11a
321
(K11a
321
)
A knot diagram
1
Linearized knot diagam
7 9 1 8 10 2 11 3 5 6 4
Solving Sequence
5,9
10 6
3,11
2 7 1 8 4
c
9
c
5
c
10
c
2
c
6
c
1
c
8
c
4
c
3
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h1073u
25
+ 10099u
24
+ ··· + 16b − 21648, −299u
25
− 2899u
24
+ ··· + 32a + 7504,
u
26
+ 11u
25
+ ··· + 16u − 32i
I
u
2
= hu
3
a + u
4
− u
3
− au − u
2
+ b − a, u
3
a − u
4
+ 2u
3
+ a
2
− au + 2u
2
− 2a − 4u, u
5
− u
4
− 2u
3
+ u
2
+ u + 1i
I
u
3
= h−325652548336533a
7
u
4
− 216522091497175a
6
u
4
+ ··· + 461842568426094a − 37300538969198,
2a
7
u
4
+ 3a
6
u
4
+ ··· + 63a + 36, u
5
− u
4
− 2u
3
+ u
2
+ u + 1i
I
u
4
= hu
15
− 2u
14
− 8u
13
+ 16u
12
+ 23u
11
− 49u
10
− 30u
9
+ 74u
8
+ 21u
7
− 63u
6
− 11u
5
+ 33u
4
+ 3u
3
− 9u
2
+ b + 2,
− u
14
+ u
13
+ 8u
12
− 8u
11
− 24u
10
+ 24u
9
+ 36u
8
− 34u
7
− 34u
6
+ 25u
5
+ 24u
4
− 9u
3
− 10u
2
+ a + 3,
u
16
− 9u
14
+ u
13
+ 33u
12
− 6u
11
− 64u
10
+ 13u
9
+ 73u
8
− 12u
7
− 52u
6
+ 4u
5
+ 22u
4
− 4u
2
+ 1i
* 4 irreducible components of dim
C
= 0, with total 92 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
= h1073u
25
+ 10099u
24
+ · · · + 16b − 21648, −299u
25
− 2899u
24
+ · · · +
32a + 7504, u
26
+ 11u
25
+ · · · + 16u − 32i
(i) Arc colorings
a
5
=
0
u
a
9
=
1
0
a
10
=
1
−u
2
a
6
=
u
−u
3
+ u
a
3
=
299
32
u
25
+
2899
32
u
24
+ ··· + 301u −
469
2
−67.0625u
25
− 631.188u
24
+ ··· − 1534u + 1353
a
11
=
−u
2
+ 1
u
4
− 2u
2
a
2
=
2445
32
u
25
+
23097
32
u
24
+ ··· + 1835u −
3175
2
−67.0625u
25
− 631.188u
24
+ ··· − 1534u + 1353
a
7
=
−13.7500u
25
− 133.250u
24
+ ··· − 383.500u + 320.500
4u
25
+ 42u
24
+ ··· +
377
2
u − 136
a
1
=
1181
16
u
25
+
5595
8
u
24
+ ··· + 1708u − 1515
107
16
u
25
+
871
16
u
24
+ ··· − 43u − 22
a
8
=
39
4
u
25
+
365
4
u
24
+ ··· + 197u −
367
2
−4u
25
− 42u
24
+ ··· −
375
2
u + 136
a
4
=
5
4
u
25
+
75
4
u
24
+ ··· +
863
4
u − 128
185
4
u
25
+
891
2
u
24
+ ··· + 1245u − 1048
a
4
=
5
4
u
25
+
75
4
u
24
+ ··· +
863
4
u − 128
185
4
u
25
+
891
2
u
24
+ ··· + 1245u − 1048
(ii) Obstruction class = −1
(iii) Cusp Shapes =
333
2
u
25
+ 1571u
24
+ ··· + 3724u − 3326
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
c
8
u
26
+ 7u
24
+ ··· + 3u − 1
c
3
, c
11
u
26
− 12u
25
+ ··· − 448u + 32
c
4
, c
7
u
26
− 9u
24
+ ··· − 16u
2
− 1
c
5
, c
9
, c
10
u
26
+ 11u
25
+ ··· + 16u − 32
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
8
y
26
+ 14y
25
+ ··· − y + 1
c
3
, c
11
y
26
+ 10y
25
+ ··· − 27136y + 1024
c
4
, c
7
y
26
− 18y
25
+ ··· + 32y + 1
c
5
, c
9
, c
10
y
26
− 23y
25
+ ··· − 5888y + 1024
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.383322 + 0.913347I
a = 0.15913 − 1.78657I
b = −0.55889 − 1.30495I
−2.65503 + 11.68360I 5.29865 − 8.17521I
u = 0.383322 − 0.913347I
a = 0.15913 + 1.78657I
b = −0.55889 + 1.30495I
−2.65503 − 11.68360I 5.29865 + 8.17521I
u = −0.828242 + 0.616056I
a = 0.43855 + 1.53930I
b = −0.081709 + 0.666053I
−1.85940 − 2.41843I 9.7124 + 14.3057I
u = −0.828242 − 0.616056I
a = 0.43855 − 1.53930I
b = −0.081709 − 0.666053I
−1.85940 + 2.41843I 9.7124 − 14.3057I
u = 0.317740 + 0.989994I
a = −0.13580 + 1.61988I
b = 0.424496 + 1.163430I
−5.41034 + 5.29072I 3.13484 − 6.09748I
u = 0.317740 − 0.989994I
a = −0.13580 − 1.61988I
b = 0.424496 − 1.163430I
−5.41034 − 5.29072I 3.13484 + 6.09748I
u = 0.867391 + 0.763321I
a = 0.748452 − 0.780722I
b = 0.380945 − 1.145790I
−1.25182 − 6.02050I 5.93358 + 4.78066I
u = 0.867391 − 0.763321I
a = 0.748452 + 0.780722I
b = 0.380945 + 1.145790I
−1.25182 + 6.02050I 5.93358 − 4.78066I
u = 0.604803 + 0.424043I
a = 0.576639 + 0.245391I
b = 0.695203 − 0.396515I
3.26437 + 1.57845I 12.40306 − 2.05363I
u = 0.604803 − 0.424043I
a = 0.576639 − 0.245391I
b = 0.695203 + 0.396515I
3.26437 − 1.57845I 12.40306 + 2.05363I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.155329 + 0.682857I
a = −0.12123 − 1.47536I
b = −0.595161 − 0.658480I
1.79534 + 1.92657I 9.32234 − 4.27733I
u = 0.155329 − 0.682857I
a = −0.12123 + 1.47536I
b = −0.595161 + 0.658480I
1.79534 − 1.92657I 9.32234 + 4.27733I
u = 1.081110 + 0.752925I
a = −0.476440 + 0.754455I
b = −0.236698 + 1.023340I
−3.21650 + 0.73193I 6.23274 + 2.78423I
u = 1.081110 − 0.752925I
a = −0.476440 − 0.754455I
b = −0.236698 − 1.023340I
−3.21650 − 0.73193I 6.23274 − 2.78423I
u = −1.37365 + 0.35020I
a = −0.829144 − 1.069810I
b = 0.726167 − 0.875974I
6.54594 − 5.84781I 12.9077 + 6.2870I
u = −1.37365 − 0.35020I
a = −0.829144 + 1.069810I
b = 0.726167 + 0.875974I
6.54594 + 5.84781I 12.9077 − 6.2870I
u = −1.47715
a = −0.340449
b = 0.812944
7.01191 13.1000
u = −1.51143 + 0.09637I
a = 0.142803 + 0.338489I
b = −0.920008 − 0.217229I
10.23750 − 3.38664I 16.0962 + 0.I
u = −1.51143 − 0.09637I
a = 0.142803 − 0.338489I
b = −0.920008 + 0.217229I
10.23750 + 3.38664I 16.0962 + 0.I
u = −1.47229 + 0.38599I
a = 0.852447 + 0.991797I
b = −0.618131 + 1.238700I
0.31031 − 10.20530I 7.00000 + 6.34949I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.47229 − 0.38599I
a = 0.852447 − 0.991797I
b = −0.618131 − 1.238700I
0.31031 + 10.20530I 7.00000 − 6.34949I
u = −1.48560 + 0.35379I
a = −0.921287 − 1.008460I
b = 0.73457 − 1.37086I
3.3294 − 16.2583I 0. + 8.72442I
u = −1.48560 − 0.35379I
a = −0.921287 + 1.008460I
b = 0.73457 + 1.37086I
3.3294 + 16.2583I 0. − 8.72442I
u = 0.423114
a = 0.218860
b = −0.331232
0.617191 16.1820
u = −1.71146 + 0.07064I
a = −0.123322 − 0.123466I
b = −0.191640 − 0.759101I
8.12481 + 2.87714I 0
u = −1.71146 − 0.07064I
a = −0.123322 + 0.123466I
b = −0.191640 + 0.759101I
8.12481 − 2.87714I 0
7
II. I
u
2
= hu
3
a + u
4
− u
3
− au − u
2
+ b − a, u
3
a − u
4
+ 2u
3
+ a
2
− au + 2u
2
−
2a − 4u, u
5
− u
4
− 2u
3
+ u
2
+ u + 1i
(i) Arc colorings
a
5
=
0
u
a
9
=
1
0
a
10
=
1
−u
2
a
6
=
u
−u
3
+ u
a
3
=
a
−u
3
a − u
4
+ u
3
+ au + u
2
+ a
a
11
=
−u
2
+ 1
u
4
− 2u
2
a
2
=
u
3
a + u
4
− u
3
− au − u
2
−u
3
a − u
4
+ u
3
+ au + u
2
+ a
a
7
=
u
4
a − u
3
a − u
2
a − u
3
− u
2
+ 3u
u
2
− 2
a
1
=
−u
4
+ u
2
a + u
3
+ u
2
− a − u + 1
−u
4
a + 2u
2
a − u
2
+ u + 1
a
8
=
−u
3
a + au + a + u − 1
−u
4
− u
2
a + 3u
2
− 1
a
4
=
−u
3
a − u
4
+ 2au + 2u
2
− 1
−a − u
a
4
=
−u
3
a − u
4
+ 2au + 2u
2
− 1
−a − u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −8u
3
+ 16u + 10
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
c
8
u
10
+ 2u
9
+ ··· + 8u + 17
c
3
, c
11
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
2
c
4
, c
7
u
10
+ 2u
9
+ 3u
8
+ 4u
6
+ 15u
4
− 16u
3
+ 33u
2
− 20u + 7
c
5
, c
9
, c
10
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
2
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
8
y
10
+ 6y
9
+ ··· + 786y + 289
c
3
, c
11
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
2
c
4
, c
7
y
10
+ 2y
9
+ ··· + 62y + 49
c
5
, c
9
, c
10
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
2
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.21774
a = 1.29401 + 0.59312I
b = −0.466896 + 0.941886I
−0.132640 4.96230
u = −1.21774
a = 1.29401 − 0.59312I
b = −0.466896 − 0.941886I
−0.132640 4.96230
u = −0.309916 + 0.549911I
a = −0.422523 − 1.226950I
b = 0.617609 − 1.263280I
−4.27660 − 3.06116I 3.03023 + 8.86130I
u = −0.309916 + 0.549911I
a = 1.86122 + 1.78470I
b = −0.060281 + 1.331670I
−4.27660 − 3.06116I 3.03023 + 8.86130I
u = −0.309916 − 0.549911I
a = −0.422523 + 1.226950I
b = 0.617609 + 1.263280I
−4.27660 + 3.06116I 3.03023 − 8.86130I
u = −0.309916 − 0.549911I
a = 1.86122 − 1.78470I
b = −0.060281 − 1.331670I
−4.27660 + 3.06116I 3.03023 − 8.86130I
u = 1.41878 + 0.21917I
a = 1.00071 − 1.33190I
b = −0.547449 − 1.293710I
6.81032 + 8.80167I 11.48863 − 6.99717I
u = 1.41878 + 0.21917I
a = −0.233411 + 0.238092I
b = 1.45702 − 0.30917I
6.81032 + 8.80167I 11.48863 − 6.99717I
u = 1.41878 − 0.21917I
a = 1.00071 + 1.33190I
b = −0.547449 + 1.293710I
6.81032 − 8.80167I 11.48863 + 6.99717I
u = 1.41878 − 0.21917I
a = −0.233411 − 0.238092I
b = 1.45702 + 0.30917I
6.81032 − 8.80167I 11.48863 + 6.99717I
11
III. I
u
3
= h−3.26 × 10
14
a
7
u
4
− 2.17 × 10
14
a
6
u
4
+ · · · + 4.62 × 10
14
a − 3.73 ×
10
13
, 2a
7
u
4
+ 3a
6
u
4
+ · · · + 63a + 36, u
5
− u
4
− 2u
3
+ u
2
+ u + 1i
(i) Arc colorings
a
5
=
0
u
a
9
=
1
0
a
10
=
1
−u
2
a
6
=
u
−u
3
+ u
a
3
=
a
1.78373a
7
u
4
+ 1.18598a
6
u
4
+ ··· − 2.52970a + 0.204311
a
11
=
−u
2
+ 1
u
4
− 2u
2
a
2
=
−1.78373a
7
u
4
− 1.18598a
6
u
4
+ ··· + 3.52970a − 0.204311
1.78373a
7
u
4
+ 1.18598a
6
u
4
+ ··· − 2.52970a + 0.204311
a
7
=
−0.513662a
7
u
4
− 0.154648a
6
u
4
+ ··· + 1.00013a + 0.425409
0.452703a
7
u
4
+ 0.296357a
6
u
4
+ ··· − 0.697071a − 0.200491
a
1
=
−0.431150a
7
u
4
− 0.236002a
6
u
4
+ ··· + 1.67334a − 0.859074
1.74389a
7
u
4
+ 0.846631a
6
u
4
+ ··· − 3.09895a + 1.01675
a
8
=
0.158932a
7
u
4
+ 0.0166854a
6
u
4
+ ··· + 0.0570178a + 1.29770
0.0505083a
7
u
4
− 0.709704a
6
u
4
+ ··· + 0.671481a + 1.16410
a
4
=
−0.381857a
7
u
4
+ 0.0243899a
6
u
4
+ ··· + 1.70012a + 0.510808
−1.20422a
7
u
4
− 0.158188a
6
u
4
+ ··· + 1.44338a − 0.285170
a
4
=
−0.381857a
7
u
4
+ 0.0243899a
6
u
4
+ ··· + 1.70012a + 0.510808
−1.20422a
7
u
4
− 0.158188a
6
u
4
+ ··· + 1.44338a − 0.285170
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
52949256522924
91283920109957
a
7
u
4
+
90213951943262
91283920109957
a
6
u
4
+ ··· +
111428618111312
91283920109957
a +
970857959574538
91283920109957
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
c
8
u
40
− u
39
+ ··· + 112u + 32
c
3
, c
11
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
8
c
4
, c
7
u
40
− 7u
39
+ ··· + 80u + 32
c
5
, c
9
, c
10
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
8
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
8
y
40
+ 29y
39
+ ··· + 8960y + 1024
c
3
, c
11
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
8
c
4
, c
7
y
40
+ 5y
39
+ ··· + 9984y + 1024
c
5
, c
9
, c
10
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
8
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.21774
a = −1.207790 + 0.238764I
b = 1.020160 + 0.833032I
3.33884 + 4.40083I 8.22546 − 3.49859I
u = −1.21774
a = −1.207790 − 0.238764I
b = 1.020160 − 0.833032I
3.33884 − 4.40083I 8.22546 + 3.49859I
u = −1.21774
a = 0.256260 + 0.476517I
b = −0.23486 + 1.89553I
−2.20462 − 1.53058I 3.99626 + 4.43065I
u = −1.21774
a = 0.256260 − 0.476517I
b = −0.23486 − 1.89553I
−2.20462 + 1.53058I 3.99626 − 4.43065I
u = −1.21774
a = 0.40240 + 1.64523I
b = −0.00279 + 1.47385I
−2.20462 + 1.53058I 3.99626 − 4.43065I
u = −1.21774
a = 0.40240 − 1.64523I
b = −0.00279 − 1.47385I
−2.20462 − 1.53058I 3.99626 + 4.43065I
u = −1.21774
a = −1.80751 + 0.70455I
b = 0.067800 + 0.664970I
3.33884 − 4.40083I 8.22546 + 3.49859I
u = −1.21774
a = −1.80751 − 0.70455I
b = 0.067800 − 0.664970I
3.33884 + 4.40083I 8.22546 − 3.49859I
u = −0.309916 + 0.549911I
a = −0.614210 − 0.356072I
b = −1.112460 − 0.022805I
1.26686 − 5.93141I 7.25943 + 7.92923I
u = −0.309916 + 0.549911I
a = −0.077663 + 0.645448I
b = 0.540737 − 0.024289I
−2.20462 − 1.53058I 3.99626 + 4.43065I
15
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.309916 + 0.549911I
a = −0.69063 − 1.44845I
b = −0.631776 − 0.881136I
1.26686 + 2.87025I 7.25943 + 0.93206I
u = −0.309916 + 0.549911I
a = 0.72433 + 1.72452I
b = −0.28691 + 1.51546I
−4.27660 3.03023 + 0.I
u = −0.309916 + 0.549911I
a = −1.94655 − 0.78265I
b = −0.060228 − 1.074110I
−4.27660 3.03023 + 0.I
u = −0.309916 + 0.549911I
a = 0.72536 − 2.06070I
b = 0.330888 − 0.359958I
1.26686 + 2.87025I 7.25943 + 0.93206I
u = −0.309916 + 0.549911I
a = 0.50296 + 2.30075I
b = −0.127790 + 1.025730I
−2.20462 − 1.53058I 3.99626 + 4.43065I
u = −0.309916 + 0.549911I
a = −0.41156 − 2.99999I
b = 0.451097 − 1.069650I
1.26686 − 5.93141I 7.25943 + 7.92923I
u = −0.309916 − 0.549911I
a = −0.614210 + 0.356072I
b = −1.112460 + 0.022805I
1.26686 + 5.93141I 7.25943 − 7.92923I
u = −0.309916 − 0.549911I
a = −0.077663 − 0.645448I
b = 0.540737 + 0.024289I
−2.20462 + 1.53058I 3.99626 − 4.43065I
u = −0.309916 − 0.549911I
a = −0.69063 + 1.44845I
b = −0.631776 + 0.881136I
1.26686 − 2.87025I 7.25943 − 0.93206I
u = −0.309916 − 0.549911I
a = 0.72433 − 1.72452I
b = −0.28691 − 1.51546I
−4.27660 3.03023 + 0.I
16
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.309916 − 0.549911I
a = −1.94655 + 0.78265I
b = −0.060228 + 1.074110I
−4.27660 3.03023 + 0.I
u = −0.309916 − 0.549911I
a = 0.72536 + 2.06070I
b = 0.330888 + 0.359958I
1.26686 − 2.87025I 7.25943 − 0.93206I
u = −0.309916 − 0.549911I
a = 0.50296 − 2.30075I
b = −0.127790 − 1.025730I
−2.20462 + 1.53058I 3.99626 − 4.43065I
u = −0.309916 − 0.549911I
a = −0.41156 + 2.99999I
b = 0.451097 + 1.069650I
1.26686 + 5.93141I 7.25943 − 7.92923I
u = 1.41878 + 0.21917I
a = −0.862919 + 0.408494I
b = 0.68021 + 1.39772I
1.26686 + 2.87025I 7.25943 + 0.93206I
u = 1.41878 + 0.21917I
a = 0.787041 − 0.329401I
b = −1.02988 − 1.04062I
1.26686 + 5.93141I 7.25943 − 7.92923I
u = 1.41878 + 0.21917I
a = 1.194210 + 0.076658I
b = −0.161461 − 0.775177I
1.26686 + 2.87025I 7.25943 + 0.93206I
u = 1.41878 + 0.21917I
a = 0.407015 − 1.193670I
b = −0.464952 − 0.997444I
6.81032 11.48863 + 0.I
u = 1.41878 + 0.21917I
a = −0.808970 + 1.033880I
b = 0.427482 + 1.218940I
3.33884 + 4.40083I 8.22546 − 3.49859I
u = 1.41878 + 0.21917I
a = −1.37363 + 0.36155I
b = 0.228681 + 1.161970I
1.26686 + 5.93141I 7.25943 − 7.92923I
17
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.41878 + 0.21917I
a = 0.307395 − 0.017583I
b = −0.982401 + 0.242528I
3.33884 + 4.40083I 8.22546 − 3.49859I
u = 1.41878 + 0.21917I
a = −0.0055411 − 0.0806818I
b = 0.848456 − 0.805185I
6.81032 11.48863 + 0.I
u = 1.41878 − 0.21917I
a = −0.862919 − 0.408494I
b = 0.68021 − 1.39772I
1.26686 − 2.87025I 7.25943 − 0.93206I
u = 1.41878 − 0.21917I
a = 0.787041 + 0.329401I
b = −1.02988 + 1.04062I
1.26686 − 5.93141I 7.25943 + 7.92923I
u = 1.41878 − 0.21917I
a = 1.194210 − 0.076658I
b = −0.161461 + 0.775177I
1.26686 − 2.87025I 7.25943 − 0.93206I
u = 1.41878 − 0.21917I
a = 0.407015 + 1.193670I
b = −0.464952 + 0.997444I
6.81032 11.48863 + 0.I
u = 1.41878 − 0.21917I
a = −0.808970 − 1.033880I
b = 0.427482 − 1.218940I
3.33884 − 4.40083I 8.22546 + 3.49859I
u = 1.41878 − 0.21917I
a = −1.37363 − 0.36155I
b = 0.228681 − 1.161970I
1.26686 − 5.93141I 7.25943 + 7.92923I
u = 1.41878 − 0.21917I
a = 0.307395 + 0.017583I
b = −0.982401 − 0.242528I
3.33884 − 4.40083I 8.22546 + 3.49859I
u = 1.41878 − 0.21917I
a = −0.0055411 + 0.0806818I
b = 0.848456 + 0.805185I
6.81032 11.48863 + 0.I
18
IV.
I
u
4
= hu
15
−2u
14
+· · ·+b+2, −u
14
+u
13
+· · ·+a+3, u
16
−9u
14
+· · ·−4u
2
+1i
(i) Arc colorings
a
5
=
0
u
a
9
=
1
0
a
10
=
1
−u
2
a
6
=
u
−u
3
+ u
a
3
=
u
14
− u
13
+ ··· + 10u
2
− 3
−u
15
+ 2u
14
+ ··· + 9u
2
− 2
a
11
=
−u
2
+ 1
u
4
− 2u
2
a
2
=
u
15
− u
14
+ ··· + u
2
− 1
−u
15
+ 2u
14
+ ··· + 9u
2
− 2
a
7
=
−u
14
− u
13
+ ··· − u + 2
u
13
− 7u
11
+ ··· + 3u − 1
a
1
=
u
15
− u
14
+ ··· − 3u + 1
2u
15
− 2u
14
+ ··· − u + 1
a
8
=
−u
14
+ 8u
12
+ ··· − 12u
2
+ 2
u
13
− 7u
11
+ ··· + 2u − 1
a
4
=
−u
13
+ 7u
11
− u
10
− 18u
9
+ 4u
8
+ 21u
7
− 4u
6
− 12u
5
+ 2u
3
+ u
2
+ 3u
−u
15
+ 2u
14
+ ··· + 3u − 2
a
4
=
−u
13
+ 7u
11
− u
10
− 18u
9
+ 4u
8
+ 21u
7
− 4u
6
− 12u
5
+ 2u
3
+ u
2
+ 3u
−u
15
+ 2u
14
+ ··· + 3u − 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = u
15
− 5u
14
− 11u
13
+ 38u
12
+ 42u
11
− 112u
10
− 77u
9
+ 161u
8
+
82u
7
− 122u
6
− 63u
5
+ 48u
4
+ 28u
3
+ 2u + 5
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
u
16
+ 8u
14
+ ··· − u + 1
c
2
, c
6
u
16
+ 8u
14
+ ··· + u + 1
c
3
u
16
+ 3u
15
+ ··· + 5u
2
+ 1
c
4
, c
7
u
16
− 3u
13
− u
12
− u
11
+ 8u
8
+ 2u
7
+ 6u
6
+ 3u
5
+ 10u
4
+ 3u
2
+ 1
c
5
u
16
− 9u
14
+ ··· − 4u
2
+ 1
c
9
, c
10
u
16
− 9u
14
+ ··· − 4u
2
+ 1
c
11
u
16
− 3u
15
+ ··· + 5u
2
+ 1
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
8
y
16
+ 16y
15
+ ··· + 13y + 1
c
3
, c
11
y
16
+ 7y
15
+ ··· + 10y + 1
c
4
, c
7
y
16
− 2y
14
+ ··· + 6y + 1
c
5
, c
9
, c
10
y
16
− 18y
15
+ ··· − 8y + 1
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.932576 + 0.558604I
a = 0.83677 − 1.43673I
b = −0.031814 − 0.697076I
−2.00312 + 2.11071I −0.36261 + 5.84578I
u = 0.932576 − 0.558604I
a = 0.83677 + 1.43673I
b = −0.031814 + 0.697076I
−2.00312 − 2.11071I −0.36261 − 5.84578I
u = −0.758635 + 0.439917I
a = −0.543641 − 0.719000I
b = 0.033972 − 1.283280I
−4.35479 − 2.08547I 2.28739 + 3.71145I
u = −0.758635 − 0.439917I
a = −0.543641 + 0.719000I
b = 0.033972 + 1.283280I
−4.35479 + 2.08547I 2.28739 − 3.71145I
u = −1.270170 + 0.042100I
a = −0.117828 − 1.114430I
b = −0.13344 − 1.70790I
−1.36561 + 1.03179I 13.09233 + 0.83056I
u = −1.270170 − 0.042100I
a = −0.117828 + 1.114430I
b = −0.13344 + 1.70790I
−1.36561 − 1.03179I 13.09233 − 0.83056I
u = 1.299950 + 0.158892I
a = −1.49957 + 0.33616I
b = 0.717514 + 0.694169I
4.26074 + 5.75964I 11.30648 − 7.65537I
u = 1.299950 − 0.158892I
a = −1.49957 − 0.33616I
b = 0.717514 − 0.694169I
4.26074 − 5.75964I 11.30648 + 7.65537I
u = 1.44241 + 0.18942I
a = 0.942839 − 0.151798I
b = −0.559613 − 1.118820I
1.52375 + 4.32708I 9.46348 − 3.89019I
u = 1.44241 − 0.18942I
a = 0.942839 + 0.151798I
b = −0.559613 + 1.118820I
1.52375 − 4.32708I 9.46348 + 3.89019I
22
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.389768 + 0.361348I
a = −1.42793 − 0.61604I
b = 0.199143 − 1.346600I
−4.35506 − 1.95343I 2.10403 + 1.81382I
u = −0.389768 − 0.361348I
a = −1.42793 + 0.61604I
b = 0.199143 + 1.346600I
−4.35506 + 1.95343I 2.10403 − 1.81382I
u = 0.380311 + 0.321242I
a = −1.37704 + 2.58113I
b = −0.462275 + 0.600749I
1.00222 − 3.96560I 4.29089 + 5.86867I
u = 0.380311 − 0.321242I
a = −1.37704 − 2.58113I
b = −0.462275 − 0.600749I
1.00222 + 3.96560I 4.29089 − 5.86867I
u = −1.63668 + 0.04505I
a = 0.186402 + 0.341093I
b = 0.236509 + 0.446950I
8.58175 + 2.59504I 15.8180 + 1.0523I
u = −1.63668 − 0.04505I
a = 0.186402 − 0.341093I
b = 0.236509 − 0.446950I
8.58175 − 2.59504I 15.8180 − 1.0523I
23
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
8
(u
10
+ 2u
9
+ ··· + 8u + 17)(u
16
+ 8u
14
+ ··· − u + 1)
· (u
26
+ 7u
24
+ ··· + 3u − 1)(u
40
− u
39
+ ··· + 112u + 32)
c
2
, c
6
(u
10
+ 2u
9
+ ··· + 8u + 17)(u
16
+ 8u
14
+ ··· + u + 1)
· (u
26
+ 7u
24
+ ··· + 3u − 1)(u
40
− u
39
+ ··· + 112u + 32)
c
3
((u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
10
)(u
16
+ 3u
15
+ ··· + 5u
2
+ 1)
· (u
26
− 12u
25
+ ··· − 448u + 32)
c
4
, c
7
(u
10
+ 2u
9
+ 3u
8
+ 4u
6
+ 15u
4
− 16u
3
+ 33u
2
− 20u + 7)
· (u
16
− 3u
13
− u
12
− u
11
+ 8u
8
+ 2u
7
+ 6u
6
+ 3u
5
+ 10u
4
+ 3u
2
+ 1)
· (u
26
− 9u
24
+ ··· − 16u
2
− 1)(u
40
− 7u
39
+ ··· + 80u + 32)
c
5
((u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
10
)(u
16
− 9u
14
+ ··· − 4u
2
+ 1)
· (u
26
+ 11u
25
+ ··· + 16u − 32)
c
9
, c
10
((u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
10
)(u
16
− 9u
14
+ ··· − 4u
2
+ 1)
· (u
26
+ 11u
25
+ ··· + 16u − 32)
c
11
((u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
10
)(u
16
− 3u
15
+ ··· + 5u
2
+ 1)
· (u
26
− 12u
25
+ ··· − 448u + 32)
24
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
8
(y
10
+ 6y
9
+ ··· + 786y + 289)(y
16
+ 16y
15
+ ··· + 13y + 1)
· (y
26
+ 14y
25
+ ··· − y + 1)(y
40
+ 29y
39
+ ··· + 8960y + 1024)
c
3
, c
11
((y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
10
)(y
16
+ 7y
15
+ ··· + 10y + 1)
· (y
26
+ 10y
25
+ ··· − 27136y + 1024)
c
4
, c
7
(y
10
+ 2y
9
+ ··· + 62y + 49)(y
16
− 2y
14
+ ··· + 6y + 1)
· (y
26
− 18y
25
+ ··· + 32y + 1)(y
40
+ 5y
39
+ ··· + 9984y + 1024)
c
5
, c
9
, c
10
((y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
10
)(y
16
− 18y
15
+ ··· − 8y + 1)
· (y
26
− 23y
25
+ ··· − 5888y + 1024)
25
