12a
0441
(K12a
0441
)
A knot diagram
1
Linearized knot diagam
3 6 10 9 2 5 11 12 1 8 7 4
Solving Sequence
7,11
8 12
4,9
5 1 6 10 3 2
c
7
c
11
c
8
c
4
c
12
c
6
c
10
c
3
c
2
c
1
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h3.27711 × 10
102
u
101
+ 1.55836 × 10
103
u
100
+ ··· + 2.62772 × 10
103
b − 1.25743 × 10
103
,
3.78313 × 10
102
u
101
− 5.58370 × 10
102
u
100
+ ··· + 2.62772 × 10
103
a − 4.51200 × 10
103
, u
102
+ 2u
101
+ ··· + 4u − 1i
I
u
2
= hb − u + 1, u
2
+ a + 1, u
3
− u
2
+ 2u − 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
= h3.28 × 10
102
u
101
+ 1.56 × 10
103
u
100
+ · · · + 2.63 × 10
103
b − 1.26 ×
10
103
, 3.78 × 10
102
u
101
− 5.58 × 10
102
u
100
+ · · · + 2.63 × 10
103
a − 4.51 ×
10
103
, u
102
+ 2u
101
+ · · · + 4u − 1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
8
=
1
u
2
a
12
=
−u
u
a
4
=
−0.143970u
101
+ 0.212492u
100
+ ··· − 15.9951u + 1.71708
−0.124713u
101
− 0.593046u
100
+ ··· − 1.79673u + 0.478524
a
9
=
−u
4
− u
2
+ 1
u
4
+ 2u
2
a
5
=
−0.0438647u
101
+ 0.121507u
100
+ ··· − 17.6760u + 1.94288
0.0129440u
101
+ 0.0941687u
100
+ ··· − 2.42475u + 0.661696
a
1
=
0.340303u
101
+ 0.920651u
100
+ ··· + 4.12833u − 3.41343
0.0802727u
101
− 0.159772u
100
+ ··· + 5.51631u − 0.420576
a
6
=
0.280386u
101
+ 0.439282u
100
+ ··· + 4.90809u − 0.660980
0.0907918u
101
+ 0.172191u
100
+ ··· + 2.45351u − 0.598287
a
10
=
u
u
3
+ u
a
3
=
−0.0822981u
101
+ 0.0664369u
100
+ ··· − 18.3878u + 2.28500
0.0138280u
101
+ 0.101020u
100
+ ··· − 3.05023u + 0.777047
a
2
=
−0.0489390u
101
− 0.0545099u
100
+ ··· − 0.777862u − 1.55095
0.00990874u
101
− 0.00655573u
100
+ ··· + 2.52993u + 0.271094
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.789125u
101
− 1.26697u
100
+ ··· − 29.4788u − 4.11553
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
102
+ 32u
101
+ ··· − 3u + 1
c
2
, c
5
u
102
+ 4u
101
+ ··· + 11u + 1
c
3
u
102
+ 2u
101
+ ··· + 5470u − 5977
c
4
u
102
+ 4u
101
+ ··· − 19212u + 1231
c
7
, c
10
, c
11
u
102
− 2u
101
+ ··· − 4u − 1
c
8
u
102
+ 2u
101
+ ··· − 18596u − 1873
c
9
u
102
− 7u
101
+ ··· − 12u + 8
c
12
u
102
+ 10u
101
+ ··· + u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
102
+ 80y
101
+ ··· + 523y + 1
c
2
, c
5
y
102
− 32y
101
+ ··· + 3y + 1
c
3
y
102
− 126y
101
+ ··· − 2034750148y + 35724529
c
4
y
102
− 98y
101
+ ··· − 154232356y + 1515361
c
7
, c
10
, c
11
y
102
+ 90y
101
+ ··· − 76y + 1
c
8
y
102
− 14y
101
+ ··· − 28907108y + 3508129
c
9
y
102
− 21y
101
+ ··· − 2512y + 64
c
12
y
102
+ 4y
101
+ ··· + 3y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.342733 + 0.923254I
a = 1.25977 + 1.12229I
b = −0.051328 − 0.792366I
−2.25655 − 4.00745I 0
u = −0.342733 − 0.923254I
a = 1.25977 − 1.12229I
b = −0.051328 + 0.792366I
−2.25655 + 4.00745I 0
u = −0.514550 + 0.838295I
a = 1.20538 + 1.04569I
b = 0.070366 − 0.834664I
3.88303 − 9.31616I 0
u = −0.514550 − 0.838295I
a = 1.20538 − 1.04569I
b = 0.070366 + 0.834664I
3.88303 + 9.31616I 0
u = 0.425257 + 0.838879I
a = 0.879897 + 0.420710I
b = −0.375466 + 0.246656I
−1.98033 − 3.36359I 0
u = 0.425257 − 0.838879I
a = 0.879897 − 0.420710I
b = −0.375466 − 0.246656I
−1.98033 + 3.36359I 0
u = −0.500531 + 0.793245I
a = −1.22432 − 1.03190I
b = −0.093334 + 0.814325I
4.68549 − 3.34925I 0
u = −0.500531 − 0.793245I
a = −1.22432 + 1.03190I
b = −0.093334 − 0.814325I
4.68549 + 3.34925I 0
u = 0.933119 + 0.035557I
a = −0.0065528 + 0.1389500I
b = −0.001034 − 0.823033I
−0.53243 + 2.66744I 0
u = 0.933119 − 0.035557I
a = −0.0065528 − 0.1389500I
b = −0.001034 + 0.823033I
−0.53243 − 2.66744I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.808708 + 0.440383I
a = −0.208416 − 0.088095I
b = 0.060032 − 0.647083I
0.21594 − 5.19806I 0
u = 0.808708 − 0.440383I
a = −0.208416 + 0.088095I
b = 0.060032 + 0.647083I
0.21594 + 5.19806I 0
u = −0.010693 + 1.087270I
a = −1.62121 − 0.96416I
b = 0.706796 + 0.696680I
1.33913 − 1.67285I 0
u = −0.010693 − 1.087270I
a = −1.62121 + 0.96416I
b = 0.706796 − 0.696680I
1.33913 + 1.67285I 0
u = 0.740386 + 0.492813I
a = 0.260593 + 0.176271I
b = −0.072170 + 0.583829I
0.478204 + 0.201766I 0
u = 0.740386 − 0.492813I
a = 0.260593 − 0.176271I
b = −0.072170 − 0.583829I
0.478204 − 0.201766I 0
u = −0.812573 + 0.288229I
a = −0.117709 − 0.083189I
b = 0.73296 + 1.64728I
2.13668 + 13.96830I −6.00000 − 9.62755I
u = −0.812573 − 0.288229I
a = −0.117709 + 0.083189I
b = 0.73296 − 1.64728I
2.13668 − 13.96830I −6.00000 + 9.62755I
u = 0.829100 + 0.228200I
a = −0.0236605 + 0.0272508I
b = −0.027412 − 0.754278I
−3.97163 − 1.15270I −20.5841 + 5.1449I
u = 0.829100 − 0.228200I
a = −0.0236605 − 0.0272508I
b = −0.027412 + 0.754278I
−3.97163 + 1.15270I −20.5841 − 5.1449I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.790346 + 0.296589I
a = 0.153251 + 0.039686I
b = −0.73825 − 1.64533I
3.07625 + 7.87052I −4.36541 − 5.15887I
u = −0.790346 − 0.296589I
a = 0.153251 − 0.039686I
b = −0.73825 + 1.64533I
3.07625 − 7.87052I −4.36541 + 5.15887I
u = −0.199745 + 1.154830I
a = 1.47863 + 1.38460I
b = −0.302032 − 1.143370I
−0.89312 + 2.34840I 0
u = −0.199745 − 1.154830I
a = 1.47863 − 1.38460I
b = −0.302032 + 1.143370I
−0.89312 − 2.34840I 0
u = −0.766287 + 0.215154I
a = 0.0300001 + 0.0787510I
b = 0.73843 + 1.63200I
−4.47188 + 8.10704I −11.13307 − 8.33149I
u = −0.766287 − 0.215154I
a = 0.0300001 − 0.0787510I
b = 0.73843 − 1.63200I
−4.47188 − 8.10704I −11.13307 + 8.33149I
u = 0.500154 + 1.103880I
a = 1.049060 + 0.042967I
b = −0.630409 + 0.460401I
2.74383 − 7.71085I 0
u = 0.500154 − 1.103880I
a = 1.049060 − 0.042967I
b = −0.630409 − 0.460401I
2.74383 + 7.71085I 0
u = 0.155063 + 1.233840I
a = 1.24065 + 1.16763I
b = −1.10883 − 1.73815I
5.11217 + 0.61098I 0
u = 0.155063 − 1.233840I
a = 1.24065 − 1.16763I
b = −1.10883 + 1.73815I
5.11217 − 0.61098I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.452368 + 1.162730I
a = −1.143030 + 0.022639I
b = 0.723069 − 0.486545I
3.16141 − 2.23441I 0
u = 0.452368 − 1.162730I
a = −1.143030 − 0.022639I
b = 0.723069 + 0.486545I
3.16141 + 2.23441I 0
u = 0.038972 + 1.250760I
a = −1.002410 − 0.513576I
b = 0.98835 + 1.28441I
5.01539 − 4.42939I 0
u = 0.038972 − 1.250760I
a = −1.002410 + 0.513576I
b = 0.98835 − 1.28441I
5.01539 + 4.42939I 0
u = 0.197981 + 1.258870I
a = −2.35159 − 0.10811I
b = 1.89635 − 0.03836I
2.06036 − 2.18071I 0
u = 0.197981 − 1.258870I
a = −2.35159 + 0.10811I
b = 1.89635 + 0.03836I
2.06036 + 2.18071I 0
u = −0.686380 + 0.231259I
a = 0.086597 − 0.289788I
b = −0.73508 − 1.64042I
−0.56630 + 4.76337I −4.66700 − 7.02795I
u = −0.686380 − 0.231259I
a = 0.086597 + 0.289788I
b = −0.73508 + 1.64042I
−0.56630 − 4.76337I −4.66700 + 7.02795I
u = 0.223234 + 1.299150I
a = 2.27543 + 2.56027I
b = −2.10409 − 2.82514I
1.70310 − 2.94491I 0
u = 0.223234 − 1.299150I
a = 2.27543 − 2.56027I
b = −2.10409 + 2.82514I
1.70310 + 2.94491I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.657256 + 0.131190I
a = 0.225297 + 0.506371I
b = 0.77257 + 1.69014I
−3.90267 + 0.82212I −12.21728 − 6.17449I
u = −0.657256 − 0.131190I
a = 0.225297 − 0.506371I
b = 0.77257 − 1.69014I
−3.90267 − 0.82212I −12.21728 + 6.17449I
u = −0.617707 + 0.239610I
a = 1.37527 + 0.42240I
b = 0.739097 − 0.917208I
3.02844 + 6.45887I −4.21756 − 8.81537I
u = −0.617707 − 0.239610I
a = 1.37527 − 0.42240I
b = 0.739097 + 0.917208I
3.02844 − 6.45887I −4.21756 + 8.81537I
u = −0.177916 + 1.330800I
a = −0.99335 + 1.18279I
b = 1.55957 + 0.12336I
1.96203 + 2.33421I 0
u = −0.177916 − 1.330800I
a = −0.99335 − 1.18279I
b = 1.55957 − 0.12336I
1.96203 − 2.33421I 0
u = 0.225615 + 1.345060I
a = 2.80377 + 1.41185I
b = −2.43909 − 1.61759I
6.34710 − 6.20555I 0
u = 0.225615 − 1.345060I
a = 2.80377 − 1.41185I
b = −2.43909 + 1.61759I
6.34710 + 6.20555I 0
u = 0.210413 + 1.349260I
a = −2.82627 − 1.27891I
b = 2.43475 + 1.45854I
6.53621 − 0.46405I 0
u = 0.210413 − 1.349260I
a = −2.82627 + 1.27891I
b = 2.43475 − 1.45854I
6.53621 + 0.46405I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.564461 + 0.288826I
a = −1.45930 − 0.55769I
b = −0.656253 + 0.805623I
4.06468 + 0.52556I −1.22749 − 3.19069I
u = −0.564461 − 0.288826I
a = −1.45930 + 0.55769I
b = −0.656253 − 0.805623I
4.06468 − 0.52556I −1.22749 + 3.19069I
u = −0.257602 + 1.349260I
a = −2.53428 − 0.90364I
b = 1.69422 + 1.98927I
0.78505 + 4.13766I 0
u = −0.257602 − 1.349260I
a = −2.53428 + 0.90364I
b = 1.69422 − 1.98927I
0.78505 − 4.13766I 0
u = 0.242875 + 1.359570I
a = 0.97200 − 1.04626I
b = −0.72711 + 1.42868I
3.38448 − 3.66037I 0
u = 0.242875 − 1.359570I
a = 0.97200 + 1.04626I
b = −0.72711 − 1.42868I
3.38448 + 3.66037I 0
u = 0.602639 + 0.125822I
a = −0.448733 − 0.049040I
b = 0.340562 + 0.820327I
−1.36014 − 0.57030I −7.00686 + 0.66688I
u = 0.602639 − 0.125822I
a = −0.448733 + 0.049040I
b = 0.340562 − 0.820327I
−1.36014 + 0.57030I −7.00686 − 0.66688I
u = −0.152168 + 1.381700I
a = −2.36104 − 1.32263I
b = 1.38536 + 1.86708I
9.51148 − 1.78647I 0
u = −0.152168 − 1.381700I
a = −2.36104 + 1.32263I
b = 1.38536 − 1.86708I
9.51148 + 1.78647I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.058050 + 1.390210I
a = −0.214325 − 0.385890I
b = 0.432491 + 1.037990I
4.90639 − 4.31612I 0
u = 0.058050 − 1.390210I
a = −0.214325 + 0.385890I
b = 0.432491 − 1.037990I
4.90639 + 4.31612I 0
u = −0.100985 + 1.388210I
a = 0.439921 − 0.436767I
b = −0.848224 − 0.452009I
6.93748 − 0.32378I 0
u = −0.100985 − 1.388210I
a = 0.439921 + 0.436767I
b = −0.848224 + 0.452009I
6.93748 + 0.32378I 0
u = −0.178930 + 1.391970I
a = 2.40118 + 1.27682I
b = −1.45376 − 1.92801I
10.02930 + 4.70521I 0
u = −0.178930 − 1.391970I
a = 2.40118 − 1.27682I
b = −1.45376 + 1.92801I
10.02930 − 4.70521I 0
u = 0.593982
a = 2.73604
b = −2.20828
−2.38410 54.6630
u = 0.583003 + 0.101933I
a = 2.45217 + 0.05429I
b = −1.70633 + 0.09811I
1.74385 − 3.26779I 2.88737 − 10.90513I
u = 0.583003 − 0.101933I
a = 2.45217 − 0.05429I
b = −1.70633 − 0.09811I
1.74385 + 3.26779I 2.88737 + 10.90513I
u = −0.190695 + 0.559763I
a = −1.34414 − 1.17459I
b = −0.160913 + 0.440826I
1.11243 − 1.44612I 0.13718 + 1.97472I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.190695 − 0.559763I
a = −1.34414 + 1.17459I
b = −0.160913 − 0.440826I
1.11243 + 1.44612I 0.13718 − 1.97472I
u = −0.246055 + 1.387440I
a = 0.121500 + 1.311960I
b = 0.773792 − 0.480688I
8.20256 + 9.62941I 0
u = −0.246055 − 1.387440I
a = 0.121500 − 1.311960I
b = 0.773792 + 0.480688I
8.20256 − 9.62941I 0
u = −0.22191 + 1.39757I
a = 0.020878 − 1.176100I
b = −0.822452 + 0.305397I
9.42255 + 3.42449I 0
u = −0.22191 − 1.39757I
a = 0.020878 + 1.176100I
b = −0.822452 − 0.305397I
9.42255 − 3.42449I 0
u = −0.27472 + 1.38951I
a = 2.35251 + 1.00781I
b = −1.61512 − 1.94063I
4.58757 + 8.26514I 0
u = −0.27472 − 1.38951I
a = 2.35251 − 1.00781I
b = −1.61512 + 1.94063I
4.58757 − 8.26514I 0
u = 0.34342 + 1.37583I
a = −1.072820 + 0.491427I
b = 0.745414 − 0.899850I
1.06522 − 5.38443I 0
u = 0.34342 − 1.37583I
a = −1.072820 − 0.491427I
b = 0.745414 + 0.899850I
1.06522 + 5.38443I 0
u = −0.31148 + 1.38686I
a = −2.25082 − 0.95011I
b = 1.61105 + 1.90755I
0.60926 + 12.00430I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.31148 − 1.38686I
a = −2.25082 + 0.95011I
b = 1.61105 − 1.90755I
0.60926 − 12.00430I 0
u = 0.546311 + 0.122192I
a = −2.39457 − 0.12609I
b = 1.57755 − 0.07278I
1.85856 + 2.29830I −0.8280 − 14.5266I
u = 0.546311 − 0.122192I
a = −2.39457 + 0.12609I
b = 1.57755 + 0.07278I
1.85856 − 2.29830I −0.8280 + 14.5266I
u = −0.31557 + 1.42872I
a = 2.20776 + 1.04807I
b = −1.59195 − 1.92018I
8.5800 + 11.8770I 0
u = −0.31557 − 1.42872I
a = 2.20776 − 1.04807I
b = −1.59195 + 1.92018I
8.5800 − 11.8770I 0
u = −0.32703 + 1.42851I
a = −2.18439 − 1.04009I
b = 1.58858 + 1.91809I
7.6091 + 18.0913I 0
u = −0.32703 − 1.42851I
a = −2.18439 + 1.04009I
b = 1.58858 − 1.91809I
7.6091 − 18.0913I 0
u = −0.394024 + 0.351464I
a = 1.012870 − 0.727446I
b = −0.69461 − 1.41217I
4.60683 + 2.47380I −0.27300 − 5.84452I
u = −0.394024 − 0.351464I
a = 1.012870 + 0.727446I
b = −0.69461 + 1.41217I
4.60683 − 2.47380I −0.27300 + 5.84452I
u = 0.29807 + 1.47853I
a = 0.803266 − 0.456206I
b = −0.489347 + 0.902235I
6.74208 − 3.64259I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.29807 − 1.47853I
a = 0.803266 + 0.456206I
b = −0.489347 − 0.902235I
6.74208 + 3.64259I 0
u = 0.32601 + 1.47662I
a = −0.852223 + 0.429271I
b = 0.532308 − 0.869967I
6.32365 − 9.37051I 0
u = 0.32601 − 1.47662I
a = −0.852223 − 0.429271I
b = 0.532308 + 0.869967I
6.32365 + 9.37051I 0
u = −0.04746 + 1.51688I
a = −0.149728 − 0.206078I
b = −0.283967 − 0.439872I
12.42370 − 1.87684I 0
u = −0.04746 − 1.51688I
a = −0.149728 + 0.206078I
b = −0.283967 + 0.439872I
12.42370 + 1.87684I 0
u = −0.02637 + 1.52770I
a = 0.192831 + 0.142910I
b = 0.225667 + 0.481937I
11.9305 − 7.9869I 0
u = −0.02637 − 1.52770I
a = 0.192831 − 0.142910I
b = 0.225667 − 0.481937I
11.9305 + 7.9869I 0
u = −0.274164 + 0.383680I
a = −1.44345 + 0.76664I
b = 0.73919 + 1.26681I
4.13708 − 3.56002I −0.866491 + 0.092998I
u = −0.274164 − 0.383680I
a = −1.44345 − 0.76664I
b = 0.73919 − 1.26681I
4.13708 + 3.56002I −0.866491 − 0.092998I
u = −0.469679
a = 2.06635
b = 1.26384
−2.34235 7.23550
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.157431 + 0.042000I
a = −3.47332 − 1.95737I
b = 0.632255 + 0.234499I
−1.37921 − 0.33811I −8.16224 + 0.09301I
u = 0.157431 − 0.042000I
a = −3.47332 + 1.95737I
b = 0.632255 − 0.234499I
−1.37921 + 0.33811I −8.16224 − 0.09301I
15
II. I
u
2
= hb − u + 1, u
2
+ a + 1, u
3
− u
2
+ 2u − 1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
8
=
1
u
2
a
12
=
−u
u
a
4
=
−u
2
− 1
u − 1
a
9
=
u
u
2
− u + 1
a
5
=
−u
2
+ u − 2
−1
a
1
=
u
2
− u + 1
1
a
6
=
−u
2
+ u − 1
−1
a
10
=
u
u
2
− u + 1
a
3
=
−u
2
+ u − 2
−1
a
2
=
−1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −5u
2
+ 4u − 16
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
12
(u − 1)
3
c
3
, c
4
u
3
− u
2
+ 1
c
5
, c
6
(u + 1)
3
c
7
u
3
− u
2
+ 2u − 1
c
8
u
3
+ u
2
− 1
c
9
u
3
c
10
, c
11
u
3
+ u
2
+ 2u + 1
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
12
(y −1)
3
c
3
, c
4
, c
8
y
3
− y
2
+ 2y −1
c
7
, c
10
, c
11
y
3
+ 3y
2
+ 2y −1
c
9
y
3
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.215080 + 1.307140I
a = 0.662359 − 0.562280I
b = −0.78492 + 1.30714I
1.37919 − 2.82812I −6.82789 + 2.41717I
u = 0.215080 − 1.307140I
a = 0.662359 + 0.562280I
b = −0.78492 − 1.30714I
1.37919 + 2.82812I −6.82789 − 2.41717I
u = 0.569840
a = −1.32472
b = −0.430160
−2.75839 −15.3440
19
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
3
)(u
102
+ 32u
101
+ ··· − 3u + 1)
c
2
((u − 1)
3
)(u
102
+ 4u
101
+ ··· + 11u + 1)
c
3
(u
3
− u
2
+ 1)(u
102
+ 2u
101
+ ··· + 5470u − 5977)
c
4
(u
3
− u
2
+ 1)(u
102
+ 4u
101
+ ··· − 19212u + 1231)
c
5
((u + 1)
3
)(u
102
+ 4u
101
+ ··· + 11u + 1)
c
6
((u + 1)
3
)(u
102
+ 32u
101
+ ··· − 3u + 1)
c
7
(u
3
− u
2
+ 2u − 1)(u
102
− 2u
101
+ ··· − 4u − 1)
c
8
(u
3
+ u
2
− 1)(u
102
+ 2u
101
+ ··· − 18596u − 1873)
c
9
u
3
(u
102
− 7u
101
+ ··· − 12u + 8)
c
10
, c
11
(u
3
+ u
2
+ 2u + 1)(u
102
− 2u
101
+ ··· − 4u − 1)
c
12
((u − 1)
3
)(u
102
+ 10u
101
+ ··· + u − 1)
20
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
((y −1)
3
)(y
102
+ 80y
101
+ ··· + 523y + 1)
c
2
, c
5
((y −1)
3
)(y
102
− 32y
101
+ ··· + 3y + 1)
c
3
(y
3
− y
2
+ 2y −1)(y
102
− 126y
101
+ ··· − 2.03475 × 10
9
y + 3.57245 × 10
7
)
c
4
(y
3
− y
2
+ 2y −1)(y
102
− 98y
101
+ ··· − 1.54232 × 10
8
y + 1515361)
c
7
, c
10
, c
11
(y
3
+ 3y
2
+ 2y −1)(y
102
+ 90y
101
+ ··· − 76y + 1)
c
8
(y
3
− y
2
+ 2y −1)(y
102
− 14y
101
+ ··· − 2.89071 × 10
7
y + 3508129)
c
9
y
3
(y
102
− 21y
101
+ ··· − 2512y + 64)
c
12
((y −1)
3
)(y
102
+ 4y
101
+ ··· + 3y + 1)
21
