12a
0137
(K12a
0137
)
A knot diagram
1
Linearized knot diagam
3 5 8 9 2 10 11 1 6 12 7 4
Solving Sequence
2,5
3
6,9
10 7 1 4 8 12 11
c
2
c
5
c
9
c
6
c
1
c
4
c
8
c
12
c
11
c
3
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h6.13816 × 10
191
u
110
− 1.13429 × 10
193
u
109
+ ··· + 2.24718 × 10
193
b − 3.38769 × 10
193
,
− 1.81134 × 10
193
u
110
+ 6.26196 × 10
193
u
109
+ ··· + 2.24718 × 10
193
a + 3.37392 × 10
193
,
u
111
− 3u
110
+ ··· − 8u + 1i
I
u
2
= hb − 2, a − 1, u
2
+ u + 1i
I
u
3
= hb + 1, a + u + 1, u
2
+ u + 1i
* 3 irreducible components of dim
C
= 0, with total 115 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
= h6.14 × 10
191
u
110
− 1.13 × 10
193
u
109
+ · · · + 2.25 × 10
193
b − 3.39 ×
10
193
, −1.81 × 10
193
u
110
+ 6.26 × 10
193
u
109
+ · · · + 2.25 × 10
193
a + 3.37 ×
10
193
, u
111
− 3u
110
+ · · · − 8u + 1i
(i) Arc colorings
a
2
=
1
0
a
5
=
0
u
a
3
=
1
−u
2
a
6
=
u
u
a
9
=
0.806049u
110
− 2.78659u
109
+ ··· + 32.2491u − 1.50140
−0.0273149u
110
+ 0.504759u
109
+ ··· − 8.15785u + 1.50753
a
10
=
1.23473u
110
− 4.63145u
109
+ ··· + 39.4124u − 2.29265
0.401363u
110
− 1.34010u
109
+ ··· − 0.994453u + 0.716275
a
7
=
−0.344800u
110
+ 2.01151u
109
+ ··· − 9.75297u − 2.65220
−0.941826u
110
+ 2.82073u
109
+ ··· − 2.64014u + 0.726247
a
1
=
u
2
+ 1
−u
4
a
4
=
0.325295u
110
− 1.05138u
109
+ ··· − 0.0877722u + 3.79641
0.344661u
110
− 0.920101u
109
+ ··· − 2.58288u + 0.162347
a
8
=
1.04968u
110
− 3.66787u
109
+ ··· + 30.1172u − 0.718132
0.479923u
110
− 1.04472u
109
+ ··· − 3.71313u + 0.942185
a
12
=
−0.193835u
110
+ 0.246390u
109
+ ··· − 8.59881u + 2.39820
0.0697190u
110
− 0.380589u
109
+ ··· + 1.11872u − 0.310933
a
11
=
1.30011u
110
− 2.29710u
109
+ ··· + 18.8682u + 0.678898
−1.16327u
110
+ 3.92263u
109
+ ··· − 19.1527u + 3.07306
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.199727u
110
− 1.12797u
109
+ ··· + 25.1841u − 1.58105
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
111
+ 41u
110
+ ··· − 12u − 1
c
2
, c
5
u
111
+ 3u
110
+ ··· − 8u − 1
c
3
u
111
− 2u
110
+ ··· + 128151u − 22181
c
4
u
111
+ 39u
109
+ ··· − 10571037u − 2188019
c
6
, c
9
u
111
− 3u
110
+ ··· + 3962u − 1217
c
7
, c
11
u
111
+ 3u
110
+ ··· + 2u − 1
c
8
u
111
+ 3u
110
+ ··· − 2u − 1
c
10
u
111
− 61u
110
+ ··· − 8u + 1
c
12
u
111
+ 11u
110
+ ··· − 16u + 16
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
111
+ 61y
110
+ ··· − 2780y −1
c
2
, c
5
y
111
+ 41y
110
+ ··· − 12y −1
c
3
y
111
+ 150y
110
+ ··· − 11615036801y −491996761
c
4
y
111
+ 78y
110
+ ··· + 215220189102279y −4787427144361
c
6
, c
9
y
111
− 99y
110
+ ··· − 22891192y −1481089
c
7
, c
11
y
111
+ 61y
110
+ ··· − 8y −1
c
8
y
111
+ 13y
110
+ ··· − 8y −1
c
10
y
111
− 19y
110
+ ··· + 148y −1
c
12
y
111
− 25y
110
+ ··· + 6272y −256
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.151572 + 0.991463I
a = −0.888867 − 0.508229I
b = −1.66325 − 0.01061I
−3.59561 − 0.34680I 0
u = 0.151572 − 0.991463I
a = −0.888867 + 0.508229I
b = −1.66325 + 0.01061I
−3.59561 + 0.34680I 0
u = 0.258560 + 0.953606I
a = 0.820900 + 0.539762I
b = 1.79814 − 0.31279I
−1.60150 + 4.05760I 0
u = 0.258560 − 0.953606I
a = 0.820900 − 0.539762I
b = 1.79814 + 0.31279I
−1.60150 − 4.05760I 0
u = 0.700734 + 0.735786I
a = 0.388751 − 1.180800I
b = −0.545202 + 0.253821I
9.12536 − 4.91085I 0
u = 0.700734 − 0.735786I
a = 0.388751 + 1.180800I
b = −0.545202 − 0.253821I
9.12536 + 4.91085I 0
u = −0.452673 + 0.873202I
a = 2.34656 − 0.61539I
b = 2.78531 − 1.07755I
0.001017 − 0.573653I 0
u = −0.452673 − 0.873202I
a = 2.34656 + 0.61539I
b = 2.78531 + 1.07755I
0.001017 + 0.573653I 0
u = 0.574894 + 0.794669I
a = 0.401800 − 0.342049I
b = 1.84011 − 0.11929I
0.66452 + 3.75930I 0
u = 0.574894 − 0.794669I
a = 0.401800 + 0.342049I
b = 1.84011 + 0.11929I
0.66452 − 3.75930I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.762307 + 0.679648I
a = 0.596090 − 0.841569I
b = 0.707490 − 0.483429I
5.76477 − 1.56136I 0
u = 0.762307 − 0.679648I
a = 0.596090 + 0.841569I
b = 0.707490 + 0.483429I
5.76477 + 1.56136I 0
u = −0.503793 + 0.893374I
a = −2.95406 + 1.43653I
b = −3.62966 + 1.39140I
0.29861 − 3.79341I 0
u = −0.503793 − 0.893374I
a = −2.95406 − 1.43653I
b = −3.62966 − 1.39140I
0.29861 + 3.79341I 0
u = 0.682390 + 0.771033I
a = −0.408080 + 1.072650I
b = 0.360693 − 0.288234I
5.68044 + 0.15489I 0
u = 0.682390 − 0.771033I
a = −0.408080 − 1.072650I
b = 0.360693 + 0.288234I
5.68044 − 0.15489I 0
u = −0.591641 + 0.849125I
a = 2.80917 − 1.82162I
b = 3.46325 − 0.58936I
6.39356 + 2.13485I 0
u = −0.591641 − 0.849125I
a = 2.80917 + 1.82162I
b = 3.46325 + 0.58936I
6.39356 − 2.13485I 0
u = −0.574926 + 0.863175I
a = −2.78033 + 1.84517I
b = −3.49720 + 0.84587I
2.81370 − 2.28141I 0
u = −0.574926 − 0.863175I
a = −2.78033 − 1.84517I
b = −3.49720 − 0.84587I
2.81370 + 2.28141I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.813992 + 0.499000I
a = 0.446497 − 1.221160I
b = 0.181652 + 0.047950I
2.21997 − 7.60792I 0
u = 0.813992 − 0.499000I
a = 0.446497 + 1.221160I
b = 0.181652 − 0.047950I
2.21997 + 7.60792I 0
u = −0.586237 + 0.879911I
a = 2.78417 − 1.86801I
b = 3.72891 − 0.83367I
6.29471 − 6.78751I 0
u = −0.586237 − 0.879911I
a = 2.78417 + 1.86801I
b = 3.72891 + 0.83367I
6.29471 + 6.78751I 0
u = −0.479587 + 0.810655I
a = −2.03914 + 1.62005I
b = −1.82668 + 1.01950I
0.575579 − 0.242431I 0
u = −0.479587 − 0.810655I
a = −2.03914 − 1.62005I
b = −1.82668 − 1.01950I
0.575579 + 0.242431I 0
u = 0.715946 + 0.802237I
a = 0.539436 − 1.067170I
b = −0.257897 + 0.053696I
9.93624 + 4.63451I 0
u = 0.715946 − 0.802237I
a = 0.539436 + 1.067170I
b = −0.257897 − 0.053696I
9.93624 − 4.63451I 0
u = −0.854505 + 0.665544I
a = −0.796795 − 0.332626I
b = −0.176428 − 0.335951I
2.95184 − 4.02036I 0
u = −0.854505 − 0.665544I
a = −0.796795 + 0.332626I
b = −0.176428 + 0.335951I
2.95184 + 4.02036I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.586692 + 0.921955I
a = −0.528186 + 0.484546I
b = −1.025630 − 0.779401I
0.240812 + 0.859822I 0
u = 0.586692 − 0.921955I
a = −0.528186 − 0.484546I
b = −1.025630 + 0.779401I
0.240812 − 0.859822I 0
u = 0.941357 + 0.564368I
a = 0.73528 − 1.28253I
b = −0.268509 − 0.334879I
6.96139 − 7.48818I 0
u = 0.941357 − 0.564368I
a = 0.73528 + 1.28253I
b = −0.268509 + 0.334879I
6.96139 + 7.48818I 0
u = −0.227715 + 0.870897I
a = −1.132120 + 0.819750I
b = −1.00126 + 2.27287I
4.59030 + 2.48721I 0
u = −0.227715 − 0.870897I
a = −1.132120 − 0.819750I
b = −1.00126 − 2.27287I
4.59030 − 2.48721I 0
u = −0.469961 + 0.996253I
a = 0.117592 − 0.706494I
b = −0.176725 − 0.538862I
−0.29591 − 2.82467I 0
u = −0.469961 − 0.996253I
a = 0.117592 + 0.706494I
b = −0.176725 + 0.538862I
−0.29591 + 2.82467I 0
u = 0.725179 + 0.524774I
a = −0.325303 + 1.068910I
b = −0.477568 − 0.087742I
0.75510 − 3.03844I 0
u = 0.725179 − 0.524774I
a = −0.325303 − 1.068910I
b = −0.477568 + 0.087742I
0.75510 + 3.03844I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.554611 + 0.696207I
a = −0.223070 + 0.519748I
b = −1.336370 − 0.225481I
−0.019953 − 1.212380I 0
u = 0.554611 − 0.696207I
a = −0.223070 − 0.519748I
b = −1.336370 + 0.225481I
−0.019953 + 1.212380I 0
u = 0.962589 + 0.556575I
a = −0.75736 + 1.32394I
b = 0.378198 + 0.314058I
10.3327 − 12.4597I 0
u = 0.962589 − 0.556575I
a = −0.75736 − 1.32394I
b = 0.378198 − 0.314058I
10.3327 + 12.4597I 0
u = 0.943879 + 0.593618I
a = −0.77992 + 1.24019I
b = 0.250347 + 0.480235I
11.11290 − 3.11428I 0
u = 0.943879 − 0.593618I
a = −0.77992 − 1.24019I
b = 0.250347 − 0.480235I
11.11290 + 3.11428I 0
u = 0.057724 + 1.127700I
a = −0.818291 − 0.459279I
b = −1.60759 − 0.56216I
−4.49052 − 1.47159I 0
u = 0.057724 − 1.127700I
a = −0.818291 + 0.459279I
b = −1.60759 + 0.56216I
−4.49052 + 1.47159I 0
u = 0.668394 + 0.918370I
a = 0.808515 − 0.261517I
b = 1.93517 − 1.09112I
5.23269 + 5.06395I 0
u = 0.668394 − 0.918370I
a = 0.808515 + 0.261517I
b = 1.93517 + 1.09112I
5.23269 − 5.06395I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.823991 + 0.245283I
a = −0.372283 − 0.132431I
b = 0.027700 + 0.356730I
3.33552 + 0.83572I 0
u = −0.823991 − 0.245283I
a = −0.372283 + 0.132431I
b = 0.027700 − 0.356730I
3.33552 − 0.83572I 0
u = 0.601782 + 0.972682I
a = 0.703124 − 0.423032I
b = 1.42206 + 0.41755I
−0.91047 + 5.90697I 0
u = 0.601782 − 0.972682I
a = 0.703124 + 0.423032I
b = 1.42206 − 0.41755I
−0.91047 − 5.90697I 0
u = 0.705390 + 0.901522I
a = −0.841518 + 0.355883I
b = −1.72949 + 1.16337I
9.63753 + 0.79597I 0
u = 0.705390 − 0.901522I
a = −0.841518 − 0.355883I
b = −1.72949 − 1.16337I
9.63753 − 0.79597I 0
u = −0.099316 + 0.839474I
a = −0.821647 + 0.664821I
b = −0.20449 + 2.25163I
4.28144 − 5.96457I 0. + 5.29148I
u = −0.099316 − 0.839474I
a = −0.821647 − 0.664821I
b = −0.20449 − 2.25163I
4.28144 + 5.96457I 0. − 5.29148I
u = 0.673062 + 0.946975I
a = −0.868424 + 0.223066I
b = −2.02019 + 1.21063I
8.48686 + 10.20060I 0
u = 0.673062 − 0.946975I
a = −0.868424 − 0.223066I
b = −2.02019 − 1.21063I
8.48686 − 10.20060I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.510107 + 1.048430I
a = −0.087829 − 0.482061I
b = −0.458579 − 0.366228I
−0.30671 − 2.85278I 0
u = −0.510107 − 1.048430I
a = −0.087829 + 0.482061I
b = −0.458579 + 0.366228I
−0.30671 + 2.85278I 0
u = −1.071010 + 0.486667I
a = −0.610862 − 0.476506I
b = 0.456865 − 0.021950I
6.08148 − 1.84087I 0
u = −1.071010 − 0.486667I
a = −0.610862 + 0.476506I
b = 0.456865 + 0.021950I
6.08148 + 1.84087I 0
u = −1.103540 + 0.452944I
a = 0.574168 + 0.510120I
b = −0.530356 − 0.076491I
9.73834 + 2.68285I 0
u = −1.103540 − 0.452944I
a = 0.574168 − 0.510120I
b = −0.530356 + 0.076491I
9.73834 − 2.68285I 0
u = −0.754105 + 0.931578I
a = 0.769831 + 0.401589I
b = 0.728793 + 0.726801I
2.18684 − 1.93079I 0
u = −0.754105 − 0.931578I
a = 0.769831 − 0.401589I
b = 0.728793 − 0.726801I
2.18684 + 1.93079I 0
u = 0.002586 + 1.199940I
a = 0.736504 + 0.468001I
b = 1.46749 + 0.91439I
−3.75632 − 5.69149I 0
u = 0.002586 − 1.199940I
a = 0.736504 − 0.468001I
b = 1.46749 − 0.91439I
−3.75632 + 5.69149I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.687416 + 0.991173I
a = −0.919889 + 0.614023I
b = −1.220630 + 0.402447I
4.82666 + 7.06196I 0
u = 0.687416 − 0.991173I
a = −0.919889 − 0.614023I
b = −1.220630 − 0.402447I
4.82666 − 7.06196I 0
u = −0.518497 + 0.591175I
a = 1.036080 − 0.036679I
b = 0.639685 − 0.395378I
0.95922 − 1.38701I 3.62313 + 4.03872I
u = −0.518497 − 0.591175I
a = 1.036080 + 0.036679I
b = 0.639685 + 0.395378I
0.95922 + 1.38701I 3.62313 − 4.03872I
u = −1.099180 + 0.521315I
a = 0.645774 + 0.505681I
b = −0.539820 + 0.112610I
9.66501 − 6.42879I 0
u = −1.099180 − 0.521315I
a = 0.645774 − 0.505681I
b = −0.539820 − 0.112610I
9.66501 + 6.42879I 0
u = −0.184337 + 0.753351I
a = 1.043900 − 0.529630I
b = 0.52687 − 1.73885I
1.17620 − 1.56366I 2.66486 + 2.86045I
u = −0.184337 − 0.753351I
a = 1.043900 + 0.529630I
b = 0.52687 + 1.73885I
1.17620 + 1.56366I 2.66486 − 2.86045I
u = 0.638797 + 1.047900I
a = 0.976434 − 0.378779I
b = 1.93206 − 0.21548I
−0.75752 + 8.27205I 0
u = 0.638797 − 1.047900I
a = 0.976434 + 0.378779I
b = 1.93206 + 0.21548I
−0.75752 − 8.27205I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.060387 + 0.767194I
a = 1.37998 + 0.44429I
b = 1.122470 − 0.118951I
0.16533 − 2.35261I 2.77573 + 4.98016I
u = −0.060387 − 0.767194I
a = 1.37998 − 0.44429I
b = 1.122470 + 0.118951I
0.16533 + 2.35261I 2.77573 − 4.98016I
u = 0.656616 + 1.078440I
a = −1.090710 + 0.369060I
b = −2.14362 + 0.50659I
0.51181 + 13.10760I 0
u = 0.656616 − 1.078440I
a = −1.090710 − 0.369060I
b = −2.14362 − 0.50659I
0.51181 − 13.10760I 0
u = −0.131918 + 1.294100I
a = 0.517379 + 0.471372I
b = 0.82271 + 1.42156I
−0.44496 − 5.50904I 0
u = −0.131918 − 1.294100I
a = 0.517379 − 0.471372I
b = 0.82271 − 1.42156I
−0.44496 + 5.50904I 0
u = −0.629427 + 1.140000I
a = 0.409419 + 0.186743I
b = 1.024250 + 0.332219I
0.79695 − 6.19473I 0
u = −0.629427 − 1.140000I
a = 0.409419 − 0.186743I
b = 1.024250 − 0.332219I
0.79695 + 6.19473I 0
u = −0.184178 + 1.304150I
a = −0.433758 − 0.444358I
b = −0.52426 − 1.44209I
3.38019 − 1.36129I 0
u = −0.184178 − 1.304150I
a = −0.433758 + 0.444358I
b = −0.52426 + 1.44209I
3.38019 + 1.36129I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.732792 + 1.097870I
a = 1.281690 − 0.535052I
b = 1.97203 − 1.33997I
9.54930 + 9.25447I 0
u = 0.732792 − 1.097870I
a = 1.281690 + 0.535052I
b = 1.97203 + 1.33997I
9.54930 − 9.25447I 0
u = 0.719066 + 1.108810I
a = −1.285890 + 0.478952I
b = −2.15316 + 1.26035I
5.2786 + 13.5702I 0
u = 0.719066 − 1.108810I
a = −1.285890 − 0.478952I
b = −2.15316 − 1.26035I
5.2786 − 13.5702I 0
u = 0.723621 + 1.120700I
a = 1.325790 − 0.469571I
b = 2.25081 − 1.36835I
8.5830 + 18.6152I 0
u = 0.723621 − 1.120700I
a = 1.325790 + 0.469571I
b = 2.25081 + 1.36835I
8.5830 − 18.6152I 0
u = −0.122528 + 1.331290I
a = −0.503591 − 0.529859I
b = −0.86356 − 1.63805I
2.80751 − 10.21780I 0
u = −0.122528 − 1.331290I
a = −0.503591 + 0.529859I
b = −0.86356 + 1.63805I
2.80751 + 10.21780I 0
u = −0.792316 + 1.155410I
a = 0.701131 + 0.128222I
b = 1.30642 + 0.86455I
4.06504 − 4.83337I 0
u = −0.792316 − 1.155410I
a = 0.701131 − 0.128222I
b = 1.30642 − 0.86455I
4.06504 + 4.83337I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.826959 + 1.146610I
a = −0.751232 − 0.139656I
b = −1.27812 − 1.00796I
7.78064 − 0.43369I 0
u = −0.826959 − 1.146610I
a = −0.751232 + 0.139656I
b = −1.27812 + 1.00796I
7.78064 + 0.43369I 0
u = −0.79655 + 1.18655I
a = −0.707249 − 0.080958I
b = −1.44030 − 0.86582I
7.52726 − 9.46426I 0
u = −0.79655 − 1.18655I
a = −0.707249 + 0.080958I
b = −1.44030 + 0.86582I
7.52726 + 9.46426I 0
u = −0.384256 + 0.053866I
a = −4.33938 − 0.12550I
b = −0.502514 − 0.052716I
6.78584 − 4.52007I 3.14532 + 3.49869I
u = −0.384256 − 0.053866I
a = −4.33938 + 0.12550I
b = −0.502514 + 0.052716I
6.78584 + 4.52007I 3.14532 − 3.49869I
u = −0.333373
a = 4.52744
b = 0.535469
3.19926 −0.0131130
u = 0.136187 + 0.228465I
a = 1.88069 + 0.93129I
b = −0.365190 − 0.698875I
−0.37869 − 1.54324I −0.57658 + 5.32657I
u = 0.136187 − 0.228465I
a = 1.88069 − 0.93129I
b = −0.365190 + 0.698875I
−0.37869 + 1.54324I −0.57658 − 5.32657I
u = 0.122192 + 0.109380I
a = 0.52539 + 4.38815I
b = 0.567044 − 0.364579I
0.33050 − 1.99725I 1.05958 + 4.02569I
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.122192 − 0.109380I
a = 0.52539 − 4.38815I
b = 0.567044 + 0.364579I
0.33050 + 1.99725I 1.05958 − 4.02569I
16
II. I
u
2
= hb − 2, a − 1, u
2
+ u + 1i
(i) Arc colorings
a
2
=
1
0
a
5
=
0
u
a
3
=
1
u + 1
a
6
=
u
u
a
9
=
1
2
a
10
=
−u
−u + 1
a
7
=
−1
−u − 1
a
1
=
−u
−u
a
4
=
−u
−u
a
8
=
−u
−u + 1
a
12
=
−u
−u
a
11
=
−2u − 1
−2u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 8u + 4
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
5
, c
7
, c
9
u
2
− u + 1
c
2
, c
6
, c
8
c
10
, c
11
u
2
+ u + 1
c
12
u
2
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
7
, c
8
, c
9
c
10
, c
11
y
2
+ y + 1
c
12
y
2
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = 1.00000
b = 2.00000
− 4.05977I 0. + 6.92820I
u = −0.500000 − 0.866025I
a = 1.00000
b = 2.00000
4.05977I 0. − 6.92820I
20
III. I
u
3
= hb + 1, a + u + 1, u
2
+ u + 1i
(i) Arc colorings
a
2
=
1
0
a
5
=
0
u
a
3
=
1
u + 1
a
6
=
u
u
a
9
=
−u − 1
−1
a
10
=
−u
0
a
7
=
u + 1
u
a
1
=
−u
−u
a
4
=
u + 1
u + 1
a
8
=
−u
0
a
12
=
−u
−u
a
11
=
−u + 1
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 3
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
7
c
9
u
2
− u + 1
c
2
, c
6
, c
8
c
10
, c
11
u
2
+ u + 1
c
3
, c
4
(u + 1)
2
c
12
u
2
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
7
, c
8
c
9
, c
10
, c
11
y
2
+ y + 1
c
3
, c
4
(y −1)
2
c
12
y
2
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = −0.500000 − 0.866025I
b = −1.00000
0 3.00000
u = −0.500000 − 0.866025I
a = −0.500000 + 0.866025I
b = −1.00000
0 3.00000
24
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
2
)(u
111
+ 41u
110
+ ··· − 12u − 1)
c
2
((u
2
+ u + 1)
2
)(u
111
+ 3u
110
+ ··· − 8u − 1)
c
3
((u + 1)
2
)(u
2
− u + 1)(u
111
− 2u
110
+ ··· + 128151u − 22181)
c
4
((u + 1)
2
)(u
2
− u + 1)(u
111
+ 39u
109
+ ··· − 1.05710 × 10
7
u − 2188019)
c
5
((u
2
− u + 1)
2
)(u
111
+ 3u
110
+ ··· − 8u − 1)
c
6
((u
2
+ u + 1)
2
)(u
111
− 3u
110
+ ··· + 3962u − 1217)
c
7
((u
2
− u + 1)
2
)(u
111
+ 3u
110
+ ··· + 2u − 1)
c
8
((u
2
+ u + 1)
2
)(u
111
+ 3u
110
+ ··· − 2u − 1)
c
9
((u
2
− u + 1)
2
)(u
111
− 3u
110
+ ··· + 3962u − 1217)
c
10
((u
2
+ u + 1)
2
)(u
111
− 61u
110
+ ··· − 8u + 1)
c
11
((u
2
+ u + 1)
2
)(u
111
+ 3u
110
+ ··· + 2u − 1)
c
12
u
4
(u
111
+ 11u
110
+ ··· − 16u + 16)
25
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
2
)(y
111
+ 61y
110
+ ··· − 2780y −1)
c
2
, c
5
((y
2
+ y + 1)
2
)(y
111
+ 41y
110
+ ··· − 12y −1)
c
3
(y −1)
2
(y
2
+ y + 1)
· (y
111
+ 150y
110
+ ··· − 11615036801y −491996761)
c
4
(y −1)
2
(y
2
+ y + 1)
· (y
111
+ 78y
110
+ ··· + 215220189102279y −4787427144361)
c
6
, c
9
((y
2
+ y + 1)
2
)(y
111
− 99y
110
+ ··· − 2.28912 × 10
7
y −1481089)
c
7
, c
11
((y
2
+ y + 1)
2
)(y
111
+ 61y
110
+ ··· − 8y −1)
c
8
((y
2
+ y + 1)
2
)(y
111
+ 13y
110
+ ··· − 8y −1)
c
10
((y
2
+ y + 1)
2
)(y
111
− 19y
110
+ ··· + 148y −1)
c
12
y
4
(y
111
− 25y
110
+ ··· + 6272y −256)
26
