12a
0246
(K12a
0246
)
A knot diagram
1
Linearized knot diagam
3 6 7 10 8 2 1 11 12 5 9 4
Solving Sequence
2,7
6 3
4,10
5 11 1 8 12 9
c
6
c
2
c
3
c
4
c
10
c
1
c
7
c
12
c
9
c
5
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h2u
84
− u
83
+ ··· + b + u, −2u
84
+ 2u
83
+ ··· + a − 2, u
86
− 2u
85
+ ··· + u + 1i
I
u
2
= h−u
2
+ b − 1, u
2
+ a, u
4
+ u
2
− u + 1i
I
u
3
= h−u
5
− u
3
+ b − u − 1, a + u + 1, u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1i
* 3 irreducible components of dim
C
= 0, with total 96 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
= h2u
84
−u
83
+· · ·+b+u, −2u
84
+2u
83
+· · ·+a−2, u
86
−2u
85
+· · ·+u+1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
u
2
a
3
=
u
u
3
+ u
a
4
=
−u
3
u
3
+ u
a
10
=
2u
84
− 2u
83
+ ··· − 2u
2
+ 2
−2u
84
+ u
83
+ ··· + 2u
2
− u
a
5
=
u
16
+ 3u
14
+ 5u
12
+ 4u
10
+ 3u
8
+ 2u
6
+ 2u
4
+ 1
u
18
+ 4u
16
+ 9u
14
+ 12u
12
+ 11u
10
+ 6u
8
+ 2u
6
+ u
2
a
11
=
u
81
− u
80
+ ··· + u + 1
u
83
− u
82
+ ··· − u
3
− 2u
a
1
=
u
3
u
5
+ u
3
+ u
a
8
=
u
8
+ u
6
+ u
4
+ 1
u
10
+ 2u
8
+ 3u
6
+ 2u
4
+ u
2
a
12
=
−u
11
− 2u
9
− 2u
7
+ u
3
u
11
+ 3u
9
+ 4u
7
+ 3u
5
+ u
3
+ u
a
9
=
u
84
− u
83
+ ··· + u + 2
−u
84
+ u
83
+ ··· + u
2
− u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
85
+ 8u
84
+ ··· + 13u − 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
86
+ 42u
85
+ ··· − 5u + 1
c
2
, c
6
u
86
− 2u
85
+ ··· + u + 1
c
3
u
86
+ 2u
85
+ ··· − 1288u + 1480
c
4
, c
10
u
86
− u
85
+ ··· − 1024u − 1024
c
5
, c
12
u
86
+ 6u
85
+ ··· + 2399u + 61
c
7
u
86
− 10u
85
+ ··· − 1635u + 175
c
8
, c
9
, c
11
u
86
− 11u
85
+ ··· + 10u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
86
+ 6y
85
+ ··· − 53y + 1
c
2
, c
6
y
86
+ 42y
85
+ ··· − 5y + 1
c
3
y
86
− 30y
85
+ ··· − 83985424y + 2190400
c
4
, c
10
y
86
− 63y
85
+ ··· + 524288y + 1048576
c
5
, c
12
y
86
+ 78y
85
+ ··· − 4956101y + 3721
c
7
y
86
− 6y
85
+ ··· − 286925y + 30625
c
8
, c
9
, c
11
y
86
− 89y
85
+ ··· − 20y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.288549 + 0.972974I
a = 1.75493 + 0.78387I
b = −0.71441 − 1.39976I
−2.22116 + 0.63715I 0
u = −0.288549 − 0.972974I
a = 1.75493 − 0.78387I
b = −0.71441 + 1.39976I
−2.22116 − 0.63715I 0
u = −0.594363 + 0.827888I
a = −0.91851 − 1.96253I
b = 0.014524 + 1.303580I
−9.68745 + 4.03436I 0
u = −0.594363 − 0.827888I
a = −0.91851 + 1.96253I
b = 0.014524 − 1.303580I
−9.68745 − 4.03436I 0
u = −0.638296 + 0.718655I
a = 0.621829 + 1.066280I
b = −1.11853 − 1.20118I
−9.35445 − 8.83622I 0
u = −0.638296 − 0.718655I
a = 0.621829 − 1.066280I
b = −1.11853 + 1.20118I
−9.35445 + 8.83622I 0
u = −0.555957 + 0.776754I
a = 1.16780 + 1.58425I
b = −0.34327 − 1.64073I
−2.77437 + 0.31938I 0
u = −0.555957 − 0.776754I
a = 1.16780 − 1.58425I
b = −0.34327 + 1.64073I
−2.77437 − 0.31938I 0
u = 0.581383 + 0.747816I
a = −0.883363 + 0.244616I
b = −0.160269 + 0.234378I
−4.82698 + 2.27835I −7.05026 + 0.I
u = 0.581383 − 0.747816I
a = −0.883363 − 0.244616I
b = −0.160269 − 0.234378I
−4.82698 − 2.27835I −7.05026 + 0.I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.596508 + 0.722178I
a = −0.96022 − 1.17170I
b = 0.89133 + 1.57341I
−2.57785 − 4.86252I −5.77848 + 6.73279I
u = −0.596508 − 0.722178I
a = −0.96022 + 1.17170I
b = 0.89133 − 1.57341I
−2.57785 + 4.86252I −5.77848 − 6.73279I
u = −0.165912 + 1.053050I
a = −1.46305 − 1.21359I
b = 0.58657 + 1.44609I
−8.18316 + 2.86607I 0
u = −0.165912 − 1.053050I
a = −1.46305 + 1.21359I
b = 0.58657 − 1.44609I
−8.18316 − 2.86607I 0
u = 0.349534 + 1.027830I
a = −1.12480 + 0.89092I
b = 0.106873 − 0.233450I
−4.50001 + 0.99756I 0
u = 0.349534 − 1.027830I
a = −1.12480 − 0.89092I
b = 0.106873 + 0.233450I
−4.50001 − 0.99756I 0
u = 0.472766 + 0.978829I
a = 0.632946 − 0.143360I
b = −0.0900200 + 0.0714641I
−0.31789 + 2.37544I 0
u = 0.472766 − 0.978829I
a = 0.632946 + 0.143360I
b = −0.0900200 − 0.0714641I
−0.31789 − 2.37544I 0
u = −0.409816 + 1.044080I
a = −2.51537 + 0.29188I
b = 1.78380 + 1.41570I
−3.34460 − 3.00265I 0
u = −0.409816 − 1.044080I
a = −2.51537 − 0.29188I
b = 1.78380 − 1.41570I
−3.34460 + 3.00265I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.662896 + 0.554239I
a = −0.209758 + 0.606442I
b = 0.607340 + 0.402687I
−2.86044 + 2.76662I −5.58462 − 3.68598I
u = 0.662896 − 0.554239I
a = −0.209758 − 0.606442I
b = 0.607340 − 0.402687I
−2.86044 − 2.76662I −5.58462 + 3.68598I
u = 0.569259 + 0.995615I
a = −0.950968 − 0.816360I
b = 0.354473 − 0.196976I
−4.15735 + 2.02652I 0
u = 0.569259 − 0.995615I
a = −0.950968 + 0.816360I
b = 0.354473 + 0.196976I
−4.15735 − 2.02652I 0
u = 0.789520 + 0.286900I
a = 0.055631 + 0.848882I
b = −3.06816 − 0.09259I
−11.5254 − 10.8225I −8.61250 + 5.48206I
u = 0.789520 − 0.286900I
a = 0.055631 − 0.848882I
b = −3.06816 + 0.09259I
−11.5254 + 10.8225I −8.61250 − 5.48206I
u = 0.524013 + 1.035860I
a = 0.017411 + 0.996158I
b = −0.225482 − 0.283637I
0.34446 + 3.37846I 0
u = 0.524013 − 1.035860I
a = 0.017411 − 0.996158I
b = −0.225482 + 0.283637I
0.34446 − 3.37846I 0
u = −0.286242 + 1.129260I
a = −0.253145 + 0.710934I
b = 0.598687 − 0.429451I
−4.99538 + 0.14999I 0
u = −0.286242 − 1.129260I
a = −0.253145 − 0.710934I
b = 0.598687 + 0.429451I
−4.99538 − 0.14999I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.537821 + 0.631209I
a = 0.450398 − 0.045646I
b = 0.001813 − 0.214183I
0.69758 + 1.71362I 1.48385 − 4.15054I
u = 0.537821 − 0.631209I
a = 0.450398 + 0.045646I
b = 0.001813 + 0.214183I
0.69758 − 1.71362I 1.48385 + 4.15054I
u = −0.726874 + 0.393872I
a = 0.112798 + 0.574879I
b = 1.17469 + 0.88530I
−3.62779 + 4.95156I −6.26943 − 4.18360I
u = −0.726874 − 0.393872I
a = 0.112798 − 0.574879I
b = 1.17469 − 0.88530I
−3.62779 − 4.95156I −6.26943 + 4.18360I
u = −0.498379 + 1.066840I
a = −2.07471 + 1.96310I
b = 2.57897 + 0.42300I
−2.71273 − 3.72235I 0
u = −0.498379 − 1.066840I
a = −2.07471 − 1.96310I
b = 2.57897 − 0.42300I
−2.71273 + 3.72235I 0
u = 0.770621 + 0.275590I
a = −0.157069 − 1.026500I
b = 2.99026 + 0.32459I
−4.69326 − 6.52919I −6.81472 + 5.27474I
u = 0.770621 − 0.275590I
a = −0.157069 + 1.026500I
b = 2.99026 − 0.32459I
−4.69326 + 6.52919I −6.81472 − 5.27474I
u = −0.767665 + 0.262811I
a = −0.492258 + 0.383127I
b = −0.563795 + 1.146430I
−7.06528 + 3.78113I −8.10408 − 2.38629I
u = −0.767665 − 0.262811I
a = −0.492258 − 0.383127I
b = −0.563795 − 1.146430I
−7.06528 − 3.78113I −8.10408 + 2.38629I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.277554 + 1.162930I
a = −3.44039 − 1.29200I
b = 2.31723 − 1.08605I
−9.10196 − 3.37594I 0
u = 0.277554 − 1.162930I
a = −3.44039 + 1.29200I
b = 2.31723 + 1.08605I
−9.10196 + 3.37594I 0
u = 0.296845 + 1.162430I
a = 2.88869 + 1.49562I
b = −2.07890 + 0.99513I
−9.33402 + 2.30663I 0
u = 0.296845 − 1.162430I
a = 2.88869 − 1.49562I
b = −2.07890 − 0.99513I
−9.33402 − 2.30663I 0
u = −0.287047 + 1.165100I
a = 0.45506 − 1.42515I
b = −1.20531 + 0.95369I
−11.41770 + 0.56506I 0
u = −0.287047 − 1.165100I
a = 0.45506 + 1.42515I
b = −1.20531 − 0.95369I
−11.41770 − 0.56506I 0
u = 0.768626 + 0.218313I
a = 0.077135 − 1.268350I
b = 2.17103 + 0.10227I
−12.50220 + 2.89654I −9.84851 − 1.14586I
u = 0.768626 − 0.218313I
a = 0.077135 + 1.268350I
b = 2.17103 − 0.10227I
−12.50220 − 2.89654I −9.84851 + 1.14586I
u = 0.757922 + 0.251411I
a = 0.071124 + 1.222860I
b = −2.56236 − 0.49445I
−5.06705 − 0.94141I −7.86259 − 0.41236I
u = 0.757922 − 0.251411I
a = 0.071124 − 1.222860I
b = −2.56236 + 0.49445I
−5.06705 + 0.94141I −7.86259 + 0.41236I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.262587 + 1.173330I
a = 3.53054 + 0.94911I
b = −2.41749 + 1.15092I
−16.0850 − 7.6716I 0
u = 0.262587 − 1.173330I
a = 3.53054 − 0.94911I
b = −2.41749 − 1.15092I
−16.0850 + 7.6716I 0
u = 0.519924 + 1.085570I
a = 1.03946 − 1.48640I
b = −0.148695 + 1.038150I
−3.28429 + 5.87626I 0
u = 0.519924 − 1.085570I
a = 1.03946 + 1.48640I
b = −0.148695 − 1.038150I
−3.28429 − 5.87626I 0
u = −0.541621 + 1.081200I
a = 0.68625 − 1.95841I
b = −1.88134 + 0.43680I
−0.49878 − 7.28560I 0
u = −0.541621 − 1.081200I
a = 0.68625 + 1.95841I
b = −1.88134 − 0.43680I
−0.49878 + 7.28560I 0
u = −0.432231 + 1.134090I
a = 2.07510 − 0.96389I
b = −2.17476 − 0.86834I
−11.08480 − 3.93749I 0
u = −0.432231 − 1.134090I
a = 2.07510 + 0.96389I
b = −2.17476 + 0.86834I
−11.08480 + 3.93749I 0
u = 0.313991 + 1.175220I
a = −2.43370 − 1.04010I
b = 1.75385 − 1.21759I
−16.7193 + 6.3367I 0
u = 0.313991 − 1.175220I
a = −2.43370 + 1.04010I
b = 1.75385 + 1.21759I
−16.7193 − 6.3367I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.726678 + 0.290250I
a = 0.272140 − 0.169725I
b = 0.280985 − 0.574993I
−0.80863 + 3.09743I −0.14695 − 3.21978I
u = −0.726678 − 0.290250I
a = 0.272140 + 0.169725I
b = 0.280985 + 0.574993I
−0.80863 − 3.09743I −0.14695 + 3.21978I
u = −0.571260 + 1.092910I
a = 0.24119 + 1.91899I
b = 1.49187 − 1.07630I
−5.67694 − 9.90189I 0
u = −0.571260 − 1.092910I
a = 0.24119 − 1.91899I
b = 1.49187 + 1.07630I
−5.67694 + 9.90189I 0
u = 0.590836 + 0.487016I
a = 0.033582 − 0.610913I
b = −0.555184 + 0.176196I
1.95612 + 1.07254I 2.32786 − 4.06564I
u = 0.590836 − 0.487016I
a = 0.033582 + 0.610913I
b = −0.555184 − 0.176196I
1.95612 − 1.07254I 2.32786 + 4.06564I
u = −0.651259 + 0.383779I
a = −0.297043 − 0.580610I
b = −1.327010 − 0.235305I
1.52038 + 2.62568I 0.05256 − 5.40036I
u = −0.651259 − 0.383779I
a = −0.297043 + 0.580610I
b = −1.327010 + 0.235305I
1.52038 − 2.62568I 0.05256 + 5.40036I
u = −0.546113 + 1.127960I
a = −0.819362 − 0.114303I
b = 0.342254 + 0.774577I
−3.23683 − 7.93121I 0
u = −0.546113 − 1.127960I
a = −0.819362 + 0.114303I
b = 0.342254 − 0.774577I
−3.23683 + 7.93121I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.541262 + 1.146140I
a = 3.19594 + 2.07479I
b = −3.56382 + 0.39183I
−7.67401 + 5.81428I 0
u = 0.541262 − 1.146140I
a = 3.19594 − 2.07479I
b = −3.56382 − 0.39183I
−7.67401 − 5.81428I 0
u = −0.547225 + 1.147030I
a = 1.53697 + 0.31279I
b = −0.57924 − 1.56428I
−9.65180 − 8.70743I 0
u = −0.547225 − 1.147030I
a = 1.53697 − 0.31279I
b = −0.57924 + 1.56428I
−9.65180 + 8.70743I 0
u = 0.552216 + 1.145020I
a = −3.19958 − 2.81060I
b = 3.91549 − 0.11091I
−7.24107 + 11.48790I 0
u = 0.552216 − 1.145020I
a = −3.19958 + 2.81060I
b = 3.91549 + 0.11091I
−7.24107 − 11.48790I 0
u = 0.530994 + 1.156470I
a = −2.44372 − 1.78900I
b = 3.09953 − 0.05061I
−15.2418 + 1.9452I 0
u = 0.530994 − 1.156470I
a = −2.44372 + 1.78900I
b = 3.09953 + 0.05061I
−15.2418 − 1.9452I 0
u = 0.560925 + 1.148440I
a = 2.81719 + 3.06743I
b = −3.87039 − 0.10151I
−14.0649 + 15.8670I 0
u = 0.560925 − 1.148440I
a = 2.81719 − 3.06743I
b = −3.87039 + 0.10151I
−14.0649 − 15.8670I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.594714 + 0.341461I
a = −0.122682 + 1.010820I
b = 0.410591 − 0.962437I
−1.16613 − 1.42530I −4.02664 + 0.35446I
u = 0.594714 − 0.341461I
a = −0.122682 − 1.010820I
b = 0.410591 + 0.962437I
−1.16613 + 1.42530I −4.02664 − 0.35446I
u = −0.659724
a = −1.04511
b = −1.45516
−7.94428 −10.6470
u = −0.497755 + 0.426248I
a = 0.749388 + 1.023230I
b = 1.51286 − 0.69421I
−0.808182 − 0.442640I −5.58197 − 2.36706I
u = −0.497755 − 0.426248I
a = 0.749388 − 1.023230I
b = 1.51286 + 0.69421I
−0.808182 + 0.442640I −5.58197 + 2.36706I
u = −0.333193
a = 1.59751
b = 0.781978
−0.970966 −9.92870
13
II. I
u
2
= h−u
2
+ b − 1, u
2
+ a, u
4
+ u
2
− u + 1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
u
2
a
3
=
u
u
3
+ u
a
4
=
−u
3
u
3
+ u
a
10
=
−u
2
u
2
+ 1
a
5
=
−u
3
u
3
+ u
a
11
=
−u
2
u
2
+ 1
a
1
=
u
3
u
2
a
8
=
−u
3
+ u
2
− u + 1
−u
2
+ u − 1
a
12
=
u
3
− u
2
+ u − 1
u
2
− u + 1
a
9
=
−u
3
− u + 1
u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −5u
3
− 4u
2
− u − 6
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
4
− 2u
3
+ 3u
2
− u + 1
c
2
, c
5
, c
12
u
4
+ u
2
+ u + 1
c
3
u
4
+ 3u
3
+ 4u
2
+ 3u + 2
c
4
, c
10
u
4
c
6
u
4
+ u
2
− u + 1
c
7
u
4
+ 2u
3
+ 3u
2
+ u + 1
c
8
, c
9
(u − 1)
4
c
11
(u + 1)
4
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
4
+ 2y
3
+ 7y
2
+ 5y + 1
c
2
, c
5
, c
6
c
12
y
4
+ 2y
3
+ 3y
2
+ y + 1
c
3
y
4
− y
3
+ 2y
2
+ 7y + 4
c
4
, c
10
y
4
c
8
, c
9
, c
11
(y −1)
4
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.547424 + 0.585652I
a = 0.043315 − 0.641200I
b = 0.956685 + 0.641200I
−0.66484 + 1.39709I −4.37800 − 4.77865I
u = 0.547424 − 0.585652I
a = 0.043315 + 0.641200I
b = 0.956685 − 0.641200I
−0.66484 − 1.39709I −4.37800 + 4.77865I
u = −0.547424 + 1.120870I
a = 0.95668 + 1.22719I
b = 0.043315 − 1.227190I
−4.26996 − 7.64338I −11.12200 + 5.79053I
u = −0.547424 − 1.120870I
a = 0.95668 − 1.22719I
b = 0.043315 + 1.227190I
−4.26996 + 7.64338I −11.12200 − 5.79053I
17
III. I
u
3
= h−u
5
− u
3
+ b − u − 1, a + u + 1, u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
u
2
a
3
=
u
u
3
+ u
a
4
=
−u
3
u
3
+ u
a
10
=
−u − 1
u
5
+ u
3
+ u + 1
a
5
=
−u
3
u
3
+ u
a
11
=
−u − 1
u
5
+ u
3
+ u + 1
a
1
=
u
3
u
5
+ u
3
+ u
a
8
=
u
4
+ u
2
+ u + 1
−2u
5
− u
4
− 3u
3
− 2u
2
− 3u − 2
a
12
=
−u
4
− u
2
− u − 1
2u
5
+ u
4
+ 3u
3
+ 2u
2
+ 3u + 2
a
9
=
u
4
+ u
2
−u
5
− u
4
− 2u
3
− 2u
2
− 2u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −u
4
− 5u
3
− u
2
− 4u − 11
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
6
− 3u
5
+ 4u
4
− 2u
3
+ 1
c
2
, c
5
, c
12
u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1
c
3
(u
3
− u
2
+ 1)
2
c
4
, c
10
u
6
c
6
u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1
c
7
u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1
c
8
, c
9
(u − 1)
6
c
11
(u + 1)
6
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1
c
2
, c
5
, c
6
c
12
y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1
c
3
(y
3
− y
2
+ 2y −1)
2
c
4
, c
10
y
6
c
8
, c
9
, c
11
(y −1)
6
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.498832 + 1.001300I
a = −1.49883 − 1.00130I
b = 1.41613 − 0.43668I
−1.91067 + 2.82812I −4.93045 − 2.21599I
u = 0.498832 − 1.001300I
a = −1.49883 + 1.00130I
b = 1.41613 + 0.43668I
−1.91067 − 2.82812I −4.93045 + 2.21599I
u = −0.284920 + 1.115140I
a = −0.715080 − 1.115140I
b = −0.162359 + 0.635452I
−6.04826 −14.8442 + 0.2733I
u = −0.284920 − 1.115140I
a = −0.715080 + 1.115140I
b = −0.162359 − 0.635452I
−6.04826 −14.8442 − 0.2733I
u = −0.713912 + 0.305839I
a = −0.286088 − 0.305839I
b = 0.246226 + 0.998963I
−1.91067 + 2.82812I −7.72532 − 2.61835I
u = −0.713912 − 0.305839I
a = −0.286088 + 0.305839I
b = 0.246226 − 0.998963I
−1.91067 − 2.82812I −7.72532 + 2.61835I
21
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
4
− 2u
3
+ 3u
2
− u + 1)(u
6
− 3u
5
+ 4u
4
− 2u
3
+ 1)
· (u
86
+ 42u
85
+ ··· − 5u + 1)
c
2
(u
4
+ u
2
+ u + 1)(u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
· (u
86
− 2u
85
+ ··· + u + 1)
c
3
(u
3
− u
2
+ 1)
2
(u
4
+ 3u
3
+ 4u
2
+ 3u + 2)
· (u
86
+ 2u
85
+ ··· − 1288u + 1480)
c
4
, c
10
u
10
(u
86
− u
85
+ ··· − 1024u − 1024)
c
5
, c
12
(u
4
+ u
2
+ u + 1)(u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
· (u
86
+ 6u
85
+ ··· + 2399u + 61)
c
6
(u
4
+ u
2
− u + 1)(u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)
· (u
86
− 2u
85
+ ··· + u + 1)
c
7
(u
4
+ 2u
3
+ 3u
2
+ u + 1)(u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1)
· (u
86
− 10u
85
+ ··· − 1635u + 175)
c
8
, c
9
((u − 1)
10
)(u
86
− 11u
85
+ ··· + 10u − 1)
c
11
((u + 1)
10
)(u
86
− 11u
85
+ ··· + 10u − 1)
22
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
4
+ 2y
3
+ 7y
2
+ 5y + 1)(y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1)
· (y
86
+ 6y
85
+ ··· − 53y + 1)
c
2
, c
6
(y
4
+ 2y
3
+ 3y
2
+ y + 1)(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
· (y
86
+ 42y
85
+ ··· − 5y + 1)
c
3
(y
3
− y
2
+ 2y −1)
2
(y
4
− y
3
+ 2y
2
+ 7y + 4)
· (y
86
− 30y
85
+ ··· − 83985424y + 2190400)
c
4
, c
10
y
10
(y
86
− 63y
85
+ ··· + 524288y + 1048576)
c
5
, c
12
(y
4
+ 2y
3
+ 3y
2
+ y + 1)(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
· (y
86
+ 78y
85
+ ··· − 4956101y + 3721)
c
7
(y
4
+ 2y
3
+ 7y
2
+ 5y + 1)(y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1)
· (y
86
− 6y
85
+ ··· − 286925y + 30625)
c
8
, c
9
, c
11
((y −1)
10
)(y
86
− 89y
85
+ ··· − 20y + 1)
23
