12a
1037
(K12a
1037
)
A knot diagram
1
Linearized knot diagam
4 7 8 10 12 3 2 11 5 1 6 9
Solving Sequence
2,7
3 8
4,11
9 1 6 12 5 10
c
2
c
7
c
3
c
8
c
1
c
6
c
11
c
5
c
10
c
4
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h9u
38
− 54u
37
+ ··· + 2b − 61u, 3u
38
− 9u
37
+ ··· + 2a + 21, u
39
− 6u
38
+ ··· + 38u − 4i
I
u
2
= h−3949624u
17
a
3
− 3395926u
17
a
2
+ ··· + 4044931a − 2562506, 2u
17
a
3
− 2u
17
a
2
+ ··· − 35a + 20,
u
18
+ u
17
+ ··· − 3u − 1i
I
u
3
= h−u
18
− 2u
17
+ ··· + b + 1, 2u
18
+ 2u
17
+ ··· + a + 1, u
19
+ u
18
+ ··· − 2u − 1i
* 3 irreducible components of dim
C
= 0, with total 130 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
=
h9u
38
−54u
37
+· · ·+2b−61u, 3u
38
−9u
37
+· · ·+2a+21, u
39
−6u
38
+· · ·+38u−4i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
3
=
1
u
2
a
8
=
−u
u
a
4
=
−u
4
− u
2
+ 1
u
4
+ 2u
2
a
11
=
−
3
2
u
38
+
9
2
u
37
+ ··· + 97u −
21
2
−
9
2
u
38
+ 27u
37
+ ··· −
483
2
u
2
+
61
2
u
a
9
=
5
4
u
38
− 6u
37
+ ··· −
293
4
u + 8
3
2
u
38
− 9u
37
+ ··· −
35
2
u + 1
a
1
=
u
8
+ 3u
6
+ u
4
− 2u
2
+ 1
−u
8
− 4u
6
− 4u
4
a
6
=
u
u
3
+ u
a
12
=
3
2
u
38
−
13
2
u
37
+ ··· + 104u −
25
2
5
2
u
38
− 15u
37
+ ··· −
433
2
u + 26
a
5
=
7
4
u
38
− 8u
37
+ ··· −
183
4
u + 6
−
3
2
u
38
+ 5u
37
+ ··· −
5
2
u + 1
a
10
=
−4u
38
+
43
2
u
37
+ ··· +
267
2
u −
29
2
−
5
2
u
38
+ 15u
37
+ ··· +
277
2
u − 16
(ii) Obstruction class = −1
(iii) Cusp Shapes = −15u
38
+ 90u
37
+ ··· + 1046u − 146
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
39
− 8u
38
+ ··· + 6840u + 6208
c
2
, c
6
, c
7
u
39
+ 6u
38
+ ··· + 38u + 4
c
3
u
39
− 6u
38
+ ··· + 2982u + 612
c
4
, c
5
, c
9
c
11
u
39
+ 16u
37
+ ··· + 2u + 1
c
8
, c
10
u
39
+ 3u
38
+ ··· + 7u + 1
c
12
u
39
+ 40u
38
+ ··· + 5898240u + 262144
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
39
+ 24y
38
+ ··· + 872760000y −38539264
c
2
, c
6
, c
7
y
39
+ 36y
38
+ ··· + 236y −16
c
3
y
39
+ 10y
38
+ ··· + 2009772y −374544
c
4
, c
5
, c
9
c
11
y
39
+ 32y
38
+ ··· + 8y −1
c
8
, c
10
y
39
+ 9y
38
+ ··· + 17y −1
c
12
y
39
+ 6y
38
+ ··· + 876173328384y −68719476736
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.621412 + 0.721365I
a = −0.932835 − 0.396053I
b = 0.564441 − 0.374185I
7.47477 − 1.00733I 0.507207 − 0.734789I
u = 0.621412 − 0.721365I
a = −0.932835 + 0.396053I
b = 0.564441 + 0.374185I
7.47477 + 1.00733I 0.507207 + 0.734789I
u = 0.795732 + 0.401330I
a = 0.036813 − 0.325741I
b = 0.905438 + 0.766145I
6.46497 − 3.87487I −4.28170 + 7.09893I
u = 0.795732 − 0.401330I
a = 0.036813 + 0.325741I
b = 0.905438 − 0.766145I
6.46497 + 3.87487I −4.28170 − 7.09893I
u = −0.405140 + 1.083670I
a = −1.234740 − 0.069956I
b = 0.818856 + 0.510836I
5.48677 − 2.23109I 0
u = −0.405140 − 1.083670I
a = −1.234740 + 0.069956I
b = 0.818856 − 0.510836I
5.48677 + 2.23109I 0
u = 0.566335 + 0.612658I
a = 1.17391 + 1.37819I
b = −0.758745 + 0.525385I
9.36820 + 9.41842I −5.95786 − 3.44024I
u = 0.566335 − 0.612658I
a = 1.17391 − 1.37819I
b = −0.758745 − 0.525385I
9.36820 − 9.41842I −5.95786 + 3.44024I
u = 0.732516 + 0.383228I
a = −0.169603 + 0.225290I
b = −1.72263 − 1.08880I
8.5551 − 13.8295I −7.67024 + 8.80490I
u = 0.732516 − 0.383228I
a = −0.169603 − 0.225290I
b = −1.72263 + 1.08880I
8.5551 + 13.8295I −7.67024 − 8.80490I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.783601 + 0.096059I
a = 0.053303 + 0.259416I
b = 0.792876 − 1.059160I
2.48065 + 6.48872I −10.45492 − 8.33183I
u = −0.783601 − 0.096059I
a = 0.053303 − 0.259416I
b = 0.792876 + 1.059160I
2.48065 − 6.48872I −10.45492 + 8.33183I
u = −0.103803 + 1.209710I
a = 0.50605 − 2.21549I
b = −0.99422 + 1.38736I
0.35295 + 1.88325I 0
u = −0.103803 − 1.209710I
a = 0.50605 + 2.21549I
b = −0.99422 − 1.38736I
0.35295 − 1.88325I 0
u = 0.099527 + 1.231270I
a = −0.018915 + 0.867476I
b = 0.177931 − 0.711431I
2.95447 − 1.60320I 0
u = 0.099527 − 1.231270I
a = −0.018915 − 0.867476I
b = 0.177931 + 0.711431I
2.95447 + 1.60320I 0
u = 0.613014 + 0.336552I
a = 0.306076 + 0.500256I
b = 1.107600 + 0.121686I
−0.59947 − 3.61547I −14.0789 + 6.2920I
u = 0.613014 − 0.336552I
a = 0.306076 − 0.500256I
b = 1.107600 − 0.121686I
−0.59947 + 3.61547I −14.0789 − 6.2920I
u = −0.314712 + 1.271460I
a = 0.51202 + 1.94415I
b = 0.25798 − 1.51458I
6.72838 + 10.43640I 0
u = −0.314712 − 1.271460I
a = 0.51202 − 1.94415I
b = 0.25798 + 1.51458I
6.72838 − 10.43640I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.196182 + 1.345270I
a = 1.37134 − 1.61017I
b = −1.43122 + 0.67225I
1.84241 + 3.16143I 0
u = −0.196182 − 1.345270I
a = 1.37134 + 1.61017I
b = −1.43122 − 0.67225I
1.84241 − 3.16143I 0
u = 0.471183 + 0.367555I
a = 0.164394 − 0.998156I
b = −0.313414 − 0.259898I
−0.148043 + 0.231843I −12.86061 + 0.25911I
u = 0.471183 − 0.367555I
a = 0.164394 + 0.998156I
b = −0.313414 + 0.259898I
−0.148043 − 0.231843I −12.86061 − 0.25911I
u = 0.20386 + 1.42529I
a = 0.545416 + 0.979984I
b = −1.12807 − 1.21432I
5.54119 − 2.38108I 0
u = 0.20386 − 1.42529I
a = 0.545416 − 0.979984I
b = −1.12807 + 1.21432I
5.54119 + 2.38108I 0
u = −0.544157 + 0.117730I
a = −0.462056 − 0.632512I
b = −1.46475 − 0.17702I
−2.80387 + 0.48049I −15.5833 − 11.0293I
u = −0.544157 − 0.117730I
a = −0.462056 + 0.632512I
b = −1.46475 + 0.17702I
−2.80387 − 0.48049I −15.5833 + 11.0293I
u = 0.23475 + 1.43146I
a = −1.36069 − 1.22018I
b = 2.12508 + 0.89186I
5.07499 − 6.73147I 0
u = 0.23475 − 1.43146I
a = −1.36069 + 1.22018I
b = 2.12508 − 0.89186I
5.07499 + 6.73147I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.27692 + 1.46170I
a = 1.06115 + 2.55968I
b = −2.14021 − 2.00162I
14.4904 − 17.5068I 0
u = 0.27692 − 1.46170I
a = 1.06115 − 2.55968I
b = −2.14021 + 2.00162I
14.4904 + 17.5068I 0
u = 0.29538 + 1.47814I
a = −0.44941 − 1.62298I
b = 1.08264 + 1.26742I
12.5250 − 7.8307I 0
u = 0.29538 − 1.47814I
a = −0.44941 + 1.62298I
b = 1.08264 − 1.26742I
12.5250 + 7.8307I 0
u = 0.15804 + 1.50183I
a = 0.492863 − 0.131153I
b = 0.409338 + 0.771966I
16.2651 + 6.9065I 0
u = 0.15804 − 1.50183I
a = 0.492863 + 0.131153I
b = 0.409338 − 0.771966I
16.2651 − 6.9065I 0
u = 0.12529 + 1.53061I
a = −0.513286 − 0.068115I
b = −0.160716 − 0.114876I
15.0110 − 3.4153I 0
u = 0.12529 − 1.53061I
a = −0.513286 + 0.068115I
b = −0.160716 + 0.114876I
15.0110 + 3.4153I 0
u = 0.307285
a = 0.836404
b = −0.256404
−0.549271 −17.8940
8
II. I
u
2
= h−3.95 × 10
6
a
3
u
17
− 3.40 × 10
6
a
2
u
17
+ · · · + 4.04 × 10
6
a − 2.56 ×
10
6
, 2u
17
a
3
− 2u
17
a
2
+ · · · − 35a + 20, u
18
+ u
17
+ · · · − 3u − 1i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
3
=
1
u
2
a
8
=
−u
u
a
4
=
−u
4
− u
2
+ 1
u
4
+ 2u
2
a
11
=
a
3.35053a
3
u
17
+ 2.88082a
2
u
17
+ ··· − 3.43138a + 2.17382
a
9
=
−0.326524a
3
u
17
− 0.760371a
2
u
17
+ ··· + 0.486927a + 2.37802
−0.385925a
3
u
17
+ 0.993532a
2
u
17
+ ··· − 1.17433a − 0.846691
a
1
=
u
8
+ 3u
6
+ u
4
− 2u
2
+ 1
−u
8
− 4u
6
− 4u
4
a
6
=
u
u
3
+ u
a
12
=
−0.203610a
3
u
17
− 0.760371a
2
u
17
+ ··· + 3.55812a + 0.378015
3.23037a
3
u
17
+ 2.58904a
2
u
17
+ ··· − 2.53286a + 1.26567
a
5
=
0.340485a
3
u
17
+ 0.00777567a
2
u
17
+ ··· − 0.614410a + 2.33064
1.51848a
3
u
17
+ 2.60572a
2
u
17
+ ··· − 0.901601a − 3.30391
a
10
=
−1.24583a
3
u
17
− 0.857607a
2
u
17
+ ··· + 0.857607a + 1.07142
−2.10677a
3
u
17
− 0.544094a
2
u
17
+ ··· − 1.00647a + 2.61074
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
8518448
1178805
u
17
a
3
−
1539632
1178805
u
17
a
2
+ ··· +
5989952
1178805
a −
19770202
1178805
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
18
− 3u
17
+ ··· − 3u + 3)
4
c
2
, c
6
, c
7
(u
18
− u
17
+ ··· + 3u − 1)
4
c
3
(u
18
+ u
17
+ ··· + 13u − 5)
4
c
4
, c
5
, c
9
c
11
u
72
− u
71
+ ··· − 2u + 1
c
8
, c
10
u
72
− 21u
71
+ ··· − 139378u + 9841
c
12
(u
2
− u + 1)
36
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
18
+ 13y
17
+ ··· − 75y + 9)
4
c
2
, c
6
, c
7
(y
18
+ 17y
17
+ ··· − 7y + 1)
4
c
3
(y
18
+ 5y
17
+ ··· − 39y + 25)
4
c
4
, c
5
, c
9
c
11
y
72
+ 63y
71
+ ··· + 144y + 1
c
8
, c
10
y
72
+ 27y
71
+ ··· + 5486973168y + 96845281
c
12
(y
2
+ y + 1)
36
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.215059 + 1.214380I
a = 0.84158 + 1.15506I
b = −0.634182 − 0.545920I
2.78152 − 1.19685I −9.05526 + 0.16546I
u = 0.215059 + 1.214380I
a = −1.42648 + 0.34743I
b = 1.159740 − 0.702226I
2.78152 − 1.19685I −9.05526 + 0.16546I
u = 0.215059 + 1.214380I
a = 0.47279 + 1.95213I
b = −1.09686 − 1.42735I
2.78152 − 5.25662I −9.05526 + 7.09366I
u = 0.215059 + 1.214380I
a = 1.12086 − 2.19684I
b = −0.24685 + 1.59627I
2.78152 − 5.25662I −9.05526 + 7.09366I
u = 0.215059 − 1.214380I
a = 0.84158 − 1.15506I
b = −0.634182 + 0.545920I
2.78152 + 1.19685I −9.05526 − 0.16546I
u = 0.215059 − 1.214380I
a = −1.42648 − 0.34743I
b = 1.159740 + 0.702226I
2.78152 + 1.19685I −9.05526 − 0.16546I
u = 0.215059 − 1.214380I
a = 0.47279 − 1.95213I
b = −1.09686 + 1.42735I
2.78152 + 5.25662I −9.05526 − 7.09366I
u = 0.215059 − 1.214380I
a = 1.12086 + 2.19684I
b = −0.24685 − 1.59627I
2.78152 + 5.25662I −9.05526 − 7.09366I
u = −0.678984 + 0.355286I
a = −0.159736 + 0.522088I
b = 0.094560 + 0.657341I
3.04600 + 3.68439I −9.06596 − 2.59573I
u = −0.678984 + 0.355286I
a = −0.090805 − 0.507402I
b = 1.283080 − 0.167605I
3.04600 + 7.74416I −9.06596 − 9.52393I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.678984 + 0.355286I
a = −0.447651 − 0.097294I
b = −1.80893 + 1.31318I
3.04600 + 7.74416I −9.06596 − 9.52393I
u = −0.678984 + 0.355286I
a = −0.094718 + 0.246577I
b = 1.160460 − 0.774719I
3.04600 + 3.68439I −9.06596 − 2.59573I
u = −0.678984 − 0.355286I
a = −0.159736 − 0.522088I
b = 0.094560 − 0.657341I
3.04600 − 3.68439I −9.06596 + 2.59573I
u = −0.678984 − 0.355286I
a = −0.090805 + 0.507402I
b = 1.283080 + 0.167605I
3.04600 − 7.74416I −9.06596 + 9.52393I
u = −0.678984 − 0.355286I
a = −0.447651 + 0.097294I
b = −1.80893 − 1.31318I
3.04600 − 7.74416I −9.06596 + 9.52393I
u = −0.678984 − 0.355286I
a = −0.094718 − 0.246577I
b = 1.160460 + 0.774719I
3.04600 − 3.68439I −9.06596 + 2.59573I
u = 0.590027 + 0.406016I
a = −0.747467 + 0.817649I
b = −2.24434 − 0.81502I
7.36099 + 0.14420I −3.68331 + 0.52947I
u = 0.590027 + 0.406016I
a = −0.493746 − 0.244011I
b = 1.61229 + 0.75954I
7.36099 − 3.91557I −3.68331 + 7.45767I
u = 0.590027 + 0.406016I
a = −0.74761 − 1.57796I
b = 0.477339 + 0.169725I
7.36099 + 0.14420I −3.68331 + 0.52947I
u = 0.590027 + 0.406016I
a = 0.58284 + 1.91894I
b = −1.28763 + 1.09338I
7.36099 − 3.91557I −3.68331 + 7.45767I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.590027 − 0.406016I
a = −0.747467 − 0.817649I
b = −2.24434 + 0.81502I
7.36099 − 0.14420I −3.68331 − 0.52947I
u = 0.590027 − 0.406016I
a = −0.493746 + 0.244011I
b = 1.61229 − 0.75954I
7.36099 + 3.91557I −3.68331 − 7.45767I
u = 0.590027 − 0.406016I
a = −0.74761 + 1.57796I
b = 0.477339 − 0.169725I
7.36099 − 0.14420I −3.68331 − 0.52947I
u = 0.590027 − 0.406016I
a = 0.58284 − 1.91894I
b = −1.28763 − 1.09338I
7.36099 + 3.91557I −3.68331 − 7.45767I
u = −0.482433 + 0.528989I
a = 0.676484 + 0.200897I
b = 0.587231 − 0.287840I
3.80604 + 0.24294I −7.23943 − 3.48661I
u = −0.482433 + 0.528989I
a = −0.126601 + 1.382480I
b = −0.170952 − 0.123200I
3.80604 − 3.81683I −7.23943 + 3.44160I
u = −0.482433 + 0.528989I
a = −1.09882 + 0.99815I
b = 0.515901 + 0.123082I
3.80604 + 0.24294I −7.23943 − 3.48661I
u = −0.482433 + 0.528989I
a = 1.37618 − 1.61626I
b = −0.523299 − 0.749761I
3.80604 − 3.81683I −7.23943 + 3.44160I
u = −0.482433 − 0.528989I
a = 0.676484 − 0.200897I
b = 0.587231 + 0.287840I
3.80604 − 0.24294I −7.23943 + 3.48661I
u = −0.482433 − 0.528989I
a = −0.126601 − 1.382480I
b = −0.170952 + 0.123200I
3.80604 + 3.81683I −7.23943 − 3.44160I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.482433 − 0.528989I
a = −1.09882 − 0.99815I
b = 0.515901 − 0.123082I
3.80604 − 0.24294I −7.23943 + 3.48661I
u = −0.482433 − 0.528989I
a = 1.37618 + 1.61626I
b = −0.523299 + 0.749761I
3.80604 + 3.81683I −7.23943 − 3.44160I
u = −0.076050 + 1.298790I
a = −0.919925 + 0.243405I
b = 1.86099 − 0.27931I
8.28842 − 0.45801I −3.80878 − 0.75660I
u = −0.076050 + 1.298790I
a = −1.44427 + 1.22259I
b = 0.176652 − 0.618705I
8.28842 + 3.60176I −3.80878 − 7.68480I
u = −0.076050 + 1.298790I
a = −1.82203 − 2.73302I
b = 1.65533 + 2.74318I
8.28842 + 3.60176I −3.80878 − 7.68480I
u = −0.076050 + 1.298790I
a = 1.24500 + 3.34050I
b = −0.93713 − 2.36947I
8.28842 − 0.45801I −3.80878 − 0.75660I
u = −0.076050 − 1.298790I
a = −0.919925 − 0.243405I
b = 1.86099 + 0.27931I
8.28842 + 0.45801I −3.80878 + 0.75660I
u = −0.076050 − 1.298790I
a = −1.44427 − 1.22259I
b = 0.176652 + 0.618705I
8.28842 − 3.60176I −3.80878 + 7.68480I
u = −0.076050 − 1.298790I
a = −1.82203 + 2.73302I
b = 1.65533 − 2.74318I
8.28842 − 3.60176I −3.80878 + 7.68480I
u = −0.076050 − 1.298790I
a = 1.24500 − 3.34050I
b = −0.93713 + 2.36947I
8.28842 + 0.45801I −3.80878 + 0.75660I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.663049
a = 0.064959 + 0.400733I
b = −1.208060 + 0.381728I
−0.89775 + 2.02988I −14.3720 − 3.4641I
u = 0.663049
a = 0.064959 − 0.400733I
b = −1.208060 − 0.381728I
−0.89775 − 2.02988I −14.3720 + 3.4641I
u = 0.663049
a = 0.287724 + 0.210132I
b = 0.70420 − 1.25443I
−0.89775 + 2.02988I −14.3720 − 3.4641I
u = 0.663049
a = 0.287724 − 0.210132I
b = 0.70420 + 1.25443I
−0.89775 − 2.02988I −14.3720 + 3.4641I
u = −0.17132 + 1.45278I
a = 0.520335 + 0.799536I
b = 0.70398 − 1.43202I
10.07990 − 1.47092I −3.51114 + 3.72120I
u = −0.17132 + 1.45278I
a = 1.156310 − 0.321118I
b = −1.65049 + 0.62665I
10.07990 − 1.47092I −3.51114 + 3.72120I
u = −0.17132 + 1.45278I
a = −1.017530 + 0.809538I
b = 1.64441 − 0.36076I
10.07990 + 2.58885I −3.51114 − 3.20700I
u = −0.17132 + 1.45278I
a = −0.235110 + 0.403267I
b = −0.473689 − 0.056257I
10.07990 + 2.58885I −3.51114 − 3.20700I
u = −0.17132 − 1.45278I
a = 0.520335 − 0.799536I
b = 0.70398 + 1.43202I
10.07990 + 1.47092I −3.51114 − 3.72120I
u = −0.17132 − 1.45278I
a = 1.156310 + 0.321118I
b = −1.65049 − 0.62665I
10.07990 + 1.47092I −3.51114 − 3.72120I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.17132 − 1.45278I
a = −1.017530 − 0.809538I
b = 1.64441 + 0.36076I
10.07990 − 2.58885I −3.51114 + 3.20700I
u = −0.17132 − 1.45278I
a = −0.235110 − 0.403267I
b = −0.473689 + 0.056257I
10.07990 − 2.58885I −3.51114 + 3.20700I
u = −0.25789 + 1.44398I
a = −0.335626 − 0.777806I
b = −0.277963 + 1.122660I
8.82504 + 7.10521I −4.98695 − 2.40068I
u = −0.25789 + 1.44398I
a = −1.55330 + 1.39269I
b = 2.26174 − 1.13867I
8.8250 + 11.1650I −4.98695 − 9.32888I
u = −0.25789 + 1.44398I
a = −0.73749 + 2.01471I
b = 1.35360 − 1.66105I
8.82504 + 7.10521I −4.98695 − 2.40068I
u = −0.25789 + 1.44398I
a = 1.01866 − 2.94049I
b = −2.33331 + 2.33940I
8.8250 + 11.1650I −4.98695 − 9.32888I
u = −0.25789 − 1.44398I
a = −0.335626 + 0.777806I
b = −0.277963 − 1.122660I
8.82504 − 7.10521I −4.98695 + 2.40068I
u = −0.25789 − 1.44398I
a = −1.55330 − 1.39269I
b = 2.26174 + 1.13867I
8.8250 − 11.1650I −4.98695 + 9.32888I
u = −0.25789 − 1.44398I
a = −0.73749 − 2.01471I
b = 1.35360 + 1.66105I
8.82504 − 7.10521I −4.98695 + 2.40068I
u = −0.25789 − 1.44398I
a = 1.01866 + 2.94049I
b = −2.33331 − 2.33940I
8.8250 − 11.1650I −4.98695 + 9.32888I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.22144 + 1.45044I
a = 0.166678 − 0.743458I
b = −0.801939 + 0.292853I
13.32210 − 2.84406I −0.473205 + 0.137261I
u = 0.22144 + 1.45044I
a = 1.90706 − 0.23597I
b = −0.96942 + 1.60449I
13.3221 − 6.9038I −0.47320 + 7.06546I
u = 0.22144 + 1.45044I
a = −1.26293 − 2.59937I
b = 1.81388 + 2.27983I
13.3221 − 6.9038I −0.47320 + 7.06546I
u = 0.22144 + 1.45044I
a = 1.96674 + 2.71895I
b = −2.98421 − 1.50369I
13.32210 − 2.84406I −0.473205 + 0.137261I
u = 0.22144 − 1.45044I
a = 0.166678 + 0.743458I
b = −0.801939 − 0.292853I
13.32210 + 2.84406I −0.473205 − 0.137261I
u = 0.22144 − 1.45044I
a = 1.90706 + 0.23597I
b = −0.96942 − 1.60449I
13.3221 + 6.9038I −0.47320 − 7.06546I
u = 0.22144 − 1.45044I
a = −1.26293 + 2.59937I
b = 1.81388 − 2.27983I
13.3221 + 6.9038I −0.47320 − 7.06546I
u = 0.22144 − 1.45044I
a = 1.96674 − 2.71895I
b = −2.98421 + 1.50369I
13.32210 + 2.84406I −0.473205 − 0.137261I
u = −0.382766
a = 1.24526 + 0.85582I
b = 0.29856 − 1.81148I
4.31288 − 2.02988I −13.9800 + 3.4641I
u = −0.382766
a = 1.24526 − 0.85582I
b = 0.29856 + 1.81148I
4.31288 + 2.02988I −13.9800 − 3.4641I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.382766
a = 0.11239 + 3.20734I
b = 0.785287 + 0.065805I
4.31288 + 2.02988I −13.9800 − 3.4641I
u = −0.382766
a = 0.11239 − 3.20734I
b = 0.785287 − 0.065805I
4.31288 − 2.02988I −13.9800 + 3.4641I
19
III.
I
u
3
= h−u
18
−2u
17
+· · ·+b+1, 2u
18
+2u
17
+· · ·+a+1, u
19
+u
18
+· · ·−2u−1i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
3
=
1
u
2
a
8
=
−u
u
a
4
=
−u
4
− u
2
+ 1
u
4
+ 2u
2
a
11
=
−2u
18
− 2u
17
+ ··· + 4u − 1
u
18
+ 2u
17
+ ··· − 3u − 1
a
9
=
2u
18
+ 17u
16
+ ··· − 4u − 1
−u
18
− 8u
16
+ ··· + u
3
− u
2
a
1
=
u
8
+ 3u
6
+ u
4
− 2u
2
+ 1
−u
8
− 4u
6
− 4u
4
a
6
=
u
u
3
+ u
a
12
=
−2u
18
− u
17
+ ··· + 3u − 1
u
18
+ u
17
+ ··· − 2u
2
− 2u
a
5
=
−2u
18
− 4u
17
+ ··· + 5u + 4
2u
17
+ 2u
16
+ ··· − 2u − 2
a
10
=
−u
18
− u
17
+ ··· + u − 1
u
18
+ 2u
17
+ ··· − 3u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = u
17
+ u
16
+ 9u
15
+ 6u
14
+ 28u
13
+ 11u
12
+ 31u
11
+ u
10
− 8u
9
−
14u
8
− 33u
7
− 7u
6
− 12u
5
− 5u
3
− 5u
2
− 6u − 5
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
19
+ 5u
18
+ ··· − 6u − 1
c
2
u
19
+ u
18
+ ··· − 2u − 1
c
3
u
19
− u
18
+ ··· + 2u − 1
c
4
, c
11
u
19
+ 11u
17
+ ··· + 11u
2
− 1
c
5
, c
9
u
19
+ 11u
17
+ ··· − 11u
2
+ 1
c
6
, c
7
u
19
− u
18
+ ··· − 2u + 1
c
8
, c
10
u
19
+ 3u
18
+ ··· − 3u − 1
c
12
u
19
− 3u
18
+ ··· − 3u + 1
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
19
+ 11y
18
+ ··· − 4y −1
c
2
, c
6
, c
7
y
19
+ 19y
18
+ ··· − 14y
2
− 1
c
3
y
19
+ 5y
18
+ ··· − 4y −1
c
4
, c
5
, c
9
c
11
y
19
+ 22y
18
+ ··· + 22y −1
c
8
, c
10
y
19
+ 3y
18
+ ··· − 5y −1
c
12
y
19
+ 5y
18
+ ··· − 3y −1
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.235288 + 0.915709I
a = −1.411480 − 0.044591I
b = 0.746747 + 0.027293I
5.44511 − 1.35552I −4.89852 − 1.07017I
u = −0.235288 − 0.915709I
a = −1.411480 + 0.044591I
b = 0.746747 − 0.027293I
5.44511 + 1.35552I −4.89852 + 1.07017I
u = −0.708819 + 0.304677I
a = −0.177007 − 0.019901I
b = 0.774542 − 0.956982I
3.79141 + 5.07606I −6.47879 − 7.14339I
u = −0.708819 − 0.304677I
a = −0.177007 + 0.019901I
b = 0.774542 + 0.956982I
3.79141 − 5.07606I −6.47879 + 7.14339I
u = 0.608408 + 0.473769I
a = −0.453736 − 0.906033I
b = 1.159460 + 0.033720I
6.60042 − 2.09094I −5.46216 + 3.45807I
u = 0.608408 − 0.473769I
a = −0.453736 + 0.906033I
b = 1.159460 − 0.033720I
6.60042 + 2.09094I −5.46216 − 3.45807I
u = −0.031829 + 1.293340I
a = −0.22504 − 2.60016I
b = 0.99670 + 2.02747I
8.34281 + 2.44030I −3.33990 − 0.56667I
u = −0.031829 − 1.293340I
a = −0.22504 + 2.60016I
b = 0.99670 − 2.02747I
8.34281 − 2.44030I −3.33990 + 0.56667I
u = 0.171821 + 1.297070I
a = 0.93833 + 1.52105I
b = −1.117650 − 0.751284I
1.46611 − 2.46863I −11.04601 + 1.02417I
u = 0.171821 − 1.297070I
a = 0.93833 − 1.52105I
b = −1.117650 + 0.751284I
1.46611 + 2.46863I −11.04601 − 1.02417I
23
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.17378 + 1.42845I
a = 1.014020 − 0.128298I
b = −1.88482 + 0.07849I
10.85170 + 0.51651I −1.208225 − 0.024037I
u = −0.17378 − 1.42845I
a = 1.014020 + 0.128298I
b = −1.88482 − 0.07849I
10.85170 − 0.51651I −1.208225 + 0.024037I
u = −0.27003 + 1.43292I
a = −0.26706 + 1.90078I
b = 0.98783 − 1.87047I
9.37856 + 8.63319I −3.01636 − 7.40521I
u = −0.27003 − 1.43292I
a = −0.26706 − 1.90078I
b = 0.98783 + 1.87047I
9.37856 − 8.63319I −3.01636 + 7.40521I
u = 0.21619 + 1.46250I
a = −1.28775 − 1.23021I
b = 1.198330 + 0.453553I
12.79670 − 5.06751I −2.04376 + 3.02477I
u = 0.21619 − 1.46250I
a = −1.28775 + 1.23021I
b = 1.198330 − 0.453553I
12.79670 + 5.06751I −2.04376 − 3.02477I
u = 0.516155
a = −0.717462
b = −1.29834
−2.60799 −11.0690
u = −0.334750 + 0.331722I
a = −1.77154 + 1.50786I
b = −0.211963 − 0.541557I
5.13870 − 1.64426I −3.47177 − 1.01784I
u = −0.334750 − 0.331722I
a = −1.77154 − 1.50786I
b = −0.211963 + 0.541557I
5.13870 + 1.64426I −3.47177 + 1.01784I
24
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
18
− 3u
17
+ ··· − 3u + 3)
4
)(u
19
+ 5u
18
+ ··· − 6u − 1)
· (u
39
− 8u
38
+ ··· + 6840u + 6208)
c
2
((u
18
− u
17
+ ··· + 3u − 1)
4
)(u
19
+ u
18
+ ··· − 2u − 1)
· (u
39
+ 6u
38
+ ··· + 38u + 4)
c
3
((u
18
+ u
17
+ ··· + 13u − 5)
4
)(u
19
− u
18
+ ··· + 2u − 1)
· (u
39
− 6u
38
+ ··· + 2982u + 612)
c
4
, c
11
(u
19
+ 11u
17
+ ··· + 11u
2
− 1)(u
39
+ 16u
37
+ ··· + 2u + 1)
· (u
72
− u
71
+ ··· − 2u + 1)
c
5
, c
9
(u
19
+ 11u
17
+ ··· − 11u
2
+ 1)(u
39
+ 16u
37
+ ··· + 2u + 1)
· (u
72
− u
71
+ ··· − 2u + 1)
c
6
, c
7
((u
18
− u
17
+ ··· + 3u − 1)
4
)(u
19
− u
18
+ ··· − 2u + 1)
· (u
39
+ 6u
38
+ ··· + 38u + 4)
c
8
, c
10
(u
19
+ 3u
18
+ ··· − 3u − 1)(u
39
+ 3u
38
+ ··· + 7u + 1)
· (u
72
− 21u
71
+ ··· − 139378u + 9841)
c
12
((u
2
− u + 1)
36
)(u
19
− 3u
18
+ ··· − 3u + 1)
· (u
39
+ 40u
38
+ ··· + 5898240u + 262144)
25
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
18
+ 13y
17
+ ··· − 75y + 9)
4
)(y
19
+ 11y
18
+ ··· − 4y −1)
· (y
39
+ 24y
38
+ ··· + 872760000y −38539264)
c
2
, c
6
, c
7
((y
18
+ 17y
17
+ ··· − 7y + 1)
4
)(y
19
+ 19y
18
+ ··· − 14y
2
− 1)
· (y
39
+ 36y
38
+ ··· + 236y −16)
c
3
((y
18
+ 5y
17
+ ··· − 39y + 25)
4
)(y
19
+ 5y
18
+ ··· − 4y −1)
· (y
39
+ 10y
38
+ ··· + 2009772y −374544)
c
4
, c
5
, c
9
c
11
(y
19
+ 22y
18
+ ··· + 22y −1)(y
39
+ 32y
38
+ ··· + 8y −1)
· (y
72
+ 63y
71
+ ··· + 144y + 1)
c
8
, c
10
(y
19
+ 3y
18
+ ··· − 5y −1)(y
39
+ 9y
38
+ ··· + 17y −1)
· (y
72
+ 27y
71
+ ··· + 5486973168y + 96845281)
c
12
((y
2
+ y + 1)
36
)(y
19
+ 5y
18
+ ··· − 3y −1)
· (y
39
+ 6y
38
+ ··· + 876173328384y −68719476736)
26
