12a
0911
(K12a
0911
)
A knot diagram
1
Linearized knot diagam
4 6 9 2 10 12 1 11 5 3 8 7
Solving Sequence
1,8
7 12
3,6
2 11 9 4 10 5
c
7
c
12
c
6
c
2
c
11
c
8
c
3
c
10
c
5
c
1
, c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h2.55005 × 10
55
u
99
+ 1.78130 × 10
55
u
98
+ ··· + 1.02735 × 10
54
b − 1.90596 × 10
55
,
− 2.30960 × 10
54
u
99
− 2.60296 × 10
53
u
98
+ ··· + 1.02735 × 10
54
a + 2.71064 × 10
54
, u
100
+ 2u
99
+ ··· + u − 1i
I
u
2
= h2u
4
− 2u
3
− 7u
2
+ 7b − 2u − 1, 6u
4
+ 8u
3
− 7u
2
+ 7a − 6u + 4, u
5
+ u
4
− 2u
3
− u
2
+ u − 1i
* 2 irreducible components of dim
C
= 0, with total 105 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
= h2.55×10
55
u
99
+1.78×10
55
u
98
+· · ·+1.03×10
54
b−1.91×10
55
, −2.31×
10
54
u
99
−2.60×10
53
u
98
+· · ·+1.03×10
54
a+2.71×10
54
, u
100
+ 2 u
99
+· · ·+u−1i
(i) Arc colorings
a
1
=
0
u
a
8
=
1
0
a
7
=
1
−u
2
a
12
=
u
−u
3
+ u
a
3
=
2.24811u
99
+ 0.253365u
98
+ ··· − 0.644151u − 2.63847
−24.8215u
99
− 17.3387u
98
+ ··· − 31.6225u + 18.5521
a
6
=
−u
2
+ 1
u
4
− 2u
2
a
2
=
−12.8554u
99
− 10.3071u
98
+ ··· − 19.7406u + 8.23996
−33.1829u
99
− 22.7159u
98
+ ··· − 41.6270u + 24.6702
a
11
=
−u
3
+ 2u
−u
3
+ u
a
9
=
u
6
− 3u
4
+ 2u
2
+ 1
u
6
− 2u
4
+ u
2
a
4
=
−11.4644u
99
− 9.40616u
98
+ ··· − 18.1363u + 7.33735
−43.7815u
99
− 29.8900u
98
+ ··· − 57.0219u + 32.7738
a
10
=
−0.735233u
99
− 0.0386406u
98
+ ··· − 3.61695u + 0.645082
19.0168u
99
+ 13.0073u
98
+ ··· + 23.4427u − 14.2277
a
5
=
3.85489u
99
+ 2.47469u
98
+ ··· + 4.29212u − 2.64226
−15.8972u
99
− 10.5712u
98
+ ··· − 22.7675u + 12.2305
(ii) Obstruction class = −1
(iii) Cusp Shapes = 76.2668u
99
+ 56.8751u
98
+ ··· + 75.3902u − 55.1984
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
100
− 6u
99
+ ··· + 1149u − 49
c
2
7(7u
100
+ 35u
99
+ ··· + 385706u − 40879)
c
3
7(7u
100
− 147u
99
+ ··· − 311196u − 14099)
c
5
, c
9
u
100
+ 2u
99
+ ··· + 5u + 1
c
6
, c
7
, c
12
u
100
+ 2u
99
+ ··· + u − 1
c
8
, c
11
u
100
− 6u
99
+ ··· + 25745u − 4025
c
10
u
100
+ 3u
99
+ ··· + 17472u + 1568
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
100
− 54y
99
+ ··· − 355685y + 2401
c
2
49(49y
100
− 12187y
99
+ ··· − 3.62058 × 10
10
y + 1.67109 × 10
9
)
c
3
49(49y
100
− 14049y
99
+ ··· − 6.34678 × 10
10
y + 1.98782 × 10
8
)
c
5
, c
9
y
100
− 54y
99
+ ··· − 7y + 1
c
6
, c
7
, c
12
y
100
− 82y
99
+ ··· − 7y + 1
c
8
, c
11
y
100
+ 70y
99
+ ··· − 361276175y + 16200625
c
10
y
100
− 33y
99
+ ··· − 259083776y + 2458624
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.066180 + 0.860765I
a = 0.87155 − 2.12153I
b = 0.61301 − 1.78801I
7.76831 + 1.78382I 0
u = 0.066180 − 0.860765I
a = 0.87155 + 2.12153I
b = 0.61301 + 1.78801I
7.76831 − 1.78382I 0
u = 0.125303 + 0.844813I
a = 0.00052 + 3.24559I
b = 0.34459 + 2.71163I
5.8756 − 13.5209I 0
u = 0.125303 − 0.844813I
a = 0.00052 − 3.24559I
b = 0.34459 − 2.71163I
5.8756 + 13.5209I 0
u = −0.135762 + 0.841793I
a = −0.00022 + 2.29080I
b = −0.26671 + 1.96639I
2.30679 + 7.72312I 0
u = −0.135762 − 0.841793I
a = −0.00022 − 2.29080I
b = −0.26671 − 1.96639I
2.30679 − 7.72312I 0
u = 0.084808 + 0.824876I
a = −0.25875 − 3.34323I
b = −0.49311 − 2.87868I
8.93550 − 6.71171I 0. + 5.58180I
u = 0.084808 − 0.824876I
a = −0.25875 + 3.34323I
b = −0.49311 + 2.87868I
8.93550 + 6.71171I 0. − 5.58180I
u = 1.118570 + 0.355935I
a = −0.411676 + 1.064340I
b = 1.17459 + 1.01033I
4.54352 − 1.52298I 0
u = 1.118570 − 0.355935I
a = −0.411676 − 1.064340I
b = 1.17459 − 1.01033I
4.54352 + 1.52298I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.063459 + 0.823553I
a = 0.01587 − 2.41880I
b = 0.28053 − 1.98760I
5.17789 + 2.75522I 0
u = −0.063459 − 0.823553I
a = 0.01587 + 2.41880I
b = 0.28053 + 1.98760I
5.17789 − 2.75522I 0
u = 0.133069 + 0.812087I
a = −1.17414 + 1.37179I
b = −0.71986 + 1.37933I
7.53948 − 2.72894I 0. + 4.33750I
u = 0.133069 − 0.812087I
a = −1.17414 − 1.37179I
b = −0.71986 − 1.37933I
7.53948 + 2.72894I 0. − 4.33750I
u = −1.108750 + 0.404553I
a = 1.233170 + 0.565323I
b = −0.21427 + 1.54803I
−0.67251 − 3.23097I 0
u = −1.108750 − 0.404553I
a = 1.233170 − 0.565323I
b = −0.21427 − 1.54803I
−0.67251 + 3.23097I 0
u = 1.127540 + 0.406548I
a = −1.80128 + 0.82756I
b = 0.19262 + 2.25353I
2.80795 + 9.01655I 0
u = 1.127540 − 0.406548I
a = −1.80128 − 0.82756I
b = 0.19262 − 2.25353I
2.80795 − 9.01655I 0
u = −1.20312
a = 0.236367
b = −0.701550
−2.51628 0
u = −0.026000 + 0.786577I
a = −4.29155 − 2.82581I
b = −2.37520 − 1.76189I
4.40963 + 0.13433I −4.43140 + 2.83159I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.026000 − 0.786577I
a = −4.29155 + 2.82581I
b = −2.37520 + 1.76189I
4.40963 − 0.13433I −4.43140 − 2.83159I
u = −0.072981 + 0.768562I
a = 1.287060 + 0.166439I
b = 1.65682 + 0.13967I
2.78890 + 4.95396I −0.93576 − 7.70957I
u = −0.072981 − 0.768562I
a = 1.287060 − 0.166439I
b = 1.65682 − 0.13967I
2.78890 − 4.95396I −0.93576 + 7.70957I
u = −0.603154 + 0.480578I
a = 0.531251 + 0.247738I
b = −0.116625 − 0.232744I
−2.41423 + 3.09068I −4.65212 − 8.27933I
u = −0.603154 − 0.480578I
a = 0.531251 − 0.247738I
b = −0.116625 + 0.232744I
−2.41423 − 3.09068I −4.65212 + 8.27933I
u = 1.179710 + 0.372781I
a = 1.87644 − 0.67092I
b = −0.29893 − 2.56412I
5.58223 + 2.39089I 0
u = 1.179710 − 0.372781I
a = 1.87644 + 0.67092I
b = −0.29893 + 2.56412I
5.58223 − 2.39089I 0
u = −1.208580 + 0.298352I
a = 0.138130 + 0.798805I
b = −1.39785 − 0.70786I
−0.659627 − 1.083600I 0
u = −1.208580 − 0.298352I
a = 0.138130 − 0.798805I
b = −1.39785 + 0.70786I
−0.659627 + 1.083600I 0
u = −0.368759 + 0.658434I
a = −0.200364 + 0.148708I
b = 0.192399 + 0.236039I
−1.61628 + 0.90792I 0.73056 + 3.87410I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.368759 − 0.658434I
a = −0.200364 − 0.148708I
b = 0.192399 − 0.236039I
−1.61628 − 0.90792I 0.73056 − 3.87410I
u = 0.046166 + 0.753218I
a = 0.29339 + 1.60136I
b = −0.337923 + 1.301070I
1.06739 − 1.59292I −4.21907 + 0.71852I
u = 0.046166 − 0.753218I
a = 0.29339 − 1.60136I
b = −0.337923 − 1.301070I
1.06739 + 1.59292I −4.21907 − 0.71852I
u = −1.207020 + 0.373783I
a = −1.187900 − 0.686360I
b = 0.29346 − 1.83954I
1.66457 + 1.55604I 0
u = −1.207020 − 0.373783I
a = −1.187900 + 0.686360I
b = 0.29346 + 1.83954I
1.66457 − 1.55604I 0
u = 1.26388
a = −10.1850
b = 15.3307
−3.96123 0
u = 1.199860 + 0.413091I
a = 0.88673 − 1.23671I
b = −0.98804 − 1.51467I
4.27981 − 6.34812I 0
u = 1.199860 − 0.413091I
a = 0.88673 + 1.23671I
b = −0.98804 + 1.51467I
4.27981 + 6.34812I 0
u = 0.535734 + 0.490182I
a = −0.857560 + 0.337611I
b = 0.035042 − 0.510932I
0.80071 − 9.15581I −3.31075 + 8.99009I
u = 0.535734 − 0.490182I
a = −0.857560 − 0.337611I
b = 0.035042 + 0.510932I
0.80071 + 9.15581I −3.31075 − 8.99009I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.026695 + 0.718976I
a = −0.03361 + 3.09163I
b = −0.29804 + 2.61186I
0.46493 − 1.57636I −3.62391 + 3.74056I
u = 0.026695 − 0.718976I
a = −0.03361 − 3.09163I
b = −0.29804 − 2.61186I
0.46493 + 1.57636I −3.62391 − 3.74056I
u = 1.244710 + 0.302263I
a = −1.125240 + 0.246242I
b = 0.684228 + 0.684322I
−2.61355 − 2.20912I 0
u = 1.244710 − 0.302263I
a = −1.125240 − 0.246242I
b = 0.684228 − 0.684322I
−2.61355 + 2.20912I 0
u = 0.425289 + 0.569271I
a = 0.679374 + 0.345318I
b = −0.322505 + 0.245223I
1.16837 + 5.35171I −2.33945 − 3.24419I
u = 0.425289 − 0.569271I
a = 0.679374 − 0.345318I
b = −0.322505 − 0.245223I
1.16837 − 5.35171I −2.33945 + 3.24419I
u = −1.247730 + 0.335150I
a = 0.14268 − 2.59678I
b = 1.90497 − 1.37567I
0.63837 + 3.90975I 0
u = −1.247730 − 0.335150I
a = 0.14268 + 2.59678I
b = 1.90497 + 1.37567I
0.63837 − 3.90975I 0
u = 1.302980 + 0.076339I
a = −0.177078 − 0.842270I
b = 0.451240 + 0.097844I
−4.78110 − 2.15974I 0
u = 1.302980 − 0.076339I
a = −0.177078 + 0.842270I
b = 0.451240 − 0.097844I
−4.78110 + 2.15974I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.276810 + 0.291243I
a = −1.64166 + 0.89025I
b = 1.52030 + 2.34735I
−3.42645 − 2.04331I 0
u = 1.276810 − 0.291243I
a = −1.64166 − 0.89025I
b = 1.52030 − 2.34735I
−3.42645 + 2.04331I 0
u = −1.31785
a = 0.616471
b = −0.733009
−2.21898 0
u = −1.329660 + 0.009805I
a = 0.667787 − 0.376017I
b = 1.83737 − 0.03557I
−7.24915 + 0.12420I 0
u = −1.329660 − 0.009805I
a = 0.667787 + 0.376017I
b = 1.83737 + 0.03557I
−7.24915 − 0.12420I 0
u = 1.286520 + 0.342616I
a = 3.62577 + 1.50468I
b = 3.04784 − 2.13233I
0.32064 − 4.20537I 0
u = 1.286520 − 0.342616I
a = 3.62577 − 1.50468I
b = 3.04784 + 2.13233I
0.32064 + 4.20537I 0
u = −1.295980 + 0.307916I
a = 1.52481 + 0.84597I
b = −0.74775 + 3.02913I
−3.68022 + 5.30134I 0
u = −1.295980 − 0.307916I
a = 1.52481 − 0.84597I
b = −0.74775 − 3.02913I
−3.68022 − 5.30134I 0
u = 1.336150 + 0.037532I
a = −0.668166 − 1.189430I
b = −0.974750 − 0.539922I
−6.23871 − 3.34970I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.336150 − 0.037532I
a = −0.668166 + 1.189430I
b = −0.974750 + 0.539922I
−6.23871 + 3.34970I 0
u = −1.334610 + 0.104729I
a = −0.401638 − 0.914443I
b = −0.867103 − 0.055077I
−1.56741 + 5.50751I 0
u = −1.334610 − 0.104729I
a = −0.401638 + 0.914443I
b = −0.867103 + 0.055077I
−1.56741 − 5.50751I 0
u = −1.302260 + 0.324685I
a = 0.584203 + 0.491239I
b = −0.02040 + 1.86856I
−3.15215 + 5.49182I 0
u = −1.302260 − 0.324685I
a = 0.584203 − 0.491239I
b = −0.02040 − 1.86856I
−3.15215 − 5.49182I 0
u = 1.314960 + 0.333665I
a = −0.223233 − 0.758788I
b = −1.76656 + 0.86515I
−1.55939 − 8.93980I 0
u = 1.314960 − 0.333665I
a = −0.223233 + 0.758788I
b = −1.76656 − 0.86515I
−1.55939 + 8.93980I 0
u = 1.312470 + 0.363962I
a = 1.36690 − 0.90680I
b = −0.79085 − 1.96456I
0.87397 − 7.02667I 0
u = 1.312470 − 0.363962I
a = 1.36690 + 0.90680I
b = −0.79085 + 1.96456I
0.87397 + 7.02667I 0
u = −1.314330 + 0.390094I
a = −1.37366 − 0.34309I
b = −0.22659 − 1.87215I
3.45510 + 2.70339I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.314330 − 0.390094I
a = −1.37366 + 0.34309I
b = −0.22659 + 1.87215I
3.45510 − 2.70339I 0
u = −1.325260 + 0.363911I
a = −1.78448 − 1.24566I
b = 1.18856 − 2.94620I
4.51646 + 10.99010I 0
u = −1.325260 − 0.363911I
a = −1.78448 + 1.24566I
b = 1.18856 + 2.94620I
4.51646 − 10.99010I 0
u = −1.37954
a = 0.525786
b = −0.307804
−2.27657 0
u = −1.354270 + 0.350897I
a = 1.105460 − 0.077103I
b = 0.31851 + 1.50383I
2.85303 + 6.92434I 0
u = −1.354270 − 0.350897I
a = 1.105460 + 0.077103I
b = 0.31851 − 1.50383I
2.85303 − 6.92434I 0
u = −1.351770 + 0.370394I
a = 1.77739 + 1.17880I
b = −0.84705 + 2.89589I
1.2299 + 17.8925I 0
u = −1.351770 − 0.370394I
a = 1.77739 − 1.17880I
b = −0.84705 − 2.89589I
1.2299 − 17.8925I 0
u = 1.356960 + 0.367547I
a = −1.26141 + 0.86468I
b = 0.72317 + 2.11532I
−2.39184 − 12.07600I 0
u = 1.356960 − 0.367547I
a = −1.26141 − 0.86468I
b = 0.72317 − 2.11532I
−2.39184 + 12.07600I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.403610 + 0.172759I
a = −0.357432 + 0.140146I
b = 0.045150 + 0.705809I
−4.64740 − 2.81144I 0
u = −1.403610 − 0.172759I
a = −0.357432 − 0.140146I
b = 0.045150 − 0.705809I
−4.64740 + 2.81144I 0
u = −1.40977 + 0.11256I
a = 0.350963 + 0.532406I
b = 0.973998 − 0.537090I
−5.38865 + 11.04220I 0
u = −1.40977 − 0.11256I
a = 0.350963 − 0.532406I
b = 0.973998 + 0.537090I
−5.38865 − 11.04220I 0
u = 0.467110 + 0.337848I
a = −0.393316 − 0.183041I
b = 0.684027 − 0.159400I
3.31994 + 0.86651I 0.20729 + 2.64307I
u = 0.467110 − 0.337848I
a = −0.393316 + 0.183041I
b = 0.684027 + 0.159400I
3.31994 − 0.86651I 0.20729 − 2.64307I
u = 1.42891 + 0.10467I
a = −0.245132 + 0.379566I
b = −0.596256 − 0.199428I
−8.90921 − 4.87685I 0
u = 1.42891 − 0.10467I
a = −0.245132 − 0.379566I
b = −0.596256 + 0.199428I
−8.90921 + 4.87685I 0
u = 0.366259 + 0.423550I
a = 0.494904 − 1.198700I
b = −0.184808 + 0.420618I
3.66081 − 3.79622I 0.61652 + 6.81445I
u = 0.366259 − 0.423550I
a = 0.494904 + 1.198700I
b = −0.184808 − 0.420618I
3.66081 + 3.79622I 0.61652 − 6.81445I
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.43401 + 0.23684I
a = 0.0739934 + 0.0177622I
b = −0.028722 + 0.371217I
−7.39038 − 4.13584I 0
u = 1.43401 − 0.23684I
a = 0.0739934 − 0.0177622I
b = −0.028722 − 0.371217I
−7.39038 + 4.13584I 0
u = −0.394376 + 0.192389I
a = 2.48574 − 1.37904I
b = 0.140530 + 0.493595I
−1.01019 + 2.66805I −7.45912 − 8.19865I
u = −0.394376 − 0.192389I
a = 2.48574 + 1.37904I
b = 0.140530 − 0.493595I
−1.01019 − 2.66805I −7.45912 + 8.19865I
u = −0.228390 + 0.315226I
a = 0.343800 − 0.503868I
b = −0.014070 + 0.387664I
−0.128347 + 0.852424I −3.12509 − 7.92655I
u = −0.228390 − 0.315226I
a = 0.343800 + 0.503868I
b = −0.014070 − 0.387664I
−0.128347 − 0.852424I −3.12509 + 7.92655I
u = 0.359461
a = −3.42432
b = −0.325755
−2.17491 −8.86230
u = −0.140389 + 0.309477I
a = 0.29923 + 1.54706I
b = −0.33446 + 1.69351I
−0.198785 − 0.797982I 1.07929 − 8.34309I
u = −0.140389 − 0.309477I
a = 0.29923 − 1.54706I
b = −0.33446 − 1.69351I
−0.198785 + 0.797982I 1.07929 + 8.34309I
u = 0.337339
a = −3.34460
b = −0.411638
−2.17651 −7.62400
14
II. I
u
2
= h2u
4
− 2u
3
− 7u
2
+ 7b − 2u − 1, 6u
4
+ 8u
3
− 7u
2
+ 7a − 6u +
4, u
5
+ u
4
− 2u
3
− u
2
+ u − 1i
(i) Arc colorings
a
1
=
0
u
a
8
=
1
0
a
7
=
1
−u
2
a
12
=
u
−u
3
+ u
a
3
=
−
6
7
u
4
−
8
7
u
3
+ u
2
+
6
7
u −
4
7
−
2
7
u
4
+
2
7
u
3
+ u
2
+
2
7
u +
1
7
a
6
=
−u
2
+ 1
u
4
− 2u
2
a
2
=
−u
4
− u
3
+ 2u
2
+ u − 1
−
4
7
u
4
+
4
7
u
3
+ ··· +
4
7
u +
2
7
a
11
=
−u
3
+ 2u
−u
3
+ u
a
9
=
−u
3
+ 2u
u
4
− u
3
− u
2
+ 2u − 1
a
4
=
−u
4
− u
3
+ 2u
2
+ u − 1
−
4
7
u
4
+
4
7
u
3
+ ··· −
3
7
u +
2
7
a
10
=
−u
3
+ 2u
−u
3
+ u
a
5
=
0
−u
(ii) Obstruction class = 1
(iii) Cusp Shapes =
143
49
u
4
−
514
49
u
3
−
44
7
u
2
+
767
49
u −
726
49
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
5
c
2
7(7u
5
− 30u
4
+ 41u
3
− 26u
2
+ 8u − 1)
c
3
7(7u
5
+ 12u
4
+ 2u
3
+ 7u
2
+ 1)
c
4
(u + 1)
5
c
5
u
5
− u
4
+ 2u
3
− u
2
+ u − 1
c
6
, c
7
u
5
+ u
4
− 2u
3
− u
2
+ u − 1
c
8
u
5
− 3u
4
+ 4u
3
− u
2
− u + 1
c
9
u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1
c
10
u
5
c
11
u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1
c
12
u
5
− u
4
− 2u
3
+ u
2
+ u + 1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y −1)
5
c
2
49(49y
5
− 326y
4
+ 233y
3
− 80y
2
+ 12y −1)
c
3
49(49y
5
− 116y
4
− 164y
3
− 73y
2
− 14y −1)
c
5
, c
9
y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1
c
6
, c
7
, c
12
y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1
c
8
, c
11
y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1
c
10
y
5
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.21774
a = −1.99330
b = 1.86133
−4.04602 −17.6010
u = 0.309916 + 0.549911I
a = −0.161754 + 0.941741I
b = −0.025747 + 0.535921I
−1.97403 − 1.53058I −6.24587 + 6.13700I
u = 0.309916 − 0.549911I
a = −0.161754 − 0.941741I
b = −0.025747 − 0.535921I
−1.97403 + 1.53058I −6.24587 − 6.13700I
u = −1.41878 + 0.21917I
a = 0.229832 + 0.160224I
b = −0.047773 + 0.514129I
−7.51750 + 4.40083I −11.4232 − 13.5655I
u = −1.41878 − 0.21917I
a = 0.229832 − 0.160224I
b = −0.047773 − 0.514129I
−7.51750 − 4.40083I −11.4232 + 13.5655I
18
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
5
)(u
100
− 6u
99
+ ··· + 1149u − 49)
c
2
49(7u
5
− 30u
4
+ 41u
3
− 26u
2
+ 8u − 1)
· (7u
100
+ 35u
99
+ ··· + 385706u − 40879)
c
3
49(7u
5
+ 12u
4
+ 2u
3
+ 7u
2
+ 1)
· (7u
100
− 147u
99
+ ··· − 311196u − 14099)
c
4
((u + 1)
5
)(u
100
− 6u
99
+ ··· + 1149u − 49)
c
5
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)(u
100
+ 2u
99
+ ··· + 5u + 1)
c
6
, c
7
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)(u
100
+ 2u
99
+ ··· + u − 1)
c
8
(u
5
− 3u
4
+ 4u
3
− u
2
− u + 1)(u
100
− 6u
99
+ ··· + 25745u − 4025)
c
9
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)(u
100
+ 2u
99
+ ··· + 5u + 1)
c
10
u
5
(u
100
+ 3u
99
+ ··· + 17472u + 1568)
c
11
(u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1)(u
100
− 6u
99
+ ··· + 25745u − 4025)
c
12
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)(u
100
+ 2u
99
+ ··· + u − 1)
19
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y −1)
5
)(y
100
− 54y
99
+ ··· − 355685y + 2401)
c
2
2401(49y
5
− 326y
4
+ 233y
3
− 80y
2
+ 12y −1)
· (49y
100
− 12187y
99
+ ··· − 36205848648y + 1671092641)
c
3
2401(49y
5
− 116y
4
− 164y
3
− 73y
2
− 14y −1)
· (49y
100
− 14049y
99
+ ··· − 63467769418y + 198781801)
c
5
, c
9
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)(y
100
− 54y
99
+ ··· − 7y + 1)
c
6
, c
7
, c
12
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)(y
100
− 82y
99
+ ··· − 7y + 1)
c
8
, c
11
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)
· (y
100
+ 70y
99
+ ··· − 361276175y + 16200625)
c
10
y
5
(y
100
− 33y
99
+ ··· − 2.59084 × 10
8
y + 2458624)
20
