12a
0844
(K12a
0844
)
A knot diagram
1
Linearized knot diagam
4 5 9 2 11 10 12 3 7 1 8 6
Solving Sequence
7,12 3,8
9 4 10 6 1 11 5 2
c
7
c
8
c
3
c
9
c
6
c
12
c
11
c
5
c
2
c
1
, c
4
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h7.31418 × 10
587
u
129
+ 1.42814 × 10
588
u
128
+ ··· + 1.49614 × 10
590
b + 2.54492 × 10
590
,
1.23726 × 10
589
u
129
+ 1.96379 × 10
589
u
128
+ ··· + 3.44111 × 10
591
a + 6.43358 × 10
592
,
u
130
+ 2u
129
+ ··· + 4232u − 4232i
I
u
2
= h6u
19
+ 3u
18
+ ··· + b + 13, −2u
19
+ u
18
+ ··· + a + 2, u
20
+ 10u
18
+ ··· + 3u + 1i
I
u
3
= h4u
8
+ u
6
+ 4u
5
+ 2u
4
+ 5u
3
− u
2
+ 7b − u + 3,
− 4u
8
+ 7u
7
− 15u
6
+ 10u
5
− 16u
4
+ 9u
3
− 13u
2
+ 7a + u − 3, u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1i
* 3 irreducible components of dim
C
= 0, with total 159 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
= h7.31 × 10
587
u
129
+ 1.43 × 10
588
u
128
+ · · · + 1.50 × 10
590
b + 2.54 ×
10
590
, 1.24 × 10
589
u
129
+ 1.96 × 10
589
u
128
+ · · · + 3.44 × 10
591
a + 6.43 ×
10
592
, u
130
+ 2u
129
+ · · · + 4232u − 4232i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
3
=
−0.00359551u
129
− 0.00570685u
128
+ ··· + 66.2600u − 18.6962
−0.00488871u
129
− 0.00954553u
128
+ ··· + 62.4474u − 1.70099
a
8
=
1
−u
2
a
9
=
0.000787540u
129
+ 0.00474240u
128
+ ··· + 31.4660u − 17.0069
0.00284266u
129
+ 0.00595084u
128
+ ··· + 0.0159490u − 1.74523
a
4
=
−0.00565176u
129
− 0.00744750u
128
+ ··· + 59.4935u − 12.5896
−0.000553067u
129
− 0.000371621u
128
+ ··· − 1.21646u + 13.1924
a
10
=
−0.00205512u
129
− 0.00120844u
128
+ ··· + 31.4501u − 15.2617
0.00284266u
129
+ 0.00595084u
128
+ ··· + 0.0159490u − 1.74523
a
6
=
0.00535830u
129
+ 0.0124217u
128
+ ··· − 21.2452u − 4.11354
0.00265702u
129
+ 0.00676648u
128
+ ··· − 32.0678u + 7.80220
a
1
=
0.00169895u
129
+ 0.00692070u
128
+ ··· + 8.87400u − 21.6666
−0.00256817u
129
− 0.00715091u
128
+ ··· + 18.3812u + 9.46098
a
11
=
−u
u
3
+ u
a
5
=
0.00831517u
129
+ 0.0204715u
128
+ ··· − 31.2624u − 9.85356
0.00238806u
129
+ 0.00614912u
128
+ ··· − 25.5243u + 4.50253
a
2
=
0.00237606u
129
+ 0.00902992u
128
+ ··· + 13.9603u − 35.8227
−0.00167924u
129
− 0.00170185u
128
+ ··· + 43.7419u − 26.9090
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.0137665u
129
+ 0.0271520u
128
+ ··· − 158.707u − 13.2029
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
4
u
130
− 14u
129
+ ··· + 35u − 49
c
3
, c
8
u
130
+ u
129
+ ··· − 60928u + 25088
c
5
u
130
+ u
129
+ ··· − 15153510u − 893777
c
6
, c
9
u
130
− 3u
129
+ ··· + 4534u − 71
c
7
, c
11
u
130
− 2u
129
+ ··· − 4232u − 4232
c
10
u
130
+ 18u
129
+ ··· − 8409u + 1079
c
12
u
130
+ 10u
129
+ ··· − 27u − 9
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
y
130
− 122y
129
+ ··· − 5929y + 2401
c
3
, c
8
y
130
− 69y
129
+ ··· − 11984437248y + 629407744
c
5
y
130
+ 13y
129
+ ··· + 20581982318772y + 798837325729
c
6
, c
9
y
130
+ 81y
129
+ ··· − 16239788y + 5041
c
7
, c
11
y
130
+ 86y
129
+ ··· + 519774240y + 17909824
c
10
y
130
− 26y
129
+ ··· − 102045441y + 1164241
c
12
y
130
− 6y
129
+ ··· + 2151y + 81
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.207403 + 0.977252I
a = −2.13432 + 1.44213I
b = −1.29939 + 0.83567I
−5.39383 − 0.67456I 0
u = −0.207403 − 0.977252I
a = −2.13432 − 1.44213I
b = −1.29939 − 0.83567I
−5.39383 + 0.67456I 0
u = 0.870481 + 0.482230I
a = 0.136852 + 0.115419I
b = −1.231720 − 0.550774I
−7.57713 − 2.60992I 0
u = 0.870481 − 0.482230I
a = 0.136852 − 0.115419I
b = −1.231720 + 0.550774I
−7.57713 + 2.60992I 0
u = −0.207306 + 0.968285I
a = 0.552789 − 1.258600I
b = 0.851569 − 0.056422I
−1.20363 − 3.45389I 0
u = −0.207306 − 0.968285I
a = 0.552789 + 1.258600I
b = 0.851569 + 0.056422I
−1.20363 + 3.45389I 0
u = 0.045460 + 0.986316I
a = 0.031164 + 1.041930I
b = 0.420336 − 0.550031I
−4.06225 + 0.19731I 0
u = 0.045460 − 0.986316I
a = 0.031164 − 1.041930I
b = 0.420336 + 0.550031I
−4.06225 − 0.19731I 0
u = 0.355513 + 0.900991I
a = 0.542870 − 0.433386I
b = −0.353756 + 0.490944I
3.12587 + 4.37430I 0
u = 0.355513 − 0.900991I
a = 0.542870 + 0.433386I
b = −0.353756 − 0.490944I
3.12587 − 4.37430I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.052715 + 1.033720I
a = −0.288223 + 0.352604I
b = 0.134358 + 0.922567I
−1.62444 − 1.37557I 0
u = 0.052715 − 1.033720I
a = −0.288223 − 0.352604I
b = 0.134358 − 0.922567I
−1.62444 + 1.37557I 0
u = −0.959148 + 0.078977I
a = 1.057860 − 0.294072I
b = −1.78753 + 0.77001I
1.39635 + 3.23709I 0
u = −0.959148 − 0.078977I
a = 1.057860 + 0.294072I
b = −1.78753 − 0.77001I
1.39635 − 3.23709I 0
u = −0.140669 + 1.028800I
a = −2.12933 − 0.04020I
b = −0.645111 − 0.983937I
−2.45297 − 3.70553I 0
u = −0.140669 − 1.028800I
a = −2.12933 + 0.04020I
b = −0.645111 + 0.983937I
−2.45297 + 3.70553I 0
u = 0.523222 + 0.802656I
a = 2.49879 + 4.67344I
b = 4.65998 + 0.06588I
−0.42547 + 2.53758I 0
u = 0.523222 − 0.802656I
a = 2.49879 − 4.67344I
b = 4.65998 − 0.06588I
−0.42547 − 2.53758I 0
u = 0.309325 + 0.872790I
a = −2.03045 − 1.07152I
b = −0.499650 − 0.281157I
−8.13468 + 7.32693I 0
u = 0.309325 − 0.872790I
a = −2.03045 + 1.07152I
b = −0.499650 + 0.281157I
−8.13468 − 7.32693I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.009940 + 0.380275I
a = −0.749459 − 0.478953I
b = 0.790741 + 0.283640I
5.03065 − 2.91197I 0
u = 1.009940 − 0.380275I
a = −0.749459 + 0.478953I
b = 0.790741 − 0.283640I
5.03065 + 2.91197I 0
u = 0.556506 + 0.727484I
a = 0.297857 − 0.675164I
b = −0.389439 + 0.331391I
3.62319 − 0.56871I 0
u = 0.556506 − 0.727484I
a = 0.297857 + 0.675164I
b = −0.389439 − 0.331391I
3.62319 + 0.56871I 0
u = −0.541139 + 0.952132I
a = 0.147250 + 0.918610I
b = −0.178510 + 0.299329I
1.88655 − 1.65023I 0
u = −0.541139 − 0.952132I
a = 0.147250 − 0.918610I
b = −0.178510 − 0.299329I
1.88655 + 1.65023I 0
u = −0.290943 + 1.071750I
a = 0.359265 + 0.121506I
b = 0.669032 − 0.344390I
−1.67452 − 3.13091I 0
u = −0.290943 − 1.071750I
a = 0.359265 − 0.121506I
b = 0.669032 + 0.344390I
−1.67452 + 3.13091I 0
u = 0.296795 + 1.075410I
a = −2.91041 − 0.47249I
b = −2.50052 + 0.95290I
1.16491 + 5.17903I 0
u = 0.296795 − 1.075410I
a = −2.91041 + 0.47249I
b = −2.50052 − 0.95290I
1.16491 − 5.17903I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.750310 + 0.427363I
a = 0.068052 + 0.564511I
b = 0.697843 + 0.441677I
−1.53269 − 6.33362I 0
u = −0.750310 − 0.427363I
a = 0.068052 − 0.564511I
b = 0.697843 − 0.441677I
−1.53269 + 6.33362I 0
u = 0.016383 + 0.861091I
a = 2.51607 + 0.55432I
b = 0.481827 + 0.674512I
−1.42660 + 2.83814I 0
u = 0.016383 − 0.861091I
a = 2.51607 − 0.55432I
b = 0.481827 − 0.674512I
−1.42660 − 2.83814I 0
u = −0.666858 + 0.939090I
a = −0.214878 + 0.171005I
b = −0.409765 + 0.257143I
0.38694 − 2.59415I 0
u = −0.666858 − 0.939090I
a = −0.214878 − 0.171005I
b = −0.409765 − 0.257143I
0.38694 + 2.59415I 0
u = 1.172230 + 0.057028I
a = 0.688708 + 1.000700I
b = −1.222240 − 0.451724I
0.47369 − 5.68832I 0
u = 1.172230 − 0.057028I
a = 0.688708 − 1.000700I
b = −1.222240 + 0.451724I
0.47369 + 5.68832I 0
u = −0.646682 + 0.508924I
a = −0.607220 + 0.928340I
b = −1.117150 − 0.578316I
0.75859 − 3.24972I 0
u = −0.646682 − 0.508924I
a = −0.607220 − 0.928340I
b = −1.117150 + 0.578316I
0.75859 + 3.24972I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.306526 + 0.755382I
a = −0.326678 − 0.381872I
b = −0.881679 − 0.168136I
−4.78653 − 1.59407I 0
u = −0.306526 − 0.755382I
a = −0.326678 + 0.381872I
b = −0.881679 + 0.168136I
−4.78653 + 1.59407I 0
u = 0.788563 + 0.204340I
a = 0.534729 + 0.656471I
b = 1.170900 − 0.040856I
−6.57708 − 7.15153I 0
u = 0.788563 − 0.204340I
a = 0.534729 − 0.656471I
b = 1.170900 + 0.040856I
−6.57708 + 7.15153I 0
u = 0.067187 + 0.805703I
a = 3.65880 − 1.74203I
b = 1.37055 − 1.72420I
0.47179 + 1.76850I 0
u = 0.067187 − 0.805703I
a = 3.65880 + 1.74203I
b = 1.37055 + 1.72420I
0.47179 − 1.76850I 0
u = 0.071155 + 1.217340I
a = 1.093210 + 0.732066I
b = 0.782484 − 0.448149I
−4.64544 + 1.87466I 0
u = 0.071155 − 1.217340I
a = 1.093210 − 0.732066I
b = 0.782484 + 0.448149I
−4.64544 − 1.87466I 0
u = −0.220315 + 1.200090I
a = −1.96529 − 0.03345I
b = −1.327500 − 0.345449I
−0.99196 − 4.71706I 0
u = −0.220315 − 1.200090I
a = −1.96529 + 0.03345I
b = −1.327500 + 0.345449I
−0.99196 + 4.71706I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.813144 + 0.914977I
a = −0.183806 − 0.173935I
b = 0.358860 + 0.079720I
1.52846 + 7.35278I 0
u = 0.813144 − 0.914977I
a = −0.183806 + 0.173935I
b = 0.358860 − 0.079720I
1.52846 − 7.35278I 0
u = −0.759942
a = 0.944622
b = 0.523634
−2.56238 −1.14050
u = 0.010388 + 1.247310I
a = 1.65859 − 0.36936I
b = 1.80529 − 1.08613I
−4.78176 + 1.13220I 0
u = 0.010388 − 1.247310I
a = 1.65859 + 0.36936I
b = 1.80529 + 1.08613I
−4.78176 − 1.13220I 0
u = −0.721881 + 1.025220I
a = −0.015244 − 0.728804I
b = −0.0448569 − 0.0263149I
−3.08113 + 0.81431I 0
u = −0.721881 − 1.025220I
a = −0.015244 + 0.728804I
b = −0.0448569 + 0.0263149I
−3.08113 − 0.81431I 0
u = 0.309343 + 1.237480I
a = 1.89400 + 0.83926I
b = 2.28057 − 0.00970I
−5.66140 + 2.87702I 0
u = 0.309343 − 1.237480I
a = 1.89400 − 0.83926I
b = 2.28057 + 0.00970I
−5.66140 − 2.87702I 0
u = 0.265868 + 1.248280I
a = 2.24133 + 0.22130I
b = 2.26417 − 0.63628I
−4.41116 + 8.47604I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.265868 − 1.248280I
a = 2.24133 − 0.22130I
b = 2.26417 + 0.63628I
−4.41116 − 8.47604I 0
u = −1.274750 + 0.149399I
a = −0.629685 − 0.215734I
b = 2.13894 − 0.43531I
3.35673 + 7.72625I 0
u = −1.274750 − 0.149399I
a = −0.629685 + 0.215734I
b = 2.13894 + 0.43531I
3.35673 − 7.72625I 0
u = 0.439475 + 1.206410I
a = −1.61258 − 1.11031I
b = −2.07853 − 0.22200I
−4.00841 + 7.89339I 0
u = 0.439475 − 1.206410I
a = −1.61258 + 1.11031I
b = −2.07853 + 0.22200I
−4.00841 − 7.89339I 0
u = 0.596326 + 1.151090I
a = −0.118605 + 0.317783I
b = 0.077208 − 0.472785I
2.56590 + 8.61563I 0
u = 0.596326 − 1.151090I
a = −0.118605 − 0.317783I
b = 0.077208 + 0.472785I
2.56590 − 8.61563I 0
u = −0.385070 + 1.240120I
a = −0.444387 − 0.153876I
b = −0.861742 + 0.514358I
−6.87980 − 5.59995I 0
u = −0.385070 − 1.240120I
a = −0.444387 + 0.153876I
b = −0.861742 − 0.514358I
−6.87980 + 5.59995I 0
u = 1.050980 + 0.804516I
a = 0.321098 + 0.405591I
b = −0.288639 − 0.548025I
1.95452 − 0.73217I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.050980 − 0.804516I
a = 0.321098 − 0.405591I
b = −0.288639 + 0.548025I
1.95452 + 0.73217I 0
u = 0.297996 + 0.596894I
a = −0.54817 + 1.51250I
b = 1.05023 + 1.30928I
−0.131132 + 1.178100I −1.130855 − 0.687358I
u = 0.297996 − 0.596894I
a = −0.54817 − 1.51250I
b = 1.05023 − 1.30928I
−0.131132 − 1.178100I −1.130855 + 0.687358I
u = 0.537857 + 1.232880I
a = 1.39056 + 1.09863I
b = 1.89489 + 0.20264I
−9.7181 + 12.1998I 0
u = 0.537857 − 1.232880I
a = 1.39056 − 1.09863I
b = 1.89489 − 0.20264I
−9.7181 − 12.1998I 0
u = −0.447868 + 0.446054I
a = −0.179300 − 0.673744I
b = −0.583300 − 0.734247I
3.14662 − 2.57828I 3.70857 + 3.51309I
u = −0.447868 − 0.446054I
a = −0.179300 + 0.673744I
b = −0.583300 + 0.734247I
3.14662 + 2.57828I 3.70857 − 3.51309I
u = −0.619320 + 0.098741I
a = 0.64193 − 1.63021I
b = 0.111781 − 0.294175I
−2.97910 − 1.77302I −5.16591 + 3.41651I
u = −0.619320 − 0.098741I
a = 0.64193 + 1.63021I
b = 0.111781 + 0.294175I
−2.97910 + 1.77302I −5.16591 − 3.41651I
u = −0.246238 + 1.353050I
a = 1.73313 − 0.06279I
b = 1.43771 + 0.98489I
−12.25150 − 6.55987I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.246238 − 1.353050I
a = 1.73313 + 0.06279I
b = 1.43771 − 0.98489I
−12.25150 + 6.55987I 0
u = −0.329709 + 1.346510I
a = 1.69685 − 0.19298I
b = 1.74640 + 0.33574I
−6.71754 − 9.96409I 0
u = −0.329709 − 1.346510I
a = 1.69685 + 0.19298I
b = 1.74640 − 0.33574I
−6.71754 + 9.96409I 0
u = 0.615817 + 1.246730I
a = −1.61173 − 0.21772I
b = −1.13458 + 2.31191I
−2.89630 + 0.85409I 0
u = 0.615817 − 1.246730I
a = −1.61173 + 0.21772I
b = −1.13458 − 2.31191I
−2.89630 − 0.85409I 0
u = 0.599539 + 0.031257I
a = −0.134478 − 1.293650I
b = −1.000210 + 0.123339I
−0.63869 − 3.79000I −3.28691 + 6.67650I
u = 0.599539 − 0.031257I
a = −0.134478 + 1.293650I
b = −1.000210 − 0.123339I
−0.63869 + 3.79000I −3.28691 − 6.67650I
u = −0.526568 + 1.297290I
a = −1.84964 + 0.47697I
b = −1.97035 − 1.49638I
−2.38605 − 8.61930I 0
u = −0.526568 − 1.297290I
a = −1.84964 − 0.47697I
b = −1.97035 + 1.49638I
−2.38605 + 8.61930I 0
u = −1.281120 + 0.570799I
a = −0.023425 − 0.158691I
b = 1.51149 − 0.04289I
−5.37237 − 2.41269I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.281120 − 0.570799I
a = −0.023425 + 0.158691I
b = 1.51149 + 0.04289I
−5.37237 + 2.41269I 0
u = 0.527514 + 0.253658I
a = −0.797736 − 0.405039I
b = 0.920390 + 0.384396I
−1.385150 − 0.269456I −6.74039 + 0.20784I
u = 0.527514 − 0.253658I
a = −0.797736 + 0.405039I
b = 0.920390 − 0.384396I
−1.385150 + 0.269456I −6.74039 − 0.20784I
u = −0.40824 + 1.38572I
a = −1.26301 + 0.82009I
b = −2.21976 + 0.37082I
−2.96488 − 2.11966I 0
u = −0.40824 − 1.38572I
a = −1.26301 − 0.82009I
b = −2.21976 − 0.37082I
−2.96488 + 2.11966I 0
u = −0.73422 + 1.25225I
a = 0.343833 − 0.161391I
b = 0.770766 − 0.683082I
−4.71583 − 3.31857I 0
u = −0.73422 − 1.25225I
a = 0.343833 + 0.161391I
b = 0.770766 + 0.683082I
−4.71583 + 3.31857I 0
u = −0.152962 + 0.522678I
a = 0.052409 + 1.203110I
b = 0.483156 + 1.065560I
−0.169062 + 1.292200I −1.82953 + 1.55175I
u = −0.152962 − 0.522678I
a = 0.052409 − 1.203110I
b = 0.483156 − 1.065560I
−0.169062 − 1.292200I −1.82953 − 1.55175I
u = 0.57273 + 1.34557I
a = 0.043546 − 0.393122I
b = −0.046931 + 0.648616I
−3.56917 + 11.75340I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.57273 − 1.34557I
a = 0.043546 + 0.393122I
b = −0.046931 − 0.648616I
−3.56917 − 11.75340I 0
u = 0.21861 + 1.45249I
a = −1.55078 − 0.43115I
b = −1.99666 + 0.19901I
−13.95940 + 1.16927I 0
u = 0.21861 − 1.45249I
a = −1.55078 + 0.43115I
b = −1.99666 − 0.19901I
−13.95940 − 1.16927I 0
u = −1.46184 + 0.14608I
a = 0.403978 + 0.285131I
b = −2.20414 + 0.22320I
−2.13477 + 11.78310I 0
u = −1.46184 − 0.14608I
a = 0.403978 − 0.285131I
b = −2.20414 − 0.22320I
−2.13477 − 11.78310I 0
u = 0.83100 + 1.21302I
a = 1.51363 + 0.78715I
b = 1.65210 − 2.11701I
−2.38061 + 5.66774I 0
u = 0.83100 − 1.21302I
a = 1.51363 − 0.78715I
b = 1.65210 + 2.11701I
−2.38061 − 5.66774I 0
u = −0.63063 + 1.35580I
a = 1.67755 − 0.66075I
b = 2.30117 + 1.31250I
−0.4865 − 14.3089I 0
u = −0.63063 − 1.35580I
a = 1.67755 + 0.66075I
b = 2.30117 − 1.31250I
−0.4865 + 14.3089I 0
u = −0.496424 + 0.067253I
a = −0.814201 + 0.734293I
b = −0.176043 + 0.243992I
1.35306 − 0.46632I 5.92593 + 0.52773I
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.496424 − 0.067253I
a = −0.814201 − 0.734293I
b = −0.176043 − 0.243992I
1.35306 + 0.46632I 5.92593 − 0.52773I
u = 0.27528 + 1.53209I
a = −0.326210 − 0.865487I
b = −1.56706 − 2.53672I
−5.23503 + 0.36072I 0
u = 0.27528 − 1.53209I
a = −0.326210 + 0.865487I
b = −1.56706 + 2.53672I
−5.23503 − 0.36072I 0
u = 0.49715 + 1.47956I
a = 1.149740 + 0.115198I
b = 0.98122 − 1.87029I
−9.92744 − 2.15814I 0
u = 0.49715 − 1.47956I
a = 1.149740 − 0.115198I
b = 0.98122 + 1.87029I
−9.92744 + 2.15814I 0
u = 0.114561 + 0.422618I
a = 0.04206 − 1.51538I
b = −0.990252 − 0.965223I
3.19605 − 2.75030I 3.06253 − 0.82065I
u = 0.114561 − 0.422618I
a = 0.04206 + 1.51538I
b = −0.990252 + 0.965223I
3.19605 + 2.75030I 3.06253 + 0.82065I
u = −0.68600 + 1.42782I
a = −1.50251 + 0.67794I
b = −2.37448 − 1.09688I
−6.2538 − 19.1081I 0
u = −0.68600 − 1.42782I
a = −1.50251 − 0.67794I
b = −2.37448 + 1.09688I
−6.2538 + 19.1081I 0
u = 0.004684 + 0.408362I
a = 0.302795 + 1.341510I
b = 1.054940 + 0.893360I
−1.18088 − 6.70646I −4.08150 − 4.57276I
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.004684 − 0.408362I
a = 0.302795 − 1.341510I
b = 1.054940 − 0.893360I
−1.18088 + 6.70646I −4.08150 + 4.57276I
u = −0.66292 + 1.46328I
a = 0.992938 − 0.740700I
b = 1.88185 + 0.17259I
−8.72321 − 5.31358I 0
u = −0.66292 − 1.46328I
a = 0.992938 + 0.740700I
b = 1.88185 − 0.17259I
−8.72321 + 5.31358I 0
u = 0.97842 + 1.30276I
a = −1.17137 − 0.82987I
b = −1.62857 + 1.80768I
−8.70050 + 9.40227I 0
u = 0.97842 − 1.30276I
a = −1.17137 + 0.82987I
b = −1.62857 − 1.80768I
−8.70050 − 9.40227I 0
u = 0.311547
a = −2.15815
b = 0.727000
−1.15012 −10.3680
u = −0.17602 + 1.70075I
a = 1.44258 − 0.11537I
b = 3.36651 + 0.80561I
−3.37537 + 1.30670I 0
u = −0.17602 − 1.70075I
a = 1.44258 + 0.11537I
b = 3.36651 − 0.80561I
−3.37537 − 1.30670I 0
u = −0.28889 + 1.89577I
a = −1.058340 + 0.167814I
b = −2.66309 − 1.00421I
−9.16387 + 4.05703I 0
u = −0.28889 − 1.89577I
a = −1.058340 − 0.167814I
b = −2.66309 + 1.00421I
−9.16387 − 4.05703I 0
17
II.
I
u
2
= h6u
19
+3u
18
+· · ·+b+13, −2u
19
+u
18
+· · ·+a+2, u
20
+10u
18
+· · ·+3u+1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
3
=
2u
19
− u
18
+ ··· + u − 2
−6u
19
− 3u
18
+ ··· − 38u − 13
a
8
=
1
−u
2
a
9
=
u
19
− u
18
+ ··· + 7u + 2
u
19
+ 10u
17
+ ··· + 12u + 3
a
4
=
11u
19
+ 107u
17
+ ··· + 55u + 13
6u
19
− 9u
18
+ ··· − 7u − 14
a
10
=
−u
18
− 9u
16
+ ··· − 5u − 1
u
19
+ 10u
17
+ ··· + 12u + 3
a
6
=
u
19
+ 9u
17
+ ··· + u − 1
−3u
19
+ u
18
+ ··· − 14u + 3
a
1
=
2u
18
+ 19u
16
+ ··· + 10u + 3
−u
19
− u
18
+ ··· − 15u − 4
a
11
=
−u
u
3
+ u
a
5
=
u
19
+ 9u
17
+ ··· + 5u
2
+ u
−3u
19
+ u
18
+ ··· − 14u + 2
a
2
=
−5u
19
+ 2u
18
+ ··· − 17u − 4
−9u
19
+ 5u
18
+ ··· − 16u + 7
(ii) Obstruction class = 1
(iii) Cusp Shapes
= 45u
19
−24u
18
+ 450u
17
−100u
16
+ 1858u
15
+ 99u
14
+ 4342u
13
+ 1215u
12
+ 6677u
11
+
2779u
10
+7228u
9
+3175u
8
+5442u
7
+2099u
6
+2685u
5
+752u
4
+842u
3
+115u
2
+129u−17
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
u
20
+ 4u
19
+ ··· − 5u + 1
c
3
u
20
− 6u
18
+ ··· − 3u + 1
c
4
u
20
− 4u
19
+ ··· + 5u + 1
c
5
u
20
− 3u
19
+ ··· + 5u
3
+ 1
c
6
u
20
− 3u
19
+ ··· + 10u
2
+ 1
c
7
u
20
+ 10u
18
+ ··· + 3u + 1
c
8
u
20
− 6u
18
+ ··· + 3u + 1
c
9
u
20
+ 3u
19
+ ··· + 10u
2
+ 1
c
10
u
20
− 4u
18
+ ··· + 5u + 1
c
11
u
20
+ 10u
18
+ ··· − 3u + 1
c
12
u
20
− 5u
17
+ ··· + 3u + 1
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
y
20
− 20y
19
+ ··· − y + 1
c
3
, c
8
y
20
− 12y
19
+ ··· − 9y + 1
c
5
y
20
− 5y
19
+ ··· + 6y
2
+ 1
c
6
, c
9
y
20
+ 15y
19
+ ··· + 20y + 1
c
7
, c
11
y
20
+ 20y
19
+ ··· + 15y + 1
c
10
y
20
− 8y
19
+ ··· − 5y + 1
c
12
y
20
+ 6y
18
+ ··· − 5y + 1
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.329203 + 1.094160I
a = 2.14620 + 0.32651I
b = 1.22206 − 0.80890I
−1.53784 + 4.32358I −6.41394 − 6.31106I
u = 0.329203 − 1.094160I
a = 2.14620 − 0.32651I
b = 1.22206 + 0.80890I
−1.53784 − 4.32358I −6.41394 + 6.31106I
u = −0.457051 + 0.680670I
a = −1.47560 − 0.75165I
b = −0.443653 − 0.900964I
1.16478 − 2.39395I 1.54588 + 3.97709I
u = −0.457051 − 0.680670I
a = −1.47560 + 0.75165I
b = −0.443653 + 0.900964I
1.16478 + 2.39395I 1.54588 − 3.97709I
u = −0.574386 + 0.534332I
a = 0.980231 + 0.358160I
b = 0.826345 + 0.385404I
−3.84276 − 1.04802I −4.21027 + 1.93550I
u = −0.574386 − 0.534332I
a = 0.980231 − 0.358160I
b = 0.826345 − 0.385404I
−3.84276 + 1.04802I −4.21027 − 1.93550I
u = 0.371455 + 0.685308I
a = 4.10221 − 5.25780I
b = −1.58450 − 4.16112I
−0.30091 + 3.00431I 3.31212 + 12.78342I
u = 0.371455 − 0.685308I
a = 4.10221 + 5.25780I
b = −1.58450 + 4.16112I
−0.30091 − 3.00431I 3.31212 − 12.78342I
u = −0.163354 + 1.255280I
a = −0.694587 + 0.456216I
b = −0.682571 − 0.835680I
−4.47222 − 1.54255I −4.86257 − 3.43959I
u = −0.163354 − 1.255280I
a = −0.694587 − 0.456216I
b = −0.682571 + 0.835680I
−4.47222 + 1.54255I −4.86257 + 3.43959I
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.211407 + 0.674773I
a = 0.153610 − 0.354903I
b = 0.814387 + 0.670029I
2.73376 − 3.43447I −1.29601 + 4.99499I
u = −0.211407 − 0.674773I
a = 0.153610 + 0.354903I
b = 0.814387 − 0.670029I
2.73376 + 3.43447I −1.29601 − 4.99499I
u = 0.591819 + 1.167140I
a = −1.65614 − 0.78307I
b = −1.37496 + 0.87177I
−8.01378 + 8.58732I −5.27072 − 5.92160I
u = 0.591819 − 1.167140I
a = −1.65614 + 0.78307I
b = −1.37496 − 0.87177I
−8.01378 − 8.58732I −5.27072 + 5.92160I
u = −0.220491 + 0.519453I
a = −0.534636 − 0.251741I
b = −1.016770 − 0.802496I
−1.21585 − 7.07402I −6.1302 + 16.7431I
u = −0.220491 − 0.519453I
a = −0.534636 + 0.251741I
b = −1.016770 + 0.802496I
−1.21585 + 7.07402I −6.1302 − 16.7431I
u = 0.09236 + 1.53921I
a = −1.64944 + 0.37517I
b = −3.01493 + 1.40555I
−3.72172 − 0.64910I −8.97978 − 3.00915I
u = 0.09236 − 1.53921I
a = −1.64944 − 0.37517I
b = −3.01493 − 1.40555I
−3.72172 + 0.64910I −8.97978 + 3.00915I
u = 0.24185 + 1.69545I
a = 1.128150 − 0.070054I
b = 1.75459 − 1.46603I
−10.40230 − 2.81932I −12.19450 + 3.27289I
u = 0.24185 − 1.69545I
a = 1.128150 + 0.070054I
b = 1.75459 + 1.46603I
−10.40230 + 2.81932I −12.19450 − 3.27289I
22
III. I
u
3
= h4u
8
+ u
6
+ 4u
5
+ 2u
4
+ 5u
3
− u
2
+ 7b − u + 3, −4u
8
+ 7u
7
+ · · · +
7a − 3, u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
3
=
4
7
u
8
− u
7
+ ··· −
1
7
u +
3
7
−
4
7
u
8
−
1
7
u
6
+ ··· +
1
7
u −
3
7
a
8
=
1
−u
2
a
9
=
1
−u
2
a
4
=
4
7
u
8
− u
7
+ ··· −
1
7
u +
3
7
−
4
7
u
8
−
1
7
u
6
+ ··· +
1
7
u −
3
7
a
10
=
u
2
+ 1
−u
2
a
6
=
u
4
+ u
2
+ 1
−u
4
a
1
=
u
8
+ u
6
+ u
4
− 1
−u
8
+ u
7
− u
6
+ 2u
5
− u
4
+ 2u
3
+ 2u + 1
a
11
=
−u
u
3
+ u
a
5
=
−u
8
− u
6
− u
4
+ 1
u
8
− u
7
+ u
6
− 2u
5
+ u
4
− 2u
3
− 2u − 1
a
2
=
11
7
u
8
− u
7
+ ··· −
1
7
u −
4
7
−
11
7
u
8
+ u
7
+ ··· +
15
7
u +
4
7
(ii) Obstruction class = 1
(iii) Cusp Shapes =
5
49
u
8
−
16
7
u
7
+
241
49
u
6
−
184
49
u
5
+
307
49
u
4
−
342
49
u
3
+
361
49
u
2
+
95
49
u +
30
49
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
9
c
3
, c
8
u
9
c
4
(u + 1)
9
c
5
, c
10
u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1
c
6
u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1
c
7
u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1
c
9
u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1
c
11
u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1
c
12
u
9
− 5u
8
+ 12u
7
− 15u
6
+ 9u
5
+ u
4
− 4u
3
+ 2u
2
+ u − 1
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y − 1)
9
c
3
, c
8
y
9
c
5
, c
10
y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y − 1
c
6
, c
9
y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y − 1
c
7
, c
11
y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y − 1
c
12
y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y − 1
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.140343 + 0.966856I
a = −0.903964 + 0.094390I
b = −0.852846 − 0.158943I
−3.42837 − 2.09337I −6.52230 + 4.24226I
u = −0.140343 − 0.966856I
a = −0.903964 − 0.094390I
b = −0.852846 + 0.158943I
−3.42837 + 2.09337I −6.52230 − 4.24226I
u = −0.628449 + 0.875112I
a = 0.53175 + 1.59553I
b = −1.55776 + 1.17662I
−1.02799 − 2.45442I −8.21790 + 4.39771I
u = −0.628449 − 0.875112I
a = 0.53175 − 1.59553I
b = −1.55776 − 1.17662I
−1.02799 + 2.45442I −8.21790 − 4.39771I
u = 0.796005 + 0.733148I
a = −0.476406 + 0.294981I
b = 0.390088 + 0.527698I
2.72642 − 1.33617I 0.84367 + 3.27176I
u = 0.796005 − 0.733148I
a = −0.476406 − 0.294981I
b = 0.390088 − 0.527698I
2.72642 + 1.33617I 0.84367 − 3.27176I
u = 0.728966 + 0.986295I
a = 0.352455 − 0.113243I
b = −0.007269 − 0.556797I
1.95319 + 7.08493I 3.61934 − 1.74309I
u = 0.728966 − 0.986295I
a = 0.352455 + 0.113243I
b = −0.007269 + 0.556797I
1.95319 − 7.08493I 3.61934 + 1.74309I
u = −0.512358
a = 1.42091
b = −0.373004
−0.446489 3.16660
26
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
2
((u − 1)
9
)(u
20
+ 4u
19
+ ··· − 5u + 1)(u
130
− 14u
129
+ ··· + 35u − 49)
c
3
u
9
(u
20
− 6u
18
+ ··· − 3u + 1)(u
130
+ u
129
+ ··· − 60928u + 25088)
c
4
((u + 1)
9
)(u
20
− 4u
19
+ ··· + 5u + 1)(u
130
− 14u
129
+ ··· + 35u − 49)
c
5
(u
9
− u
8
+ ··· − u + 1)(u
20
− 3u
19
+ ··· + 5u
3
+ 1)
· (u
130
+ u
129
+ ··· − 15153510u − 893777)
c
6
(u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1)
· (u
20
− 3u
19
+ ··· + 10u
2
+ 1)(u
130
− 3u
129
+ ··· + 4534u − 71)
c
7
(u
9
− u
8
+ ··· + u + 1)(u
20
+ 10u
18
+ ··· + 3u + 1)
· (u
130
− 2u
129
+ ··· − 4232u − 4232)
c
8
u
9
(u
20
− 6u
18
+ ··· + 3u + 1)(u
130
+ u
129
+ ··· − 60928u + 25088)
c
9
(u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
· (u
20
+ 3u
19
+ ··· + 10u
2
+ 1)(u
130
− 3u
129
+ ··· + 4534u − 71)
c
10
(u
9
− u
8
+ ··· − u + 1)(u
20
− 4u
18
+ ··· + 5u + 1)
· (u
130
+ 18u
129
+ ··· − 8409u + 1079)
c
11
(u
9
+ u
8
+ ··· + u − 1)(u
20
+ 10u
18
+ ··· − 3u + 1)
· (u
130
− 2u
129
+ ··· − 4232u − 4232)
c
12
(u
9
− 5u
8
+ 12u
7
− 15u
6
+ 9u
5
+ u
4
− 4u
3
+ 2u
2
+ u − 1)
· (u
20
− 5u
17
+ ··· + 3u + 1)(u
130
+ 10u
129
+ ··· − 27u − 9)
27
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
((y − 1)
9
)(y
20
− 20y
19
+ ··· − y + 1)
· (y
130
− 122y
129
+ ··· − 5929y + 2401)
c
3
, c
8
y
9
(y
20
− 12y
19
+ ··· − 9y + 1)
· (y
130
− 69y
129
+ ··· − 11984437248y + 629407744)
c
5
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y − 1)
· (y
20
− 5y
19
+ ··· + 6y
2
+ 1)
· (y
130
+ 13y
129
+ ··· + 20581982318772y + 798837325729)
c
6
, c
9
(y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y − 1)
· (y
20
+ 15y
19
+ ··· + 20y + 1)
· (y
130
+ 81y
129
+ ··· − 16239788y + 5041)
c
7
, c
11
(y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y − 1)
· (y
20
+ 20y
19
+ ··· + 15y + 1)
· (y
130
+ 86y
129
+ ··· + 519774240y + 17909824)
c
10
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y − 1)
· (y
20
− 8y
19
+ ··· − 5y + 1)
· (y
130
− 26y
129
+ ··· − 102045441y + 1164241)
c
12
(y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y − 1)
· (y
20
+ 6y
18
+ ··· − 5y + 1)(y
130
− 6y
129
+ ··· + 2151y + 81)
28
