12a
0496
(K12a
0496
)
A knot diagram
1
Linearized knot diagam
3 7 8 9 10 2 6 11 12 1 4 5
Solving Sequence
2,7
3
1,10
11 6 8 4 5 12 9
c
2
c
1
c
10
c
6
c
7
c
3
c
5
c
12
c
9
c
4
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−1734730u
63
+ 7359550u
62
+ ··· + 238897b + 11914608,
− 8636494u
63
+ 40140921u
62
+ ··· + 1672279a + 84242322, u
64
− 5u
63
+ ··· − 46u + 7i
I
u
2
= h150u
46
a − 680138u
46
+ ··· − 95994a − 523234, −6u
46
a + 4u
46
+ ··· + 2a − 4,
u
47
+ 2u
46
+ ··· + 6u
2
− 1i
I
u
3
= h2u
19
− 3u
18
+ ··· + b − 3, 2u
19
− 2u
18
+ ··· + a − 1, u
20
− 2u
19
+ ··· − 2u + 1i
I
u
4
= h−2u
2
+ b − u + 1, −2u
2
+ a − u, u
3
+ u
2
− 1i
I
u
5
= h−u
2
+ b − 2u, −u
2
+ a − u + 1, u
3
+ u
2
− 1i
I
v
1
= ha, b − 1, v + 1i
* 6 irreducible components of dim
C
= 0, with total 185 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−1.73 × 10
6
u
63
+ 7.36 × 10
6
u
62
+ · · · + 2.39 × 10
5
b + 1.19 × 10
7
, −8.64 ×
10
6
u
63
+4.01×10
7
u
62
+· · ·+1.67×10
6
a+8.42×10
7
, u
64
−5u
63
+· · ·−46u+7i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
3
=
1
u
2
a
1
=
−u
2
+ 1
−u
4
a
10
=
5.16451u
63
− 24.0037u
62
+ ··· + 303.319u − 50.3758
7.26141u
63
− 30.8064u
62
+ ··· + 292.630u − 49.8734
a
11
=
2.48151u
63
− 20.2200u
62
+ ··· + 322.081u − 53.6177
−7.81243u
63
+ 18.6263u
62
+ ··· + 60.5318u − 17.3706
a
6
=
u
u
a
8
=
−u
3
−u
3
+ u
a
4
=
−u
8
+ u
6
− u
4
+ 1
−u
8
+ 2u
6
− 2u
4
+ 2u
2
a
5
=
16.0754u
63
− 59.9879u
62
+ ··· + 275.423u − 35.9390
18.6758u
63
− 76.4973u
62
+ ··· + 561.005u − 87.3529
a
12
=
3.22947u
63
− 27.3703u
62
+ ··· + 454.241u − 78.3087
−10.5895u
63
+ 24.5239u
62
+ ··· + 149.285u − 35.7643
a
9
=
2.61568u
63
− 11.2817u
62
+ ··· + 143.423u − 21.8542
1.79666u
63
− 8.38758u
62
+ ··· + 99.4670u − 18.3098
(ii) Obstruction class = −1
(iii) Cusp Shapes =
185551
238897
u
63
+
3341470
238897
u
62
+ ··· −
143830148
238897
u +
29363823
238897
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
64
+ 23u
63
+ ··· + 464u + 49
c
2
, c
6
u
64
− 5u
63
+ ··· − 46u + 7
c
3
u
64
+ 7u
63
+ ··· − 34358u + 14287
c
4
, c
12
u
64
+ 3u
63
+ ··· − u − 1
c
5
, c
11
u
64
+ 2u
63
+ ··· − 2u + 1
c
8
, c
10
u
64
− 10u
63
+ ··· + 14u + 1
c
9
u
64
− 34u
63
+ ··· + 22u − 7
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
64
+ 41y
63
+ ··· + 127704y + 2401
c
2
, c
6
y
64
− 23y
63
+ ··· − 464y + 49
c
3
y
64
− 21y
63
+ ··· − 4975613696y + 204118369
c
4
, c
12
y
64
− 35y
63
+ ··· − 77y + 1
c
5
, c
11
y
64
− 14y
63
+ ··· − 14y + 1
c
8
, c
10
y
64
− 26y
63
+ ··· − 118y + 1
c
9
y
64
+ 22y
62
+ ··· − 946y + 49
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.697962 + 0.708130I
a = −1.67956 − 1.76520I
b = −0.852517 − 0.546831I
3.23555 − 0.09263I 0
u = −0.697962 − 0.708130I
a = −1.67956 + 1.76520I
b = −0.852517 + 0.546831I
3.23555 + 0.09263I 0
u = 1.00820
a = 1.45537
b = 2.94663
−1.74441 −5.99190
u = 0.639156 + 0.782956I
a = −1.10014 + 2.11562I
b = −1.50171 + 1.10683I
2.98257 + 5.54336I 0. − 6.27222I
u = 0.639156 − 0.782956I
a = −1.10014 − 2.11562I
b = −1.50171 − 1.10683I
2.98257 − 5.54336I 0. + 6.27222I
u = 0.728093 + 0.711367I
a = 0.68572 + 1.76281I
b = −0.46330 + 1.96744I
3.52720 − 0.00884I 0
u = 0.728093 − 0.711367I
a = 0.68572 − 1.76281I
b = −0.46330 − 1.96744I
3.52720 + 0.00884I 0
u = 0.572354 + 0.786065I
a = −0.051150 + 0.959296I
b = −0.059433 + 0.598116I
2.29221 + 1.37861I 3.68261 − 1.26528I
u = 0.572354 − 0.786065I
a = −0.051150 − 0.959296I
b = −0.059433 − 0.598116I
2.29221 − 1.37861I 3.68261 + 1.26528I
u = 0.804285 + 0.524113I
a = 0.190288 − 1.042600I
b = 1.091820 − 0.891582I
1.03742 − 3.37211I −1.80469 + 6.78145I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.804285 − 0.524113I
a = 0.190288 + 1.042600I
b = 1.091820 + 0.891582I
1.03742 + 3.37211I −1.80469 − 6.78145I
u = 0.634325 + 0.833636I
a = 1.54312 − 2.00028I
b = 1.54828 − 0.43921I
1.2900 + 14.4309I 0
u = 0.634325 − 0.833636I
a = 1.54312 + 2.00028I
b = 1.54828 + 0.43921I
1.2900 − 14.4309I 0
u = −0.932588 + 0.007398I
a = 0.415698 + 0.467945I
b = −0.186759 − 0.248263I
−1.339460 + 0.449150I −6.56145 − 1.67611I
u = −0.932588 − 0.007398I
a = 0.415698 − 0.467945I
b = −0.186759 + 0.248263I
−1.339460 − 0.449150I −6.56145 + 1.67611I
u = −1.071850 + 0.068659I
a = 0.669015 + 1.069670I
b = 1.293700 + 0.264092I
−2.98372 + 5.03113I 0
u = −1.071850 − 0.068659I
a = 0.669015 − 1.069670I
b = 1.293700 − 0.264092I
−2.98372 − 5.03113I 0
u = 1.07680
a = −0.786660
b = −1.75843
−6.33617 −14.1800
u = −0.592507 + 0.702795I
a = 0.752269 + 0.978771I
b = 0.174748 + 0.081898I
−1.043970 − 0.946914I −6.98595 + 0.I
u = −0.592507 − 0.702795I
a = 0.752269 − 0.978771I
b = 0.174748 − 0.081898I
−1.043970 + 0.946914I −6.98595 + 0.I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.736786 + 0.817581I
a = 0.149009 − 1.133040I
b = 0.832202 − 0.663254I
4.13608 − 1.87912I 0
u = 0.736786 − 0.817581I
a = 0.149009 + 1.133040I
b = 0.832202 + 0.663254I
4.13608 + 1.87912I 0
u = −1.117060 + 0.109814I
a = −0.807439 − 0.795984I
b = −2.03240 − 0.10781I
−5.2527 + 13.7489I 0
u = −1.117060 − 0.109814I
a = −0.807439 + 0.795984I
b = −2.03240 + 0.10781I
−5.2527 − 13.7489I 0
u = −0.856164 + 0.736535I
a = −0.84854 − 2.26839I
b = −1.46492 − 1.86228I
6.33526 + 4.44087I 0
u = −0.856164 − 0.736535I
a = −0.84854 + 2.26839I
b = −1.46492 + 1.86228I
6.33526 − 4.44087I 0
u = −0.868762 + 0.731876I
a = −2.00888 − 1.13797I
b = −2.31883 − 0.53167I
6.29588 + 1.13543I 0
u = −0.868762 − 0.731876I
a = −2.00888 + 1.13797I
b = −2.31883 + 0.53167I
6.29588 − 1.13543I 0
u = −1.15307
a = 0.601343
b = 0.930830
−3.58190 0
u = 0.986087 + 0.603160I
a = 0.759306 − 0.700975I
b = 0.609793 + 0.181630I
0.175719 − 1.083750I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.986087 − 0.603160I
a = 0.759306 + 0.700975I
b = 0.609793 − 0.181630I
0.175719 + 1.083750I 0
u = 1.062550 + 0.468285I
a = −0.200162 + 0.267131I
b = −1.041540 + 0.047587I
−1.95009 − 8.80692I 0
u = 1.062550 − 0.468285I
a = −0.200162 − 0.267131I
b = −1.041540 − 0.047587I
−1.95009 + 8.80692I 0
u = −0.846265 + 0.805401I
a = 1.84643 + 0.87650I
b = 1.95412 − 0.27824I
6.28695 − 5.68542I 0
u = −0.846265 − 0.805401I
a = 1.84643 − 0.87650I
b = 1.95412 + 0.27824I
6.28695 + 5.68542I 0
u = 1.044360 + 0.535925I
a = −0.297767 − 0.010643I
b = 0.287388 − 1.086830I
−2.64693 + 6.82839I 0
u = 1.044360 − 0.535925I
a = −0.297767 + 0.010643I
b = 0.287388 + 1.086830I
−2.64693 − 6.82839I 0
u = 0.965327 + 0.681396I
a = −1.83686 − 0.09440I
b = −1.57566 − 1.07217I
2.80623 − 5.34875I 0
u = 0.965327 − 0.681396I
a = −1.83686 + 0.09440I
b = −1.57566 + 1.07217I
2.80623 + 5.34875I 0
u = −0.982823 + 0.674637I
a = −1.31717 − 1.51958I
b = −2.48194 − 2.08681I
2.37380 + 5.42471I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.982823 − 0.674637I
a = −1.31717 + 1.51958I
b = −2.48194 + 2.08681I
2.37380 − 5.42471I 0
u = −1.172950 + 0.233278I
a = −0.046370 + 0.198660I
b = 0.219915 + 0.658412I
−3.53632 − 1.31927I 0
u = −1.172950 − 0.233278I
a = −0.046370 − 0.198660I
b = 0.219915 − 0.658412I
−3.53632 + 1.31927I 0
u = −0.904136 + 0.786401I
a = 0.45867 + 2.05749I
b = 1.62123 + 1.88253I
6.10887 + 11.63470I 0
u = −0.904136 − 0.786401I
a = 0.45867 − 2.05749I
b = 1.62123 − 1.88253I
6.10887 − 11.63470I 0
u = −1.016970 + 0.654432I
a = 0.747567 + 0.699678I
b = 1.53161 + 1.07598I
−2.27025 + 6.19345I 0
u = −1.016970 − 0.654432I
a = 0.747567 − 0.699678I
b = 1.53161 − 1.07598I
−2.27025 − 6.19345I 0
u = 0.303108 + 0.722084I
a = 0.781154 − 0.316034I
b = −0.878500 + 0.638191I
−0.52027 − 11.41630I −2.49256 + 8.08162I
u = 0.303108 − 0.722084I
a = 0.781154 + 0.316034I
b = −0.878500 − 0.638191I
−0.52027 + 11.41630I −2.49256 − 8.08162I
u = 0.981513 + 0.732663I
a = 1.019970 − 0.631499I
b = 1.48785 − 0.02952I
3.38294 − 3.93081I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.981513 − 0.732663I
a = 1.019970 + 0.631499I
b = 1.48785 + 0.02952I
3.38294 + 3.93081I 0
u = 0.154501 + 0.750893I
a = 0.336028 + 0.604708I
b = −0.436498 − 0.329752I
0.75067 + 4.55551I 2.40157 − 10.29146I
u = 0.154501 − 0.750893I
a = 0.336028 − 0.604708I
b = −0.436498 + 0.329752I
0.75067 − 4.55551I 2.40157 + 10.29146I
u = 1.023840 + 0.691795I
a = −1.96311 + 1.54995I
b = −2.78367 + 1.14339I
1.82985 − 11.12330I 0
u = 1.023840 − 0.691795I
a = −1.96311 − 1.54995I
b = −2.78367 − 1.14339I
1.82985 + 11.12330I 0
u = 1.052550 + 0.676673I
a = −0.954979 + 0.296922I
b = −1.312160 + 0.307764I
0.87367 − 6.91136I 0
u = 1.052550 − 0.676673I
a = −0.954979 − 0.296922I
b = −1.312160 − 0.307764I
0.87367 + 6.91136I 0
u = 1.043210 + 0.709927I
a = 1.67256 − 1.84369I
b = 2.98654 − 1.78795I
0.0504 − 20.2068I 0
u = 1.043210 − 0.709927I
a = 1.67256 + 1.84369I
b = 2.98654 + 1.78795I
0.0504 + 20.2068I 0
u = 0.361556 + 0.559052I
a = −0.400060 − 0.573207I
b = 1.044170 − 0.600052I
1.50411 − 3.41073I 3.06252 + 7.09437I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.361556 − 0.559052I
a = −0.400060 + 0.573207I
b = 1.044170 + 0.600052I
1.50411 + 3.41073I 3.06252 − 7.09437I
u = −0.640733
a = 0.559622
b = −0.336776
−0.999154 −9.88350
u = 0.320846 + 0.345616I
a = 0.856259 − 0.836701I
b = 0.815333 + 0.325629I
1.85294 + 0.24098I 3.67461 + 0.64977I
u = 0.320846 − 0.345616I
a = 0.856259 + 0.836701I
b = 0.815333 − 0.325629I
1.85294 − 0.24098I 3.67461 − 0.64977I
11
II. I
u
2
= h150u
46
a − 680138u
46
+ · · · − 95994a − 523234, −6u
46
a + 4u
46
+
· · · + 2a − 4, u
47
+ 2u
46
+ · · · + 6u
2
− 1i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
3
=
1
u
2
a
1
=
−u
2
+ 1
−u
4
a
10
=
a
−0.000413819au
46
+ 1.87636u
46
+ ··· + 0.264828a + 1.44350
a
11
=
−0.312516au
46
− 2.77156u
46
+ ··· + 1.59798a + 2.72797
0.149146au
46
− 1.41248u
46
+ ··· + 0.312516a + 4.77156
a
6
=
u
u
a
8
=
−u
3
−u
3
+ u
a
4
=
−u
8
+ u
6
− u
4
+ 1
−u
8
+ 2u
6
− 2u
4
+ 2u
2
a
5
=
−0.368892au
46
+ 0.918130u
46
+ ··· + 1.87636a + 1.91354
−0.640937au
46
+ 1.83838u
46
+ ··· + 1.17418a + 1.06763
a
12
=
−0.205293au
46
− 2.92275u
46
+ ··· + 1.65932a + 1.52194
0.251020au
46
− 1.41523u
46
+ ··· + 0.0771994a + 3.97178
a
9
=
−0.503113au
46
+ 2.92316u
46
+ ··· + 2.81239a − 1.78677
−0.111028au
46
+ 2.22787u
46
+ ··· + 1.45331a − 3.31010
(ii) Obstruction class = −1
(iii) Cusp Shapes = −u
46
− 6u
45
+ ··· − 25u − 17
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
(u
47
+ 16u
46
+ ··· + 12u + 1)
2
c
2
, c
6
(u
47
+ 2u
46
+ ··· + 6u
2
− 1)
2
c
3
(u
47
− 2u
46
+ ··· + 122u − 37)
2
c
4
, c
12
u
94
+ 10u
92
+ ··· − 7u + 1
c
5
, c
11
u
94
− 4u
92
+ ··· − 18201u + 761
c
8
, c
10
u
94
+ 7u
93
+ ··· + 74u + 19
c
9
(u
47
+ 23u
46
+ ··· + 12u + 8)
2
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
(y
47
+ 32y
46
+ ··· + 12y −1)
2
c
2
, c
6
(y
47
− 16y
46
+ ··· + 12y −1)
2
c
3
(y
47
− 16y
46
+ ··· + 37824y −1369)
2
c
4
, c
12
y
94
+ 20y
93
+ ··· + 9y + 1
c
5
, c
11
y
94
− 8y
93
+ ··· − 190343767y + 579121
c
8
, c
10
y
94
+ 33y
93
+ ··· − 11366y + 361
c
9
(y
47
− 7y
46
+ ··· + 1424y −64)
2
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.776349 + 0.661422I
a = 0.758981 + 0.193716I
b = 1.77645 + 0.49361I
1.10849 + 5.40536I −0.41152 − 9.36246I
u = −0.776349 + 0.661422I
a = 0.54263 − 3.15148I
b = −0.76174 − 2.41245I
1.10849 + 5.40536I −0.41152 − 9.36246I
u = −0.776349 − 0.661422I
a = 0.758981 − 0.193716I
b = 1.77645 − 0.49361I
1.10849 − 5.40536I −0.41152 + 9.36246I
u = −0.776349 − 0.661422I
a = 0.54263 + 3.15148I
b = −0.76174 + 2.41245I
1.10849 − 5.40536I −0.41152 + 9.36246I
u = 1.019790 + 0.092510I
a = 0.68972 − 1.40592I
b = 1.70152 − 0.86662I
−2.43130 − 5.51015I −4.82916 + 8.03335I
u = 1.019790 + 0.092510I
a = 0.029262 + 0.176413I
b = 0.12157 − 1.45314I
−2.43130 − 5.51015I −4.82916 + 8.03335I
u = 1.019790 − 0.092510I
a = 0.68972 + 1.40592I
b = 1.70152 + 0.86662I
−2.43130 + 5.51015I −4.82916 − 8.03335I
u = 1.019790 − 0.092510I
a = 0.029262 − 0.176413I
b = 0.12157 + 1.45314I
−2.43130 + 5.51015I −4.82916 − 8.03335I
u = 0.648071 + 0.723212I
a = −0.736502 − 0.524748I
b = −1.243130 + 0.114753I
−0.49007 + 4.87876I −5.65107 − 6.38090I
u = 0.648071 + 0.723212I
a = −1.79929 + 2.64042I
b = −1.93267 + 0.81735I
−0.49007 + 4.87876I −5.65107 − 6.38090I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.648071 − 0.723212I
a = −0.736502 + 0.524748I
b = −1.243130 − 0.114753I
−0.49007 − 4.87876I −5.65107 + 6.38090I
u = 0.648071 − 0.723212I
a = −1.79929 − 2.64042I
b = −1.93267 − 0.81735I
−0.49007 − 4.87876I −5.65107 + 6.38090I
u = −0.681587 + 0.784410I
a = −0.42546 + 2.27854I
b = 1.20914 + 1.53709I
3.54465 − 5.47609I 3.45857 + 5.88892I
u = −0.681587 + 0.784410I
a = −1.85767 − 1.81979I
b = −1.80898 − 0.69665I
3.54465 − 5.47609I 3.45857 + 5.88892I
u = −0.681587 − 0.784410I
a = −0.42546 − 2.27854I
b = 1.20914 − 1.53709I
3.54465 + 5.47609I 3.45857 − 5.88892I
u = −0.681587 − 0.784410I
a = −1.85767 + 1.81979I
b = −1.80898 + 0.69665I
3.54465 + 5.47609I 3.45857 − 5.88892I
u = −1.048580 + 0.022164I
a = 0.670100 + 0.764343I
b = 2.00093 − 0.27133I
−5.85788 + 4.38390I −13.6960 − 5.4679I
u = −1.048580 + 0.022164I
a = −1.05745 + 1.50356I
b = −1.65854 + 1.43422I
−5.85788 + 4.38390I −13.6960 − 5.4679I
u = −1.048580 − 0.022164I
a = 0.670100 − 0.764343I
b = 2.00093 + 0.27133I
−5.85788 − 4.38390I −13.6960 + 5.4679I
u = −1.048580 − 0.022164I
a = −1.05745 − 1.50356I
b = −1.65854 − 1.43422I
−5.85788 − 4.38390I −13.6960 + 5.4679I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.643340 + 0.833331I
a = −1.20226 − 0.85122I
b = −1.027200 − 0.118397I
−0.23631 − 6.14773I −6.28409 + 6.42865I
u = −0.643340 + 0.833331I
a = 1.43841 + 1.82679I
b = 1.45781 + 0.21030I
−0.23631 − 6.14773I −6.28409 + 6.42865I
u = −0.643340 − 0.833331I
a = −1.20226 + 0.85122I
b = −1.027200 + 0.118397I
−0.23631 + 6.14773I −6.28409 − 6.42865I
u = −0.643340 − 0.833331I
a = 1.43841 − 1.82679I
b = 1.45781 − 0.21030I
−0.23631 + 6.14773I −6.28409 − 6.42865I
u = 1.07542
a = −0.782008 + 0.163949I
b = −1.74468 + 0.12456I
−6.33500 −14.0910
u = 1.07542
a = −0.782008 − 0.163949I
b = −1.74468 − 0.12456I
−6.33500 −14.0910
u = 0.642944 + 0.643850I
a = −1.078100 − 0.664840I
b = 0.621290 − 1.023730I
−1.02865 − 3.62128I −7.85432 + 4.03793I
u = 0.642944 + 0.643850I
a = 1.48670 − 1.74194I
b = 1.18147 − 1.47113I
−1.02865 − 3.62128I −7.85432 + 4.03793I
u = 0.642944 − 0.643850I
a = −1.078100 + 0.664840I
b = 0.621290 + 1.023730I
−1.02865 + 3.62128I −7.85432 − 4.03793I
u = 0.642944 − 0.643850I
a = 1.48670 + 1.74194I
b = 1.18147 + 1.47113I
−1.02865 + 3.62128I −7.85432 − 4.03793I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.574541 + 0.684773I
a = 0.906959 + 0.595184I
b = 0.189356 − 0.393389I
−1.09201 − 0.99704I −7.43094 + 0.59298I
u = −0.574541 + 0.684773I
a = 0.68672 + 1.27674I
b = 0.036037 + 0.532121I
−1.09201 − 0.99704I −7.43094 + 0.59298I
u = −0.574541 − 0.684773I
a = 0.906959 − 0.595184I
b = 0.189356 + 0.393389I
−1.09201 + 0.99704I −7.43094 − 0.59298I
u = −0.574541 − 0.684773I
a = 0.68672 − 1.27674I
b = 0.036037 − 0.532121I
−1.09201 + 0.99704I −7.43094 − 0.59298I
u = 1.108130 + 0.117843I
a = 0.197788 − 0.818395I
b = 0.958445 − 0.713043I
−6.80256 − 5.57711I −13.3130 + 6.5645I
u = 1.108130 + 0.117843I
a = −0.640637 + 0.530645I
b = −1.88288 − 0.12291I
−6.80256 − 5.57711I −13.3130 + 6.5645I
u = 1.108130 − 0.117843I
a = 0.197788 + 0.818395I
b = 0.958445 + 0.713043I
−6.80256 + 5.57711I −13.3130 − 6.5645I
u = 1.108130 − 0.117843I
a = −0.640637 − 0.530645I
b = −1.88288 + 0.12291I
−6.80256 + 5.57711I −13.3130 − 6.5645I
u = 0.809770 + 0.776587I
a = 0.33531 + 1.81344I
b = −0.40943 + 1.85077I
5.52793 − 3.37748I 7.24336 + 9.19029I
u = 0.809770 + 0.776587I
a = 2.04613 − 1.57298I
b = 2.13651 + 0.08512I
5.52793 − 3.37748I 7.24336 + 9.19029I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.809770 − 0.776587I
a = 0.33531 − 1.81344I
b = −0.40943 − 1.85077I
5.52793 + 3.37748I 7.24336 − 9.19029I
u = 0.809770 − 0.776587I
a = 2.04613 + 1.57298I
b = 2.13651 − 0.08512I
5.52793 + 3.37748I 7.24336 − 9.19029I
u = −0.804168 + 0.325690I
a = 1.032170 + 0.238929I
b = 0.199742 − 0.568143I
−0.561606 − 0.847966I −6.35285 + 0.66182I
u = −0.804168 + 0.325690I
a = −0.424709 + 0.510863I
b = −1.48737 + 0.88084I
−0.561606 − 0.847966I −6.35285 + 0.66182I
u = −0.804168 − 0.325690I
a = 1.032170 − 0.238929I
b = 0.199742 + 0.568143I
−0.561606 + 0.847966I −6.35285 − 0.66182I
u = −0.804168 − 0.325690I
a = −0.424709 − 0.510863I
b = −1.48737 − 0.88084I
−0.561606 + 0.847966I −6.35285 − 0.66182I
u = −0.938082 + 0.646765I
a = 0.267718 + 1.012250I
b = −0.225138 + 0.137298I
0.600942 − 0.316659I −1.40018 + 2.53507I
u = −0.938082 + 0.646765I
a = −2.64915 − 0.16749I
b = −3.17830 + 1.10512I
0.600942 − 0.316659I −1.40018 + 2.53507I
u = −0.938082 − 0.646765I
a = 0.267718 − 1.012250I
b = −0.225138 − 0.137298I
0.600942 + 0.316659I −1.40018 − 2.53507I
u = −0.938082 − 0.646765I
a = −2.64915 + 0.16749I
b = −3.17830 − 1.10512I
0.600942 + 0.316659I −1.40018 − 2.53507I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.029320 + 0.521102I
a = −0.235544 + 0.360586I
b = 0.352893 + 1.295700I
−4.35818 + 1.21721I −12.24472 − 0.73106I
u = −1.029320 + 0.521102I
a = 0.303321 + 0.053585I
b = −0.374463 − 0.238009I
−4.35818 + 1.21721I −12.24472 − 0.73106I
u = −1.029320 − 0.521102I
a = −0.235544 − 0.360586I
b = 0.352893 − 1.295700I
−4.35818 − 1.21721I −12.24472 + 0.73106I
u = −1.029320 − 0.521102I
a = 0.303321 − 0.053585I
b = −0.374463 + 0.238009I
−4.35818 − 1.21721I −12.24472 + 0.73106I
u = 0.993847 + 0.647375I
a = 0.845776 + 0.381787I
b = 0.25649 + 1.68941I
−2.06171 − 1.47775I −9.32770 + 1.15281I
u = 0.993847 + 0.647375I
a = 1.69546 − 1.77990I
b = 2.04398 − 1.89942I
−2.06171 − 1.47775I −9.32770 + 1.15281I
u = 0.993847 − 0.647375I
a = 0.845776 − 0.381787I
b = 0.25649 − 1.68941I
−2.06171 + 1.47775I −9.32770 − 1.15281I
u = 0.993847 − 0.647375I
a = 1.69546 + 1.77990I
b = 2.04398 + 1.89942I
−2.06171 + 1.47775I −9.32770 − 1.15281I
u = 0.927543 + 0.748868I
a = −1.71080 − 0.09887I
b = −1.58120 − 0.72712I
5.16961 − 2.37615I 6.79993 − 5.84948I
u = 0.927543 + 0.748868I
a = 0.90921 − 2.19048I
b = 2.50095 − 2.03389I
5.16961 − 2.37615I 6.79993 − 5.84948I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.927543 − 0.748868I
a = −1.71080 + 0.09887I
b = −1.58120 + 0.72712I
5.16961 + 2.37615I 6.79993 + 5.84948I
u = 0.927543 − 0.748868I
a = 0.90921 + 2.19048I
b = 2.50095 + 2.03389I
5.16961 + 2.37615I 6.79993 + 5.84948I
u = 0.881371 + 0.803017I
a = −0.165659 + 0.325119I
b = −0.222654 + 0.344546I
4.05779 − 2.99996I −17.5576 + 5.0015I
u = 0.881371 + 0.803017I
a = 0.96433 − 1.49953I
b = 1.88261 − 0.69916I
4.05779 − 2.99996I −17.5576 + 5.0015I
u = 0.881371 − 0.803017I
a = −0.165659 − 0.325119I
b = −0.222654 − 0.344546I
4.05779 + 2.99996I −17.5576 − 5.0015I
u = 0.881371 − 0.803017I
a = 0.96433 + 1.49953I
b = 1.88261 + 0.69916I
4.05779 + 2.99996I −17.5576 − 5.0015I
u = −1.013000 + 0.648985I
a = 0.219984 + 0.625623I
b = 1.04442 + 1.12606I
−2.32658 + 6.17353I −9.42839 − 5.54710I
u = −1.013000 + 0.648985I
a = 1.22370 + 0.78552I
b = 1.87218 + 1.11325I
−2.32658 + 6.17353I −9.42839 − 5.54710I
u = −1.013000 − 0.648985I
a = 0.219984 − 0.625623I
b = 1.04442 − 1.12606I
−2.32658 − 6.17353I −9.42839 + 5.54710I
u = −1.013000 − 0.648985I
a = 1.22370 − 0.78552I
b = 1.87218 − 1.11325I
−2.32658 − 6.17353I −9.42839 + 5.54710I
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.005010 + 0.672828I
a = 0.372572 + 1.043990I
b = 0.911748 + 0.658883I
−1.54872 − 10.24500I −7.55162 + 10.89875I
u = 1.005010 + 0.672828I
a = −2.02921 + 2.22835I
b = −3.53175 + 1.94128I
−1.54872 − 10.24500I −7.55162 + 10.89875I
u = 1.005010 − 0.672828I
a = 0.372572 − 1.043990I
b = 0.911748 − 0.658883I
−1.54872 + 10.24500I −7.55162 − 10.89875I
u = 1.005010 − 0.672828I
a = −2.02921 − 2.22835I
b = −3.53175 − 1.94128I
−1.54872 + 10.24500I −7.55162 − 10.89875I
u = −1.006600 + 0.704989I
a = 2.21682 + 0.31076I
b = 2.76853 − 1.14567I
2.56157 + 11.10870I 0. − 10.69982I
u = −1.006600 + 0.704989I
a = −1.58865 − 2.12298I
b = −2.56665 − 2.07037I
2.56157 + 11.10870I 0. − 10.69982I
u = −1.006600 − 0.704989I
a = 2.21682 − 0.31076I
b = 2.76853 + 1.14567I
2.56157 − 11.10870I 0. + 10.69982I
u = −1.006600 − 0.704989I
a = −1.58865 + 2.12298I
b = −2.56665 + 2.07037I
2.56157 − 11.10870I 0. + 10.69982I
u = −0.276974 + 0.708893I
a = 0.995607 + 0.328280I
b = −0.612898 − 0.567032I
−2.20701 + 3.21583I −8.52754 − 5.71295I
u = −0.276974 + 0.708893I
a = −0.096933 − 0.250118I
b = 0.332782 + 0.564920I
−2.20701 + 3.21583I −8.52754 − 5.71295I
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.276974 − 0.708893I
a = 0.995607 − 0.328280I
b = −0.612898 + 0.567032I
−2.20701 − 3.21583I −8.52754 + 5.71295I
u = −0.276974 − 0.708893I
a = −0.096933 + 0.250118I
b = 0.332782 − 0.564920I
−2.20701 − 3.21583I −8.52754 + 5.71295I
u = −1.039600 + 0.713019I
a = −0.72514 − 1.39716I
b = −1.38896 − 1.50717I
−1.43938 + 11.93490I −7.71369 − 10.76632I
u = −1.039600 + 0.713019I
a = 1.43644 + 1.73632I
b = 2.81521 + 1.68606I
−1.43938 + 11.93490I −7.71369 − 10.76632I
u = −1.039600 − 0.713019I
a = −0.72514 + 1.39716I
b = −1.38896 + 1.50717I
−1.43938 − 11.93490I −7.71369 + 10.76632I
u = −1.039600 − 0.713019I
a = 1.43644 − 1.73632I
b = 2.81521 − 1.68606I
−1.43938 − 11.93490I −7.71369 + 10.76632I
u = −0.169763 + 0.526481I
a = −0.621754 − 0.410489I
b = 0.870560 + 0.773366I
1.28051 + 3.72235I 3.63725 − 7.32254I
u = −0.169763 + 0.526481I
a = 1.34819 − 1.75846I
b = −0.644969 − 0.030356I
1.28051 + 3.72235I 3.63725 − 7.32254I
u = −0.169763 − 0.526481I
a = −0.621754 + 0.410489I
b = 0.870560 − 0.773366I
1.28051 − 3.72235I 3.63725 + 7.32254I
u = −0.169763 − 0.526481I
a = 1.34819 + 1.75846I
b = −0.644969 + 0.030356I
1.28051 − 3.72235I 3.63725 + 7.32254I
23
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.427714 + 0.128339I
a = 0.96062 − 1.18896I
b = −0.45366 − 1.58721I
−1.40151 − 3.87082I −11.36079 + 7.52746I
u = 0.427714 + 0.128339I
a = −2.25370 − 2.21196I
b = 0.494622 − 0.881617I
−1.40151 − 3.87082I −11.36079 + 7.52746I
u = 0.427714 − 0.128339I
a = 0.96062 + 1.18896I
b = −0.45366 + 1.58721I
−1.40151 + 3.87082I −11.36079 − 7.52746I
u = 0.427714 − 0.128339I
a = −2.25370 + 2.21196I
b = 0.494622 + 0.881617I
−1.40151 + 3.87082I −11.36079 − 7.52746I
24
III.
I
u
3
= h2u
19
−3u
18
+· · ·+b−3, 2u
19
−2u
18
+· · ·+a−1, u
20
−2u
19
+· · ·−2u+1i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
3
=
1
u
2
a
1
=
−u
2
+ 1
−u
4
a
10
=
−2u
19
+ 2u
18
+ ··· − 4u + 1
−2u
19
+ 3u
18
+ ··· − 4u + 3
a
11
=
−5u
19
+ 4u
18
+ ··· − 8u + 2
−6u
19
+ 7u
18
+ ··· − 8u + 5
a
6
=
u
u
a
8
=
−u
3
−u
3
+ u
a
4
=
−u
8
+ u
6
− u
4
+ 1
−u
8
+ 2u
6
− 2u
4
+ 2u
2
a
5
=
3u
19
− 6u
18
+ ··· + 7u − 4
−3u
18
+ u
17
+ ··· + 2u − 3
a
12
=
−3u
19
+ 3u
18
+ ··· − 5u + 2
−3u
19
+ 4u
18
+ ··· − 5u + 3
a
9
=
−2u
19
+ 8u
17
+ ··· − u − 2
−4u
19
+ 4u
18
+ ··· − 5u + 2
(ii) Obstruction class = 1
(iii) Cusp Shapes
= 17u
19
− 22u
18
− 55u
17
+ 85u
16
+ 124u
15
− 210u
14
− 184u
13
+ 368u
12
+ 178u
11
−
463u
10
− 107u
9
+ 450u
8
− 8u
7
− 291u
6
+ 62u
5
+ 123u
4
− 47u
3
− 26u
2
+ 33u − 20
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
20
− 8u
19
+ ··· + 2u + 1
c
2
u
20
− 2u
19
+ ··· − 2u + 1
c
3
u
20
− u
18
+ ··· − 3u
2
+ 1
c
4
, c
12
u
20
− 2u
19
+ ··· − u + 1
c
5
, c
11
u
20
+ u
19
+ ··· + 2u + 1
c
6
u
20
+ 2u
19
+ ··· + 2u + 1
c
7
u
20
+ 8u
19
+ ··· − 2u + 1
c
8
, c
10
u
20
+ 5u
19
+ ··· + 4u + 1
c
9
u
20
− 15u
19
+ ··· − 348u + 25
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
20
+ 12y
19
+ ··· − 14y + 1
c
2
, c
6
y
20
− 8y
19
+ ··· + 2y + 1
c
3
y
20
− 2y
19
+ ··· − 6y + 1
c
4
, c
12
y
20
+ 4y
19
+ ··· + 5y + 1
c
5
, c
11
y
20
+ 5y
19
+ ··· + 4y + 1
c
8
, c
10
y
20
+ 17y
19
+ ··· + 20y + 1
c
9
y
20
+ 7y
19
+ ··· − 9504y + 625
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.666143 + 0.783105I
a = −1.27315 + 1.74718I
b = −1.67471 + 0.68682I
1.76978 + 5.48057I −2.80463 − 5.80608I
u = 0.666143 − 0.783105I
a = −1.27315 − 1.74718I
b = −1.67471 − 0.68682I
1.76978 − 5.48057I −2.80463 + 5.80608I
u = −1.040020 + 0.070690I
a = 0.193110 + 1.103820I
b = 0.906546 + 0.225670I
−4.13829 + 5.28856I −10.94237 − 7.77287I
u = −1.040020 − 0.070690I
a = 0.193110 − 1.103820I
b = 0.906546 − 0.225670I
−4.13829 − 5.28856I −10.94237 + 7.77287I
u = 0.714204 + 0.615617I
a = 0.21064 − 1.74863I
b = 1.41852 − 1.64526I
−0.02013 − 4.56194I −4.71384 + 7.99241I
u = 0.714204 − 0.615617I
a = 0.21064 + 1.74863I
b = 1.41852 + 1.64526I
−0.02013 + 4.56194I −4.71384 − 7.99241I
u = −0.698035 + 0.580142I
a = −0.27138 + 1.49983I
b = −0.520510 + 0.448149I
−0.17060 − 2.73692I −3.32837 + 3.91179I
u = −0.698035 − 0.580142I
a = −0.27138 − 1.49983I
b = −0.520510 − 0.448149I
−0.17060 + 2.73692I −3.32837 − 3.91179I
u = 1.120920 + 0.219372I
a = −0.035895 + 0.344729I
b = −0.332239 + 0.792126I
−3.60919 + 1.16294I −14.7378 + 11.3130I
u = 1.120920 − 0.219372I
a = −0.035895 − 0.344729I
b = −0.332239 − 0.792126I
−3.60919 − 1.16294I −14.7378 − 11.3130I
28
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.972477 + 0.632866I
a = 1.46152 − 0.77839I
b = 1.301680 + 0.237230I
−0.839247 − 0.384926I −6.85126 − 2.25388I
u = 0.972477 − 0.632866I
a = 1.46152 + 0.77839I
b = 1.301680 − 0.237230I
−0.839247 + 0.384926I −6.85126 + 2.25388I
u = −0.991864 + 0.607465I
a = 0.928383 − 0.088421I
b = 1.70546 − 0.09808I
−1.12841 + 7.50023I −4.46736 − 9.20296I
u = −0.991864 − 0.607465I
a = 0.928383 + 0.088421I
b = 1.70546 + 0.09808I
−1.12841 − 7.50023I −4.46736 + 9.20296I
u = −0.869777 + 0.801650I
a = −0.679339 − 1.075670I
b = −1.202540 − 0.582098I
4.47518 + 2.98841I 6.85305 − 4.79073I
u = −0.869777 − 0.801650I
a = −0.679339 + 1.075670I
b = −1.202540 + 0.582098I
4.47518 − 2.98841I 6.85305 + 4.79073I
u = 1.013830 + 0.698724I
a = −1.55497 + 1.69525I
b = −2.43716 + 1.26705I
0.71948 − 11.08790I −5.09964 + 10.57150I
u = 1.013830 − 0.698724I
a = −1.55497 − 1.69525I
b = −2.43716 − 1.26705I
0.71948 + 11.08790I −5.09964 − 10.57150I
u = 0.112132 + 0.472540I
a = −1.47892 + 0.01768I
b = 0.334951 − 0.743675I
−0.34843 − 3.78733I −1.90782 + 6.91613I
u = 0.112132 − 0.472540I
a = −1.47892 − 0.01768I
b = 0.334951 + 0.743675I
−0.34843 + 3.78733I −1.90782 − 6.91613I
29
IV. I
u
4
= h−2u
2
+ b − u + 1, −2u
2
+ a − u, u
3
+ u
2
− 1i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
3
=
1
u
2
a
1
=
−u
2
+ 1
−u
2
− u + 1
a
10
=
2u
2
+ u
2u
2
+ u − 1
a
11
=
u
2
+ u + 1
u
2
a
6
=
u
u
a
8
=
u
2
− 1
u
2
+ u − 1
a
4
=
u
u
a
5
=
−u
2
+ u + 2
−u
2
+ 2
a
12
=
u
2
+ u + 2
u
2
+ 1
a
9
=
2u
2
+ u
2u
2
+ u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 2u
2
− u − 2
30
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
3
− u
2
+ 2u − 1
c
2
u
3
+ u
2
− 1
c
4
, c
5
, c
6
u
3
− u
2
+ 1
c
7
u
3
+ u
2
+ 2u + 1
c
8
, c
10
(u + 1)
3
c
9
u
3
c
11
, c
12
u
3
− u − 1
31
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
7
y
3
+ 3y
2
+ 2y −1
c
2
, c
4
, c
5
c
6
y
3
− y
2
+ 2y −1
c
8
, c
10
(y −1)
3
c
9
y
3
c
11
, c
12
y
3
− 2y
2
+ y −1
32
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.877439 + 0.744862I
a = −0.44728 − 1.86942I
b = −1.44728 − 1.86942I
4.66906 + 2.82812I −0.69240 − 3.35914I
u = −0.877439 − 0.744862I
a = −0.44728 + 1.86942I
b = −1.44728 + 1.86942I
4.66906 − 2.82812I −0.69240 + 3.35914I
u = 0.754878
a = 1.89456
b = 0.894558
0.531480 −1.61520
33
V. I
u
5
= h−u
2
+ b − 2u, −u
2
+ a − u + 1, u
3
+ u
2
− 1i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
3
=
1
u
2
a
1
=
−u
2
+ 1
−u
2
− u + 1
a
10
=
u
2
+ u − 1
u
2
+ 2u
a
11
=
u
u + 1
a
6
=
u
u
a
8
=
u
2
− 1
u
2
+ u − 1
a
4
=
u
u
a
5
=
u
2
+ u − 1
−2
a
12
=
−u
2
+ u
−u
2
+ u + 1
a
9
=
u
2
+ u − 1
u
2
+ 2u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 2u
2
− u − 2
34
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
3
− u
2
+ 2u − 1
c
2
u
3
+ u
2
− 1
c
4
, c
5
u
3
− u − 1
c
6
, c
11
, c
12
u
3
− u
2
+ 1
c
7
u
3
+ u
2
+ 2u + 1
c
8
, c
10
(u + 1)
3
c
9
u
3
35
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
7
y
3
+ 3y
2
+ 2y −1
c
2
, c
6
, c
11
c
12
y
3
− y
2
+ 2y −1
c
4
, c
5
y
3
− 2y
2
+ y −1
c
8
, c
10
(y −1)
3
c
9
y
3
36
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.877439 + 0.744862I
a = −1.66236 − 0.56228I
b = −1.53980 + 0.18258I
4.66906 + 2.82812I −0.69240 − 3.35914I
u = −0.877439 − 0.744862I
a = −1.66236 + 0.56228I
b = −1.53980 − 0.18258I
4.66906 − 2.82812I −0.69240 + 3.35914I
u = 0.754878
a = 0.324718
b = 2.07960
0.531480 −1.61520
37
VI. I
v
1
= ha, b − 1, v + 1i
(i) Arc colorings
a
2
=
1
0
a
7
=
−1
0
a
3
=
1
0
a
1
=
1
0
a
10
=
0
1
a
11
=
1
1
a
6
=
−1
0
a
8
=
−1
0
a
4
=
1
0
a
5
=
−1
1
a
12
=
0
1
a
9
=
0
1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 6
38
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
6
, c
7
, c
9
u
c
4
, c
5
, c
8
c
10
, c
11
, c
12
u − 1
39
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
6
, c
7
, c
9
y
c
4
, c
5
, c
8
c
10
, c
11
, c
12
y −1
40
(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
41
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u(u
3
− u
2
+ 2u − 1)
2
(u
20
− 8u
19
+ ··· + 2u + 1)
· ((u
47
+ 16u
46
+ ··· + 12u + 1)
2
)(u
64
+ 23u
63
+ ··· + 464u + 49)
c
2
u(u
3
+ u
2
− 1)
2
(u
20
− 2u
19
+ ··· − 2u + 1)
· ((u
47
+ 2u
46
+ ··· + 6u
2
− 1)
2
)(u
64
− 5u
63
+ ··· − 46u + 7)
c
3
u(u
3
− u
2
+ 2u − 1)
2
(u
20
− u
18
+ ··· − 3u
2
+ 1)
· ((u
47
− 2u
46
+ ··· + 122u − 37)
2
)(u
64
+ 7u
63
+ ··· − 34358u + 14287)
c
4
, c
12
(u − 1)(u
3
− u − 1)(u
3
− u
2
+ 1)(u
20
− 2u
19
+ ··· − u + 1)
· (u
64
+ 3u
63
+ ··· − u − 1)(u
94
+ 10u
92
+ ··· − 7u + 1)
c
5
, c
11
(u − 1)(u
3
− u − 1)(u
3
− u
2
+ 1)(u
20
+ u
19
+ ··· + 2u + 1)
· (u
64
+ 2u
63
+ ··· − 2u + 1)(u
94
− 4u
92
+ ··· − 18201u + 761)
c
6
u(u
3
− u
2
+ 1)
2
(u
20
+ 2u
19
+ ··· + 2u + 1)
· ((u
47
+ 2u
46
+ ··· + 6u
2
− 1)
2
)(u
64
− 5u
63
+ ··· − 46u + 7)
c
7
u(u
3
+ u
2
+ 2u + 1)
2
(u
20
+ 8u
19
+ ··· − 2u + 1)
· ((u
47
+ 16u
46
+ ··· + 12u + 1)
2
)(u
64
+ 23u
63
+ ··· + 464u + 49)
c
8
, c
10
(u − 1)(u + 1)
6
(u
20
+ 5u
19
+ ··· + 4u + 1)(u
64
− 10u
63
+ ··· + 14u + 1)
· (u
94
+ 7u
93
+ ··· + 74u + 19)
c
9
u
7
(u
20
− 15u
19
+ ··· − 348u + 25)(u
47
+ 23u
46
+ ··· + 12u + 8)
2
· (u
64
− 34u
63
+ ··· + 22u − 7)
42
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
y(y
3
+ 3y
2
+ 2y −1)
2
(y
20
+ 12y
19
+ ··· − 14y + 1)
· ((y
47
+ 32y
46
+ ··· + 12y −1)
2
)(y
64
+ 41y
63
+ ··· + 127704y + 2401)
c
2
, c
6
y(y
3
− y
2
+ 2y −1)
2
(y
20
− 8y
19
+ ··· + 2y + 1)
· ((y
47
− 16y
46
+ ··· + 12y −1)
2
)(y
64
− 23y
63
+ ··· − 464y + 49)
c
3
y(y
3
+ 3y
2
+ 2y −1)
2
(y
20
− 2y
19
+ ··· − 6y + 1)
· (y
47
− 16y
46
+ ··· + 37824y −1369)
2
· (y
64
− 21y
63
+ ··· − 4975613696y + 204118369)
c
4
, c
12
(y −1)(y
3
− 2y
2
+ y −1)(y
3
− y
2
+ 2y −1)(y
20
+ 4y
19
+ ··· + 5y + 1)
· (y
64
− 35y
63
+ ··· − 77y + 1)(y
94
+ 20y
93
+ ··· + 9y + 1)
c
5
, c
11
(y −1)(y
3
− 2y
2
+ y −1)(y
3
− y
2
+ 2y −1)(y
20
+ 5y
19
+ ··· + 4y + 1)
· (y
64
− 14y
63
+ ··· − 14y + 1)
· (y
94
− 8y
93
+ ··· − 190343767y + 579121)
c
8
, c
10
((y −1)
7
)(y
20
+ 17y
19
+ ··· + 20y + 1)(y
64
− 26y
63
+ ··· − 118y + 1)
· (y
94
+ 33y
93
+ ··· − 11366y + 361)
c
9
y
7
(y
20
+ 7y
19
+ ··· − 9504y + 625)(y
47
− 7y
46
+ ··· + 1424y −64)
2
· (y
64
+ 22y
62
+ ··· − 946y + 49)
43
