12a
0904
(K12a
0904
)
A knot diagram
1
Linearized knot diagam
4 6 8 1 9 10 11 12 2 7 3 5
Solving Sequence
6,10
7 11
3,8
4 12 2 1 9 5
c
6
c
10
c
7
c
3
c
11
c
2
c
1
c
9
c
5
c
4
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−6.80736 × 10
21
u
48
+ 8.45127 × 10
22
u
47
+ ··· + 9.47444 × 10
18
b − 6.36777 × 10
22
,
− 9.78381 × 10
22
u
48
+ 1.20822 × 10
24
u
47
+ ··· + 1.42117 × 10
20
a − 8.78994 × 10
23
,
u
49
− 14u
48
+ ··· + 15u − 15i
I
u
2
= h15u
32
+ 51u
31
+ ··· + 4b + 29, 29u
32
a − 51u
32
+ ··· + 59a − 55, u
33
+ 4u
32
+ ··· + 4u + 1i
I
u
3
= h212u
18
+ 746u
17
+ ··· + b − 143, 284u
18
+ 993u
17
+ ··· + a − 188, u
19
+ 5u
18
+ ··· + 2u − 1i
I
u
4
= hb + 1, a
4
+ 2a
3
− a
2
− 2a + 3, u − 1i
I
u
5
= hb − 1, a
2
− a − 1, u − 1i
I
v
1
= ha, b + 1, v −1i
* 6 irreducible components of dim
C
= 0, with total 141 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−6.81 × 10
21
u
48
+ 8.45 × 10
22
u
47
+ · · · + 9.47 × 10
18
b − 6.37 ×
10
22
, −9.78 × 10
22
u
48
+ 1.21 × 10
24
u
47
+ · · · + 1.42 × 10
20
a − 8.79 ×
10
23
, u
49
− 14u
48
+ · · · + 15u − 15i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
7
=
1
u
2
a
11
=
−u
−u
3
+ u
a
3
=
688.436u
48
− 8501.60u
47
+ ··· − 2513.66u + 6185.02
718.497u
48
− 8920.08u
47
+ ··· − 2579.49u + 6721.00
a
8
=
−u
2
+ 1
−u
4
+ 2u
2
a
4
=
464.635u
48
− 5815.98u
47
+ ··· − 1526.92u + 4698.07
105.044u
48
− 1301.83u
47
+ ··· − 294.460u + 1043.20
a
12
=
−1047.35u
48
+ 13271.5u
47
+ ··· + 2929.33u − 11815.0
−455.203u
48
+ 5771.76u
47
+ ··· + 1265.32u − 5159.50
a
2
=
−30.0619u
48
+ 418.482u
47
+ ··· + 65.8259u − 535.978
718.497u
48
− 8920.08u
47
+ ··· − 2579.49u + 6721.00
a
1
=
−868.372u
48
+ 10931.9u
47
+ ··· + 2757.74u − 9184.05
−367.877u
48
+ 4676.46u
47
+ ··· + 980.968u − 4262.61
a
9
=
1011.69u
48
− 12824.6u
47
+ ··· − 2762.90u + 11491.1
790.230u
48
− 10008.2u
47
+ ··· − 2225.63u + 8882.16
a
5
=
158.515u
48
− 2047.43u
47
+ ··· − 269.436u + 2139.17
1034.37u
48
− 13113.2u
47
+ ··· − 2833.39u + 11749.5
(ii) Obstruction class = −1
(iii) Cusp Shapes =
15967610317655355889704
9474437016710709037
u
48
−
200050054562027319399210
9474437016710709037
u
47
+ ··· −
55240295833948105225005
9474437016710709037
u +
160054166406768266614452
9474437016710709037
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
12
u
49
− 9u
48
+ ··· − 75u + 15
c
2
, c
11
u
49
+ 2u
48
+ ··· − 12u − 3
c
3
, c
9
u
49
− 6u
47
+ ··· − 35u − 11
c
5
, c
8
u
49
+ 4u
48
+ ··· − 3u − 1
c
6
, c
7
, c
10
u
49
+ 14u
48
+ ··· + 15u + 15
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
12
y
49
+ 47y
48
+ ··· + 3495y −225
c
2
, c
11
y
49
− 6y
48
+ ··· + 120y −9
c
3
, c
9
y
49
− 12y
48
+ ··· + 1005y −121
c
5
, c
8
y
49
− 42y
48
+ ··· + 141y −1
c
6
, c
7
, c
10
y
49
− 54y
48
+ ··· + 1245y −225
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.433047 + 0.879529I
a = 0.291430 + 0.391337I
b = 0.597708 − 0.538193I
1.03664 − 4.43730I 0
u = −0.433047 − 0.879529I
a = 0.291430 − 0.391337I
b = 0.597708 + 0.538193I
1.03664 + 4.43730I 0
u = −0.615786 + 0.757323I
a = −0.367363 + 0.678499I
b = 0.991856 + 0.906798I
0.46282 + 9.75261I 0
u = −0.615786 − 0.757323I
a = −0.367363 − 0.678499I
b = 0.991856 − 0.906798I
0.46282 − 9.75261I 0
u = −0.590062 + 0.843539I
a = 0.443919 − 0.597588I
b = −0.998349 − 0.951834I
6.6188 + 13.7974I 0
u = −0.590062 − 0.843539I
a = 0.443919 + 0.597588I
b = −0.998349 + 0.951834I
6.6188 − 13.7974I 0
u = −0.584945 + 0.950148I
a = −0.331095 − 0.287711I
b = −0.601232 + 0.675624I
6.74131 − 7.96419I 0
u = −0.584945 − 0.950148I
a = −0.331095 + 0.287711I
b = −0.601232 − 0.675624I
6.74131 + 7.96419I 0
u = −0.725664 + 0.466170I
a = 0.696467 + 0.277718I
b = 1.038160 − 0.508456I
7.88801 + 1.77959I 0
u = −0.725664 − 0.466170I
a = 0.696467 − 0.277718I
b = 1.038160 + 0.508456I
7.88801 − 1.77959I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.570337 + 0.621546I
a = 0.317455 − 0.880503I
b = −1.009850 − 0.870823I
1.36125 + 4.73215I 0. − 6.17410I
u = −0.570337 − 0.621546I
a = 0.317455 + 0.880503I
b = −1.009850 + 0.870823I
1.36125 − 4.73215I 0. + 6.17410I
u = 0.289625 + 0.769569I
a = 0.291612 − 0.422229I
b = −0.369416 + 0.242506I
2.10039 − 1.64969I 0. + 3.17462I
u = 0.289625 − 0.769569I
a = 0.291612 + 0.422229I
b = −0.369416 − 0.242506I
2.10039 + 1.64969I 0. − 3.17462I
u = 1.242710 + 0.016595I
a = 1.16528 + 1.29445I
b = 0.319236 + 0.418793I
3.15210 + 0.59306I 0
u = 1.242710 − 0.016595I
a = 1.16528 − 1.29445I
b = 0.319236 − 0.418793I
3.15210 − 0.59306I 0
u = −0.345736 + 0.608967I
a = −0.681550 + 1.075440I
b = 1.043400 + 0.803583I
8.99740 + 2.00742I 3.69703 − 4.15633I
u = −0.345736 − 0.608967I
a = −0.681550 − 1.075440I
b = 1.043400 − 0.803583I
8.99740 − 2.00742I 3.69703 + 4.15633I
u = 1.346140 + 0.047168I
a = −0.443611 − 1.201140I
b = −0.109835 − 0.592401I
−2.79905 + 0.29382I 0
u = 1.346140 − 0.047168I
a = −0.443611 + 1.201140I
b = −0.109835 + 0.592401I
−2.79905 − 0.29382I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.350884 + 0.523383I
a = −0.515791 − 0.746507I
b = −0.768093 + 0.310045I
1.91939 − 0.70956I 1.318828 + 0.280442I
u = −0.350884 − 0.523383I
a = −0.515791 + 0.746507I
b = −0.768093 − 0.310045I
1.91939 + 0.70956I 1.318828 − 0.280442I
u = −1.42373
a = −0.459235
b = −1.58471
−3.37509 0
u = −1.43526 + 0.05673I
a = 0.470759 − 0.012708I
b = 1.64110 − 0.14774I
1.28248 + 0.95897I 0
u = −1.43526 − 0.05673I
a = 0.470759 + 0.012708I
b = 1.64110 + 0.14774I
1.28248 − 0.95897I 0
u = −1.44574 + 0.13037I
a = −0.285354 − 0.092403I
b = −1.051010 − 0.180394I
−3.51728 + 4.30782I 0
u = −1.44574 − 0.13037I
a = −0.285354 + 0.092403I
b = −1.051010 + 0.180394I
−3.51728 − 4.30782I 0
u = 1.44985 + 0.18119I
a = 0.29317 − 2.09746I
b = 0.90354 − 1.19821I
3.18263 − 4.79396I 0
u = 1.44985 − 0.18119I
a = 0.29317 + 2.09746I
b = 0.90354 + 1.19821I
3.18263 + 4.79396I 0
u = 1.47749 + 0.03978I
a = −0.19780 + 2.30854I
b = −0.31875 + 1.60961I
−6.62186 − 2.92931I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.47749 − 0.03978I
a = −0.19780 − 2.30854I
b = −0.31875 − 1.60961I
−6.62186 + 2.92931I 0
u = −1.49311
a = 0.281474
b = 1.04778
−7.43487 0
u = 0.479702
a = −1.05468
b = 0.263235
−0.947319 −10.8700
u = 1.54367 + 0.20987I
a = −0.37262 + 1.86764I
b = −1.11448 + 1.32193I
−5.62131 − 7.81657I 0
u = 1.54367 − 0.20987I
a = −0.37262 − 1.86764I
b = −1.11448 − 1.32193I
−5.62131 + 7.81657I 0
u = 1.56434 + 0.25553I
a = 0.27338 − 1.74910I
b = 1.17492 − 1.28124I
−6.6890 − 13.4975I 0
u = 1.56434 − 0.25553I
a = 0.27338 + 1.74910I
b = 1.17492 + 1.28124I
−6.6890 + 13.4975I 0
u = 1.56308 + 0.29110I
a = −0.17723 + 1.71857I
b = −1.20463 + 1.25726I
−0.3997 − 17.9676I 0
u = 1.56308 − 0.29110I
a = −0.17723 − 1.71857I
b = −1.20463 − 1.25726I
−0.3997 + 17.9676I 0
u = −0.359518 + 0.130940I
a = 0.10471 − 2.15999I
b = −0.436809 − 1.042280I
−0.50334 + 2.29820I −0.41049 + 7.94845I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.359518 − 0.130940I
a = 0.10471 + 2.15999I
b = −0.436809 + 1.042280I
−0.50334 − 2.29820I −0.41049 − 7.94845I
u = 1.67836 + 0.27620I
a = −0.010084 + 0.531761I
b = −0.356849 + 0.558291I
−5.86325 − 0.66633I 0
u = 1.67836 − 0.27620I
a = −0.010084 − 0.531761I
b = −0.356849 − 0.558291I
−5.86325 + 0.66633I 0
u = 1.70957 + 0.15400I
a = 0.077778 − 0.702600I
b = 0.354253 − 0.806660I
−1.46119 + 3.06033I 0
u = 1.70957 − 0.15400I
a = 0.077778 + 0.702600I
b = 0.354253 + 0.806660I
−1.46119 − 3.06033I 0
u = 1.67687 + 0.48704I
a = −0.069085 − 0.340576I
b = 0.328404 − 0.384973I
−2.14546 − 4.63461I 0
u = 1.67687 − 0.48704I
a = −0.069085 + 0.340576I
b = 0.328404 + 0.384973I
−2.14546 + 4.63461I 0
u = 0.133847 + 0.185778I
a = −4.35816 + 3.14536I
b = 1.083580 + 0.119708I
6.62641 − 0.11786I 5.86559 − 0.14016I
u = 0.133847 − 0.185778I
a = −4.35816 − 3.14536I
b = 1.083580 − 0.119708I
6.62641 + 0.11786I 5.86559 + 0.14016I
9
II. I
u
2
= h15u
32
+ 51u
31
+ · · · + 4b + 29, 29u
32
a − 51u
32
+ · · · + 59a −
55, u
33
+ 4u
32
+ · · · + 4u + 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
7
=
1
u
2
a
11
=
−u
−u
3
+ u
a
3
=
a
−3.75000u
32
− 12.7500u
31
+ ··· − 14.2500u − 7.25000
a
8
=
−u
2
+ 1
−u
4
+ 2u
2
a
4
=
u
32
+ 5u
31
+ ··· + a + 4
−5.75000u
32
− 16.7500u
31
+ ··· − 17.2500u − 7.25000
a
12
=
15
4
u
32
a + 7u
32
+ ··· +
29
4
a + 4
1
a
2
=
15
4
u
32
+
51
4
u
31
+ ··· + a +
29
4
−3.75000u
32
− 12.7500u
31
+ ··· − 14.2500u − 7.25000
a
1
=
1
4
u
32
a +
23
4
u
32
+ ··· +
5
4
a +
13
4
1
4
u
32
a + u
32
+ ··· +
1
4
a +
3
2
a
9
=
−
3
4
u
32
a −
27
4
u
32
+ ··· +
7
4
a −
19
4
11
4
u
32
a +
31
4
u
31
a + ··· +
13
4
a − 1
a
5
=
1
2
u
31
a +
27
4
u
32
+ ··· −
1
2
a +
15
4
−
5
4
u
32
a +
1
4
u
32
+ ··· −
3
4
a +
5
4
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
183
4
u
32
−
515
4
u
31
+ ··· −
397
4
u −
289
4
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
12
(u
33
+ 7u
32
+ ··· + 6u + 2)
2
c
2
, c
11
u
66
− 3u
65
+ ··· − 422u + 59
c
3
, c
9
u
66
− 5u
64
+ ··· − 7821u + 1213
c
5
, c
8
u
66
+ 2u
65
+ ··· − 195u − 107
c
6
, c
7
, c
10
(u
33
− 4u
32
+ ··· + 4u − 1)
2
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
12
(y
33
+ 33y
32
+ ··· + 84y −4)
2
c
2
, c
11
y
66
+ 29y
65
+ ··· + 16970y + 3481
c
3
, c
9
y
66
− 10y
65
+ ··· − 30663517y + 1471369
c
5
, c
8
y
66
− 2y
65
+ ··· − 846945y + 11449
c
6
, c
7
, c
10
(y
33
− 34y
32
+ ··· + 20y −1)
2
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.688220 + 0.730433I
a = 0.679420 + 0.177115I
b = −0.390156 + 0.737285I
1.96145 − 1.06750I −5.04121 − 0.08113I
u = 0.688220 + 0.730433I
a = 0.070121 − 0.168584I
b = −0.172925 − 0.537570I
1.96145 − 1.06750I −5.04121 − 0.08113I
u = 0.688220 − 0.730433I
a = 0.679420 − 0.177115I
b = −0.390156 − 0.737285I
1.96145 + 1.06750I −5.04121 + 0.08113I
u = 0.688220 − 0.730433I
a = 0.070121 + 0.168584I
b = −0.172925 + 0.537570I
1.96145 + 1.06750I −5.04121 + 0.08113I
u = 0.480050 + 0.852324I
a = 0.708758 + 0.499855I
b = −0.697285 + 0.596564I
2.63544 − 4.29581I −2.69433 + 7.14256I
u = 0.480050 + 0.852324I
a = −0.267358 − 0.076310I
b = 0.280856 − 1.024980I
2.63544 − 4.29581I −2.69433 + 7.14256I
u = 0.480050 − 0.852324I
a = 0.708758 − 0.499855I
b = −0.697285 − 0.596564I
2.63544 + 4.29581I −2.69433 − 7.14256I
u = 0.480050 − 0.852324I
a = −0.267358 + 0.076310I
b = 0.280856 + 1.024980I
2.63544 + 4.29581I −2.69433 − 7.14256I
u = 0.554324 + 0.780221I
a = −0.574660 − 0.354350I
b = 0.531601 − 0.665036I
−1.79727 − 2.60552I −13.6142 + 5.4970I
u = 0.554324 + 0.780221I
a = 0.202674 + 0.210448I
b = −0.201059 + 0.756653I
−1.79727 − 2.60552I −13.6142 + 5.4970I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.554324 − 0.780221I
a = −0.574660 + 0.354350I
b = 0.531601 + 0.665036I
−1.79727 + 2.60552I −13.6142 − 5.4970I
u = 0.554324 − 0.780221I
a = 0.202674 − 0.210448I
b = −0.201059 − 0.756653I
−1.79727 + 2.60552I −13.6142 − 5.4970I
u = 1.104540 + 0.315968I
a = 1.345920 + 0.217380I
b = 0.894831 + 0.743190I
4.76058 + 1.84769I −1.10325 − 3.83345I
u = 1.104540 + 0.315968I
a = 0.491156 + 0.257639I
b = −1.047590 − 0.033948I
4.76058 + 1.84769I −1.10325 − 3.83345I
u = 1.104540 − 0.315968I
a = 1.345920 − 0.217380I
b = 0.894831 − 0.743190I
4.76058 − 1.84769I −1.10325 + 3.83345I
u = 1.104540 − 0.315968I
a = 0.491156 − 0.257639I
b = −1.047590 + 0.033948I
4.76058 − 1.84769I −1.10325 + 3.83345I
u = 0.790477 + 0.166609I
a = −0.492307 − 0.049240I
b = 1.009260 − 0.056854I
−0.369987 + 0.040866I −12.86224 − 3.13604I
u = 0.790477 + 0.166609I
a = −1.58891 + 0.20558I
b = −0.621928 − 0.174825I
−0.369987 + 0.040866I −12.86224 − 3.13604I
u = 0.790477 − 0.166609I
a = −0.492307 + 0.049240I
b = 1.009260 + 0.056854I
−0.369987 − 0.040866I −12.86224 + 3.13604I
u = 0.790477 − 0.166609I
a = −1.58891 − 0.20558I
b = −0.621928 + 0.174825I
−0.369987 − 0.040866I −12.86224 + 3.13604I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.369130 + 0.132853I
a = −0.09548 − 1.97539I
b = −0.224121 − 0.177252I
3.24445 + 7.69327I 0. − 7.24679I
u = −1.369130 + 0.132853I
a = 0.24344 + 2.54788I
b = 0.98575 + 1.95064I
3.24445 + 7.69327I 0. − 7.24679I
u = −1.369130 − 0.132853I
a = −0.09548 + 1.97539I
b = −0.224121 + 0.177252I
3.24445 − 7.69327I 0. + 7.24679I
u = −1.369130 − 0.132853I
a = 0.24344 − 2.54788I
b = 0.98575 − 1.95064I
3.24445 − 7.69327I 0. + 7.24679I
u = 0.091448 + 0.602007I
a = −0.482645 − 0.043727I
b = 0.96667 − 1.18249I
7.79919 − 5.26371I 6.25290 + 5.11827I
u = 0.091448 + 0.602007I
a = 1.66371 + 1.56662I
b = −0.743717 − 0.076925I
7.79919 − 5.26371I 6.25290 + 5.11827I
u = 0.091448 − 0.602007I
a = −0.482645 + 0.043727I
b = 0.96667 + 1.18249I
7.79919 + 5.26371I 6.25290 − 5.11827I
u = 0.091448 − 0.602007I
a = 1.66371 − 1.56662I
b = −0.743717 + 0.076925I
7.79919 + 5.26371I 6.25290 − 5.11827I
u = 0.295713 + 0.495961I
a = 0.445625 + 0.069876I
b = −0.983847 + 0.868746I
1.12370 − 2.92332I 1.70980 + 9.60306I
u = 0.295713 + 0.495961I
a = −0.32255 − 1.99227I
b = 0.538393 − 0.020450I
1.12370 − 2.92332I 1.70980 + 9.60306I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.295713 − 0.495961I
a = 0.445625 − 0.069876I
b = −0.983847 − 0.868746I
1.12370 + 2.92332I 1.70980 − 9.60306I
u = 0.295713 − 0.495961I
a = −0.32255 + 1.99227I
b = 0.538393 + 0.020450I
1.12370 + 2.92332I 1.70980 − 9.60306I
u = −1.46348 + 0.10101I
a = 0.44263 + 1.42953I
b = −0.025005 + 0.390093I
−4.66470 + 4.86669I 0
u = −1.46348 + 0.10101I
a = −0.82750 − 1.78327I
b = −1.49894 − 1.50915I
−4.66470 + 4.86669I 0
u = −1.46348 − 0.10101I
a = 0.44263 − 1.42953I
b = −0.025005 − 0.390093I
−4.66470 − 4.86669I 0
u = −1.46348 − 0.10101I
a = −0.82750 + 1.78327I
b = −1.49894 + 1.50915I
−4.66470 − 4.86669I 0
u = 1.47320 + 0.07823I
a = −0.53451 − 1.56310I
b = 0.852179 − 0.743106I
−0.43816 − 7.73793I 0
u = 1.47320 + 0.07823I
a = −1.21527 − 1.81095I
b = −1.54751 − 1.85479I
−0.43816 − 7.73793I 0
u = 1.47320 − 0.07823I
a = −0.53451 + 1.56310I
b = 0.852179 + 0.743106I
−0.43816 + 7.73793I 0
u = 1.47320 − 0.07823I
a = −1.21527 + 1.81095I
b = −1.54751 + 1.85479I
−0.43816 + 7.73793I 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.47653 + 0.02582I
a = 0.25574 + 2.09823I
b = −0.519028 + 1.042790I
−7.05002 − 3.03427I 0
u = 1.47653 + 0.02582I
a = 0.66250 + 2.39252I
b = 0.93805 + 2.16023I
−7.05002 − 3.03427I 0
u = 1.47653 − 0.02582I
a = 0.25574 − 2.09823I
b = −0.519028 − 1.042790I
−7.05002 + 3.03427I 0
u = 1.47653 − 0.02582I
a = 0.66250 − 2.39252I
b = 0.93805 − 2.16023I
−7.05002 + 3.03427I 0
u = −1.50178
a = 1.12928
b = 1.75374
−7.38654 0
u = −1.50178
a = −0.528148
b = 0.504772
−7.38654 0
u = −0.379813 + 0.219018I
a = 0.941104 + 0.583452I
b = −0.68195 + 1.37498I
5.69458 + 6.59044I −4.79082 − 11.54571I
u = −0.379813 + 0.219018I
a = −3.39928 + 1.92428I
b = 0.478064 + 0.766315I
5.69458 + 6.59044I −4.79082 − 11.54571I
u = −0.379813 − 0.219018I
a = 0.941104 − 0.583452I
b = −0.68195 − 1.37498I
5.69458 − 6.59044I −4.79082 + 11.54571I
u = −0.379813 − 0.219018I
a = −3.39928 − 1.92428I
b = 0.478064 − 0.766315I
5.69458 − 6.59044I −4.79082 + 11.54571I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.53334 + 0.30744I
a = 0.112187 − 1.334420I
b = −0.953189 − 0.799052I
−3.91413 + 8.53917I 0
u = −1.53334 + 0.30744I
a = −0.25894 + 1.45981I
b = 0.55378 + 1.45773I
−3.91413 + 8.53917I 0
u = −1.53334 − 0.30744I
a = 0.112187 + 1.334420I
b = −0.953189 + 0.799052I
−3.91413 − 8.53917I 0
u = −1.53334 − 0.30744I
a = −0.25894 − 1.45981I
b = 0.55378 − 1.45773I
−3.91413 − 8.53917I 0
u = −1.54739 + 0.26541I
a = −0.039423 + 1.371380I
b = 0.908815 + 1.009530I
−8.68011 + 6.44112I 0
u = −1.54739 + 0.26541I
a = 0.158864 − 1.400900I
b = −0.478500 − 1.253630I
−8.68011 + 6.44112I 0
u = −1.54739 − 0.26541I
a = −0.039423 − 1.371380I
b = 0.908815 − 1.009530I
−8.68011 − 6.44112I 0
u = −1.54739 − 0.26541I
a = 0.158864 + 1.400900I
b = −0.478500 + 1.253630I
−8.68011 − 6.44112I 0
u = −1.56285 + 0.20190I
a = −0.071729 + 1.298250I
b = 0.153519 + 1.034830I
−5.52357 + 4.35615I 0
u = −1.56285 + 0.20190I
a = −0.137539 − 1.379700I
b = −1.05103 − 1.18343I
−5.52357 + 4.35615I 0
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.56285 − 0.20190I
a = −0.071729 − 1.298250I
b = 0.153519 − 1.034830I
−5.52357 − 4.35615I 0
u = −1.56285 − 0.20190I
a = −0.137539 + 1.379700I
b = −1.05103 + 1.18343I
−5.52357 − 4.35615I 0
u = −0.347602 + 0.080852I
a = −0.655893 − 1.111460I
b = 0.36827 − 1.44393I
−0.95777 + 2.63463I −16.6257 − 9.2457I
u = −0.347602 + 0.080852I
a = 2.23956 − 3.37366I
b = −0.251523 − 0.844773I
−0.95777 + 2.63463I −16.6257 − 9.2457I
u = −0.347602 − 0.080852I
a = −0.655893 + 1.111460I
b = 0.36827 + 1.44393I
−0.95777 − 2.63463I −16.6257 + 9.2457I
u = −0.347602 − 0.080852I
a = 2.23956 + 3.37366I
b = −0.251523 + 0.844773I
−0.95777 − 2.63463I −16.6257 + 9.2457I
19
III. I
u
3
= h212u
18
+ 746u
17
+ · · · + b − 143, 284u
18
+ 993u
17
+ · · · + a −
188, u
19
+ 5u
18
+ · · · + 2u − 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
7
=
1
u
2
a
11
=
−u
−u
3
+ u
a
3
=
−284u
18
− 993u
17
+ ··· − 507u + 188
−212u
18
− 746u
17
+ ··· − 382u + 143
a
8
=
−u
2
+ 1
−u
4
+ 2u
2
a
4
=
−125u
18
− 439u
17
+ ··· − 231u + 84
−121u
18
− 418u
17
+ ··· − 206u + 78
a
12
=
−8u
18
− 28u
17
+ ··· − 9u + 2
−8u
18
− 27u
17
+ ··· − 13u + 4
a
2
=
−72u
18
− 247u
17
+ ··· − 125u + 45
−212u
18
− 746u
17
+ ··· − 382u + 143
a
1
=
113u
18
+ 413u
17
+ ··· + 225u − 85
42u
18
+ 157u
17
+ ··· + 91u − 33
a
9
=
−7u
18
− 28u
17
+ ··· − 14u + 6
−u
18
− 4u
17
+ ··· + 6u
2
− u
a
5
=
−24u
18
− 90u
17
+ ··· − 53u + 19
−6u
18
− 23u
17
+ ··· − 18u + 6
(ii) Obstruction class = 1
(iii) Cusp Shapes =
481u
18
+1689u
17
−2037u
16
−11897u
15
+396u
14
+29834u
13
+893u
12
−33357u
11
+32607u
10
+
32616u
9
−71759u
8
−37583u
7
+31476u
6
−11450u
5
−17741u
4
+2407u
3
−1866u
2
+897u−326
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
12
u
19
− 6u
18
+ ··· + 26u − 5
c
2
, c
11
u
19
+ u
18
+ ··· − u − 1
c
3
, c
9
u
19
− u
18
+ ··· − 2u + 1
c
4
u
19
+ 6u
18
+ ··· + 26u + 5
c
5
, c
8
u
19
− 3u
18
+ ··· + 2u − 1
c
6
, c
7
u
19
+ 5u
18
+ ··· + 2u − 1
c
10
u
19
− 5u
18
+ ··· + 2u + 1
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
12
y
19
+ 18y
18
+ ··· − 274y −25
c
2
, c
11
y
19
+ 17y
18
+ ··· − y −1
c
3
, c
9
y
19
+ 3y
18
+ ··· + 4y −1
c
5
, c
8
y
19
+ y
18
+ ··· + 2y
2
− 1
c
6
, c
7
, c
10
y
19
− 23y
18
+ ··· − 4y −1
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.498057 + 1.043760I
a = 0.283992 + 0.099100I
b = −0.303973 + 0.557666I
1.56873 − 2.00654I −9.89274 + 9.93240I
u = 0.498057 − 1.043760I
a = 0.283992 − 0.099100I
b = −0.303973 − 0.557666I
1.56873 + 2.00654I −9.89274 − 9.93240I
u = 0.451443 + 0.518954I
a = −0.557415 − 0.674007I
b = 0.450465 − 0.810572I
−0.60471 − 2.88406I −5.24973 + 8.32085I
u = 0.451443 − 0.518954I
a = −0.557415 + 0.674007I
b = 0.450465 + 0.810572I
−0.60471 + 2.88406I −5.24973 − 8.32085I
u = −1.401300 + 0.103496I
a = 0.31694 − 2.44376I
b = −0.28108 − 1.40718I
1.85698 + 7.44641I −5.10787 − 5.92651I
u = −1.401300 − 0.103496I
a = 0.31694 + 2.44376I
b = −0.28108 + 1.40718I
1.85698 − 7.44641I −5.10787 + 5.92651I
u = −1.46931 + 0.03702I
a = 0.02353 + 2.55490I
b = 0.19956 + 1.75659I
−6.25421 + 3.36017I −1.28351 − 7.80982I
u = −1.46931 − 0.03702I
a = 0.02353 − 2.55490I
b = 0.19956 − 1.75659I
−6.25421 − 3.36017I −1.28351 + 7.80982I
u = −1.52868 + 0.21520I
a = 0.01958 + 1.60043I
b = 0.723515 + 1.210650I
−7.27853 + 5.82567I −6.96095 − 4.30133I
u = −1.52868 − 0.21520I
a = 0.01958 − 1.60043I
b = 0.723515 − 1.210650I
−7.27853 − 5.82567I −6.96095 + 4.30133I
23
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.55777 + 0.32580I
a = 0.130960 − 1.131790I
b = −0.680192 − 0.953517I
−5.16950 + 6.79128I −6.65966 − 5.16941I
u = −1.55777 − 0.32580I
a = 0.130960 + 1.131790I
b = −0.680192 + 0.953517I
−5.16950 − 6.79128I −6.65966 + 5.16941I
u = 1.59297 + 0.30534I
a = 0.1137980 − 0.0630215I
b = 0.539987 − 0.108988I
−1.95391 − 4.34795I −1.36568 − 2.53861I
u = 1.59297 − 0.30534I
a = 0.1137980 + 0.0630215I
b = 0.539987 + 0.108988I
−1.95391 + 4.34795I −1.36568 + 2.53861I
u = −0.141191 + 0.350131I
a = 1.98607 − 1.57595I
b = −0.088324 + 0.883311I
6.39041 − 5.95192I 2.01493 + 4.29419I
u = −0.141191 − 0.350131I
a = 1.98607 + 1.57595I
b = −0.088324 − 0.883311I
6.39041 + 5.95192I 2.01493 − 4.29419I
u = 1.62979
a = −0.128710
b = −0.551653
−5.85643 −10.0770
u = 0.240888 + 0.205962I
a = −1.75310 − 2.18070I
b = 0.215866 − 1.094370I
−0.43147 − 2.68369I 3.04354 + 11.76064I
u = 0.240888 − 0.205962I
a = −1.75310 + 2.18070I
b = 0.215866 + 1.094370I
−0.43147 + 2.68369I 3.04354 − 11.76064I
24
IV. I
u
4
= hb + 1, a
4
+ 2a
3
− a
2
− 2a + 3, u − 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
1
a
7
=
1
1
a
11
=
−1
0
a
3
=
a
−1
a
8
=
0
1
a
4
=
a
a − 1
a
12
=
−a − 1
1
a
2
=
a + 1
−1
a
1
=
−a
3
− a
2
+ 2a + 1
−a
3
+ 2a − 2
a
9
=
a
2
+ 2a + 1
−a
a
5
=
−a
3
− 2a
2
− a + 1
a
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
12
(u
2
+ 2)
2
c
2
, c
6
, c
7
c
11
(u − 1)
4
c
3
, c
9
u
4
+ 2u
3
− u
2
− 2u + 3
c
5
, c
8
u
4
− 2u
3
− u
2
+ 2u + 3
c
10
(u + 1)
4
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
12
(y + 2)
4
c
2
, c
6
, c
7
c
10
, c
11
(y −1)
4
c
3
, c
5
, c
8
c
9
y
4
− 6y
3
+ 15y
2
− 10y + 9
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0.752489 + 0.564561I
b = −1.00000
4.93480 0
u = 1.00000
a = 0.752489 − 0.564561I
b = −1.00000
4.93480 0
u = 1.00000
a = −1.75249 + 0.56456I
b = −1.00000
4.93480 0
u = 1.00000
a = −1.75249 − 0.56456I
b = −1.00000
4.93480 0
28
V. I
u
5
= hb − 1, a
2
− a − 1, u − 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
1
a
7
=
1
1
a
11
=
−1
0
a
3
=
a
1
a
8
=
0
1
a
4
=
a
a + 1
a
12
=
a − 1
1
a
2
=
a − 1
1
a
1
=
a − 1
1
a
9
=
−a + 2
a
a
5
=
a
a + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 10
29
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
12
u
2
c
2
, c
10
, c
11
(u + 1)
2
c
3
, c
5
, c
8
c
9
u
2
− u − 1
c
6
, c
7
(u − 1)
2
30
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
12
y
2
c
2
, c
6
, c
7
c
10
, c
11
(y −1)
2
c
3
, c
5
, c
8
c
9
y
2
− 3y + 1
31
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −0.618034
b = 1.00000
0 10.0000
u = 1.00000
a = 1.61803
b = 1.00000
0 10.0000
32
VI. I
v
1
= ha, b + 1, v − 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
1
0
a
7
=
1
0
a
11
=
1
0
a
3
=
0
−1
a
8
=
1
0
a
4
=
1
−1
a
12
=
1
−1
a
2
=
1
−1
a
1
=
1
−1
a
9
=
2
−1
a
5
=
−1
1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 6
33
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
6
c
7
, c
10
, c
12
u
c
2
, c
3
, c
5
c
8
, c
9
, c
11
u − 1
34
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
6
c
7
, c
10
, c
12
y
c
2
, c
3
, c
5
c
8
, c
9
, c
11
y −1
35
(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
36
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
12
u
3
(u
2
+ 2)
2
(u
19
− 6u
18
+ ··· + 26u − 5)(u
33
+ 7u
32
+ ··· + 6u + 2)
2
· (u
49
− 9u
48
+ ··· − 75u + 15)
c
2
, c
11
((u − 1)
5
)(u + 1)
2
(u
19
+ u
18
+ ··· − u − 1)(u
49
+ 2u
48
+ ··· − 12u − 3)
· (u
66
− 3u
65
+ ··· − 422u + 59)
c
3
, c
9
(u − 1)(u
2
− u − 1)(u
4
+ 2u
3
+ ··· − 2u + 3)(u
19
− u
18
+ ··· − 2u + 1)
· (u
49
− 6u
47
+ ··· − 35u − 11)(u
66
− 5u
64
+ ··· − 7821u + 1213)
c
4
u
3
(u
2
+ 2)
2
(u
19
+ 6u
18
+ ··· + 26u + 5)(u
33
+ 7u
32
+ ··· + 6u + 2)
2
· (u
49
− 9u
48
+ ··· − 75u + 15)
c
5
, c
8
(u − 1)(u
2
− u − 1)(u
4
− 2u
3
+ ··· + 2u + 3)(u
19
− 3u
18
+ ··· + 2u − 1)
· (u
49
+ 4u
48
+ ··· − 3u − 1)(u
66
+ 2u
65
+ ··· − 195u − 107)
c
6
, c
7
u(u − 1)
6
(u
19
+ 5u
18
+ ··· + 2u − 1)(u
33
− 4u
32
+ ··· + 4u − 1)
2
· (u
49
+ 14u
48
+ ··· + 15u + 15)
c
10
u(u + 1)
6
(u
19
− 5u
18
+ ··· + 2u + 1)(u
33
− 4u
32
+ ··· + 4u − 1)
2
· (u
49
+ 14u
48
+ ··· + 15u + 15)
37
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
12
y
3
(y + 2)
4
(y
19
+ 18y
18
+ ··· − 274y −25)
· ((y
33
+ 33y
32
+ ··· + 84y −4)
2
)(y
49
+ 47y
48
+ ··· + 3495y −225)
c
2
, c
11
((y −1)
7
)(y
19
+ 17y
18
+ ··· − y −1)(y
49
− 6y
48
+ ··· + 120y −9)
· (y
66
+ 29y
65
+ ··· + 16970y + 3481)
c
3
, c
9
(y −1)(y
2
− 3y + 1)(y
4
− 6y
3
+ ··· − 10y + 9)(y
19
+ 3y
18
+ ··· + 4y −1)
· (y
49
− 12y
48
+ ··· + 1005y −121)
· (y
66
− 10y
65
+ ··· − 30663517y + 1471369)
c
5
, c
8
(y −1)(y
2
− 3y + 1)(y
4
− 6y
3
+ ··· − 10y + 9)(y
19
+ y
18
+ ··· + 2y
2
− 1)
· (y
49
− 42y
48
+ ··· + 141y −1)(y
66
− 2y
65
+ ··· − 846945y + 11449)
c
6
, c
7
, c
10
y(y −1)
6
(y
19
− 23y
18
+ ··· − 4y −1)(y
33
− 34y
32
+ ··· + 20y −1)
2
· (y
49
− 54y
48
+ ··· + 1245y −225)
38
