12n
0700
(K12n
0700
)
A knot diagram
1
Linearized knot diagam
4 5 9 12 10 11 3 12 7 6 2 9
Solving Sequence
6,10
11
2,7
12 5 3 4 1 9 8
c
10
c
6
c
11
c
5
c
2
c
4
c
1
c
9
c
8
c
3
, c
7
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h12u
31
− 42u
30
+ ··· + b + 13, −13u
31
+ 41u
30
+ ··· + 2a − 20, u
32
− 5u
31
+ ··· − 8u − 2i
I
u
2
= h−3u
15
− 2u
14
+ ··· + b − 3, 3u
15
− 22u
13
+ ··· + 2a + 5, u
16
+ 2u
15
+ ··· − 3u + 2i
I
u
3
= h−u
14
− u
13
+ 5u
12
+ 4u
11
− 10u
10
− 5u
9
+ 9u
8
− 2u
6
+ 4u
5
− 2u
4
− 2u
3
− au + b − u + 1,
− u
14
a − 5u
14
+ ··· + 3a + 12,
u
15
+ u
14
− 6u
13
− 5u
12
+ 14u
11
+ 8u
10
− 14u
9
− u
8
+ 2u
7
− 8u
6
+ 6u
5
+ 4u
4
− 2u
3
+ 2u
2
− 2u − 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
= h12u
31
− 42u
30
+ · · · + b + 13, −13u
31
+ 41u
30
+ · · · + 2a − 20, u
32
−
5u
31
+ · · · − 8u − 2i
(i) Arc colorings
a
6
=
0
u
a
10
=
1
0
a
11
=
1
−u
2
a
2
=
13
2
u
31
−
41
2
u
30
+ ··· +
69
2
u + 10
−12u
31
+ 42u
30
+ ··· − 62u − 13
a
7
=
u
−u
3
+ u
a
12
=
17
2
u
31
−
61
2
u
30
+ ··· +
103
2
u + 12
−12u
31
+ 42u
30
+ ··· − 79u − 17
a
5
=
−u
u
a
3
=
−
1
2
u
31
+
15
2
u
30
+ ··· −
49
2
u − 2
−5u
31
+ 14u
30
+ ··· − 3u − 1
a
4
=
7
2
u
31
−
15
2
u
30
+ ··· +
15
2
u + 5
−5u
31
+ 14u
30
+ ··· − 3u − 1
a
1
=
−
9
2
u
31
+
31
2
u
30
+ ··· −
39
2
u − 5
12u
31
− 42u
30
+ ··· + 79u + 17
a
9
=
−u
4
+ u
2
+ 1
u
6
− 2u
4
+ u
2
a
8
=
−
27
2
u
31
+
99
2
u
30
+ ··· −
199
2
u − 21
19u
31
− 71u
30
+ ··· + 139u + 29
(ii) Obstruction class = −1
(iii) Cusp Shapes = 19u
31
−65u
30
−138u
29
+ 623u
28
+ 427u
27
−2612u
26
−1023u
25
+
6228u
24
+ 3091u
23
− 8672u
22
− 8566u
21
+ 4803u
20
+ 15237u
19
+ 6582u
18
− 14312u
17
−
16767u
16
+ 1566u
15
+ 14326u
14
+ 11332u
13
− 1711u
12
− 10557u
11
− 6164u
10
+ 1148u
9
+
3788u
8
+ 3056u
7
+ 240u
6
− 1226u
5
− 540u
4
− 312u
3
+ 110u
2
+ 80u + 16
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
32
− 17u
31
+ ··· − 308u + 178
c
2
, c
11
u
32
+ 2u
31
+ ··· − 11u + 1
c
3
, c
8
, c
12
u
32
+ 23u
30
+ ··· + u − 1
c
4
u
32
+ 29u
31
+ ··· + 393216u + 32768
c
5
, c
6
, c
10
u
32
− 5u
31
+ ··· − 8u − 2
c
7
u
32
+ u
31
+ ··· + 221u − 97
c
9
u
32
+ 15u
31
+ ··· + 964u + 86
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
32
− 33y
31
+ ··· − 1623172y + 31684
c
2
, c
11
y
32
+ 14y
31
+ ··· − 73y + 1
c
3
, c
8
, c
12
y
32
+ 46y
31
+ ··· + 13y + 1
c
4
y
32
− 9y
31
+ ··· − 5368709120y + 1073741824
c
5
, c
6
, c
10
y
32
− 29y
31
+ ··· − 60y + 4
c
7
y
32
+ 25y
31
+ ··· − 27307y + 9409
c
9
y
32
+ 7y
31
+ ··· − 138956y + 7396
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.856862 + 0.544335I
a = −0.529669 + 0.145017I
b = −0.374915 + 0.412577I
−7.76454 − 4.88822I 4.38586 + 5.79440I
u = −0.856862 − 0.544335I
a = −0.529669 − 0.145017I
b = −0.374915 − 0.412577I
−7.76454 + 4.88822I 4.38586 − 5.79440I
u = −0.300083 + 0.868605I
a = 0.628210 + 0.007038I
b = 0.194628 − 0.543554I
−9.54364 − 0.04641I 0.192477 − 0.463915I
u = −0.300083 − 0.868605I
a = 0.628210 − 0.007038I
b = 0.194628 + 0.543554I
−9.54364 + 0.04641I 0.192477 + 0.463915I
u = −0.982425 + 0.459735I
a = 0.063117 − 0.663220I
b = −0.242898 − 0.680581I
−8.42524 + 6.40056I 6.06353 − 2.39705I
u = −0.982425 − 0.459735I
a = 0.063117 + 0.663220I
b = −0.242898 + 0.680581I
−8.42524 − 6.40056I 6.06353 + 2.39705I
u = −0.211672 + 0.838103I
a = −0.712628 − 1.047410I
b = −1.028680 + 0.375549I
−10.8094 − 11.0307I 3.82556 + 6.27574I
u = −0.211672 − 0.838103I
a = −0.712628 + 1.047410I
b = −1.028680 − 0.375549I
−10.8094 + 11.0307I 3.82556 − 6.27574I
u = −1.229180 + 0.220961I
a = 0.111894 + 0.489674I
b = 0.245737 + 0.577172I
1.77560 + 0.48261I 9.87124 + 2.81544I
u = −1.229180 − 0.220961I
a = 0.111894 − 0.489674I
b = 0.245737 − 0.577172I
1.77560 − 0.48261I 9.87124 − 2.81544I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.262910 + 0.254948I
a = 0.070086 − 0.361128I
b = −0.003556 − 0.473942I
1.17420 − 4.36507I 10.02842 + 6.42012I
u = −1.262910 − 0.254948I
a = 0.070086 + 0.361128I
b = −0.003556 + 0.473942I
1.17420 + 4.36507I 10.02842 − 6.42012I
u = 1.287670 + 0.253472I
a = −1.52393 + 0.12920I
b = 1.99507 + 0.21991I
1.37746 + 2.34487I 8.41481 − 0.55216I
u = 1.287670 − 0.253472I
a = −1.52393 − 0.12920I
b = 1.99507 − 0.21991I
1.37746 − 2.34487I 8.41481 + 0.55216I
u = −0.098169 + 0.677929I
a = 0.71726 + 1.41090I
b = 1.026900 − 0.347744I
−1.60725 − 3.69611I 3.29803 + 2.27748I
u = −0.098169 − 0.677929I
a = 0.71726 − 1.41090I
b = 1.026900 + 0.347744I
−1.60725 + 3.69611I 3.29803 − 2.27748I
u = −0.015798 + 0.674807I
a = −0.638339 − 0.789035I
b = −0.542531 + 0.418291I
−2.66882 + 1.00290I 3.62847 − 3.27774I
u = −0.015798 − 0.674807I
a = −0.638339 + 0.789035I
b = −0.542531 − 0.418291I
−2.66882 − 1.00290I 3.62847 + 3.27774I
u = 1.342160 + 0.077096I
a = 1.55439 − 1.39862I
b = −2.19406 + 1.75733I
5.49774 − 0.90354I 12.53276 + 1.80769I
u = 1.342160 − 0.077096I
a = 1.55439 + 1.39862I
b = −2.19406 − 1.75733I
5.49774 + 0.90354I 12.53276 − 1.80769I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.330040 + 0.281861I
a = 2.47693 − 0.37891I
b = −3.40120 − 0.19418I
2.89499 + 7.19326I 8.98916 − 5.05295I
u = 1.330040 − 0.281861I
a = 2.47693 + 0.37891I
b = −3.40120 + 0.19418I
2.89499 − 7.19326I 8.98916 + 5.05295I
u = 1.39497 + 0.35222I
a = −2.21296 + 0.14720I
b = 3.13885 + 0.57412I
−5.7214 + 15.3218I 8.04302 − 7.62554I
u = 1.39497 − 0.35222I
a = −2.21296 − 0.14720I
b = 3.13885 − 0.57412I
−5.7214 − 15.3218I 8.04302 + 7.62554I
u = 1.45144 + 0.37096I
a = 0.664841 + 0.529951I
b = −0.768383 − 1.015820I
−3.96493 + 4.54692I 0
u = 1.45144 − 0.37096I
a = 0.664841 − 0.529951I
b = −0.768383 + 1.015820I
−3.96493 − 4.54692I 0
u = 1.49869 + 0.06046I
a = −1.30572 − 0.89485I
b = 1.90276 + 1.42005I
0.09897 + 6.38740I 10.66369 − 5.63916I
u = 1.49869 − 0.06046I
a = −1.30572 + 0.89485I
b = 1.90276 − 1.42005I
0.09897 − 6.38740I 10.66369 + 5.63916I
u = 0.475802
a = −0.529412
b = 0.251895
0.724697 12.9880
u = −1.57937
a = 0.0469240
b = 0.0741106
7.86571 −16.8850
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.296068 + 0.129818I
a = 0.37776 + 2.13705I
b = 0.389271 + 0.583672I
0.49245 + 1.79175I 2.45715 − 5.83736I
u = −0.296068 − 0.129818I
a = 0.37776 − 2.13705I
b = 0.389271 − 0.583672I
0.49245 − 1.79175I 2.45715 + 5.83736I
8
II. I
u
2
=
h−3u
15
−2u
14
+· · ·+b−3, 3u
15
−22u
13
+· · ·+2a+5, u
16
+2u
15
+· · ·−3u+2i
(i) Arc colorings
a
6
=
0
u
a
10
=
1
0
a
11
=
1
−u
2
a
2
=
−
3
2
u
15
+ 11u
13
+ ··· + 4u −
5
2
3u
15
+ 2u
14
+ ··· − 7u + 3
a
7
=
u
−u
3
+ u
a
12
=
1
2
u
15
− 3u
13
+ ··· + 2u +
1
2
−u
15
+ 7u
13
+ ··· + u − 1
a
5
=
−u
u
a
3
=
1
2
u
15
+ 2u
14
+ ··· − 2u −
1
2
u
15
− 7u
13
+ ··· − u + 1
a
4
=
−
1
2
u
15
+ u
14
+ ··· + u −
3
2
u
15
− 7u
13
+ ··· − u + 1
a
1
=
3
2
u
15
+ u
14
+ ··· − u +
3
2
−u
15
+ 7u
13
+ ··· + u − 1
a
9
=
−u
4
+ u
2
+ 1
u
6
− 2u
4
+ u
2
a
8
=
−
7
2
u
15
− 3u
14
+ ··· + 13u −
11
2
4u
15
+ 3u
14
+ ··· − 16u + 7
(ii) Obstruction class = 1
(iii) Cusp Shapes =
4u
15
+4u
14
−25u
13
−14u
12
+63u
11
−69u
9
+59u
8
+8u
7
−72u
6
+47u
5
−18u
3
+25u
2
−16u+16
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
16
− 14u
15
+ ··· − 41u + 4
c
2
, c
11
u
16
+ 2u
15
+ ··· + 2u + 1
c
3
, c
8
u
16
+ 6u
14
+ ··· + 4u + 1
c
4
u
16
+ 2u
15
+ ··· + 2u + 1
c
5
, c
6
u
16
− 2u
15
+ ··· + 3u + 2
c
7
u
16
− u
15
+ ··· + u
2
+ 1
c
9
u
16
− 6u
15
+ ··· − 7u + 2
c
10
u
16
+ 2u
15
+ ··· − 3u + 2
c
12
u
16
+ 6u
14
+ ··· − 4u + 1
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
16
− 16y
15
+ ··· − 97y + 16
c
2
, c
11
y
16
− 4y
15
+ ··· − 8y + 1
c
3
, c
8
, c
12
y
16
+ 12y
15
+ ··· − 10y + 1
c
4
y
16
− 8y
15
+ ··· − 4y + 1
c
5
, c
6
, c
10
y
16
− 16y
15
+ ··· − y + 4
c
7
y
16
+ 15y
15
+ ··· + 2y + 1
c
9
y
16
− 6y
14
+ ··· + 7y + 4
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.137400 + 0.146818I
a = −0.149955 + 0.449115I
b = −0.236497 + 0.488807I
1.79945 − 1.49089I 10.63523 + 4.79741I
u = 1.137400 − 0.146818I
a = −0.149955 − 0.449115I
b = −0.236497 − 0.488807I
1.79945 + 1.49089I 10.63523 − 4.79741I
u = 0.199163 + 0.721319I
a = −0.606622 + 1.036950I
b = −0.868785 − 0.231047I
−0.63802 + 4.76461I 9.16165 − 6.96874I
u = 0.199163 − 0.721319I
a = −0.606622 − 1.036950I
b = −0.868785 + 0.231047I
−0.63802 − 4.76461I 9.16165 + 6.96874I
u = −1.242630 + 0.215465I
a = 2.27494 + 1.85843I
b = −3.22733 − 1.81917I
−4.26568 − 2.08418I 10.49854 + 3.93307I
u = −1.242630 − 0.215465I
a = 2.27494 − 1.85843I
b = −3.22733 + 1.81917I
−4.26568 + 2.08418I 10.49854 − 3.93307I
u = 0.571020 + 0.339582I
a = 0.039795 + 0.842875I
b = −0.263501 + 0.494812I
1.12725 − 1.33975I 12.02351 + 1.24817I
u = 0.571020 − 0.339582I
a = 0.039795 − 0.842875I
b = −0.263501 − 0.494812I
1.12725 + 1.33975I 12.02351 − 1.24817I
u = −0.141358 + 0.640937I
a = −0.679498 − 1.144790I
b = 0.829793 − 0.273689I
−7.63694 − 0.91148I 3.93951 + 0.55564I
u = −0.141358 − 0.640937I
a = −0.679498 + 1.144790I
b = 0.829793 + 0.273689I
−7.63694 + 0.91148I 3.93951 − 0.55564I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.369690 + 0.297062I
a = 0.132211 − 0.195026I
b = 0.239022 − 0.227851I
−2.78866 + 4.38420I 9.70308 − 2.57288I
u = 1.369690 − 0.297062I
a = 0.132211 + 0.195026I
b = 0.239022 + 0.227851I
−2.78866 − 4.38420I 9.70308 + 2.57288I
u = −1.376870 + 0.303108I
a = −1.97992 − 0.37746I
b = 2.84050 − 0.08041I
4.35415 − 8.50155I 13.9603 + 7.3316I
u = −1.376870 − 0.303108I
a = −1.97992 + 0.37746I
b = 2.84050 + 0.08041I
4.35415 + 8.50155I 13.9603 − 7.3316I
u = −1.51641 + 0.01833I
a = −0.780954 − 0.139106I
b = 1.186800 + 0.196628I
8.04846 + 0.00268I 26.0782 − 3.0287I
u = −1.51641 − 0.01833I
a = −0.780954 + 0.139106I
b = 1.186800 − 0.196628I
8.04846 − 0.00268I 26.0782 + 3.0287I
13
III.
I
u
3
= h−u
14
−u
13
+· · ·+b+1, −u
14
a−5u
14
+· · ·+3a+12, u
15
+u
14
+· · ·−2u−1i
(i) Arc colorings
a
6
=
0
u
a
10
=
1
0
a
11
=
1
−u
2
a
2
=
a
u
14
+ u
13
+ ··· + u − 1
a
7
=
u
−u
3
+ u
a
12
=
u
13
a + u
14
+ ··· + a − 1
−u
13
a − u
12
a + ··· − a − 1
a
5
=
−u
u
a
3
=
u
14
+ u
13
+ ··· + a + u
−u
12
− u
11
+ ··· + au − 1
a
4
=
u
13
a + u
14
+ ··· + a − 1
−u
13
a − u
12
a + ··· − a − 1
a
1
=
−2u
13
a − u
14
+ ··· − a + 2
2u
13
a + u
13
+ ··· + 2a + 1
a
9
=
−u
4
+ u
2
+ 1
u
6
− 2u
4
+ u
2
a
8
=
−3u
14
+ u
13
+ ··· + a + 6
2u
14
− 2u
13
+ ··· − au − 3
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 4u
12
− 20u
10
+ 4u
9
+ 36u
8
− 16u
7
− 20u
6
+ 20u
5
− 12u
4
− 4u
3
+ 12u
2
− 4u + 6
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
15
+ 13u
14
+ ··· + 8u − 1)
2
c
2
, c
11
u
30
+ 13u
29
+ ··· − 198u − 23
c
3
, c
8
, c
12
u
30
− u
29
+ ··· + 356u + 599
c
4
(u − 1)
30
c
5
, c
6
, c
10
(u
15
+ u
14
+ ··· − 2u − 1)
2
c
7
u
30
+ u
29
+ ··· + 48394u − 9199
c
9
(u
15
− 3u
14
+ ··· + 4u
2
− 1)
2
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
15
− 29y
14
+ ··· + 8y −1)
2
c
2
, c
11
y
30
− 5y
29
+ ··· + 7808y + 529
c
3
, c
8
, c
12
y
30
+ 39y
29
+ ··· + 402780y + 358801
c
4
(y −1)
30
c
5
, c
6
, c
10
(y
15
− 13y
14
+ ··· + 8y −1)
2
c
7
y
30
+ 27y
29
+ ··· − 796940y + 84621601
c
9
(y
15
+ 7y
14
+ ··· + 8y −1)
2
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.897290 + 0.288232I
a = −0.503485 − 0.559425I
b = 0.416988 − 0.227974I
0.184105 − 0.159076I 5.79403 − 0.85194I
u = 0.897290 + 0.288232I
a = −0.347272 + 0.365622I
b = 0.290527 + 0.647087I
0.184105 − 0.159076I 5.79403 − 0.85194I
u = 0.897290 − 0.288232I
a = −0.503485 + 0.559425I
b = 0.416988 + 0.227974I
0.184105 + 0.159076I 5.79403 + 0.85194I
u = 0.897290 − 0.288232I
a = −0.347272 − 0.365622I
b = 0.290527 − 0.647087I
0.184105 + 0.159076I 5.79403 + 0.85194I
u = 0.200931 + 0.760138I
a = 0.347773 − 0.900603I
b = 0.695074 + 0.555297I
−2.05700 + 4.11725I 2.59688 − 3.71929I
u = 0.200931 + 0.760138I
a = −0.908735 + 0.674195I
b = −0.754461 − 0.083397I
−2.05700 + 4.11725I 2.59688 − 3.71929I
u = 0.200931 − 0.760138I
a = 0.347773 + 0.900603I
b = 0.695074 − 0.555297I
−2.05700 − 4.11725I 2.59688 + 3.71929I
u = 0.200931 − 0.760138I
a = −0.908735 − 0.674195I
b = −0.754461 + 0.083397I
−2.05700 − 4.11725I 2.59688 + 3.71929I
u = −1.224710 + 0.250895I
a = 2.08574 + 1.21971I
b = −3.86630 − 0.92593I
−5.28079 − 1.64925I 1.60633 + 0.16522I
u = −1.224710 + 0.250895I
a = −2.88112 − 1.34627I
b = 2.86043 + 0.97048I
−5.28079 − 1.64925I 1.60633 + 0.16522I
17
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.224710 − 0.250895I
a = 2.08574 − 1.21971I
b = −3.86630 + 0.92593I
−5.28079 + 1.64925I 1.60633 − 0.16522I
u = −1.224710 − 0.250895I
a = −2.88112 + 1.34627I
b = 2.86043 − 0.97048I
−5.28079 + 1.64925I 1.60633 − 0.16522I
u = −0.074720 + 0.708028I
a = 0.611710 + 0.650680I
b = −1.60975 − 0.81488I
−8.75399 − 1.81248I −1.85619 + 4.33913I
u = −0.074720 + 0.708028I
a = 0.90095 − 2.36865I
b = 0.506407 − 0.384488I
−8.75399 − 1.81248I −1.85619 + 4.33913I
u = −0.074720 − 0.708028I
a = 0.611710 − 0.650680I
b = −1.60975 + 0.81488I
−8.75399 + 1.81248I −1.85619 − 4.33913I
u = −0.074720 − 0.708028I
a = 0.90095 + 2.36865I
b = 0.506407 + 0.384488I
−8.75399 + 1.81248I −1.85619 − 4.33913I
u = 1.30332
a = −1.64310 + 0.40643I
b = 2.14148 + 0.52971I
−1.05425 9.03940
u = 1.30332
a = −1.64310 − 0.40643I
b = 2.14148 − 0.52971I
−1.05425 9.03940
u = 1.314200 + 0.295245I
a = −0.346248 + 1.242720I
b = 1.35266 − 2.62536I
−4.39644 + 5.45324I 3.99532 − 6.35130I
u = 1.314200 + 0.295245I
a = −0.55258 + 2.12183I
b = 0.82195 − 1.53095I
−4.39644 + 5.45324I 3.99532 − 6.35130I
18
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.314200 − 0.295245I
a = −0.346248 − 1.242720I
b = 1.35266 + 2.62536I
−4.39644 − 5.45324I 3.99532 + 6.35130I
u = 1.314200 − 0.295245I
a = −0.55258 − 2.12183I
b = 0.82195 + 1.53095I
−4.39644 − 5.45324I 3.99532 + 6.35130I
u = −1.378140 + 0.316043I
a = −1.70922 − 0.18417I
b = 2.62416 − 0.47024I
2.93922 − 8.01682I 7.04132 + 4.89679I
u = −1.378140 + 0.316043I
a = 1.88334 + 0.09068I
b = −2.41375 + 0.28637I
2.93922 − 8.01682I 7.04132 + 4.89679I
u = −1.378140 − 0.316043I
a = −1.70922 + 0.18417I
b = 2.62416 + 0.47024I
2.93922 + 8.01682I 7.04132 − 4.89679I
u = −1.378140 − 0.316043I
a = 1.88334 − 0.09068I
b = −2.41375 − 0.28637I
2.93922 + 8.01682I 7.04132 − 4.89679I
u = −1.43385
a = −1.16104
b = 1.90536
7.22226 9.97710
u = −1.43385
a = 1.32884
b = −1.66477
7.22226 9.97710
u = −0.339181
a = −2.02164 + 3.01582I
b = −0.685704 − 1.022910I
−5.98181 8.62820
u = −0.339181
a = −2.02164 − 3.01582I
b = −0.685704 + 1.022910I
−5.98181 8.62820
19
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
15
+ 13u
14
+ ··· + 8u − 1)
2
)(u
16
− 14u
15
+ ··· − 41u + 4)
· (u
32
− 17u
31
+ ··· − 308u + 178)
c
2
, c
11
(u
16
+ 2u
15
+ ··· + 2u + 1)(u
30
+ 13u
29
+ ··· − 198u − 23)
· (u
32
+ 2u
31
+ ··· − 11u + 1)
c
3
, c
8
(u
16
+ 6u
14
+ ··· + 4u + 1)(u
30
− u
29
+ ··· + 356u + 599)
· (u
32
+ 23u
30
+ ··· + u − 1)
c
4
((u − 1)
30
)(u
16
+ 2u
15
+ ··· + 2u + 1)
· (u
32
+ 29u
31
+ ··· + 393216u + 32768)
c
5
, c
6
((u
15
+ u
14
+ ··· − 2u − 1)
2
)(u
16
− 2u
15
+ ··· + 3u + 2)
· (u
32
− 5u
31
+ ··· − 8u − 2)
c
7
(u
16
− u
15
+ ··· + u
2
+ 1)(u
30
+ u
29
+ ··· + 48394u − 9199)
· (u
32
+ u
31
+ ··· + 221u − 97)
c
9
((u
15
− 3u
14
+ ··· + 4u
2
− 1)
2
)(u
16
− 6u
15
+ ··· − 7u + 2)
· (u
32
+ 15u
31
+ ··· + 964u + 86)
c
10
((u
15
+ u
14
+ ··· − 2u − 1)
2
)(u
16
+ 2u
15
+ ··· − 3u + 2)
· (u
32
− 5u
31
+ ··· − 8u − 2)
c
12
(u
16
+ 6u
14
+ ··· − 4u + 1)(u
30
− u
29
+ ··· + 356u + 599)
· (u
32
+ 23u
30
+ ··· + u − 1)
20
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
15
− 29y
14
+ ··· + 8y −1)
2
)(y
16
− 16y
15
+ ··· − 97y + 16)
· (y
32
− 33y
31
+ ··· − 1623172y + 31684)
c
2
, c
11
(y
16
− 4y
15
+ ··· − 8y + 1)(y
30
− 5y
29
+ ··· + 7808y + 529)
· (y
32
+ 14y
31
+ ··· − 73y + 1)
c
3
, c
8
, c
12
(y
16
+ 12y
15
+ ··· − 10y + 1)(y
30
+ 39y
29
+ ··· + 402780y + 358801)
· (y
32
+ 46y
31
+ ··· + 13y + 1)
c
4
((y −1)
30
)(y
16
− 8y
15
+ ··· − 4y + 1)
· (y
32
− 9y
31
+ ··· − 5368709120y + 1073741824)
c
5
, c
6
, c
10
((y
15
− 13y
14
+ ··· + 8y −1)
2
)(y
16
− 16y
15
+ ··· − y + 4)
· (y
32
− 29y
31
+ ··· − 60y + 4)
c
7
(y
16
+ 15y
15
+ ··· + 2y + 1)
· (y
30
+ 27y
29
+ ··· − 796940y + 84621601)
· (y
32
+ 25y
31
+ ··· − 27307y + 9409)
c
9
((y
15
+ 7y
14
+ ··· + 8y −1)
2
)(y
16
− 6y
14
+ ··· + 7y + 4)
· (y
32
+ 7y
31
+ ··· − 138956y + 7396)
21
