12a
0699
(K12a
0699
)
A knot diagram
1
Linearized knot diagam
3 8 6 10 1 9 11 2 12 5 7 4
Solving Sequence
2,8
3 9
1,11
7 6 4 5 10 12
c
2
c
8
c
1
c
7
c
6
c
3
c
5
c
10
c
12
c
4
, c
9
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−7.11942 × 10
639
u
171
− 2.78587 × 10
640
u
170
+ ··· + 7.11957 × 10
639
b − 5.07255 × 10
642
,
− 7.87299 × 10
640
u
171
+ 1.65662 × 10
641
u
170
+ ··· + 1.58766 × 10
642
a + 4.05831 × 10
644
,
u
172
+ 4u
171
+ ··· + 3076u + 892i
I
u
2
= h−1.03311 × 10
27
u
41
+ 2.27460 × 10
27
u
40
+ ··· + 6.16398 × 10
26
b − 1.34436 × 10
27
,
− 1.12761 × 10
27
u
41
+ 5.58166 × 10
27
u
40
+ ··· + 1.23280 × 10
27
a + 2.62673 × 10
28
,
u
42
− 3u
41
+ ··· − 12u + 4i
* 2 irreducible components of dim
C
= 0, with total 214 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−7.12 × 10
639
u
171
− 2.79 × 10
640
u
170
+ · · · + 7.12 × 10
639
b − 5.07 ×
10
642
, −7.87 × 10
640
u
171
+ 1.66 × 10
641
u
170
+ · · · + 1.59 × 10
642
a + 4.06 ×
10
644
, u
172
+ 4u
171
+ · · · + 3076u + 892i
(i) Arc colorings
a
2
=
1
0
a
8
=
0
u
a
3
=
1
−u
2
a
9
=
u
u
a
1
=
u
2
+ 1
−u
4
a
11
=
0.0495885u
171
− 0.104343u
170
+ ··· − 649.335u − 255.615
0.999979u
171
+ 3.91298u
170
+ ··· + 2666.54u + 712.480
a
7
=
0.665404u
171
+ 2.88035u
170
+ ··· + 2516.78u + 747.159
0.126747u
171
+ 1.77211u
170
+ ··· + 3409.29u + 1301.02
a
6
=
0.287095u
171
+ 0.685769u
170
+ ··· − 221.459u − 186.229
−0.251562u
171
− 0.422463u
170
+ ··· + 671.045u + 367.632
a
4
=
0.342578u
171
+ 1.55098u
170
+ ··· + 1632.44u + 505.425
0.337631u
171
+ 1.40966u
170
+ ··· + 1320.67u + 394.445
a
5
=
0.544119u
171
+ 2.29704u
170
+ ··· + 1923.71u + 555.144
−0.235368u
171
+ 0.434597u
170
+ ··· + 2601.45u + 1111.53
a
10
=
−0.0899103u
171
− 0.494492u
170
+ ··· − 786.015u − 270.909
0.825414u
171
+ 3.01234u
170
+ ··· + 1579.13u + 313.228
a
12
=
−0.406398u
171
− 1.22172u
170
+ ··· − 330.601u + 14.3430
−0.116379u
171
− 0.131742u
170
+ ··· + 311.010u + 166.678
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.257423u
171
− 2.68415u
170
+ ··· − 4456.58u − 1644.95
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
172
+ 76u
171
+ ··· + 25122848u + 795664
c
2
, c
8
u
172
+ 4u
171
+ ··· + 3076u + 892
c
3
81(81u
172
+ 2313u
171
+ ··· + 27u + 1)
c
4
, c
10
9(9u
172
− 21u
171
+ ··· + 3804472u + 145372)
c
5
u
172
− 3u
171
+ ··· + 1853937u + 164349
c
6
u
172
− 5u
171
+ ··· − 7246383780u + 366700275
c
7
, c
11
9(9u
172
− 30u
171
+ ··· + 1621697u + 523514)
c
9
u
172
− 13u
171
+ ··· − 15667632934u + 1387956497
c
12
u
172
+ 17u
171
+ ··· + 338848083u + 26871588
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
172
+ 48y
171
+ ··· + 43751823032704y + 633081200896
c
2
, c
8
y
172
+ 76y
171
+ ··· + 25122848y + 795664
c
3
6561(6561y
172
− 327483y
171
+ ··· + 571y + 1)
c
4
, c
10
81(81y
172
− 9927y
171
+ ··· − 4.86749 × 10
12
y + 2.11330 × 10
10
)
c
5
y
172
− 9y
171
+ ··· + 646282891935y + 27010593801
c
6
y
172
− 23y
171
+ ··· − 1.08 × 10
19
y + 1.34 × 10
17
c
7
, c
11
81(81y
172
+ 7650y
171
+ ··· + 6.61151 × 10
12
y + 2.74067 × 10
11
)
c
9
y
172
− 63y
171
+ ··· − 2.69 × 10
19
y + 1.93 × 10
18
c
12
y
172
+ 31y
171
+ ··· + 33369002886734055y + 722082241641744
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.444314 + 0.896690I
a = 1.113900 + 0.174810I
b = 2.66959 − 1.09722I
−4.76658 − 4.24724I 0
u = −0.444314 − 0.896690I
a = 1.113900 − 0.174810I
b = 2.66959 + 1.09722I
−4.76658 + 4.24724I 0
u = −0.677854 + 0.721137I
a = 0.405323 + 0.565729I
b = 0.645666 + 0.622245I
4.17273 − 0.06185I 0
u = −0.677854 − 0.721137I
a = 0.405323 − 0.565729I
b = 0.645666 − 0.622245I
4.17273 + 0.06185I 0
u = −0.957946 + 0.326646I
a = −0.645620 + 0.881778I
b = −0.649863 − 0.453342I
−1.18665 − 3.57370I 0
u = −0.957946 − 0.326646I
a = −0.645620 − 0.881778I
b = −0.649863 + 0.453342I
−1.18665 + 3.57370I 0
u = 0.595294 + 0.786960I
a = 0.773630 − 0.035104I
b = 0.627151 + 0.821745I
0.88993 + 1.85918I 0
u = 0.595294 − 0.786960I
a = 0.773630 + 0.035104I
b = 0.627151 − 0.821745I
0.88993 − 1.85918I 0
u = 0.922311 + 0.350507I
a = 0.138078 + 0.904791I
b = 0.436870 − 0.791878I
1.64081 − 1.77100I 0
u = 0.922311 − 0.350507I
a = 0.138078 − 0.904791I
b = 0.436870 + 0.791878I
1.64081 + 1.77100I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.504799 + 0.880123I
a = 1.57977 − 1.78074I
b = 1.82823 − 1.63741I
−1.62431 + 2.07905I 0
u = 0.504799 − 0.880123I
a = 1.57977 + 1.78074I
b = 1.82823 + 1.63741I
−1.62431 − 2.07905I 0
u = −0.775463 + 0.607818I
a = −0.785572 − 0.443717I
b = −0.666606 + 0.025546I
3.02226 + 3.08004I 0
u = −0.775463 − 0.607818I
a = −0.785572 + 0.443717I
b = −0.666606 − 0.025546I
3.02226 − 3.08004I 0
u = −0.918010 + 0.344848I
a = −0.168441 − 0.974586I
b = −0.088221 + 0.940929I
0.83568 + 5.69605I 0
u = −0.918010 − 0.344848I
a = −0.168441 + 0.974586I
b = −0.088221 − 0.940929I
0.83568 − 5.69605I 0
u = 0.863576 + 0.542838I
a = 0.870045 + 0.274052I
b = 0.565989 − 0.009645I
1.22443 − 1.30449I 0
u = 0.863576 − 0.542838I
a = 0.870045 − 0.274052I
b = 0.565989 + 0.009645I
1.22443 + 1.30449I 0
u = −0.438231 + 0.875440I
a = 0.283520 − 1.028340I
b = −1.046310 − 0.298808I
−4.68377 + 0.63646I 0
u = −0.438231 − 0.875440I
a = 0.283520 + 1.028340I
b = −1.046310 + 0.298808I
−4.68377 − 0.63646I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.335203 + 0.918267I
a = 0.352550 + 0.576852I
b = −0.380013 − 0.337924I
−2.95880 + 2.07571I 0
u = −0.335203 − 0.918267I
a = 0.352550 − 0.576852I
b = −0.380013 + 0.337924I
−2.95880 − 2.07571I 0
u = 0.345935 + 0.964013I
a = −1.032810 − 0.922639I
b = −2.23306 − 0.29354I
−7.39431 + 0.13825I 0
u = 0.345935 − 0.964013I
a = −1.032810 + 0.922639I
b = −2.23306 + 0.29354I
−7.39431 − 0.13825I 0
u = 0.517845 + 0.820411I
a = −0.687604 − 0.880904I
b = −0.611455 + 1.264570I
0.817136 + 1.106290I 0
u = 0.517845 − 0.820411I
a = −0.687604 + 0.880904I
b = −0.611455 − 1.264570I
0.817136 − 1.106290I 0
u = −0.680910 + 0.690973I
a = 0.327286 − 1.001280I
b = −0.674580 + 0.669526I
0.01320 + 2.08002I 0
u = −0.680910 − 0.690973I
a = 0.327286 + 1.001280I
b = −0.674580 − 0.669526I
0.01320 − 2.08002I 0
u = 0.448811 + 0.853822I
a = 0.985866 + 0.278785I
b = 2.51959 + 1.06869I
0.017064 + 1.122660I 0
u = 0.448811 − 0.853822I
a = 0.985866 − 0.278785I
b = 2.51959 − 1.06869I
0.017064 − 1.122660I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.713920 + 0.751808I
a = −0.600950 − 0.769742I
b = 0.826454 − 0.958050I
−2.49145 − 4.60127I 0
u = 0.713920 − 0.751808I
a = −0.600950 + 0.769742I
b = 0.826454 + 0.958050I
−2.49145 + 4.60127I 0
u = 0.526737 + 0.893857I
a = −1.048730 − 0.367243I
b = −3.28141 − 0.07709I
0.56641 + 3.12116I 0
u = 0.526737 − 0.893857I
a = −1.048730 + 0.367243I
b = −3.28141 + 0.07709I
0.56641 − 3.12116I 0
u = −0.141666 + 1.028690I
a = −0.250314 − 0.119199I
b = −0.87760 − 1.18524I
−5.97488 + 0.13240I 0
u = −0.141666 − 1.028690I
a = −0.250314 + 0.119199I
b = −0.87760 + 1.18524I
−5.97488 − 0.13240I 0
u = 0.895020 + 0.528313I
a = −0.182144 − 1.282520I
b = 0.034532 + 0.643268I
−0.37073 − 8.17547I 0
u = 0.895020 − 0.528313I
a = −0.182144 + 1.282520I
b = 0.034532 − 0.643268I
−0.37073 + 8.17547I 0
u = 0.770491 + 0.573420I
a = 1.091530 − 0.128106I
b = 1.059010 + 0.053499I
2.47051 + 2.46378I 0
u = 0.770491 − 0.573420I
a = 1.091530 + 0.128106I
b = 1.059010 − 0.053499I
2.47051 − 2.46378I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.916707 + 0.490817I
a = −0.005551 − 1.190440I
b = −0.252125 + 0.527816I
0.63068 + 3.00510I 0
u = −0.916707 − 0.490817I
a = −0.005551 + 1.190440I
b = −0.252125 − 0.527816I
0.63068 − 3.00510I 0
u = 0.825637 + 0.472579I
a = −1.142920 + 0.377601I
b = −0.928136 + 0.049806I
−0.52169 − 8.45025I 0
u = 0.825637 − 0.472579I
a = −1.142920 − 0.377601I
b = −0.928136 − 0.049806I
−0.52169 + 8.45025I 0
u = 0.066014 + 1.047780I
a = −0.146720 + 0.681990I
b = −0.033766 + 0.628880I
−2.79005 + 2.53157I 0
u = 0.066014 − 1.047780I
a = −0.146720 − 0.681990I
b = −0.033766 − 0.628880I
−2.79005 − 2.53157I 0
u = 0.483322 + 0.932023I
a = 0.258193 + 0.772674I
b = −0.108470 − 0.108813I
−0.31059 + 2.59895I 0
u = 0.483322 − 0.932023I
a = 0.258193 − 0.772674I
b = −0.108470 + 0.108813I
−0.31059 − 2.59895I 0
u = 0.492063 + 0.809699I
a = −0.59461 + 1.53435I
b = −0.606376 + 0.926960I
−1.41878 + 2.03132I 0
u = 0.492063 − 0.809699I
a = −0.59461 − 1.53435I
b = −0.606376 − 0.926960I
−1.41878 − 2.03132I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.494341 + 0.931042I
a = −0.471579 + 0.598238I
b = 0.06205 − 1.89940I
−2.32153 − 7.32120I 0
u = −0.494341 − 0.931042I
a = −0.471579 − 0.598238I
b = 0.06205 + 1.89940I
−2.32153 + 7.32120I 0
u = −0.250076 + 0.907912I
a = 1.45144 − 0.85887I
b = 2.20724 − 0.96331I
−7.40070 + 5.79515I 0
u = −0.250076 − 0.907912I
a = 1.45144 + 0.85887I
b = 2.20724 + 0.96331I
−7.40070 − 5.79515I 0
u = −0.453438 + 0.810747I
a = −0.855395 + 0.376915I
b = −3.97782 + 0.23710I
−1.86220 + 3.43609I 0
u = −0.453438 − 0.810747I
a = −0.855395 − 0.376915I
b = −3.97782 − 0.23710I
−1.86220 − 3.43609I 0
u = −0.500829 + 0.961519I
a = −0.456635 − 0.650896I
b = −0.513687 − 0.947118I
−3.89524 − 5.47159I 0
u = −0.500829 − 0.961519I
a = −0.456635 + 0.650896I
b = −0.513687 + 0.947118I
−3.89524 + 5.47159I 0
u = −0.687457 + 0.852804I
a = −0.640423 + 0.466864I
b = 0.65771 + 1.71387I
2.36278 − 2.64451I 0
u = −0.687457 − 0.852804I
a = −0.640423 − 0.466864I
b = 0.65771 − 1.71387I
2.36278 + 2.64451I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.983258 + 0.491988I
a = −0.030148 + 1.309630I
b = 0.184575 − 0.506908I
−3.9406 + 14.6159I 0
u = −0.983258 − 0.491988I
a = −0.030148 − 1.309630I
b = 0.184575 + 0.506908I
−3.9406 − 14.6159I 0
u = −0.608206 + 0.920459I
a = 0.909484 − 0.146029I
b = 2.83949 − 1.09248I
−0.65442 − 7.07658I 0
u = −0.608206 − 0.920459I
a = 0.909484 + 0.146029I
b = 2.83949 + 1.09248I
−0.65442 + 7.07658I 0
u = 1.043730 + 0.400521I
a = −0.002038 + 1.272240I
b = −0.130457 − 0.265102I
−0.75717 − 5.35150I 0
u = 1.043730 − 0.400521I
a = −0.002038 − 1.272240I
b = −0.130457 + 0.265102I
−0.75717 + 5.35150I 0
u = −0.443758 + 1.029070I
a = −0.812766 + 0.575345I
b = −2.10372 + 0.01711I
−4.04121 − 1.06499I 0
u = −0.443758 − 1.029070I
a = −0.812766 − 0.575345I
b = −2.10372 − 0.01711I
−4.04121 + 1.06499I 0
u = 0.550328 + 0.976342I
a = 1.220270 − 0.061283I
b = 2.46456 + 0.96409I
−6.08593 + 5.33871I 0
u = 0.550328 − 0.976342I
a = 1.220270 + 0.061283I
b = 2.46456 − 0.96409I
−6.08593 − 5.33871I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.534046 + 0.687237I
a = 0.488493 + 1.308980I
b = −0.825614 + 0.285354I
−5.15017 − 0.92884I 0
u = 0.534046 − 0.687237I
a = 0.488493 − 1.308980I
b = −0.825614 − 0.285354I
−5.15017 + 0.92884I 0
u = 0.639818 + 0.932642I
a = 0.065731 + 0.670333I
b = −0.611179 + 0.503384I
0.42180 + 3.01163I 0
u = 0.639818 − 0.932642I
a = 0.065731 − 0.670333I
b = −0.611179 − 0.503384I
0.42180 − 3.01163I 0
u = −0.593721 + 0.621763I
a = −0.49669 + 1.63921I
b = −0.021292 + 0.181530I
−4.13144 + 6.46662I 0
u = −0.593721 − 0.621763I
a = −0.49669 − 1.63921I
b = −0.021292 − 0.181530I
−4.13144 − 6.46662I 0
u = −0.640769 + 0.946193I
a = −0.542601 − 0.438875I
b = −0.452294 + 0.070085I
3.48415 − 5.05283I 0
u = −0.640769 − 0.946193I
a = −0.542601 + 0.438875I
b = −0.452294 − 0.070085I
3.48415 + 5.05283I 0
u = −0.636379 + 0.567392I
a = 0.236798 − 1.099070I
b = −0.382560 + 0.366833I
0.17613 + 1.99144I 0
u = −0.636379 − 0.567392I
a = 0.236798 + 1.099070I
b = −0.382560 − 0.366833I
0.17613 − 1.99144I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.581960 + 0.991557I
a = −1.42283 + 0.05743I
b = −2.72033 + 0.32539I
−5.24765 − 11.16740I 0
u = −0.581960 − 0.991557I
a = −1.42283 − 0.05743I
b = −2.72033 − 0.32539I
−5.24765 + 11.16740I 0
u = 0.666047 + 0.938720I
a = −0.826880 − 0.303795I
b = −0.56790 − 1.81639I
−3.06633 + 9.89751I 0
u = 0.666047 − 0.938720I
a = −0.826880 + 0.303795I
b = −0.56790 + 1.81639I
−3.06633 − 9.89751I 0
u = −0.063640 + 1.150590I
a = −0.917822 + 0.379717I
b = −2.67930 − 0.03013I
−5.70391 + 1.36026I 0
u = −0.063640 − 1.150590I
a = −0.917822 − 0.379717I
b = −2.67930 + 0.03013I
−5.70391 − 1.36026I 0
u = −0.149823 + 1.151860I
a = 1.137490 − 0.237386I
b = 2.86725 − 0.57716I
−11.44810 + 0.42410I 0
u = −0.149823 − 1.151860I
a = 1.137490 + 0.237386I
b = 2.86725 + 0.57716I
−11.44810 − 0.42410I 0
u = −0.912722 + 0.726373I
a = 0.526428 − 0.541434I
b = 0.338926 − 0.134167I
2.03330 + 0.16994I 0
u = −0.912722 − 0.726373I
a = 0.526428 + 0.541434I
b = 0.338926 + 0.134167I
2.03330 − 0.16994I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.510475 + 1.062640I
a = 1.124650 + 0.115723I
b = 3.43709 + 0.05722I
−7.89103 + 10.03170I 0
u = 0.510475 − 1.062640I
a = 1.124650 − 0.115723I
b = 3.43709 − 0.05722I
−7.89103 − 10.03170I 0
u = 0.086602 + 1.178420I
a = −0.075206 − 0.992788I
b = 0.281628 − 0.697506I
−6.14702 − 6.30554I 0
u = 0.086602 − 1.178420I
a = −0.075206 + 0.992788I
b = 0.281628 + 0.697506I
−6.14702 + 6.30554I 0
u = −0.765738 + 0.904306I
a = −0.376451 + 0.390915I
b = −0.330694 − 0.884347I
−2.78263 − 4.87703I 0
u = −0.765738 − 0.904306I
a = −0.376451 − 0.390915I
b = −0.330694 + 0.884347I
−2.78263 + 4.87703I 0
u = −0.642305 + 1.004790I
a = 0.860395 − 0.045405I
b = 2.00356 − 0.77879I
−1.02976 − 7.05861I 0
u = −0.642305 − 1.004790I
a = 0.860395 + 0.045405I
b = 2.00356 + 0.77879I
−1.02976 + 7.05861I 0
u = 0.347976 + 1.152370I
a = −0.848161 − 0.539875I
b = −2.61179 − 0.70726I
−8.96205 − 2.66335I 0
u = 0.347976 − 1.152370I
a = −0.848161 + 0.539875I
b = −2.61179 + 0.70726I
−8.96205 + 2.66335I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.045994 + 1.208720I
a = 1.050720 + 0.240655I
b = 2.84566 + 0.14258I
−6.97404 − 6.28993I 0
u = −0.045994 − 1.208720I
a = 1.050720 − 0.240655I
b = 2.84566 − 0.14258I
−6.97404 + 6.28993I 0
u = −0.782595 + 0.049312I
a = 0.46790 − 1.74852I
b = 0.432361 − 0.211392I
−6.35993 + 3.64195I 0
u = −0.782595 − 0.049312I
a = 0.46790 + 1.74852I
b = 0.432361 + 0.211392I
−6.35993 − 3.64195I 0
u = −0.017393 + 1.216130I
a = −0.672124 + 0.276089I
b = −1.73944 + 0.12978I
−5.25398 + 0.42939I 0
u = −0.017393 − 1.216130I
a = −0.672124 − 0.276089I
b = −1.73944 − 0.12978I
−5.25398 − 0.42939I 0
u = −0.479079 + 1.118270I
a = 1.194660 − 0.647803I
b = 2.15933 − 0.47152I
−9.40889 − 7.95906I 0
u = −0.479079 − 1.118270I
a = 1.194660 + 0.647803I
b = 2.15933 + 0.47152I
−9.40889 + 7.95906I 0
u = −0.680586 + 0.384722I
a = −0.45789 + 1.66515I
b = −0.391882 − 0.402950I
−6.73975 + 2.79464I 0
u = −0.680586 − 0.384722I
a = −0.45789 − 1.66515I
b = −0.391882 + 0.402950I
−6.73975 − 2.79464I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.588182 + 1.071450I
a = −1.162080 + 0.322983I
b = −2.95236 + 0.21370I
−8.64367 − 7.69534I 0
u = −0.588182 − 1.071450I
a = −1.162080 − 0.322983I
b = −2.95236 − 0.21370I
−8.64367 + 7.69534I 0
u = −0.668192 + 1.026540I
a = 0.409160 + 0.683331I
b = 0.816883 + 0.570220I
1.76470 − 8.54105I 0
u = −0.668192 − 1.026540I
a = 0.409160 − 0.683331I
b = 0.816883 − 0.570220I
1.76470 + 8.54105I 0
u = −0.686852 + 0.355106I
a = 0.238540 + 0.364318I
b = −0.164540 − 1.328740I
−0.55444 − 5.45753I 0
u = −0.686852 − 0.355106I
a = 0.238540 − 0.364318I
b = −0.164540 + 1.328740I
−0.55444 + 5.45753I 0
u = 0.656562 + 1.055890I
a = −0.080967 + 0.925475I
b = −0.393859 + 0.568642I
1.01648 + 2.93624I 0
u = 0.656562 − 1.055890I
a = −0.080967 − 0.925475I
b = −0.393859 − 0.568642I
1.01648 − 2.93624I 0
u = 0.927455 + 0.837277I
a = −0.498101 − 0.646233I
b = −0.240552 + 0.301119I
−3.68777 + 0.43923I 0
u = 0.927455 − 0.837277I
a = −0.498101 + 0.646233I
b = −0.240552 − 0.301119I
−3.68777 − 0.43923I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.699378 + 1.039980I
a = −0.638584 + 0.397046I
b = −2.25743 + 0.14449I
−3.30595 − 0.95623I 0
u = −0.699378 − 1.039980I
a = −0.638584 − 0.397046I
b = −2.25743 − 0.14449I
−3.30595 + 0.95623I 0
u = 0.642665 + 1.101750I
a = 0.345170 − 0.963796I
b = 0.719881 − 0.810505I
−2.4061 + 13.9409I 0
u = 0.642665 − 1.101750I
a = 0.345170 + 0.963796I
b = 0.719881 + 0.810505I
−2.4061 − 13.9409I 0
u = 0.264077 + 0.673674I
a = 1.29152 + 1.18764I
b = 0.74869 − 1.27455I
−6.07103 − 6.32932I 0
u = 0.264077 − 0.673674I
a = 1.29152 − 1.18764I
b = 0.74869 + 1.27455I
−6.07103 + 6.32932I 0
u = 0.681599 + 1.082700I
a = 0.134370 + 0.657059I
b = 0.258268 + 0.589139I
−0.41201 + 7.03495I 0
u = 0.681599 − 1.082700I
a = 0.134370 − 0.657059I
b = 0.258268 − 0.589139I
−0.41201 − 7.03495I 0
u = −0.540420 + 1.162560I
a = −0.227643 − 1.141750I
b = −0.537698 − 0.701552I
0.61489 − 4.28687I 0
u = −0.540420 − 1.162560I
a = −0.227643 + 1.141750I
b = −0.537698 + 0.701552I
0.61489 + 4.28687I 0
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.788810 + 1.011920I
a = 0.513013 − 0.355072I
b = 0.744637 − 0.365076I
1.14956 − 6.41226I 0
u = −0.788810 − 1.011920I
a = 0.513013 + 0.355072I
b = 0.744637 + 0.365076I
1.14956 + 6.41226I 0
u = −0.331418 + 1.252360I
a = −1.249400 − 0.109446I
b = −2.51498 + 0.24385I
−10.45800 − 0.42555I 0
u = −0.331418 − 1.252360I
a = −1.249400 + 0.109446I
b = −2.51498 − 0.24385I
−10.45800 + 0.42555I 0
u = 0.684588 + 1.105040I
a = −1.075300 − 0.180460I
b = −2.91900 − 0.36811I
−2.1363 + 14.0057I 0
u = 0.684588 − 1.105040I
a = −1.075300 + 0.180460I
b = −2.91900 + 0.36811I
−2.1363 − 14.0057I 0
u = −0.675386 + 1.113300I
a = 1.016630 − 0.060912I
b = 2.74757 − 0.36531I
−1.25825 − 8.83169I 0
u = −0.675386 − 1.113300I
a = 1.016630 + 0.060912I
b = 2.74757 + 0.36531I
−1.25825 + 8.83169I 0
u = 0.643791 + 1.146680I
a = 0.814069 + 0.253912I
b = 2.50860 − 0.11570I
−0.69877 + 7.44187I 0
u = 0.643791 − 1.146680I
a = 0.814069 − 0.253912I
b = 2.50860 + 0.11570I
−0.69877 − 7.44187I 0
18
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.641094 + 1.173750I
a = 0.827861 − 0.036357I
b = 2.80341 + 0.02929I
−1.63938 − 11.40190I 0
u = −0.641094 − 1.173750I
a = 0.827861 + 0.036357I
b = 2.80341 − 0.02929I
−1.63938 + 11.40190I 0
u = 1.230200 + 0.547429I
a = −0.555397 − 0.725269I
b = −0.743641 + 0.362584I
−3.71179 + 8.04112I 0
u = 1.230200 − 0.547429I
a = −0.555397 + 0.725269I
b = −0.743641 − 0.362584I
−3.71179 − 8.04112I 0
u = −0.700559 + 1.151710I
a = −1.113040 + 0.098573I
b = −2.84418 + 0.36066I
−5.9883 − 20.7343I 0
u = −0.700559 − 1.151710I
a = −1.113040 − 0.098573I
b = −2.84418 − 0.36066I
−5.9883 + 20.7343I 0
u = 0.044583 + 1.354140I
a = 1.027920 − 0.307042I
b = 2.58481 − 0.16838I
−11.1025 + 11.7776I 0
u = 0.044583 − 1.354140I
a = 1.027920 + 0.307042I
b = 2.58481 + 0.16838I
−11.1025 − 11.7776I 0
u = 0.589855 + 0.190021I
a = 0.451091 − 0.236965I
b = 0.337803 + 0.590121I
1.34897 + 0.76998I 6.26626 + 0.I
u = 0.589855 − 0.190021I
a = 0.451091 + 0.236965I
b = 0.337803 − 0.590121I
1.34897 − 0.76998I 6.26626 + 0.I
19
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.695522 + 1.197130I
a = 1.111910 + 0.102479I
b = 2.56009 + 0.32524I
−3.20590 + 11.58900I 0
u = 0.695522 − 1.197130I
a = 1.111910 − 0.102479I
b = 2.56009 − 0.32524I
−3.20590 − 11.58900I 0
u = −0.493134 + 0.360737I
a = 1.56042 + 0.66302I
b = 1.47103 + 0.28255I
3.12020 − 0.18336I −2.94808 − 7.99808I
u = −0.493134 − 0.360737I
a = 1.56042 − 0.66302I
b = 1.47103 − 0.28255I
3.12020 + 0.18336I −2.94808 + 7.99808I
u = −0.085533 + 1.410320I
a = −0.656461 + 0.151825I
b = −2.57331 − 0.09531I
−5.19581 + 1.79129I 0
u = −0.085533 − 1.410320I
a = −0.656461 − 0.151825I
b = −2.57331 + 0.09531I
−5.19581 − 1.79129I 0
u = 0.85937 + 1.12846I
a = −0.695878 − 0.351679I
b = −1.97981 − 0.32748I
−4.47939 + 6.42168I 0
u = 0.85937 − 1.12846I
a = −0.695878 + 0.351679I
b = −1.97981 + 0.32748I
−4.47939 − 6.42168I 0
u = 0.149090 + 0.552591I
a = −2.19797 + 0.21508I
b = −1.086190 + 0.367660I
−6.08787 + 2.36077I −0.72546 − 4.88715I
u = 0.149090 − 0.552591I
a = −2.19797 − 0.21508I
b = −1.086190 − 0.367660I
−6.08787 − 2.36077I −0.72546 + 4.88715I
20
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.526520 + 0.009788I
a = −0.83493 + 2.23542I
b = 0.154430 − 0.532936I
−5.62509 − 6.13069I −4.55808 + 5.07224I
u = 0.526520 − 0.009788I
a = −0.83493 − 2.23542I
b = 0.154430 + 0.532936I
−5.62509 + 6.13069I −4.55808 − 5.07224I
u = 0.080883 + 0.504788I
a = 1.35114 − 0.49765I
b = −0.103492 + 0.329879I
0.09172 + 1.48182I 1.10401 − 6.82765I
u = 0.080883 − 0.504788I
a = 1.35114 + 0.49765I
b = −0.103492 − 0.329879I
0.09172 − 1.48182I 1.10401 + 6.82765I
u = 0.45593 + 1.44403I
a = −0.816241 − 0.322591I
b = −2.07775 − 0.09937I
−7.37538 − 0.60806I 0
u = 0.45593 − 1.44403I
a = −0.816241 + 0.322591I
b = −2.07775 + 0.09937I
−7.37538 + 0.60806I 0
u = −0.371918 + 0.304593I
a = 1.30164 + 0.81341I
b = −0.175204 + 0.221393I
−2.52818 + 1.71195I 0.314881 − 0.743084I
u = −0.371918 − 0.304593I
a = 1.30164 − 0.81341I
b = −0.175204 − 0.221393I
−2.52818 − 1.71195I 0.314881 + 0.743084I
u = 0.311051 + 0.325277I
a = 2.40292 + 1.19843I
b = 0.722627 + 0.700650I
−1.25312 + 1.06674I −2.78809 + 2.45086I
u = 0.311051 − 0.325277I
a = 2.40292 − 1.19843I
b = 0.722627 − 0.700650I
−1.25312 − 1.06674I −2.78809 − 2.45086I
21
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.17671 + 1.63164I
a = −0.916678 − 0.094055I
b = −2.27792 − 0.07750I
−7.53781 − 0.80656I 0
u = 0.17671 − 1.63164I
a = −0.916678 + 0.094055I
b = −2.27792 + 0.07750I
−7.53781 + 0.80656I 0
22
II. I
u
2
= h−1.03 × 10
27
u
41
+ 2.27 × 10
27
u
40
+ · · · + 6.16 × 10
26
b − 1.34 ×
10
27
, −1.13 × 10
27
u
41
+ 5.58 × 10
27
u
40
+ · · · + 1.23 × 10
27
a + 2.63 ×
10
28
, u
42
− 3u
41
+ · · · − 12u + 4i
(i) Arc colorings
a
2
=
1
0
a
8
=
0
u
a
3
=
1
−u
2
a
9
=
u
u
a
1
=
u
2
+ 1
−u
4
a
11
=
0.914675u
41
− 4.52764u
40
+ ··· + 43.2049u − 21.3071
1.67604u
41
− 3.69014u
40
+ ··· + 25.7051u + 2.18099
a
7
=
0.321019u
41
+ 0.427292u
40
+ ··· − 10.9313u + 0.848029
0.312907u
41
+ 0.724784u
40
+ ··· − 1.01865u − 0.172662
a
6
=
1.21086u
41
− 1.30270u
40
+ ··· − 7.62094u − 0.244597
1.20275u
41
− 1.00521u
40
+ ··· + 2.29168u − 1.26529
a
4
=
−6.09759u
41
+ 14.8985u
40
+ ··· − 50.9545u + 5.80510
−2.01286u
41
+ 2.95185u
40
+ ··· + 30.2819u − 17.7960
a
5
=
0.143670u
41
+ 1.45287u
40
+ ··· − 24.1725u + 7.93115
0.0767440u
41
+ 2.64553u
40
+ ··· − 16.0943u + 3.98975
a
10
=
−3.52625u
41
+ 7.07224u
40
+ ··· − 15.3843u + 0.0420225
0.999593u
41
− 7.15450u
40
+ ··· + 69.8060u − 21.8925
a
12
=
3.45400u
41
− 6.72978u
40
+ ··· + 0.860421u + 8.02329
0.514126u
41
− 0.0217617u
40
+ ··· − 3.07885u + 9.55373
(ii) Obstruction class = 1
(iii) Cusp Shapes = −7.30738u
41
+ 27.5774u
40
+ ··· − 223.601u + 70.9079
23
(iv) u-Polynomials at the component
24
Crossings u-Polynomials at each crossing
c
1
u
42
− 23u
41
+ ··· − 288u + 16
c
2
u
42
− 3u
41
+ ··· − 12u + 4
c
3
81(81u
42
+ 468u
41
+ ··· − 2u + 1)
c
4
9(9u
42
+ 12u
41
+ ··· − 94u
2
+ 4)
c
5
u
42
+ 2u
41
+ ··· − 666u + 81
c
6
u
42
− 8u
41
+ ··· − 147u + 9
c
7
9(9u
42
+ 3u
41
+ ··· + 2u + 1)
c
8
u
42
+ 3u
41
+ ··· + 12u + 4
c
9
u
42
− 6u
41
+ ··· + 11u + 1
c
10
9(9u
42
− 12u
41
+ ··· − 94u
2
+ 4)
c
11
9(9u
42
− 3u
41
+ ··· − 2u + 1)
c
12
u
42
− 6u
41
+ ··· − 114u + 45
25
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
42
− y
41
+ ··· + 3968y + 256
c
2
, c
8
y
42
+ 23y
41
+ ··· + 288y + 16
c
3
6561(6561y
42
+ 20736y
41
+ ··· + 18y + 1)
c
4
, c
10
81(81y
42
− 2124y
41
+ ··· − 752y + 16)
c
5
y
42
− 2y
41
+ ··· − 475470y + 6561
c
6
y
42
+ 12y
41
+ ··· + 333y + 81
c
7
, c
11
81(81y
42
+ 2169y
41
+ ··· + 42y + 1)
c
9
y
42
− 4y
41
+ ··· − 67y + 1
c
12
y
42
− 14y
41
+ ··· + 21744y + 2025
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.563818 + 0.783332I
a = −1.372980 − 0.034283I
b = −1.57586 − 0.12497I
−1.49097 − 1.91309I −5.52424 + 0.23480I
u = −0.563818 − 0.783332I
a = −1.372980 + 0.034283I
b = −1.57586 + 0.12497I
−1.49097 + 1.91309I −5.52424 − 0.23480I
u = 0.860436 + 0.657451I
a = 0.473071 + 0.303820I
b = 0.444469 − 0.266171I
2.80332 − 0.24930I 8.06497 − 0.49027I
u = 0.860436 − 0.657451I
a = 0.473071 − 0.303820I
b = 0.444469 + 0.266171I
2.80332 + 0.24930I 8.06497 + 0.49027I
u = 0.667459 + 0.853078I
a = 0.550041 + 0.395826I
b = −0.82773 + 1.73658I
2.71792 + 2.58413I 15.5853 − 1.5314I
u = 0.667459 − 0.853078I
a = 0.550041 − 0.395826I
b = −0.82773 − 1.73658I
2.71792 − 2.58413I 15.5853 + 1.5314I
u = −1.010930 + 0.402711I
a = −0.040373 − 1.099230I
b = −0.158279 + 0.566491I
0.57146 + 3.74872I 2.00000 − 8.25312I
u = −1.010930 − 0.402711I
a = −0.040373 + 1.099230I
b = −0.158279 − 0.566491I
0.57146 − 3.74872I 2.00000 + 8.25312I
u = −0.577447 + 0.679015I
a = 0.412929 − 0.510408I
b = −2.03783 − 0.04867I
−1.13051 + 3.98189I 3.62847 − 5.76103I
u = −0.577447 − 0.679015I
a = 0.412929 + 0.510408I
b = −2.03783 + 0.04867I
−1.13051 − 3.98189I 3.62847 + 5.76103I
28
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.122112 + 1.112880I
a = −0.770907 + 0.431127I
b = −2.83538 − 0.14710I
−6.60379 + 1.75566I −10.76262 − 4.13273I
u = −0.122112 − 1.112880I
a = −0.770907 − 0.431127I
b = −2.83538 + 0.14710I
−6.60379 − 1.75566I −10.76262 + 4.13273I
u = 0.148404 + 1.132450I
a = −1.097020 − 0.475151I
b = −2.63446 − 0.24182I
−8.20407 − 1.38929I −7.76314 + 0.51690I
u = 0.148404 − 1.132450I
a = −1.097020 + 0.475151I
b = −2.63446 + 0.24182I
−8.20407 + 1.38929I −7.76314 − 0.51690I
u = 0.499018 + 1.039060I
a = 1.249980 + 0.180036I
b = 3.02802 − 0.04065I
−6.91399 + 9.62031I −2.08220 − 8.01037I
u = 0.499018 − 1.039060I
a = 1.249980 − 0.180036I
b = 3.02802 + 0.04065I
−6.91399 − 9.62031I −2.08220 + 8.01037I
u = 0.925813 + 0.712394I
a = −0.808216 − 0.611579I
b = −0.909433 − 0.176185I
−3.92497 + 7.45356I −4.40923 − 6.14039I
u = 0.925813 − 0.712394I
a = −0.808216 + 0.611579I
b = −0.909433 + 0.176185I
−3.92497 − 7.45356I −4.40923 + 6.14039I
u = 0.024384 + 0.825784I
a = −1.267420 + 0.584240I
b = −0.503982 + 0.581943I
−6.92696 + 2.02105I −10.29980 − 2.02118I
u = 0.024384 − 0.825784I
a = −1.267420 − 0.584240I
b = −0.503982 − 0.581943I
−6.92696 − 2.02105I −10.29980 + 2.02118I
29
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.608797 + 1.008580I
a = 0.511607 − 0.137433I
b = 1.26424 − 1.81546I
−2.20869 − 8.74828I −1.92950 + 9.44348I
u = −0.608797 − 1.008580I
a = 0.511607 + 0.137433I
b = 1.26424 + 1.81546I
−2.20869 + 8.74828I −1.92950 − 9.44348I
u = −0.611648 + 0.538823I
a = −0.513265 + 0.591162I
b = −0.05513 − 1.82049I
−1.27077 − 5.51591I −3.02404 + 6.05282I
u = −0.611648 − 0.538823I
a = −0.513265 − 0.591162I
b = −0.05513 + 1.82049I
−1.27077 + 5.51591I −3.02404 − 6.05282I
u = 0.406524 + 0.696325I
a = 1.06505 + 1.34521I
b = 0.937363 − 0.603903I
−5.62358 − 5.80911I −0.343863 + 0.667863I
u = 0.406524 − 0.696325I
a = 1.06505 − 1.34521I
b = 0.937363 + 0.603903I
−5.62358 + 5.80911I −0.343863 − 0.667863I
u = 0.554081 + 0.522321I
a = 1.055830 − 0.593791I
b = 1.31839 − 0.53447I
3.28793 + 0.50450I 6.85198 − 10.49433I
u = 0.554081 − 0.522321I
a = 1.055830 + 0.593791I
b = 1.31839 + 0.53447I
3.28793 − 0.50450I 6.85198 + 10.49433I
u = −0.085049 + 0.734033I
a = −0.850831 − 0.553454I
b = 0.51315 − 1.41912I
−5.03826 − 2.62235I −6.35926 + 2.69903I
u = −0.085049 − 0.734033I
a = −0.850831 + 0.553454I
b = 0.51315 + 1.41912I
−5.03826 + 2.62235I −6.35926 − 2.69903I
30
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.750966 + 1.028920I
a = 0.282233 + 0.287681I
b = 0.709891 + 0.035727I
1.70245 + 6.22898I 0
u = 0.750966 − 1.028920I
a = 0.282233 − 0.287681I
b = 0.709891 − 0.035727I
1.70245 − 6.22898I 0
u = 0.580162 + 1.137410I
a = −0.171548 + 0.971937I
b = −0.391770 + 0.429968I
1.26236 + 4.17076I 0
u = 0.580162 − 1.137410I
a = −0.171548 − 0.971937I
b = −0.391770 − 0.429968I
1.26236 − 4.17076I 0
u = −0.172202 + 1.320470I
a = −0.571462 + 0.147285I
b = −2.12354 − 0.36231I
−4.83194 + 1.37631I 0
u = −0.172202 − 1.320470I
a = −0.571462 − 0.147285I
b = −2.12354 + 0.36231I
−4.83194 − 1.37631I 0
u = −0.681291 + 1.164370I
a = 0.943500 − 0.089394I
b = 2.65687 − 0.24599I
−1.73219 − 9.80641I 0
u = −0.681291 − 1.164370I
a = 0.943500 + 0.089394I
b = 2.65687 + 0.24599I
−1.73219 + 9.80641I 0
u = 0.283616 + 0.531969I
a = −1.056520 − 0.902883I
b = 0.12982 + 1.54742I
0.225842 − 0.306784I 0.616854 − 0.137025I
u = 0.283616 − 0.531969I
a = −1.056520 + 0.902883I
b = 0.12982 − 1.54742I
0.225842 + 0.306784I 0.616854 + 0.137025I
31
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.23243 + 1.65235I
a = −0.857020 − 0.113009I
b = −2.28215 − 0.06621I
−7.66355 − 0.80423I 0
u = 0.23243 − 1.65235I
a = −0.857020 + 0.113009I
b = −2.28215 + 0.06621I
−7.66355 + 0.80423I 0
32
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
42
− 23u
41
+ ··· − 288u + 16)
· (u
172
+ 76u
171
+ ··· + 25122848u + 795664)
c
2
(u
42
− 3u
41
+ ··· − 12u + 4)(u
172
+ 4u
171
+ ··· + 3076u + 892)
c
3
6561(81u
42
+ 468u
41
+ ··· − 2u + 1)
· (81u
172
+ 2313u
171
+ ··· + 27u + 1)
c
4
81(9u
42
+ 12u
41
+ ··· − 94u
2
+ 4)
· (9u
172
− 21u
171
+ ··· + 3804472u + 145372)
c
5
(u
42
+ 2u
41
+ ··· − 666u + 81)
· (u
172
− 3u
171
+ ··· + 1853937u + 164349)
c
6
(u
42
− 8u
41
+ ··· − 147u + 9)
· (u
172
− 5u
171
+ ··· − 7246383780u + 366700275)
c
7
81(9u
42
+ 3u
41
+ ··· + 2u + 1)
· (9u
172
− 30u
171
+ ··· + 1621697u + 523514)
c
8
(u
42
+ 3u
41
+ ··· + 12u + 4)(u
172
+ 4u
171
+ ··· + 3076u + 892)
c
9
(u
42
− 6u
41
+ ··· + 11u + 1)
· (u
172
− 13u
171
+ ··· − 15667632934u + 1387956497)
c
10
81(9u
42
− 12u
41
+ ··· − 94u
2
+ 4)
· (9u
172
− 21u
171
+ ··· + 3804472u + 145372)
c
11
81(9u
42
− 3u
41
+ ··· − 2u + 1)
· (9u
172
− 30u
171
+ ··· + 1621697u + 523514)
c
12
(u
42
− 6u
41
+ ··· − 114u + 45)
· (u
172
+ 17u
171
+ ··· + 338848083u + 26871588)
33
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
42
− y
41
+ ··· + 3968y + 256)
· (y
172
+ 48y
171
+ ··· + 43751823032704y + 633081200896)
c
2
, c
8
(y
42
+ 23y
41
+ ··· + 288y + 16)
· (y
172
+ 76y
171
+ ··· + 25122848y + 795664)
c
3
43046721(6561y
42
+ 20736y
41
+ ··· + 18y + 1)
· (6561y
172
− 327483y
171
+ ··· + 571y + 1)
c
4
, c
10
6561(81y
42
− 2124y
41
+ ··· − 752y + 16)
· (81y
172
− 9927y
171
+ ··· − 4867492246160y + 21133018384)
c
5
(y
42
− 2y
41
+ ··· − 475470y + 6561)
· (y
172
− 9y
171
+ ··· + 646282891935y + 27010593801)
c
6
(y
42
+ 12y
41
+ ··· + 333y + 81)
· (y
172
− 23y
171
+ ··· − 1.08 × 10
19
y + 1.34 × 10
17
)
c
7
, c
11
6561(81y
42
+ 2169y
41
+ ··· + 42y + 1)
· (81y
172
+ 7650y
171
+ ··· + 6611505111207y + 274066908196)
c
9
(y
42
− 4y
41
+ ··· − 67y + 1)
· (y
172
− 63y
171
+ ··· − 2.69 × 10
19
y + 1.93 × 10
18
)
c
12
(y
42
− 14y
41
+ ··· + 21744y + 2025)
· (y
172
+ 31y
171
+ ··· + 33369002886734055y + 722082241641744)
34
