12a
0487
(K12a
0487
)
A knot diagram
1
Linearized knot diagam
3 6 11 12 8 2 10 1 4 7 9 5
Solving Sequence
2,7
6
3,11
4 1 10 8 5 9 12
c
6
c
2
c
3
c
1
c
10
c
7
c
5
c
9
c
12
c
4
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h6.97834 × 10
541
u
174
+ 6.18922 × 10
542
u
173
+ ··· + 5.84381 × 10
542
b + 4.55462 × 10
545
,
3.74109 × 10
545
u
174
+ 1.30601 × 10
546
u
173
+ ··· + 6.52753 × 10
545
a + 4.73645 × 10
547
,
u
175
+ 4u
174
+ ··· + 6175u + 1117i
I
u
2
= h8832633158u
43
+ 28505051997u
42
+ ··· + 4990744411b + 36995583025,
53295260397u
43
− 140240440915u
42
+ ··· + 4990744411a − 80983955218,
u
44
− u
43
+ ··· − 5u + 1i
* 2 irreducible components of dim
C
= 0, with total 219 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
= h6.98 × 10
541
u
174
+ 6.19 × 10
542
u
173
+ · · · + 5.84 × 10
542
b + 4.55 ×
10
545
, 3.74 × 10
545
u
174
+ 1.31 × 10
546
u
173
+ · · · + 6.53 × 10
545
a + 4.74 ×
10
547
, u
175
+ 4u
174
+ · · · + 6175u + 1117i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
u
2
a
3
=
u
u
3
+ u
a
11
=
−0.573125u
174
− 2.00077u
173
+ ··· − 1079.69u − 72.5611
−0.119414u
174
− 1.05911u
173
+ ··· − 3832.66u − 779.393
a
4
=
0.669635u
174
+ 0.835488u
173
+ ··· − 6116.01u − 1455.53
−0.256227u
174
− 0.356799u
173
+ ··· + 2129.74u + 508.045
a
1
=
u
3
u
5
+ u
3
+ u
a
10
=
−0.453711u
174
− 0.941658u
173
+ ··· + 2752.96u + 706.832
−0.119414u
174
− 1.05911u
173
+ ··· − 3832.66u − 779.393
a
8
=
−2.07547u
174
− 7.00149u
173
+ ··· − 3353.22u − 202.885
0.0526862u
174
− 0.663567u
173
+ ··· − 4427.74u − 936.746
a
5
=
0.104480u
174
+ 1.55732u
173
+ ··· + 5981.79u + 1247.39
0.0420972u
174
− 0.484376u
173
+ ··· − 2892.27u − 619.913
a
9
=
−2.09026u
174
− 7.90330u
173
+ ··· − 8049.25u − 1190.52
−0.0104941u
174
− 0.486964u
173
+ ··· − 2360.15u − 486.146
a
12
=
1.05839u
174
+ 5.35345u
173
+ ··· + 11562.0u + 2160.82
−0.305282u
174
− 1.96470u
173
+ ··· − 5457.81u − 1056.61
(ii) Obstruction class = −1
(iii) Cusp Shapes = −1.32452u
174
− 4.02580u
173
+ ··· + 31.4211u + 283.875
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
175
+ 84u
174
+ ··· − 21510473u − 1247689
c
2
, c
6
u
175
− 4u
174
+ ··· + 6175u − 1117
c
3
u
175
+ 5u
174
+ ··· − 200903543u − 14492227
c
4
, c
12
u
175
+ u
174
+ ··· + 38u − 1
c
5
u
175
− 9u
174
+ ··· + 1244051648u − 87632999
c
7
, c
10
u
175
− 14u
174
+ ··· + 444875u − 24751
c
8
u
175
− 3u
174
+ ··· − 3228u − 745
c
9
u
175
− u
174
+ ··· − 1852932u − 499117
c
11
u
175
+ 13u
174
+ ··· − 2u + 97
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
175
+ 28y
174
+ ··· − 85299694583841y −1556727840721
c
2
, c
6
y
175
+ 84y
174
+ ··· − 21510473y −1247689
c
3
y
175
− 37y
174
+ ··· + 10887680210935327y −210024643419529
c
4
, c
12
y
175
− 127y
174
+ ··· − 180y −1
c
5
y
175
+ 27y
174
+ ··· + 136692045245606196y −7679542513734001
c
7
, c
10
y
175
+ 94y
174
+ ··· − 17564282207y −612612001
c
8
y
175
− 29y
174
+ ··· + 14232894y −555025
c
9
y
175
+ 29y
174
+ ··· − 22256433571302y −249117779689
c
11
y
175
− 27y
174
+ ··· + 580452y −9409
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.325956 + 0.949466I
a = −2.60340 + 1.92275I
b = 0.005403 − 0.767784I
1.58192 − 4.67301I 0
u = 0.325956 − 0.949466I
a = −2.60340 − 1.92275I
b = 0.005403 + 0.767784I
1.58192 + 4.67301I 0
u = −0.987821 + 0.189772I
a = −0.326720 − 0.404313I
b = −0.347434 − 1.012110I
−0.65552 + 1.79433I 0
u = −0.987821 − 0.189772I
a = −0.326720 + 0.404313I
b = −0.347434 + 1.012110I
−0.65552 − 1.79433I 0
u = −0.364947 + 0.924553I
a = −1.54353 − 1.00452I
b = −0.452814 − 0.602040I
−2.29353 − 2.27823I 0
u = −0.364947 − 0.924553I
a = −1.54353 + 1.00452I
b = −0.452814 + 0.602040I
−2.29353 + 2.27823I 0
u = −0.813844 + 0.565118I
a = −0.413123 − 1.262400I
b = −0.701528 − 1.210640I
2.87174 + 4.67293I 0
u = −0.813844 − 0.565118I
a = −0.413123 + 1.262400I
b = −0.701528 + 1.210640I
2.87174 − 4.67293I 0
u = −0.958683 + 0.245748I
a = 1.142750 + 0.622428I
b = 0.609432 + 0.907836I
3.30252 + 1.79502I 0
u = −0.958683 − 0.245748I
a = 1.142750 − 0.622428I
b = 0.609432 − 0.907836I
3.30252 − 1.79502I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.271679 + 0.975980I
a = −1.59863 + 1.69105I
b = −0.043481 + 0.141822I
1.68466 + 6.98103I 0
u = 0.271679 − 0.975980I
a = −1.59863 − 1.69105I
b = −0.043481 − 0.141822I
1.68466 − 6.98103I 0
u = −0.249223 + 0.951198I
a = 0.022733 − 1.350770I
b = −0.090871 + 1.315720I
−4.79455 − 2.50479I 0
u = −0.249223 − 0.951198I
a = 0.022733 + 1.350770I
b = −0.090871 − 1.315720I
−4.79455 + 2.50479I 0
u = −0.950176 + 0.364365I
a = 0.941037 + 0.799797I
b = 0.670816 + 1.243370I
3.1539 + 14.7991I 0
u = −0.950176 − 0.364365I
a = 0.941037 − 0.799797I
b = 0.670816 − 1.243370I
3.1539 − 14.7991I 0
u = −0.355020 + 0.959098I
a = −0.194170 + 1.160960I
b = −0.273227 − 1.323650I
−5.19352 + 0.07694I 0
u = −0.355020 − 0.959098I
a = −0.194170 − 1.160960I
b = −0.273227 + 1.323650I
−5.19352 − 0.07694I 0
u = 0.407927 + 0.886173I
a = −0.729651 + 0.787225I
b = −0.927594 + 1.034960I
2.29763 − 1.16801I 0
u = 0.407927 − 0.886173I
a = −0.729651 − 0.787225I
b = −0.927594 − 1.034960I
2.29763 + 1.16801I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.143310 + 1.014600I
a = 0.543110 − 0.814198I
b = −0.230486 + 1.383780I
−5.13023 − 2.18375I 0
u = 0.143310 − 1.014600I
a = 0.543110 + 0.814198I
b = −0.230486 − 1.383780I
−5.13023 + 2.18375I 0
u = 0.961868 + 0.363103I
a = 0.933450 − 0.715334I
b = 0.588144 − 1.160490I
−1.48419 − 8.82684I 0
u = 0.961868 − 0.363103I
a = 0.933450 + 0.715334I
b = 0.588144 + 1.160490I
−1.48419 + 8.82684I 0
u = 0.414434 + 0.874408I
a = −1.80192 + 1.45961I
b = −0.658138 − 1.119250I
2.31978 + 4.58023I 0
u = 0.414434 − 0.874408I
a = −1.80192 − 1.45961I
b = −0.658138 + 1.119250I
2.31978 − 4.58023I 0
u = −0.902569 + 0.345482I
a = 1.55696 − 0.21348I
b = 0.665240 − 0.822100I
3.57840 − 3.20414I 0
u = −0.902569 − 0.345482I
a = 1.55696 + 0.21348I
b = 0.665240 + 0.822100I
3.57840 + 3.20414I 0
u = −0.356050 + 0.898168I
a = −2.25572 − 2.08663I
b = −0.218914 + 0.896821I
−2.18994 − 0.67486I 0
u = −0.356050 − 0.898168I
a = −2.25572 + 2.08663I
b = −0.218914 − 0.896821I
−2.18994 + 0.67486I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.680433 + 0.677818I
a = −0.572994 + 1.149020I
b = −0.839860 + 0.269339I
4.68042 − 0.92261I 0
u = 0.680433 − 0.677818I
a = −0.572994 − 1.149020I
b = −0.839860 − 0.269339I
4.68042 + 0.92261I 0
u = −0.568795 + 0.764886I
a = −1.41968 − 1.20891I
b = −1.273990 + 0.431196I
5.45673 − 2.09442I 0
u = −0.568795 − 0.764886I
a = −1.41968 + 1.20891I
b = −1.273990 − 0.431196I
5.45673 + 2.09442I 0
u = 0.958711 + 0.434750I
a = −0.255889 + 0.807548I
b = −0.417655 + 1.259020I
0.23870 − 5.12314I 0
u = 0.958711 − 0.434750I
a = −0.255889 − 0.807548I
b = −0.417655 − 1.259020I
0.23870 + 5.12314I 0
u = −0.518573 + 0.917086I
a = −1.07979 − 1.09258I
b = −1.56419 − 0.26869I
4.99730 − 2.25058I 0
u = −0.518573 − 0.917086I
a = −1.07979 + 1.09258I
b = −1.56419 + 0.26869I
4.99730 + 2.25058I 0
u = −0.273045 + 1.019310I
a = 0.570187 + 0.122249I
b = 0.303173 + 0.378363I
−1.17420 − 2.79461I 0
u = −0.273045 − 1.019310I
a = 0.570187 − 0.122249I
b = 0.303173 − 0.378363I
−1.17420 + 2.79461I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.148278 + 1.051400I
a = 0.608011 − 0.731055I
b = 0.688728 − 0.200996I
−3.85938 − 1.61276I 0
u = 0.148278 − 1.051400I
a = 0.608011 + 0.731055I
b = 0.688728 + 0.200996I
−3.85938 + 1.61276I 0
u = −0.155373 + 1.052830I
a = 0.611196 + 1.200530I
b = 0.945554 + 0.107943I
1.04897 + 6.48994I 0
u = −0.155373 − 1.052830I
a = 0.611196 − 1.200530I
b = 0.945554 − 0.107943I
1.04897 − 6.48994I 0
u = −0.761759 + 0.541233I
a = 0.849597 − 0.002654I
b = 0.399416 + 0.813177I
1.31816 − 0.63282I 0
u = −0.761759 − 0.541233I
a = 0.849597 + 0.002654I
b = 0.399416 − 0.813177I
1.31816 + 0.63282I 0
u = 0.820029 + 0.709079I
a = 0.910069 + 0.628289I
b = 0.444111 + 0.577934I
6.25198 − 1.81788I 0
u = 0.820029 − 0.709079I
a = 0.910069 − 0.628289I
b = 0.444111 − 0.577934I
6.25198 + 1.81788I 0
u = 0.322487 + 1.039360I
a = 0.511525 − 1.204290I
b = −0.27949 + 1.45121I
−4.22651 − 3.50011I 0
u = 0.322487 − 1.039360I
a = 0.511525 + 1.204290I
b = −0.27949 − 1.45121I
−4.22651 + 3.50011I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.496814 + 0.970984I
a = −0.796063 + 1.124390I
b = −1.278770 + 0.259072I
1.41529 + 2.64820I 0
u = 0.496814 − 0.970984I
a = −0.796063 − 1.124390I
b = −1.278770 − 0.259072I
1.41529 − 2.64820I 0
u = 0.751149 + 0.508223I
a = 0.749854 + 0.217362I
b = 0.613536 − 0.689882I
6.29900 + 5.67352I 0
u = 0.751149 − 0.508223I
a = 0.749854 − 0.217362I
b = 0.613536 + 0.689882I
6.29900 − 5.67352I 0
u = −0.426630 + 1.022100I
a = −0.973462 − 0.343443I
b = 0.11014 + 1.71170I
−3.59033 − 7.63415I 0
u = −0.426630 − 1.022100I
a = −0.973462 + 0.343443I
b = 0.11014 − 1.71170I
−3.59033 + 7.63415I 0
u = −0.658238 + 0.588206I
a = −0.478003 − 0.070068I
b = −0.426802 + 0.496050I
0.68565 − 1.44589I 0
u = −0.658238 − 0.588206I
a = −0.478003 + 0.070068I
b = −0.426802 − 0.496050I
0.68565 + 1.44589I 0
u = −0.495890 + 1.002680I
a = −0.60282 − 1.54683I
b = −1.49918 − 0.22333I
4.62733 − 2.83690I 0
u = −0.495890 − 1.002680I
a = −0.60282 + 1.54683I
b = −1.49918 + 0.22333I
4.62733 + 2.83690I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.765897 + 0.432538I
a = 1.71158 + 0.31154I
b = 1.116070 − 0.385780I
5.91294 + 8.43978I 0
u = −0.765897 − 0.432538I
a = 1.71158 − 0.31154I
b = 1.116070 + 0.385780I
5.91294 − 8.43978I 0
u = 0.760598 + 0.439737I
a = 1.54975 − 0.23049I
b = 0.848605 + 0.347580I
0.98319 − 3.49570I 0
u = 0.760598 − 0.439737I
a = 1.54975 + 0.23049I
b = 0.848605 − 0.347580I
0.98319 + 3.49570I 0
u = 0.766928 + 0.416428I
a = −0.719294 + 0.979594I
b = −0.552496 + 1.202390I
−0.25620 − 4.09535I 0
u = 0.766928 − 0.416428I
a = −0.719294 − 0.979594I
b = −0.552496 − 1.202390I
−0.25620 + 4.09535I 0
u = −0.796033 + 0.338196I
a = 0.381984 + 0.564663I
b = −0.083477 + 0.949279I
−0.144602 − 0.552072I 0
u = −0.796033 − 0.338196I
a = 0.381984 − 0.564663I
b = −0.083477 − 0.949279I
−0.144602 + 0.552072I 0
u = 0.667731 + 0.541222I
a = 1.079430 + 0.339682I
b = 0.472468 − 0.994102I
4.96437 − 5.68893I 0
u = 0.667731 − 0.541222I
a = 1.079430 − 0.339682I
b = 0.472468 + 0.994102I
4.96437 + 5.68893I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.594857 + 0.974758I
a = −1.295740 + 0.259836I
b = −1.082400 − 0.484273I
3.76035 + 5.86797I 0
u = 0.594857 − 0.974758I
a = −1.295740 − 0.259836I
b = −1.082400 + 0.484273I
3.76035 − 5.86797I 0
u = 0.402021 + 1.069680I
a = −0.514803 + 0.273745I
b = 0.24583 − 1.45429I
−6.87012 + 3.96919I 0
u = 0.402021 − 1.069680I
a = −0.514803 − 0.273745I
b = 0.24583 + 1.45429I
−6.87012 − 3.96919I 0
u = 0.503163 + 1.027550I
a = 0.247457 + 0.752143I
b = −0.934020 + 0.706950I
2.67225 + 0.27392I 0
u = 0.503163 − 1.027550I
a = 0.247457 − 0.752143I
b = −0.934020 − 0.706950I
2.67225 − 0.27392I 0
u = −0.455220 + 1.053460I
a = 1.94394 + 0.24485I
b = 0.37972 − 1.37114I
−3.32146 + 1.11549I 0
u = −0.455220 − 1.053460I
a = 1.94394 − 0.24485I
b = 0.37972 + 1.37114I
−3.32146 − 1.11549I 0
u = −0.269551 + 1.116900I
a = 0.810587 + 0.735572I
b = −0.442477 − 1.279560I
−1.29673 + 2.79738I 0
u = −0.269551 − 1.116900I
a = 0.810587 − 0.735572I
b = −0.442477 + 1.279560I
−1.29673 − 2.79738I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.246138 + 1.124620I
a = 0.255257 + 0.807824I
b = −0.185139 − 1.202140I
−3.53226 + 4.39070I 0
u = 0.246138 − 1.124620I
a = 0.255257 − 0.807824I
b = −0.185139 + 1.202140I
−3.53226 − 4.39070I 0
u = −0.559059 + 1.010450I
a = −2.41585 + 0.25340I
b = −0.398085 + 1.054620I
−3.72966 − 5.79595I 0
u = −0.559059 − 1.010450I
a = −2.41585 − 0.25340I
b = −0.398085 − 1.054620I
−3.72966 + 5.79595I 0
u = 0.803976 + 0.238232I
a = 0.433329 − 0.554170I
b = −0.284435 − 0.859679I
0.97451 + 1.31302I 0
u = 0.803976 − 0.238232I
a = 0.433329 + 0.554170I
b = −0.284435 + 0.859679I
0.97451 − 1.31302I 0
u = 0.509321 + 0.664565I
a = −1.65235 + 0.68133I
b = −1.014050 − 0.435231I
2.36501 + 1.47315I 0
u = 0.509321 − 0.664565I
a = −1.65235 − 0.68133I
b = −1.014050 + 0.435231I
2.36501 − 1.47315I 0
u = −0.575736 + 0.603125I
a = −0.76919 − 2.05804I
b = −0.228343 − 0.973153I
−2.47835 + 1.22081I 0
u = −0.575736 − 0.603125I
a = −0.76919 + 2.05804I
b = −0.228343 + 0.973153I
−2.47835 − 1.22081I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.566197 + 1.022380I
a = −0.401563 − 0.132568I
b = −0.681159 − 0.132368I
−0.66270 − 3.30582I 0
u = −0.566197 − 1.022380I
a = −0.401563 + 0.132568I
b = −0.681159 + 0.132368I
−0.66270 + 3.30582I 0
u = −0.858863 + 0.793976I
a = 1.035520 − 0.355962I
b = 0.381527 − 0.787545I
1.42313 − 4.08662I 0
u = −0.858863 − 0.793976I
a = 1.035520 + 0.355962I
b = 0.381527 + 0.787545I
1.42313 + 4.08662I 0
u = −0.759389 + 0.895606I
a = 0.231638 + 0.618251I
b = 0.257803 + 0.627572I
1.10685 − 1.89670I 0
u = −0.759389 − 0.895606I
a = 0.231638 − 0.618251I
b = 0.257803 − 0.627572I
1.10685 + 1.89670I 0
u = 0.449251 + 1.088340I
a = 1.82740 − 0.47237I
b = 0.545522 + 1.176210I
−6.52018 + 3.15690I 0
u = 0.449251 − 1.088340I
a = 1.82740 + 0.47237I
b = 0.545522 − 1.176210I
−6.52018 − 3.15690I 0
u = −0.218588 + 0.792950I
a = 0.876250 + 0.366706I
b = −0.24118 − 1.62448I
−2.29717 + 4.70301I 0
u = −0.218588 − 0.792950I
a = 0.876250 − 0.366706I
b = −0.24118 + 1.62448I
−2.29717 − 4.70301I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.179211 + 0.801413I
a = 1.332670 − 0.064493I
b = −0.458872 + 0.301069I
2.10855 − 0.54428I 0
u = 0.179211 − 0.801413I
a = 1.332670 + 0.064493I
b = −0.458872 − 0.301069I
2.10855 + 0.54428I 0
u = 0.576339 + 1.036900I
a = 1.54726 − 1.44567I
b = 0.334840 + 1.105570I
3.47285 + 10.53450I 0
u = 0.576339 − 1.036900I
a = 1.54726 + 1.44567I
b = 0.334840 − 1.105570I
3.47285 − 10.53450I 0
u = 0.546083 + 1.060290I
a = −2.38013 + 0.42911I
b = −0.433506 − 1.312240I
−2.67849 + 10.16570I 0
u = 0.546083 − 1.060290I
a = −2.38013 − 0.42911I
b = −0.433506 + 1.312240I
−2.67849 − 10.16570I 0
u = −0.605895 + 1.028620I
a = 1.62777 + 0.94825I
b = 0.298703 − 1.009030I
−0.12086 − 4.53150I 0
u = −0.605895 − 1.028620I
a = 1.62777 − 0.94825I
b = 0.298703 + 1.009030I
−0.12086 + 4.53150I 0
u = 0.919248 + 0.773367I
a = 0.863423 + 0.408281I
b = 0.460087 + 0.883218I
5.76777 + 9.94226I 0
u = 0.919248 − 0.773367I
a = 0.863423 − 0.408281I
b = 0.460087 − 0.883218I
5.76777 − 9.94226I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.558362 + 0.562107I
a = −1.348790 − 0.413307I
b = −0.849932 − 0.932238I
4.07234 + 3.99322I 0
u = 0.558362 − 0.562107I
a = −1.348790 + 0.413307I
b = −0.849932 + 0.932238I
4.07234 − 3.99322I 0
u = −0.720684 + 0.323222I
a = −1.026560 − 0.737859I
b = −0.72078 − 1.27260I
2.94140 + 5.54948I 0
u = −0.720684 − 0.323222I
a = −1.026560 + 0.737859I
b = −0.72078 + 1.27260I
2.94140 − 5.54948I 0
u = 0.466862 + 1.125240I
a = −1.14857 + 1.28762I
b = −0.792186 − 0.704403I
2.58142 + 6.54092I 0
u = 0.466862 − 1.125240I
a = −1.14857 − 1.28762I
b = −0.792186 + 0.704403I
2.58142 − 6.54092I 0
u = 0.624112 + 1.051420I
a = 1.10605 − 0.93099I
b = 0.388091 + 0.899336I
4.68913 − 0.45476I 0
u = 0.624112 − 1.051420I
a = 1.10605 + 0.93099I
b = 0.388091 − 0.899336I
4.68913 + 0.45476I 0
u = −0.526396 + 0.561216I
a = −1.86509 − 0.25062I
b = −1.257360 + 0.359860I
5.92930 − 1.34148I 0
u = −0.526396 − 0.561216I
a = −1.86509 + 0.25062I
b = −1.257360 − 0.359860I
5.92930 + 1.34148I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.734683 + 0.987861I
a = −0.050324 − 0.915854I
b = 0.315532 − 0.525973I
5.41367 + 7.62668I 0
u = 0.734683 − 0.987861I
a = −0.050324 + 0.915854I
b = 0.315532 + 0.525973I
5.41367 − 7.62668I 0
u = −0.645692 + 1.059480I
a = −1.78732 − 0.20482I
b = −0.78428 + 1.37915I
1.34897 − 10.14670I 0
u = −0.645692 − 1.059480I
a = −1.78732 + 0.20482I
b = −0.78428 − 1.37915I
1.34897 + 10.14670I 0
u = −0.558326 + 1.110590I
a = 1.63188 + 0.24669I
b = 0.127459 − 0.998161I
−2.43708 − 4.43907I 0
u = −0.558326 − 1.110590I
a = 1.63188 − 0.24669I
b = 0.127459 + 0.998161I
−2.43708 + 4.43907I 0
u = −0.386158 + 1.183130I
a = 1.53230 + 0.80555I
b = 0.754290 − 0.873124I
−0.97659 − 7.06232I 0
u = −0.386158 − 1.183130I
a = 1.53230 − 0.80555I
b = 0.754290 + 0.873124I
−0.97659 + 7.06232I 0
u = 0.598716 + 1.091230I
a = 0.741163 − 0.769460I
b = 1.048400 − 0.267201I
−0.95123 + 8.64684I 0
u = 0.598716 − 1.091230I
a = 0.741163 + 0.769460I
b = 1.048400 + 0.267201I
−0.95123 − 8.64684I 0
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.591098 + 1.097700I
a = −1.85741 + 0.49004I
b = −0.61582 − 1.34571I
−2.27551 + 9.22283I 0
u = 0.591098 − 1.097700I
a = −1.85741 − 0.49004I
b = −0.61582 + 1.34571I
−2.27551 − 9.22283I 0
u = −0.555456 + 1.117940I
a = −1.87785 − 0.92689I
b = −0.72380 + 1.41438I
0.63511 − 10.41790I 0
u = −0.555456 − 1.117940I
a = −1.87785 + 0.92689I
b = −0.72380 − 1.41438I
0.63511 + 10.41790I 0
u = −0.598964 + 1.095590I
a = 0.703315 + 0.946528I
b = 1.297040 + 0.315015I
3.9446 − 13.6046I 0
u = −0.598964 − 1.095590I
a = 0.703315 − 0.946528I
b = 1.297040 − 0.315015I
3.9446 + 13.6046I 0
u = −0.308397 + 1.213650I
a = 0.0617268 − 0.1019490I
b = 0.451809 + 0.980520I
−1.50068 − 2.16308I 0
u = −0.308397 − 1.213650I
a = 0.0617268 + 0.1019490I
b = 0.451809 − 0.980520I
−1.50068 + 2.16308I 0
u = 0.529809 + 1.139950I
a = 1.53069 − 0.12486I
b = −0.026059 + 0.793127I
−1.70649 + 3.54591I 0
u = 0.529809 − 1.139950I
a = 1.53069 + 0.12486I
b = −0.026059 − 0.793127I
−1.70649 − 3.54591I 0
18
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.075390 + 1.273190I
a = 0.340398 − 0.675235I
b = −0.102613 + 1.238680I
−6.07274 − 2.25115I 0
u = 0.075390 − 1.273190I
a = 0.340398 + 0.675235I
b = −0.102613 − 1.238680I
−6.07274 + 2.25115I 0
u = 0.567731 + 0.443149I
a = −1.27593 + 1.43039I
b = −0.292054 + 1.241830I
−0.89122 − 5.63124I 0
u = 0.567731 − 0.443149I
a = −1.27593 − 1.43039I
b = −0.292054 − 1.241830I
−0.89122 + 5.63124I 0
u = −0.679466 + 1.096420I
a = 0.559580 + 0.487472I
b = 0.668454 + 0.637480I
1.41704 − 2.60645I 0
u = −0.679466 − 1.096420I
a = 0.559580 − 0.487472I
b = 0.668454 − 0.637480I
1.41704 + 2.60645I 0
u = 0.886631 + 0.953977I
a = −0.134430 − 0.539825I
b = 0.269339 − 0.777930I
5.26370 − 3.43300I 0
u = 0.886631 − 0.953977I
a = −0.134430 + 0.539825I
b = 0.269339 + 0.777930I
5.26370 + 3.43300I 0
u = 0.656274 + 1.164820I
a = −1.41021 + 0.29407I
b = −0.45392 − 1.40970I
−2.04067 + 11.00890I 0
u = 0.656274 − 1.164820I
a = −1.41021 − 0.29407I
b = −0.45392 + 1.40970I
−2.04067 − 11.00890I 0
19
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.640315 + 1.181560I
a = 1.76448 + 0.55979I
b = 0.70592 − 1.33255I
0.6576 − 20.5856I 0
u = −0.640315 − 1.181560I
a = 1.76448 − 0.55979I
b = 0.70592 + 1.33255I
0.6576 + 20.5856I 0
u = −0.146827 + 1.336480I
a = −0.072758 − 0.483193I
b = 0.484983 + 1.240810I
−2.83020 + 11.27430I 0
u = −0.146827 − 1.336480I
a = −0.072758 + 0.483193I
b = 0.484983 − 1.240810I
−2.83020 − 11.27430I 0
u = 0.645400 + 1.184680I
a = 1.72120 − 0.50615I
b = 0.632692 + 1.251560I
−3.9939 + 14.6608I 0
u = 0.645400 − 1.184680I
a = 1.72120 + 0.50615I
b = 0.632692 − 1.251560I
−3.9939 − 14.6608I 0
u = 0.585627 + 0.273015I
a = −1.340080 + 0.036599I
b = −0.929285 + 0.570884I
5.04701 − 2.33430I 14.6697 + 3.6058I
u = 0.585627 − 0.273015I
a = −1.340080 − 0.036599I
b = −0.929285 − 0.570884I
5.04701 + 2.33430I 14.6697 − 3.6058I
u = −0.592121 + 1.220270I
a = −1.169560 − 0.573379I
b = −0.423759 + 1.185280I
−3.76157 − 7.38668I 0
u = −0.592121 − 1.220270I
a = −1.169560 + 0.573379I
b = −0.423759 − 1.185280I
−3.76157 + 7.38668I 0
20
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.154588 + 1.371260I
a = 0.055089 + 0.485475I
b = 0.392112 − 1.157750I
−7.55406 − 5.15323I 0
u = 0.154588 − 1.371260I
a = 0.055089 − 0.485475I
b = 0.392112 + 1.157750I
−7.55406 + 5.15323I 0
u = −0.648359 + 1.241730I
a = 1.53087 + 0.47268I
b = 0.621845 − 1.012720I
0.28944 − 7.65428I 0
u = −0.648359 − 1.241730I
a = 1.53087 − 0.47268I
b = 0.621845 + 1.012720I
0.28944 + 7.65428I 0
u = −0.179217 + 1.400100I
a = 0.096298 − 0.947605I
b = 0.097648 + 0.784942I
−4.96897 − 3.19396I 0
u = −0.179217 − 1.400100I
a = 0.096298 + 0.947605I
b = 0.097648 − 0.784942I
−4.96897 + 3.19396I 0
u = 0.558960 + 0.126450I
a = 1.17289 − 1.54891I
b = 0.234299 − 1.114390I
−3.91368 + 0.73164I −1.161521 − 0.793422I
u = 0.558960 − 0.126450I
a = 1.17289 + 1.54891I
b = 0.234299 + 1.114390I
−3.91368 − 0.73164I −1.161521 + 0.793422I
u = −0.566382
a = 0.832786
b = −0.100616
1.79126 5.72490
u = −0.30720 + 1.43422I
a = 0.340251 + 0.401393I
b = −0.112925 − 1.033040I
−6.07518 − 2.94551I 0
21
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.30720 − 1.43422I
a = 0.340251 − 0.401393I
b = −0.112925 + 1.033040I
−6.07518 + 2.94551I 0
u = −0.437946 + 0.278853I
a = 0.17874 + 2.26188I
b = 0.042219 + 1.282240I
−1.19734 − 4.89372I 4.41481 + 6.02885I
u = −0.437946 − 0.278853I
a = 0.17874 − 2.26188I
b = 0.042219 − 1.282240I
−1.19734 + 4.89372I 4.41481 − 6.02885I
u = −0.420408 + 0.235229I
a = 0.276055 − 0.729433I
b = −0.237874 + 0.329361I
0.471378 − 1.039480I 6.84675 + 6.48709I
u = −0.420408 − 0.235229I
a = 0.276055 + 0.729433I
b = −0.237874 − 0.329361I
0.471378 + 1.039480I 6.84675 − 6.48709I
22
II.
I
u
2
= h8.83 × 10
9
u
43
+ 2.85 × 10
10
u
42
+ · · · + 4.99 × 10
9
b + 3.70 × 10
10
, 5.33 ×
10
10
u
43
−1.40×10
11
u
42
+· · ·+4.99×10
9
a−8.10×10
10
, u
44
−u
43
+· · ·−5u+1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
u
2
a
3
=
u
u
3
+ u
a
11
=
−10.6788u
43
+ 28.1001u
42
+ ··· − 103.108u + 16.2268
−1.76980u
43
− 5.71158u
42
+ ··· + 34.5415u − 7.41284
a
4
=
−26.0038u
43
+ 15.2796u
42
+ ··· + 131.350u − 31.6020
7.53241u
43
− 1.10771u
42
+ ··· − 33.6298u + 7.29658
a
1
=
u
3
u
5
+ u
3
+ u
a
10
=
−8.90902u
43
+ 33.8117u
42
+ ··· − 137.649u + 23.6397
−1.76980u
43
− 5.71158u
42
+ ··· + 34.5415u − 7.41284
a
8
=
−17.8553u
43
+ 30.2134u
42
+ ··· − 26.4883u + 3.72155
9.24027u
43
− 20.7299u
42
+ ··· + 66.3772u − 9.44318
a
5
=
3.14764u
43
+ 17.2758u
42
+ ··· − 185.352u + 33.8212
−14.3476u
43
+ 11.8548u
42
+ ··· + 35.6168u − 9.43295
a
9
=
−12.8155u
43
+ 22.0132u
42
+ ··· − 8.91018u + 1.63258
5.44390u
43
− 15.5538u
42
+ ··· + 62.3290u − 9.34964
a
12
=
−11.1592u
43
+ 40.9840u
42
+ ··· − 205.341u + 33.4786
23.4851u
43
− 36.3767u
42
+ ··· + 44.9311u − 3.86733
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −
192849487866
4990744411
u
43
−
83303496455
4990744411
u
42
+ ··· +
2009823972600
4990744411
u −
371947337450
4990744411
23
(iv) u-Polynomials at the component
24
Crossings u-Polynomials at each crossing
c
1
u
44
− 25u
43
+ ··· − 11u + 1
c
2
u
44
+ u
43
+ ··· + 5u + 1
c
3
u
44
− 4u
42
+ ··· + 23u + 25
c
4
u
44
+ 2u
43
+ ··· − 4u + 1
c
5
u
44
− 2u
43
+ ··· + 74u + 25
c
6
u
44
− u
43
+ ··· − 5u + 1
c
7
u
44
+ 15u
43
+ ··· + 7u + 1
c
8
u
44
− 2u
43
+ ··· − 2u
2
+ 1
c
9
u
44
+ 3u
42
+ ··· − 4u + 1
c
10
u
44
− 15u
43
+ ··· − 7u + 1
c
11
u
44
− 6u
43
+ ··· − 8u + 1
c
12
u
44
− 2u
43
+ ··· + 4u + 1
25
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
44
+ y
43
+ ··· + 11y + 1
c
2
, c
6
y
44
+ 25y
43
+ ··· + 11y + 1
c
3
y
44
− 8y
43
+ ··· − 3629y + 625
c
4
, c
12
y
44
− 34y
43
+ ··· − 14y + 1
c
5
y
44
− 4y
43
+ ··· + 3274y + 625
c
7
, c
10
y
44
+ 23y
43
+ ··· + 37y + 1
c
8
y
44
− 16y
43
+ ··· − 4y + 1
c
9
y
44
+ 6y
43
+ ··· + 24y + 1
c
11
y
44
− 18y
43
+ ··· + 14y + 1
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.308157 + 0.987633I
a = 1.16862 + 0.93312I
b = −0.21599 − 1.57354I
−3.22606 + 3.75156I 2.55999 − 3.15479I
u = −0.308157 − 0.987633I
a = 1.16862 − 0.93312I
b = −0.21599 + 1.57354I
−3.22606 − 3.75156I 2.55999 + 3.15479I
u = 0.315393 + 1.002290I
a = 0.311564 + 0.823089I
b = 0.000777 − 1.252100I
−5.29368 + 3.15763I −4.09773 − 5.41114I
u = 0.315393 − 1.002290I
a = 0.311564 − 0.823089I
b = 0.000777 + 1.252100I
−5.29368 − 3.15763I −4.09773 + 5.41114I
u = −0.811207 + 0.489422I
a = −0.380863 − 0.948948I
b = −0.463995 − 1.292540I
0.95609 + 4.94263I 8.91748 − 4.91019I
u = −0.811207 − 0.489422I
a = −0.380863 + 0.948948I
b = −0.463995 + 1.292540I
0.95609 − 4.94263I 8.91748 + 4.91019I
u = 0.551995 + 0.918179I
a = −0.824676 + 0.819111I
b = −0.947684 + 0.175996I
1.74529 + 2.25308I 7.16464 + 0.I
u = 0.551995 − 0.918179I
a = −0.824676 − 0.819111I
b = −0.947684 − 0.175996I
1.74529 − 2.25308I 7.16464 + 0.I
u = −0.305558 + 1.034290I
a = 1.91005 + 2.16726I
b = 0.351249 − 0.651952I
1.37900 − 7.60672I 0.66870 + 12.81699I
u = −0.305558 − 1.034290I
a = 1.91005 − 2.16726I
b = 0.351249 + 0.651952I
1.37900 + 7.60672I 0.66870 − 12.81699I
28
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.245789 + 0.884474I
a = 0.27791 − 1.69712I
b = −0.163334 + 1.324920I
−4.74341 − 0.88044I 0.889226 + 0.400447I
u = 0.245789 − 0.884474I
a = 0.27791 + 1.69712I
b = −0.163334 − 1.324920I
−4.74341 + 0.88044I 0.889226 − 0.400447I
u = −0.213057 + 0.880428I
a = −0.212781 − 0.099889I
b = −0.06661 + 1.47962I
−2.65962 − 5.94295I 2.31883 + 8.60007I
u = −0.213057 − 0.880428I
a = −0.212781 + 0.099889I
b = −0.06661 − 1.47962I
−2.65962 + 5.94295I 2.31883 − 8.60007I
u = −0.479059 + 0.997167I
a = −0.81176 − 1.41693I
b = −1.60442 − 0.17277I
4.08940 − 2.90277I 0. + 6.41959I
u = −0.479059 − 0.997167I
a = −0.81176 + 1.41693I
b = −1.60442 + 0.17277I
4.08940 + 2.90277I 0. − 6.41959I
u = 0.871285 + 0.183068I
a = 0.295474 − 0.420513I
b = −0.143959 − 0.917305I
−0.837506 + 0.694451I −3.73124 + 0.53910I
u = 0.871285 − 0.183068I
a = 0.295474 + 0.420513I
b = −0.143959 + 0.917305I
−0.837506 − 0.694451I −3.73124 − 0.53910I
u = −0.273129 + 0.795130I
a = 2.32282 + 2.13261I
b = 0.379363 + 0.497324I
2.30016 + 5.13733I 8.82905 − 4.63431I
u = −0.273129 − 0.795130I
a = 2.32282 − 2.13261I
b = 0.379363 − 0.497324I
2.30016 − 5.13733I 8.82905 + 4.63431I
29
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.735552 + 0.903542I
a = −0.218764 − 0.441825I
b = 0.130785 − 0.413943I
5.21381 − 8.37867I 4.00000 + 9.26873I
u = −0.735552 − 0.903542I
a = −0.218764 + 0.441825I
b = 0.130785 + 0.413943I
5.21381 + 8.37867I 4.00000 − 9.26873I
u = −0.811075 + 0.857875I
a = −0.699674 + 0.182942I
b = 0.031035 + 0.488766I
5.38331 + 2.57251I 0
u = −0.811075 − 0.857875I
a = −0.699674 − 0.182942I
b = 0.031035 − 0.488766I
5.38331 − 2.57251I 0
u = −0.451124 + 0.667034I
a = −1.54989 − 1.13540I
b = −1.362930 + 0.228015I
5.20489 − 0.98576I 8.15267 − 3.45564I
u = −0.451124 − 0.667034I
a = −1.54989 + 1.13540I
b = −1.362930 − 0.228015I
5.20489 + 0.98576I 8.15267 + 3.45564I
u = 0.696382 + 0.971335I
a = −0.641482 + 0.568672I
b = −0.567542 + 0.498560I
1.56607 + 2.26987I 14.6992 + 0.I
u = 0.696382 − 0.971335I
a = −0.641482 − 0.568672I
b = −0.567542 − 0.498560I
1.56607 − 2.26987I 14.6992 + 0.I
u = 0.515589 + 1.093630I
a = 1.82107 − 0.24845I
b = 0.124563 + 0.868536I
−3.57585 + 3.87439I 0
u = 0.515589 − 1.093630I
a = 1.82107 + 0.24845I
b = 0.124563 − 0.868536I
−3.57585 − 3.87439I 0
30
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.597100 + 1.089810I
a = −1.82849 − 0.46447I
b = −0.52934 + 1.45945I
−0.90931 − 10.19890I 0
u = −0.597100 − 1.089810I
a = −1.82849 + 0.46447I
b = −0.52934 − 1.45945I
−0.90931 + 10.19890I 0
u = 0.311016 + 0.625703I
a = 1.82403 − 1.95875I
b = −0.015549 − 0.613118I
−1.52816 − 0.17234I 4.03079 + 1.10747I
u = 0.311016 − 0.625703I
a = 1.82403 + 1.95875I
b = −0.015549 + 0.613118I
−1.52816 + 0.17234I 4.03079 − 1.10747I
u = 0.572521 + 0.394365I
a = −1.97593 + 0.06581I
b = −0.771844 − 0.836458I
3.15409 + 2.92855I 6.03002 − 2.32219I
u = 0.572521 − 0.394365I
a = −1.97593 − 0.06581I
b = −0.771844 + 0.836458I
3.15409 − 2.92855I 6.03002 + 2.32219I
u = 0.580346 + 1.200560I
a = −1.58115 + 0.56532I
b = −0.672883 − 1.046750I
−0.04185 + 7.52820I 0
u = 0.580346 − 1.200560I
a = −1.58115 − 0.56532I
b = −0.672883 + 1.046750I
−0.04185 − 7.52820I 0
u = 0.150514 + 1.352220I
a = −0.157281 + 0.557104I
b = −0.129821 − 1.126760I
−6.27108 + 4.02109I 0
u = 0.150514 − 1.352220I
a = −0.157281 − 0.557104I
b = −0.129821 + 1.126760I
−6.27108 − 4.02109I 0
31
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.220429 + 1.392290I
a = 0.109335 − 0.963032I
b = −0.116262 + 0.796153I
−4.95880 + 2.98569I 0
u = 0.220429 − 1.392290I
a = 0.109335 + 0.963032I
b = −0.116262 − 0.796153I
−4.95880 − 2.98569I 0
u = 0.453757 + 0.195053I
a = −1.65813 + 1.80893I
b = −0.745603 + 0.882162I
3.05324 − 2.78726I 8.38024 + 3.32043I
u = 0.453757 − 0.195053I
a = −1.65813 − 1.80893I
b = −0.745603 − 0.882162I
3.05324 + 2.78726I 8.38024 − 3.32043I
32
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
44
− 25u
43
+ ··· − 11u + 1)
· (u
175
+ 84u
174
+ ··· − 21510473u − 1247689)
c
2
(u
44
+ u
43
+ ··· + 5u + 1)(u
175
− 4u
174
+ ··· + 6175u − 1117)
c
3
(u
44
− 4u
42
+ ··· + 23u + 25)
· (u
175
+ 5u
174
+ ··· − 200903543u − 14492227)
c
4
(u
44
+ 2u
43
+ ··· − 4u + 1)(u
175
+ u
174
+ ··· + 38u − 1)
c
5
(u
44
− 2u
43
+ ··· + 74u + 25)
· (u
175
− 9u
174
+ ··· + 1244051648u − 87632999)
c
6
(u
44
− u
43
+ ··· − 5u + 1)(u
175
− 4u
174
+ ··· + 6175u − 1117)
c
7
(u
44
+ 15u
43
+ ··· + 7u + 1)(u
175
− 14u
174
+ ··· + 444875u − 24751)
c
8
(u
44
− 2u
43
+ ··· − 2u
2
+ 1)(u
175
− 3u
174
+ ··· − 3228u − 745)
c
9
(u
44
+ 3u
42
+ ··· − 4u + 1)(u
175
− u
174
+ ··· − 1852932u − 499117)
c
10
(u
44
− 15u
43
+ ··· − 7u + 1)(u
175
− 14u
174
+ ··· + 444875u − 24751)
c
11
(u
44
− 6u
43
+ ··· − 8u + 1)(u
175
+ 13u
174
+ ··· − 2u + 97)
c
12
(u
44
− 2u
43
+ ··· + 4u + 1)(u
175
+ u
174
+ ··· + 38u − 1)
33
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
44
+ y
43
+ ··· + 11y + 1)
· (y
175
+ 28y
174
+ ··· − 85299694583841y −1556727840721)
c
2
, c
6
(y
44
+ 25y
43
+ ··· + 11y + 1)
· (y
175
+ 84y
174
+ ··· − 21510473y −1247689)
c
3
(y
44
− 8y
43
+ ··· − 3629y + 625)
· (y
175
− 37y
174
+ ··· + 10887680210935327y −210024643419529)
c
4
, c
12
(y
44
− 34y
43
+ ··· − 14y + 1)(y
175
− 127y
174
+ ··· − 180y −1)
c
5
(y
44
− 4y
43
+ ··· + 3274y + 625)
· (y
175
+ 27y
174
+ ··· + 136692045245606196y −7679542513734001)
c
7
, c
10
(y
44
+ 23y
43
+ ··· + 37y + 1)
· (y
175
+ 94y
174
+ ··· − 17564282207y −612612001)
c
8
(y
44
− 16y
43
+ ··· − 4y + 1)
· (y
175
− 29y
174
+ ··· + 14232894y −555025)
c
9
(y
44
+ 6y
43
+ ··· + 24y + 1)
· (y
175
+ 29y
174
+ ··· − 22256433571302y −249117779689)
c
11
(y
44
− 18y
43
+ ··· + 14y + 1)(y
175
− 27y
174
+ ··· + 580452y −9409)
34
