12a
0939
(K12a
0939
)
A knot diagram
1
Linearized knot diagam
4 6 9 1 3 12 11 2 5 8 7 10
Solving Sequence
1,4
2
5,9
10 3 6 8 11 7 12
c
1
c
4
c
9
c
3
c
5
c
8
c
10
c
7
c
12
c
2
, c
6
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h8191u
30
− 26107u
29
+ ··· + 32768b − 33535, 263u
30
− 1185u
29
+ ··· + 512a − 233,
u
31
− 4u
30
+ ··· − 6u − 1i
I
u
2
= h−2.55785 × 10
49
u
51
− 2.68690 × 10
50
u
50
+ ··· + 5.56688 × 10
49
b − 6.70004 × 10
48
,
− 8.26170 × 10
49
u
51
− 6.92304 × 10
50
u
50
+ ··· + 5.56688 × 10
49
a − 1.67397 × 10
49
, u
52
+ 9u
51
+ ··· + 2u + 1i
I
u
3
= h16b
4
− 8b
3
+ 4b
2
+ 1, a, u − 1i
* 3 irreducible components of dim
C
= 0, with total 87 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
= h8191u
30
− 26107u
29
+ · · · + 32768b − 33535, 263u
30
− 1185u
29
+
· · · + 512a − 233, u
31
− 4u
30
+ · · · − 6u − 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
5
=
−u
u
a
9
=
−0.513672u
30
+ 2.31445u
29
+ ··· + 9.14648u + 0.455078
−0.249969u
30
+ 0.796722u
29
+ ··· + 4.14828u + 1.02341
a
10
=
−0.531281u
30
+ 2.21890u
29
+ ··· + 9.57047u + 0.398468
−0.232361u
30
+ 0.892273u
29
+ ··· + 3.72430u + 1.08002
a
3
=
−
1
4
u
30
+
3
4
u
29
+ ··· +
7
4
u +
5
4
1
4
u
30
−
3
4
u
29
+ ··· −
7
4
u −
1
4
a
6
=
1
4
u
30
−
5
4
u
29
+ ··· −
3
4
u +
1
4
−
1
4
u
30
+
5
4
u
29
+ ··· −
1
4
u −
1
4
a
8
=
−0.570282u
30
+ 2.52328u
29
+ ··· + 12.2498u + 1.21872
−0.415955u
30
+ 1.69305u
29
+ ··· + 3.98602u + 1.00580
a
11
=
−0.207794u
30
+ 1.06973u
29
+ ··· + 1.39249u − 2.33078
0.0252075u
30
− 0.209045u
29
+ ··· + 3.75287u + 0.573425
a
7
=
0.253632u
30
− 1.26767u
29
+ ··· + 3.22989u + 0.245880
−0.258606u
30
+ 1.29205u
29
+ ··· − 0.203064u − 0.240417
a
12
=
0.249969u
30
− 1.24985u
29
+ ··· − 1.74985u + 2.25003
−0.249939u
30
+ 1.24969u
29
+ ··· − 2.25031u − 0.250061
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
77823
65536
u
30
+
372731
65536
u
29
+ ··· +
1036283
65536
u +
151551
65536
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
4
c
5
u
31
+ 4u
30
+ ··· − 6u + 1
c
3
u
31
+ 3u
30
+ ··· + 1408u + 512
c
6
, c
7
, c
10
c
11
u
31
+ 17u
29
+ ··· + 21u + 4
c
8
, c
9
16(16u
31
− 8u
30
+ ··· + 2u + 1)
c
12
u
31
− 6u
30
+ ··· + 27315u − 4448
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
y
31
+ 16y
30
+ ··· + 12y −1
c
3
y
31
+ 9y
30
+ ··· − 4407296y −262144
c
6
, c
7
, c
10
c
11
y
31
+ 34y
30
+ ··· + 113y −16
c
8
, c
9
256(256y
31
+ 3136y
30
+ ··· − 8y −1)
c
12
y
31
+ 14y
30
+ ··· + 1208087401y −19784704
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.800565 + 0.436099I
a = 0.467719 − 0.621707I
b = 0.042876 + 0.178508I
−2.45428 − 1.56605I −13.61992 + 2.18672I
u = 0.800565 − 0.436099I
a = 0.467719 + 0.621707I
b = 0.042876 − 0.178508I
−2.45428 + 1.56605I −13.61992 − 2.18672I
u = 0.939744 + 0.617749I
a = −0.276998 + 0.717790I
b = −0.195037 − 0.177639I
−9.79482 − 2.45438I −10.97758 + 0.07663I
u = 0.939744 − 0.617749I
a = −0.276998 − 0.717790I
b = −0.195037 + 0.177639I
−9.79482 + 2.45438I −10.97758 − 0.07663I
u = −0.402521 + 1.052770I
a = 1.48918 − 0.01324I
b = −2.36845 − 0.55108I
−6.57575 + 7.07387I −5.61246 − 7.92227I
u = −0.402521 − 1.052770I
a = 1.48918 + 0.01324I
b = −2.36845 + 0.55108I
−6.57575 − 7.07387I −5.61246 + 7.92227I
u = 0.107232 + 1.154900I
a = −0.99728 − 1.98978I
b = 1.52737 + 1.79295I
5.77342 − 3.85223I 6.43651 + 8.75740I
u = 0.107232 − 1.154900I
a = −0.99728 + 1.98978I
b = 1.52737 − 1.79295I
5.77342 + 3.85223I 6.43651 − 8.75740I
u = −0.031472 + 1.171320I
a = 1.78512 + 1.47159I
b = −2.36086 − 1.47488I
7.04254 + 1.37301I 10.49996 − 3.37928I
u = −0.031472 − 1.171320I
a = 1.78512 − 1.47159I
b = −2.36086 + 1.47488I
7.04254 − 1.37301I 10.49996 + 3.37928I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.239386 + 1.151830I
a = 0.43439 + 1.74523I
b = −0.99450 − 1.41076I
−1.64522 − 7.50176I −1.21134 + 8.53156I
u = 0.239386 − 1.151830I
a = 0.43439 − 1.74523I
b = −0.99450 + 1.41076I
−1.64522 + 7.50176I −1.21134 − 8.53156I
u = −0.220760 + 1.161050I
a = −1.76111 − 0.50636I
b = 2.49381 + 0.76768I
2.81930 + 5.65791I 0.15142 − 9.03827I
u = −0.220760 − 1.161050I
a = −1.76111 + 0.50636I
b = 2.49381 − 0.76768I
2.81930 − 5.65791I 0.15142 + 9.03827I
u = 1.288550 + 0.093987I
a = 0.043092 − 0.447446I
b = 0.0329599 − 0.0695309I
−1.04564 + 1.63981I 6.17963 − 7.92782I
u = 1.288550 − 0.093987I
a = 0.043092 + 0.447446I
b = 0.0329599 + 0.0695309I
−1.04564 − 1.63981I 6.17963 + 7.92782I
u = −0.374044 + 1.323230I
a = −1.254180 − 0.415556I
b = 2.28135 + 0.63320I
3.67791 + 5.94522I −1.46633 − 3.99996I
u = −0.374044 − 1.323230I
a = −1.254180 + 0.415556I
b = 2.28135 − 0.63320I
3.67791 − 5.94522I −1.46633 + 3.99996I
u = 1.362480 + 0.213737I
a = −0.065860 + 0.497813I
b = −0.0818984 + 0.0915721I
−7.91870 + 3.73515I −1.51291 − 6.54236I
u = 1.362480 − 0.213737I
a = −0.065860 − 0.497813I
b = −0.0818984 − 0.0915721I
−7.91870 − 3.73515I −1.51291 + 6.54236I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.587473
a = −0.910340
b = 0.138975
−0.937510 −9.83160
u = −0.46571 + 1.36110I
a = 1.146720 + 0.344361I
b = −2.28464 − 0.57619I
8.82124 + 9.22714I 0. − 4.14697I
u = −0.46571 − 1.36110I
a = 1.146720 − 0.344361I
b = −2.28464 + 0.57619I
8.82124 − 9.22714I 0. + 4.14697I
u = −0.51997 + 1.36983I
a = −1.102860 − 0.305056I
b = 2.29782 + 0.55309I
7.8389 + 13.6494I 0. − 9.33794I
u = −0.51997 − 1.36983I
a = −1.102860 + 0.305056I
b = 2.29782 − 0.55309I
7.8389 − 13.6494I 0. + 9.33794I
u = −0.56513 + 1.37037I
a = 1.072670 + 0.273505I
b = −2.31235 − 0.53883I
0.3710 + 16.6633I −4.00000 − 8.48351I
u = −0.56513 − 1.37037I
a = 1.072670 − 0.273505I
b = −2.31235 + 0.53883I
0.3710 − 16.6633I −4.00000 + 8.48351I
u = −0.289932 + 0.249849I
a = 0.75811 − 1.38910I
b = −0.713923 − 0.779751I
−7.22830 − 2.70173I −3.88344 + 0.84995I
u = −0.289932 − 0.249849I
a = 0.75811 + 1.38910I
b = −0.713923 + 0.779751I
−7.22830 + 2.70173I −3.88344 − 0.84995I
u = −0.162159 + 0.123669I
a = −0.78355 + 2.04524I
b = 0.315969 + 0.529227I
−0.035297 − 1.217330I −0.51919 + 5.04787I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.162159 − 0.123669I
a = −0.78355 − 2.04524I
b = 0.315969 − 0.529227I
−0.035297 + 1.217330I −0.51919 − 5.04787I
8
II.
I
u
2
= h−2.56×10
49
u
51
−2.69×10
50
u
50
+· · ·+5.57×10
49
b−6.70×10
48
, −8.26×
10
49
u
51
−6.92×10
50
u
50
+· · ·+5.57×10
49
a−1.67×10
49
, u
52
+9u
51
+· · ·+2u+1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
5
=
−u
u
a
9
=
1.48408u
51
+ 12.4361u
50
+ ··· + 0.432390u + 0.300702
0.459476u
51
+ 4.82658u
50
+ ··· + 1.54387u + 0.120355
a
10
=
2.14845u
51
+ 18.8762u
50
+ ··· + 1.91732u + 0.0713913
−0.204897u
51
− 1.61347u
50
+ ··· + 0.0589368u + 0.349666
a
3
=
−0.454836u
51
− 3.70365u
50
+ ··· + 0.118831u − 2.10367
−1
a
6
=
−u
51
− 9u
50
+ ··· − 2u − 2
0.389875u
51
+ 3.14977u
50
+ ··· − 1.19399u + 0.454836
a
8
=
1.71919u
51
+ 15.1586u
50
+ ··· + 1.61912u − 0.499551
−0.581045u
51
− 4.87305u
50
+ ··· + 0.0957750u − 0.486136
a
11
=
2.21012u
51
+ 19.1322u
50
+ ··· + 1.52373u + 0.737565
0.0271207u
51
+ 0.332337u
50
+ ··· − 0.0316556u + 0.591378
a
7
=
0.374845u
51
+ 3.05555u
50
+ ··· − 0.280563u − 1.56949
0.163327u
51
+ 1.34419u
50
+ ··· + 0.258641u + 0.309612
a
12
=
−1.73325u
51
− 14.9638u
50
+ ··· − 1.02224u − 0.206327
0.0199941u
51
− 0.206960u
50
+ ··· − 0.299254u − 0.214321
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.177316u
51
− 0.0575527u
50
+ ··· − 3.07266u − 2.10781
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
4
c
5
u
52
− 9u
51
+ ··· − 2u + 1
c
3
(u
26
− u
25
+ ··· − u + 1)
2
c
6
, c
7
, c
10
c
11
(u
26
+ u
25
+ ··· − u + 1)
2
c
8
, c
9
u
52
− u
51
+ ··· + 307498u + 234119
c
12
(u
26
− 5u
25
+ ··· − 5u + 3)
2
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
y
52
+ 35y
51
+ ··· − 22y
2
+ 1
c
3
(y
26
+ 9y
25
+ ··· + 5y + 1)
2
c
6
, c
7
, c
10
c
11
(y
26
+ 29y
25
+ ··· + 5y + 1)
2
c
8
, c
9
y
52
+ 27y
51
+ ··· + 786128549344y + 54811706161
c
12
(y
26
+ 13y
25
+ ··· + 161y + 9)
2
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.918656 + 0.362726I
a = 0.880173 − 0.718377I
b = −0.246680 + 0.221124I
−1.37714 + 1.77746I 0
u = −0.918656 − 0.362726I
a = 0.880173 + 0.718377I
b = −0.246680 − 0.221124I
−1.37714 − 1.77746I 0
u = −1.019230 + 0.119379I
a = −0.732005 + 0.889313I
b = 0.0937238 − 0.0409991I
4.21235 + 4.00629I 0
u = −1.019230 − 0.119379I
a = −0.732005 − 0.889313I
b = 0.0937238 + 0.0409991I
4.21235 − 4.00629I 0
u = 0.529993 + 0.937993I
a = 1.051030 − 0.221738I
b = −1.48213 + 0.45619I
−8.60065 − 2.88146I 0
u = 0.529993 − 0.937993I
a = 1.051030 + 0.221738I
b = −1.48213 − 0.45619I
−8.60065 + 2.88146I 0
u = −0.098395 + 1.086290I
a = −0.518587 + 0.731973I
b = 1.42167 + 0.24596I
2.31474 + 2.50037I 0
u = −0.098395 − 1.086290I
a = −0.518587 − 0.731973I
b = 1.42167 − 0.24596I
2.31474 − 2.50037I 0
u = −0.200224 + 1.087680I
a = 0.444964 − 0.821616I
b = −1.263110 − 0.333811I
−4.97071 + 4.90123I 0
u = −0.200224 − 1.087680I
a = 0.444964 + 0.821616I
b = −1.263110 + 0.333811I
−4.97071 − 4.90123I 0
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.107950 + 0.028133I
a = 0.633285 − 0.899169I
b = −0.0683414 − 0.0608682I
3.43843 + 7.92757I 0
u = −1.107950 − 0.028133I
a = 0.633285 + 0.899169I
b = −0.0683414 + 0.0608682I
3.43843 − 7.92757I 0
u = 0.335074 + 1.062310I
a = −0.914403 + 0.360247I
b = 1.52164 − 0.33683I
−0.43348 − 2.64715I 0
u = 0.335074 − 1.062310I
a = −0.914403 − 0.360247I
b = 1.52164 + 0.33683I
−0.43348 + 2.64715I 0
u = −0.023027 + 1.115250I
a = 0.385985 − 0.303188I
b = −2.70055 + 0.20079I
3.35189 − 0.99254I 0
u = −0.023027 − 1.115250I
a = 0.385985 + 0.303188I
b = −2.70055 − 0.20079I
3.35189 + 0.99254I 0
u = 0.015623 + 1.126090I
a = 0.584075 − 0.533445I
b = −1.70190 − 0.03427I
3.17562 − 1.00551I 0
u = 0.015623 − 1.126090I
a = 0.584075 + 0.533445I
b = −1.70190 + 0.03427I
3.17562 + 1.00551I 0
u = 0.242499 + 0.805416I
a = 0.116576 + 0.817043I
b = 1.13571 + 1.80548I
−3.13796 + 2.46970I −7.58807 − 2.77943I
u = 0.242499 − 0.805416I
a = 0.116576 − 0.817043I
b = 1.13571 − 1.80548I
−3.13796 − 2.46970I −7.58807 + 2.77943I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.059936 + 0.827194I
a = −0.554765 − 0.357827I
b = 0.17463 − 2.28039I
3.35189 + 0.99254I −2.96284 − 6.67512I
u = −0.059936 − 0.827194I
a = −0.554765 + 0.357827I
b = 0.17463 + 2.28039I
3.35189 − 0.99254I −2.96284 + 6.67512I
u = −1.170810 + 0.041488I
a = −0.568970 − 0.897264I
b = 0.0500480 − 0.1320520I
−3.82921 − 10.57850I 0
u = −1.170810 − 0.041488I
a = −0.568970 + 0.897264I
b = 0.0500480 + 0.1320520I
−3.82921 + 10.57850I 0
u = 0.068858 + 1.173240I
a = −0.279445 + 0.520393I
b = 2.10779 + 0.88556I
−3.13796 − 2.46970I 0
u = 0.068858 − 1.173240I
a = −0.279445 − 0.520393I
b = 2.10779 − 0.88556I
−3.13796 + 2.46970I 0
u = −0.698738 + 0.390612I
a = −0.30488 − 1.41316I
b = −0.425347 − 0.027800I
−8.60065 − 2.88146I −9.60306 + 2.87824I
u = −0.698738 − 0.390612I
a = −0.30488 + 1.41316I
b = −0.425347 + 0.027800I
−8.60065 + 2.88146I −9.60306 − 2.87824I
u = −0.583877 + 0.110063I
a = 0.87448 + 1.62178I
b = 0.317378 − 0.232077I
−0.43348 − 2.64715I −8.54618 + 3.67555I
u = −0.583877 − 0.110063I
a = 0.87448 − 1.62178I
b = 0.317378 + 0.232077I
−0.43348 + 2.64715I −8.54618 − 3.67555I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.26012 + 1.43593I
a = −0.727197 + 0.249900I
b = 1.66512 − 0.35502I
−1.37714 − 1.77746I 0
u = 0.26012 − 1.43593I
a = −0.727197 − 0.249900I
b = 1.66512 + 0.35502I
−1.37714 + 1.77746I 0
u = 0.44108 + 1.39128I
a = 0.781571 − 0.212164I
b = −1.64968 + 0.38783I
4.21235 − 4.00629I 0
u = 0.44108 − 1.39128I
a = 0.781571 + 0.212164I
b = −1.64968 − 0.38783I
4.21235 + 4.00629I 0
u = −0.70545 + 1.30058I
a = 0.671732 − 0.288948I
b = −1.172470 + 0.380087I
1.26907 + 4.47678I 0
u = −0.70545 − 1.30058I
a = 0.671732 + 0.288948I
b = −1.172470 − 0.380087I
1.26907 − 4.47678I 0
u = −0.60226 + 1.35652I
a = −0.660919 + 0.268780I
b = 1.268500 − 0.415860I
7.87691 + 1.94179I 0
u = −0.60226 − 1.35652I
a = −0.660919 − 0.268780I
b = 1.268500 + 0.415860I
7.87691 − 1.94179I 0
u = 0.53710 + 1.39983I
a = −0.793041 + 0.178882I
b = 1.65515 − 0.41186I
3.43843 − 7.92757I 0
u = 0.53710 − 1.39983I
a = −0.793041 − 0.178882I
b = 1.65515 + 0.41186I
3.43843 + 7.92757I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.51689 + 1.42731I
a = 0.648075 − 0.258123I
b = −1.36159 + 0.41343I
7.87691 − 1.94179I 0
u = −0.51689 − 1.42731I
a = 0.648075 + 0.258123I
b = −1.36159 − 0.41343I
7.87691 + 1.94179I 0
u = 0.61099 + 1.40315I
a = 0.798709 − 0.153496I
b = −1.66142 + 0.43078I
−3.82921 − 10.57850I 0
u = 0.61099 − 1.40315I
a = 0.798709 + 0.153496I
b = −1.66142 − 0.43078I
−3.82921 + 10.57850I 0
u = 0.427010 + 0.044189I
a = 1.70872 − 1.69549I
b = −1.048330 − 0.899889I
−4.97071 − 4.90123I −7.70149 + 2.20839I
u = 0.427010 − 0.044189I
a = 1.70872 + 1.69549I
b = −1.048330 + 0.899889I
−4.97071 + 4.90123I −7.70149 − 2.20839I
u = −0.44590 + 1.51192I
a = −0.638031 + 0.253035I
b = 1.43809 − 0.38336I
1.26907 − 4.47678I 0
u = −0.44590 − 1.51192I
a = −0.638031 − 0.253035I
b = 1.43809 + 0.38336I
1.26907 + 4.47678I 0
u = −0.065431 + 0.334054I
a = −2.21650 − 1.39141I
b = −0.444808 − 1.021440I
3.17562 + 1.00551I −1.57769 − 3.62739I
u = −0.065431 − 0.334054I
a = −2.21650 + 1.39141I
b = −0.444808 + 1.021440I
3.17562 − 1.00551I −1.57769 + 3.62739I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.248411 + 0.140739I
a = −1.17063 + 3.22092I
b = 0.876909 + 0.937890I
2.31474 − 2.50037I −4.62782 + 3.68649I
u = 0.248411 − 0.140739I
a = −1.17063 − 3.22092I
b = 0.876909 − 0.937890I
2.31474 + 2.50037I −4.62782 − 3.68649I
17
III. I
u
3
= h16b
4
− 8b
3
+ 4b
2
+ 1, a, u − 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
1
a
2
=
1
1
a
5
=
−1
1
a
9
=
0
b
a
10
=
−b
2b
a
3
=
0
1
a
6
=
−1
0
a
8
=
b
2b
a
11
=
4b
3
− b
8b
3
+ 2b
a
7
=
−4b
3
− 2b
2
−
1
2
8b
3
− 4b
2
− 1
a
12
=
2b
2
+ 1
−4b
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = b
2
− 10
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
4
c
3
u
4
c
4
, c
5
(u + 1)
4
c
6
, c
7
u
4
+ u
3
+ 3u
2
+ 2u + 1
c
8
16(16u
4
+ 8u
3
+ 4u
2
+ 1)
c
9
16(16u
4
− 8u
3
+ 4u
2
+ 1)
c
10
, c
11
u
4
− u
3
+ 3u
2
− 2u + 1
c
12
u
4
− u
3
+ u
2
+ 1
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
(y −1)
4
c
3
y
4
c
6
, c
7
, c
10
c
11
y
4
+ 5y
3
+ 7y
2
+ 2y + 1
c
8
, c
9
256(256y
4
+ 64y
3
+ 48y
2
+ 8y + 1)
c
12
y
4
+ y
3
+ 3y
2
+ 2y + 1
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0
b = 0.425904 + 0.455646I
−8.43568 − 3.16396I −10.02622 + 0.38812I
u = 1.00000
a = 0
b = 0.425904 − 0.455646I
−8.43568 + 3.16396I −10.02622 − 0.38812I
u = 1.00000
a = 0
b = −0.175904 + 0.360171I
−1.43393 + 1.41510I −10.09878 − 0.12671I
u = 1.00000
a = 0
b = −0.175904 − 0.360171I
−1.43393 − 1.41510I −10.09878 + 0.12671I
21
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
2
((u − 1)
4
)(u
31
+ 4u
30
+ ··· − 6u + 1)(u
52
− 9u
51
+ ··· − 2u + 1)
c
3
u
4
(u
26
− u
25
+ ··· − u + 1)
2
(u
31
+ 3u
30
+ ··· + 1408u + 512)
c
4
, c
5
((u + 1)
4
)(u
31
+ 4u
30
+ ··· − 6u + 1)(u
52
− 9u
51
+ ··· − 2u + 1)
c
6
, c
7
(u
4
+ u
3
+ 3u
2
+ 2u + 1)(u
26
+ u
25
+ ··· − u + 1)
2
· (u
31
+ 17u
29
+ ··· + 21u + 4)
c
8
256(16u
4
+ 8u
3
+ 4u
2
+ 1)(16u
31
− 8u
30
+ ··· + 2u + 1)
· (u
52
− u
51
+ ··· + 307498u + 234119)
c
9
256(16u
4
− 8u
3
+ 4u
2
+ 1)(16u
31
− 8u
30
+ ··· + 2u + 1)
· (u
52
− u
51
+ ··· + 307498u + 234119)
c
10
, c
11
(u
4
− u
3
+ 3u
2
− 2u + 1)(u
26
+ u
25
+ ··· − u + 1)
2
· (u
31
+ 17u
29
+ ··· + 21u + 4)
c
12
(u
4
− u
3
+ u
2
+ 1)(u
26
− 5u
25
+ ··· − 5u + 3)
2
· (u
31
− 6u
30
+ ··· + 27315u − 4448)
22
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
((y −1)
4
)(y
31
+ 16y
30
+ ··· + 12y −1)(y
52
+ 35y
51
+ ··· − 22y
2
+ 1)
c
3
y
4
(y
26
+ 9y
25
+ ··· + 5y + 1)
2
· (y
31
+ 9y
30
+ ··· − 4407296y −262144)
c
6
, c
7
, c
10
c
11
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)(y
26
+ 29y
25
+ ··· + 5y + 1)
2
· (y
31
+ 34y
30
+ ··· + 113y −16)
c
8
, c
9
65536(256y
4
+ 64y
3
+ 48y
2
+ 8y + 1)
· (256y
31
+ 3136y
30
+ ··· − 8y −1)
· (y
52
+ 27y
51
+ ··· + 786128549344y + 54811706161)
c
12
(y
4
+ y
3
+ 3y
2
+ 2y + 1)(y
26
+ 13y
25
+ ··· + 161y + 9)
2
· (y
31
+ 14y
30
+ ··· + 1208087401y −19784704)
23
