12n
0256
(K12n
0256
)
A knot diagram
1
Linearized knot diagam
3 5 9 2 12 9 11 4 6 5 7 10
Solving Sequence
4,8
9
3,11
7 12 6 5 2 1 10
c
8
c
3
c
7
c
11
c
6
c
5
c
2
c
1
c
10
c
4
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.09302 × 10
148
u
37
+ 5.18676 × 10
147
u
36
+ ··· + 1.58247 × 10
151
b − 4.86012 × 10
152
,
2.92144 × 10
150
u
37
− 1.72552 × 10
150
u
36
+ ··· + 1.55082 × 10
153
a + 1.44230 × 10
155
,
u
38
− u
37
+ ··· + 86016u − 25088i
I
u
2
= h−2796800274u
16
+ 1230170348u
15
+ ··· + 5782655035b + 1488757467,
8417711u
16
+ 1589468u
15
+ ··· + 2844395a − 43377763, u
17
+ 6u
15
+ ··· − 3u − 1i
I
v
1
= ha, 82026v
8
− 2033115v
7
+ ··· + 764761b − 1552510,
7v
9
− 3v
8
+ 2v
7
+ 14v
6
− 23v
5
− 33v
4
− v
3
+ 8v
2
+ v −1i
* 3 irreducible components of dim
C
= 0, with total 64 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−1.09 × 10
148
u
37
+ 5.19 × 10
147
u
36
+ · · · + 1.58 × 10
151
b − 4.86 ×
10
152
, 2.92 × 10
150
u
37
− 1.73 × 10
150
u
36
+ · · · + 1.55 × 10
153
a + 1.44 ×
10
155
, u
38
− u
37
+ · · · + 86016u − 25088i
(i) Arc colorings
a
4
=
0
u
a
8
=
1
0
a
9
=
1
u
2
a
3
=
u
u
3
+ u
a
11
=
−0.00188380u
37
+ 0.00111265u
36
+ ··· + 197.770u − 93.0023
0.000690707u
37
− 0.000327764u
36
+ ··· − 62.7881u + 30.7122
a
7
=
0.000436226u
37
+ 0.0000991808u
36
+ ··· − 6.16448u + 31.7162
−0.000741300u
37
+ 0.000253145u
36
+ ··· + 56.6644u − 36.9869
a
12
=
−0.00175578u
37
+ 0.000884992u
36
+ ··· + 151.445u − 59.3558
0.00132438u
37
− 0.000436480u
36
+ ··· − 91.0821u + 52.7513
a
6
=
−0.000858868u
37
+ 0.000550093u
36
+ ··· + 85.6095u − 18.7030
−0.00126665u
37
+ 0.000467679u
36
+ ··· + 96.7862u − 58.1657
a
5
=
−0.000317398u
37
+ 0.000185140u
36
+ ··· + 29.3852u − 8.54883
−0.0000363695u
37
+ 0.0000373746u
36
+ ··· + 8.27143u − 5.50537
a
2
=
0.000305502u
37
− 0.000161572u
36
+ ··· − 24.5272u + 6.36156
0.0000100886u
37
+ 3.10588 × 10
−7
u
36
+ ··· + 0.142083u + 1.42366
a
1
=
0.000281029u
37
− 0.000147765u
36
+ ··· − 21.1138u + 3.04347
−0.0000370696u
37
+ 0.0000142949u
36
+ ··· + 3.85910u − 2.16206
a
10
=
−0.00191915u
37
+ 0.00125145u
36
+ ··· + 217.235u − 96.5925
0.000789868u
37
− 0.000393658u
36
+ ··· − 72.9083u + 33.0324
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.00823228u
37
− 0.00319378u
36
+ ··· − 645.161u + 373.502
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
38
+ 46u
36
+ ··· + 6958u + 2401
c
2
, c
4
u
38
− 16u
37
+ ··· + 378u − 49
c
3
, c
8
u
38
− u
37
+ ··· + 86016u − 25088
c
5
u
38
+ 4u
37
+ ··· − 114u − 17
c
6
, c
9
u
38
− 3u
37
+ ··· − 446u + 44
c
7
, c
11
u
38
− 2u
37
+ ··· − 3904u − 5873
c
10
u
38
+ u
37
+ ··· + 40881797u + 3617129
c
12
u
38
+ u
37
+ ··· + 79046u − 14009
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
38
+ 92y
37
+ ··· + 262856678y + 5764801
c
2
, c
4
y
38
+ 46y
36
+ ··· − 6958y + 2401
c
3
, c
8
y
38
+ 69y
37
+ ··· + 3750756352y + 629407744
c
5
y
38
− 6y
37
+ ··· − 8270y + 289
c
6
, c
9
y
38
+ 35y
37
+ ··· − 111884y + 1936
c
7
, c
11
y
38
− 12y
37
+ ··· − 781291844y + 34492129
c
10
y
38
− 107y
37
+ ··· − 346184004395873y + 13083622202641
c
12
y
38
− 69y
37
+ ··· − 9544952050y + 196252081
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.542649 + 0.614305I
a = −0.125480 + 0.480523I
b = 0.653832 + 0.819508I
1.68943 + 7.69679I −0.16453 − 13.04445I
u = −0.542649 − 0.614305I
a = −0.125480 − 0.480523I
b = 0.653832 − 0.819508I
1.68943 − 7.69679I −0.16453 + 13.04445I
u = 0.072090 + 0.744709I
a = 0.128090 − 1.010850I
b = 0.532310 − 0.601577I
3.31755 + 0.54950I 6.15791 + 2.31967I
u = 0.072090 − 0.744709I
a = 0.128090 + 1.010850I
b = 0.532310 + 0.601577I
3.31755 − 0.54950I 6.15791 − 2.31967I
u = −0.554003 + 0.499646I
a = 0.564998 + 0.241017I
b = 0.158389 − 0.923477I
−1.38624 + 1.33481I −2.97345 − 3.66862I
u = −0.554003 − 0.499646I
a = 0.564998 − 0.241017I
b = 0.158389 + 0.923477I
−1.38624 − 1.33481I −2.97345 + 3.66862I
u = 0.434969 + 0.601443I
a = 0.958601 − 0.178438I
b = −0.481321 − 0.092957I
1.48961 + 0.57943I 5.02569 − 0.39325I
u = 0.434969 − 0.601443I
a = 0.958601 + 0.178438I
b = −0.481321 + 0.092957I
1.48961 − 0.57943I 5.02569 + 0.39325I
u = 0.606671 + 0.412287I
a = 2.69689 + 1.44150I
b = −0.080725 + 1.288340I
−4.47346 + 0.84284I −11.66035 − 0.97344I
u = 0.606671 − 0.412287I
a = 2.69689 − 1.44150I
b = −0.080725 − 1.288340I
−4.47346 − 0.84284I −11.66035 + 0.97344I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.185752 + 1.318190I
a = 0.527217 + 0.328502I
b = −0.165255 + 1.390640I
−2.12322 − 4.24125I −4.26882 + 3.51292I
u = 0.185752 − 1.318190I
a = 0.527217 − 0.328502I
b = −0.165255 − 1.390640I
−2.12322 + 4.24125I −4.26882 − 3.51292I
u = 0.626028 + 0.000453I
a = −0.113573 + 1.317400I
b = −0.686643 − 0.521082I
0.61462 + 3.26287I −1.84851 − 7.14359I
u = 0.626028 − 0.000453I
a = −0.113573 − 1.317400I
b = −0.686643 + 0.521082I
0.61462 − 3.26287I −1.84851 + 7.14359I
u = 0.220678 + 0.522522I
a = −7.64643 + 0.56839I
b = 0.541758 − 0.847309I
−0.41969 − 2.46857I 5.02234 + 6.21524I
u = 0.220678 − 0.522522I
a = −7.64643 − 0.56839I
b = 0.541758 + 0.847309I
−0.41969 + 2.46857I 5.02234 − 6.21524I
u = 0.134435 + 0.540176I
a = 0.616458 + 0.177082I
b = −0.685607 − 0.966646I
0.34862 + 2.64648I 0.38453 − 4.62015I
u = 0.134435 − 0.540176I
a = 0.616458 − 0.177082I
b = −0.685607 + 0.966646I
0.34862 − 2.64648I 0.38453 + 4.62015I
u = −0.487313
a = 1.16119
b = 0.259706
−1.21395 −9.56810
u = −1.68632 + 0.08026I
a = 0.347568 − 0.381381I
b = −1.09335 − 0.89962I
1.94242 + 0.25898I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.68632 − 0.08026I
a = 0.347568 + 0.381381I
b = −1.09335 + 0.89962I
1.94242 − 0.25898I 0
u = 1.86202
a = 0.274789
b = −0.588779
−6.81012 0
u = −0.78573 + 1.74324I
a = −0.675257 + 0.449148I
b = 1.84271 + 0.04920I
6.33444 − 4.25779I 0
u = −0.78573 − 1.74324I
a = −0.675257 − 0.449148I
b = 1.84271 − 0.04920I
6.33444 + 4.25779I 0
u = 0.36940 + 1.96319I
a = −1.064530 − 0.184890I
b = 1.214130 − 0.199590I
10.56750 − 4.02468I 0
u = 0.36940 − 1.96319I
a = −1.064530 + 0.184890I
b = 1.214130 + 0.199590I
10.56750 + 4.02468I 0
u = 1.13922 + 2.02195I
a = 0.845877 + 0.411862I
b = −1.26404 + 1.60251I
17.0081 − 15.1515I 0
u = 1.13922 − 2.02195I
a = 0.845877 − 0.411862I
b = −1.26404 − 1.60251I
17.0081 + 15.1515I 0
u = −1.07898 + 2.08221I
a = 0.758885 − 0.409729I
b = −1.06379 − 1.81417I
16.6139 + 6.3485I 0
u = −1.07898 − 2.08221I
a = 0.758885 + 0.409729I
b = −1.06379 + 1.81417I
16.6139 − 6.3485I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.95530 + 1.96183I
a = −0.358887 − 0.264473I
b = 1.99385 + 0.02082I
8.32107 − 2.64989I 0
u = 1.95530 − 1.96183I
a = −0.358887 + 0.264473I
b = 1.99385 − 0.02082I
8.32107 + 2.64989I 0
u = −0.18789 + 2.88116I
a = 0.553430 − 0.032065I
b = −1.87447 + 1.62365I
18.1843 + 3.4592I 0
u = −0.18789 − 2.88116I
a = 0.553430 + 0.032065I
b = −1.87447 − 1.62365I
18.1843 − 3.4592I 0
u = −0.89301 + 2.76858I
a = −0.653362 + 0.138354I
b = 1.57197 + 0.58418I
12.09730 + 5.36685I 0
u = −0.89301 − 2.76858I
a = −0.653362 − 0.138354I
b = 1.57197 − 0.58418I
12.09730 − 5.36685I 0
u = −0.20333 + 3.10034I
a = 0.594985 − 0.039653I
b = −1.94922 − 1.37711I
19.1617 + 5.3151I 0
u = −0.20333 − 3.10034I
a = 0.594985 + 0.039653I
b = −1.94922 + 1.37711I
19.1617 − 5.3151I 0
8
II.
I
u
2
= h−2.80 × 10
9
u
16
+ 1.23 × 10
9
u
15
+ · · · + 5.78 × 10
9
b + 1.49 × 10
9
, 8.42 ×
10
6
u
16
+1.59×10
6
u
15
+· · · +2.84×10
6
a−4.34×10
7
, u
17
+6u
15
+· · · −3u −1i
(i) Arc colorings
a
4
=
0
u
a
8
=
1
0
a
9
=
1
u
2
a
3
=
u
u
3
+ u
a
11
=
−2.95940u
16
− 0.558807u
15
+ ··· + 7.83137u + 15.2503
0.483653u
16
− 0.212735u
15
+ ··· − 1.67509u − 0.257452
a
7
=
2.84567u
16
− 2.41889u
15
+ ··· − 21.8102u + 1.32723
0.0829079u
16
− 0.0995122u
15
+ ··· − 1.83555u − 0.881897
a
12
=
1.42944u
16
− 2.13476u
15
+ ··· − 12.9726u + 6.25927
0.355787u
16
− 0.159534u
15
+ ··· − 2.01409u − 0.833403
a
6
=
2.12965u
16
− 2.32997u
15
+ ··· − 19.2348u + 2.86422
0.223987u
16
− 0.211458u
15
+ ··· − 2.28481u − 0.792978
a
5
=
−1.08969u
16
+ 0.114263u
15
+ ··· + 3.70066u + 2.95645
0.141079u
16
− 0.111945u
15
+ ··· − 0.449264u + 0.0889186
a
2
=
1.18986u
16
− 0.118103u
15
+ ··· − 3.40302u − 2.98180
0.0172629u
16
+ 0.0956716u
15
+ ··· + 1.13318u − 0.143448
a
1
=
1.23077u
16
− 0.226208u
15
+ ··· − 4.14992u − 2.86754
0.0648607u
16
+ 0.00369480u
15
+ ··· + 0.102878u − 0.137290
a
10
=
−4.27308u
16
− 0.233087u
15
+ ··· + 13.8168u + 17.9997
0.377489u
16
− 0.184057u
15
+ ··· − 1.56233u − 0.0206505
(ii) Obstruction class = 1
(iii) Cusp Shapes =
45091796106
5782655035
u
16
−
12435236787
5782655035
u
15
+ ··· −
43331514147
1156531007
u −
96632179643
5782655035
9
(iv) u-Polynomials at the component
10
Crossings u-Polynomials at each crossing
c
1
u
17
− 8u
16
+ ··· + 3u − 1
c
2
u
17
+ 6u
16
+ ··· + u + 1
c
3
u
17
+ 6u
15
+ ··· − 3u + 1
c
4
u
17
− 6u
16
+ ··· + u − 1
c
5
u
17
− 6u
16
+ ··· + 3u − 1
c
6
u
17
− 3u
16
+ ··· − 6u
2
− 1
c
7
u
17
+ 6u
15
+ ··· + 3u + 1
c
8
u
17
+ 6u
15
+ ··· − 3u − 1
c
9
u
17
+ 3u
16
+ ··· + 6u
2
+ 1
c
10
u
17
+ 3u
16
+ ··· + 6u + 1
c
11
u
17
+ 6u
15
+ ··· + 3u − 1
c
12
u
17
− 5u
16
+ ··· + 5u − 1
11
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
17
+ 8y
16
+ ··· − 25y −1
c
2
, c
4
y
17
− 8y
16
+ ··· + 3y −1
c
3
, c
8
y
17
+ 12y
16
+ ··· + 3y −1
c
5
y
17
+ 2y
16
+ ··· + 19y −1
c
6
, c
9
y
17
+ 3y
16
+ ··· − 12y −1
c
7
, c
11
y
17
+ 12y
16
+ ··· − 3y −1
c
10
y
17
− 19y
16
+ ··· − 2y −1
c
12
y
17
− 17y
16
+ ··· + 7y −1
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.123817 + 0.916477I
a = −0.399407 + 0.909736I
b = −0.302924 + 0.816439I
2.61790 − 2.40485I 3.33881 + 2.22795I
u = 0.123817 − 0.916477I
a = −0.399407 − 0.909736I
b = −0.302924 − 0.816439I
2.61790 + 2.40485I 3.33881 − 2.22795I
u = −0.519605 + 0.973810I
a = −0.251920 − 0.419212I
b = −0.199212 − 0.760976I
1.04490 + 6.61108I −1.52634 − 5.44334I
u = −0.519605 − 0.973810I
a = −0.251920 + 0.419212I
b = −0.199212 + 0.760976I
1.04490 − 6.61108I −1.52634 + 5.44334I
u = −0.718697 + 0.273065I
a = 1.408880 − 0.113300I
b = −0.503625 + 0.659985I
1.14952 − 2.21103I 2.23770 + 3.38646I
u = −0.718697 − 0.273065I
a = 1.408880 + 0.113300I
b = −0.503625 − 0.659985I
1.14952 + 2.21103I 2.23770 − 3.38646I
u = 0.535223 + 1.162140I
a = −0.615278 − 0.480409I
b = −0.154895 − 1.305200I
−1.12324 − 5.07181I −0.31929 + 6.91281I
u = 0.535223 − 1.162140I
a = −0.615278 + 0.480409I
b = −0.154895 + 1.305200I
−1.12324 + 5.07181I −0.31929 − 6.91281I
u = −0.259361 + 1.266310I
a = −0.251583 + 0.034431I
b = −0.27641 + 1.42034I
0.516364 − 0.300871I 0.207427 + 0.470649I
u = −0.259361 − 1.266310I
a = −0.251583 − 0.034431I
b = −0.27641 − 1.42034I
0.516364 + 0.300871I 0.207427 − 0.470649I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.642620 + 0.176331I
a = −0.79573 − 4.21005I
b = 0.06025 − 1.48960I
−3.99885 + 0.50220I −2.39894 + 6.28246I
u = 0.642620 − 0.176331I
a = −0.79573 + 4.21005I
b = 0.06025 + 1.48960I
−3.99885 − 0.50220I −2.39894 − 6.28246I
u = −0.314004 + 0.270023I
a = 12.21260 + 4.46195I
b = 0.368087 − 0.696391I
−0.26934 − 3.00568I −3.5088 − 14.7647I
u = −0.314004 − 0.270023I
a = 12.21260 − 4.46195I
b = 0.368087 + 0.696391I
−0.26934 + 3.00568I −3.5088 + 14.7647I
u = 1.73212
a = 0.299870
b = −0.404382
−6.94010 −36.0810
u = −0.35606 + 2.09120I
a = −0.957501 + 0.103745I
b = 1.210930 + 0.258234I
10.11250 + 4.21829I −4.98986 − 4.99941I
u = −0.35606 − 2.09120I
a = −0.957501 − 0.103745I
b = 1.210930 − 0.258234I
10.11250 − 4.21829I −4.98986 + 4.99941I
15
III. I
v
1
= ha, 8.20 × 10
4
v
8
− 2.03 × 10
6
v
7
+ · · · + 7.65 × 10
5
b − 1.55 ×
10
6
, 7v
9
− 3v
8
+ · · · + v − 1i
(i) Arc colorings
a
4
=
v
0
a
8
=
1
0
a
9
=
1
0
a
3
=
v
0
a
11
=
0
−0.107257v
8
+ 2.65850v
7
+ ··· − 0.280187v + 2.03006
a
7
=
1
2.14626v
8
+ 0.185889v
7
+ ··· − 0.429870v + 1.30771
a
12
=
−0.107257v
8
+ 2.65850v
7
+ ··· − 0.280187v + 2.03006
−1.38456v
8
+ 4.21937v
7
+ ··· − 2.55986v + 1.77273
a
6
=
2.14626v
8
+ 0.185889v
7
+ ··· − 0.429870v + 2.30771
2.14626v
8
+ 0.185889v
7
+ ··· − 0.429870v + 1.30771
a
5
=
−1.01346v
8
− 0.464403v
7
+ ··· + 1.07485v + 0.182471
7v
8
− 3v
7
+ 2v
6
+ 14v
5
− 23v
4
− 33v
3
− v
2
+ 8v + 1
a
2
=
1.01346v
8
+ 0.464403v
7
+ ··· − 0.0748548v − 0.182471
−7v
8
+ 3v
7
− 2v
6
− 14v
5
+ 23v
4
+ 33v
3
+ v
2
− 8v − 1
a
1
=
1.01346v
8
+ 0.464403v
7
+ ··· − 1.07485v − 0.182471
−7v
8
+ 3v
7
− 2v
6
− 14v
5
+ 23v
4
+ 33v
3
+ v
2
− 8v − 1
a
10
=
−5.30121v
8
+ 5.22147v
7
+ ··· − 3.83160v + 0.359036
−7.44747v
8
+ 5.03558v
7
+ ··· − 3.40173v − 1.94867
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
6992041
764761
v
8
+
5331628
764761
v
7
−
6285069
764761
v
6
−
9541876
764761
v
5
+
21850087
764761
v
4
+
25370276
764761
v
3
−
321417
764761
v
2
+
135859
764761
v +
1854463
764761
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
9
c
3
, c
8
u
9
c
4
(u + 1)
9
c
5
u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
2
+ u + 1
c
6
u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1
c
7
u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1
c
9
u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1
c
10
, c
12
u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1
c
11
u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y − 1)
9
c
3
, c
8
y
9
c
5
y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y − 1
c
6
, c
9
y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y − 1
c
7
, c
11
y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y − 1
c
10
, c
12
y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y − 1
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −0.903964 + 0.094390I
a = 0
b = −0.140343 + 0.966856I
−3.42837 − 2.09337I −6.52230 + 4.24226I
v = −0.903964 − 0.094390I
a = 0
b = −0.140343 − 0.966856I
−3.42837 + 2.09337I −6.52230 − 4.24226I
v = 1.42091
a = 0
b = −0.512358
−0.446489 3.16660
v = −0.476406 + 0.294981I
a = 0
b = 0.796005 + 0.733148I
2.72642 − 1.33617I 0.84367 + 3.27176I
v = −0.476406 − 0.294981I
a = 0
b = 0.796005 − 0.733148I
2.72642 + 1.33617I 0.84367 − 3.27176I
v = 0.352455 + 0.113243I
a = 0
b = 0.728966 − 0.986295I
1.95319 − 7.08493I 3.61934 + 1.74309I
v = 0.352455 − 0.113243I
a = 0
b = 0.728966 + 0.986295I
1.95319 + 7.08493I 3.61934 − 1.74309I
v = 0.53175 + 1.59553I
a = 0
b = −0.628449 + 0.875112I
−1.02799 − 2.45442I −8.21790 + 4.39771I
v = 0.53175 − 1.59553I
a = 0
b = −0.628449 − 0.875112I
−1.02799 + 2.45442I −8.21790 − 4.39771I
19
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
9
)(u
17
− 8u
16
+ ··· + 3u − 1)(u
38
+ 46u
36
+ ··· + 6958u + 2401)
c
2
((u − 1)
9
)(u
17
+ 6u
16
+ ··· + u + 1)(u
38
− 16u
37
+ ··· + 378u − 49)
c
3
u
9
(u
17
+ 6u
15
+ ··· − 3u + 1)(u
38
− u
37
+ ··· + 86016u − 25088)
c
4
((u + 1)
9
)(u
17
− 6u
16
+ ··· + u − 1)(u
38
− 16u
37
+ ··· + 378u − 49)
c
5
(u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
2
+ u + 1)
· (u
17
− 6u
16
+ ··· + 3u − 1)(u
38
+ 4u
37
+ ··· − 114u − 17)
c
6
(u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1)
· (u
17
− 3u
16
+ ··· − 6u
2
− 1)(u
38
− 3u
37
+ ··· − 446u + 44)
c
7
(u
9
− u
8
+ ··· + u + 1)(u
17
+ 6u
15
+ ··· + 3u + 1)
· (u
38
− 2u
37
+ ··· − 3904u − 5873)
c
8
u
9
(u
17
+ 6u
15
+ ··· − 3u − 1)(u
38
− u
37
+ ··· + 86016u − 25088)
c
9
(u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
· (u
17
+ 3u
16
+ ··· + 6u
2
+ 1)(u
38
− 3u
37
+ ··· − 446u + 44)
c
10
(u
9
+ u
8
+ ··· − u − 1)(u
17
+ 3u
16
+ ··· + 6u + 1)
· (u
38
+ u
37
+ ··· + 40881797u + 3617129)
c
11
(u
9
+ u
8
+ ··· + u − 1)(u
17
+ 6u
15
+ ··· + 3u − 1)
· (u
38
− 2u
37
+ ··· − 3904u − 5873)
c
12
(u
9
+ u
8
+ ··· − u − 1)(u
17
− 5u
16
+ ··· + 5u − 1)
· (u
38
+ u
37
+ ··· + 79046u − 14009)
20
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y − 1)
9
)(y
17
+ 8y
16
+ ··· − 25y − 1)
· (y
38
+ 92y
37
+ ··· + 262856678y + 5764801)
c
2
, c
4
((y − 1)
9
)(y
17
− 8y
16
+ ··· + 3y − 1)(y
38
+ 46y
36
+ ··· − 6958y + 2401)
c
3
, c
8
y
9
(y
17
+ 12y
16
+ ··· + 3y − 1)
· (y
38
+ 69y
37
+ ··· + 3750756352y + 629407744)
c
5
(y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y − 1)
· (y
17
+ 2y
16
+ ··· + 19y − 1)(y
38
− 6y
37
+ ··· − 8270y + 289)
c
6
, c
9
(y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y − 1)
· (y
17
+ 3y
16
+ ··· − 12y − 1)(y
38
+ 35y
37
+ ··· − 111884y + 1936)
c
7
, c
11
(y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y − 1)
· (y
17
+ 12y
16
+ ··· − 3y − 1)
· (y
38
− 12y
37
+ ··· − 781291844y + 34492129)
c
10
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y − 1)
· (y
17
− 19y
16
+ ··· − 2y − 1)
· (y
38
− 107y
37
+ ··· − 346184004395873y + 13083622202641)
c
12
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y − 1)
· (y
17
− 17y
16
+ ··· + 7y − 1)
· (y
38
− 69y
37
+ ··· − 9544952050y + 196252081)
21
