12n
0002
(K12n
0002
)
A knot diagram
1
Linearized knot diagam
3 5 6 9 2 9 11 5 12 7 1 10
Solving Sequence
2,5
3 6
1,10
12 9 4 8 11 7
c
2
c
5
c
1
c
12
c
9
c
4
c
8
c
11
c
7
c
3
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h1.50952 × 10
19
u
57
− 1.17965 × 10
20
u
56
+ ··· + 8.90580 × 10
18
b − 7.29842 × 10
18
,
− 1.00393 × 10
18
u
57
+ 3.12591 × 10
18
u
56
+ ··· + 4.45290 × 10
18
a + 3.47008 × 10
18
, u
58
− 8u
57
+ ··· − 2u + 1i
I
u
2
= h−a
5
+ a
4
u + 5a
3
u + 5a
3
+ a
2
− 5au + 3b − 3a + u + 1, a
6
− 4a
4
u − 4a
4
+ a
3
+ 4a
2
u + 1, u
2
+ u + 1i
I
u
3
= h−u
3
+ u
2
+ b − 1, u
4
− u
3
+ 2u
2
+ a, u
5
− u
4
+ 2u
3
− u
2
+ u − 1i
* 3 irreducible components of dim
C
= 0, with total 75 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
= h1.51×10
19
u
57
−1.18×10
20
u
56
+· · ·+8.91×10
18
b−7.30×10
18
, −1.00×
10
18
u
57
+3.13×10
18
u
56
+· · ·+4.45×10
18
a+3.47×10
18
, u
58
−8u
57
+· · ·−2u+1i
(i) Arc colorings
a
2
=
1
0
a
5
=
0
u
a
3
=
1
−u
2
a
6
=
u
u
a
1
=
u
2
+ 1
−u
4
a
10
=
0.225455u
57
− 0.701994u
56
+ ··· − 6.72656u − 0.779286
−1.69498u
57
+ 13.2459u
56
+ ··· − 1.76418u + 0.819513
a
12
=
−0.0574055u
57
− 0.455661u
56
+ ··· + 3.20301u + 1.10290
0.153541u
57
− 1.95463u
56
+ ··· + 0.280763u − 0.208388
a
9
=
−0.439374u
57
+ 3.08799u
56
+ ··· − 7.87466u − 0.429764
−1.22559u
57
+ 7.69945u
56
+ ··· + 0.535607u − 0.892059
a
4
=
u
4
+ u
2
+ 1
u
4
a
8
=
−0.439374u
57
+ 3.08799u
56
+ ··· − 7.87466u − 0.429764
−2.54116u
57
+ 16.5796u
56
+ ··· + 0.950230u − 1.31906
a
11
=
−0.144303u
57
+ 0.234853u
56
+ ··· + 4.42130u + 0.826807
0.637447u
57
− 5.42639u
56
+ ··· + 1.41189u − 0.810401
a
7
=
−u
2
− 1
−0.0312500u
57
+ 0.218750u
56
+ ··· + 1.03125u
2
+ 1.96875u
(ii) Obstruction class = −1
(iii) Cusp Shapes =
11962378823504572851
4452900487453949456
u
57
−
51305067713791607137
2226450243726974728
u
56
+ ··· +
42176209722625714401
4452900487453949456
u −
11662141419335258151
2226450243726974728
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
58
+ 36u
57
+ ··· + 38u + 1
c
2
, c
5
u
58
+ 8u
57
+ ··· + 2u + 1
c
3
u
58
− 8u
57
+ ··· − 10u + 1
c
4
, c
8
u
58
+ 2u
57
+ ··· + 22528u
2
− 4096
c
6
u
58
− 4u
57
+ ··· + 2u − 1
c
7
, c
10
u
58
+ 3u
57
+ ··· + 96u + 32
c
9
, c
12
u
58
+ 8u
57
+ ··· − 8u − 1
c
11
u
58
− 24u
57
+ ··· + 160u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
58
− 20y
57
+ ··· + 1622y + 1
c
2
, c
5
y
58
+ 36y
57
+ ··· + 38y + 1
c
3
y
58
− 76y
57
+ ··· + 38y + 1
c
4
, c
8
y
58
− 70y
57
+ ··· − 184549376y + 16777216
c
6
y
58
− 76y
57
+ ··· + 34y + 1
c
7
, c
10
y
58
− 39y
57
+ ··· − 11776y + 1024
c
9
, c
12
y
58
− 24y
57
+ ··· + 160y + 1
c
11
y
58
+ 28y
57
+ ··· − 15092y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.275952 + 0.968192I
a = −0.000155 + 0.297955I
b = 1.10303 − 1.31729I
−0.96404 + 7.38208I 0
u = 0.275952 − 0.968192I
a = −0.000155 − 0.297955I
b = 1.10303 + 1.31729I
−0.96404 − 7.38208I 0
u = 0.978634 + 0.050547I
a = −0.55182 + 2.57301I
b = 0.022208 − 0.782754I
−4.75178 − 2.65507I 0
u = 0.978634 − 0.050547I
a = −0.55182 − 2.57301I
b = 0.022208 + 0.782754I
−4.75178 + 2.65507I 0
u = 1.023510 + 0.155528I
a = −0.27153 − 2.55040I
b = 0.021646 + 0.911291I
−8.49450 − 9.39894I 0
u = 1.023510 − 0.155528I
a = −0.27153 + 2.55040I
b = 0.021646 − 0.911291I
−8.49450 + 9.39894I 0
u = 1.039610 + 0.094873I
a = 0.51869 + 1.62894I
b = 0.260631 − 0.513525I
−10.45060 − 3.04051I 0
u = 1.039610 − 0.094873I
a = 0.51869 − 1.62894I
b = 0.260631 + 0.513525I
−10.45060 + 3.04051I 0
u = 0.955917
a = 1.03957
b = −1.17742
−3.08584 0
u = −0.171249 + 1.030670I
a = −0.063866 + 0.965609I
b = 1.090800 + 0.593842I
−0.92134 − 2.15292I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.171249 − 1.030670I
a = −0.063866 − 0.965609I
b = 1.090800 − 0.593842I
−0.92134 + 2.15292I 0
u = 0.093713 + 0.946838I
a = −0.553562 − 0.684632I
b = −1.49296 + 1.41946I
0.65102 + 1.70576I 0
u = 0.093713 − 0.946838I
a = −0.553562 + 0.684632I
b = −1.49296 − 1.41946I
0.65102 − 1.70576I 0
u = −0.385585 + 0.867994I
a = −0.485247 + 0.372815I
b = −0.175174 + 0.510497I
−0.35129 − 1.66089I 0
u = −0.385585 − 0.867994I
a = −0.485247 − 0.372815I
b = −0.175174 − 0.510497I
−0.35129 + 1.66089I 0
u = −0.505582 + 0.803238I
a = −2.09011 − 2.61641I
b = −2.09154 − 2.96921I
1.74781 − 1.62369I 0. + 24.7327I
u = −0.505582 − 0.803238I
a = −2.09011 + 2.61641I
b = −2.09154 + 2.96921I
1.74781 + 1.62369I 0. − 24.7327I
u = −0.561420 + 0.898597I
a = 2.07464 + 1.60753I
b = 1.43908 + 1.62628I
1.38531 − 2.69246I 0
u = −0.561420 − 0.898597I
a = 2.07464 − 1.60753I
b = 1.43908 − 1.62628I
1.38531 + 2.69246I 0
u = −0.726204 + 0.589006I
a = 0.00616 + 1.68117I
b = −0.547028 + 1.145170I
−0.969194 + 0.999280I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.726204 − 0.589006I
a = 0.00616 − 1.68117I
b = −0.547028 − 1.145170I
−0.969194 − 0.999280I 0
u = 0.175532 + 1.051230I
a = 0.428231 − 0.504967I
b = 0.019179 − 0.580968I
−3.55927 + 2.47567I 0
u = 0.175532 − 1.051230I
a = 0.428231 + 0.504967I
b = 0.019179 + 0.580968I
−3.55927 − 2.47567I 0
u = −0.024346 + 0.878987I
a = −1.212630 + 0.073534I
b = −2.14746 + 0.60990I
1.218520 − 0.673498I −4.18882 − 1.05925I
u = −0.024346 − 0.878987I
a = −1.212630 − 0.073534I
b = −2.14746 − 0.60990I
1.218520 + 0.673498I −4.18882 + 1.05925I
u = −0.704127 + 0.981644I
a = −1.74849 + 0.22678I
b = −1.64792 − 0.60728I
−2.05852 − 6.41903I 0
u = −0.704127 − 0.981644I
a = −1.74849 − 0.22678I
b = −1.64792 + 0.60728I
−2.05852 + 6.41903I 0
u = −0.692017 + 0.375664I
a = 0.372198 − 0.642161I
b = 0.920888 − 0.097592I
−0.81151 − 3.99437I −2.30538 + 5.50801I
u = −0.692017 − 0.375664I
a = 0.372198 + 0.642161I
b = 0.920888 + 0.097592I
−0.81151 + 3.99437I −2.30538 − 5.50801I
u = −0.629338 + 1.046620I
a = 0.677631 − 0.327862I
b = 0.848161 + 0.573228I
−2.61151 − 1.02917I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.629338 − 1.046620I
a = 0.677631 + 0.327862I
b = 0.848161 − 0.573228I
−2.61151 + 1.02917I 0
u = −0.171554 + 1.234280I
a = 0.966951 − 0.171109I
b = 1.74065 − 1.48643I
−6.43951 − 0.95824I 0
u = −0.171554 − 1.234280I
a = 0.966951 + 0.171109I
b = 1.74065 + 1.48643I
−6.43951 + 0.95824I 0
u = 0.463795 + 1.173060I
a = 0.245701 − 0.546846I
b = 0.27203 − 1.99888I
−4.70507 + 4.20146I 0
u = 0.463795 − 1.173060I
a = 0.245701 + 0.546846I
b = 0.27203 + 1.99888I
−4.70507 − 4.20146I 0
u = −0.276279 + 1.243530I
a = −0.500340 − 0.211080I
b = −1.57432 + 1.01324I
−5.50368 − 7.01216I 0
u = −0.276279 − 1.243530I
a = −0.500340 + 0.211080I
b = −1.57432 − 1.01324I
−5.50368 + 7.01216I 0
u = 0.305286 + 0.606062I
a = 0.384294 + 0.040597I
b = 0.905016 − 1.068230I
0.07617 − 4.63797I −3.02109 + 8.51541I
u = 0.305286 − 0.606062I
a = 0.384294 − 0.040597I
b = 0.905016 + 1.068230I
0.07617 + 4.63797I −3.02109 − 8.51541I
u = 0.646890
a = −1.12299
b = 0.559207
−1.53774 −8.16170
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.490058 + 1.298210I
a = −0.386776 + 0.469667I
b = −0.38414 + 2.46629I
−7.08177 + 5.14263I 0
u = 0.490058 − 1.298210I
a = −0.386776 − 0.469667I
b = −0.38414 − 2.46629I
−7.08177 − 5.14263I 0
u = 0.463084 + 1.320050I
a = −1.47034 − 0.97801I
b = −3.91851 − 1.65445I
−9.03269 + 2.43239I 0
u = 0.463084 − 1.320050I
a = −1.47034 + 0.97801I
b = −3.91851 + 1.65445I
−9.03269 − 2.43239I 0
u = 0.520231 + 1.298750I
a = 1.84530 + 0.28310I
b = 4.74633 + 0.27848I
−8.59701 + 8.01455I 0
u = 0.520231 − 1.298750I
a = 1.84530 − 0.28310I
b = 4.74633 − 0.27848I
−8.59701 − 8.01455I 0
u = 0.581889 + 1.286040I
a = −1.72412 − 0.78764I
b = −4.59705 − 1.31483I
−11.9798 + 15.1518I 0
u = 0.581889 − 1.286040I
a = −1.72412 + 0.78764I
b = −4.59705 + 1.31483I
−11.9798 − 15.1518I 0
u = 0.55851 + 1.31422I
a = 1.055310 + 0.777623I
b = 2.64117 + 1.02259I
−14.2321 + 8.7482I 0
u = 0.55851 − 1.31422I
a = 1.055310 − 0.777623I
b = 2.64117 − 1.02259I
−14.2321 − 8.7482I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.38902 + 1.37780I
a = 1.64061 + 0.55483I
b = 4.47101 + 0.66773I
−13.4742 − 4.4404I 0
u = 0.38902 − 1.37780I
a = 1.64061 − 0.55483I
b = 4.47101 − 0.66773I
−13.4742 + 4.4404I 0
u = 0.44158 + 1.37511I
a = −1.169000 − 0.047468I
b = −3.16209 − 0.19464I
−15.1541 + 2.2033I 0
u = 0.44158 − 1.37511I
a = −1.169000 + 0.047468I
b = −3.16209 + 0.19464I
−15.1541 − 2.2033I 0
u = 0.342722 + 0.311153I
a = −1.206810 + 0.383647I
b = 0.526147 + 0.412647I
−1.48988 − 0.34469I −6.13134 + 1.29951I
u = 0.342722 − 0.311153I
a = −1.206810 − 0.383647I
b = 0.526147 − 0.412647I
−1.48988 + 0.34469I −6.13134 − 1.29951I
u = −0.096823 + 0.143742I
a = −4.23922 − 1.64875I
b = −0.980677 + 0.184228I
1.73915 − 0.71529I 3.95862 + 0.54158I
u = −0.096823 − 0.143742I
a = −4.23922 + 1.64875I
b = −0.980677 − 0.184228I
1.73915 + 0.71529I 3.95862 − 0.54158I
10
II.
I
u
2
= ha
4
u + 5a
3
u + · · · − 3a + 1, a
6
− 4a
4
u − 4a
4
+ a
3
+ 4a
2
u + 1, u
2
+ u + 1i
(i) Arc colorings
a
2
=
1
0
a
5
=
0
u
a
3
=
1
u + 1
a
6
=
u
u
a
1
=
−u
−u
a
10
=
a
−
1
3
a
4
u −
5
3
a
3
u + ··· + a −
1
3
a
12
=
−
1
3
a
5
u +
2
3
a
3
u + ··· +
1
3
a
2
−
1
3
a
−
1
3
a
5
u +
1
3
a
4
u + ··· −
1
3
a −
2
3
a
9
=
0
1
3
a
4
u −
7
3
a
3
u + ··· +
7
3
a
2
−
5
3
a
4
=
0
u
a
8
=
0
1
3
a
4
u −
7
3
a
3
u + ··· +
7
3
a
2
−
5
3
a
11
=
−
2
3
a
5
u +
7
3
a
3
u + ··· +
5
3
a
2
+
4
3
a
−
2
3
a
5
u +
1
3
a
4
u + ··· +
4
3
a −
2
3
a
7
=
u
a
5
+ a
4
u − 3a
3
u − 3a
3
+ 5a
2
+ 2au − u − 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 5a
5
u + 2a
5
+ a
4
u − 6a
3
u + 9a
3
+ 5a
2
u + 6a
2
−2au − 6a + 2u − 4
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
(u
2
− u + 1)
6
c
2
(u
2
+ u + 1)
6
c
4
, c
8
u
12
c
6
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
2
c
7
, c
12
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
2
c
9
, c
10
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)
2
c
11
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
2
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
5
(y
2
+ y + 1)
6
c
4
, c
8
y
12
c
6
, c
11
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
2
c
7
, c
9
, c
10
c
12
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = 0.984649 + 0.174545I
b = −0.036219 − 0.476146I
− 7.72290I 0.57335 + 8.68103I
u = −0.500000 + 0.866025I
a = −0.643485 − 0.765459I
b = −0.69657 − 1.97490I
3.66314I −3.68173 − 0.75872I
u = −0.500000 + 0.866025I
a = −0.532492 − 0.210196I
b = −0.171113 − 0.913331I
−1.89061 − 1.10558I −7.73749 + 2.70506I
u = −0.500000 + 0.866025I
a = 0.448281 + 0.356054I
b = −0.341341 + 0.317450I
−1.89061 − 2.95419I −4.53097 + 3.97184I
u = −0.500000 + 0.866025I
a = −1.62479 − 0.64137I
b = −0.867745 + 0.078785I
1.89061 − 1.10558I 0.765607 + 0.616236I
u = −0.500000 + 0.866025I
a = 1.36783 + 1.08642I
b = 1.61298 + 2.10212I
1.89061 − 2.95419I 4.61123 + 3.83711I
u = −0.500000 − 0.866025I
a = −0.643485 + 0.765459I
b = −0.69657 + 1.97490I
7.72290I 0.57335 − 8.68103I
u = −0.500000 − 0.866025I
a = 0.984649 − 0.174545I
b = −0.036219 + 0.476146I
− 3.66314I −3.68173 + 0.75872I
u = −0.500000 − 0.866025I
a = −0.532492 + 0.210196I
b = −0.171113 + 0.913331I
−1.89061 + 1.10558I −7.73749 − 2.70506I
u = −0.500000 − 0.866025I
a = 0.448281 − 0.356054I
b = −0.341341 − 0.317450I
−1.89061 + 2.95419I −4.53097 − 3.97184I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 − 0.866025I
a = −1.62479 + 0.64137I
b = −0.867745 − 0.078785I
1.89061 + 1.10558I 0.765607 − 0.616236I
u = −0.500000 − 0.866025I
a = 1.36783 − 1.08642I
b = 1.61298 − 2.10212I
1.89061 + 2.95419I 4.61123 − 3.83711I
15
III. I
u
3
= h−u
3
+ u
2
+ b − 1, u
4
− u
3
+ 2u
2
+ a, u
5
− u
4
+ 2u
3
− u
2
+ u − 1i
(i) Arc colorings
a
2
=
1
0
a
5
=
0
u
a
3
=
1
−u
2
a
6
=
u
u
a
1
=
u
2
+ 1
−u
4
a
10
=
−u
4
+ u
3
− 2u
2
u
3
− u
2
+ 1
a
12
=
−u
4
+ u
3
− u
2
+ 1
−u
4
+ u
3
− u
2
+ 1
a
9
=
−u
2
− 1
u
4
a
4
=
u
4
+ u
2
+ 1
u
4
a
8
=
−u
2
− 1
2u
4
+ u
2
a
11
=
−u
4
+ u
3
− 2u
2
u
3
− u
2
+ 1
a
7
=
−u
2
− 1
2u
4
+ u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 3u
4
+ 3u
3
− 4u
2
+ 8u − 3
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
5
− 3u
4
+ 4u
3
− u
2
− u + 1
c
2
u
5
− u
4
+ 2u
3
− u
2
+ u − 1
c
3
, c
4
u
5
+ u
4
− 2u
3
− u
2
+ u − 1
c
5
u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1
c
6
u
5
− 5u
4
+ 8u
3
− 3u
2
− u − 1
c
7
, c
10
u
5
c
8
u
5
− u
4
− 2u
3
+ u
2
+ u + 1
c
9
, c
11
(u + 1)
5
c
12
(u − 1)
5
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
5
− y
4
+ 8y
3
− 3y
2
+ 3y − 1
c
2
, c
5
y
5
+ 3y
4
+ 4y
3
+ y
2
− y − 1
c
3
, c
4
, c
8
y
5
− 5y
4
+ 8y
3
− 3y
2
− y − 1
c
6
y
5
− 9y
4
+ 32y
3
− 35y
2
− 5y − 1
c
7
, c
10
y
5
c
9
, c
11
, c
12
(y − 1)
5
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.339110 + 0.822375I
a = 1.76766 + 0.21690I
b = 2.21033 + 0.28529I
1.31583 − 1.53058I −1.50865 + 9.87103I
u = −0.339110 − 0.822375I
a = 1.76766 − 0.21690I
b = 2.21033 − 0.28529I
1.31583 + 1.53058I −1.50865 − 9.87103I
u = 0.766826
a = −1.07090
b = 0.862888
−0.756147 3.17260
u = 0.455697 + 1.200150I
a = 0.267792 − 0.471915I
b = 0.35822 − 2.07480I
−4.22763 + 4.40083I 0.92237 − 5.80708I
u = 0.455697 − 1.200150I
a = 0.267792 + 0.471915I
b = 0.35822 + 2.07480I
−4.22763 − 4.40083I 0.92237 + 5.80708I
19
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
6
)(u
5
− 3u
4
+ ··· − u + 1)(u
58
+ 36u
57
+ ··· + 38u + 1)
c
2
((u
2
+ u + 1)
6
)(u
5
− u
4
+ ··· + u − 1)(u
58
+ 8u
57
+ ··· + 2u + 1)
c
3
((u
2
− u + 1)
6
)(u
5
+ u
4
+ ··· + u − 1)(u
58
− 8u
57
+ ··· − 10u + 1)
c
4
u
12
(u
5
+ u
4
+ ··· + u − 1)(u
58
+ 2u
57
+ ··· + 22528u
2
− 4096)
c
5
((u
2
− u + 1)
6
)(u
5
+ u
4
+ ··· + u + 1)(u
58
+ 8u
57
+ ··· + 2u + 1)
c
6
(u
5
− 5u
4
+ 8u
3
− 3u
2
− u − 1)(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
2
· (u
58
− 4u
57
+ ··· + 2u − 1)
c
7
u
5
(u
6
+ u
5
+ ··· + u + 1)
2
(u
58
+ 3u
57
+ ··· + 96u + 32)
c
8
u
12
(u
5
− u
4
+ ··· + u + 1)(u
58
+ 2u
57
+ ··· + 22528u
2
− 4096)
c
9
((u + 1)
5
)(u
6
− u
5
+ ··· − u + 1)
2
(u
58
+ 8u
57
+ ··· − 8u − 1)
c
10
u
5
(u
6
− u
5
+ ··· − u + 1)
2
(u
58
+ 3u
57
+ ··· + 96u + 32)
c
11
(u + 1)
5
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
2
· (u
58
− 24u
57
+ ··· + 160u + 1)
c
12
((u − 1)
5
)(u
6
+ u
5
+ ··· + u + 1)
2
(u
58
+ 8u
57
+ ··· − 8u − 1)
20
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
2
+ y + 1)
6
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y − 1)
· (y
58
− 20y
57
+ ··· + 1622y + 1)
c
2
, c
5
((y
2
+ y + 1)
6
)(y
5
+ 3y
4
+ ··· − y − 1)(y
58
+ 36y
57
+ ··· + 38y + 1)
c
3
(y
2
+ y + 1)
6
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y − 1)
· (y
58
− 76y
57
+ ··· + 38y + 1)
c
4
, c
8
y
12
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y − 1)
· (y
58
− 70y
57
+ ··· − 184549376y + 16777216)
c
6
(y
5
− 9y
4
+ 32y
3
− 35y
2
− 5y − 1)(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
2
· (y
58
− 76y
57
+ ··· + 34y + 1)
c
7
, c
10
y
5
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
· (y
58
− 39y
57
+ ··· − 11776y + 1024)
c
9
, c
12
(y − 1)
5
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
· (y
58
− 24y
57
+ ··· + 160y + 1)
c
11
(y − 1)
5
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
2
· (y
58
+ 28y
57
+ ··· − 15092y + 1)
21
