12n
0377
(K12n
0377
)
A knot diagram
1
Linearized knot diagam
3 6 8 11 2 11 1 4 12 4 7 9
Solving Sequence
4,9
8
1,3
2 7 12 10 11 5 6
c
8
c
3
c
1
c
7
c
12
c
9
c
10
c
4
c
6
c
2
, c
5
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−117109314812117u
21
− 185021907483518u
20
+ ··· + 71466899580913b − 239788584214052,
a − 1, u
22
+ 2u
21
+ ··· + 5u + 1i
I
u
2
= h49557u
15
− 41829u
14
+ ··· + 54911b + 38554, a + 1, u
16
− u
15
+ ··· + 2u + 1i
I
u
3
= h1927557535u
13
− 1956930209u
12
+ ··· + 24185780481b − 19316532454,
60475263347u
13
+ 4869248027u
12
+ ··· + 24185780481a + 118878628659,
u
14
− 6u
12
+ u
11
− 7u
10
+ 127u
8
− 27u
7
− 371u
6
+ 81u
5
+ 482u
4
− 41u
3
− 201u
2
+ 21u − 1i
I
u
4
= hb, a − 1, u − 1i
I
u
5
= hb, a − u − 2, u
2
+ u − 1i
* 5 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−1.17 × 10
14
u
21
− 1.85 × 10
14
u
20
+ · · · + 7.15 × 10
13
b − 2.40 ×
10
14
, a − 1, u
22
+ 2u
21
+ · · · + 5u + 1i
(i) Arc colorings
a
4
=
0
u
a
9
=
1
0
a
8
=
1
u
2
a
1
=
1
1.63865u
21
+ 2.58892u
20
+ ··· + 9.18338u + 3.35524
a
3
=
−u
−u
3
+ u
a
2
=
−0.203702u
21
− 0.308210u
20
+ ··· − 1.80327u + 0.311615
1.78179u
21
+ 2.92653u
20
+ ··· + 10.6944u + 3.94443
a
7
=
1.63865u
21
+ 2.58892u
20
+ ··· + 9.18338u + 4.35524
−0.810203u
21
− 1.40823u
20
+ ··· − 4.36829u − 3.21832
a
12
=
−1.63865u
21
− 2.58892u
20
+ ··· − 9.18338u − 2.35524
1.63865u
21
+ 2.58892u
20
+ ··· + 9.18338u + 3.35524
a
10
=
−2.24515u
21
− 3.68894u
20
+ ··· − 11.7484u − 4.88518
0.606501u
21
+ 1.10002u
20
+ ··· + 2.56501u + 2.52994
a
11
=
−2.24515u
21
− 3.68894u
20
+ ··· − 11.7484u − 4.88518
0.436584u
21
+ 0.693675u
20
+ ··· + 0.803325u + 1.72857
a
5
=
0.851249u
21
+ 1.42218u
20
+ ··· + 7.28853u + 2.44520
−1.23619u
21
− 2.26646u
20
+ ··· − 9.46092u − 3.86352
a
6
=
0.573533u
21
+ 0.906242u
20
+ ··· + 4.56014u + 1.08378
−2.19732u
21
− 3.69644u
20
+ ··· − 15.9510u − 6.18859
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
797326516733960
71466899580913
u
21
+
1296483474868809
71466899580913
u
20
+ ··· +
4697397509475603
71466899580913
u +
2248576824709077
71466899580913
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
22
+ 4u
21
+ ··· − 126u + 25
c
2
, c
5
u
22
+ 8u
21
+ ··· + 12u + 5
c
3
, c
8
u
22
+ 2u
21
+ ··· + 5u + 1
c
4
, c
10
u
22
+ 28u
20
+ ··· − 2525u + 1849
c
6
, c
11
u
22
+ 3u
21
+ ··· + 11u + 1
c
7
u
22
− 15u
21
+ ··· − 384u + 64
c
9
, c
12
u
22
+ 11u
21
+ ··· + 36u + 5
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
22
+ 44y
21
+ ··· − 15326y + 625
c
2
, c
5
y
22
− 4y
21
+ ··· + 126y + 25
c
3
, c
8
y
22
− 26y
21
+ ··· − 5y + 1
c
4
, c
10
y
22
+ 56y
21
+ ··· − 20797825y + 3418801
c
6
, c
11
y
22
− 39y
21
+ ··· + 71y + 1
c
7
y
22
+ 7y
21
+ ··· + 32768y + 4096
c
9
, c
12
y
22
+ 3y
21
+ ··· − 96y + 25
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.620794 + 0.535509I
a = 1.00000
b = 0.269144 − 0.300532I
−1.73171 + 0.39209I −6.82911 − 0.72643I
u = −0.620794 − 0.535509I
a = 1.00000
b = 0.269144 + 0.300532I
−1.73171 − 0.39209I −6.82911 + 0.72643I
u = −0.105696 + 0.706053I
a = 1.00000
b = −0.063961 + 0.862281I
−3.10436 + 1.56753I −1.37917 − 0.82636I
u = −0.105696 − 0.706053I
a = 1.00000
b = −0.063961 − 0.862281I
−3.10436 − 1.56753I −1.37917 + 0.82636I
u = 1.333060 + 0.198330I
a = 1.00000
b = 0.723572 − 0.172331I
2.84189 + 0.60050I 3.92920 + 0.28556I
u = 1.333060 − 0.198330I
a = 1.00000
b = 0.723572 + 0.172331I
2.84189 − 0.60050I 3.92920 − 0.28556I
u = −0.056495 + 0.552181I
a = 1.00000
b = −0.487168 − 1.034230I
−0.79249 + 2.57985I 0.76440 − 3.56435I
u = −0.056495 − 0.552181I
a = 1.00000
b = −0.487168 + 1.034230I
−0.79249 − 2.57985I 0.76440 + 3.56435I
u = −1.41493 + 0.47947I
a = 1.00000
b = 0.921745 − 0.224366I
1.50957 − 6.23042I 2.89462 + 2.84257I
u = −1.41493 − 0.47947I
a = 1.00000
b = 0.921745 + 0.224366I
1.50957 + 6.23042I 2.89462 − 2.84257I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.290445 + 0.380257I
a = 1.00000
b = −0.658679 − 0.004198I
1.41421 + 0.48473I 7.29881 − 2.06718I
u = 0.290445 − 0.380257I
a = 1.00000
b = −0.658679 + 0.004198I
1.41421 − 0.48473I 7.29881 + 2.06718I
u = 1.52781 + 0.03204I
a = 1.00000
b = 1.09000 − 1.35357I
15.9443 − 3.5566I 4.85061 + 2.05487I
u = 1.52781 − 0.03204I
a = 1.00000
b = 1.09000 + 1.35357I
15.9443 + 3.5566I 4.85061 − 2.05487I
u = −1.58478 + 0.02890I
a = 1.00000
b = 1.25856 + 1.26328I
16.5982 − 4.1754I 5.36851 + 2.13460I
u = −1.58478 − 0.02890I
a = 1.00000
b = 1.25856 − 1.26328I
16.5982 + 4.1754I 5.36851 − 2.13460I
u = −0.369059 + 0.081714I
a = 1.00000
b = −0.113829 + 1.356110I
−3.96081 − 3.52484I 7.30433 + 8.96045I
u = −0.369059 − 0.081714I
a = 1.00000
b = −0.113829 − 1.356110I
−3.96081 + 3.52484I 7.30433 − 8.96045I
u = 1.74996 + 0.63959I
a = 1.00000
b = 1.32824 + 1.03454I
17.0359 + 5.3783I 5.15920 − 2.10879I
u = 1.74996 − 0.63959I
a = 1.00000
b = 1.32824 − 1.03454I
17.0359 − 5.3783I 5.15920 + 2.10879I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.74953 + 0.66838I
a = 1.00000
b = 1.23238 − 1.16964I
16.7528 − 13.3075I 4.63861 + 6.01533I
u = −1.74953 − 0.66838I
a = 1.00000
b = 1.23238 + 1.16964I
16.7528 + 13.3075I 4.63861 − 6.01533I
7
II.
I
u
2
= h49557u
15
−41829u
14
+· · ·+54911b+38554, a+1, u
16
−u
15
+· · ·+2u+1i
(i) Arc colorings
a
4
=
0
u
a
9
=
1
0
a
8
=
1
u
2
a
1
=
−1
−0.902497u
15
+ 0.761760u
14
+ ··· − 1.46801u − 0.702118
a
3
=
−u
−u
3
+ u
a
2
=
0.370636u
15
− 0.375917u
14
+ ··· − 1.18397u − 1.14074
−0.914371u
15
+ 0.649196u
14
+ ··· − 0.644115u − 0.556100
a
7
=
0.902497u
15
− 0.761760u
14
+ ··· + 1.46801u + 1.70212
0.217570u
15
− 0.135273u
14
+ ··· + 1.32194u − 1.08969
a
12
=
0.902497u
15
− 0.761760u
14
+ ··· + 1.46801u − 0.297882
−0.902497u
15
+ 0.761760u
14
+ ··· − 1.46801u − 0.702118
a
10
=
−0.314290u
15
+ 0.250569u
14
+ ··· − 1.33004u − 0.932545
−0.588206u
15
+ 0.511191u
14
+ ··· − 0.137969u + 1.23043
a
11
=
−0.314290u
15
+ 0.250569u
14
+ ··· − 1.33004u − 0.932545
−0.880243u
15
+ 0.779480u
14
+ ··· + 0.303764u + 1.29415
a
5
=
−0.110615u
15
− 0.168272u
14
+ ··· + 0.347162u + 0.575021
−0.320883u
15
− 0.226038u
14
+ ··· + 4.37586u + 0.584109
a
6
=
0.327475u
15
− 0.297354u
14
+ ··· − 1.08177u + 0.899237
−0.366539u
15
+ 0.127953u
14
+ ··· + 4.97174u + 1.11795
(ii) Obstruction class = 1
(iii) Cusp Shapes =
57612
54911
u
15
−
210798
54911
u
14
+ ··· +
882421
54911
u +
37697
54911
8
(iv) u-Polynomials at the component
9
Crossings u-Polynomials at each crossing
c
1
u
16
− 5u
15
+ ··· − 9u + 1
c
2
u
16
+ 5u
15
+ ··· + 5u + 1
c
3
u
16
+ u
15
+ ··· − 2u + 1
c
4
u
16
− u
15
+ ··· + 2u + 1
c
5
u
16
− 5u
15
+ ··· − 5u + 1
c
6
u
16
+ 2u
15
+ ··· + 2u + 1
c
7
u
16
− 3u
15
+ ··· − u + 1
c
8
u
16
− u
15
+ ··· + 2u + 1
c
9
u
16
+ 8u
15
+ ··· + 23u + 5
c
10
u
16
+ u
15
+ ··· − 2u + 1
c
11
u
16
− 2u
15
+ ··· − 2u + 1
c
12
u
16
− 8u
15
+ ··· − 23u + 5
10
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
16
+ 11y
15
+ ··· − 9y + 1
c
2
, c
5
y
16
− 5y
15
+ ··· − 9y + 1
c
3
, c
8
y
16
− 11y
15
+ ··· + 4y + 1
c
4
, c
10
y
16
+ 15y
15
+ ··· − 8y + 1
c
6
, c
11
y
16
− 12y
15
+ ··· − 4y + 1
c
7
y
16
+ 7y
15
+ ··· − 5y + 1
c
9
, c
12
y
16
+ 6y
15
+ ··· − 139y + 25
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.954777 + 0.142609I
a = −1.00000
b = −0.455945 − 1.267540I
−0.95352 − 2.33937I 3.69928 + 2.27145I
u = −0.954777 − 0.142609I
a = −1.00000
b = −0.455945 + 1.267540I
−0.95352 + 2.33937I 3.69928 − 2.27145I
u = 0.845388 + 0.160874I
a = −1.00000
b = −0.42793 − 1.42727I
0.65993 + 3.36157I 4.55859 − 4.29560I
u = 0.845388 − 0.160874I
a = −1.00000
b = −0.42793 + 1.42727I
0.65993 − 3.36157I 4.55859 + 4.29560I
u = −0.661594 + 0.474483I
a = −1.00000
b = −0.654799 + 0.242436I
−0.903865 + 0.284978I 4.15730 + 0.76962I
u = −0.661594 − 0.474483I
a = −1.00000
b = −0.654799 − 0.242436I
−0.903865 − 0.284978I 4.15730 − 0.76962I
u = −0.030530 + 1.200850I
a = −1.00000
b = 0.643145 + 0.122983I
9.47497 + 3.82028I 0.82572 − 2.11435I
u = −0.030530 − 1.200850I
a = −1.00000
b = 0.643145 − 0.122983I
9.47497 − 3.82028I 0.82572 + 2.11435I
u = 1.329520 + 0.350471I
a = −1.00000
b = −1.140330 − 0.634965I
3.99670 + 2.81389I 5.17513 − 2.85413I
u = 1.329520 − 0.350471I
a = −1.00000
b = −1.140330 + 0.634965I
3.99670 − 2.81389I 5.17513 + 2.85413I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.38404 + 0.60477I
a = −1.00000
b = −0.826464 + 0.694550I
1.21063 − 7.51551I 0.30224 + 8.63073I
u = −1.38404 − 0.60477I
a = −1.00000
b = −0.826464 − 0.694550I
1.21063 + 7.51551I 0.30224 − 8.63073I
u = 1.48217 + 0.35127I
a = −1.00000
b = −0.941782 − 0.971401I
3.96834 + 3.49267I 6.27073 − 2.05893I
u = 1.48217 − 0.35127I
a = −1.00000
b = −0.941782 + 0.971401I
3.96834 − 3.49267I 6.27073 + 2.05893I
u = −0.126135 + 0.368078I
a = −1.00000
b = −0.195896 − 1.263040I
−4.29370 + 3.24685I −6.98898 + 1.98047I
u = −0.126135 − 0.368078I
a = −1.00000
b = −0.195896 + 1.263040I
−4.29370 − 3.24685I −6.98898 − 1.98047I
14
III.
I
u
3
= h1.93 × 10
9
u
13
− 1.96 × 10
9
u
12
+ · · · + 2.42 × 10
10
b − 1.93 × 10
10
, 6.05 ×
10
10
u
13
+4.87×10
9
u
12
+· · ·+2.42×10
10
a+1.19×10
11
, u
14
−6u
12
+· · ·+21u−1i
(i) Arc colorings
a
4
=
0
u
a
9
=
1
0
a
8
=
1
u
2
a
1
=
−2.50045u
13
− 0.201327u
12
+ ··· + 498.185u − 4.91523
−0.0796980u
13
+ 0.0809124u
12
+ ··· + 1.72742u + 0.798673
a
3
=
−u
−u
3
+ u
a
2
=
−2.42075u
13
− 0.282239u
12
+ ··· + 496.457u − 4.71390
−0.0369901u
13
+ 0.00188849u
12
+ ··· + 5.23369u + 0.516434
a
7
=
−2.50045u
13
− 0.201327u
12
+ ··· + 498.185u − 3.91523
−0.0796980u
13
+ 0.0809124u
12
+ ··· + 1.72742u + 0.798673
a
12
=
−2.42075u
13
− 0.282239u
12
+ ··· + 496.457u − 5.71390
−0.0796980u
13
+ 0.0809124u
12
+ ··· + 1.72742u + 0.798673
a
10
=
2.45112u
13
+ 0.157103u
12
+ ··· − 490.012u + 11.1679
−0.137834u
13
+ 0.206995u
12
+ ··· − 7.06018u − 0.434576
a
11
=
2.45112u
13
+ 0.157103u
12
+ ··· − 490.012u + 11.1679
−0.0855064u
13
+ 0.157616u
12
+ ··· − 7.90821u − 0.277473
a
5
=
1.90624u
13
− 0.119682u
12
+ ··· − 392.906u + 68.8828
0.0998596u
13
+ 0.0125182u
12
+ ··· − 24.2787u + 2.08825
a
6
=
2.12010u
13
+ 0.153572u
12
+ ··· − 440.511u + 24.1292
0.00222918u
13
+ 0.0614998u
12
+ ··· − 12.0319u + 0.363834
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
6739667375
24185780481
u
13
+
3644507297
24185780481
u
12
+ ··· −
1559248921091
24185780481
u +
342583935034
24185780481
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
7
+ 4u
5
+ u
4
− 6u
3
+ 3u
2
− 2u + 1)
2
c
2
, c
5
(u
7
− 2u
6
+ 2u
5
+ u
4
− 2u
3
+ 3u
2
− 2u + 1)
2
c
3
, c
8
u
14
− 6u
12
+ ··· + 21u − 1
c
4
, c
10
u
14
+ 2u
13
+ ··· + 2543u + 563
c
6
, c
11
u
14
− 3u
13
+ ··· − 666u − 297
c
7
(u + 1)
14
c
9
, c
12
(u
7
− 3u
6
+ 3u
5
+ 2u
4
− 6u
3
+ 3u
2
+ 3u − 2)
2
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
7
+ 8y
6
+ 4y
5
− 53y
4
+ 14y
3
+ 13y
2
− 2y −1)
2
c
2
, c
5
(y
7
+ 4y
5
− y
4
− 6y
3
− 3y
2
− 2y −1)
2
c
3
, c
8
y
14
− 12y
13
+ ··· − 39y + 1
c
4
, c
10
y
14
+ 36y
13
+ ··· − 1927943y + 316969
c
6
, c
11
y
14
− 23y
13
+ ··· − 641358y + 88209
c
7
(y −1)
14
c
9
, c
12
(y
7
− 3y
6
+ 9y
5
− 16y
4
+ 30y
3
− 37y
2
+ 21y −4)
2
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.215940 + 0.220023I
a = −1.54528 − 0.08333I
b = −1.25449 + 0.70767I
5.41964 − 2.53884I 12.86344 + 1.81085I
u = −1.215940 − 0.220023I
a = −1.54528 + 0.08333I
b = −1.25449 − 0.70767I
5.41964 + 2.53884I 12.86344 − 1.81085I
u = 0.758211
a = −2.80601
b = −0.613130
0.459094 13.7190
u = −1.400900 + 0.122011I
a = −1.010470 + 0.394732I
b = −0.833081 + 1.114220I
3.62587 − 4.72329I 4.98093 + 9.17288I
u = −1.400900 − 0.122011I
a = −1.010470 − 0.394732I
b = −0.833081 − 1.114220I
3.62587 + 4.72329I 4.98093 − 9.17288I
u = 1.36740 + 0.67627I
a = −0.858613 + 0.335410I
b = −0.833081 − 1.114220I
3.62587 + 4.72329I 4.98093 − 9.17288I
u = 1.36740 − 0.67627I
a = −0.858613 − 0.335410I
b = −0.833081 + 1.114220I
3.62587 − 4.72329I 4.98093 + 9.17288I
u = 1.89730 + 0.23868I
a = −0.645256 − 0.034794I
b = −1.25449 − 0.70767I
5.41964 + 2.53884I 12.86344 − 1.81085I
u = 1.89730 − 0.23868I
a = −0.645256 + 0.034794I
b = −1.25449 + 0.70767I
5.41964 − 2.53884I 12.86344 + 1.81085I
u = 0.0517518 + 0.0475534I
a = 21.1195 + 23.2984I
b = 0.894131 + 0.113662I
10.46420 + 3.91715I 10.79602 − 3.00324I
18
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.0517518 − 0.0475534I
a = 21.1195 − 23.2984I
b = 0.894131 − 0.113662I
10.46420 − 3.91715I 10.79602 + 3.00324I
u = −2.12755
a = −0.356378
b = −0.613130
0.459094 13.7190
u = −0.01495 + 2.21004I
a = 0.0213576 − 0.0235612I
b = 0.894131 + 0.113662I
10.46420 + 3.91715I 10.79602 − 3.00324I
u = −0.01495 − 2.21004I
a = 0.0213576 + 0.0235612I
b = 0.894131 − 0.113662I
10.46420 − 3.91715I 10.79602 + 3.00324I
19
IV. I
u
4
= hb, a − 1, u − 1i
(i) Arc colorings
a
4
=
0
1
a
9
=
1
0
a
8
=
1
1
a
1
=
1
0
a
3
=
−1
0
a
2
=
1
0
a
7
=
0
1
a
12
=
1
0
a
10
=
1
0
a
11
=
1
1
a
5
=
−1
0
a
6
=
−1
0
(ii) Obstruction class = −1
(iii) Cusp Shapes = 6
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
c
9
, c
12
u
c
3
, c
4
, c
6
c
7
, c
8
, c
10
c
11
u − 1
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
9
, c
12
y
c
3
, c
4
, c
6
c
7
, c
8
, c
10
c
11
y −1
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 1.00000
b = 0
1.64493 6.00000
23
V. I
u
5
= hb, a − u − 2, u
2
+ u − 1i
(i) Arc colorings
a
4
=
0
u
a
9
=
1
0
a
8
=
1
−u + 1
a
1
=
u + 2
0
a
3
=
−u
−u + 1
a
2
=
2
−u + 1
a
7
=
−u − 1
−u + 1
a
12
=
u + 2
0
a
10
=
1
0
a
11
=
1
−u + 1
a
5
=
−u
−u + 1
a
6
=
−u − 2
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −5
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
11
(u − 1)
2
c
3
, c
4
u
2
− u − 1
c
5
, c
6
, c
7
(u + 1)
2
c
8
, c
10
u
2
+ u − 1
c
9
, c
12
u
2
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
7
, c
11
(y −1)
2
c
3
, c
4
, c
8
c
10
y
2
− 3y + 1
c
9
, c
12
y
2
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.618034
a = 2.61803
b = 0
0 −5.00000
u = −1.61803
a = 0.381966
b = 0
0 −5.00000
27
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u(u − 1)
2
(u
7
+ 4u
5
+ u
4
− 6u
3
+ 3u
2
− 2u + 1)
2
· (u
16
− 5u
15
+ ··· − 9u + 1)(u
22
+ 4u
21
+ ··· − 126u + 25)
c
2
u(u − 1)
2
(u
7
− 2u
6
+ 2u
5
+ u
4
− 2u
3
+ 3u
2
− 2u + 1)
2
· (u
16
+ 5u
15
+ ··· + 5u + 1)(u
22
+ 8u
21
+ ··· + 12u + 5)
c
3
(u − 1)(u
2
− u − 1)(u
14
− 6u
12
+ ··· + 21u − 1)(u
16
+ u
15
+ ··· − 2u + 1)
· (u
22
+ 2u
21
+ ··· + 5u + 1)
c
4
(u − 1)(u
2
− u − 1)(u
14
+ 2u
13
+ ··· + 2543u + 563)
· (u
16
− u
15
+ ··· + 2u + 1)(u
22
+ 28u
20
+ ··· − 2525u + 1849)
c
5
u(u + 1)
2
(u
7
− 2u
6
+ 2u
5
+ u
4
− 2u
3
+ 3u
2
− 2u + 1)
2
· (u
16
− 5u
15
+ ··· − 5u + 1)(u
22
+ 8u
21
+ ··· + 12u + 5)
c
6
(u − 1)(u + 1)
2
(u
14
− 3u
13
+ ··· − 666u − 297)
· (u
16
+ 2u
15
+ ··· + 2u + 1)(u
22
+ 3u
21
+ ··· + 11u + 1)
c
7
(u − 1)(u + 1)
16
(u
16
− 3u
15
+ ··· − u + 1)
· (u
22
− 15u
21
+ ··· − 384u + 64)
c
8
(u − 1)(u
2
+ u − 1)(u
14
− 6u
12
+ ··· + 21u − 1)(u
16
− u
15
+ ··· + 2u + 1)
· (u
22
+ 2u
21
+ ··· + 5u + 1)
c
9
u
3
(u
7
− 3u
6
+ 3u
5
+ 2u
4
− 6u
3
+ 3u
2
+ 3u − 2)
2
· (u
16
+ 8u
15
+ ··· + 23u + 5)(u
22
+ 11u
21
+ ··· + 36u + 5)
c
10
(u − 1)(u
2
+ u − 1)(u
14
+ 2u
13
+ ··· + 2543u + 563)
· (u
16
+ u
15
+ ··· − 2u + 1)(u
22
+ 28u
20
+ ··· − 2525u + 1849)
c
11
((u − 1)
3
)(u
14
− 3u
13
+ ··· − 666u − 297)(u
16
− 2u
15
+ ··· − 2u + 1)
· (u
22
+ 3u
21
+ ··· + 11u + 1)
c
12
u
3
(u
7
− 3u
6
+ 3u
5
+ 2u
4
− 6u
3
+ 3u
2
+ 3u − 2)
2
· (u
16
− 8u
15
+ ··· − 23u + 5)(u
22
+ 11u
21
+ ··· + 36u + 5)
28
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y(y −1)
2
(y
7
+ 8y
6
+ 4y
5
− 53y
4
+ 14y
3
+ 13y
2
− 2y −1)
2
· (y
16
+ 11y
15
+ ··· − 9y + 1)(y
22
+ 44y
21
+ ··· − 15326y + 625)
c
2
, c
5
y(y −1)
2
(y
7
+ 4y
5
− y
4
− 6y
3
− 3y
2
− 2y −1)
2
· (y
16
− 5y
15
+ ··· − 9y + 1)(y
22
− 4y
21
+ ··· + 126y + 25)
c
3
, c
8
(y −1)(y
2
− 3y + 1)(y
14
− 12y
13
+ ··· − 39y + 1)
· (y
16
− 11y
15
+ ··· + 4y + 1)(y
22
− 26y
21
+ ··· − 5y + 1)
c
4
, c
10
(y −1)(y
2
− 3y + 1)(y
14
+ 36y
13
+ ··· − 1927943y + 316969)
· (y
16
+ 15y
15
+ ··· − 8y + 1)
· (y
22
+ 56y
21
+ ··· − 20797825y + 3418801)
c
6
, c
11
((y −1)
3
)(y
14
− 23y
13
+ ··· − 641358y + 88209)
· (y
16
− 12y
15
+ ··· − 4y + 1)(y
22
− 39y
21
+ ··· + 71y + 1)
c
7
((y −1)
17
)(y
16
+ 7y
15
+ ··· − 5y + 1)
· (y
22
+ 7y
21
+ ··· + 32768y + 4096)
c
9
, c
12
y
3
(y
7
− 3y
6
+ 9y
5
− 16y
4
+ 30y
3
− 37y
2
+ 21y −4)
2
· (y
16
+ 6y
15
+ ··· − 139y + 25)(y
22
+ 3y
21
+ ··· − 96y + 25)
29
