12a
1091
(K12a
1091
)
A knot diagram
1
Linearized knot diagam
4 7 10 1 11 9 3 12 2 5 8 6
Solving Sequence
8,12 3,9
7 2 10 6 1 11 5 4
c
8
c
7
c
2
c
9
c
6
c
12
c
11
c
5
c
4
c
1
, c
3
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−6.39310 × 10
837
u
160
+ 4.58819 × 10
837
u
159
+ ··· + 1.25873 × 10
837
b + 1.99542 × 10
842
,
1.45185 × 10
842
u
160
− 7.32509 × 10
841
u
159
+ ··· + 2.86374 × 10
841
a − 5.38127 × 10
846
,
u
161
− 43u
159
+ ··· + 23192u − 22751i
I
u
2
= h−1.30052 × 10
27
u
42
+ 5.58534 × 10
27
u
41
+ ··· + 5.17611 × 10
24
b − 1.73362 × 10
27
,
− 5.05339 × 10
27
u
42
+ 2.24625 × 10
28
u
41
+ ··· + 5.17611 × 10
24
a − 8.77138 × 10
27
, u
43
− 5u
42
+ ··· + 9u − 1i
* 2 irreducible components of dim
C
= 0, with total 204 representations.
1
The image of knot diagram is generated by the software “Draw programme” developed by An-
drew Bartholomew(http://www.layer8.co.uk/maths/draw/index.htm#Running-draw), where we modi-
fied some parts for our purpose(https://github.com/CATsTAILs/LinksPainter).
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
1
I. I
u
1
= h−6.39 × 10
837
u
160
+ 4.59 × 10
837
u
159
+ · · · + 1.26 × 10
837
b + 2.00 ×
10
842
, 1.45 × 10
842
u
160
− 7.33 × 10
841
u
159
+ · · · + 2.86 × 10
841
a − 5.38 ×
10
846
, u
161
− 43u
159
+ · · · + 23192u − 22751i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
3
=
−5.06979u
160
+ 2.55788u
159
+ ··· − 468625.u + 187911.
5.07901u
160
− 3.64509u
159
+ ··· + 375636.u − 158527.
a
9
=
1
−u
2
a
7
=
10.6826u
160
− 9.77082u
159
+ ··· + 576831.u − 269285.
−24.6702u
160
+ 21.3731u
159
+ ··· − 1.39803 × 10
6
u + 645587.
a
2
=
1.12700u
160
− 6.54266u
159
+ ··· − 510744.u + 142501.
1.25989u
160
+ 0.372663u
159
+ ··· + 244271.u − 82982.0
a
10
=
−80.0417u
160
+ 75.0777u
159
+ ··· − 4.05107 × 10
6
u + 1.94173 × 10
6
28.1384u
160
− 23.4524u
159
+ ··· + 1.66699 × 10
6
u − 759659.
a
6
=
26.3009u
160
− 22.6628u
159
+ ··· + 1.50521 × 10
6
u − 692577.
−35.0998u
160
+ 29.6020u
159
+ ··· − 2.05235 × 10
6
u + 938893.
a
1
=
74.7417u
160
− 62.5278u
159
+ ··· + 4.47416 × 10
6
u − 2.02663 × 10
6
−45.8026u
160
+ 37.7780u
159
+ ··· − 2.80124 × 10
6
u + 1.25943 × 10
6
a
11
=
−u
u
a
5
=
21.0485u
160
− 18.9227u
159
+ ··· + 1.14409 × 10
6
u − 534703.
−29.8474u
160
+ 25.8619u
159
+ ··· − 1.69123 × 10
6
u + 781019.
a
4
=
−23.3510u
160
+ 15.7838u
159
+ ··· − 1.78107 × 10
6
u + 747855.
−11.4670u
160
+ 12.3883u
159
+ ··· − 382645.u + 221297.
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −357.352u
160
+ 338.730u
159
+ ··· − 1.76787 × 10
7
u + 8.55098 × 10
6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
161
− 6u
160
+ ··· − 60405u + 2525
c
2
, c
7
u
161
+ u
160
+ ··· + 62875u + 20690
c
3
u
161
+ u
160
+ ··· + 6424407u − 1081037
c
5
, c
10
u
161
− 5u
160
+ ··· − 34377u − 24287
c
6
u
161
+ 4u
160
+ ··· + 209706558586u + 17633051719
c
8
, c
11
u
161
− 43u
159
+ ··· + 23192u + 22751
c
9
u
161
+ 5u
160
+ ··· + 5900566245u − 806431049
c
12
u
161
+ 2u
160
+ ··· + 297854463u − 20528044
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
161
+ 104y
160
+ ··· − 44901925y −6375625
c
2
, c
7
y
161
− 95y
160
+ ··· + 56848574785y −428076100
c
3
y
161
+ 13y
160
+ ··· − 81817610068445y −1168640995369
c
5
, c
10
y
161
− 71y
160
+ ··· − 8324930855y −589858369
c
6
y
161
− 44y
160
+ ··· + 4.98 × 10
21
y −3.11 × 10
20
c
8
, c
11
y
161
− 86y
160
+ ··· + 30379536528y −517608001
c
9
y
161
+ 29y
160
+ ··· − 3.95 × 10
19
y −6.50 × 10
17
c
12
y
161
+ 36y
160
+ ··· − 32685559262828287y −421400590465936
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.950374 + 0.325702I
a = 0.393996 − 0.385326I
b = 0.169698 + 0.056372I
1.60788 − 1.20779I 0
u = −0.950374 − 0.325702I
a = 0.393996 + 0.385326I
b = 0.169698 − 0.056372I
1.60788 + 1.20779I 0
u = −0.072510 + 0.991759I
a = −0.559105 − 0.563435I
b = 1.205640 − 0.484119I
6.47296 − 7.82720I 0
u = −0.072510 − 0.991759I
a = −0.559105 + 0.563435I
b = 1.205640 + 0.484119I
6.47296 + 7.82720I 0
u = −0.993352 + 0.197972I
a = 2.56889 + 0.55840I
b = −1.30419 + 0.69007I
0.61248 − 4.81440I 0
u = −0.993352 − 0.197972I
a = 2.56889 − 0.55840I
b = −1.30419 − 0.69007I
0.61248 + 4.81440I 0
u = 0.902874 + 0.463441I
a = 1.336050 − 0.193210I
b = −0.871684 − 0.901749I
−0.08463 + 5.13600I 0
u = 0.902874 − 0.463441I
a = 1.336050 + 0.193210I
b = −0.871684 + 0.901749I
−0.08463 − 5.13600I 0
u = −0.955013 + 0.229039I
a = −2.93997 − 0.42458I
b = 1.50313 − 0.49893I
3.79930 − 8.84455I 0
u = −0.955013 − 0.229039I
a = −2.93997 + 0.42458I
b = 1.50313 + 0.49893I
3.79930 + 8.84455I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.173656 + 0.965528I
a = 0.467423 + 0.277205I
b = −1.156730 + 0.326183I
1.90577 − 4.13490I 0
u = −0.173656 − 0.965528I
a = 0.467423 − 0.277205I
b = −1.156730 − 0.326183I
1.90577 + 4.13490I 0
u = 0.363651 + 0.909552I
a = 0.282299 − 0.406949I
b = −0.623074 − 0.340925I
−1.77610 − 2.50851I 0
u = 0.363651 − 0.909552I
a = 0.282299 + 0.406949I
b = −0.623074 + 0.340925I
−1.77610 + 2.50851I 0
u = −0.133671 + 0.967135I
a = 0.363269 + 0.968622I
b = −0.060760 + 1.024230I
−0.48025 + 8.06330I 0
u = −0.133671 − 0.967135I
a = 0.363269 − 0.968622I
b = −0.060760 − 1.024230I
−0.48025 − 8.06330I 0
u = −0.923789 + 0.443969I
a = 0.26507 + 1.48143I
b = −0.951484 − 0.034762I
4.76381 + 0.13098I 0
u = −0.923789 − 0.443969I
a = 0.26507 − 1.48143I
b = −0.951484 + 0.034762I
4.76381 − 0.13098I 0
u = 0.794847 + 0.656611I
a = 0.210662 + 0.974229I
b = −0.875222 + 0.010488I
6.86027 + 2.36778I 0
u = 0.794847 − 0.656611I
a = 0.210662 − 0.974229I
b = −0.875222 − 0.010488I
6.86027 − 2.36778I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.990904 + 0.328079I
a = 0.276707 + 0.562545I
b = −0.696982 + 0.658755I
−2.70689 + 1.93033I 0
u = 0.990904 − 0.328079I
a = 0.276707 − 0.562545I
b = −0.696982 − 0.658755I
−2.70689 − 1.93033I 0
u = 0.955110 + 0.432923I
a = −0.730781 − 0.042302I
b = 0.519570 + 0.834793I
0.31187 + 3.75114I 0
u = 0.955110 − 0.432923I
a = −0.730781 + 0.042302I
b = 0.519570 − 0.834793I
0.31187 − 3.75114I 0
u = 1.023370 + 0.258291I
a = −0.437416 − 1.185920I
b = 0.685995 − 0.525139I
1.01774 + 6.80120I 0
u = 1.023370 − 0.258291I
a = −0.437416 + 1.185920I
b = 0.685995 + 0.525139I
1.01774 − 6.80120I 0
u = 0.836063 + 0.420493I
a = −1.70373 + 0.81945I
b = 0.969989 + 0.648626I
1.31743 + 5.01058I 0
u = 0.836063 − 0.420493I
a = −1.70373 − 0.81945I
b = 0.969989 − 0.648626I
1.31743 − 5.01058I 0
u = 0.633559 + 0.685378I
a = −0.527296 − 0.412378I
b = −0.933157 + 0.296491I
−3.10634 − 1.77812I 0
u = 0.633559 − 0.685378I
a = −0.527296 + 0.412378I
b = −0.933157 − 0.296491I
−3.10634 + 1.77812I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.048950 + 0.218293I
a = 1.050050 + 0.088161I
b = −0.710613 + 1.195320I
−1.32350 − 3.70585I 0
u = −1.048950 − 0.218293I
a = 1.050050 − 0.088161I
b = −0.710613 − 1.195320I
−1.32350 + 3.70585I 0
u = −0.926103 + 0.043767I
a = −2.15843 + 4.41436I
b = −0.854807 + 0.525279I
3.09316 − 2.11983I 0
u = −0.926103 − 0.043767I
a = −2.15843 − 4.41436I
b = −0.854807 − 0.525279I
3.09316 + 2.11983I 0
u = −1.066240 + 0.148110I
a = −3.43481 − 1.07592I
b = 1.010390 − 0.473750I
3.77843 − 2.44545I 0
u = −1.066240 − 0.148110I
a = −3.43481 + 1.07592I
b = 1.010390 + 0.473750I
3.77843 + 2.44545I 0
u = 0.944602 + 0.520467I
a = 0.167943 + 1.200010I
b = 0.965227 + 0.370418I
1.82846 + 10.45490I 0
u = 0.944602 − 0.520467I
a = 0.167943 − 1.200010I
b = 0.965227 − 0.370418I
1.82846 − 10.45490I 0
u = 0.946178 + 0.536677I
a = 0.370509 − 0.948938I
b = −0.880008 − 0.511022I
−2.15295 + 6.49551I 0
u = 0.946178 − 0.536677I
a = 0.370509 + 0.948938I
b = −0.880008 + 0.511022I
−2.15295 − 6.49551I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.662436 + 0.623903I
a = 1.028290 + 0.834059I
b = 1.059350 − 0.145601I
0.96205 − 5.94168I 0
u = 0.662436 − 0.623903I
a = 1.028290 − 0.834059I
b = 1.059350 + 0.145601I
0.96205 + 5.94168I 0
u = −1.087020 + 0.168140I
a = 0.436478 + 0.788002I
b = −0.183843 + 0.032853I
3.59860 + 0.07650I 0
u = −1.087020 − 0.168140I
a = 0.436478 − 0.788002I
b = −0.183843 − 0.032853I
3.59860 − 0.07650I 0
u = −1.049320 + 0.371160I
a = −0.222543 − 0.140301I
b = 0.202947 − 0.964642I
−0.000052 + 0.961895I 0
u = −1.049320 − 0.371160I
a = −0.222543 + 0.140301I
b = 0.202947 + 0.964642I
−0.000052 − 0.961895I 0
u = −0.875918 + 0.103730I
a = 2.03283 − 1.31093I
b = 0.799114 + 0.511328I
3.04543 + 1.62804I 0
u = −0.875918 − 0.103730I
a = 2.03283 + 1.31093I
b = 0.799114 − 0.511328I
3.04543 − 1.62804I 0
u = −0.841656 + 0.044934I
a = 0.16926 + 1.84266I
b = −0.38662 − 1.39931I
−2.50794 + 2.48803I 0
u = −0.841656 − 0.044934I
a = 0.16926 − 1.84266I
b = −0.38662 + 1.39931I
−2.50794 − 2.48803I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.796866 + 0.244137I
a = −1.061210 + 0.068995I
b = 1.257450 + 0.612779I
3.30258 + 6.67390I 0
u = −0.796866 − 0.244137I
a = −1.061210 − 0.068995I
b = 1.257450 − 0.612779I
3.30258 − 6.67390I 0
u = 0.814659 + 0.159634I
a = −0.871559 + 0.272351I
b = 0.807308 − 0.821539I
0.94128 − 1.98249I 0
u = 0.814659 − 0.159634I
a = −0.871559 − 0.272351I
b = 0.807308 + 0.821539I
0.94128 + 1.98249I 0
u = 0.252024 + 1.147930I
a = −0.038822 − 0.459122I
b = 1.39368 − 0.48426I
3.97747 + 2.64873I 0
u = 0.252024 − 1.147930I
a = −0.038822 + 0.459122I
b = 1.39368 + 0.48426I
3.97747 − 2.64873I 0
u = −1.114150 + 0.402874I
a = 2.58183 + 1.28478I
b = −1.226860 + 0.255437I
9.37549 − 4.01193I 0
u = −1.114150 − 0.402874I
a = 2.58183 − 1.28478I
b = −1.226860 − 0.255437I
9.37549 + 4.01193I 0
u = −0.791974 + 0.157432I
a = 0.265101 + 0.320836I
b = −1.030410 − 0.730490I
−0.11674 + 3.08623I 0
u = −0.791974 − 0.157432I
a = 0.265101 − 0.320836I
b = −1.030410 + 0.730490I
−0.11674 − 3.08623I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.014317 + 0.799111I
a = −0.676822 + 0.294373I
b = 1.241560 − 0.201321I
4.16113 − 3.92910I 0
u = 0.014317 − 0.799111I
a = −0.676822 − 0.294373I
b = 1.241560 + 0.201321I
4.16113 + 3.92910I 0
u = −1.097850 + 0.496437I
a = −0.808536 − 0.037056I
b = −0.169521 − 0.579602I
6.15852 − 1.21053I 0
u = −1.097850 − 0.496437I
a = −0.808536 + 0.037056I
b = −0.169521 + 0.579602I
6.15852 + 1.21053I 0
u = 0.033762 + 0.791489I
a = −0.79759 − 1.72609I
b = −0.117292 − 0.771044I
−5.45941 + 1.36823I 0
u = 0.033762 − 0.791489I
a = −0.79759 + 1.72609I
b = −0.117292 + 0.771044I
−5.45941 − 1.36823I 0
u = 0.785570 + 0.051564I
a = −4.81959 − 0.73771I
b = 0.828167 − 0.031471I
−0.30806 − 5.16477I 0
u = 0.785570 − 0.051564I
a = −4.81959 + 0.73771I
b = 0.828167 + 0.031471I
−0.30806 + 5.16477I 0
u = −1.184560 + 0.266383I
a = −2.57917 − 0.56752I
b = 1.106790 − 0.256566I
4.24337 − 3.13114I 0
u = −1.184560 − 0.266383I
a = −2.57917 + 0.56752I
b = 1.106790 + 0.256566I
4.24337 + 3.13114I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.275379 + 1.183100I
a = 0.367775 − 0.409936I
b = −1.31774 − 0.54177I
3.41290 + 13.66070I 0
u = −0.275379 − 1.183100I
a = 0.367775 + 0.409936I
b = −1.31774 + 0.54177I
3.41290 − 13.66070I 0
u = 0.784212
a = 4.93069
b = −0.828307
−4.42162 0
u = 1.194880 + 0.268287I
a = −0.356072 − 0.444064I
b = 0.014716 + 1.171310I
1.95698 + 3.36078I 0
u = 1.194880 − 0.268287I
a = −0.356072 + 0.444064I
b = 0.014716 − 1.171310I
1.95698 − 3.36078I 0
u = 0.750525 + 0.971488I
a = −0.423895 + 0.819516I
b = 0.889804 + 0.129233I
−1.87142 + 1.91362I 0
u = 0.750525 − 0.971488I
a = −0.423895 − 0.819516I
b = 0.889804 − 0.129233I
−1.87142 − 1.91362I 0
u = −0.249738 + 0.717625I
a = 1.70201 + 0.75465I
b = −0.143646 + 0.490394I
−2.54043 − 4.81653I 0
u = −0.249738 − 0.717625I
a = 1.70201 − 0.75465I
b = −0.143646 − 0.490394I
−2.54043 + 4.81653I 0
u = 1.057840 + 0.659438I
a = 1.49849 − 1.64923I
b = −1.069830 − 0.095667I
7.74010 + 2.88014I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.057840 − 0.659438I
a = 1.49849 + 1.64923I
b = −1.069830 + 0.095667I
7.74010 − 2.88014I 0
u = −0.691215 + 0.294815I
a = 0.289608 − 1.087610I
b = 0.819546 − 0.317304I
1.38946 − 1.66923I 0
u = −0.691215 − 0.294815I
a = 0.289608 + 1.087610I
b = 0.819546 + 0.317304I
1.38946 + 1.66923I 0
u = −0.086248 + 0.741503I
a = −0.246964 + 0.667509I
b = 0.141184 + 0.757421I
3.30597 − 3.17657I 0
u = −0.086248 − 0.741503I
a = −0.246964 − 0.667509I
b = 0.141184 − 0.757421I
3.30597 + 3.17657I 0
u = 1.051730 + 0.682378I
a = −0.200801 + 0.021955I
b = 0.629989 − 0.128704I
−0.72570 + 4.16457I 0
u = 1.051730 − 0.682378I
a = −0.200801 − 0.021955I
b = 0.629989 + 0.128704I
−0.72570 − 4.16457I 0
u = 0.542256 + 1.134990I
a = −0.888463 − 0.217508I
b = 0.928594 − 0.125798I
−1.79231 + 0.58528I 0
u = 0.542256 − 1.134990I
a = −0.888463 + 0.217508I
b = 0.928594 + 0.125798I
−1.79231 − 0.58528I 0
u = 0.538354 + 0.507318I
a = −0.187718 − 0.615248I
b = −0.505655 + 0.830666I
−1.07550 − 1.11618I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.538354 − 0.507318I
a = −0.187718 + 0.615248I
b = −0.505655 − 0.830666I
−1.07550 + 1.11618I 0
u = 0.141501 + 1.253470I
a = 0.924660 + 0.167727I
b = −0.925758 + 0.178230I
−1.23918 − 4.98850I 0
u = 0.141501 − 1.253470I
a = 0.924660 − 0.167727I
b = −0.925758 − 0.178230I
−1.23918 + 4.98850I 0
u = 1.227100 + 0.388147I
a = 0.386210 + 0.443945I
b = 0.142871 − 1.021830I
7.19910 + 7.20219I 0
u = 1.227100 − 0.388147I
a = 0.386210 − 0.443945I
b = 0.142871 + 1.021830I
7.19910 − 7.20219I 0
u = 1.283860 + 0.197190I
a = 1.85782 − 0.24238I
b = −1.39271 + 0.39227I
12.15770 + 2.16342I 0
u = 1.283860 − 0.197190I
a = 1.85782 + 0.24238I
b = −1.39271 − 0.39227I
12.15770 − 2.16342I 0
u = 1.163390 + 0.588438I
a = 0.094949 − 0.291251I
b = −0.427811 + 0.447608I
0.72346 + 7.97520I 0
u = 1.163390 − 0.588438I
a = 0.094949 + 0.291251I
b = −0.427811 − 0.447608I
0.72346 − 7.97520I 0
u = 1.218890 + 0.469664I
a = −2.09340 + 0.77780I
b = 1.45635 + 0.24580I
7.68884 + 8.51436I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.218890 − 0.469664I
a = −2.09340 − 0.77780I
b = 1.45635 − 0.24580I
7.68884 − 8.51436I 0
u = 0.488312 + 0.487819I
a = 0.549771 + 0.405455I
b = 0.070979 − 0.755869I
−0.976204 + 0.110519I 0
u = 0.488312 − 0.487819I
a = 0.549771 − 0.405455I
b = 0.070979 + 0.755869I
−0.976204 − 0.110519I 0
u = −1.225560 + 0.463896I
a = −1.67421 − 1.18222I
b = 1.246410 − 0.082879I
7.75605 − 0.60215I 0
u = −1.225560 − 0.463896I
a = −1.67421 + 1.18222I
b = 1.246410 + 0.082879I
7.75605 + 0.60215I 0
u = 1.237590 + 0.437420I
a = 2.01148 − 0.66167I
b = −1.46536 − 0.39893I
6.37169 + 8.20229I 0
u = 1.237590 − 0.437420I
a = 2.01148 + 0.66167I
b = −1.46536 + 0.39893I
6.37169 − 8.20229I 0
u = −0.067862 + 0.681199I
a = 0.176085 − 0.260940I
b = −1.176730 + 0.387839I
2.58142 − 4.00230I 0
u = −0.067862 − 0.681199I
a = 0.176085 + 0.260940I
b = −1.176730 − 0.387839I
2.58142 + 4.00230I 0
u = −0.940533 + 0.941896I
a = −0.277371 − 0.435324I
b = −0.988739 − 0.802148I
6.24717 − 0.29908I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.940533 − 0.941896I
a = −0.277371 + 0.435324I
b = −0.988739 + 0.802148I
6.24717 + 0.29908I 0
u = −0.283208 + 1.306100I
a = 0.390236 + 0.305867I
b = −1.294480 + 0.218177I
1.63786 − 4.30834I 0
u = −0.283208 − 1.306100I
a = 0.390236 − 0.305867I
b = −1.294480 − 0.218177I
1.63786 + 4.30834I 0
u = −0.392797 + 1.286680I
a = −0.267809 + 0.366326I
b = 1.34240 + 0.55580I
−0.76603 + 6.89558I 0
u = −0.392797 − 1.286680I
a = −0.267809 − 0.366326I
b = 1.34240 − 0.55580I
−0.76603 − 6.89558I 0
u = −0.327204 + 0.555531I
a = 0.636996 − 1.229940I
b = −1.111360 − 0.326258I
7.00072 + 0.30811I 0
u = −0.327204 − 0.555531I
a = 0.636996 + 1.229940I
b = −1.111360 + 0.326258I
7.00072 − 0.30811I 0
u = 1.376410 + 0.069310I
a = −1.71327 + 0.08014I
b = 1.43509 − 0.41398I
6.96615 − 2.50132I 0
u = 1.376410 − 0.069310I
a = −1.71327 − 0.08014I
b = 1.43509 + 0.41398I
6.96615 + 2.50132I 0
u = −1.269100 + 0.552397I
a = −0.523171 + 0.253472I
b = −0.194441 − 1.243000I
3.00122 − 13.54100I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.269100 − 0.552397I
a = −0.523171 − 0.253472I
b = −0.194441 + 1.243000I
3.00122 + 13.54100I 0
u = 1.308780 + 0.465341I
a = 1.83742 − 0.78805I
b = −1.34417 − 0.51184I
6.33671 + 9.08273I 0
u = 1.308780 − 0.465341I
a = 1.83742 + 0.78805I
b = −1.34417 + 0.51184I
6.33671 − 9.08273I 0
u = 1.306810 + 0.475630I
a = −1.89328 + 0.92128I
b = 1.286200 + 0.577959I
10.7154 + 12.9263I 0
u = 1.306810 − 0.475630I
a = −1.89328 − 0.92128I
b = 1.286200 − 0.577959I
10.7154 − 12.9263I 0
u = −1.352590 + 0.377037I
a = −1.48051 − 0.51240I
b = 1.59871 + 0.29351I
9.28418 − 7.57796I 0
u = −1.352590 − 0.377037I
a = −1.48051 + 0.51240I
b = 1.59871 − 0.29351I
9.28418 + 7.57796I 0
u = 1.36189 + 0.38376I
a = 0.327869 + 0.177645I
b = 0.309449 − 1.229080I
4.22039 − 3.23688I 0
u = 1.36189 − 0.38376I
a = 0.327869 − 0.177645I
b = 0.309449 + 1.229080I
4.22039 + 3.23688I 0
u = −1.40996 + 0.21702I
a = 1.87955 + 0.05582I
b = −1.003870 + 0.065130I
5.05593 − 0.34565I 0
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.40996 − 0.21702I
a = 1.87955 − 0.05582I
b = −1.003870 − 0.065130I
5.05593 + 0.34565I 0
u = −1.32026 + 0.58348I
a = 0.429953 − 0.159621I
b = 0.314367 + 1.291950I
−1.06924 − 7.01836I 0
u = −1.32026 − 0.58348I
a = 0.429953 + 0.159621I
b = 0.314367 − 1.291950I
−1.06924 + 7.01836I 0
u = 1.27599 + 0.67937I
a = −1.58847 + 0.91676I
b = 1.059540 + 0.231478I
0.81247 + 6.07654I 0
u = 1.27599 − 0.67937I
a = −1.58847 − 0.91676I
b = 1.059540 − 0.231478I
0.81247 − 6.07654I 0
u = 1.33885 + 0.58073I
a = 1.76165 − 0.76077I
b = −1.076530 − 0.340845I
2.70539 + 11.25400I 0
u = 1.33885 − 0.58073I
a = 1.76165 + 0.76077I
b = −1.076530 + 0.340845I
2.70539 − 11.25400I 0
u = −1.30757 + 0.65669I
a = 1.58455 + 1.05180I
b = −1.35553 + 0.64430I
6.7085 − 20.1549I 0
u = −1.30757 − 0.65669I
a = 1.58455 − 1.05180I
b = −1.35553 − 0.64430I
6.7085 + 20.1549I 0
u = −1.37349 + 0.51903I
a = −1.311600 − 0.480971I
b = 1.259940 + 0.325657I
10.47850 + 2.18356I 0
18
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.37349 − 0.51903I
a = −1.311600 + 0.480971I
b = 1.259940 − 0.325657I
10.47850 − 2.18356I 0
u = −1.37819 + 0.50716I
a = 1.44237 + 0.63470I
b = −1.221120 + 0.079457I
5.55494 − 1.82210I 0
u = −1.37819 − 0.50716I
a = 1.44237 − 0.63470I
b = −1.221120 − 0.079457I
5.55494 + 1.82210I 0
u = −0.22057 + 1.45474I
a = −0.127654 − 1.048490I
b = 0.15390 − 1.45082I
−5.07831 + 0.54261I 0
u = −0.22057 − 1.45474I
a = −0.127654 + 1.048490I
b = 0.15390 + 1.45082I
−5.07831 − 0.54261I 0
u = −1.42771 + 0.44318I
a = 1.40615 + 0.46494I
b = −1.42123 − 0.11571I
6.18667 − 2.09350I 0
u = −1.42771 − 0.44318I
a = 1.40615 − 0.46494I
b = −1.42123 + 0.11571I
6.18667 + 2.09350I 0
u = −1.32376 + 0.69830I
a = −1.44255 − 1.02867I
b = 1.34377 − 0.66711I
2.36737 − 13.86820I 0
u = −1.32376 − 0.69830I
a = −1.44255 + 1.02867I
b = 1.34377 + 0.66711I
2.36737 + 13.86820I 0
u = −1.24712 + 0.84386I
a = 1.08987 + 1.19487I
b = −1.24793 + 0.76502I
7.40283 − 6.91839I 0
19
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.24712 − 0.84386I
a = 1.08987 − 1.19487I
b = −1.24793 − 0.76502I
7.40283 + 6.91839I 0
u = 1.41867 + 0.51798I
a = −1.46126 + 0.74622I
b = 1.45701 + 0.63495I
8.02706 + 3.82363I 0
u = 1.41867 − 0.51798I
a = −1.46126 − 0.74622I
b = 1.45701 − 0.63495I
8.02706 − 3.82363I 0
u = 1.51830 + 0.17387I
a = 1.51539 − 0.19146I
b = −1.42599 + 0.37167I
10.05230 − 8.50067I 0
u = 1.51830 − 0.17387I
a = 1.51539 + 0.19146I
b = −1.42599 − 0.37167I
10.05230 + 8.50067I 0
u = 0.168197 + 0.431680I
a = 0.875183 − 0.334368I
b = −0.201001 − 0.533588I
−0.915726 − 0.687361I 0
u = 0.168197 − 0.431680I
a = 0.875183 + 0.334368I
b = −0.201001 + 0.533588I
−0.915726 + 0.687361I 0
u = −0.343804 + 0.090921I
a = 0.94819 − 1.32544I
b = 0.941762 − 0.385718I
1.45487 − 1.58972I −2.00000 − 2.74536I
u = −0.343804 − 0.090921I
a = 0.94819 + 1.32544I
b = 0.941762 + 0.385718I
1.45487 + 1.58972I −2.00000 + 2.74536I
u = 0.280701 + 0.097255I
a = −0.97322 + 1.50126I
b = 0.690430 − 0.592461I
0.71411 − 2.06955I −3.17684 + 3.40929I
20
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.280701 − 0.097255I
a = −0.97322 − 1.50126I
b = 0.690430 + 0.592461I
0.71411 + 2.06955I −3.17684 − 3.40929I
21
II.
I
u
2
= h−1.30×10
27
u
42
+5.59×10
27
u
41
+· · ·+5.18×10
24
b−1.73×10
27
, −5.05×
10
27
u
42
+2.25×10
28
u
41
+· · ·+5.18×10
24
a−8.77×10
27
, u
43
−5u
42
+· · ·+9u−1i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
3
=
976.290u
42
− 4339.64u
41
+ ··· − 12563.5u + 1694.59
251.254u
42
− 1079.06u
41
+ ··· − 2631.38u + 334.926
a
9
=
1
−u
2
a
7
=
690.201u
42
− 3223.52u
41
+ ··· − 11234.8u + 1666.48
1063.08u
42
− 4649.80u
41
+ ··· − 12523.5u + 1690.74
a
2
=
1946.84u
42
− 8537.33u
41
+ ··· − 22943.6u + 3065.48
−1757.20u
42
+ 7761.50u
41
+ ··· + 21933.8u − 3006.41
a
10
=
−381.102u
42
+ 1690.92u
41
+ ··· + 4259.64u − 572.007
−571.317u
42
+ 2488.17u
41
+ ··· + 6264.83u − 823.904
a
6
=
−417.569u
42
+ 1685.77u
41
+ ··· + 2645.87u − 251.748
1435.87u
42
− 6302.74u
41
+ ··· − 17081.9u + 2320.31
a
1
=
−3563.78u
42
+ 15715.5u
41
+ ··· + 43934.5u − 5998.17
3561.78u
42
− 15706.5u
41
+ ··· − 43899.5u + 5987.17
a
11
=
−u
u
a
5
=
−196.119u
42
+ 664.940u
41
+ ··· − 606.796u + 222.805
1214.42u
42
− 5281.91u
41
+ ··· − 13829.2u + 1845.76
a
4
=
−5669.06u
42
+ 25125.2u
41
+ ··· + 72661.1u − 10052.1
2770.71u
42
− 12334.0u
41
+ ··· − 36228.9u + 5041.16
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −
39731743503703556572717582173
5176114318849511714698289
u
42
+
176212969798214825520092916434
5176114318849511714698289
u
41
+ ··· +
528850699858818575212985731870
5176114318849511714698289
u −
73356324113368931490575946909
5176114318849511714698289
22
(iv) u-Polynomials at the component
23
Crossings u-Polynomials at each crossing
c
1
u
43
− 7u
42
+ ··· + 10u − 1
c
2
u
43
− 10u
41
+ ··· − 4u − 1
c
3
u
43
− 2u
41
+ ··· + 4u − 1
c
4
u
43
+ 7u
42
+ ··· + 10u + 1
c
5
u
43
+ 4u
42
+ ··· − 2u − 1
c
6
u
43
+ 13u
42
+ ··· − 7u + 1
c
7
u
43
− 10u
41
+ ··· − 4u + 1
c
8
u
43
− 5u
42
+ ··· + 9u − 1
c
9
u
43
+ 8u
42
+ ··· − 6u + 1
c
10
u
43
− 4u
42
+ ··· − 2u + 1
c
11
u
43
+ 5u
42
+ ··· + 9u + 1
c
12
u
43
+ u
42
+ ··· − 4u + 1
24
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
43
+ 27y
42
+ ··· − 18y −1
c
2
, c
7
y
43
− 20y
42
+ ··· + 32y −1
c
3
y
43
− 4y
42
+ ··· − 30y −1
c
5
, c
10
y
43
− 4y
42
+ ··· − 16y −1
c
6
y
43
+ 15y
42
+ ··· + 43y −1
c
8
, c
11
y
43
− 15y
42
+ ··· + 27y −1
c
9
y
43
− 24y
42
+ ··· − 10y −1
c
12
y
43
+ 3y
42
+ ··· − 112y −1
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.018036 + 1.005850I
a = −0.865587 − 0.572541I
b = 0.703586 − 0.069280I
−1.55180 − 4.33690I 0
u = 0.018036 − 1.005850I
a = −0.865587 + 0.572541I
b = 0.703586 + 0.069280I
−1.55180 + 4.33690I 0
u = −0.967617 + 0.119302I
a = −0.548131 + 0.149417I
b = 0.514103 − 0.815458I
1.61658 − 2.29495I 4.61864 + 2.93274I
u = −0.967617 − 0.119302I
a = −0.548131 − 0.149417I
b = 0.514103 + 0.815458I
1.61658 + 2.29495I 4.61864 − 2.93274I
u = −1.020430 + 0.293177I
a = 0.354342 − 0.854539I
b = 0.693053 + 0.548437I
3.33625 + 1.27021I 0
u = −1.020430 − 0.293177I
a = 0.354342 + 0.854539I
b = 0.693053 − 0.548437I
3.33625 − 1.27021I 0
u = 0.967778 + 0.438117I
a = 1.164550 − 0.206473I
b = −0.756698 − 0.918811I
−1.36209 + 4.95710I 0
u = 0.967778 − 0.438117I
a = 1.164550 + 0.206473I
b = −0.756698 + 0.918811I
−1.36209 − 4.95710I 0
u = −0.783383 + 0.470302I
a = −0.204859 − 1.011670I
b = −0.858982 + 0.087111I
7.75302 − 2.17548I 9.56983 + 2.53983I
u = −0.783383 − 0.470302I
a = −0.204859 + 1.011670I
b = −0.858982 − 0.087111I
7.75302 + 2.17548I 9.56983 − 2.53983I
27
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.898121 + 0.033912I
a = −2.34558 + 3.49066I
b = −0.856628 + 0.518902I
3.05821 − 2.10222I −47.3234 − 50.9827I
u = −0.898121 − 0.033912I
a = −2.34558 − 3.49066I
b = −0.856628 − 0.518902I
3.05821 + 2.10222I −47.3234 + 50.9827I
u = 0.675502 + 0.929007I
a = 0.479383 − 0.025545I
b = −0.762703 + 0.350472I
−2.75030 + 0.36331I 0
u = 0.675502 − 0.929007I
a = 0.479383 + 0.025545I
b = −0.762703 − 0.350472I
−2.75030 − 0.36331I 0
u = −0.770362 + 0.201775I
a = 0.277954 − 0.244414I
b = 0.767500 − 0.404339I
1.87369 − 2.08777I 5.28642 + 7.07196I
u = −0.770362 − 0.201775I
a = 0.277954 + 0.244414I
b = 0.767500 + 0.404339I
1.87369 + 2.08777I 5.28642 − 7.07196I
u = 1.070160 + 0.552468I
a = 0.738078 − 0.337807I
b = −0.415913 − 0.621412I
−1.36368 + 5.06561I 0
u = 1.070160 − 0.552468I
a = 0.738078 + 0.337807I
b = −0.415913 + 0.621412I
−1.36368 − 5.06561I 0
u = −1.112120 + 0.484369I
a = 1.95574 + 1.34639I
b = −1.139400 + 0.010371I
8.99490 − 1.86585I 0
u = −1.112120 − 0.484369I
a = 1.95574 − 1.34639I
b = −1.139400 − 0.010371I
8.99490 + 1.86585I 0
28
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.115720 + 0.510206I
a = −0.258006 + 1.066870I
b = 0.490522 + 0.130491I
1.55198 + 8.82913I 0
u = 1.115720 − 0.510206I
a = −0.258006 − 1.066870I
b = 0.490522 − 0.130491I
1.55198 − 8.82913I 0
u = 0.739430 + 0.158190I
a = 0.16306 − 1.69152I
b = −0.457958 + 1.315660I
−2.87881 − 2.25807I −11.65616 − 2.03401I
u = 0.739430 − 0.158190I
a = 0.16306 + 1.69152I
b = −0.457958 − 1.315660I
−2.87881 + 2.25807I −11.65616 + 2.03401I
u = 0.858125 + 0.903741I
a = −0.167400 + 0.587060I
b = −1.001110 + 0.631626I
5.77802 + 0.61199I 0
u = 0.858125 − 0.903741I
a = −0.167400 − 0.587060I
b = −1.001110 − 0.631626I
5.77802 − 0.61199I 0
u = −0.179188 + 1.256430I
a = −0.373285 − 0.110297I
b = 1.260690 − 0.185553I
1.14741 − 4.73512I 0
u = −0.179188 − 1.256430I
a = −0.373285 + 0.110297I
b = 1.260690 + 0.185553I
1.14741 + 4.73512I 0
u = 1.266850 + 0.376482I
a = −2.00362 + 0.42464I
b = 1.48678 + 0.29090I
6.43713 + 9.46442I 0
u = 1.266850 − 0.376482I
a = −2.00362 − 0.42464I
b = 1.48678 − 0.29090I
6.43713 − 9.46442I 0
29
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.256468 + 0.623041I
a = 0.63391 − 1.37530I
b = −1.103980 − 0.529718I
−1.27564 + 4.14509I −4.10122 − 5.10933I
u = 0.256468 − 0.623041I
a = 0.63391 + 1.37530I
b = −1.103980 + 0.529718I
−1.27564 − 4.14509I −4.10122 + 5.10933I
u = 0.122323 + 1.392290I
a = −0.100494 + 1.092750I
b = 0.004112 + 1.384690I
−5.15083 − 0.32395I 0
u = 0.122323 − 1.392290I
a = −0.100494 − 1.092750I
b = 0.004112 − 1.384690I
−5.15083 + 0.32395I 0
u = 1.247040 + 0.664885I
a = 1.49607 − 1.14603I
b = −1.34820 − 0.52760I
7.37503 + 5.86162I 0
u = 1.247040 − 0.664885I
a = 1.49607 + 1.14603I
b = −1.34820 + 0.52760I
7.37503 − 5.86162I 0
u = 0.581841 + 0.029202I
a = −2.60703 + 1.14090I
b = 1.301390 + 0.502509I
2.92133 + 7.68807I 0.83209 − 7.89037I
u = 0.581841 − 0.029202I
a = −2.60703 − 1.14090I
b = 1.301390 − 0.502509I
2.92133 − 7.68807I 0.83209 + 7.89037I
u = 0.522271 + 0.225026I
a = 4.03290 − 0.02892I
b = 0.537672 + 0.044936I
−0.91454 − 5.09998I −7.09887 + 2.47578I
u = 0.522271 − 0.225026I
a = 4.03290 + 0.02892I
b = 0.537672 − 0.044936I
−0.91454 + 5.09998I −7.09887 − 2.47578I
30
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.42156 + 0.41997I
a = −1.56789 − 0.55679I
b = 1.201850 − 0.125310I
5.72726 − 1.48386I 0
u = −1.42156 − 0.41997I
a = −1.56789 + 0.55679I
b = 1.201850 + 0.125310I
5.72726 + 1.48386I 0
u = 0.422479
a = −5.50822
b = −0.519385
−4.97926 −11.8730
31
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
43
− 7u
42
+ ··· + 10u − 1)(u
161
− 6u
160
+ ··· − 60405u + 2525)
c
2
(u
43
− 10u
41
+ ··· − 4u − 1)(u
161
+ u
160
+ ··· + 62875u + 20690)
c
3
(u
43
− 2u
41
+ ··· + 4u − 1)(u
161
+ u
160
+ ··· + 6424407u − 1081037)
c
4
(u
43
+ 7u
42
+ ··· + 10u + 1)(u
161
− 6u
160
+ ··· − 60405u + 2525)
c
5
(u
43
+ 4u
42
+ ··· − 2u − 1)(u
161
− 5u
160
+ ··· − 34377u − 24287)
c
6
(u
43
+ 13u
42
+ ··· − 7u + 1)
· (u
161
+ 4u
160
+ ··· + 209706558586u + 17633051719)
c
7
(u
43
− 10u
41
+ ··· − 4u + 1)(u
161
+ u
160
+ ··· + 62875u + 20690)
c
8
(u
43
− 5u
42
+ ··· + 9u − 1)(u
161
− 43u
159
+ ··· + 23192u + 22751)
c
9
(u
43
+ 8u
42
+ ··· − 6u + 1)
· (u
161
+ 5u
160
+ ··· + 5900566245u − 806431049)
c
10
(u
43
− 4u
42
+ ··· − 2u + 1)(u
161
− 5u
160
+ ··· − 34377u − 24287)
c
11
(u
43
+ 5u
42
+ ··· + 9u + 1)(u
161
− 43u
159
+ ··· + 23192u + 22751)
c
12
(u
43
+ u
42
+ ··· − 4u + 1)
· (u
161
+ 2u
160
+ ··· + 297854463u − 20528044)
32
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y
43
+ 27y
42
+ ··· − 18y −1)
· (y
161
+ 104y
160
+ ··· − 44901925y −6375625)
c
2
, c
7
(y
43
− 20y
42
+ ··· + 32y −1)
· (y
161
− 95y
160
+ ··· + 56848574785y −428076100)
c
3
(y
43
− 4y
42
+ ··· − 30y −1)
· (y
161
+ 13y
160
+ ··· − 81817610068445y −1168640995369)
c
5
, c
10
(y
43
− 4y
42
+ ··· − 16y −1)
· (y
161
− 71y
160
+ ··· − 8324930855y −589858369)
c
6
(y
43
+ 15y
42
+ ··· + 43y −1)
· (y
161
− 44y
160
+ ··· + 4.98 × 10
21
y −3.11 × 10
20
)
c
8
, c
11
(y
43
− 15y
42
+ ··· + 27y −1)
· (y
161
− 86y
160
+ ··· + 30379536528y −517608001)
c
9
(y
43
− 24y
42
+ ··· − 10y −1)
· (y
161
+ 29y
160
+ ··· − 3.95 × 10
19
y −6.50 × 10
17
)
c
12
(y
43
+ 3y
42
+ ··· − 112y −1)
· (y
161
+ 36y
160
+ ··· − 32685559262828287y −421400590465936)
33
