11n
150
(K11n
150
)
A knot diagram
1
Linearized knot diagam
9 8 1 2 3 1 11 5 4 8 7
Solving Sequence
2,8 3,5
6 9 1 4 10 11 7
c
2
c
5
c
8
c
1
c
4
c
9
c
10
c
7
c
3
, c
6
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h2575706427464u
21
− 75635053703013u
20
+ ··· + 105076803822638b − 642339227026933,
1743319071217019u
21
+ 1770759336218560u
20
+ ··· + 525384019113190a − 4689968007233431,
u
22
− 4u
20
+ ··· − 14u + 5i
I
u
2
= h7.75318 × 10
41
u
23
+ 7.31958 × 10
41
u
22
+ ··· + 5.04425 × 10
43
b + 5.71288 × 10
43
,
− 3.32426 × 10
43
u
23
− 4.90017 × 10
43
u
22
+ ··· + 9.24779 × 10
44
a + 2.28923 × 10
45
,
u
24
+ u
23
+ ··· − 14u + 11i
I
u
3
= h−u
2
+ b + 1, u
8
− u
7
− 2u
6
+ u
5
+ 3u
4
− 4u
2
+ a + u + 2, u
9
− 2u
7
− u
6
+ 2u
5
+ 2u
4
− 2u
3
− u
2
+ u + 1i
* 3 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
=
h2.58×10
12
u
21
−7.56×10
13
u
20
+· · ·+1.05×10
14
b−6.42×10
14
, 1.74×10
15
u
21
+
1.77 × 10
15
u
20
+ · · · + 5.25 × 10
14
a − 4.69 × 10
15
, u
22
− 4u
20
+ · · · − 14u + 5i
(i) Arc colorings
a
2
=
1
0
a
8
=
0
u
a
3
=
1
u
2
a
5
=
−3.31818u
21
− 3.37041u
20
+ ··· − 24.1967u + 8.92674
−0.0245126u
21
+ 0.719807u
20
+ ··· + 0.565515u + 6.11304
a
6
=
−6.91563u
21
− 7.12434u
20
+ ··· − 55.3570u + 19.6657
−3.62984u
21
− 2.30969u
20
+ ··· − 34.0023u + 24.8827
a
9
=
10.1768u
21
+ 5.97138u
20
+ ··· + 106.076u − 77.2357
−3.37041u
21
− 3.62196u
20
+ ··· − 37.5278u + 16.5909
a
1
=
15.2289u
21
+ 12.3246u
20
+ ··· + 150.786u − 83.4067
5.97138u
21
+ 2.84888u
20
+ ··· + 65.2393u − 50.8839
a
4
=
−3.29367u
21
− 4.09022u
20
+ ··· − 24.7622u + 2.81370
−0.0245126u
21
+ 0.719807u
20
+ ··· + 0.565515u + 6.11304
a
10
=
14.2670u
21
+ 10.4261u
20
+ ··· + 149.374u − 93.7040
−4.09022u
21
− 4.45473u
20
+ ··· − 43.2977u + 16.4683
a
11
=
14.2670u
21
+ 10.4261u
20
+ ··· + 149.374u − 93.7040
2.71761u
21
− 0.249682u
20
+ ··· + 31.3329u − 35.6622
a
7
=
5.68713u
21
+ 4.69087u
20
+ ··· + 59.0094u − 36.8288
−0.0869368u
21
+ 1.65095u
20
+ ··· − 4.06164u + 14.6425
a
7
=
5.68713u
21
+ 4.69087u
20
+ ··· + 59.0094u − 36.8288
−0.0869368u
21
+ 1.65095u
20
+ ··· − 4.06164u + 14.6425
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
46675218577444
52538401911319
u
21
+
154724488953125
52538401911319
u
20
+ ··· +
718281907576011
52538401911319
u +
149853052606131
52538401911319
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
u
22
− u
21
+ ··· − u + 1
c
2
, c
9
u
22
− 4u
20
+ ··· + 14u + 5
c
3
, c
5
u
22
+ 2u
21
+ ··· − 2u + 1
c
4
u
22
+ 14u
21
+ ··· + 11u + 2
c
6
, c
7
, c
10
c
11
u
22
− 5u
21
+ ··· − 3u + 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
22
+ 9y
21
+ ··· + 21y + 1
c
2
, c
9
y
22
− 8y
21
+ ··· − 246y + 25
c
3
, c
5
y
22
− 28y
21
+ ··· − 10y + 1
c
4
y
22
+ 36y
20
+ ··· + 71y + 4
c
6
, c
7
, c
10
c
11
y
22
+ 19y
21
+ ··· + 7y + 16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.428754 + 0.878103I
a = 0.455413 − 0.257667I
b = −0.663346 − 0.941102I
3.69794 + 2.45328I −0.65552 − 2.28211I
u = −0.428754 − 0.878103I
a = 0.455413 + 0.257667I
b = −0.663346 + 0.941102I
3.69794 − 2.45328I −0.65552 + 2.28211I
u = 1.026780 + 0.294583I
a = −0.083593 + 0.649774I
b = 1.19477 + 1.51394I
−1.94956 − 5.83716I −9.57717 + 8.35225I
u = 1.026780 − 0.294583I
a = −0.083593 − 0.649774I
b = 1.19477 − 1.51394I
−1.94956 + 5.83716I −9.57717 − 8.35225I
u = −0.897797 + 0.074279I
a = −0.270012 − 0.839152I
b = 1.34747 − 1.07987I
−5.71309 + 1.52838I −12.61169 − 4.44312I
u = −0.897797 − 0.074279I
a = −0.270012 + 0.839152I
b = 1.34747 + 1.07987I
−5.71309 − 1.52838I −12.61169 + 4.44312I
u = −0.827838 + 0.234233I
a = 0.995620 − 0.629938I
b = 0.282736 − 0.453819I
−0.21957 − 2.12717I −6.07714 + 3.56253I
u = −0.827838 − 0.234233I
a = 0.995620 + 0.629938I
b = 0.282736 + 0.453819I
−0.21957 + 2.12717I −6.07714 − 3.56253I
u = 0.760691 + 0.206194I
a = 1.08312 − 1.47957I
b = 0.677862 − 0.440050I
7.68733 − 4.10610I −10.22463 + 1.15969I
u = 0.760691 − 0.206194I
a = 1.08312 + 1.47957I
b = 0.677862 + 0.440050I
7.68733 + 4.10610I −10.22463 − 1.15969I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.717385 + 0.176237I
a = −0.728362 − 1.017690I
b = 1.46505 − 0.64978I
−1.45123 − 2.66218I −7.52164 − 0.32161I
u = 0.717385 − 0.176237I
a = −0.728362 + 1.017690I
b = 1.46505 + 0.64978I
−1.45123 + 2.66218I −7.52164 + 0.32161I
u = 0.432579 + 0.567805I
a = 0.799059 + 0.423606I
b = 0.023080 + 0.517895I
−0.808492 − 0.857573I −6.91603 + 4.94465I
u = 0.432579 − 0.567805I
a = 0.799059 − 0.423606I
b = 0.023080 − 0.517895I
−0.808492 + 0.857573I −6.91603 − 4.94465I
u = 0.520005 + 1.238630I
a = 0.802607 + 0.196282I
b = −0.175628 + 0.287507I
−0.077811 − 0.121037I −6.01835 − 0.40486I
u = 0.520005 − 1.238630I
a = 0.802607 − 0.196282I
b = −0.175628 − 0.287507I
−0.077811 + 0.121037I −6.01835 + 0.40486I
u = −1.42815 + 0.70349I
a = 0.194878 + 0.926631I
b = 0.782653 + 1.033470I
−3.38864 + 4.05517I −5.85659 − 2.92403I
u = −1.42815 − 0.70349I
a = 0.194878 − 0.926631I
b = 0.782653 − 1.033470I
−3.38864 − 4.05517I −5.85659 + 2.92403I
u = 1.40689 + 1.02797I
a = 0.033035 − 0.885936I
b = 0.95797 − 1.12718I
−6.62431 − 9.59009I −7.42347 + 6.05850I
u = 1.40689 − 1.02797I
a = 0.033035 + 0.885936I
b = 0.95797 + 1.12718I
−6.62431 + 9.59009I −7.42347 − 6.05850I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.28179 + 1.24184I
a = −0.081765 + 0.868752I
b = 1.10739 + 1.14097I
−1.8446 + 14.7873I −3.61777 − 8.09852I
u = −1.28179 − 1.24184I
a = −0.081765 − 0.868752I
b = 1.10739 − 1.14097I
−1.8446 − 14.7873I −3.61777 + 8.09852I
7
II. I
u
2
= h7.75 × 10
41
u
23
+ 7.32 × 10
41
u
22
+ · · · + 5.04 × 10
43
b + 5.71 ×
10
43
, −3.32 × 10
43
u
23
− 4.90 × 10
43
u
22
+ · · · + 9.25 × 10
44
a + 2.29 ×
10
45
, u
24
+ u
23
+ · · · − 14u + 11i
(i) Arc colorings
a
2
=
1
0
a
8
=
0
u
a
3
=
1
u
2
a
5
=
0.0359466u
23
+ 0.0529875u
22
+ ··· + 21.0925u − 2.47544
−0.0153703u
23
− 0.0145107u
22
+ ··· − 3.98454u − 1.13255
a
6
=
0.0411054u
23
+ 0.0645644u
22
+ ··· + 24.9202u − 1.53033
−0.0161448u
23
− 0.0160826u
22
+ ··· − 3.95144u − 1.20315
a
9
=
−0.0967087u
23
− 0.0561866u
22
+ ··· − 8.43223u + 1.35926
0.00738052u
23
+ 0.0148442u
22
+ ··· + 5.23380u + 0.445645
a
1
=
−0.00456662u
23
+ 0.0198549u
22
+ ··· + 4.17439u + 3.32554
0.0109435u
23
+ 0.0143386u
22
+ ··· + 6.53516u − 0.554396
a
4
=
0.0513169u
23
+ 0.0674983u
22
+ ··· + 25.0770u − 1.34288
−0.0153703u
23
− 0.0145107u
22
+ ··· − 3.98454u − 1.13255
a
10
=
0.0201213u
23
+ 0.0353821u
22
+ ··· + 6.23353u + 6.83415
0.0302784u
23
+ 0.0259611u
22
+ ··· + 11.9102u − 1.00459
a
11
=
0.0201213u
23
+ 0.0353821u
22
+ ··· + 6.23353u + 6.83415
0.0323398u
23
+ 0.0261261u
22
+ ··· + 11.9025u − 1.17246
a
7
=
0.123802u
23
+ 0.132537u
22
+ ··· + 51.6121u − 2.14655
−0.0158132u
23
− 0.0205158u
22
+ ··· − 6.87114u − 2.42748
a
7
=
0.123802u
23
+ 0.132537u
22
+ ··· + 51.6121u − 2.14655
−0.0158132u
23
− 0.0205158u
22
+ ··· − 6.87114u − 2.42748
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.0238112u
23
− 0.0116625u
22
+ ··· − 9.75202u + 2.94951
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
u
24
− 3u
23
+ ··· − 12u + 5
c
2
, c
9
u
24
− u
23
+ ··· + 14u + 11
c
3
, c
5
u
24
+ u
23
+ ··· − 188u + 145
c
4
(u
12
− 5u
11
+ ··· + 3u
2
+ 1)
2
c
6
, c
7
, c
10
c
11
(u
12
+ 3u
11
+ ··· − 2u + 1)
2
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
24
− 5y
23
+ ··· + 116y + 25
c
2
, c
9
y
24
− 9y
23
+ ··· + 7812y + 121
c
3
, c
5
y
24
− 9y
23
+ ··· − 29544y + 21025
c
4
(y
12
+ y
11
+ ··· + 6y + 1)
2
c
6
, c
7
, c
10
c
11
(y
12
+ 9y
11
+ ··· − 6y + 1)
2
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.822375 + 0.544420I
a = −0.43573 + 1.79593I
b = −0.096849 + 0.815314I
−2.20294 − 4.46082I −11.64801 + 4.72827I
u = 0.822375 − 0.544420I
a = −0.43573 − 1.79593I
b = −0.096849 − 0.815314I
−2.20294 + 4.46082I −11.64801 − 4.72827I
u = −0.994835 + 0.204013I
a = −0.365805 − 0.706116I
b = −0.897414 − 0.962359I
0.29247 + 3.33657I −9.82297 − 1.92424I
u = −0.994835 − 0.204013I
a = −0.365805 + 0.706116I
b = −0.897414 + 0.962359I
0.29247 − 3.33657I −9.82297 + 1.92424I
u = −0.258569 + 0.999486I
a = 0.336204 − 1.107620I
b = −1.00664 − 1.21018I
3.00704 + 5.40399I −1.47702 − 8.56336I
u = −0.258569 − 0.999486I
a = 0.336204 + 1.107620I
b = −1.00664 + 1.21018I
3.00704 − 5.40399I −1.47702 + 8.56336I
u = 0.564663 + 0.948037I
a = 0.267910 + 1.052460I
b = −0.897414 + 0.962359I
0.29247 − 3.33657I −9.82297 + 1.92424I
u = 0.564663 − 0.948037I
a = 0.267910 − 1.052460I
b = −0.897414 − 0.962359I
0.29247 + 3.33657I −9.82297 − 1.92424I
u = −0.759985 + 0.083928I
a = −1.94007 − 1.80669I
b = 0.225615 − 0.583583I
−5.22591 − 0.91968I −15.5307 + 7.1820I
u = −0.759985 − 0.083928I
a = −1.94007 + 1.80669I
b = 0.225615 + 0.583583I
−5.22591 + 0.91968I −15.5307 − 7.1820I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.681064 + 0.334584I
a = −2.49696 − 0.18183I
b = 0.492148 − 0.450600I
−0.39191 − 6.22910I −3.95991 + 11.28166I
u = 0.681064 − 0.334584I
a = −2.49696 + 0.18183I
b = 0.492148 + 0.450600I
−0.39191 + 6.22910I −3.95991 − 11.28166I
u = −0.484578 + 1.315260I
a = 0.434565 − 0.649908I
b = −1.216860 − 0.709160I
4.52125 + 2.53747I 2.43865 − 1.71275I
u = −0.484578 − 1.315260I
a = 0.434565 + 0.649908I
b = −1.216860 + 0.709160I
4.52125 − 2.53747I 2.43865 + 1.71275I
u = 1.52705 + 0.88894I
a = −0.014991 + 0.572943I
b = −1.00664 + 1.21018I
3.00704 − 5.40399I −1.47702 + 8.56336I
u = 1.52705 − 0.88894I
a = −0.014991 − 0.572943I
b = −1.00664 − 1.21018I
3.00704 + 5.40399I −1.47702 − 8.56336I
u = 0.021881 + 0.164630I
a = −1.82275 + 3.64426I
b = −1.216860 − 0.709160I
4.52125 + 2.53747I 2.43865 − 1.71275I
u = 0.021881 − 0.164630I
a = −1.82275 − 3.64426I
b = −1.216860 + 0.709160I
4.52125 − 2.53747I 2.43865 + 1.71275I
u = −1.63601 + 1.50675I
a = 0.001439 + 0.368895I
b = 0.492148 + 0.450600I
−0.39191 + 6.22910I −3.95991 − 11.28166I
u = −1.63601 − 1.50675I
a = 0.001439 − 0.368895I
b = 0.492148 − 0.450600I
−0.39191 − 6.22910I −3.95991 + 11.28166I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.88393 + 1.22339I
a = −0.139202 + 0.262568I
b = −0.096849 + 0.815314I
−2.20294 − 4.46082I −11.64801 + 4.72827I
u = −1.88393 − 1.22339I
a = −0.139202 − 0.262568I
b = −0.096849 − 0.815314I
−2.20294 + 4.46082I −11.64801 − 4.72827I
u = 1.90087 + 1.52654I
a = −0.051888 − 0.269749I
b = 0.225615 − 0.583583I
−5.22591 − 0.91968I −15.5307 + 7.1820I
u = 1.90087 − 1.52654I
a = −0.051888 + 0.269749I
b = 0.225615 + 0.583583I
−5.22591 + 0.91968I −15.5307 − 7.1820I
13
III. I
u
3
= h−u
2
+ b + 1, u
8
− u
7
− 2u
6
+ u
5
+ 3u
4
− 4u
2
+ a + u + 2, u
9
−
2u
7
− u
6
+ 2u
5
+ 2u
4
− 2u
3
− u
2
+ u + 1i
(i) Arc colorings
a
2
=
1
0
a
8
=
0
u
a
3
=
1
u
2
a
5
=
−u
8
+ u
7
+ 2u
6
− u
5
− 3u
4
+ 4u
2
− u − 2
u
2
− 1
a
6
=
−u
8
+ u
7
+ 2u
6
− u
5
− 3u
4
+ 3u
2
− u − 2
−u
4
+ u
2
− 1
a
9
=
−2u
8
+ u
7
+ 3u
6
− 3u
4
− u
3
+ 4u
2
− 2u − 1
−u
8
+ 2u
6
+ u
5
− 2u
4
− 2u
3
+ 2u
2
+ u − 1
a
1
=
u
8
− 2u
7
− u
6
+ 2u
5
+ 2u
4
− u
3
− 3u
2
+ 3u
u
8
− u
7
− 2u
6
+ u
5
+ 3u
4
− 4u
2
+ u + 2
a
4
=
−u
8
+ u
7
+ 2u
6
− u
5
− 3u
4
+ 3u
2
− u − 1
u
2
− 1
a
10
=
−u
8
+ u
7
+ u
6
− u
5
− u
4
+ 2u
2
− 2u
−u
8
+ 2u
6
+ u
5
− 2u
4
− u
3
+ 2u
2
− 1
a
11
=
−u
8
+ u
7
+ u
6
− u
5
− u
4
+ 2u
2
− 2u
−2u
8
+ 4u
6
+ u
5
− 4u
4
− 2u
3
+ 4u
2
− 2
a
7
=
2u
8
− 4u
6
− u
5
+ 4u
4
+ 3u
3
− 5u
2
− u + 3
u
7
− u
6
− u
5
+ u
3
+ u
2
− 2u + 1
a
7
=
2u
8
− 4u
6
− u
5
+ 4u
4
+ 3u
3
− 5u
2
− u + 3
u
7
− u
6
− u
5
+ u
3
+ u
2
− 2u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 6u
7
− 2u
6
− 7u
5
− 4u
4
+ 7u
3
+ 8u
2
− 9u
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
u
9
+ u
8
− u
7
− 2u
6
+ 2u
5
+ 2u
4
− u
3
− 2u
2
+ 1
c
2
, c
9
u
9
− 2u
7
− u
6
+ 2u
5
+ 2u
4
− 2u
3
− u
2
+ u + 1
c
3
, c
5
u
9
+ 4u
8
+ 8u
7
+ 13u
6
+ 18u
5
+ 18u
4
+ 14u
3
+ 9u
2
+ 3u + 1
c
4
u
9
− 5u
8
+ 12u
7
− 15u
6
+ 10u
5
− 3u
4
+ 2u
3
− 2u
2
+ 1
c
6
, c
7
u
9
− 2u
8
+ 7u
7
− 10u
6
+ 16u
5
− 16u
4
+ 13u
3
− 9u
2
+ 2u − 1
c
10
, c
11
u
9
+ 2u
8
+ 7u
7
+ 10u
6
+ 16u
5
+ 16u
4
+ 13u
3
+ 9u
2
+ 2u + 1
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
9
− 3y
8
+ 9y
7
− 14y
6
+ 18y
5
− 18y
4
+ 13y
3
− 8y
2
+ 4y −1
c
2
, c
9
y
9
− 4y
8
+ 8y
7
− 13y
6
+ 18y
5
− 18y
4
+ 14y
3
− 9y
2
+ 3y −1
c
3
, c
5
y
9
− 4y
7
+ 3y
6
+ 14y
5
− 14y
4
− 46y
3
− 33y
2
− 9y −1
c
4
y
9
− y
8
+ 14y
7
− 11y
6
+ 38y
5
− 19y
4
+ 22y
3
+ 2y
2
+ 4y −1
c
6
, c
7
, c
10
c
11
y
9
+ 10y
8
+ 41y
7
+ 86y
6
+ 86y
5
+ 4y
4
− 75y
3
− 61y
2
− 14y −1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.697125 + 0.630614I
a = −0.113094 + 1.126000I
b = −0.911691 + 0.879233I
1.14384 − 3.68908I 0.51130 + 5.82682I
u = 0.697125 − 0.630614I
a = −0.113094 − 1.126000I
b = −0.911691 − 0.879233I
1.14384 + 3.68908I 0.51130 − 5.82682I
u = −0.706353 + 0.887392I
a = 0.174357 − 0.757557I
b = −1.28853 − 1.25362I
3.87432 + 3.77454I −0.80820 − 6.90291I
u = −0.706353 − 0.887392I
a = 0.174357 + 0.757557I
b = −1.28853 + 1.25362I
3.87432 − 3.77454I −0.80820 + 6.90291I
u = −1.20053
a = −0.693833
b = 0.441270
−4.78668 −8.18270
u = 1.180420 + 0.249688I
a = −0.628101 + 0.278164I
b = 0.331044 + 0.589474I
−0.89563 − 5.00672I −4.18305 + 4.27017I
u = 1.180420 − 0.249688I
a = −0.628101 − 0.278164I
b = 0.331044 − 0.589474I
−0.89563 + 5.00672I −4.18305 − 4.27017I
u = −0.570926 + 0.421204I
a = −0.58625 − 1.89814I
b = −0.851457 − 0.480952I
8.14041 + 4.21823I 7.07132 − 5.34400I
u = −0.570926 − 0.421204I
a = −0.58625 + 1.89814I
b = −0.851457 + 0.480952I
8.14041 − 4.21823I 7.07132 + 5.34400I
17
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
8
(u
9
+ u
8
+ ··· − 2u
2
+ 1)(u
22
− u
21
+ ··· − u + 1)
· (u
24
− 3u
23
+ ··· − 12u + 5)
c
2
, c
9
(u
9
− 2u
7
− u
6
+ 2u
5
+ 2u
4
− 2u
3
− u
2
+ u + 1)
· (u
22
− 4u
20
+ ··· + 14u + 5)(u
24
− u
23
+ ··· + 14u + 11)
c
3
, c
5
(u
9
+ 4u
8
+ 8u
7
+ 13u
6
+ 18u
5
+ 18u
4
+ 14u
3
+ 9u
2
+ 3u + 1)
· (u
22
+ 2u
21
+ ··· − 2u + 1)(u
24
+ u
23
+ ··· − 188u + 145)
c
4
(u
9
− 5u
8
+ 12u
7
− 15u
6
+ 10u
5
− 3u
4
+ 2u
3
− 2u
2
+ 1)
· ((u
12
− 5u
11
+ ··· + 3u
2
+ 1)
2
)(u
22
+ 14u
21
+ ··· + 11u + 2)
c
6
, c
7
(u
9
− 2u
8
+ 7u
7
− 10u
6
+ 16u
5
− 16u
4
+ 13u
3
− 9u
2
+ 2u − 1)
· ((u
12
+ 3u
11
+ ··· − 2u + 1)
2
)(u
22
− 5u
21
+ ··· − 3u + 4)
c
10
, c
11
(u
9
+ 2u
8
+ 7u
7
+ 10u
6
+ 16u
5
+ 16u
4
+ 13u
3
+ 9u
2
+ 2u + 1)
· ((u
12
+ 3u
11
+ ··· − 2u + 1)
2
)(u
22
− 5u
21
+ ··· − 3u + 4)
18
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
8
(y
9
− 3y
8
+ 9y
7
− 14y
6
+ 18y
5
− 18y
4
+ 13y
3
− 8y
2
+ 4y −1)
· (y
22
+ 9y
21
+ ··· + 21y + 1)(y
24
− 5y
23
+ ··· + 116y + 25)
c
2
, c
9
(y
9
− 4y
8
+ 8y
7
− 13y
6
+ 18y
5
− 18y
4
+ 14y
3
− 9y
2
+ 3y −1)
· (y
22
− 8y
21
+ ··· − 246y + 25)(y
24
− 9y
23
+ ··· + 7812y + 121)
c
3
, c
5
(y
9
− 4y
7
+ 3y
6
+ 14y
5
− 14y
4
− 46y
3
− 33y
2
− 9y −1)
· (y
22
− 28y
21
+ ··· − 10y + 1)(y
24
− 9y
23
+ ··· − 29544y + 21025)
c
4
(y
9
− y
8
+ 14y
7
− 11y
6
+ 38y
5
− 19y
4
+ 22y
3
+ 2y
2
+ 4y −1)
· ((y
12
+ y
11
+ ··· + 6y + 1)
2
)(y
22
+ 36y
20
+ ··· + 71y + 4)
c
6
, c
7
, c
10
c
11
(y
9
+ 10y
8
+ 41y
7
+ 86y
6
+ 86y
5
+ 4y
4
− 75y
3
− 61y
2
− 14y −1)
· ((y
12
+ 9y
11
+ ··· − 6y + 1)
2
)(y
22
+ 19y
21
+ ··· + 7y + 16)
19
