12a
0261
(K12a
0261
)
A knot diagram
1
Linearized knot diagam
3 6 7 11 9 2 10 5 1 12 4 8
Solving Sequence
2,6
3 7 4
1,9
10 5 8 12 11
c
2
c
6
c
3
c
1
c
9
c
5
c
8
c
12
c
11
c
4
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−8.93536 × 10
235
u
147
+ 2.60233 × 10
236
u
146
+ ··· + 1.61998 × 10
236
b − 4.36700 × 10
235
,
− 5.05436 × 10
236
u
147
+ 9.67804 × 10
236
u
146
+ ··· + 1.61998 × 10
236
a − 1.50588 × 10
236
,
u
148
− 2u
147
+ ··· − u + 1i
I
u
2
= h−2u
27
− u
26
+ ··· + b − 1, −u
27
+ 2u
26
+ ··· + a + 2, u
28
− u
27
+ ··· − u + 1i
* 2 irreducible components of dim
C
= 0, with total 176 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−8.94 × 10
235
u
147
+ 2.60 × 10
236
u
146
+ · · · + 1.62 × 10
236
b − 4.37 ×
10
235
, −5.05 × 10
236
u
147
+ 9.68 × 10
236
u
146
+ · · · + 1.62 × 10
236
a − 1.51 ×
10
236
, u
148
− 2u
147
+ · · · − u + 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u
2
a
7
=
u
u
a
4
=
u
4
+ u
2
+ 1
u
4
a
1
=
u
2
+ 1
−u
4
a
9
=
3.12001u
147
− 5.97417u
146
+ ··· + 5.16617u + 0.929564
0.551572u
147
− 1.60639u
146
+ ··· + 6.60221u + 0.269571
a
10
=
4.90742u
147
− 9.88405u
146
+ ··· + 10.2567u + 2.03757
2.74186u
147
− 5.25117u
146
+ ··· + 8.07769u − 0.659708
a
5
=
−3.44700u
147
+ 7.67545u
146
+ ··· − 9.69461u − 4.30138
0.766780u
147
− 0.0367417u
146
+ ··· − 4.96169u + 0.0605707
a
8
=
−8.83933u
147
+ 17.8206u
146
+ ··· − 16.2453u − 4.37980
−5.65335u
147
+ 10.1649u
146
+ ··· − 8.27590u + 3.13104
a
12
=
1.17140u
147
− 3.95676u
146
+ ··· + 19.3209u − 11.3326
−3.30282u
147
+ 6.39633u
146
+ ··· + 3.20990u − 0.536014
a
11
=
0.0723142u
147
− 1.55046u
146
+ ··· + 13.5943u − 10.7505
−5.50146u
147
+ 9.54017u
146
+ ··· + 1.68224u + 0.127919
(ii) Obstruction class = −1
(iii) Cusp Shapes = 1.08525u
147
+ 1.56569u
146
+ ··· + 11.7001u + 5.09065
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
148
+ 76u
147
+ ··· + 11u + 1
c
2
, c
6
u
148
− 2u
147
+ ··· − u + 1
c
3
u
148
+ 2u
147
+ ··· − 7627619u + 456713
c
4
, c
11
u
148
+ 34u
146
+ ··· + u + 1
c
5
, c
8
u
148
− u
147
+ ··· + 24734u + 1843
c
7
u
148
+ 23u
147
+ ··· + 58u + 1
c
9
u
148
+ 13u
147
+ ··· + 1242562u + 100697
c
10
u
148
+ 68u
147
+ ··· + 19u + 1
c
12
u
148
− 3u
147
+ ··· + 52u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
148
− 4y
147
+ ··· + 103y + 1
c
2
, c
6
y
148
+ 76y
147
+ ··· + 11y + 1
c
3
y
148
− 84y
147
+ ··· − 9230611190501y + 208586764369
c
4
, c
11
y
148
+ 68y
147
+ ··· + 19y + 1
c
5
, c
8
y
148
− 113y
147
+ ··· − 509628010y + 3396649
c
7
y
148
− 5y
147
+ ··· − 358y + 1
c
9
y
148
+ 35y
147
+ ··· + 1833695584058y + 10139885809
c
10
y
148
+ 36y
147
+ ··· + 171y + 1
c
12
y
148
+ 7y
147
+ ··· − 98y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.094195 + 0.999336I
a = 0.328602 + 1.117010I
b = 0.137573 + 1.237080I
−3.16447 + 2.18690I 0
u = −0.094195 − 0.999336I
a = 0.328602 − 1.117010I
b = 0.137573 − 1.237080I
−3.16447 − 2.18690I 0
u = 0.978749 + 0.166975I
a = −1.062100 + 0.222854I
b = 0.688357 − 0.219779I
−3.72173 + 1.72799I 0
u = 0.978749 − 0.166975I
a = −1.062100 − 0.222854I
b = 0.688357 + 0.219779I
−3.72173 − 1.72799I 0
u = 0.975795 + 0.323601I
a = −1.196330 + 0.307608I
b = 0.647571 + 0.063171I
−3.83865 − 4.09059I 0
u = 0.975795 − 0.323601I
a = −1.196330 − 0.307608I
b = 0.647571 − 0.063171I
−3.83865 + 4.09059I 0
u = −0.507310 + 0.823566I
a = −0.492109 − 1.107460I
b = −1.46561 − 1.24894I
−4.54359 − 4.56469I 0
u = −0.507310 − 0.823566I
a = −0.492109 + 1.107460I
b = −1.46561 + 1.24894I
−4.54359 + 4.56469I 0
u = −0.849870 + 0.428582I
a = 1.272750 + 0.396740I
b = −0.341656 + 0.132103I
−2.83362 + 0.78922I 0
u = −0.849870 − 0.428582I
a = 1.272750 − 0.396740I
b = −0.341656 − 0.132103I
−2.83362 − 0.78922I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.598151 + 0.864715I
a = 0.372791 + 0.774854I
b = 0.53248 + 1.50869I
2.23245 − 1.64680I 0
u = 0.598151 − 0.864715I
a = 0.372791 − 0.774854I
b = 0.53248 − 1.50869I
2.23245 + 1.64680I 0
u = −0.230852 + 1.041610I
a = −0.051708 + 0.534460I
b = −0.390975 + 0.018729I
−3.72477 + 1.28933I 0
u = −0.230852 − 1.041610I
a = −0.051708 − 0.534460I
b = −0.390975 − 0.018729I
−3.72477 − 1.28933I 0
u = 0.614295 + 0.699956I
a = 0.995978 + 0.461045I
b = −0.204773 + 0.104363I
2.70556 + 6.39419I 0
u = 0.614295 − 0.699956I
a = 0.995978 − 0.461045I
b = −0.204773 − 0.104363I
2.70556 − 6.39419I 0
u = 0.705243 + 0.804106I
a = 0.355815 − 1.028880I
b = 0.442914 − 1.019280I
1.67100 + 6.12333I 0
u = 0.705243 − 0.804106I
a = 0.355815 + 1.028880I
b = 0.442914 + 1.019280I
1.67100 − 6.12333I 0
u = −0.302256 + 0.876460I
a = 0.038881 + 0.179502I
b = 1.33544 + 1.59186I
0.94391 − 1.34144I 0
u = −0.302256 − 0.876460I
a = 0.038881 − 0.179502I
b = 1.33544 − 1.59186I
0.94391 + 1.34144I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.457920 + 0.801622I
a = 0.568224 + 0.576181I
b = −0.150439 + 0.781837I
0.05173 + 1.90170I 0
u = 0.457920 − 0.801622I
a = 0.568224 − 0.576181I
b = −0.150439 − 0.781837I
0.05173 − 1.90170I 0
u = −0.551452 + 0.925329I
a = −0.217913 + 0.770096I
b = −0.32932 + 1.93065I
2.92622 − 2.93528I 0
u = −0.551452 − 0.925329I
a = −0.217913 − 0.770096I
b = −0.32932 − 1.93065I
2.92622 + 2.93528I 0
u = 0.729923 + 0.799401I
a = −0.834437 + 0.472703I
b = −0.406020 + 0.328911I
1.70561 − 0.73296I 0
u = 0.729923 − 0.799401I
a = −0.834437 − 0.472703I
b = −0.406020 − 0.328911I
1.70561 + 0.73296I 0
u = 0.877976 + 0.242939I
a = 1.65181 + 0.19080I
b = −0.723758 + 0.321601I
−3.7523 − 14.2406I 0
u = 0.877976 − 0.242939I
a = 1.65181 − 0.19080I
b = −0.723758 − 0.321601I
−3.7523 + 14.2406I 0
u = −0.412626 + 1.022700I
a = 0.791782 + 0.699635I
b = −0.367077 + 0.591343I
−2.37666 + 1.92149I 0
u = −0.412626 − 1.022700I
a = 0.791782 − 0.699635I
b = −0.367077 − 0.591343I
−2.37666 − 1.92149I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.803777 + 0.761287I
a = 0.942167 + 0.420110I
b = 0.277599 + 0.467456I
0.26947 + 5.93833I 0
u = −0.803777 − 0.761287I
a = 0.942167 − 0.420110I
b = 0.277599 − 0.467456I
0.26947 − 5.93833I 0
u = −0.845808 + 0.256301I
a = −1.60157 + 0.15845I
b = 0.624980 + 0.413153I
−1.42164 + 8.51643I 0
u = −0.845808 − 0.256301I
a = −1.60157 − 0.15845I
b = 0.624980 − 0.413153I
−1.42164 − 8.51643I 0
u = −0.271784 + 0.829466I
a = −0.581523 + 1.279840I
b = 0.952850 + 0.719603I
−2.40401 − 6.32586I 0
u = −0.271784 − 0.829466I
a = −0.581523 − 1.279840I
b = 0.952850 − 0.719603I
−2.40401 + 6.32586I 0
u = 0.327173 + 0.807475I
a = 0.416283 + 0.881244I
b = −0.362159 + 0.639328I
−0.30820 + 1.83950I 0
u = 0.327173 − 0.807475I
a = 0.416283 − 0.881244I
b = −0.362159 − 0.639328I
−0.30820 − 1.83950I 0
u = −0.732313 + 0.859267I
a = −0.336296 − 1.067240I
b = −0.253821 − 1.257030I
−0.05820 − 11.61000I 0
u = −0.732313 − 0.859267I
a = −0.336296 + 1.067240I
b = −0.253821 + 1.257030I
−0.05820 + 11.61000I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.538512 + 0.994874I
a = −0.334765 + 0.503156I
b = −0.832714 − 0.173183I
0.40241 + 2.45854I 0
u = 0.538512 − 0.994874I
a = −0.334765 − 0.503156I
b = −0.832714 + 0.173183I
0.40241 − 2.45854I 0
u = −0.570545 + 0.631994I
a = −1.025060 + 0.277355I
b = 0.496332 + 0.064601I
3.77932 − 1.54987I 0
u = −0.570545 − 0.631994I
a = −1.025060 − 0.277355I
b = 0.496332 − 0.064601I
3.77932 + 1.54987I 0
u = 0.350751 + 1.098840I
a = 0.934047 + 0.146504I
b = 1.074220 + 0.535335I
−1.356000 + 0.219520I 0
u = 0.350751 − 1.098840I
a = 0.934047 − 0.146504I
b = 1.074220 − 0.535335I
−1.356000 − 0.219520I 0
u = −0.399311 + 1.082190I
a = −0.64562 − 1.28019I
b = −0.39699 − 2.90380I
−6.47002 − 1.38061I 0
u = −0.399311 − 1.082190I
a = −0.64562 + 1.28019I
b = −0.39699 + 2.90380I
−6.47002 + 1.38061I 0
u = 0.496928 + 1.049490I
a = 0.414745 + 0.477428I
b = −0.173860 + 0.655148I
−0.37344 + 2.64441I 0
u = 0.496928 − 1.049490I
a = 0.414745 − 0.477428I
b = −0.173860 − 0.655148I
−0.37344 − 2.64441I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.829917 + 0.096494I
a = 0.999880 − 0.166069I
b = −0.485211 − 0.294425I
−2.47161 + 1.70417I 0. − 3.02001I
u = −0.829917 − 0.096494I
a = 0.999880 + 0.166069I
b = −0.485211 + 0.294425I
−2.47161 − 1.70417I 0. + 3.02001I
u = 0.458761 + 1.071170I
a = −0.729221 + 0.248734I
b = −0.144459 − 0.256168I
−0.50434 + 4.02422I 0
u = 0.458761 − 1.071170I
a = −0.729221 − 0.248734I
b = −0.144459 + 0.256168I
−0.50434 − 4.02422I 0
u = 0.620790 + 0.547942I
a = 0.566415 − 0.735155I
b = 0.867114 + 0.126647I
1.70567 + 2.12132I 5.97809 − 8.47541I
u = 0.620790 − 0.547942I
a = 0.566415 + 0.735155I
b = 0.867114 − 0.126647I
1.70567 − 2.12132I 5.97809 + 8.47541I
u = −0.322175 + 1.128650I
a = −1.062420 + 0.050724I
b = −1.59933 + 0.47016I
−3.32302 + 4.78199I 0
u = −0.322175 − 1.128650I
a = −1.062420 − 0.050724I
b = −1.59933 − 0.47016I
−3.32302 − 4.78199I 0
u = 0.792737 + 0.193318I
a = 1.65458 + 0.03445I
b = −0.777965 + 0.685230I
−7.48672 − 5.32621I −3.30327 + 4.49709I
u = 0.792737 − 0.193318I
a = 1.65458 − 0.03445I
b = −0.777965 − 0.685230I
−7.48672 + 5.32621I −3.30327 − 4.49709I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.456979 + 1.100050I
a = 0.237618 + 0.851844I
b = 0.18101 + 3.78515I
−0.81545 − 3.66987I 0
u = −0.456979 − 1.100050I
a = 0.237618 − 0.851844I
b = 0.18101 − 3.78515I
−0.81545 + 3.66987I 0
u = −0.715111 + 0.374405I
a = −0.195776 − 0.263669I
b = −0.364634 + 0.389793I
0.54126 + 3.54143I 3.75434 − 0.34615I
u = −0.715111 − 0.374405I
a = −0.195776 + 0.263669I
b = −0.364634 − 0.389793I
0.54126 − 3.54143I 3.75434 + 0.34615I
u = 0.420682 + 1.124150I
a = −0.330865 + 0.820359I
b = −1.08154 + 3.92517I
−4.84937 − 1.82765I 0
u = 0.420682 − 1.124150I
a = −0.330865 − 0.820359I
b = −1.08154 − 3.92517I
−4.84937 + 1.82765I 0
u = 0.594507 + 0.512607I
a = 0.605447 + 0.286351I
b = 0.325128 + 0.549340I
1.22529 + 1.67906I 5.39633 − 3.05067I
u = 0.594507 − 0.512607I
a = 0.605447 − 0.286351I
b = 0.325128 − 0.549340I
1.22529 − 1.67906I 5.39633 + 3.05067I
u = 0.450266 + 1.128750I
a = 0.86257 − 1.22449I
b = 0.74080 − 3.05187I
−7.68132 + 5.02347I 0
u = 0.450266 − 1.128750I
a = 0.86257 + 1.22449I
b = 0.74080 + 3.05187I
−7.68132 − 5.02347I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.741244 + 0.254652I
a = 0.54082 − 1.51334I
b = 0.005226 − 0.332551I
0.74086 + 7.93059I 2.74611 − 7.67444I
u = −0.741244 − 0.254652I
a = 0.54082 + 1.51334I
b = 0.005226 + 0.332551I
0.74086 − 7.93059I 2.74611 + 7.67444I
u = 0.451263 + 1.131820I
a = 0.067834 − 1.397070I
b = 0.71217 − 3.63104I
−7.67016 + 2.76940I 0
u = 0.451263 − 1.131820I
a = 0.067834 + 1.397070I
b = 0.71217 + 3.63104I
−7.67016 − 2.76940I 0
u = −0.537926 + 1.093450I
a = −0.053904 + 0.775024I
b = 1.14332 + 1.50502I
−1.12518 − 8.59303I 0
u = −0.537926 − 1.093450I
a = −0.053904 − 0.775024I
b = 1.14332 − 1.50502I
−1.12518 + 8.59303I 0
u = 0.477248 + 1.128980I
a = −0.259172 + 0.945359I
b = 0.56481 + 3.87576I
−4.44020 + 9.57309I 0
u = 0.477248 − 1.128980I
a = −0.259172 − 0.945359I
b = 0.56481 − 3.87576I
−4.44020 − 9.57309I 0
u = −0.673692 + 0.371028I
a = −1.172060 − 0.111708I
b = −0.149098 + 0.813558I
0.98324 + 3.90006I 8.23651 − 5.87685I
u = −0.673692 − 0.371028I
a = −1.172060 + 0.111708I
b = −0.149098 − 0.813558I
0.98324 − 3.90006I 8.23651 + 5.87685I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.407315 + 1.164450I
a = −0.671591 − 0.200838I
b = −0.691548 − 0.595255I
−6.13142 − 2.11386I 0
u = −0.407315 − 1.164450I
a = −0.671591 + 0.200838I
b = −0.691548 + 0.595255I
−6.13142 + 2.11386I 0
u = −0.561749 + 1.102850I
a = 0.089185 + 0.213451I
b = 0.853807 + 0.008570I
−1.59412 − 8.43476I 0
u = −0.561749 − 1.102850I
a = 0.089185 − 0.213451I
b = 0.853807 − 0.008570I
−1.59412 + 8.43476I 0
u = −0.743692 + 0.159366I
a = 1.58736 − 0.22169I
b = −0.423945 − 0.252612I
−2.52813 + 1.53343I 0.54596 − 1.85069I
u = −0.743692 − 0.159366I
a = 1.58736 + 0.22169I
b = −0.423945 + 0.252612I
−2.52813 − 1.53343I 0.54596 + 1.85069I
u = 0.521147 + 1.129620I
a = −0.927754 − 0.338704I
b = −1.12919 − 0.87813I
−0.14290 + 7.42320I 0
u = 0.521147 − 1.129620I
a = −0.927754 + 0.338704I
b = −1.12919 + 0.87813I
−0.14290 − 7.42320I 0
u = −0.744636 + 0.100857I
a = 0.815304 − 0.726174I
b = −0.370093 − 0.297368I
−2.51905 + 1.79037I −1.08608 − 3.70094I
u = −0.744636 − 0.100857I
a = 0.815304 + 0.726174I
b = −0.370093 + 0.297368I
−2.51905 − 1.79037I −1.08608 + 3.70094I
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.335342 + 1.202770I
a = −0.542905 + 0.996111I
b = 0.31098 + 2.76756I
−11.72300 − 1.63235I 0
u = 0.335342 − 1.202770I
a = −0.542905 − 0.996111I
b = 0.31098 − 2.76756I
−11.72300 + 1.63235I 0
u = −0.333069 + 0.665307I
a = 0.49623 + 1.56070I
b = 0.511761 − 0.246982I
−4.05684 + 0.78238I −2.41428 + 1.66037I
u = −0.333069 − 0.665307I
a = 0.49623 − 1.56070I
b = 0.511761 + 0.246982I
−4.05684 − 0.78238I −2.41428 − 1.66037I
u = −0.274221 + 1.226330I
a = 0.582922 + 0.982247I
b = 0.20404 + 2.58454I
−6.17524 + 4.96683I 0
u = −0.274221 − 1.226330I
a = 0.582922 − 0.982247I
b = 0.20404 − 2.58454I
−6.17524 − 4.96683I 0
u = −0.385278 + 1.196360I
a = −0.581886 − 0.779805I
b = −0.48929 − 2.04048I
−6.47605 − 2.30153I 0
u = −0.385278 − 1.196360I
a = −0.581886 + 0.779805I
b = −0.48929 + 2.04048I
−6.47605 + 2.30153I 0
u = −0.508738 + 1.149490I
a = −0.053152 − 1.122090I
b = −0.36993 − 2.95291I
−5.35931 − 6.18141I 0
u = −0.508738 − 1.149490I
a = −0.053152 + 1.122090I
b = −0.36993 + 2.95291I
−5.35931 + 6.18141I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.320549 + 1.216140I
a = −0.332873 − 0.934936I
b = −0.00186 − 2.38927I
−6.67201 − 2.21444I 0
u = −0.320549 − 1.216140I
a = −0.332873 + 0.934936I
b = −0.00186 + 2.38927I
−6.67201 + 2.21444I 0
u = 0.425964 + 1.185020I
a = 0.931362 − 0.939815I
b = 1.18213 − 2.57500I
−7.89986 − 0.93437I 0
u = 0.425964 − 1.185020I
a = 0.931362 + 0.939815I
b = 1.18213 + 2.57500I
−7.89986 + 0.93437I 0
u = 0.736916 + 0.051206I
a = −1.94600 − 0.90629I
b = 0.558879 − 0.288383I
−4.35838 − 5.05167I −3.25940 + 7.90426I
u = 0.736916 − 0.051206I
a = −1.94600 + 0.90629I
b = 0.558879 + 0.288383I
−4.35838 + 5.05167I −3.25940 − 7.90426I
u = −0.533688 + 1.145760I
a = 0.986026 − 0.494540I
b = 1.43242 − 1.08748I
−1.86160 − 12.74340I 0
u = −0.533688 − 1.145760I
a = 0.986026 + 0.494540I
b = 1.43242 + 1.08748I
−1.86160 + 12.74340I 0
u = −0.464254 + 1.176790I
a = 0.276099 − 0.367655I
b = 0.01692 − 1.52073I
−5.71204 − 6.27548I 0
u = −0.464254 − 1.176790I
a = 0.276099 + 0.367655I
b = 0.01692 + 1.52073I
−5.71204 + 6.27548I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.685527 + 0.260417I
a = −0.36382 − 1.43194I
b = 0.062293 − 0.481338I
2.36352 − 2.78842I 5.99487 + 2.61021I
u = 0.685527 − 0.260417I
a = −0.36382 + 1.43194I
b = 0.062293 + 0.481338I
2.36352 + 2.78842I 5.99487 − 2.61021I
u = 0.470524 + 1.178780I
a = −0.221532 − 1.312780I
b = −0.21240 − 3.56169I
−7.58338 + 9.46926I 0
u = 0.470524 − 1.178780I
a = −0.221532 + 1.312780I
b = −0.21240 + 3.56169I
−7.58338 − 9.46926I 0
u = 0.173472 + 1.261970I
a = 0.119485 − 1.064980I
b = −0.17683 − 2.82048I
−9.56750 − 0.58327I 0
u = 0.173472 − 1.261970I
a = 0.119485 + 1.064980I
b = −0.17683 + 2.82048I
−9.56750 + 0.58327I 0
u = −0.052055 + 0.719773I
a = −0.361204 − 0.861064I
b = −2.43699 + 0.17170I
−1.89632 + 4.43860I −2.51555 − 2.71424I
u = −0.052055 − 0.719773I
a = −0.361204 + 0.861064I
b = −2.43699 − 0.17170I
−1.89632 − 4.43860I −2.51555 + 2.71424I
u = −0.574837 + 1.147180I
a = −0.240883 − 1.033160I
b = −0.47783 − 2.68338I
−5.11108 − 6.06792I 0
u = −0.574837 − 1.147180I
a = −0.240883 + 1.033160I
b = −0.47783 + 2.68338I
−5.11108 + 6.06792I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.496998 + 1.187650I
a = 0.214421 − 0.805894I
b = 0.15155 − 2.37554I
−5.68511 − 6.41382I 0
u = −0.496998 − 1.187650I
a = 0.214421 + 0.805894I
b = 0.15155 + 2.37554I
−5.68511 + 6.41382I 0
u = 0.530606 + 1.173690I
a = −0.136138 + 1.059740I
b = −1.02384 + 3.38189I
−10.3635 + 10.2246I 0
u = 0.530606 − 1.173690I
a = −0.136138 − 1.059740I
b = −1.02384 − 3.38189I
−10.3635 − 10.2246I 0
u = 0.281268 + 1.259650I
a = −0.602164 + 0.997818I
b = −0.34220 + 2.81243I
−8.62415 − 10.46360I 0
u = 0.281268 − 1.259650I
a = −0.602164 − 0.997818I
b = −0.34220 − 2.81243I
−8.62415 + 10.46360I 0
u = −0.564926 + 1.177470I
a = 0.045954 + 1.134820I
b = 0.50216 + 3.22859I
−4.1731 − 13.7141I 0
u = −0.564926 − 1.177470I
a = 0.045954 − 1.134820I
b = 0.50216 − 3.22859I
−4.1731 + 13.7141I 0
u = 0.569389 + 1.192980I
a = −0.064758 + 1.186030I
b = −0.37213 + 3.42803I
−6.6088 + 19.5371I 0
u = 0.569389 − 1.192980I
a = −0.064758 − 1.186030I
b = −0.37213 − 3.42803I
−6.6088 − 19.5371I 0
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.347929 + 0.560423I
a = −0.31115 − 1.70958I
b = −0.73600 − 2.04863I
−0.93423 − 5.35665I 6.58639 + 7.90798I
u = −0.347929 − 0.560423I
a = −0.31115 + 1.70958I
b = −0.73600 + 2.04863I
−0.93423 + 5.35665I 6.58639 − 7.90798I
u = 0.307412 + 1.310520I
a = 0.139548 − 0.884774I
b = −0.45593 − 2.44833I
−8.72224 + 6.12567I 0
u = 0.307412 − 1.310520I
a = 0.139548 + 0.884774I
b = −0.45593 + 2.44833I
−8.72224 − 6.12567I 0
u = 0.608156 + 1.207850I
a = 0.336680 − 0.930581I
b = 0.47949 − 2.74871I
−6.60922 + 9.82175I 0
u = 0.608156 − 1.207850I
a = 0.336680 + 0.930581I
b = 0.47949 + 2.74871I
−6.60922 − 9.82175I 0
u = 0.543606 + 1.245390I
a = 0.273062 − 0.738816I
b = 0.65790 − 2.53745I
−7.09036 + 3.70510I 0
u = 0.543606 − 1.245390I
a = 0.273062 + 0.738816I
b = 0.65790 + 2.53745I
−7.09036 − 3.70510I 0
u = 0.574015 + 0.126268I
a = 1.85452 − 0.05087I
b = −1.47749 − 0.57039I
−1.72656 − 5.40426I 1.53709 + 7.31225I
u = 0.574015 − 0.126268I
a = 1.85452 + 0.05087I
b = −1.47749 + 0.57039I
−1.72656 + 5.40426I 1.53709 − 7.31225I
18
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.171226 + 0.547986I
a = 1.02157 + 2.72115I
b = −0.079412 + 1.148280I
−4.47220 − 1.61677I 0.65648 + 6.33827I
u = −0.171226 − 0.547986I
a = 1.02157 − 2.72115I
b = −0.079412 − 1.148280I
−4.47220 + 1.61677I 0.65648 − 6.33827I
u = 0.548755 + 0.018675I
a = −2.93170 − 0.57487I
b = 0.409304 − 0.558284I
−4.77059 + 1.15573I −3.66714 − 1.69774I
u = 0.548755 − 0.018675I
a = −2.93170 + 0.57487I
b = 0.409304 + 0.558284I
−4.77059 − 1.15573I −3.66714 + 1.69774I
u = 0.374365 + 0.312762I
a = 0.37147 − 1.47803I
b = 0.775279 − 0.881999I
1.59458 − 0.23339I 8.06627 + 1.34861I
u = 0.374365 − 0.312762I
a = 0.37147 + 1.47803I
b = 0.775279 + 0.881999I
1.59458 + 0.23339I 8.06627 − 1.34861I
u = −0.269833 + 0.241695I
a = −1.78785 − 1.00149I
b = 1.409520 − 0.107037I
1.59970 − 0.04753I 6.39277 − 0.92731I
u = −0.269833 − 0.241695I
a = −1.78785 + 1.00149I
b = 1.409520 + 0.107037I
1.59970 + 0.04753I 6.39277 + 0.92731I
19
II.
I
u
2
= h−2u
27
−u
26
+· · ·+b−1, −u
27
+2u
26
+· · ·+a+2, u
28
−u
27
+· · ·−u+1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u
2
a
7
=
u
u
a
4
=
u
4
+ u
2
+ 1
u
4
a
1
=
u
2
+ 1
−u
4
a
9
=
u
27
− 2u
26
+ ··· + 7u − 2
2u
27
+ u
26
+ ··· + 7u + 1
a
10
=
3u
27
− 4u
26
+ ··· + 13u − 4
2u
27
+ 2u
26
+ ··· + 6u + 2
a
5
=
−2u
27
+ 7u
26
+ ··· − 13u + 7
u
27
− 4u
26
+ ··· − 20u
2
− 4
a
8
=
−5u
27
+ 13u
26
+ ··· − 19u + 13
4u
27
+ 27u
25
+ ··· + 7u + 1
a
12
=
−8u
27
+ 2u
26
+ ··· − 7u − 9
−5u
27
+ 6u
26
+ ··· − 10u + 3
a
11
=
−7u
27
− 2u
26
+ ··· − 2u − 14
−5u
27
+ 4u
26
+ ··· − 7u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −20u
27
− 2u
26
− 135u
25
− 39u
24
− 443u
23
− 210u
22
− 851u
21
− 616u
20
− 997u
19
−
1116u
18
−637u
17
−1321u
16
−157u
15
−1001u
14
−126u
13
−478u
12
−497u
11
−165u
10
−
655u
9
− 167u
8
− 433u
7
− 242u
6
− 157u
5
− 270u
4
− 39u
3
− 171u
2
− 7u − 52
20
(iv) u-Polynomials at the component
21
Crossings u-Polynomials at each crossing
c
1
u
28
− 15u
27
+ ··· − 11u + 1
c
2
u
28
− u
27
+ ··· − u + 1
c
3
u
28
+ u
27
+ ··· + u + 1
c
4
u
28
+ u
27
+ ··· − u + 1
c
5
u
28
+ 2u
27
+ ··· − 11u
2
+ 1
c
6
u
28
+ u
27
+ ··· + u + 1
c
7
u
28
− 2u
27
+ ··· + 6u + 1
c
8
u
28
− 2u
27
+ ··· − 11u
2
+ 1
c
9
u
28
− 2u
27
+ ··· − 2u + 1
c
10
u
28
− 15u
27
+ ··· − 19u + 1
c
11
u
28
− u
27
+ ··· + u + 1
c
12
u
28
+ 2u
27
+ ··· + 2u + 1
22
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
28
− y
27
+ ··· − 5y + 1
c
2
, c
6
y
28
+ 15y
27
+ ··· + 11y + 1
c
3
y
28
− 17y
27
+ ··· + 23y + 1
c
4
, c
11
y
28
+ 15y
27
+ ··· + 19y + 1
c
5
, c
8
y
28
− 30y
27
+ ··· − 22y + 1
c
7
y
28
− 6y
27
+ ··· − 6y + 1
c
9
y
28
− 6y
27
+ ··· + 2y + 1
c
10
y
28
+ 7y
27
+ ··· − 25y + 1
c
12
y
28
+ 2y
27
+ ··· − 6y + 1
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.365439 + 0.836410I
a = −0.387851 + 0.415870I
b = 0.71789 + 1.58480I
1.32260 − 1.60130I 8.71562 + 6.45471I
u = −0.365439 − 0.836410I
a = −0.387851 − 0.415870I
b = 0.71789 − 1.58480I
1.32260 + 1.60130I 8.71562 − 6.45471I
u = 0.381716 + 1.029330I
a = 0.648516 − 0.513298I
b = 0.171375 + 0.757477I
−3.08626 − 2.62316I −1.65800 + 5.02113I
u = 0.381716 − 1.029330I
a = 0.648516 + 0.513298I
b = 0.171375 − 0.757477I
−3.08626 + 2.62316I −1.65800 − 5.02113I
u = 0.856236 + 0.280811I
a = −1.387960 + 0.082806I
b = 0.388646 + 0.076668I
−3.10049 − 0.21509I −4.06964 − 3.93322I
u = 0.856236 − 0.280811I
a = −1.387960 − 0.082806I
b = 0.388646 − 0.076668I
−3.10049 + 0.21509I −4.06964 + 3.93322I
u = −0.486112 + 0.995622I
a = −0.203990 − 0.411822I
b = −0.240558 + 0.877728I
0.80932 − 2.87184I 9.73391 + 6.16296I
u = −0.486112 − 0.995622I
a = −0.203990 + 0.411822I
b = −0.240558 − 0.877728I
0.80932 + 2.87184I 9.73391 − 6.16296I
u = −0.863022 + 0.165510I
a = 1.47605 + 0.06126I
b = −0.683724 − 0.004069I
−3.74191 + 3.30686I −2.33673 − 2.10493I
u = −0.863022 − 0.165510I
a = 1.47605 − 0.06126I
b = −0.683724 + 0.004069I
−3.74191 − 3.30686I −2.33673 + 2.10493I
25
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.490056 + 0.670198I
a = 0.417868 + 0.499022I
b = 1.194550 + 0.667265I
1.89003 − 1.13368I 6.62059 + 3.29252I
u = −0.490056 − 0.670198I
a = 0.417868 − 0.499022I
b = 1.194550 − 0.667265I
1.89003 + 1.13368I 6.62059 − 3.29252I
u = 0.649260 + 0.516295I
a = −0.978264 + 0.324319I
b = −0.747966 + 0.047309I
−0.10406 − 4.45468I 0.81082 + 4.92455I
u = 0.649260 − 0.516295I
a = −0.978264 − 0.324319I
b = −0.747966 − 0.047309I
−0.10406 + 4.45468I 0.81082 − 4.92455I
u = 0.549710 + 1.067170I
a = 0.025082 − 0.662017I
b = 0.681133 − 0.440731I
−1.81915 + 9.16310I −2.52839 − 13.26466I
u = 0.549710 − 1.067170I
a = 0.025082 + 0.662017I
b = 0.681133 + 0.440731I
−1.81915 − 9.16310I −2.52839 + 13.26466I
u = 0.348454 + 1.149410I
a = 0.658802 − 1.099010I
b = 0.92388 − 2.48074I
−7.39860 + 3.04531I −8.09341 − 4.44196I
u = 0.348454 − 1.149410I
a = 0.658802 + 1.099010I
b = 0.92388 + 2.48074I
−7.39860 − 3.04531I −8.09341 + 4.44196I
u = −0.374671 + 1.175130I
a = −0.512726 − 1.137850I
b = −0.50975 − 3.13448I
−7.86845 − 0.47406I −6.80610 + 0.20183I
u = −0.374671 − 1.175130I
a = −0.512726 + 1.137850I
b = −0.50975 + 3.13448I
−7.86845 + 0.47406I −6.80610 − 0.20183I
26
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.227894 + 0.712348I
a = 0.248942 + 1.342120I
b = −1.77286 + 1.79816I
−1.75291 + 5.42762I −1.77047 − 8.41574I
u = 0.227894 − 0.712348I
a = 0.248942 − 1.342120I
b = −1.77286 − 1.79816I
−1.75291 − 5.42762I −1.77047 + 8.41574I
u = 0.023362 + 0.732048I
a = 0.09845 + 2.19590I
b = −0.476032 + 0.772669I
−5.01732 − 1.24897I −11.27715 − 0.05900I
u = 0.023362 − 0.732048I
a = 0.09845 − 2.19590I
b = −0.476032 − 0.772669I
−5.01732 + 1.24897I −11.27715 + 0.05900I
u = −0.496859 + 1.198450I
a = −0.124720 − 1.049440I
b = −0.13620 − 3.21782I
−6.95419 − 8.20241I −4.76290 + 6.44782I
u = −0.496859 − 1.198450I
a = −0.124720 + 1.049440I
b = −0.13620 + 3.21782I
−6.95419 + 8.20241I −4.76290 − 6.44782I
u = 0.539527 + 1.190270I
a = 0.021804 − 0.999223I
b = −0.01038 − 2.64689I
−5.94690 + 5.37088I −5.57815 − 1.15124I
u = 0.539527 − 1.190270I
a = 0.021804 + 0.999223I
b = −0.01038 + 2.64689I
−5.94690 − 5.37088I −5.57815 + 1.15124I
27
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
28
− 15u
27
+ ··· − 11u + 1)(u
148
+ 76u
147
+ ··· + 11u + 1)
c
2
(u
28
− u
27
+ ··· − u + 1)(u
148
− 2u
147
+ ··· − u + 1)
c
3
(u
28
+ u
27
+ ··· + u + 1)(u
148
+ 2u
147
+ ··· − 7627619u + 456713)
c
4
(u
28
+ u
27
+ ··· − u + 1)(u
148
+ 34u
146
+ ··· + u + 1)
c
5
(u
28
+ 2u
27
+ ··· − 11u
2
+ 1)(u
148
− u
147
+ ··· + 24734u + 1843)
c
6
(u
28
+ u
27
+ ··· + u + 1)(u
148
− 2u
147
+ ··· − u + 1)
c
7
(u
28
− 2u
27
+ ··· + 6u + 1)(u
148
+ 23u
147
+ ··· + 58u + 1)
c
8
(u
28
− 2u
27
+ ··· − 11u
2
+ 1)(u
148
− u
147
+ ··· + 24734u + 1843)
c
9
(u
28
− 2u
27
+ ··· − 2u + 1)(u
148
+ 13u
147
+ ··· + 1242562u + 100697)
c
10
(u
28
− 15u
27
+ ··· − 19u + 1)(u
148
+ 68u
147
+ ··· + 19u + 1)
c
11
(u
28
− u
27
+ ··· + u + 1)(u
148
+ 34u
146
+ ··· + u + 1)
c
12
(u
28
+ 2u
27
+ ··· + 2u + 1)(u
148
− 3u
147
+ ··· + 52u + 1)
28
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
28
− y
27
+ ··· − 5y + 1)(y
148
− 4y
147
+ ··· + 103y + 1)
c
2
, c
6
(y
28
+ 15y
27
+ ··· + 11y + 1)(y
148
+ 76y
147
+ ··· + 11y + 1)
c
3
(y
28
− 17y
27
+ ··· + 23y + 1)
· (y
148
− 84y
147
+ ··· − 9230611190501y + 208586764369)
c
4
, c
11
(y
28
+ 15y
27
+ ··· + 19y + 1)(y
148
+ 68y
147
+ ··· + 19y + 1)
c
5
, c
8
(y
28
− 30y
27
+ ··· − 22y + 1)
· (y
148
− 113y
147
+ ··· − 509628010y + 3396649)
c
7
(y
28
− 6y
27
+ ··· − 6y + 1)(y
148
− 5y
147
+ ··· − 358y + 1)
c
9
(y
28
− 6y
27
+ ··· + 2y + 1)
· (y
148
+ 35y
147
+ ··· + 1833695584058y + 10139885809)
c
10
(y
28
+ 7y
27
+ ··· − 25y + 1)(y
148
+ 36y
147
+ ··· + 171y + 1)
c
12
(y
28
+ 2y
27
+ ··· − 6y + 1)(y
148
+ 7y
147
+ ··· − 98y + 1)
29
