
b = 0.33102 − 1.44442I
−0.33025 + 4.70984I 11.3417 − 11.5444I
u = 0.0579910 − 0.0764411I
a = −8.09290 − 2.32584I
b = 0.33102 + 1.44442I
−0.33025 − 4.70984I 11.3417 + 11.5444I
u = 1.96691
a = 0.0504349
b = 0.170188
7.42639 0
11
II.
I
u
2
= hu
5
−u
4
−3u
3
+u
2
+b+2u+1, 2u
9
−2u
8
+· · ·+a+6, u
10
−u
9
+· · ·+4u+1i
(i) Arc colorings
a
9
=
0
u
a
12
=
1
0
a
1
=
1
−u
2
a
4
=
−2u
9
+ 2u
8
+ 12u
7
− 9u
6
− 24u
5
+ 11u
4
+ 17u
3
− 2u − 6
−u
5
+ u
4
+ 3u
3
− u
2
− 2u − 1
a
2
=
2u
8
− 5u
7
− 5u
6
+ 17u
5
+ u
4
− 14u
3
+ u
2
− 2u + 6
u
9
− 2u
8
− 4u
7
+ 8u
6
+ 5u
5
− 9u
4
− 3u
3
+ u
2
+ 2u + 1
a
10
=
u
−u
3
+ u
a
5
=
−u
9
+ 8u
7
− 2u
6
− 18u
5
+ 5u
4
+ 13u
3
− u
2
− 5
u
8
− u
7
− 4u
6
+ 2u
5
+ 5u
4
+ u
3
− u
2
− 3u − 1
a
8
=
−u
u
a
7
=
2u
9
− 2u
8
− 14u
7
+ 12u
6
+ 32u
5
− 20u
4
− 27u
3
+ 4u
2
+ 4u + 11
u
9
− u
8
− 5u
7
+ 3u
6
+ 9u
5
− 2u
4
− 6u
3
− u
2
+ u + 1
a
3
=
2u
9
− 17u
7
+ 4u
6
+ 42u
5
− 11u
4
− 34u
3
+ 2u
2
+ u + 13
u
9
− 2u
8
− 4u
7
+ 8u
6
+ 5u
5
− 9u
4
− 2u
3
+ u
2
+ u + 1
a
6
=
3u
9
− 3u
8
− 19u
7
+ 15u
6
+ 41u
5
− 22u
4
− 33u
3
+ 3u
2
+ 5u + 12
u
9
− u
8
− 5u
7
+ 3u
6
+ 9u
5
− 2u
4
− 6u
3
− u
2
+ u + 1
a
11
=
−3u
9
+ 5u
8
+ 15u
7
− 21u
6
− 28u
5
+ 26u
4
+ 22u
3
− 2u
2
− 7u − 9
−u
3
+ 2u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −7u
9
+ 12u
8
+ 30u
7
−45u
6
−46u
5
+ 43u
4
+ 32u
3
+ 10u
2
−15u −6
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
10
+ u
9
+ u
8
+ 16u
7
+ 11u
6
+ 11u
5
+ 27u
4
+ 13u
3
+ 3u
2
− 1
c
2
u
10
+ u
9
− 3u
8
− 6u
7
− 2u
6
+ 7u
5
+ 9u
4
+ 3u
3
− 4u
2
− 4u − 1
c
3
u
10
− 6u
9
+ 13u
8
− 11u
7
− 2u
6
+ 12u
5
− 7u
4
− 5u
3
+ 8u
2
− 5u + 1
c
4
u
10
− 3u
8
+ u
7
+ 2u
6
− 2u
5
+ u
4
+ u
3
− 2u
2
− u + 1
c
5
u
10
− u
9
− 3u
8
+ 6u
7
− 2u
6
− 7u
5
+ 9u
4
− 3u
3
− 4u
2
+ 4u − 1
c
6
u
10
+ u
9
− 2u
8
− u
7
+ u
6
+ 2u
5
+ 2u
4
− u
3
− 3u
2
+ 1
c
7
u
10
+ 6u
9
+ 13u
8
+ 11u
7
− 2u
6
− 12u
5
− 7u
4
+ 5u
3
+ 8u
2
+ 5u + 1
c
8
, c
9
u
10
+ u
9
− 6u
8
− 4u
7
+ 13u
6
+ 4u
5
− 11u
4
+ 2u
3
+ 2u
2
− 4u + 1
c
10
u
10
− 3u
8
− u
7
+ 2u
6
+ 2u
5
+ u
4
− u
3
− 2u
2
+ u + 1
c
11
u
10
− u
9
− 2u
8
+ u
7
+ u
6
− 2u
5
+ 2u
4
+ u
3
− 3u
2
+ 1
c
12
u
10
− u
9
− 6u
8
+ 4u
7
+ 13u
6
− 4u
5
− 11u
4
− 2u
3
+ 2u
2
+ 4u + 1
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
10
+ y
9
+ ··· − 6y + 1
c
2
, c
5
y
10
− 7y
9
+ ··· − 8y + 1
c
3
, c
7
y
10
− 10y
9
+ 33y
8
− 43y
7
+ 42y
6
− 76y
5
+ 53y
4
− 21y
3
− 9y + 1
c
4
, c
10
y
10
− 6y
9
+ 13y
8
− 11y
7
− 2y
6
+ 12y
5
− 7y
4
− 5y
3
+ 8y
2
− 5y + 1
c
6
, c
11
y
10
− 5y
9
+ 8y
8
− 5y
7
− 7y
6
+ 12y
5
− 2y
4
− 11y
3
+ 13y
2
− 6y + 1
c
8
, c
9
, c
12
y
10
− 13y
9
+ ··· − 12y + 1
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.118050 + 0.232448I
a = −0.159280 − 1.307010I
b = −0.630949 + 1.176290I
3.06671 + 1.14968I 12.41669 − 0.09656I
u = 1.118050 − 0.232448I
a = −0.159280 + 1.307010I
b = −0.630949 − 1.176290I
3.06671 − 1.14968I 12.41669 + 0.09656I
u = −1.27546
a = −1.36835
b = −0.278715
9.38465 20.1760
u = −1.333980 + 0.226517I
a = 0.35319 + 2.32281I
b = −0.92049 − 1.72482I
3.07640 − 6.89606I 7.33660 + 9.72380I
u = −1.333980 − 0.226517I
a = 0.35319 − 2.32281I
b = −0.92049 + 1.72482I
3.07640 + 6.89606I 7.33660 − 9.72380I
u = −0.227124 + 0.579101I
a = 0.242833 + 0.178690I
b = 0.488743 − 1.032260I
−0.76904 + 4.14977I 4.72090 − 3.87430I
u = −0.227124 − 0.579101I
a = 0.242833 − 0.178690I
b = 0.488743 + 1.032260I
−0.76904 − 4.14977I 4.72090 + 3.87430I
u = 1.55280
a = −0.492950
b = 1.50160
12.6171 9.76370
u = −0.288130
a = −5.71392
b = −0.569642
6.02399 −1.25560
u = 1.89689
a = −0.298260
b = 0.472157
7.28432 −12.6330
15
III. I
u
3
= hb + a + u + 1, a
2
+ au + 3a + u + 1, u
2
+ u − 1i
(i) Arc colorings
a
9
=
0
u
a
12
=
1
0
a
1
=
1
u − 1
a
4
=
a
−a − u − 1
a
2
=
au + 2
−au + a + 2u
a
10
=
u
−u + 1
a
5
=
−au + a − u
au − 2a − 2
a
8
=
−u
u
a
7
=
a − u
−a − 1
a
3
=
u
−u
a
6
=
−u − 1
−a − 1
a
11
=
−au − a − u
au + a + u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −6au − 13a − 2u + 14
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
u
4
+ 2u
3
− 2u
2
− 3u + 1
c
3
(u + 1)
4
c
4
, c
6
u
4
+ u
3
− 3u
2
− u + 1
c
5
u
4
− 2u
3
− 2u
2
+ 3u + 1
c
7
(u − 1)
4
c
8
, c
9
(u
2
− u − 1)
2
c
10
, c
11
u
4
− u
3
− 3u
2
+ u + 1
c
12
(u
2
+ u − 1)
2
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
y
4
− 8y
3
+ 18y
2
− 13y + 1
c
3
, c
7
(y −1)
4
c
4
, c
6
, c
10
c
11
y
4
− 7y
3
+ 13y
2
− 7y + 1
c
8
, c
9
, c
12
(y
2
− 3y + 1)
2
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.618034
a = −0.522740
b = −1.09529
2.63189 21.4980
u = 0.618034
a = −3.09529
b = 1.47726
2.63189 64.4810
u = −1.61803
a = 0.355674
b = 0.262360
10.5276 16.0650
u = −1.61803
a = −1.73764
b = 2.35567
10.5276 22.9560
19
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
4
+ 2u
3
− 2u
2
− 3u + 1)
· (u
10
+ u
9
+ u
8
+ 16u
7
+ 11u
6
+ 11u
5
+ 27u
4
+ 13u
3
+ 3u
2
− 1)
· (u
64
− 6u
63
+ ··· + 392u + 49)
c
2
(u
4
+ 2u
3
− 2u
2
− 3u + 1)
· (u
10
+ u
9
− 3u
8
− 6u
7
− 2u
6
+ 7u
5
+ 9u
4
+ 3u
3
− 4u
2
− 4u − 1)
· (u
64
− 2u
63
+ ··· + 14u + 1)
c
3
(u + 1)
4
· (u
10
− 6u
9
+ 13u
8
− 11u
7
− 2u
6
+ 12u
5
− 7u
4
− 5u
3
+ 8u
2
− 5u + 1)
· (u
64
− u
63
+ ··· − 30u + 7)
c
4
(u
4
+ u
3
− 3u
2
− u + 1)(u
10
− 3u
8
+ ··· − u + 1)
· (u
64
− 2u
63
+ ··· − 649u − 23)
c
5
(u
4
− 2u
3
− 2u
2
+ 3u + 1)
· (u
10
− u
9
− 3u
8
+ 6u
7
− 2u
6
− 7u
5
+ 9u
4
− 3u
3
− 4u
2
+ 4u − 1)
· (u
64
− 2u
63
+ ··· + 14u + 1)
c
6
(u
4
+ u
3
− 3u
2
− u + 1)
· (u
10
+ u
9
− 2u
8
− u
7
+ u
6
+ 2u
5
+ 2u
4
− u
3
− 3u
2
+ 1)
· (u
64
− u
63
+ ··· + 16u + 1)
c
7
(u − 1)
4
· (u
10
+ 6u
9
+ 13u
8
+ 11u
7
− 2u
6
− 12u
5
− 7u
4
+ 5u
3
+ 8u
2
+ 5u + 1)
· (u
64
− u
63
+ ··· − 30u + 7)
c
8
, c
9
(u
2
− u − 1)
2
· (u
10
+ u
9
− 6u
8
− 4u
7
+ 13u
6
+ 4u
5
− 11u
4
+ 2u
3
+ 2u
2
− 4u + 1)
· (u
64
− 2u
63
+ ··· − 23u + 1)
c
10
(u
4
− u
3
− 3u
2
+ u + 1)(u
10
− 3u
8
+ ··· + u + 1)
· (u
64
− 2u
63
+ ··· − 649u − 23)
c
11
(u
4
− u
3
− 3u
2
+ u + 1)
· (u
10
− u
9
− 2u
8
+ u
7
+ u
6
− 2u
5
+ 2u
4
+ u
3
− 3u
2
+ 1)
· (u
64
− u
63
+ ··· + 16u + 1)
c
12
(u
2
+ u − 1)
2
· (u
10
− u
9
− 6u
8
+ 4u
7
+ 13u
6
− 4u
5
− 11u
4
− 2u
3
+ 2u
2
+ 4u + 1)
· (u
64
− 2u
63
+ ··· − 23u + 1)
20
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
4
− 8y
3
+ 18y
2
− 13y + 1)(y
10
+ y
9
+ ··· − 6y + 1)
· (y
64
− 10y
63
+ ··· − 254506y + 2401)
c
2
, c
5
(y
4
− 8y
3
+ 18y
2
− 13y + 1)(y
10
− 7y
9
+ ··· − 8y + 1)
· (y
64
− 18y
63
+ ··· − 60y + 1)
c
3
, c
7
(y −1)
4
· (y
10
− 10y
9
+ 33y
8
− 43y
7
+ 42y
6
− 76y
5
+ 53y
4
− 21y
3
− 9y + 1)
· (y
64
− 21y
63
+ ··· − 3056y + 49)
c
4
, c
10
(y
4
− 7y
3
+ 13y
2
− 7y + 1)
· (y
10
− 6y
9
+ 13y
8
− 11y
7
− 2y
6
+ 12y
5
− 7y
4
− 5y
3
+ 8y
2
− 5y + 1)
· (y
64
− 28y
63
+ ··· − 464395y + 529)
c
6
, c
11
(y
4
− 7y
3
+ 13y
2
− 7y + 1)
· (y
10
− 5y
9
+ 8y
8
− 5y
7
− 7y
6
+ 12y
5
− 2y
4
− 11y
3
+ 13y
2
− 6y + 1)
· (y
64
− 51y
63
+ ··· − 312y + 1)
c
8
, c
9
, c
12
((y
2
− 3y + 1)
2
)(y
10
− 13y
9
+ ··· − 12y + 1)
· (y
64
− 58y
63
+ ··· + 39y + 1)
21
