12a
0077
(K12a
0077
)
A knot diagram
1
Linearized knot diagam
3 5 8 2 9 10 11 4 1 12 7 6
Solving Sequence
7,11 4,8
9 12 3 10 6 1 5 2
c
7
c
8
c
11
c
3
c
10
c
6
c
12
c
5
c
2
c
1
, c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= hu
121
+ u
120
+ ··· + b + u, u
121
+ u
120
+ ··· + a − u, u
122
+ 2u
121
+ ··· + 3u + 1i
I
u
2
= hb − u, −u
3
+ a − u − 1, u
4
+ u
2
+ u + 1i
I
u
3
= hu
5
− u
4
+ 2u
3
− 2u
2
+ b + 2u − 1, −u
4
− u
2
+ a, u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1i
* 3 irreducible components of dim
C
= 0, with total 132 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
= hu
121
+u
120
+· · ·+b+u, u
121
+u
120
+· · ·+a−u, u
122
+2u
121
+· · ·+3u+1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
4
=
−u
121
− u
120
+ ··· − 4u
3
+ u
−u
121
− u
120
+ ··· − 3u
2
− u
a
8
=
1
−u
2
a
9
=
u
19
+ 4u
17
+ 8u
15
+ 8u
13
+ 3u
11
− 2u
9
− 2u
7
+ u
3
u
19
+ 5u
17
+ 12u
15
+ 17u
13
+ 15u
11
+ 9u
9
+ 4u
7
+ 2u
5
+ u
3
+ u
a
12
=
u
u
a
3
=
u
120
+ u
119
+ ··· + 4u + 1
u
120
− u
119
+ ··· − 2u
3
− u
2
a
10
=
u
3
u
3
+ u
a
6
=
−u
6
− u
4
+ 1
−u
6
− 2u
4
− u
2
a
1
=
u
11
+ 2u
9
+ 2u
7
− u
3
u
11
+ 3u
9
+ 4u
7
+ 3u
5
+ u
3
+ u
a
5
=
u
32
+ 7u
30
+ ··· + 2u
12
+ 1
u
32
+ 8u
30
+ ··· + 12u
8
+ 4u
6
a
2
=
u
117
+ u
116
+ ··· + 3u + 1
−u
119
− u
118
+ ··· − 3u
3
− 2u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
121
+ 16u
120
+ ··· + 25u + 10
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
122
+ 57u
121
+ ··· − 6u + 1
c
2
, c
4
u
122
− 11u
121
+ ··· − 10u + 1
c
3
, c
8
u
122
+ u
121
+ ··· + 3072u + 1024
c
5
u
122
− 2u
121
+ ··· − 8688533u + 4045417
c
6
u
122
+ 2u
121
+ ··· + 45832u + 4360
c
7
, c
11
u
122
− 2u
121
+ ··· − 3u + 1
c
9
u
122
+ 14u
121
+ ··· + 8849u + 409
c
10
u
122
+ 58u
121
+ ··· + 5u + 1
c
12
u
122
− 10u
121
+ ··· − 24512u + 5824
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
122
+ 27y
121
+ ··· − 66y + 1
c
2
, c
4
y
122
− 57y
121
+ ··· + 6y + 1
c
3
, c
8
y
122
− 63y
121
+ ··· − 30932992y + 1048576
c
5
y
122
− 38y
121
+ ··· − 180991027544255y + 16365398703889
c
6
y
122
− 30y
121
+ ··· − 1148670864y + 19009600
c
7
, c
11
y
122
+ 58y
121
+ ··· + 5y + 1
c
9
y
122
+ 22y
121
+ ··· + 25546025y + 167281
c
10
y
122
+ 14y
121
+ ··· + 13y + 1
c
12
y
122
+ 26y
121
+ ··· + 3082177920y + 33918976
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.147503 + 1.019890I
a = 0.160638 + 0.361005I
b = 1.257490 − 0.009631I
0.80605 − 4.42181I 0
u = −0.147503 − 1.019890I
a = 0.160638 − 0.361005I
b = 1.257490 + 0.009631I
0.80605 + 4.42181I 0
u = −0.503910 + 0.793936I
a = 0.823657 + 0.701487I
b = 0.718290 + 0.623909I
0.05395 − 4.08608I 0
u = −0.503910 − 0.793936I
a = 0.823657 − 0.701487I
b = 0.718290 − 0.623909I
0.05395 + 4.08608I 0
u = −0.187037 + 1.064040I
a = −0.257633 + 0.087294I
b = −1.56569 + 0.12591I
1.92349 + 0.97666I 0
u = −0.187037 − 1.064040I
a = −0.257633 − 0.087294I
b = −1.56569 − 0.12591I
1.92349 − 0.97666I 0
u = 0.663437 + 0.631192I
a = −2.79895 + 0.94536I
b = −0.33616 + 1.66340I
4.25458 + 10.76030I 0
u = 0.663437 − 0.631192I
a = −2.79895 − 0.94536I
b = −0.33616 − 1.66340I
4.25458 − 10.76030I 0
u = 0.664047 + 0.613237I
a = 2.86898 − 0.94744I
b = 0.30798 − 1.84487I
6.35315 + 5.04876I 0
u = 0.664047 − 0.613237I
a = 2.86898 + 0.94744I
b = 0.30798 + 1.84487I
6.35315 − 5.04876I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.580897 + 0.939576I
a = 1.40599 − 0.64077I
b = 1.31558 − 2.50343I
3.34514 − 5.92062I 0
u = 0.580897 − 0.939576I
a = 1.40599 + 0.64077I
b = 1.31558 + 2.50343I
3.34514 + 5.92062I 0
u = −0.563945 + 0.687578I
a = −0.463939 − 0.933720I
b = −0.226560 − 0.728292I
0.391182 − 0.219141I 0
u = −0.563945 − 0.687578I
a = −0.463939 + 0.933720I
b = −0.226560 + 0.728292I
0.391182 + 0.219141I 0
u = 0.247747 + 1.082810I
a = 0.246194 + 1.053460I
b = 0.771686 + 0.150808I
−3.15692 + 0.14365I 0
u = 0.247747 − 1.082810I
a = 0.246194 − 1.053460I
b = 0.771686 − 0.150808I
−3.15692 − 0.14365I 0
u = −0.557353 + 0.961980I
a = 0.942594 − 0.238886I
b = 1.147840 − 0.156245I
0.384580 − 0.022257I 0
u = −0.557353 − 0.961980I
a = 0.942594 + 0.238886I
b = 1.147840 + 0.156245I
0.384580 + 0.022257I 0
u = −0.642511 + 0.606712I
a = 0.423802 − 1.223920I
b = 0.581380 − 0.647488I
1.42902 − 4.68272I 0
u = −0.642511 − 0.606712I
a = 0.423802 + 1.223920I
b = 0.581380 + 0.647488I
1.42902 + 4.68272I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.578496 + 0.957006I
a = −1.73350 + 0.73489I
b = −1.46493 + 2.74505I
5.33977 − 0.21651I 0
u = 0.578496 − 0.957006I
a = −1.73350 − 0.73489I
b = −1.46493 − 2.74505I
5.33977 + 0.21651I 0
u = 0.545074 + 0.978382I
a = 2.55909 − 0.38765I
b = 2.14304 − 3.11468I
−0.83283 + 2.32108I 0
u = 0.545074 − 0.978382I
a = 2.55909 + 0.38765I
b = 2.14304 + 3.11468I
−0.83283 − 2.32108I 0
u = 0.676980 + 0.556127I
a = 2.75159 − 0.80208I
b = 0.29221 − 2.16620I
7.33859 + 0.89759I 0
u = 0.676980 − 0.556127I
a = 2.75159 + 0.80208I
b = 0.29221 + 2.16620I
7.33859 − 0.89759I 0
u = 0.310246 + 1.083390I
a = −0.358349 + 1.021320I
b = 0.570849 + 0.641805I
−3.70234 + 0.56339I 0
u = 0.310246 − 1.083390I
a = −0.358349 − 1.021320I
b = 0.570849 − 0.641805I
−3.70234 − 0.56339I 0
u = 0.685820 + 0.531680I
a = −2.55763 + 0.78007I
b = −0.22955 + 2.19623I
5.98830 − 4.81101I 0
u = 0.685820 − 0.531680I
a = −2.55763 − 0.78007I
b = −0.22955 − 2.19623I
5.98830 + 4.81101I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.243131 + 1.108750I
a = 1.01081 − 1.20474I
b = 2.71881 − 0.53821I
−5.30960 + 1.62774I 0
u = −0.243131 − 1.108750I
a = 1.01081 + 1.20474I
b = 2.71881 + 0.53821I
−5.30960 − 1.62774I 0
u = −0.480136 + 1.029710I
a = 0.060217 + 0.435203I
b = 0.183899 + 0.551516I
−0.61714 − 3.08115I 0
u = −0.480136 − 1.029710I
a = 0.060217 − 0.435203I
b = 0.183899 − 0.551516I
−0.61714 + 3.08115I 0
u = 0.626554 + 0.591288I
a = −3.17061 + 0.97693I
b = −0.01997 + 2.10665I
0.30602 + 2.29616I 0
u = 0.626554 − 0.591288I
a = −3.17061 − 0.97693I
b = −0.01997 − 2.10665I
0.30602 − 2.29616I 0
u = 0.232311 + 1.117320I
a = −0.580972 − 1.076570I
b = −0.823114 + 0.039156I
−4.37882 − 4.12065I 0
u = 0.232311 − 1.117320I
a = −0.580972 + 1.076570I
b = −0.823114 − 0.039156I
−4.37882 + 4.12065I 0
u = −0.557153 + 0.997293I
a = −0.679241 + 0.573310I
b = −0.974590 + 0.622642I
0.84323 − 4.34495I 0
u = −0.557153 − 0.997293I
a = −0.679241 − 0.573310I
b = −0.974590 − 0.622642I
0.84323 + 4.34495I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.217849 + 1.124370I
a = −0.187626 + 1.188830I
b = −2.03552 + 0.87762I
0.39410 + 4.66441I 0
u = −0.217849 − 1.124370I
a = −0.187626 − 1.188830I
b = −2.03552 − 0.87762I
0.39410 − 4.66441I 0
u = −0.638088 + 0.561092I
a = −0.798780 + 0.964384I
b = −0.691669 + 0.304217I
2.12882 − 0.34486I 0
u = −0.638088 − 0.561092I
a = −0.798780 − 0.964384I
b = −0.691669 − 0.304217I
2.12882 + 0.34486I 0
u = −0.334748 + 1.103830I
a = −0.83313 − 1.90432I
b = −0.29049 − 2.26529I
−6.22983 − 1.88137I 0
u = −0.334748 − 1.103830I
a = −0.83313 + 1.90432I
b = −0.29049 + 2.26529I
−6.22983 + 1.88137I 0
u = −0.773736 + 0.340441I
a = −2.27642 + 0.95926I
b = −0.64290 − 2.33332I
2.78144 + 13.02340I 0
u = −0.773736 − 0.340441I
a = −2.27642 − 0.95926I
b = −0.64290 + 2.33332I
2.78144 − 13.02340I 0
u = −0.766387 + 0.349666I
a = 2.38500 − 0.93938I
b = 0.65193 + 2.19129I
5.02651 + 7.30828I 0
u = −0.766387 − 0.349666I
a = 2.38500 + 0.93938I
b = 0.65193 − 2.19129I
5.02651 − 7.30828I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.580775 + 1.002240I
a = −2.32556 + 1.16823I
b = −1.49852 + 3.23792I
6.02309 + 3.97372I 0
u = 0.580775 − 1.002240I
a = −2.32556 − 1.16823I
b = −1.49852 − 3.23792I
6.02309 − 3.97372I 0
u = −0.222634 + 1.137130I
a = 0.04620 − 1.47787I
b = 2.02261 − 1.14560I
−1.87191 + 10.28300I 0
u = −0.222634 − 1.137130I
a = 0.04620 + 1.47787I
b = 2.02261 + 1.14560I
−1.87191 − 10.28300I 0
u = −0.742446 + 0.388031I
a = 2.41605 − 0.76410I
b = 0.78560 + 1.54744I
6.50957 + 3.19238I 0
u = −0.742446 − 0.388031I
a = 2.41605 + 0.76410I
b = 0.78560 − 1.54744I
6.50957 − 3.19238I 0
u = −0.730426 + 0.409385I
a = −2.28243 + 0.74960I
b = −0.89107 − 1.21865I
5.39473 − 2.49625I 0
u = −0.730426 − 0.409385I
a = −2.28243 − 0.74960I
b = −0.89107 + 1.21865I
5.39473 + 2.49625I 0
u = 0.351696 + 1.109570I
a = 0.94996 − 1.25525I
b = −0.412184 − 1.221590I
−5.61386 + 4.27204I 0
u = 0.351696 − 1.109570I
a = 0.94996 + 1.25525I
b = −0.412184 + 1.221590I
−5.61386 − 4.27204I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.274646 + 1.138280I
a = −0.900239 − 0.382822I
b = −0.554801 + 0.399175I
−5.66097 + 1.23463I 0
u = 0.274646 − 1.138280I
a = −0.900239 + 0.382822I
b = −0.554801 − 0.399175I
−5.66097 − 1.23463I 0
u = 0.754006 + 0.343369I
a = 0.403285 − 0.833170I
b = −1.019380 − 0.886124I
0.13714 − 6.77256I 0. + 5.74192I
u = 0.754006 − 0.343369I
a = 0.403285 + 0.833170I
b = −1.019380 + 0.886124I
0.13714 + 6.77256I 0. − 5.74192I
u = 0.582684 + 1.018360I
a = 2.41797 − 1.26623I
b = 1.46594 − 3.24790I
4.55439 + 9.71101I 0
u = 0.582684 − 1.018360I
a = 2.41797 + 1.26623I
b = 1.46594 + 3.24790I
4.55439 − 9.71101I 0
u = −0.374798 + 1.116820I
a = 0.04976 + 1.74262I
b = −0.30164 + 1.53458I
−1.26418 − 4.75234I 0
u = −0.374798 − 1.116820I
a = 0.04976 − 1.74262I
b = −0.30164 − 1.53458I
−1.26418 + 4.75234I 0
u = 0.308936 + 1.138480I
a = 1.112100 − 0.379507I
b = 0.224418 − 0.838709I
−6.04051 − 1.73738I 0
u = 0.308936 − 1.138480I
a = 1.112100 + 0.379507I
b = 0.224418 + 0.838709I
−6.04051 + 1.73738I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.741592 + 0.341947I
a = −2.68131 + 1.04936I
b = −0.29140 − 2.09408I
−0.89417 + 4.25803I 2.47020 − 4.79794I
u = −0.741592 − 0.341947I
a = −2.68131 − 1.04936I
b = −0.29140 + 2.09408I
−0.89417 − 4.25803I 2.47020 + 4.79794I
u = 0.727560 + 0.357150I
a = −0.676826 + 0.613682I
b = 0.610983 + 1.066460I
1.16636 − 2.32617I 3.33942 + 0.I
u = 0.727560 − 0.357150I
a = −0.676826 − 0.613682I
b = 0.610983 − 1.066460I
1.16636 + 2.32617I 3.33942 + 0.I
u = −0.366393 + 1.135130I
a = 0.03793 − 2.08248I
b = 0.62048 − 1.73701I
−3.47259 − 10.00020I 0
u = −0.366393 − 1.135130I
a = 0.03793 + 2.08248I
b = 0.62048 + 1.73701I
−3.47259 + 10.00020I 0
u = −0.474706 + 1.099400I
a = −0.380284 + 0.418935I
b = 0.184497 + 0.371876I
−0.60185 − 2.76992I 0
u = −0.474706 − 1.099400I
a = −0.380284 − 0.418935I
b = 0.184497 − 0.371876I
−0.60185 + 2.76992I 0
u = 0.742897 + 0.291124I
a = −0.116461 − 0.570194I
b = −0.970990 + 0.058027I
−1.35964 − 1.73759I 2.29144 − 2.31325I
u = 0.742897 − 0.291124I
a = −0.116461 + 0.570194I
b = −0.970990 − 0.058027I
−1.35964 + 1.73759I 2.29144 + 2.31325I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.505779 + 1.104550I
a = −1.00118 + 1.86287I
b = 0.58455 + 2.08301I
−4.58051 + 3.20726I 0
u = 0.505779 − 1.104550I
a = −1.00118 − 1.86287I
b = 0.58455 − 2.08301I
−4.58051 − 3.20726I 0
u = −0.519041 + 1.107540I
a = −0.142012 + 0.389842I
b = −1.316650 − 0.337487I
−4.97820 − 5.58195I 0
u = −0.519041 − 1.107540I
a = −0.142012 − 0.389842I
b = −1.316650 + 0.337487I
−4.97820 + 5.58195I 0
u = −0.484369 + 1.125250I
a = 0.819496 − 0.149267I
b = −0.112185 + 0.136501I
−2.68020 + 2.19171I 0
u = −0.484369 − 1.125250I
a = 0.819496 + 0.149267I
b = −0.112185 − 0.136501I
−2.68020 − 2.19171I 0
u = 0.536230 + 1.104700I
a = 1.03791 − 1.12148I
b = 0.04903 − 1.60825I
−2.15124 + 6.76591I 0
u = 0.536230 − 1.104700I
a = 1.03791 + 1.12148I
b = 0.04903 + 1.60825I
−2.15124 − 6.76591I 0
u = −0.576567 + 1.090460I
a = 0.82502 + 1.79493I
b = −0.26431 + 2.97096I
3.39134 − 2.48781I 0
u = −0.576567 − 1.090460I
a = 0.82502 − 1.79493I
b = −0.26431 − 2.97096I
3.39134 + 2.48781I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.715919 + 0.244608I
a = 0.402000 + 0.499492I
b = 0.881830 − 0.783285I
−1.99977 − 4.88959I −0.19185 + 6.83299I
u = 0.715919 − 0.244608I
a = 0.402000 − 0.499492I
b = 0.881830 + 0.783285I
−1.99977 + 4.88959I −0.19185 − 6.83299I
u = −0.576427 + 1.102190I
a = −1.22366 − 2.00645I
b = 0.14513 − 3.45387I
4.40913 − 8.20349I 0
u = −0.576427 − 1.102190I
a = −1.22366 + 2.00645I
b = 0.14513 + 3.45387I
4.40913 + 8.20349I 0
u = 0.563785 + 1.110100I
a = 1.62962 − 0.12987I
b = 1.27778 − 1.18135I
−1.03613 + 7.25005I 0
u = 0.563785 − 1.110100I
a = 1.62962 + 0.12987I
b = 1.27778 + 1.18135I
−1.03613 − 7.25005I 0
u = 0.529898 + 1.132100I
a = −0.10898 + 1.63343I
b = 0.97595 + 1.32102I
−4.54724 + 9.60660I 0
u = 0.529898 − 1.132100I
a = −0.10898 − 1.63343I
b = 0.97595 − 1.32102I
−4.54724 − 9.60660I 0
u = −0.564571 + 1.118020I
a = 2.15905 + 2.17034I
b = 0.21148 + 4.45037I
−3.16535 − 9.21460I 0
u = −0.564571 − 1.118020I
a = 2.15905 − 2.17034I
b = 0.21148 − 4.45037I
−3.16535 + 9.21460I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.568633 + 1.120910I
a = −1.72962 − 0.38857I
b = −1.68973 + 0.77827I
−2.14484 + 11.77480I 0
u = 0.568633 − 1.120910I
a = −1.72962 + 0.38857I
b = −1.68973 − 0.77827I
−2.14484 − 11.77480I 0
u = 0.550329 + 1.131450I
a = −0.732352 − 1.021390I
b = −1.234400 − 0.348833I
−3.80504 + 6.62461I 0
u = 0.550329 − 1.131450I
a = −0.732352 + 1.021390I
b = −1.234400 + 0.348833I
−3.80504 − 6.62461I 0
u = −0.574280 + 1.122500I
a = −1.85412 − 2.51219I
b = 0.25455 − 4.23615I
2.75092 − 12.36380I 0
u = −0.574280 − 1.122500I
a = −1.85412 + 2.51219I
b = 0.25455 + 4.23615I
2.75092 + 12.36380I 0
u = −0.573842 + 1.127650I
a = 1.94322 + 2.63754I
b = −0.34594 + 4.31971I
0.4616 − 18.0934I 0
u = −0.573842 − 1.127650I
a = 1.94322 − 2.63754I
b = −0.34594 − 4.31971I
0.4616 + 18.0934I 0
u = 0.660170 + 0.316088I
a = −0.732772 − 0.193117I
b = −0.215520 + 0.967082I
0.10486 − 2.11384I 2.75851 + 4.42684I
u = 0.660170 − 0.316088I
a = −0.732772 + 0.193117I
b = −0.215520 − 0.967082I
0.10486 + 2.11384I 2.75851 − 4.42684I
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.502135 + 0.520497I
a = −0.843249 − 0.145577I
b = −0.377248 − 0.103982I
0.921687 − 0.967284I 5.88815 + 4.44516I
u = −0.502135 − 0.520497I
a = −0.843249 + 0.145577I
b = −0.377248 + 0.103982I
0.921687 + 0.967284I 5.88815 − 4.44516I
u = −0.667655 + 0.125853I
a = 0.803991 + 0.367385I
b = 0.748284 − 0.621145I
0.08889 − 6.49361I 0.00970 + 5.09244I
u = −0.667655 − 0.125853I
a = 0.803991 − 0.367385I
b = 0.748284 + 0.621145I
0.08889 + 6.49361I 0.00970 − 5.09244I
u = −0.623496 + 0.254190I
a = 1.36029 + 0.77185I
b = −0.007159 − 0.321290I
−2.60730 + 1.09949I −2.12650 + 0.94003I
u = −0.623496 − 0.254190I
a = 1.36029 − 0.77185I
b = −0.007159 + 0.321290I
−2.60730 − 1.09949I −2.12650 − 0.94003I
u = −0.619769 + 0.095267I
a = −0.968869 − 0.258640I
b = −0.712902 + 0.333354I
2.07800 − 1.29731I 3.26116 + 0.74944I
u = −0.619769 − 0.095267I
a = −0.968869 + 0.258640I
b = −0.712902 − 0.333354I
2.07800 + 1.29731I 3.26116 − 0.74944I
u = 0.592035 + 0.190430I
a = 0.510361 + 0.710669I
b = 0.450440 − 1.161470I
−2.14348 + 1.10867I −2.68663 − 1.45232I
u = 0.592035 − 0.190430I
a = 0.510361 − 0.710669I
b = 0.450440 + 1.161470I
−2.14348 − 1.10867I −2.68663 + 1.45232I
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.191047 + 0.515704I
a = 0.83394 + 1.44078I
b = 0.862620 − 0.391075I
−1.87815 + 0.80870I −4.98554 + 0.10240I
u = 0.191047 − 0.515704I
a = 0.83394 − 1.44078I
b = 0.862620 + 0.391075I
−1.87815 − 0.80870I −4.98554 − 0.10240I
17
II. I
u
2
= hb − u, −u
3
+ a − u − 1, u
4
+ u
2
+ u + 1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
4
=
u
3
+ u + 1
u
a
8
=
1
−u
2
a
9
=
1
−u
2
a
12
=
u
u
a
3
=
u
3
+ u + 1
u
a
10
=
u
3
u
3
+ u
a
6
=
u
3
+ u
2
+ 1
u
3
+ u
2
+ u + 1
a
1
=
−u
3
− u
2
− u − 1
−u
2
− u − 1
a
5
=
u
3
+ u
2
+ u + 1
u
2
+ u + 1
a
2
=
−u
2
−u
2
− 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 3u
3
− 4u
2
− u − 2
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
4
c
3
, c
8
u
4
c
4
(u + 1)
4
c
5
, c
7
, c
9
u
4
+ u
2
+ u + 1
c
6
u
4
+ 3u
3
+ 4u
2
+ 3u + 2
c
10
u
4
− 2u
3
+ 3u
2
− u + 1
c
11
u
4
+ u
2
− u + 1
c
12
u
4
+ 2u
3
+ 3u
2
+ u + 1
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
4
c
3
, c
8
y
4
c
5
, c
7
, c
9
c
11
y
4
+ 2y
3
+ 3y
2
+ y + 1
c
6
y
4
− y
3
+ 2y
2
+ 7y + 4
c
10
, c
12
y
4
+ 2y
3
+ 7y
2
+ 5y + 1
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.547424 + 0.585652I
a = 0.851808 + 0.911292I
b = −0.547424 + 0.585652I
−0.66484 − 1.39709I −0.08162 + 2.95607I
u = −0.547424 − 0.585652I
a = 0.851808 − 0.911292I
b = −0.547424 − 0.585652I
−0.66484 + 1.39709I −0.08162 − 2.95607I
u = 0.547424 + 1.120870I
a = −0.351808 + 0.720342I
b = 0.547424 + 1.120870I
−4.26996 + 7.64338I −4.41838 − 7.23121I
u = 0.547424 − 1.120870I
a = −0.351808 − 0.720342I
b = 0.547424 − 1.120870I
−4.26996 − 7.64338I −4.41838 + 7.23121I
21
III. I
u
3
=
hu
5
−u
4
+2u
3
−2u
2
+b+2u−1, −u
4
−u
2
+a, u
6
−u
5
+2u
4
−2u
3
+2u
2
−2u+1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
4
=
u
4
+ u
2
−u
5
+ u
4
− 2u
3
+ 2u
2
− 2u + 1
a
8
=
1
−u
2
a
9
=
1
−u
2
a
12
=
u
u
a
3
=
u
4
+ u
2
−u
5
+ u
4
− 2u
3
+ 2u
2
− 2u + 1
a
10
=
u
3
u
3
+ u
a
6
=
−u
5
+ u
4
− 2u
3
+ 2u
2
− 2u + 2
−u
5
− 2u
3
+ u
2
− 2u + 1
a
1
=
−u
4
− u
2
+ u − 1
2u
5
− u
4
+ 3u
3
− 2u
2
+ 3u − 2
a
5
=
u
4
+ u
2
− u + 1
−2u
5
+ u
4
− 3u
3
+ 2u
2
− 3u + 2
a
2
=
u − 1
u
5
+ u
3
+ u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = u
4
+ 3u
3
+ u
2
+ 4u − 5
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
6
c
3
, c
8
u
6
c
4
(u + 1)
6
c
5
, c
7
, c
9
u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1
c
6
(u
3
− u
2
+ 1)
2
c
10
u
6
− 3u
5
+ 4u
4
− 2u
3
+ 1
c
11
u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1
c
12
u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
6
c
3
, c
8
y
6
c
5
, c
7
, c
9
c
11
y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1
c
6
(y
3
− y
2
+ 2y −1)
2
c
10
, c
12
y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.498832 + 1.001300I
a = −1.183530 + 0.507021I
b = −1.39861 − 0.80012I
−1.91067 − 2.82812I −4.05004 + 3.74291I
u = −0.498832 − 1.001300I
a = −1.183530 − 0.507021I
b = −1.39861 + 0.80012I
−1.91067 + 2.82812I −4.05004 − 3.74291I
u = 0.284920 + 1.115140I
a = −0.215080 − 0.841795I
b = −0.784920 − 0.841795I
−6.04826 −7.19479 + 0.27335I
u = 0.284920 − 1.115140I
a = −0.215080 + 0.841795I
b = −0.784920 + 0.841795I
−6.04826 −7.19479 − 0.27335I
u = 0.713912 + 0.305839I
a = 0.398606 + 0.800120I
b = 0.183526 − 0.507021I
−1.91067 − 2.82812I −1.25517 + 3.34054I
u = 0.713912 − 0.305839I
a = 0.398606 − 0.800120I
b = 0.183526 + 0.507021I
−1.91067 + 2.82812I −1.25517 − 3.34054I
25
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
10
)(u
122
+ 57u
121
+ ··· − 6u + 1)
c
2
((u − 1)
10
)(u
122
− 11u
121
+ ··· − 10u + 1)
c
3
, c
8
u
10
(u
122
+ u
121
+ ··· + 3072u + 1024)
c
4
((u + 1)
10
)(u
122
− 11u
121
+ ··· − 10u + 1)
c
5
(u
4
+ u
2
+ u + 1)(u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
· (u
122
− 2u
121
+ ··· − 8688533u + 4045417)
c
6
(u
3
− u
2
+ 1)
2
(u
4
+ 3u
3
+ 4u
2
+ 3u + 2)
· (u
122
+ 2u
121
+ ··· + 45832u + 4360)
c
7
(u
4
+ u
2
+ u + 1)(u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
· (u
122
− 2u
121
+ ··· − 3u + 1)
c
9
(u
4
+ u
2
+ u + 1)(u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
· (u
122
+ 14u
121
+ ··· + 8849u + 409)
c
10
(u
4
− 2u
3
+ 3u
2
− u + 1)(u
6
− 3u
5
+ 4u
4
− 2u
3
+ 1)
· (u
122
+ 58u
121
+ ··· + 5u + 1)
c
11
(u
4
+ u
2
− u + 1)(u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)
· (u
122
− 2u
121
+ ··· − 3u + 1)
c
12
(u
4
+ 2u
3
+ 3u
2
+ u + 1)(u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1)
· (u
122
− 10u
121
+ ··· − 24512u + 5824)
26
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
10
)(y
122
+ 27y
121
+ ··· − 66y + 1)
c
2
, c
4
((y −1)
10
)(y
122
− 57y
121
+ ··· + 6y + 1)
c
3
, c
8
y
10
(y
122
− 63y
121
+ ··· − 3.09330 × 10
7
y + 1048576)
c
5
(y
4
+ 2y
3
+ 3y
2
+ y + 1)(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
· (y
122
− 38y
121
+ ··· − 180991027544255y + 16365398703889)
c
6
(y
3
− y
2
+ 2y −1)
2
(y
4
− y
3
+ 2y
2
+ 7y + 4)
· (y
122
− 30y
121
+ ··· − 1148670864y + 19009600)
c
7
, c
11
(y
4
+ 2y
3
+ 3y
2
+ y + 1)(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
· (y
122
+ 58y
121
+ ··· + 5y + 1)
c
9
(y
4
+ 2y
3
+ 3y
2
+ y + 1)(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
· (y
122
+ 22y
121
+ ··· + 25546025y + 167281)
c
10
(y
4
+ 2y
3
+ 7y
2
+ 5y + 1)(y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1)
· (y
122
+ 14y
121
+ ··· + 13y + 1)
c
12
(y
4
+ 2y
3
+ 7y
2
+ 5y + 1)(y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1)
· (y
122
+ 26y
121
+ ··· + 3082177920y + 33918976)
27
