12a
0741
(K12a
0741
)
A knot diagram
1
Linearized knot diagam
3 8 9 11 1 10 12 2 5 7 4 6
Solving Sequence
6,10
7
1,11
5 4 9 3 12 8 2
c
6
c
10
c
5
c
4
c
9
c
3
c
12
c
7
c
2
c
1
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−9.22629 × 10
114
u
52
− 2.74007 × 10
115
u
51
+ ··· + 4.77254 × 10
116
b + 2.56825 × 10
117
,
1.04478 × 10
116
u
52
+ 3.89252 × 10
116
u
51
+ ··· + 1.90902 × 10
118
a − 3.41478 × 10
118
,
u
53
+ 2u
52
+ ··· + 329u + 160i
I
u
2
= hu
38
+ u
37
+ ··· + a + 2, 2u
38
a + 14u
38
+ ··· + 6a + 14, u
39
+ u
38
+ ··· + 2u + 1i
I
u
3
= hb − 1, 16a
4
− 32a
3
+ 16a
2
+ 1, u + 1i
I
u
4
= h−4u
2
a + au − 13u
2
+ 23b + 10a + 9u − 25, −70u
2
a + 25a
2
+ 40au + 151u
2
− 130a − 62u + 309,
u
3
− u
2
+ 2u − 1i
I
u
5
= hb + 1, 8a
3
+ 12a
2
+ 6a + 1, u − 1i
* 5 irreducible components of dim
C
= 0, with total 144 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−9.23 × 10
114
u
52
− 2.74 × 10
115
u
51
+ · · · + 4.77 × 10
116
b + 2.57 ×
10
117
, 1.04 × 10
116
u
52
+ 3.89 × 10
116
u
51
+ · · · + 1.91 × 10
118
a − 3.41 ×
10
118
, u
53
+ 2u
52
+ · · · + 329u + 160i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
7
=
1
u
2
a
1
=
−0.00547287u
52
− 0.0203902u
51
+ ··· − 5.89017u + 1.78876
0.0193320u
52
+ 0.0574133u
51
+ ··· − 12.8760u − 5.38131
a
11
=
−u
−u
3
+ u
a
5
=
0.0243283u
52
+ 0.0637946u
51
+ ··· − 4.49363u + 0.406738
0.0256578u
52
+ 0.0667823u
51
+ ··· − 17.0251u − 4.63953
a
4
=
0.0430776u
52
+ 0.111948u
51
+ ··· − 16.2352u − 2.68638
0.0138491u
52
+ 0.0344025u
51
+ ··· − 11.7889u − 3.25117
a
9
=
0.0196369u
52
+ 0.0612628u
51
+ ··· − 3.78192u − 4.37932
−0.00126582u
52
− 0.00958516u
51
+ ··· − 0.909111u + 0.348371
a
3
=
0.0151668u
52
+ 0.0328572u
51
+ ··· − 12.7531u − 1.36568
−0.0100144u
52
− 0.0235824u
51
+ ··· + 0.705795u − 0.528707
a
12
=
0.0138591u
52
+ 0.0370231u
51
+ ··· − 18.7662u − 3.59254
0.0193320u
52
+ 0.0574133u
51
+ ··· − 12.8760u − 5.38131
a
8
=
−0.0241663u
52
− 0.0663621u
51
+ ··· + 3.16247u + 1.51646
0.00213415u
52
+ 0.00509088u
51
+ ··· − 1.04158u − 0.257202
a
2
=
0.00119343u
52
− 0.0121666u
51
+ ··· − 6.31916u + 1.10586
−0.0242121u
52
− 0.0727143u
51
+ ··· + 5.31037u + 2.13761
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.102716u
52
+ 0.362833u
51
+ ··· + 2.34272u − 23.6794
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
53
+ 25u
52
+ ··· − 112u − 64
c
2
, c
8
u
53
− 3u
52
+ ··· − 12u + 8
c
3
u
53
+ 3u
52
+ ··· + 91812u + 11464
c
4
, c
5
, c
11
c
12
u
53
− u
52
+ ··· − 2u + 1
c
6
, c
10
u
53
+ 2u
52
+ ··· + 329u + 160
c
7
, c
9
128(128u
53
− 64u
52
+ ··· − 13u + 1)
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
53
+ 9y
52
+ ··· − 3840y −4096
c
2
, c
8
y
53
+ 25y
52
+ ··· − 112y −64
c
3
y
53
− 7y
52
+ ··· + 828536208y −131423296
c
4
, c
5
, c
11
c
12
y
53
+ 17y
52
+ ··· − 18y −1
c
6
, c
10
y
53
− 22y
52
+ ··· + 992401y −25600
c
7
, c
9
16384(16384y
53
− 208896y
52
+ ··· − 135y −1)
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.010500 + 0.277494I
a = −0.309112 + 0.248738I
b = −1.230130 + 0.452325I
−3.60132 − 1.23088I −8.16326 + 5.88240I
u = 1.010500 − 0.277494I
a = −0.309112 − 0.248738I
b = −1.230130 − 0.452325I
−3.60132 + 1.23088I −8.16326 − 5.88240I
u = −1.016340 + 0.336995I
a = 0.237630 + 0.305698I
b = 1.31165 + 0.53324I
−5.96983 + 5.72038I −11.2924 − 8.5433I
u = −1.016340 − 0.336995I
a = 0.237630 − 0.305698I
b = 1.31165 − 0.53324I
−5.96983 − 5.72038I −11.2924 + 8.5433I
u = 0.894368 + 0.170124I
a = −1.173990 + 0.551696I
b = 0.192195 − 0.262622I
−4.05202 + 3.78789I −10.53464 − 4.24172I
u = 0.894368 − 0.170124I
a = −1.173990 − 0.551696I
b = 0.192195 + 0.262622I
−4.05202 − 3.78789I −10.53464 + 4.24172I
u = 0.889815 + 0.158884I
a = −0.558076 + 0.216460I
b = −1.237620 + 0.182509I
−2.84156 − 0.53577I −2.03217 + 7.98267I
u = 0.889815 − 0.158884I
a = −0.558076 − 0.216460I
b = −1.237620 − 0.182509I
−2.84156 + 0.53577I −2.03217 − 7.98267I
u = 0.856411 + 0.685171I
a = 0.23931 − 1.74388I
b = 0.468215 + 0.785484I
−4.04273 + 0.39813I −11.01909 + 4.12127I
u = 0.856411 − 0.685171I
a = 0.23931 + 1.74388I
b = 0.468215 − 0.785484I
−4.04273 − 0.39813I −11.01909 − 4.12127I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.357016 + 1.088740I
a = 0.29731 + 1.45796I
b = −0.487890 − 1.101780I
0.44124 − 4.68393I −8.30547 + 4.38111I
u = −0.357016 − 1.088740I
a = 0.29731 − 1.45796I
b = −0.487890 + 1.101780I
0.44124 + 4.68393I −8.30547 − 4.38111I
u = −1.107520 + 0.302023I
a = 0.185994 + 0.166983I
b = 1.135680 + 0.628747I
−7.15683 − 1.71285I −15.0160 − 0.3603I
u = −1.107520 − 0.302023I
a = 0.185994 − 0.166983I
b = 1.135680 − 0.628747I
−7.15683 + 1.71285I −15.0160 + 0.3603I
u = −0.246858 + 1.143050I
a = 0.22408 + 1.48798I
b = −0.507181 − 1.240200I
3.35515 − 13.11250I −5.16195 + 8.65922I
u = −0.246858 − 1.143050I
a = 0.22408 − 1.48798I
b = −0.507181 + 1.240200I
3.35515 + 13.11250I −5.16195 − 8.65922I
u = 0.285314 + 1.165920I
a = −0.23055 + 1.46085I
b = 0.460429 − 1.210720I
5.76708 + 7.70183I −2.26158 − 5.23055I
u = 0.285314 − 1.165920I
a = −0.23055 − 1.46085I
b = 0.460429 + 1.210720I
5.76708 − 7.70183I −2.26158 + 5.23055I
u = −1.190920 + 0.164534I
a = 0.595741 + 0.422528I
b = 0.162888 − 0.445268I
−1.54684 + 0.49363I −7.46237 − 2.14913I
u = −1.190920 − 0.164534I
a = 0.595741 − 0.422528I
b = 0.162888 + 0.445268I
−1.54684 − 0.49363I −7.46237 + 2.14913I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.957980 + 0.787698I
a = −0.37852 − 1.57550I
b = −0.434771 + 0.898967I
−0.60629 + 4.29298I −8.00000 − 7.47231I
u = −0.957980 − 0.787698I
a = −0.37852 + 1.57550I
b = −0.434771 − 0.898967I
−0.60629 − 4.29298I −8.00000 + 7.47231I
u = 1.041380 + 0.692963I
a = 0.56731 − 1.66360I
b = 0.542920 + 0.942914I
−4.64111 − 8.53246I −11.2112 + 9.6162I
u = 1.041380 − 0.692963I
a = 0.56731 + 1.66360I
b = 0.542920 − 0.942914I
−4.64111 + 8.53246I −11.2112 − 9.6162I
u = −0.738902 + 0.118991I
a = 0.839648 + 0.253541I
b = 1.328440 + 0.061804I
−4.61573 − 3.33353I −5.28986 + 1.76068I
u = −0.738902 − 0.118991I
a = 0.839648 − 0.253541I
b = 1.328440 − 0.061804I
−4.61573 + 3.33353I −5.28986 − 1.76068I
u = 1.309210 + 0.191706I
a = −0.150987 − 0.150085I
b = −0.689475 + 0.753211I
−5.84739 + 0.86218I 0
u = 1.309210 − 0.191706I
a = −0.150987 + 0.150085I
b = −0.689475 − 0.753211I
−5.84739 − 0.86218I 0
u = 0.455502 + 1.311390I
a = −0.229330 + 1.339160I
b = 0.293604 − 1.116830I
7.73147 + 4.14673I 0
u = 0.455502 − 1.311390I
a = −0.229330 − 1.339160I
b = 0.293604 + 1.116830I
7.73147 − 4.14673I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.253370 + 0.652070I
a = −0.94701 − 1.36034I
b = −0.633605 + 1.227090I
−2.43644 + 10.92000I 0
u = −1.253370 − 0.652070I
a = −0.94701 + 1.36034I
b = −0.633605 − 1.227090I
−2.43644 − 10.92000I 0
u = −1.29214 + 0.64007I
a = −1.01211 − 1.27074I
b = −0.64920 + 1.30689I
0.0577 + 19.4085I 0
u = −1.29214 − 0.64007I
a = −1.01211 + 1.27074I
b = −0.64920 − 1.30689I
0.0577 − 19.4085I 0
u = 1.28693 + 0.65572I
a = 0.96664 − 1.27292I
b = 0.61846 + 1.29081I
2.5806 − 14.1172I 0
u = 1.28693 − 0.65572I
a = 0.96664 + 1.27292I
b = 0.61846 − 1.29081I
2.5806 + 14.1172I 0
u = 1.28431 + 0.72559I
a = 0.80342 − 1.23877I
b = 0.498243 + 1.251700I
4.89820 − 11.20600I 0
u = 1.28431 − 0.72559I
a = 0.80342 + 1.23877I
b = 0.498243 − 1.251700I
4.89820 + 11.20600I 0
u = −1.27009 + 0.77458I
a = −0.70606 − 1.24445I
b = −0.441345 + 1.205700I
4.39290 + 5.76841I 0
u = −1.27009 − 0.77458I
a = −0.70606 + 1.24445I
b = −0.441345 − 1.205700I
4.39290 − 5.76841I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.62038 + 1.36139I
a = 0.247137 + 1.266590I
b = −0.239949 − 1.046860I
6.83679 + 1.68050I 0
u = −0.62038 − 1.36139I
a = 0.247137 − 1.266590I
b = −0.239949 + 1.046860I
6.83679 − 1.68050I 0
u = −1.50653 + 0.08391I
a = 0.136195 − 0.401648I
b = 0.397232 + 0.840006I
−1.12611 − 2.71991I 0
u = −1.50653 − 0.08391I
a = 0.136195 + 0.401648I
b = 0.397232 − 0.840006I
−1.12611 + 2.71991I 0
u = −0.18082 + 1.50804I
a = −0.025191 − 1.242950I
b = −0.035651 + 0.846395I
5.62880 + 2.99985I 0
u = −0.18082 − 1.50804I
a = −0.025191 + 1.242950I
b = −0.035651 − 0.846395I
5.62880 − 2.99985I 0
u = 1.52320 + 0.19708I
a = −0.031722 − 0.366987I
b = −0.453417 + 0.944633I
−3.01084 + 7.94270I 0
u = 1.52320 − 0.19708I
a = −0.031722 + 0.366987I
b = −0.453417 − 0.944633I
−3.01084 − 7.94270I 0
u = −0.279211 + 0.248748I
a = 0.598547 − 0.883823I
b = −0.239491 + 0.269538I
−0.533461 + 0.879212I −9.52326 − 7.63662I
u = −0.279211 − 0.248748I
a = 0.598547 + 0.883823I
b = −0.239491 − 0.269538I
−0.533461 − 0.879212I −9.52326 + 7.63662I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.349659 + 0.074107I
a = −2.23401 + 1.00440I
b = 0.596328 − 0.151333I
−3.95805 + 3.86479I −11.90700 − 4.97851I
u = 0.349659 − 0.074107I
a = −2.23401 − 1.00440I
b = 0.596328 + 0.151333I
−3.95805 − 3.86479I −11.90700 + 4.97851I
u = −0.337034
a = 1.65164
b = −0.453134
−1.01554 −10.2060
10
II.
I
u
2
= hu
38
+u
37
+· · ·+a+2, 2u
38
a+14u
38
+· · ·+6a+14, u
39
+u
38
+· · ·+2u+1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
7
=
1
u
2
a
1
=
a
−u
38
− u
37
+ ··· − a − 2
a
11
=
−u
−u
3
+ u
a
5
=
−u
38
a − 4u
38
+ ··· − 2a − 2
u
5
a + u
6
− 2u
3
a − 2u
4
+ au + 2u
2
a
4
=
−u
38
a − 4u
38
+ ··· − 2a − 3
1
a
9
=
−2u
38
a − 10u
38
+ ··· − a − 10
u
38
− u
37
+ ··· + a + 4
a
3
=
−u
38
a − 3u
37
a + ··· + 12u + 7
−2u
38
− 2u
37
+ ··· + au + 2u
a
12
=
−u
38
− u
37
+ ··· − 2u − 2
−u
38
− u
37
+ ··· − a − 2
a
8
=
u
38
a + 10u
38
+ ··· + 4a + 13
−2u
38
− 2u
37
+ ··· + 2u − 1
a
2
=
−u
38
a − 11u
38
+ ··· + 24u + 6
u
37
a − u
38
+ ··· + au + 2u
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −4u
38
+ 44u
36
+ 4u
35
− 232u
34
− 40u
33
+ 752u
32
+ 192u
31
− 1620u
30
− 564u
29
+
2316u
28
+ 1092u
27
− 1948u
26
− 1380u
25
+ 284u
24
+ 980u
23
+ 1508u
22
− 16u
21
−
1892u
20
− 728u
19
+ 776u
18
+ 660u
17
+ 444u
16
− 64u
15
− 692u
14
− 332u
13
+ 236u
12
+
252u
11
+ 128u
10
+ 4u
9
− 132u
8
− 96u
7
+ 20u
6
+ 40u
5
+ 20u
4
+ 8u
3
− 8u
2
− 12u − 14
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
39
+ 19u
38
+ ··· + 2u
2
− 1)
2
c
2
, c
8
(u
39
+ u
38
+ ··· + 2u
3
− 1)
2
c
3
(u
39
− u
38
+ ··· − 18u − 17)
2
c
4
, c
5
, c
11
c
12
u
78
+ 3u
77
+ ··· + 788u + 173
c
6
, c
10
(u
39
+ u
38
+ ··· + 2u + 1)
2
c
7
, c
9
u
78
− 21u
77
+ ··· + 448674u + 57751
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
39
+ 3y
38
+ ··· + 4y −1)
2
c
2
, c
8
(y
39
+ 19y
38
+ ··· + 2y
2
− 1)
2
c
3
(y
39
− 13y
38
+ ··· + 3588y −289)
2
c
4
, c
5
, c
11
c
12
y
78
+ 47y
77
+ ··· + 318100y + 29929
c
6
, c
10
(y
39
− 21y
38
+ ··· + 2y
2
− 1)
2
c
7
, c
9
y
78
+ 27y
77
+ ··· − 879585708y + 3335178001
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.913577 + 0.379498I
a = −1.64226 − 0.07520I
b = −0.477548 + 0.774232I
1.22606 + 1.25772I −10.67108 − 2.89583I
u = −0.913577 + 0.379498I
a = 0.62112 + 1.52499I
b = −0.068253 − 1.290290I
1.22606 + 1.25772I −10.67108 − 2.89583I
u = −0.913577 − 0.379498I
a = −1.64226 + 0.07520I
b = −0.477548 − 0.774232I
1.22606 − 1.25772I −10.67108 + 2.89583I
u = −0.913577 − 0.379498I
a = 0.62112 − 1.52499I
b = −0.068253 + 1.290290I
1.22606 − 1.25772I −10.67108 + 2.89583I
u = −0.867921 + 0.539600I
a = 0.510917 + 0.983764I
b = −0.18434 − 1.52434I
3.26214 + 7.71489I −5.96279 − 8.94046I
u = −0.867921 + 0.539600I
a = −1.238810 − 0.665421I
b = −0.787918 + 1.001630I
3.26214 + 7.71489I −5.96279 − 8.94046I
u = −0.867921 − 0.539600I
a = 0.510917 − 0.983764I
b = −0.18434 + 1.52434I
3.26214 − 7.71489I −5.96279 + 8.94046I
u = −0.867921 − 0.539600I
a = −1.238810 + 0.665421I
b = −0.787918 − 1.001630I
3.26214 − 7.71489I −5.96279 + 8.94046I
u = 0.824609 + 0.517095I
a = −0.377205 + 0.997280I
b = 0.24151 − 1.45331I
5.20022 − 2.98443I −2.14009 + 4.48194I
u = 0.824609 + 0.517095I
a = 1.37439 − 0.72790I
b = 0.683848 + 1.053830I
5.20022 − 2.98443I −2.14009 + 4.48194I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.824609 − 0.517095I
a = −0.377205 − 0.997280I
b = 0.24151 + 1.45331I
5.20022 + 2.98443I −2.14009 − 4.48194I
u = 0.824609 − 0.517095I
a = 1.37439 + 0.72790I
b = 0.683848 − 1.053830I
5.20022 + 2.98443I −2.14009 − 4.48194I
u = 1.027710 + 0.074094I
a = 3.84195 + 7.80158I
b = −0.025359 + 0.910828I
−0.87783 − 3.61917I −14.0650 + 4.3346I
u = 1.027710 + 0.074094I
a = −7.85413 + 3.84314I
b = −0.015457 − 1.071100I
−0.87783 − 3.61917I −14.0650 + 4.3346I
u = 1.027710 − 0.074094I
a = 3.84195 − 7.80158I
b = −0.025359 − 0.910828I
−0.87783 + 3.61917I −14.0650 − 4.3346I
u = 1.027710 − 0.074094I
a = −7.85413 − 3.84314I
b = −0.015457 + 1.071100I
−0.87783 + 3.61917I −14.0650 − 4.3346I
u = −0.898181
a = −5.31152 + 5.23221I
b = −0.086796 − 1.011240I
1.82692 −10.3980
u = −0.898181
a = −5.31152 − 5.23221I
b = −0.086796 + 1.011240I
1.82692 −10.3980
u = 0.704254 + 0.512490I
a = −0.054845 + 0.799959I
b = 0.392937 − 1.328450I
5.54691 − 1.23434I −0.76309 + 3.43750I
u = 0.704254 + 0.512490I
a = 1.51387 − 1.03796I
b = 0.516935 + 1.213000I
5.54691 − 1.23434I −0.76309 + 3.43750I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.704254 − 0.512490I
a = −0.054845 − 0.799959I
b = 0.392937 + 1.328450I
5.54691 + 1.23434I −0.76309 − 3.43750I
u = 0.704254 − 0.512490I
a = 1.51387 + 1.03796I
b = 0.516935 − 1.213000I
5.54691 + 1.23434I −0.76309 − 3.43750I
u = −0.632327 + 0.547010I
a = −0.020576 + 0.552941I
b = −0.503524 − 1.265570I
3.92367 − 3.33294I −3.97830 + 2.50936I
u = −0.632327 + 0.547010I
a = −1.45180 − 1.22116I
b = −0.443589 + 1.320110I
3.92367 − 3.33294I −3.97830 + 2.50936I
u = −0.632327 − 0.547010I
a = −0.020576 − 0.552941I
b = −0.503524 + 1.265570I
3.92367 + 3.33294I −3.97830 − 2.50936I
u = −0.632327 − 0.547010I
a = −1.45180 + 1.22116I
b = −0.443589 − 1.320110I
3.92367 + 3.33294I −3.97830 − 2.50936I
u = −0.139221 + 0.807285I
a = 0.299849 − 0.814758I
b = −0.880048 + 0.059607I
−0.17425 − 8.12134I −7.90397 + 6.02892I
u = −0.139221 + 0.807285I
a = −0.60927 − 1.40465I
b = 0.471332 + 1.226850I
−0.17425 − 8.12134I −7.90397 + 6.02892I
u = −0.139221 − 0.807285I
a = 0.299849 + 0.814758I
b = −0.880048 − 0.059607I
−0.17425 + 8.12134I −7.90397 − 6.02892I
u = −0.139221 − 0.807285I
a = −0.60927 + 1.40465I
b = 0.471332 − 1.226850I
−0.17425 + 8.12134I −7.90397 − 6.02892I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.114960 + 0.441427I
a = 0.96280 + 1.05055I
b = 0.305249 − 1.203980I
0.79891 + 1.59434I −7.82288 − 0.43137I
u = −1.114960 + 0.441427I
a = −0.392949 + 0.110127I
b = −0.685928 + 0.085145I
0.79891 + 1.59434I −7.82288 − 0.43137I
u = −1.114960 − 0.441427I
a = 0.96280 − 1.05055I
b = 0.305249 + 1.203980I
0.79891 − 1.59434I −7.82288 + 0.43137I
u = −1.114960 − 0.441427I
a = −0.392949 − 0.110127I
b = −0.685928 − 0.085145I
0.79891 − 1.59434I −7.82288 + 0.43137I
u = −0.076025 + 0.793162I
a = 0.273987 − 0.956855I
b = −0.679913 + 0.270947I
−1.95085 − 0.25023I −10.76221 − 0.26522I
u = −0.076025 + 0.793162I
a = −0.45840 − 1.35614I
b = 0.460844 + 1.007450I
−1.95085 − 0.25023I −10.76221 − 0.26522I
u = −0.076025 − 0.793162I
a = 0.273987 + 0.956855I
b = −0.679913 − 0.270947I
−1.95085 + 0.25023I −10.76221 + 0.26522I
u = −0.076025 − 0.793162I
a = −0.45840 + 1.35614I
b = 0.460844 − 1.007450I
−1.95085 + 0.25023I −10.76221 + 0.26522I
u = 0.132738 + 0.775160I
a = −0.231485 − 0.830100I
b = 0.751940 + 0.013317I
2.28825 + 3.25758I −4.69216 − 2.50620I
u = 0.132738 + 0.775160I
a = 0.56771 − 1.46731I
b = −0.382264 + 1.186640I
2.28825 + 3.25758I −4.69216 − 2.50620I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.132738 − 0.775160I
a = −0.231485 + 0.830100I
b = 0.751940 − 0.013317I
2.28825 − 3.25758I −4.69216 + 2.50620I
u = 0.132738 − 0.775160I
a = 0.56771 + 1.46731I
b = −0.382264 − 1.186640I
2.28825 − 3.25758I −4.69216 + 2.50620I
u = 1.142370 + 0.483180I
a = −0.935088 + 1.044860I
b = −0.477838 − 1.271590I
1.19227 − 6.17588I −6.65093 + 6.87938I
u = 1.142370 + 0.483180I
a = 0.272499 − 0.151704I
b = 0.929505 − 0.024096I
1.19227 − 6.17588I −6.65093 + 6.87938I
u = 1.142370 − 0.483180I
a = −0.935088 − 1.044860I
b = −0.477838 + 1.271590I
1.19227 + 6.17588I −6.65093 − 6.87938I
u = 1.142370 − 0.483180I
a = 0.272499 + 0.151704I
b = 0.929505 + 0.024096I
1.19227 + 6.17588I −6.65093 − 6.87938I
u = −1.194180 + 0.388571I
a = 0.760362 + 0.937327I
b = 0.321822 − 0.694203I
−1.60456 + 0.66747I −9.40097 − 0.84813I
u = −1.194180 + 0.388571I
a = 0.390346 + 0.318847I
b = −0.353940 − 0.520941I
−1.60456 + 0.66747I −9.40097 − 0.84813I
u = −1.194180 − 0.388571I
a = 0.760362 − 0.937327I
b = 0.321822 + 0.694203I
−1.60456 − 0.66747I −9.40097 + 0.84813I
u = −1.194180 − 0.388571I
a = 0.390346 − 0.318847I
b = −0.353940 + 0.520941I
−1.60456 − 0.66747I −9.40097 + 0.84813I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.213030 + 0.378072I
a = −0.662575 + 1.045760I
b = −0.425457 − 0.498391I
−4.23928 + 4.12434I −12.59821 − 2.83806I
u = 1.213030 + 0.378072I
a = −0.617933 + 0.190406I
b = 0.373755 − 0.738426I
−4.23928 + 4.12434I −12.59821 − 2.83806I
u = 1.213030 − 0.378072I
a = −0.662575 − 1.045760I
b = −0.425457 + 0.498391I
−4.23928 − 4.12434I −12.59821 + 2.83806I
u = 1.213030 − 0.378072I
a = −0.617933 − 0.190406I
b = 0.373755 + 0.738426I
−4.23928 − 4.12434I −12.59821 + 2.83806I
u = 1.210580 + 0.415258I
a = −0.826285 + 1.053700I
b = −0.562463 − 0.775475I
−5.75156 − 3.95701I −14.5927 + 3.7511I
u = 1.210580 + 0.415258I
a = −0.314458 + 0.021623I
b = 0.625189 − 0.563346I
−5.75156 − 3.95701I −14.5927 + 3.7511I
u = 1.210580 − 0.415258I
a = −0.826285 − 1.053700I
b = −0.562463 + 0.775475I
−5.75156 + 3.95701I −14.5927 − 3.7511I
u = 1.210580 − 0.415258I
a = −0.314458 − 0.021623I
b = 0.625189 + 0.563346I
−5.75156 + 3.95701I −14.5927 − 3.7511I
u = 1.185450 + 0.504016I
a = −0.94362 + 1.05600I
b = −0.69021 − 1.27161I
−0.78771 − 7.98510I −8.00000 + 5.54137I
u = 1.185450 + 0.504016I
a = 0.109545 − 0.319832I
b = 1.113180 − 0.221223I
−0.78771 − 7.98510I −8.00000 + 5.54137I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.185450 − 0.504016I
a = −0.94362 − 1.05600I
b = −0.69021 + 1.27161I
−0.78771 + 7.98510I −8.00000 − 5.54137I
u = 1.185450 − 0.504016I
a = 0.109545 + 0.319832I
b = 1.113180 + 0.221223I
−0.78771 + 7.98510I −8.00000 − 5.54137I
u = −1.200000 + 0.486246I
a = 0.93326 + 1.06775I
b = 0.720212 − 1.161810I
−5.24646 + 4.91106I −13.8091 − 3.0612I
u = −1.200000 + 0.486246I
a = −0.008020 − 0.279310I
b = −1.043390 − 0.337545I
−5.24646 + 4.91106I −13.8091 − 3.0612I
u = −1.200000 − 0.486246I
a = 0.93326 − 1.06775I
b = 0.720212 + 1.161810I
−5.24646 − 4.91106I −13.8091 + 3.0612I
u = −1.200000 − 0.486246I
a = −0.008020 + 0.279310I
b = −1.043390 + 0.337545I
−5.24646 − 4.91106I −13.8091 + 3.0612I
u = −1.194900 + 0.512673I
a = 0.95104 + 1.05959I
b = 0.74829 − 1.29366I
−3.28896 + 12.96900I −10.9187 − 9.0478I
u = −1.194900 + 0.512673I
a = −0.089777 − 0.373592I
b = −1.179310 − 0.254876I
−3.28896 + 12.96900I −10.9187 − 9.0478I
u = −1.194900 − 0.512673I
a = 0.95104 − 1.05959I
b = 0.74829 + 1.29366I
−3.28896 − 12.96900I −10.9187 + 9.0478I
u = −1.194900 − 0.512673I
a = −0.089777 + 0.373592I
b = −1.179310 + 0.254876I
−3.28896 − 12.96900I −10.9187 + 9.0478I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.180542 + 0.637095I
a = 0.064504 − 0.748110I
b = 0.495256 − 0.410729I
3.93259 + 1.83013I −2.77518 − 3.69155I
u = 0.180542 + 0.637095I
a = 0.68301 − 1.84952I
b = −0.100757 + 1.244120I
3.93259 + 1.83013I −2.77518 − 3.69155I
u = 0.180542 − 0.637095I
a = 0.064504 + 0.748110I
b = 0.495256 + 0.410729I
3.93259 − 1.83013I −2.77518 + 3.69155I
u = 0.180542 − 0.637095I
a = 0.68301 + 1.84952I
b = −0.100757 − 1.244120I
3.93259 − 1.83013I −2.77518 + 3.69155I
u = −0.339086 + 0.540694I
a = −0.372018 − 0.331028I
b = −0.515841 − 0.801258I
3.03920 + 2.27932I −4.43670 − 3.34383I
u = −0.339086 + 0.540694I
a = −1.21813 − 1.86370I
b = −0.081651 + 1.313520I
3.03920 + 2.27932I −4.43670 − 3.34383I
u = −0.339086 − 0.540694I
a = −0.372018 + 0.331028I
b = −0.515841 + 0.801258I
3.03920 − 2.27932I −4.43670 + 3.34383I
u = −0.339086 − 0.540694I
a = −1.21813 + 1.86370I
b = −0.081651 − 1.313520I
3.03920 − 2.27932I −4.43670 + 3.34383I
21
III. I
u
3
= hb − 1, 16a
4
− 32a
3
+ 16a
2
+ 1, u + 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
−1
a
7
=
1
1
a
1
=
a
1
a
11
=
1
0
a
5
=
−a + 1
−1
a
4
=
−a
−1
a
9
=
−a
2
+ 2a − 1
−a
a
3
=
2a
3
− 5a
2
+ 3a − 1
2a
2
− a − 1
a
12
=
a + 1
1
a
8
=
−a
2
− a + 1
−a + 1
a
2
=
2a
3
− 9a
2
+
15
2
a −
1
4
4a
3
− 6a
2
+ 3a −
1
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 16a
2
− 16a − 16
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
2
− 2u + 2)
2
c
2
, c
8
u
4
+ 2u
2
+ 2
c
3
u
4
− 2u
2
+ 2
c
4
, c
5
, c
10
(u − 1)
4
c
6
, c
11
, c
12
(u + 1)
4
c
7
16(16u
4
+ 32u
3
+ 16u
2
+ 1)
c
9
16(16u
4
− 32u
3
+ 16u
2
+ 1)
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
2
+ 4)
2
c
2
, c
8
(y
2
+ 2y + 2)
2
c
3
(y
2
− 2y + 2)
2
c
4
, c
5
, c
6
c
10
, c
11
, c
12
(y −1)
4
c
7
, c
9
256(256y
4
− 512y
3
+ 288y
2
+ 32y + 1)
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 1.049340 + 0.227545I
b = 1.00000
−5.75727 − 3.66386I −16.0000 + 4.0000I
u = −1.00000
a = 1.049340 − 0.227545I
b = 1.00000
−5.75727 + 3.66386I −16.0000 − 4.0000I
u = −1.00000
a = −0.049342 + 0.227545I
b = 1.00000
−5.75727 + 3.66386I −16.0000 − 4.0000I
u = −1.00000
a = −0.049342 − 0.227545I
b = 1.00000
−5.75727 − 3.66386I −16.0000 + 4.0000I
25
IV. I
u
4
= h−4u
2
a + au − 13u
2
+ 23b + 10a + 9u − 25, −70u
2
a + 151u
2
+
· · · − 130a + 309, u
3
− u
2
+ 2u − 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
7
=
1
u
2
a
1
=
a
0.173913au
2
+ 0.565217u
2
+ ··· − 0.434783a + 1.08696
a
11
=
−u
−u
2
+ 3u − 1
a
5
=
0.565217au
2
− 2.11304u
2
+ ··· + 1.08696a − 4.01739
1
a
4
=
0.434783au
2
− 2.28696u
2
+ ··· + 0.913043a − 4.58261
0.869565au
2
− 0.173913u
2
+ ··· + 0.826087a + 1.43478
a
9
=
−0.852174au
2
+ 1.09043u
2
+ ··· − 1.66957a + 1.81391
0.173913au
2
− 1.23478u
2
+ ··· + 0.565217a − 2.11304
a
3
=
0.565217au
2
− 3.75304u
2
+ ··· + 1.08696a − 6.77739
0.391304au
2
+ 0.521739u
2
+ ··· + 0.521739a + 1.69565
a
12
=
0.173913au
2
+ 0.565217u
2
+ ··· + 0.565217a + 1.08696
0.173913au
2
+ 0.565217u
2
+ ··· − 0.434783a + 1.08696
a
8
=
−1.10435au
2
+ 2.90087u
2
+ ··· − 1.93913a + 6.10783
0.130435au
2
− 0.0260870u
2
+ ··· + 0.173913a − 2.23478
a
2
=
1.17391au
2
− 2.19478u
2
+ ··· + 1.56522a − 3.75304
−0.782609au
2
+ 0.956522u
2
+ ··· − 0.0434783a + 1.60870
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
2
+ 4u − 8
26
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
(u
3
− u
2
+ 2u − 1)
2
c
2
, c
8
u
6
+ u
4
+ 2u
2
+ 1
c
3
u
6
+ 5u
4
+ 10u
2
+ 1
c
4
, c
5
, c
11
c
12
(u
2
+ 1)
3
c
7
25(25u
6
+ 40u
5
+ 87u
4
+ 26u
3
+ 56u
2
+ 6u + 1)
c
9
25(25u
6
− 40u
5
+ 87u
4
− 26u
3
+ 56u
2
− 6u + 1)
c
10
(u
3
+ u
2
+ 2u + 1)
2
27
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
, c
10
(y
3
+ 3y
2
+ 2y −1)
2
c
2
, c
8
(y
3
+ y
2
+ 2y + 1)
2
c
3
(y
3
+ 5y
2
+ 10y + 1)
2
c
4
, c
5
, c
11
c
12
(y + 1)
6
c
7
, c
9
625(625y
6
+ 2750y
5
+ 8289y
4
+ 8638y
3
+ 2998y
2
+ 76y + 1)
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.215080 + 1.307140I
a = 0.024694 + 1.101050I
b = − 1.000000I
6.31400 − 2.82812I −0.49024 + 2.97945I
u = 0.215080 + 1.307140I
a = 0.17657 − 1.61809I
b = 1.000000I
6.31400 − 2.82812I −0.49024 + 2.97945I
u = 0.215080 − 1.307140I
a = 0.024694 − 1.101050I
b = 1.000000I
6.31400 + 2.82812I −0.49024 − 2.97945I
u = 0.215080 − 1.307140I
a = 0.17657 + 1.61809I
b = − 1.000000I
6.31400 + 2.82812I −0.49024 − 2.97945I
u = 0.569840
a = 2.59873 + 2.48086I
b = − 1.000000I
2.17641 −7.01950
u = 0.569840
a = 2.59873 − 2.48086I
b = 1.000000I
2.17641 −7.01950
29
V. I
u
5
= hb + 1, 8a
3
+ 12a
2
+ 6a + 1, u − 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
1
a
7
=
1
1
a
1
=
a
−1
a
11
=
−1
0
a
5
=
a + 1
−1
a
4
=
a
−1
a
9
=
a
2
+ 2a + 1
−a
a
3
=
−2a
2
−
3
2
a −
3
4
2a
2
+ a − 1
a
12
=
a − 1
−1
a
8
=
−a
2
+ a + 1
a + 1
a
2
=
2a
2
+ 3a +
1
2
4a
2
+ 4a
(ii) Obstruction class = 1
(iii) Cusp Shapes = 34a
2
+ 34a −
7
2
30
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
8
u
3
c
4
, c
5
, c
10
(u + 1)
3
c
6
, c
11
, c
12
(u − 1)
3
c
7
512(2u − 1)
3
c
9
512(2u + 1)
3
31
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
8
y
3
c
4
, c
5
, c
6
c
10
, c
11
, c
12
(y −1)
3
c
7
, c
9
262144(4y −1)
3
32
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −0.500000
b = −1.00000
−3.28987 −12.0000
u = 1.00000
a = −0.500000
b = −1.00000
−3.28987 −12.0000
u = 1.00000
a = −0.500000
b = −1.00000
−3.28987 −12.0000
33
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
3
(u
2
− 2u + 2)
2
(u
3
− u
2
+ 2u − 1)
2
(u
39
+ 19u
38
+ ··· + 2u
2
− 1)
2
· (u
53
+ 25u
52
+ ··· − 112u − 64)
c
2
, c
8
u
3
(u
4
+ 2u
2
+ 2)(u
6
+ u
4
+ 2u
2
+ 1)(u
39
+ u
38
+ ··· + 2u
3
− 1)
2
· (u
53
− 3u
52
+ ··· − 12u + 8)
c
3
u
3
(u
4
− 2u
2
+ 2)(u
6
+ 5u
4
+ 10u
2
+ 1)(u
39
− u
38
+ ··· − 18u − 17)
2
· (u
53
+ 3u
52
+ ··· + 91812u + 11464)
c
4
, c
5
((u − 1)
4
)(u + 1)
3
(u
2
+ 1)
3
(u
53
− u
52
+ ··· − 2u + 1)
· (u
78
+ 3u
77
+ ··· + 788u + 173)
c
6
((u − 1)
3
)(u + 1)
4
(u
3
− u
2
+ 2u − 1)
2
(u
39
+ u
38
+ ··· + 2u + 1)
2
· (u
53
+ 2u
52
+ ··· + 329u + 160)
c
7
26214400(2u − 1)
3
(16u
4
+ 32u
3
+ 16u
2
+ 1)
· (25u
6
+ 40u
5
+ 87u
4
+ 26u
3
+ 56u
2
+ 6u + 1)
· (128u
53
− 64u
52
+ ··· − 13u + 1)
· (u
78
− 21u
77
+ ··· + 448674u + 57751)
c
9
26214400(2u + 1)
3
(16u
4
− 32u
3
+ 16u
2
+ 1)
· (25u
6
− 40u
5
+ 87u
4
− 26u
3
+ 56u
2
− 6u + 1)
· (128u
53
− 64u
52
+ ··· − 13u + 1)
· (u
78
− 21u
77
+ ··· + 448674u + 57751)
c
10
((u − 1)
4
)(u + 1)
3
(u
3
+ u
2
+ 2u + 1)
2
(u
39
+ u
38
+ ··· + 2u + 1)
2
· (u
53
+ 2u
52
+ ··· + 329u + 160)
c
11
, c
12
((u − 1)
3
)(u + 1)
4
(u
2
+ 1)
3
(u
53
− u
52
+ ··· − 2u + 1)
· (u
78
+ 3u
77
+ ··· + 788u + 173)
34
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
3
(y
2
+ 4)
2
(y
3
+ 3y
2
+ 2y −1)
2
(y
39
+ 3y
38
+ ··· + 4y −1)
2
· (y
53
+ 9y
52
+ ··· − 3840y −4096)
c
2
, c
8
y
3
(y
2
+ 2y + 2)
2
(y
3
+ y
2
+ 2y + 1)
2
(y
39
+ 19y
38
+ ··· + 2y
2
− 1)
2
· (y
53
+ 25y
52
+ ··· − 112y −64)
c
3
y
3
(y
2
− 2y + 2)
2
(y
3
+ 5y
2
+ 10y + 1)
2
· (y
39
− 13y
38
+ ··· + 3588y −289)
2
· (y
53
− 7y
52
+ ··· + 828536208y −131423296)
c
4
, c
5
, c
11
c
12
((y −1)
7
)(y + 1)
6
(y
53
+ 17y
52
+ ··· − 18y −1)
· (y
78
+ 47y
77
+ ··· + 318100y + 29929)
c
6
, c
10
((y −1)
7
)(y
3
+ 3y
2
+ 2y −1)
2
(y
39
− 21y
38
+ ··· + 2y
2
− 1)
2
· (y
53
− 22y
52
+ ··· + 992401y −25600)
c
7
, c
9
687194767360000(4y −1)
3
(256y
4
− 512y
3
+ 288y
2
+ 32y + 1)
· (625y
6
+ 2750y
5
+ 8289y
4
+ 8638y
3
+ 2998y
2
+ 76y + 1)
· (16384y
53
− 208896y
52
+ ··· − 135y −1)
· (y
78
+ 27y
77
+ ··· − 879585708y + 3335178001)
35
