12a
0486
(K12a
0486
)
A knot diagram
1
Linearized knot diagam
3 6 11 12 7 2 1 4 5 8 9 10
Solving Sequence
3,6
2 7 1 8
5,10
9 12 4 11
c
2
c
6
c
1
c
7
c
5
c
9
c
12
c
4
c
11
c
3
, c
8
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−48599558u
68
− 169298104u
67
+ ··· + 17100943b − 315531735,
350511433u
68
+ 1020261118u
67
+ ··· + 119706601a − 2664075662, u
69
+ 5u
68
+ ··· − 11u + 7i
I
u
2
= h−352821u
46
a − 5119679u
46
+ ··· − 1763091a + 4390751, −u
46
a − 4u
46
+ ··· + 4a − 2,
u
47
− 2u
46
+ ··· − 2u + 1i
I
u
3
= hu
22
+ u
21
+ ··· + b + 3u, u
23
− 2u
22
+ ··· + a + 3, u
24
− 2u
23
+ ··· + 7u
2
+ 1i
I
u
4
= hau + b + u + 1, a
2
− 3au − 3u − 2, u
2
+ u + 1i
I
v
1
= ha, b + 1, v −1i
* 5 irreducible components of dim
C
= 0, with total 192 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−4.86 × 10
7
u
68
− 1.69 × 10
8
u
67
+ · · · + 1.71 × 10
7
b − 3.16 × 10
8
, 3.51 ×
10
8
u
68
+1.02×10
9
u
67
+· · ·+1.20×10
8
a−2.66×10
9
, u
69
+5u
68
+· · ·−11u+7i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
u
2
a
7
=
u
u
3
+ u
a
1
=
u
2
+ 1
u
2
a
8
=
u
7
+ 2u
5
+ 2u
3
+ 2u
u
7
+ u
5
+ 2u
3
+ u
a
5
=
u
3
u
5
+ u
3
+ u
a
10
=
−2.92809u
68
− 8.52301u
67
+ ··· − 75.4142u + 22.2550
2.84192u
68
+ 9.89993u
67
+ ··· − 49.7328u + 18.4511
a
9
=
−4.76650u
68
− 13.2256u
67
+ ··· − 105.769u + 29.5256
−1.57547u
68
− 5.78395u
67
+ ··· − 56.6428u + 13.2040
a
12
=
−4.76183u
68
− 9.61536u
67
+ ··· − 111.548u + 35.3483
−3.57547u
68
− 12.7839u
67
+ ··· − 42.6428u + 6.20396
a
4
=
−2.98023u
68
− 12.1415u
67
+ ··· + 22.7597u − 10.5704
−2.77581u
68
− 13.7928u
67
+ ··· + 33.0385u − 16.8236
a
11
=
8.01122u
68
+ 28.2908u
67
+ ··· + 64.2914u − 4.00348
2.70124u
68
+ 10.8019u
67
+ ··· − 12.4433u + 9.09453
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
53809100
17100943
u
68
−
239622692
17100943
u
67
+ ··· +
686921128
17100943
u −
253153132
17100943
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
69
+ 23u
68
+ ··· + 65u − 49
c
2
, c
6
u
69
− 5u
68
+ ··· − 11u − 7
c
3
, c
9
u
69
− 2u
68
+ ··· − 3u − 1
c
4
, c
8
u
69
− u
68
+ ··· − 2u − 1
c
7
u
69
+ 25u
68
+ ··· − 59915u − 3703
c
10
, c
12
u
69
+ 10u
68
+ ··· + 29u − 1
c
11
u
69
+ 38u
68
+ ··· − 64u − 7
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
69
+ 51y
68
+ ··· + 29901y −2401
c
2
, c
6
y
69
+ 23y
68
+ ··· + 65y −49
c
3
, c
9
y
69
− 6y
68
+ ··· − 33y −1
c
4
, c
8
y
69
− 29y
68
+ ··· + 76y −1
c
7
y
69
+ 3y
68
+ ··· − 816311009y −13712209
c
10
, c
12
y
69
− 42y
68
+ ··· + 27y −1
c
11
y
69
+ 50y
67
+ ··· + 134y −49
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.012222 + 1.002130I
a = −1.121370 + 0.553514I
b = 1.66113 + 0.68765I
−5.00379 − 0.12361I −9.98584 + 0.I
u = −0.012222 − 1.002130I
a = −1.121370 − 0.553514I
b = 1.66113 − 0.68765I
−5.00379 + 0.12361I −9.98584 + 0.I
u = 0.716065 + 0.706433I
a = −1.78731 − 1.65142I
b = −0.623796 − 0.900743I
0.0540759 − 0.0939258I 0
u = 0.716065 − 0.706433I
a = −1.78731 + 1.65142I
b = −0.623796 + 0.900743I
0.0540759 + 0.0939258I 0
u = −0.683285 + 0.702977I
a = −1.68834 − 0.68669I
b = −1.82191 + 0.42380I
−0.234320 − 0.001152I −2.25563 + 0.I
u = −0.683285 − 0.702977I
a = −1.68834 + 0.68669I
b = −1.82191 − 0.42380I
−0.234320 + 0.001152I −2.25563 + 0.I
u = −0.793801 + 0.571976I
a = 1.148810 + 0.200493I
b = 0.957086 − 0.158430I
−0.92159 − 2.20912I −4.61148 + 3.51139I
u = −0.793801 − 0.571976I
a = 1.148810 − 0.200493I
b = 0.957086 + 0.158430I
−0.92159 + 2.20912I −4.61148 − 3.51139I
u = 0.141687 + 1.029870I
a = −0.843291 − 0.549722I
b = 1.237290 + 0.564726I
−5.58220 + 1.94498I −10.57738 + 0.I
u = 0.141687 − 1.029870I
a = −0.843291 + 0.549722I
b = 1.237290 − 0.564726I
−5.58220 − 1.94498I −10.57738 + 0.I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.796333 + 0.677780I
a = −2.41597 + 0.72004I
b = −2.10792 + 1.43766I
0.15968 + 5.61109I 0
u = −0.796333 − 0.677780I
a = −2.41597 − 0.72004I
b = −2.10792 − 1.43766I
0.15968 − 5.61109I 0
u = 0.110513 + 1.048830I
a = −1.236350 + 0.224439I
b = 2.06677 − 0.35387I
−6.03215 + 5.53076I 0
u = 0.110513 − 1.048830I
a = −1.236350 − 0.224439I
b = 2.06677 + 0.35387I
−6.03215 − 5.53076I 0
u = −0.119600 + 0.926304I
a = 0.219849 − 0.770724I
b = −0.850774 − 0.031966I
−1.43506 − 1.95242I −2.33460 + 4.04464I
u = −0.119600 − 0.926304I
a = 0.219849 + 0.770724I
b = −0.850774 + 0.031966I
−1.43506 + 1.95242I −2.33460 − 4.04464I
u = −0.837875 + 0.662257I
a = 2.29743 − 0.93819I
b = 1.91355 − 1.36492I
1.6483 + 14.5043I 0
u = −0.837875 − 0.662257I
a = 2.29743 + 0.93819I
b = 1.91355 + 1.36492I
1.6483 − 14.5043I 0
u = 0.777141 + 0.736280I
a = 1.149780 + 0.578014I
b = 0.491520 + 0.431357I
4.40070 − 1.06842I 0
u = 0.777141 − 0.736280I
a = 1.149780 − 0.578014I
b = 0.491520 − 0.431357I
4.40070 + 1.06842I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.541394 + 0.923763I
a = −1.36122 − 1.59201I
b = 0.267146 − 0.903066I
−3.42369 + 3.69120I 0
u = 0.541394 − 0.923763I
a = −1.36122 + 1.59201I
b = 0.267146 + 0.903066I
−3.42369 − 3.69120I 0
u = −0.819723 + 0.709991I
a = −1.252450 − 0.288105I
b = −1.385820 − 0.016383I
0.87380 + 1.64675I 0
u = −0.819723 − 0.709991I
a = −1.252450 + 0.288105I
b = −1.385820 + 0.016383I
0.87380 − 1.64675I 0
u = 0.554061 + 0.946702I
a = 0.09644 − 2.39009I
b = 1.003420 − 0.616051I
−3.54428 + 0.34170I 0
u = 0.554061 − 0.946702I
a = 0.09644 + 2.39009I
b = 1.003420 + 0.616051I
−3.54428 − 0.34170I 0
u = −0.745478 + 0.805661I
a = 0.757979 − 0.428250I
b = 0.54619 − 1.38301I
2.31641 − 3.75915I 0
u = −0.745478 − 0.805661I
a = 0.757979 + 0.428250I
b = 0.54619 + 1.38301I
2.31641 + 3.75915I 0
u = 0.139797 + 1.097740I
a = 0.958448 + 0.089891I
b = −2.02653 + 0.54635I
−5.0428 + 14.1417I 0
u = 0.139797 − 1.097740I
a = 0.958448 − 0.089891I
b = −2.02653 − 0.54635I
−5.0428 − 14.1417I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.063890 + 1.113210I
a = 0.404800 + 0.058459I
b = −1.167720 − 0.501445I
−6.98700 − 3.23243I 0
u = 0.063890 − 1.113210I
a = 0.404800 − 0.058459I
b = −1.167720 + 0.501445I
−6.98700 + 3.23243I 0
u = −0.448141 + 0.761288I
a = 0.546214 − 0.397562I
b = −0.055472 − 0.575637I
0.01707 − 1.74830I −0.18091 + 2.95800I
u = −0.448141 − 0.761288I
a = 0.546214 + 0.397562I
b = −0.055472 + 0.575637I
0.01707 + 1.74830I −0.18091 − 2.95800I
u = 0.485720 + 1.018670I
a = −0.29913 + 1.96319I
b = −1.205210 + 0.213225I
−2.96219 − 7.43047I 0
u = 0.485720 − 1.018670I
a = −0.29913 − 1.96319I
b = −1.205210 − 0.213225I
−2.96219 + 7.43047I 0
u = −0.712951 + 0.920207I
a = 0.724780 − 1.103170I
b = −0.89412 − 1.16084I
1.96162 − 1.78958I 0
u = −0.712951 − 0.920207I
a = 0.724780 + 1.103170I
b = −0.89412 + 1.16084I
1.96162 + 1.78958I 0
u = −0.666247 + 0.975151I
a = 0.87734 + 2.02741I
b = 2.22184 + 0.18370I
−1.05699 − 5.23860I 0
u = −0.666247 − 0.975151I
a = 0.87734 − 2.02741I
b = 2.22184 − 0.18370I
−1.05699 + 5.23860I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.729961 + 0.368810I
a = 0.653129 + 1.020220I
b = 0.569812 + 0.486825I
−1.97006 − 5.23474I −2.27710 + 5.73809I
u = 0.729961 − 0.368810I
a = 0.653129 − 1.020220I
b = 0.569812 − 0.486825I
−1.97006 + 5.23474I −2.27710 − 5.73809I
u = 0.568755 + 1.036610I
a = 0.83010 + 1.37787I
b = −0.441338 + 0.942217I
−3.88153 + 10.01270I 0
u = 0.568755 − 1.036610I
a = 0.83010 − 1.37787I
b = −0.441338 − 0.942217I
−3.88153 − 10.01270I 0
u = −0.812502 + 0.862501I
a = 0.154560 − 0.114706I
b = −0.133160 + 0.560845I
5.21176 − 10.95100I 0
u = −0.812502 − 0.862501I
a = 0.154560 + 0.114706I
b = −0.133160 − 0.560845I
5.21176 + 10.95100I 0
u = 0.680791 + 0.980389I
a = −0.27668 − 2.49060I
b = 0.83048 − 1.24615I
−0.77573 + 5.46732I 0
u = 0.680791 − 0.980389I
a = −0.27668 + 2.49060I
b = 0.83048 + 1.24615I
−0.77573 − 5.46732I 0
u = −0.802033 + 0.901610I
a = −0.511400 − 0.076132I
b = 0.268850 + 0.356050I
5.09360 + 4.92645I 0
u = −0.802033 − 0.901610I
a = −0.511400 + 0.076132I
b = 0.268850 − 0.356050I
5.09360 − 4.92645I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.719215 + 0.976978I
a = −0.303296 + 1.329610I
b = −0.628169 + 0.547859I
3.66707 + 6.73077I 0
u = 0.719215 − 0.976978I
a = −0.303296 − 1.329610I
b = −0.628169 − 0.547859I
3.66707 − 6.73077I 0
u = −0.710906 + 1.012370I
a = 0.02535 + 3.15247I
b = 2.49262 + 1.37298I
−0.85162 − 11.29640I 0
u = −0.710906 − 1.012370I
a = 0.02535 − 3.15247I
b = 2.49262 − 1.37298I
−0.85162 + 11.29640I 0
u = −0.673456 + 1.039560I
a = −0.467776 − 1.318920I
b = −1.306860 − 0.312183I
−2.30054 − 3.29537I 0
u = −0.673456 − 1.039560I
a = −0.467776 + 1.318920I
b = −1.306860 + 0.312183I
−2.30054 + 3.29537I 0
u = −0.731358 + 1.008530I
a = 0.90677 + 1.57723I
b = 1.55923 − 0.04851I
−0.04166 − 7.47084I 0
u = −0.731358 − 1.008530I
a = 0.90677 − 1.57723I
b = 1.55923 + 0.04851I
−0.04166 + 7.47084I 0
u = 0.703757 + 0.228722I
a = 1.70911 − 0.02367I
b = 1.263340 − 0.518926I
−0.65978 + 11.64210I 1.56318 − 8.06482I
u = 0.703757 − 0.228722I
a = 1.70911 + 0.02367I
b = 1.263340 + 0.518926I
−0.65978 − 11.64210I 1.56318 + 8.06482I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.722375 + 1.033830I
a = 0.02797 − 2.99925I
b = −2.20797 − 1.41096I
0.5162 − 20.3389I 0
u = −0.722375 − 1.033830I
a = 0.02797 + 2.99925I
b = −2.20797 + 1.41096I
0.5162 + 20.3389I 0
u = 0.868018 + 0.916637I
a = 0.153455 + 0.272902I
b = 0.021429 + 0.199037I
7.87304 + 3.21385I 0
u = 0.868018 − 0.916637I
a = 0.153455 − 0.272902I
b = 0.021429 − 0.199037I
7.87304 − 3.21385I 0
u = 0.560624 + 0.241305I
a = −1.43460 − 0.41224I
b = −1.009480 + 0.562273I
−1.98795 + 3.58898I −4.22570 − 7.51690I
u = 0.560624 − 0.241305I
a = −1.43460 + 0.41224I
b = −1.009480 − 0.562273I
−1.98795 − 3.58898I −4.22570 + 7.51690I
u = 0.469463 + 0.153072I
a = −0.049678 − 0.731363I
b = −0.778060 − 0.142940I
−1.97373 − 0.10861I −3.92335 − 0.27922I
u = 0.469463 − 0.153072I
a = −0.049678 + 0.731363I
b = −0.778060 + 0.142940I
−1.97373 + 0.10861I −3.92335 + 0.27922I
u = −0.485133
a = 1.38454
b = 0.545168
1.33750 7.76510
11
II. I
u
2
= h−3.53 × 10
5
au
46
− 5.12 × 10
6
u
46
+ · · · − 1.76 × 10
6
a + 4.39 ×
10
6
, −u
46
a − 4u
46
+ · · · + 4a − 2, u
47
− 2u
46
+ · · · − 2u + 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
u
2
a
7
=
u
u
3
+ u
a
1
=
u
2
+ 1
u
2
a
8
=
u
7
+ 2u
5
+ 2u
3
+ 2u
u
7
+ u
5
+ 2u
3
+ u
a
5
=
u
3
u
5
+ u
3
+ u
a
10
=
a
0.0812428au
46
+ 1.17889u
46
+ ··· + 0.405981a − 1.01104
a
9
=
0.518544au
46
− 0.210245u
46
+ ··· + 0.695338a − 2.12702
0.532249au
46
+ 0.655745u
46
+ ··· − 0.0802495a − 1.01291
a
12
=
−0.695287au
46
− 0.870005u
46
+ ··· + 0.393056a + 3.69548
−1.22640au
46
− 0.919210u
46
+ ··· + 1.42747a + 3.22755
a
4
=
0.0795135au
46
− 3.46239u
46
+ ··· + 0.264558a + 2.53391
−0.263752au
46
− 4.29780u
46
+ ··· + 0.193759a + 4.16617
a
11
=
−0.728387au
46
− 1.21723u
46
+ ··· + 0.997171a − 0.164785
−0.241660au
46
+ 0.367629u
46
+ ··· + 0.306498a + 0.125823
(ii) Obstruction class = −1
(iii) Cusp Shapes = −9u
46
+ 12u
45
+ ··· − 25u
3
+ 11
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
(u
47
+ 16u
46
+ ··· + 6u − 1)
2
c
2
, c
6
(u
47
+ 2u
46
+ ··· − 2u − 1)
2
c
3
, c
9
u
94
+ 2u
93
+ ··· − 1357u + 617
c
4
, c
8
u
94
+ 2u
93
+ ··· − 5u − 1
c
7
(u
47
− 15u
46
+ ··· + 584u − 64)
2
c
10
, c
12
u
94
− 5u
93
+ ··· − 1230u − 479
c
11
(u
47
− 23u
46
+ ··· + 6u − 4)
2
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
47
+ 32y
46
+ ··· + 54y −1)
2
c
2
, c
6
(y
47
+ 16y
46
+ ··· + 6y −1)
2
c
3
, c
9
y
94
+ 88y
92
+ ··· − 24281739y + 380689
c
4
, c
8
y
94
+ 20y
93
+ ··· − 95y + 1
c
7
(y
47
+ 11y
46
+ ··· + 4032y −4096)
2
c
10
, c
12
y
94
+ 23y
93
+ ··· − 3235384y + 229441
c
11
(y
47
− 5y
46
+ ··· + 364y −16)
2
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.772143 + 0.642996I
a = 2.23948 − 0.62237I
b = 1.82124 + 0.57008I
−0.36535 − 5.41817I −3.72177 + 5.83848I
u = 0.772143 + 0.642996I
a = −1.95406 − 1.42975I
b = −1.57524 − 1.57601I
−0.36535 − 5.41817I −3.72177 + 5.83848I
u = 0.772143 − 0.642996I
a = 2.23948 + 0.62237I
b = 1.82124 − 0.57008I
−0.36535 + 5.41817I −3.72177 − 5.83848I
u = 0.772143 − 0.642996I
a = −1.95406 + 1.42975I
b = −1.57524 + 1.57601I
−0.36535 + 5.41817I −3.72177 − 5.83848I
u = 0.065823 + 0.985795I
a = −0.794525 + 0.145636I
b = 2.39330 − 0.83626I
−1.81519 + 5.22959I −3.91168 − 9.23109I
u = 0.065823 + 0.985795I
a = −0.11431 + 2.05371I
b = −0.289829 − 1.141580I
−1.81519 + 5.22959I −3.91168 − 9.23109I
u = 0.065823 − 0.985795I
a = −0.794525 − 0.145636I
b = 2.39330 + 0.83626I
−1.81519 − 5.22959I −3.91168 + 9.23109I
u = 0.065823 − 0.985795I
a = −0.11431 − 2.05371I
b = −0.289829 + 1.141580I
−1.81519 − 5.22959I −3.91168 + 9.23109I
u = 0.670790 + 0.783645I
a = −0.161907 + 0.672913I
b = 0.351390 + 1.295530I
2.06177 + 5.42127I −0.51305 − 9.04370I
u = 0.670790 + 0.783645I
a = −3.09541 + 0.33327I
b = −1.80019 − 1.46614I
2.06177 + 5.42127I −0.51305 − 9.04370I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.670790 − 0.783645I
a = −0.161907 − 0.672913I
b = 0.351390 − 1.295530I
2.06177 − 5.42127I −0.51305 + 9.04370I
u = 0.670790 − 0.783645I
a = −3.09541 − 0.33327I
b = −1.80019 + 1.46614I
2.06177 − 5.42127I −0.51305 + 9.04370I
u = −0.757991 + 0.707290I
a = 0.368122 + 0.935352I
b = 0.05350 + 1.55347I
3.76799 + 4.92764I 5.40903 − 6.45647I
u = −0.757991 + 0.707290I
a = −2.86375 + 1.71519I
b = −1.40822 + 2.25640I
3.76799 + 4.92764I 5.40903 − 6.45647I
u = −0.757991 − 0.707290I
a = 0.368122 − 0.935352I
b = 0.05350 − 1.55347I
3.76799 − 4.92764I 5.40903 + 6.45647I
u = −0.757991 − 0.707290I
a = −2.86375 − 1.71519I
b = −1.40822 − 2.25640I
3.76799 − 4.92764I 5.40903 + 6.45647I
u = −0.321739 + 0.904434I
a = −0.752471 − 0.181737I
b = −0.441533 − 0.190699I
−1.49879 − 2.72703I 0.31803 + 10.40316I
u = −0.321739 + 0.904434I
a = 0.83846 − 1.53264I
b = −1.206220 − 0.369321I
−1.49879 − 2.72703I 0.31803 + 10.40316I
u = −0.321739 − 0.904434I
a = −0.752471 + 0.181737I
b = −0.441533 + 0.190699I
−1.49879 + 2.72703I 0.31803 − 10.40316I
u = −0.321739 − 0.904434I
a = 0.83846 + 1.53264I
b = −1.206220 + 0.369321I
−1.49879 + 2.72703I 0.31803 − 10.40316I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.745676 + 0.749598I
a = 0.594496 + 0.931998I
b = 1.122390 − 0.539463I
4.39717 − 3.62571I 7.53098 + 3.80616I
u = −0.745676 + 0.749598I
a = 2.08257 − 1.70821I
b = 1.44620 − 1.97237I
4.39717 − 3.62571I 7.53098 + 3.80616I
u = −0.745676 − 0.749598I
a = 0.594496 − 0.931998I
b = 1.122390 + 0.539463I
4.39717 + 3.62571I 7.53098 − 3.80616I
u = −0.745676 − 0.749598I
a = 2.08257 + 1.70821I
b = 1.44620 + 1.97237I
4.39717 + 3.62571I 7.53098 − 3.80616I
u = 0.835576 + 0.654367I
a = −1.149220 − 0.808852I
b = −1.01681 − 1.08095I
3.17815 − 6.17661I 6.08040 + 7.08127I
u = 0.835576 + 0.654367I
a = 2.04035 + 0.90725I
b = 1.49419 + 1.19628I
3.17815 − 6.17661I 6.08040 + 7.08127I
u = 0.835576 − 0.654367I
a = −1.149220 + 0.808852I
b = −1.01681 + 1.08095I
3.17815 + 6.17661I 6.08040 − 7.08127I
u = 0.835576 − 0.654367I
a = 2.04035 − 0.90725I
b = 1.49419 − 1.19628I
3.17815 + 6.17661I 6.08040 − 7.08127I
u = −0.068239 + 1.072380I
a = −1.171150 − 0.335843I
b = 1.86850 + 0.88154I
−6.27292 − 4.92429I −11.80612 + 6.60421I
u = −0.068239 + 1.072380I
a = 0.361183 + 0.154733I
b = −1.61240 + 0.76863I
−6.27292 − 4.92429I −11.80612 + 6.60421I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.068239 − 1.072380I
a = −1.171150 + 0.335843I
b = 1.86850 − 0.88154I
−6.27292 + 4.92429I −11.80612 − 6.60421I
u = −0.068239 − 1.072380I
a = 0.361183 − 0.154733I
b = −1.61240 − 0.76863I
−6.27292 + 4.92429I −11.80612 − 6.60421I
u = 0.772491 + 0.749634I
a = 0.598374 + 0.785507I
b = −0.279711 + 0.391763I
4.50657 − 1.10565I 7.26389 + 0.73525I
u = 0.772491 + 0.749634I
a = 1.70588 + 0.49021I
b = 1.226170 + 0.551106I
4.50657 − 1.10565I 7.26389 + 0.73525I
u = 0.772491 − 0.749634I
a = 0.598374 − 0.785507I
b = −0.279711 − 0.391763I
4.50657 + 1.10565I 7.26389 − 0.73525I
u = 0.772491 − 0.749634I
a = 1.70588 − 0.49021I
b = 1.226170 − 0.551106I
4.50657 + 1.10565I 7.26389 − 0.73525I
u = −0.130958 + 1.104210I
a = −0.648999 − 0.190098I
b = 0.996603 + 0.502190I
−3.46438 − 5.71911I 0. + 10.73754I
u = −0.130958 + 1.104210I
a = 0.586734 − 0.214829I
b = −1.80970 − 0.34810I
−3.46438 − 5.71911I 0. + 10.73754I
u = −0.130958 − 1.104210I
a = −0.648999 + 0.190098I
b = 0.996603 − 0.502190I
−3.46438 + 5.71911I 0. − 10.73754I
u = −0.130958 − 1.104210I
a = 0.586734 + 0.214829I
b = −1.80970 + 0.34810I
−3.46438 + 5.71911I 0. − 10.73754I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.040229 + 0.879504I
a = −0.287572 − 1.222140I
b = −0.383448 − 0.507173I
−0.76455 − 2.60705I −1.60051 + 0.53932I
u = 0.040229 + 0.879504I
a = 1.77466 − 0.86226I
b = −1.47969 + 0.88535I
−0.76455 − 2.60705I −1.60051 + 0.53932I
u = 0.040229 − 0.879504I
a = −0.287572 + 1.222140I
b = −0.383448 + 0.507173I
−0.76455 + 2.60705I −1.60051 − 0.53932I
u = 0.040229 − 0.879504I
a = 1.77466 + 0.86226I
b = −1.47969 − 0.88535I
−0.76455 + 2.60705I −1.60051 − 0.53932I
u = 0.660122 + 0.938453I
a = 1.78287 + 0.59230I
b = −0.497549 + 1.192870I
1.57017 − 0.25942I −1.06368 + 3.01037I
u = 0.660122 + 0.938453I
a = 1.13707 − 2.93123I
b = 2.52010 − 1.14200I
1.57017 − 0.25942I −1.06368 + 3.01037I
u = 0.660122 − 0.938453I
a = 1.78287 − 0.59230I
b = −0.497549 − 1.192870I
1.57017 + 0.25942I −1.06368 − 3.01037I
u = 0.660122 − 0.938453I
a = 1.13707 + 2.93123I
b = 2.52010 + 1.14200I
1.57017 + 0.25942I −1.06368 − 3.01037I
u = −0.505950 + 1.033790I
a = 0.288704 + 0.762750I
b = 0.420531 − 0.175980I
−1.20472 − 1.09384I 8.06325 − 6.83134I
u = −0.505950 + 1.033790I
a = 0.02739 − 1.62004I
b = −1.061970 − 0.621817I
−1.20472 − 1.09384I 8.06325 − 6.83134I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.505950 − 1.033790I
a = 0.288704 − 0.762750I
b = 0.420531 + 0.175980I
−1.20472 + 1.09384I 8.06325 + 6.83134I
u = −0.505950 − 1.033790I
a = 0.02739 + 1.62004I
b = −1.061970 + 0.621817I
−1.20472 + 1.09384I 8.06325 + 6.83134I
u = −0.592721 + 1.003590I
a = 0.91940 − 1.82547I
b = −0.32920 − 1.50045I
−3.12533 − 1.32118I −9.86172 − 1.87297I
u = −0.592721 + 1.003590I
a = 0.98493 + 1.90479I
b = 1.44789 − 0.16408I
−3.12533 − 1.32118I −9.86172 − 1.87297I
u = −0.592721 − 1.003590I
a = 0.91940 + 1.82547I
b = −0.32920 + 1.50045I
−3.12533 + 1.32118I −9.86172 + 1.87297I
u = −0.592721 − 1.003590I
a = 0.98493 − 1.90479I
b = 1.44789 + 0.16408I
−3.12533 + 1.32118I −9.86172 + 1.87297I
u = 0.796351 + 0.877178I
a = 0.318920 + 0.558060I
b = −0.401394 + 0.125062I
7.14398 + 2.97736I 10.10091 − 3.12468I
u = 0.796351 + 0.877178I
a = 0.061883 + 0.240083I
b = 0.407103 + 0.385543I
7.14398 + 2.97736I 10.10091 − 3.12468I
u = 0.796351 − 0.877178I
a = 0.318920 − 0.558060I
b = −0.401394 − 0.125062I
7.14398 − 2.97736I 10.10091 + 3.12468I
u = 0.796351 − 0.877178I
a = 0.061883 − 0.240083I
b = 0.407103 − 0.385543I
7.14398 − 2.97736I 10.10091 + 3.12468I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.704160 + 0.960383I
a = −0.259940 − 0.426803I
b = −1.320450 − 0.145118I
3.75387 − 1.89878I 5.76587 + 2.06655I
u = −0.704160 + 0.960383I
a = 0.92784 − 3.27718I
b = −1.76239 − 1.90494I
3.75387 − 1.89878I 5.76587 + 2.06655I
u = −0.704160 − 0.960383I
a = −0.259940 + 0.426803I
b = −1.320450 + 0.145118I
3.75387 + 1.89878I 5.76587 − 2.06655I
u = −0.704160 − 0.960383I
a = 0.92784 + 3.27718I
b = −1.76239 + 1.90494I
3.75387 + 1.89878I 5.76587 − 2.06655I
u = 0.718348 + 0.965153I
a = 0.131396 + 0.525117I
b = 0.283757 + 0.615978I
3.84804 + 6.74938I 5.58868 − 6.17473I
u = 0.718348 + 0.965153I
a = −0.63010 + 2.24866I
b = −1.49467 + 0.56145I
3.84804 + 6.74938I 5.58868 − 6.17473I
u = 0.718348 − 0.965153I
a = 0.131396 − 0.525117I
b = 0.283757 − 0.615978I
3.84804 − 6.74938I 5.58868 + 6.17473I
u = 0.718348 − 0.965153I
a = −0.63010 − 2.24866I
b = −1.49467 − 0.56145I
3.84804 − 6.74938I 5.58868 + 6.17473I
u = −0.700956 + 0.987558I
a = −2.01581 + 0.26450I
b = 0.076435 + 1.404510I
2.91955 − 10.47790I 3.11327 + 11.61269I
u = −0.700956 + 0.987558I
a = −0.66356 + 3.49438I
b = 1.95608 + 2.44853I
2.91955 − 10.47790I 3.11327 + 11.61269I
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.700956 − 0.987558I
a = −2.01581 − 0.26450I
b = 0.076435 − 1.404510I
2.91955 + 10.47790I 3.11327 − 11.61269I
u = −0.700956 − 0.987558I
a = −0.66356 − 3.49438I
b = 1.95608 − 2.44853I
2.91955 + 10.47790I 3.11327 − 11.61269I
u = 0.690939 + 1.018760I
a = −1.12961 + 2.00203I
b = −2.36330 + 0.39658I
−1.48582 + 10.96820I −5.73761 − 10.34128I
u = 0.690939 + 1.018760I
a = −0.70651 − 3.00542I
b = 1.87813 − 1.65600I
−1.48582 + 10.96820I −5.73761 − 10.34128I
u = 0.690939 − 1.018760I
a = −1.12961 − 2.00203I
b = −2.36330 − 0.39658I
−1.48582 − 10.96820I −5.73761 + 10.34128I
u = 0.690939 − 1.018760I
a = −0.70651 + 3.00542I
b = 1.87813 + 1.65600I
−1.48582 − 10.96820I −5.73761 + 10.34128I
u = −0.709255 + 0.256293I
a = −0.602810 − 0.317048I
b = −0.504753 − 0.560887I
1.03622 − 3.27383I 9.01134 + 8.23853I
u = −0.709255 + 0.256293I
a = 1.58630 − 0.15907I
b = 0.991234 + 0.147920I
1.03622 − 3.27383I 9.01134 + 8.23853I
u = −0.709255 − 0.256293I
a = −0.602810 + 0.317048I
b = −0.504753 + 0.560887I
1.03622 + 3.27383I 9.01134 − 8.23853I
u = −0.709255 − 0.256293I
a = 1.58630 + 0.15907I
b = 0.991234 − 0.147920I
1.03622 + 3.27383I 9.01134 − 8.23853I
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.718603 + 1.036020I
a = −0.44695 − 1.78971I
b = 1.24131 − 1.08106I
2.01774 + 11.99080I 0. − 11.87939I
u = 0.718603 + 1.036020I
a = 0.01022 + 2.58701I
b = −1.80260 + 1.32253I
2.01774 + 11.99080I 0. − 11.87939I
u = 0.718603 − 1.036020I
a = −0.44695 + 1.78971I
b = 1.24131 + 1.08106I
2.01774 − 11.99080I 0. + 11.87939I
u = 0.718603 − 1.036020I
a = 0.01022 − 2.58701I
b = −1.80260 − 1.32253I
2.01774 − 11.99080I 0. + 11.87939I
u = −0.596911 + 0.421542I
a = −1.54344 − 0.54636I
b = −1.159750 − 0.623127I
−1.66205 − 3.33681I −4.87506 + 7.62978I
u = −0.596911 + 0.421542I
a = 1.19145 − 1.77959I
b = 0.282395 − 0.518869I
−1.66205 − 3.33681I −4.87506 + 7.62978I
u = −0.596911 − 0.421542I
a = −1.54344 + 0.54636I
b = −1.159750 + 0.623127I
−1.66205 + 3.33681I −4.87506 − 7.62978I
u = −0.596911 − 0.421542I
a = 1.19145 + 1.77959I
b = 0.282395 + 0.518869I
−1.66205 + 3.33681I −4.87506 − 7.62978I
u = −0.557302
a = 1.21547
b = 0.121806
1.15522 8.68310
u = −0.557302
a = 1.63842
b = 1.14422
1.15522 8.68310
23
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.371791 + 0.088614I
a = 1.54496 + 0.38373I
b = 0.69756 + 1.33020I
1.44196 + 3.94940I 9.27313 − 7.93438I
u = 0.371791 + 0.088614I
a = −3.03847 − 1.45398I
b = −0.608030 + 0.449499I
1.44196 + 3.94940I 9.27313 − 7.93438I
u = 0.371791 − 0.088614I
a = 1.54496 − 0.38373I
b = 0.69756 − 1.33020I
1.44196 − 3.94940I 9.27313 + 7.93438I
u = 0.371791 − 0.088614I
a = −3.03847 + 1.45398I
b = −0.608030 − 0.449499I
1.44196 − 3.94940I 9.27313 + 7.93438I
24
III.
I
u
3
= hu
22
+u
21
+· · ·+b+3u, u
23
−2u
22
+· · ·+a+3, u
24
−2u
23
+· · ·+7u
2
+1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
u
2
a
7
=
u
u
3
+ u
a
1
=
u
2
+ 1
u
2
a
8
=
u
7
+ 2u
5
+ 2u
3
+ 2u
u
7
+ u
5
+ 2u
3
+ u
a
5
=
u
3
u
5
+ u
3
+ u
a
10
=
−u
23
+ 2u
22
+ ··· − 6u − 3
−u
22
− u
21
+ ··· − 4u
2
− 3u
a
9
=
−2u
23
+ 4u
22
+ ··· − 6u − 2
−u
21
+ u
20
+ ··· − u + 1
a
12
=
u
23
− u
22
+ ··· − 6u + 1
u
23
− 3u
22
+ ··· − u − 1
a
4
=
u
23
+ u
22
+ ··· + 2u + 5
3u
23
− 4u
22
+ ··· + 4u − 1
a
11
=
−u
23
+ 2u
22
+ ··· − 6u − 2
−u
21
+ u
20
+ ··· − 2u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 18u
23
− 25u
22
+ 84u
21
− 88u
20
+ 249u
19
− 231u
18
+ 501u
17
−
393u
16
+ 767u
15
− 511u
14
+ 903u
13
− 510u
12
+ 836u
11
− 370u
10
+ 609u
9
− 232u
8
+
351u
7
− 103u
6
+ 161u
5
− 70u
4
+ 77u
3
− 52u
2
+ 22u − 9
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
24
− 8u
23
+ ··· − 14u + 1
c
2
u
24
− 2u
23
+ ··· + 7u
2
+ 1
c
3
, c
9
u
24
+ u
23
+ ··· + 6u
2
+ 1
c
4
, c
8
u
24
+ 6u
22
+ ··· − u + 1
c
6
u
24
+ 2u
23
+ ··· + 7u
2
+ 1
c
7
u
24
− 10u
23
+ ··· − 60u + 13
c
10
, c
12
u
24
+ 7u
23
+ ··· + 12u + 1
c
11
u
24
− 17u
23
+ ··· − 159u + 13
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
24
+ 20y
23
+ ··· − 38y + 1
c
2
, c
6
y
24
+ 8y
23
+ ··· + 14y + 1
c
3
, c
9
y
24
+ 7y
23
+ ··· + 12y + 1
c
4
, c
8
y
24
+ 12y
23
+ ··· + 7y + 1
c
7
y
24
− 8y
23
+ ··· + 3316y + 169
c
10
, c
12
y
24
+ 15y
23
+ ··· − 16y + 1
c
11
y
24
+ 5y
23
+ ··· + 1941y + 169
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.783109 + 0.655543I
a = −1.90898 − 0.95090I
b = −1.41891 − 1.49164I
1.38748 − 5.46519I 2.50414 + 5.64098I
u = 0.783109 − 0.655543I
a = −1.90898 + 0.95090I
b = −1.41891 + 1.49164I
1.38748 + 5.46519I 2.50414 − 5.64098I
u = 0.722134 + 0.771620I
a = 1.56857 + 0.44185I
b = 1.33569 + 1.71663I
3.32921 + 4.65722I 4.55642 − 7.86836I
u = 0.722134 − 0.771620I
a = 1.56857 − 0.44185I
b = 1.33569 − 1.71663I
3.32921 − 4.65722I 4.55642 + 7.86836I
u = −0.087858 + 1.075070I
a = −0.697208 − 0.281594I
b = 1.55008 + 0.42215I
−4.67521 − 5.07247I −5.72982 + 6.40556I
u = −0.087858 − 1.075070I
a = −0.697208 + 0.281594I
b = 1.55008 − 0.42215I
−4.67521 + 5.07247I −5.72982 − 6.40556I
u = −0.744007 + 0.782170I
a = 1.64417 + 0.32394I
b = 0.816926 − 0.127063I
3.55737 + 2.59657I 2.55184 − 4.16828I
u = −0.744007 − 0.782170I
a = 1.64417 − 0.32394I
b = 0.816926 + 0.127063I
3.55737 − 2.59657I 2.55184 + 4.16828I
u = 0.010799 + 0.915059I
a = 0.46203 + 1.54084I
b = −1.41632 − 0.54217I
−1.29285 + 3.71864I −4.48788 − 6.49334I
u = 0.010799 − 0.915059I
a = 0.46203 − 1.54084I
b = −1.41632 + 0.54217I
−1.29285 − 3.71864I −4.48788 + 6.49334I
28
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.552898 + 1.014130I
a = 0.129679 + 1.406560I
b = 0.768179 + 0.377090I
−1.86115 − 1.33351I −5.25361 − 0.66855I
u = −0.552898 − 1.014130I
a = 0.129679 − 1.406560I
b = 0.768179 − 0.377090I
−1.86115 + 1.33351I −5.25361 + 0.66855I
u = 0.694951 + 0.945102I
a = 0.70843 + 2.09621I
b = −1.69527 + 1.53542I
2.79501 + 0.77128I 2.92731 + 2.21034I
u = 0.694951 − 0.945102I
a = 0.70843 − 2.09621I
b = −1.69527 − 1.53542I
2.79501 − 0.77128I 2.92731 − 2.21034I
u = −0.710362 + 0.947085I
a = −1.26576 − 1.33668I
b = −1.044050 − 0.205193I
3.04601 − 8.14001I 1.19401 + 10.31197I
u = −0.710362 − 0.947085I
a = −1.26576 + 1.33668I
b = −1.044050 + 0.205193I
3.04601 + 8.14001I 1.19401 − 10.31197I
u = 0.700024 + 1.017760I
a = −0.36276 − 2.53749I
b = 1.85064 − 1.46863I
0.30274 + 11.07770I 0.61856 − 10.05231I
u = 0.700024 − 1.017760I
a = −0.36276 + 2.53749I
b = 1.85064 + 1.46863I
0.30274 − 11.07770I 0.61856 + 10.05231I
u = −0.659109 + 0.381913I
a = −1.157770 + 0.055314I
b = −0.615488 − 0.234859I
−0.07986 − 3.24341I 0.45676 + 7.76742I
u = −0.659109 − 0.381913I
a = −1.157770 − 0.055314I
b = −0.615488 + 0.234859I
−0.07986 + 3.24341I 0.45676 − 7.76742I
29
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.873660 + 0.917557I
a = −0.062950 − 0.211590I
b = −0.0106167 − 0.0427477I
7.80986 + 3.23033I −60.3385 − 17.9900I
u = 0.873660 − 0.917557I
a = −0.062950 + 0.211590I
b = −0.0106167 + 0.0427477I
7.80986 − 3.23033I −60.3385 + 17.9900I
u = −0.030442 + 0.453632I
a = −2.05746 − 1.42608I
b = 0.379145 − 0.677721I
0.48580 − 3.68590I −0.49927 + 5.76109I
u = −0.030442 − 0.453632I
a = −2.05746 + 1.42608I
b = 0.379145 + 0.677721I
0.48580 + 3.68590I −0.49927 − 5.76109I
30
IV. I
u
4
= hau + b + u + 1, a
2
− 3au − 3u − 2, u
2
+ u + 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
−u − 1
a
7
=
u
u + 1
a
1
=
−u
−u − 1
a
8
=
u
u + 1
a
5
=
1
0
a
10
=
a
−au − u − 1
a
9
=
au + a + u + 1
−au − u − 1
a
12
=
a − u
−au − 2u − 2
a
4
=
−u
a − 2u − 1
a
11
=
a − u
−au − 2u − 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = u − 3
31
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
6
(u
2
− u + 1)
2
c
2
(u
2
+ u + 1)
2
c
3
, c
4
, c
8
c
9
u
4
+ u
3
− u
2
− u + 1
c
7
, c
11
u
4
c
10
, c
12
(u + 1)
4
32
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
(y
2
+ y + 1)
2
c
3
, c
4
, c
8
c
9
y
4
− 3y
3
+ 5y
2
− 3y + 1
c
7
, c
11
y
4
c
10
, c
12
(y −1)
4
33
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = −1.121740 + 0.425428I
b = −0.692440 + 0.318148I
−1.64493 − 2.02988I −3.50000 + 0.86603I
u = −0.500000 + 0.866025I
a = −0.37826 + 2.17265I
b = 1.192440 + 0.547877I
−1.64493 − 2.02988I −3.50000 + 0.86603I
u = −0.500000 − 0.866025I
a = −1.121740 − 0.425428I
b = −0.692440 − 0.318148I
−1.64493 + 2.02988I −3.50000 − 0.86603I
u = −0.500000 − 0.866025I
a = −0.37826 − 2.17265I
b = 1.192440 − 0.547877I
−1.64493 + 2.02988I −3.50000 − 0.86603I
34
V. I
v
1
= ha, b + 1, v − 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
1
0
a
2
=
1
0
a
7
=
1
0
a
1
=
1
0
a
8
=
1
0
a
5
=
1
0
a
10
=
0
−1
a
9
=
1
−1
a
12
=
1
−1
a
4
=
2
−1
a
11
=
1
−1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6
35
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
7
, c
11
u
c
3
, c
4
, c
8
c
9
, c
10
, c
12
u + 1
36
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
7
, c
11
y
c
3
, c
4
, c
8
c
9
, c
10
, c
12
y −1
37
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 1.00000
a = 0
b = −1.00000
−1.64493 −6.00000
38
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
u(u
2
− u + 1)
2
(u
24
− 8u
23
+ ··· − 14u + 1)
· ((u
47
+ 16u
46
+ ··· + 6u − 1)
2
)(u
69
+ 23u
68
+ ··· + 65u − 49)
c
2
u(u
2
+ u + 1)
2
(u
24
− 2u
23
+ ··· + 7u
2
+ 1)(u
47
+ 2u
46
+ ··· − 2u − 1)
2
· (u
69
− 5u
68
+ ··· − 11u − 7)
c
3
, c
9
(u + 1)(u
4
+ u
3
− u
2
− u + 1)(u
24
+ u
23
+ ··· + 6u
2
+ 1)
· (u
69
− 2u
68
+ ··· − 3u − 1)(u
94
+ 2u
93
+ ··· − 1357u + 617)
c
4
, c
8
(u + 1)(u
4
+ u
3
− u
2
− u + 1)(u
24
+ 6u
22
+ ··· − u + 1)
· (u
69
− u
68
+ ··· − 2u − 1)(u
94
+ 2u
93
+ ··· − 5u − 1)
c
6
u(u
2
− u + 1)
2
(u
24
+ 2u
23
+ ··· + 7u
2
+ 1)(u
47
+ 2u
46
+ ··· − 2u − 1)
2
· (u
69
− 5u
68
+ ··· − 11u − 7)
c
7
u
5
(u
24
− 10u
23
+ ··· − 60u + 13)(u
47
− 15u
46
+ ··· + 584u − 64)
2
· (u
69
+ 25u
68
+ ··· − 59915u − 3703)
c
10
, c
12
((u + 1)
5
)(u
24
+ 7u
23
+ ··· + 12u + 1)(u
69
+ 10u
68
+ ··· + 29u − 1)
· (u
94
− 5u
93
+ ··· − 1230u − 479)
c
11
u
5
(u
24
− 17u
23
+ ··· − 159u + 13)(u
47
− 23u
46
+ ··· + 6u − 4)
2
· (u
69
+ 38u
68
+ ··· − 64u − 7)
39
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
y(y
2
+ y + 1)
2
(y
24
+ 20y
23
+ ··· − 38y + 1)
· ((y
47
+ 32y
46
+ ··· + 54y −1)
2
)(y
69
+ 51y
68
+ ··· + 29901y −2401)
c
2
, c
6
y(y
2
+ y + 1)
2
(y
24
+ 8y
23
+ ··· + 14y + 1)
· ((y
47
+ 16y
46
+ ··· + 6y −1)
2
)(y
69
+ 23y
68
+ ··· + 65y −49)
c
3
, c
9
(y −1)(y
4
− 3y
3
+ ··· − 3y + 1)(y
24
+ 7y
23
+ ··· + 12y + 1)
· (y
69
− 6y
68
+ ··· − 33y −1)
· (y
94
+ 88y
92
+ ··· − 24281739y + 380689)
c
4
, c
8
(y −1)(y
4
− 3y
3
+ ··· − 3y + 1)(y
24
+ 12y
23
+ ··· + 7y + 1)
· (y
69
− 29y
68
+ ··· + 76y −1)(y
94
+ 20y
93
+ ··· − 95y + 1)
c
7
y
5
(y
24
− 8y
23
+ ··· + 3316y + 169)
· (y
47
+ 11y
46
+ ··· + 4032y −4096)
2
· (y
69
+ 3y
68
+ ··· − 816311009y −13712209)
c
10
, c
12
((y −1)
5
)(y
24
+ 15y
23
+ ··· − 16y + 1)(y
69
− 42y
68
+ ··· + 27y −1)
· (y
94
+ 23y
93
+ ··· − 3235384y + 229441)
c
11
y
5
(y
24
+ 5y
23
+ ··· + 1941y + 169)(y
47
− 5y
46
+ ··· + 364y −16)
2
· (y
69
+ 50y
67
+ ··· + 134y −49)
40
