12a
0256
(K12a
0256
)
A knot diagram
1
Linearized knot diagam
3 6 7 10 12 2 11 1 5 8 4 9
Solving Sequence
2,6
3 7
4,11
8 12 1 9 5 10
c
2
c
6
c
3
c
7
c
11
c
1
c
8
c
5
c
10
c
4
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h2.56758 × 10
188
u
136
+ 1.42936 × 10
189
u
135
+ ··· + 2.47840 × 10
187
b − 1.95610 × 10
188
,
2.04389 × 10
188
u
136
+ 1.15337 × 10
189
u
135
+ ··· + 2.47840 × 10
187
a − 8.69370 × 10
187
, u
137
+ 5u
136
+ ··· − 3u − 1i
I
u
2
= h−5u
26
− u
25
+ ··· + b − 6, −5u
27
− 3u
26
+ ··· + a − 4, u
28
+ 8u
26
+ ··· − 2u + 1i
* 2 irreducible components of dim
C
= 0, with total 165 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
= h2.57 × 10
188
u
136
+ 1.43 × 10
189
u
135
+ · · · + 2.48 × 10
187
b − 1.96 ×
10
188
, 2.04 × 10
188
u
136
+ 1.15 × 10
189
u
135
+ · · · + 2.48 × 10
187
a − 8.69 ×
10
187
, u
137
+ 5u
136
+ · · · − 3u − 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
11
=
−8.24683u
136
− 46.5369u
135
+ ··· + 34.6876u + 3.50779
−10.3598u
136
− 57.6726u
135
+ ··· + 28.1421u + 7.89259
a
8
=
1.62844u
136
+ 10.3502u
135
+ ··· − 2.08567u + 3.05147
−2.24765u
136
− 7.89848u
135
+ ··· − 14.2337u − 4.99920
a
12
=
−4.73113u
136
− 29.1031u
135
+ ··· + 31.2965u + 2.98213
−4.43686u
136
− 28.1267u
135
+ ··· + 16.0148u + 4.77163
a
1
=
u
2
+ 1
−u
4
a
9
=
−0.0634631u
136
− 0.511369u
135
+ ··· + 12.2936u + 6.46153
−7.98027u
136
− 38.7088u
135
+ ··· + 0.862867u − 0.263602
a
5
=
5.35808u
136
+ 27.7315u
135
+ ··· − 11.7973u + 0.359303
6.75832u
136
+ 37.5761u
135
+ ··· − 38.0131u − 10.3110
a
10
=
−0.550892u
136
+ 1.58672u
135
+ ··· − 29.6268u − 8.41074
3.01851u
136
+ 18.3843u
135
+ ··· − 8.86141u − 5.99470
(ii) Obstruction class = −1
(iii) Cusp Shapes = 3.41230u
136
+ 7.78483u
135
+ ··· − 25.4529u − 5.81017
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
137
+ 71u
136
+ ··· − 11u − 1
c
2
, c
6
u
137
− 5u
136
+ ··· − 3u + 1
c
3
u
137
+ 5u
136
+ ··· − 28109u + 49282
c
4
, c
9
u
137
− u
136
+ ··· + 37207u + 14092
c
5
u
137
+ 18u
135
+ ··· + 38195407u + 7601057
c
7
, c
10
u
137
+ 6u
136
+ ··· − 20079u + 3169
c
8
, c
12
u
137
+ 3u
136
+ ··· − 1611854u + 205619
c
11
u
137
+ 5u
136
+ ··· + 361656u + 26671
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
137
− y
136
+ ··· + 61y −1
c
2
, c
6
y
137
+ 71y
136
+ ··· − 11y −1
c
3
y
137
− 73y
136
+ ··· + 30864949201y −2428715524
c
4
, c
9
y
137
+ 103y
136
+ ··· − 3967076151y −198584464
c
5
y
137
+ 36y
136
+ ··· − 2839868740482897y −57776067517249
c
7
, c
10
y
137
+ 90y
136
+ ··· − 824301543y −10042561
c
8
, c
12
y
137
+ 93y
136
+ ··· − 669185450976y −42279173161
c
11
y
137
− 17y
136
+ ··· + 62854050382y −711342241
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.533319 + 0.849244I
a = 0.116988 − 0.644715I
b = 0.815465 − 1.064700I
−1.12416 − 2.04890I 0
u = −0.533319 − 0.849244I
a = 0.116988 + 0.644715I
b = 0.815465 + 1.064700I
−1.12416 + 2.04890I 0
u = 0.502796 + 0.853410I
a = 0.984550 + 0.293887I
b = 0.182920 − 0.493163I
0.28337 − 1.41442I 0
u = 0.502796 − 0.853410I
a = 0.984550 − 0.293887I
b = 0.182920 + 0.493163I
0.28337 + 1.41442I 0
u = −0.957173 + 0.102971I
a = −0.25823 − 1.86243I
b = −0.162071 − 0.899505I
3.30511 − 0.01751I 0
u = −0.957173 − 0.102971I
a = −0.25823 + 1.86243I
b = −0.162071 + 0.899505I
3.30511 + 0.01751I 0
u = −0.304693 + 0.910206I
a = −0.26481 − 1.50058I
b = 0.668726 − 0.857128I
2.61366 − 5.14297I 0
u = −0.304693 − 0.910206I
a = −0.26481 + 1.50058I
b = 0.668726 + 0.857128I
2.61366 + 5.14297I 0
u = 0.596239 + 0.863165I
a = −0.958277 + 0.025577I
b = −1.86008 + 0.32518I
7.73934 − 0.81536I 0
u = 0.596239 − 0.863165I
a = −0.958277 − 0.025577I
b = −1.86008 − 0.32518I
7.73934 + 0.81536I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.069847 + 1.050040I
a = 0.0056226 + 0.0646777I
b = −1.068510 + 0.267075I
−0.0265712 − 0.0562753I 0
u = 0.069847 − 1.050040I
a = 0.0056226 − 0.0646777I
b = −1.068510 − 0.267075I
−0.0265712 + 0.0562753I 0
u = −0.325030 + 0.878832I
a = 0.456202 − 0.441515I
b = 0.286899 − 0.477025I
−0.54203 − 1.42582I 0
u = −0.325030 − 0.878832I
a = 0.456202 + 0.441515I
b = 0.286899 + 0.477025I
−0.54203 + 1.42582I 0
u = 0.617489 + 0.700364I
a = 0.17956 − 1.41511I
b = −0.130881 − 0.287691I
8.20953 + 5.56566I 0
u = 0.617489 − 0.700364I
a = 0.17956 + 1.41511I
b = −0.130881 + 0.287691I
8.20953 − 5.56566I 0
u = 0.887754 + 0.262797I
a = 0.12921 + 2.14576I
b = 0.179272 + 0.677955I
−1.93538 − 7.48838I 0
u = 0.887754 − 0.262797I
a = 0.12921 − 2.14576I
b = 0.179272 − 0.677955I
−1.93538 + 7.48838I 0
u = 0.756689 + 0.764410I
a = −0.110558 − 0.663621I
b = 0.216956 + 0.337434I
6.38454 − 5.71250I 0
u = 0.756689 − 0.764410I
a = −0.110558 + 0.663621I
b = 0.216956 − 0.337434I
6.38454 + 5.71250I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.988134 + 0.432807I
a = −0.160589 + 1.032590I
b = 0.242816 + 0.384392I
3.73770 − 1.79692I 0
u = −0.988134 − 0.432807I
a = −0.160589 − 1.032590I
b = 0.242816 − 0.384392I
3.73770 + 1.79692I 0
u = 0.575110 + 0.713441I
a = −0.217900 + 0.741038I
b = 0.99074 + 1.18801I
0.68274 + 5.78618I 0
u = 0.575110 − 0.713441I
a = −0.217900 − 0.741038I
b = 0.99074 − 1.18801I
0.68274 − 5.78618I 0
u = −0.869875 + 0.251926I
a = 0.08200 − 2.32233I
b = 0.361982 − 0.715554I
2.71900 + 13.79220I 0
u = −0.869875 − 0.251926I
a = 0.08200 + 2.32233I
b = 0.361982 + 0.715554I
2.71900 − 13.79220I 0
u = 0.490407 + 0.755910I
a = 0.636976 + 1.124530I
b = 1.099390 + 0.433924I
3.99446 + 2.04024I 0
u = 0.490407 − 0.755910I
a = 0.636976 − 1.124530I
b = 1.099390 − 0.433924I
3.99446 − 2.04024I 0
u = 0.718798 + 0.835116I
a = −0.150342 − 0.075852I
b = −1.263490 − 0.320415I
6.16457 + 11.21360I 0
u = 0.718798 − 0.835116I
a = −0.150342 + 0.075852I
b = −1.263490 + 0.320415I
6.16457 − 11.21360I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.680528 + 0.577464I
a = 0.432488 + 0.843523I
b = 0.145641 + 0.260873I
3.38601 − 0.98367I 0
u = −0.680528 − 0.577464I
a = 0.432488 − 0.843523I
b = 0.145641 − 0.260873I
3.38601 + 0.98367I 0
u = 0.354562 + 1.052920I
a = 0.343872 − 0.019856I
b = 0.104155 − 0.950397I
−1.331140 − 0.354042I 0
u = 0.354562 − 1.052920I
a = 0.343872 + 0.019856I
b = 0.104155 + 0.950397I
−1.331140 + 0.354042I 0
u = −0.166408 + 1.098790I
a = −1.50293 − 0.36380I
b = −2.64367 − 0.36084I
−4.55631 − 3.25534I 0
u = −0.166408 − 1.098790I
a = −1.50293 + 0.36380I
b = −2.64367 + 0.36084I
−4.55631 + 3.25534I 0
u = −0.472124 + 1.038700I
a = 0.407735 − 1.282440I
b = −0.063430 − 0.465076I
3.23424 − 0.51796I 0
u = −0.472124 − 1.038700I
a = 0.407735 + 1.282440I
b = −0.063430 + 0.465076I
3.23424 + 0.51796I 0
u = 0.712987 + 0.446274I
a = 1.111570 + 0.012824I
b = 0.352809 − 0.679136I
4.76931 − 1.62940I 0
u = 0.712987 − 0.446274I
a = 1.111570 − 0.012824I
b = 0.352809 + 0.679136I
4.76931 + 1.62940I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.667112 + 0.501243I
a = 0.911117 − 0.658420I
b = 0.759339 + 0.465298I
5.05813 + 0.60000I 0
u = −0.667112 − 0.501243I
a = 0.911117 + 0.658420I
b = 0.759339 − 0.465298I
5.05813 − 0.60000I 0
u = −0.546634 + 1.030390I
a = 0.267839 − 1.154730I
b = 1.10542 − 1.03275I
3.50173 − 5.32217I 0
u = −0.546634 − 1.030390I
a = 0.267839 + 1.154730I
b = 1.10542 + 1.03275I
3.50173 + 5.32217I 0
u = −0.378661 + 1.103420I
a = 0.140117 − 0.141434I
b = 0.023825 − 0.869305I
−1.35691 − 0.78518I 0
u = −0.378661 − 1.103420I
a = 0.140117 + 0.141434I
b = 0.023825 + 0.869305I
−1.35691 + 0.78518I 0
u = 0.809928 + 0.190888I
a = −0.47628 − 2.02906I
b = −0.519671 − 0.606618I
−4.37189 − 2.92393I −8.03585 + 0.I
u = 0.809928 − 0.190888I
a = −0.47628 + 2.02906I
b = −0.519671 + 0.606618I
−4.37189 + 2.92393I −8.03585 + 0.I
u = 0.419233 + 1.096630I
a = 3.28779 + 0.82729I
b = 4.00138 + 1.08547I
1.63196 − 0.57127I 0
u = 0.419233 − 1.096630I
a = 3.28779 − 0.82729I
b = 4.00138 − 1.08547I
1.63196 + 0.57127I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.309532 + 1.135070I
a = 0.637035 + 0.462955I
b = 0.92097 + 1.47589I
2.06956 + 4.03324I 0
u = −0.309532 − 1.135070I
a = 0.637035 − 0.462955I
b = 0.92097 − 1.47589I
2.06956 − 4.03324I 0
u = 0.434697 + 1.101330I
a = −1.351880 + 0.178073I
b = −2.39197 − 0.79055I
−3.75315 + 0.76063I 0
u = 0.434697 − 1.101330I
a = −1.351880 − 0.178073I
b = −2.39197 + 0.79055I
−3.75315 − 0.76063I 0
u = −0.766102 + 0.246672I
a = −0.63871 + 2.36043I
b = −0.737180 + 0.709707I
−1.48537 + 7.19229I −2.90359 − 6.29894I
u = −0.766102 − 0.246672I
a = −0.63871 − 2.36043I
b = −0.737180 − 0.709707I
−1.48537 − 7.19229I −2.90359 + 6.29894I
u = −0.749282 + 0.261094I
a = −1.229260 − 0.235481I
b = 0.372948 − 0.002355I
6.22390 + 7.17173I 1.35640 − 5.57817I
u = −0.749282 − 0.261094I
a = −1.229260 + 0.235481I
b = 0.372948 + 0.002355I
6.22390 − 7.17173I 1.35640 + 5.57817I
u = −0.450406 + 1.119820I
a = −2.04217 − 0.38943I
b = −3.24431 + 0.11454I
−4.22382 − 5.85372I 0
u = −0.450406 − 1.119820I
a = −2.04217 + 0.38943I
b = −3.24431 − 0.11454I
−4.22382 + 5.85372I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.474163 + 1.111140I
a = 1.88851 + 0.59079I
b = 3.19369 + 0.46268I
−3.45317 + 6.67791I 0
u = 0.474163 − 1.111140I
a = 1.88851 − 0.59079I
b = 3.19369 − 0.46268I
−3.45317 − 6.67791I 0
u = −0.309506 + 1.167930I
a = 1.60936 + 0.86298I
b = 2.56755 + 0.23611I
−5.73719 + 3.86942I 0
u = −0.309506 − 1.167930I
a = 1.60936 − 0.86298I
b = 2.56755 − 0.23611I
−5.73719 − 3.86942I 0
u = 0.483929 + 1.108490I
a = −3.12745 + 0.85374I
b = −3.96728 + 0.63687I
2.11058 + 7.96960I 0
u = 0.483929 − 1.108490I
a = −3.12745 − 0.85374I
b = −3.96728 − 0.63687I
2.11058 − 7.96960I 0
u = −0.447836 + 1.123900I
a = 2.17137 − 0.64014I
b = 3.28589 − 0.91335I
−4.23233 − 1.82443I 0
u = −0.447836 − 1.123900I
a = 2.17137 + 0.64014I
b = 3.28589 + 0.91335I
−4.23233 + 1.82443I 0
u = 0.579612 + 1.066840I
a = −0.372465 + 0.966588I
b = 0.159901 + 1.382820I
2.94960 + 6.58219I 0
u = 0.579612 − 1.066840I
a = −0.372465 − 0.966588I
b = 0.159901 − 1.382820I
2.94960 − 6.58219I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.446297 + 1.130490I
a = −0.347437 − 0.281460I
b = −0.428965 + 0.284776I
−4.22376 + 3.90424I 0
u = 0.446297 − 1.130490I
a = −0.347437 + 0.281460I
b = −0.428965 − 0.284776I
−4.22376 − 3.90424I 0
u = −0.628866 + 1.049280I
a = −0.509840 − 0.322071I
b = −0.802525 − 0.260188I
2.06270 − 4.14982I 0
u = −0.628866 − 1.049280I
a = −0.509840 + 0.322071I
b = −0.802525 + 0.260188I
2.06270 + 4.14982I 0
u = 0.769989 + 0.085192I
a = 0.69957 − 2.14608I
b = −0.334847 − 0.454878I
−0.21167 − 3.95519I −0.70872 + 4.40749I
u = 0.769989 − 0.085192I
a = 0.69957 + 2.14608I
b = −0.334847 + 0.454878I
−0.21167 + 3.95519I −0.70872 − 4.40749I
u = 0.690948 + 0.327915I
a = −0.534108 + 0.568309I
b = 0.437649 − 0.094786I
2.37595 − 2.88460I −0.64698 + 3.62738I
u = 0.690948 − 0.327915I
a = −0.534108 − 0.568309I
b = 0.437649 + 0.094786I
2.37595 + 2.88460I −0.64698 − 3.62738I
u = −0.761678 + 0.972727I
a = −0.513431 − 0.357447I
b = −1.164300 − 0.121244I
2.09836 − 4.33096I 0
u = −0.761678 − 0.972727I
a = −0.513431 + 0.357447I
b = −1.164300 + 0.121244I
2.09836 + 4.33096I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.494451 + 1.133360I
a = −0.945389 − 0.096475I
b = −1.19728 − 0.77220I
−0.53789 − 6.91554I 0
u = −0.494451 − 1.133360I
a = −0.945389 + 0.096475I
b = −1.19728 + 0.77220I
−0.53789 + 6.91554I 0
u = 0.535487 + 1.114710I
a = 0.528266 + 0.009933I
b = 1.046600 − 0.694471I
0.07546 + 7.60673I 0
u = 0.535487 − 1.114710I
a = 0.528266 − 0.009933I
b = 1.046600 + 0.694471I
0.07546 − 7.60673I 0
u = −0.424065 + 1.166910I
a = 1.82804 − 0.27571I
b = 2.84165 − 0.96154I
−4.83821 − 1.44208I 0
u = −0.424065 − 1.166910I
a = 1.82804 + 0.27571I
b = 2.84165 + 0.96154I
−4.83821 + 1.44208I 0
u = 0.025066 + 0.753968I
a = 0.564772 − 0.822293I
b = −0.233222 − 0.889953I
−0.93531 − 1.11977I −7.63811 + 4.58075I
u = 0.025066 − 0.753968I
a = 0.564772 + 0.822293I
b = −0.233222 + 0.889953I
−0.93531 + 1.11977I −7.63811 − 4.58075I
u = 0.295392 + 0.690589I
a = −0.451041 + 0.994000I
b = 1.086820 + 0.656532I
−0.14414 + 3.11446I −8.84863 + 1.95541I
u = 0.295392 − 0.690589I
a = −0.451041 − 0.994000I
b = 1.086820 − 0.656532I
−0.14414 − 3.11446I −8.84863 − 1.95541I
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.473615 + 1.159220I
a = −2.23868 − 0.05116I
b = −3.47114 − 0.04967I
−4.48472 − 6.82060I 0
u = −0.473615 − 1.159220I
a = −2.23868 + 0.05116I
b = −3.47114 + 0.04967I
−4.48472 + 6.82060I 0
u = −0.478731 + 0.568594I
a = 1.316230 − 0.160713I
b = 0.035393 + 0.245607I
−0.39680 − 2.11027I −3.71418 + 2.14261I
u = −0.478731 − 0.568594I
a = 1.316230 + 0.160713I
b = 0.035393 − 0.245607I
−0.39680 + 2.11027I −3.71418 − 2.14261I
u = 0.333106 + 1.214680I
a = 1.52890 − 0.65967I
b = 2.44133 − 0.21664I
−8.68461 + 0.83942I 0
u = 0.333106 − 1.214680I
a = 1.52890 + 0.65967I
b = 2.44133 + 0.21664I
−8.68461 − 0.83942I 0
u = 0.407231 + 1.196350I
a = 1.285220 + 0.287911I
b = 2.06870 + 1.29048I
−3.96480 + 0.12479I 0
u = 0.407231 − 1.196350I
a = 1.285220 − 0.287911I
b = 2.06870 − 1.29048I
−3.96480 − 0.12479I 0
u = −0.538558 + 1.145630I
a = 0.397123 + 0.477194I
b = 0.69365 + 1.54220I
3.63696 − 12.02450I 0
u = −0.538558 − 1.145630I
a = 0.397123 − 0.477194I
b = 0.69365 − 1.54220I
3.63696 + 12.02450I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.541768 + 1.153570I
a = −2.22949 + 0.90829I
b = −3.30390 + 0.95277I
−4.13786 − 12.09350I 0
u = −0.541768 − 1.153570I
a = −2.22949 − 0.90829I
b = −3.30390 − 0.95277I
−4.13786 + 12.09350I 0
u = −0.275174 + 1.252270I
a = −1.71289 − 0.25641I
b = −2.64631 + 0.39413I
−2.15174 + 10.09580I 0
u = −0.275174 − 1.252270I
a = −1.71289 + 0.25641I
b = −2.64631 − 0.39413I
−2.15174 − 10.09580I 0
u = 0.485122 + 1.187120I
a = −2.00112 + 0.05850I
b = −3.21581 + 0.44929I
−3.41641 + 8.54851I 0
u = 0.485122 − 1.187120I
a = −2.00112 − 0.05850I
b = −3.21581 − 0.44929I
−3.41641 − 8.54851I 0
u = 0.248468 + 1.263820I
a = −1.73417 + 0.22192I
b = −2.69325 − 0.19554I
−6.98987 − 3.80379I 0
u = 0.248468 − 1.263820I
a = −1.73417 − 0.22192I
b = −2.69325 + 0.19554I
−6.98987 + 3.80379I 0
u = 0.533106 + 1.180340I
a = −1.95084 − 0.63722I
b = −2.90642 − 0.73647I
−7.29057 + 7.87576I 0
u = 0.533106 − 1.180340I
a = −1.95084 + 0.63722I
b = −2.90642 + 0.73647I
−7.29057 − 7.87576I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.663096 + 0.189723I
a = 0.789921 + 0.764446I
b = −0.336996 + 0.443443I
2.13907 + 2.48571I −0.07943 − 3.19313I
u = −0.663096 − 0.189723I
a = 0.789921 − 0.764446I
b = −0.336996 − 0.443443I
2.13907 − 2.48571I −0.07943 + 3.19313I
u = −0.570930 + 1.187360I
a = 2.21296 − 0.30007I
b = 3.37522 − 0.28961I
−0.0881 − 19.0756I 0
u = −0.570930 − 1.187360I
a = 2.21296 + 0.30007I
b = 3.37522 + 0.28961I
−0.0881 + 19.0756I 0
u = −0.678581 + 0.062843I
a = 0.45807 + 2.61890I
b = −0.049753 + 0.622208I
−1.43948 + 2.51411I −3.67454 − 0.43519I
u = −0.678581 − 0.062843I
a = 0.45807 − 2.61890I
b = −0.049753 − 0.622208I
−1.43948 − 2.51411I −3.67454 + 0.43519I
u = 0.577984 + 1.189160I
a = 2.04104 + 0.21797I
b = 3.12088 + 0.35123I
−4.72940 + 12.84590I 0
u = 0.577984 − 1.189160I
a = 2.04104 − 0.21797I
b = 3.12088 − 0.35123I
−4.72940 − 12.84590I 0
u = 0.062478 + 0.661502I
a = 1.59403 + 2.45404I
b = 0.90624 + 2.55894I
3.97109 + 3.39944I −3.68341 + 1.39930I
u = 0.062478 − 0.661502I
a = 1.59403 − 2.45404I
b = 0.90624 − 2.55894I
3.97109 − 3.39944I −3.68341 − 1.39930I
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.473872 + 1.270700I
a = −1.84298 + 0.14674I
b = −2.41988 + 0.35596I
−0.86475 − 4.93494I 0
u = −0.473872 − 1.270700I
a = −1.84298 − 0.14674I
b = −2.41988 − 0.35596I
−0.86475 + 4.93494I 0
u = −0.275520 + 1.335420I
a = 1.43990 + 0.43703I
b = 2.22752 + 0.40675I
−2.14149 − 5.88208I 0
u = −0.275520 − 1.335420I
a = 1.43990 − 0.43703I
b = 2.22752 − 0.40675I
−2.14149 + 5.88208I 0
u = −0.589872 + 1.251000I
a = 1.82282 + 0.25698I
b = 2.59582 + 0.05410I
−0.11982 − 5.54446I 0
u = −0.589872 − 1.251000I
a = 1.82282 − 0.25698I
b = 2.59582 − 0.05410I
−0.11982 + 5.54446I 0
u = −0.426484 + 0.445189I
a = 0.332045 − 0.391955I
b = 1.88098 − 0.77902I
4.97034 − 3.39824I 4.02447 + 4.68678I
u = −0.426484 − 0.445189I
a = 0.332045 + 0.391955I
b = 1.88098 + 0.77902I
4.97034 + 3.39824I 4.02447 − 4.68678I
u = 0.590002
a = 0.311170
b = −0.471733
−1.25020 −8.18790
u = 0.509954 + 0.217008I
a = 0.36882 − 3.42715I
b = 0.59694 − 1.77591I
4.55501 − 3.83548I −0.52183 + 5.66712I
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.509954 − 0.217008I
a = 0.36882 + 3.42715I
b = 0.59694 + 1.77591I
4.55501 + 3.83548I −0.52183 − 5.66712I
u = −0.538359 + 0.029909I
a = 0.64786 − 3.00563I
b = 0.415245 − 0.505868I
−1.37258 − 2.04781I −4.83102 + 3.56124I
u = −0.538359 − 0.029909I
a = 0.64786 + 3.00563I
b = 0.415245 + 0.505868I
−1.37258 + 2.04781I −4.83102 − 3.56124I
u = 0.481827 + 0.203197I
a = 0.50493 + 2.88522I
b = 0.542964 + 0.155260I
−0.95953 − 2.63263I −1.29118 + 1.16569I
u = 0.481827 − 0.203197I
a = 0.50493 − 2.88522I
b = 0.542964 − 0.155260I
−0.95953 + 2.63263I −1.29118 − 1.16569I
u = 0.074277 + 0.488015I
a = −1.94274 + 0.35807I
b = 1.140730 + 0.138784I
−1.30856 + 2.47032I −1.47299 − 5.97951I
u = 0.074277 − 0.488015I
a = −1.94274 − 0.35807I
b = 1.140730 − 0.138784I
−1.30856 − 2.47032I −1.47299 + 5.97951I
18
II.
I
u
2
= h−5u
26
−u
25
+· · ·+b−6, −5u
27
−3u
26
+· · ·+a−4, u
28
+8u
26
+· · ·−2u+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
11
=
5u
27
+ 3u
26
+ ··· + 3u + 4
5u
26
+ u
25
+ ··· − 9u + 6
a
8
=
−3u
27
− 5u
26
+ ··· + 6u − 4
−4u
27
− 2u
26
+ ··· − 9u + 1
a
12
=
5u
27
+ 2u
26
+ ··· + 5u + 3
5u
26
+ 2u
25
+ ··· − 8u + 6
a
1
=
u
2
+ 1
−u
4
a
9
=
−4u
26
− 29u
24
+ ··· + 10u − 5
−2u
27
− 2u
26
+ ··· − 5u − 1
a
5
=
3u
27
− 7u
26
+ ··· + 28u − 12
4u
27
− 2u
26
+ ··· + 14u − 6
a
10
=
u
26
+ u
25
+ ··· + 4u − 2
2u
27
+ 4u
26
+ ··· − 6u + 6
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −26u
27
− 11u
26
− 209u
25
− 83u
24
− 827u
23
− 304u
22
− 2019u
21
− 677u
20
− 3292u
19
−
984u
18
− 3611u
17
− 899u
16
− 2586u
15
− 323u
14
− 1184u
13
+ 477u
12
− 630u
11
+
1072u
10
− 837u
9
+ 1200u
8
− 947u
7
+ 878u
6
− 629u
5
+ 395u
4
− 258u
3
+ 75u
2
− 53u − 10
19
(iv) u-Polynomials at the component
20
Crossings u-Polynomials at each crossing
c
1
u
28
− 16u
27
+ ··· − 10u + 1
c
2
u
28
+ 8u
26
+ ··· − 2u + 1
c
3
u
28
− 8u
26
+ ··· − 2u + 1
c
4
u
28
+ 14u
26
+ ··· − 3u + 1
c
5
u
28
− u
27
+ ··· + 2u + 1
c
6
u
28
+ 8u
26
+ ··· + 2u + 1
c
7
u
28
+ 5u
27
+ ··· − 2u + 1
c
8
u
28
+ 2u
27
+ ··· − 5u + 1
c
9
u
28
+ 14u
26
+ ··· + 3u + 1
c
10
u
28
− 5u
27
+ ··· + 2u + 1
c
11
u
28
+ 4u
26
+ ··· − 3u + 1
c
12
u
28
− 2u
27
+ ··· + 5u + 1
21
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
28
+ 32y
26
+ ··· − 6y + 1
c
2
, c
6
y
28
+ 16y
27
+ ··· + 10y + 1
c
3
y
28
− 16y
27
+ ··· + 18y + 1
c
4
, c
9
y
28
+ 28y
27
+ ··· + 33y + 1
c
5
y
28
+ y
27
+ ··· + 4y + 1
c
7
, c
10
y
28
+ 23y
27
+ ··· + 22y + 1
c
8
, c
12
y
28
+ 22y
27
+ ··· + 23y + 1
c
11
y
28
+ 8y
27
+ ··· + 5y + 1
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.927627 + 0.310266I
a = 0.476646 − 1.306430I
b = 0.141645 − 0.548306I
3.71732 − 1.33828I 2.28500 − 1.95773I
u = −0.927627 − 0.310266I
a = 0.476646 + 1.306430I
b = 0.141645 + 0.548306I
3.71732 + 1.33828I 2.28500 + 1.95773I
u = −0.429176 + 0.929211I
a = 0.516897 − 0.021782I
b = 0.055854 + 0.774875I
−0.417008 − 0.074495I −2.20975 + 1.98394I
u = −0.429176 − 0.929211I
a = 0.516897 + 0.021782I
b = 0.055854 − 0.774875I
−0.417008 + 0.074495I −2.20975 − 1.98394I
u = 0.392480 + 1.019250I
a = 1.99736 + 0.72446I
b = 1.68008 + 0.22227I
2.74271 − 1.09825I 0.07581 + 2.01930I
u = 0.392480 − 1.019250I
a = 1.99736 − 0.72446I
b = 1.68008 − 0.22227I
2.74271 + 1.09825I 0.07581 − 2.01930I
u = −0.288262 + 1.113700I
a = 1.73094 − 0.01917I
b = 2.91182 − 0.22588I
−3.52283 − 3.88968I −5.89753 + 4.23756I
u = −0.288262 − 1.113700I
a = 1.73094 + 0.01917I
b = 2.91182 + 0.22588I
−3.52283 + 3.88968I −5.89753 − 4.23756I
u = −0.440389 + 0.714722I
a = −0.514138 − 0.686596I
b = 0.808306 − 0.627817I
0.22093 − 3.57942I 0.17898 + 8.99073I
u = −0.440389 − 0.714722I
a = −0.514138 + 0.686596I
b = 0.808306 + 0.627817I
0.22093 + 3.57942I 0.17898 − 8.99073I
24
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.530263 + 1.045870I
a = −1.190230 + 0.613612I
b = −0.706757 + 0.604841I
3.76050 + 7.44396I 1.49824 − 9.02202I
u = 0.530263 − 1.045870I
a = −1.190230 − 0.613612I
b = −0.706757 − 0.604841I
3.76050 − 7.44396I 1.49824 + 9.02202I
u = 0.406570 + 1.160990I
a = 1.48927 + 0.23978I
b = 2.43638 + 1.20695I
−5.18932 + 0.02135I −11.78845 + 2.28843I
u = 0.406570 − 1.160990I
a = 1.48927 − 0.23978I
b = 2.43638 − 1.20695I
−5.18932 − 0.02135I −11.78845 − 2.28843I
u = 0.561190 + 0.517059I
a = 0.248990 − 0.696773I
b = −0.02581 − 1.46246I
5.37250 − 3.01778I 3.40635 + 1.78695I
u = 0.561190 − 0.517059I
a = 0.248990 + 0.696773I
b = −0.02581 + 1.46246I
5.37250 + 3.01778I 3.40635 − 1.78695I
u = 0.229239 + 0.711347I
a = 1.16053 + 2.42775I
b = 2.14265 + 2.15977I
4.04199 + 3.98407I −1.99854 − 10.95718I
u = 0.229239 − 0.711347I
a = 1.16053 − 2.42775I
b = 2.14265 − 2.15977I
4.04199 − 3.98407I −1.99854 + 10.95718I
u = −0.092522 + 0.736102I
a = 1.144440 − 0.744715I
b = −0.771373 − 0.011538I
−1.79219 + 2.06540I −11.53599 + 0.86230I
u = −0.092522 − 0.736102I
a = 1.144440 + 0.744715I
b = −0.771373 + 0.011538I
−1.79219 − 2.06540I −11.53599 − 0.86230I
25
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.491650 + 1.162380I
a = −2.07659 − 0.11492I
b = −3.33038 + 0.11639I
−4.57612 + 8.23220I −9.55306 − 8.45619I
u = 0.491650 − 1.162380I
a = −2.07659 + 0.11492I
b = −3.33038 − 0.11639I
−4.57612 − 8.23220I −9.55306 + 8.45619I
u = −0.671255 + 1.082300I
a = 0.546251 − 0.154259I
b = 1.118220 − 0.403693I
1.54070 − 4.46634I −8.22602 + 6.86506I
u = −0.671255 − 1.082300I
a = 0.546251 + 0.154259I
b = 1.118220 + 0.403693I
1.54070 + 4.46634I −8.22602 − 6.86506I
u = 0.697120 + 0.130845I
a = 0.38376 − 2.49764I
b = −0.314180 − 0.479622I
−1.64038 − 3.74071I −6.13159 + 6.29732I
u = 0.697120 − 0.130845I
a = 0.38376 + 2.49764I
b = −0.314180 + 0.479622I
−1.64038 + 3.74071I −6.13159 − 6.29732I
u = −0.459282 + 1.281090I
a = −1.91412 − 0.41482I
b = −2.64645 − 0.34057I
−0.96893 − 5.94168I −5.10346 + 10.57461I
u = −0.459282 − 1.281090I
a = −1.91412 + 0.41482I
b = −2.64645 + 0.34057I
−0.96893 + 5.94168I −5.10346 − 10.57461I
26
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
28
− 16u
27
+ ··· − 10u + 1)(u
137
+ 71u
136
+ ··· − 11u − 1)
c
2
(u
28
+ 8u
26
+ ··· − 2u + 1)(u
137
− 5u
136
+ ··· − 3u + 1)
c
3
(u
28
− 8u
26
+ ··· − 2u + 1)(u
137
+ 5u
136
+ ··· − 28109u + 49282)
c
4
(u
28
+ 14u
26
+ ··· − 3u + 1)(u
137
− u
136
+ ··· + 37207u + 14092)
c
5
(u
28
− u
27
+ ··· + 2u + 1)
· (u
137
+ 18u
135
+ ··· + 38195407u + 7601057)
c
6
(u
28
+ 8u
26
+ ··· + 2u + 1)(u
137
− 5u
136
+ ··· − 3u + 1)
c
7
(u
28
+ 5u
27
+ ··· − 2u + 1)(u
137
+ 6u
136
+ ··· − 20079u + 3169)
c
8
(u
28
+ 2u
27
+ ··· − 5u + 1)(u
137
+ 3u
136
+ ··· − 1611854u + 205619)
c
9
(u
28
+ 14u
26
+ ··· + 3u + 1)(u
137
− u
136
+ ··· + 37207u + 14092)
c
10
(u
28
− 5u
27
+ ··· + 2u + 1)(u
137
+ 6u
136
+ ··· − 20079u + 3169)
c
11
(u
28
+ 4u
26
+ ··· − 3u + 1)(u
137
+ 5u
136
+ ··· + 361656u + 26671)
c
12
(u
28
− 2u
27
+ ··· + 5u + 1)(u
137
+ 3u
136
+ ··· − 1611854u + 205619)
27
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
28
+ 32y
26
+ ··· − 6y + 1)(y
137
− y
136
+ ··· + 61y −1)
c
2
, c
6
(y
28
+ 16y
27
+ ··· + 10y + 1)(y
137
+ 71y
136
+ ··· − 11y −1)
c
3
(y
28
− 16y
27
+ ··· + 18y + 1)
· (y
137
− 73y
136
+ ··· + 30864949201y −2428715524)
c
4
, c
9
(y
28
+ 28y
27
+ ··· + 33y + 1)
· (y
137
+ 103y
136
+ ··· − 3967076151y −198584464)
c
5
(y
28
+ y
27
+ ··· + 4y + 1)
· (y
137
+ 36y
136
+ ··· − 2839868740482897y −57776067517249)
c
7
, c
10
(y
28
+ 23y
27
+ ··· + 22y + 1)
· (y
137
+ 90y
136
+ ··· − 824301543y −10042561)
c
8
, c
12
(y
28
+ 22y
27
+ ··· + 23y + 1)
· (y
137
+ 93y
136
+ ··· − 669185450976y −42279173161)
c
11
(y
28
+ 8y
27
+ ··· + 5y + 1)
· (y
137
− 17y
136
+ ··· + 62854050382y −711342241)
28
