12a
0895
(K12a
0895
)
A knot diagram
1
Linearized knot diagam
4 6 8 9 11 3 12 2 1 5 7 10
Solving Sequence
1,9 5,10
11 6 4 2 8 3 12 7
c
9
c
10
c
5
c
4
c
1
c
8
c
3
c
12
c
7
c
2
, c
6
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−5.76967 × 10
713
u
140
− 2.01798 × 10
714
u
139
+ ··· + 5.49307 × 10
715
b − 4.88700 × 10
716
,
− 3.01897 × 10
716
u
140
− 1.28805 × 10
717
u
139
+ ··· + 4.46587 × 10
718
a + 4.49215 × 10
719
,
u
141
+ 4u
140
+ ··· + 17088u − 2439i
I
u
2
= h7.04074 × 10
51
u
39
− 4.76153 × 10
52
u
38
+ ··· + 1.87032 × 10
52
b + 3.25362 × 10
52
,
− 9.67601 × 10
51
u
39
+ 7.48438 × 10
52
u
38
+ ··· + 1.87032 × 10
52
a + 1.84688 × 10
53
, u
40
− 7u
39
+ ··· − u + 1i
I
u
3
= h1.91827 × 10
15
u
23
− 1.49385 × 10
15
u
22
+ ··· + 6.45013 × 10
15
b − 5.92118 × 10
16
,
− 3.90530 × 10
16
u
23
+ 3.28309 × 10
16
u
22
+ ··· + 7.09515 × 10
16
a + 1.19578 × 10
18
,
u
24
+ 6u
22
+ ··· − 35u + 22i
I
u
4
= h2au + 5b + 4a + 2u − 1, 2a
2
+ au + 2a + 7, u
2
+ 1i
* 4 irreducible components of dim
C
= 0, with total 209 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−5.77 × 10
713
u
140
− 2.02 × 10
714
u
139
+ · · · + 5.49 × 10
715
b − 4.89 ×
10
716
, −3.02 × 10
716
u
140
− 1.29 × 10
717
u
139
+ · · · + 4.47 × 10
718
a + 4.49 ×
10
719
, u
141
+ 4u
140
+ · · · + 17088u − 2439i
(i) Arc colorings
a
1
=
0
u
a
9
=
1
0
a
5
=
0.00676008u
140
+ 0.0288421u
139
+ ··· + 29.7986u − 10.0588
0.0105035u
140
+ 0.0367369u
139
+ ··· − 98.0007u + 8.89665
a
10
=
1
u
2
a
11
=
−0.00145415u
140
− 0.0330147u
139
+ ··· − 461.608u + 67.9518
0.000487711u
140
+ 0.000914384u
139
+ ··· − 29.1630u + 4.04438
a
6
=
0.0698353u
140
+ 0.335805u
139
+ ··· + 725.297u − 128.431
−0.0172725u
140
− 0.0588641u
139
+ ··· + 170.894u − 17.6429
a
4
=
0.0172636u
140
+ 0.0655790u
139
+ ··· − 68.2021u − 1.16219
0.0105035u
140
+ 0.0367369u
139
+ ··· − 98.0007u + 8.89665
a
2
=
0.0273329u
140
+ 0.108049u
139
+ ··· − 59.1992u + 4.91525
0.00133350u
140
+ 0.00670385u
139
+ ··· + 22.2324u − 4.11296
a
8
=
−0.00194108u
140
+ 0.0360596u
139
+ ··· + 750.730u − 108.524
0.000164712u
140
+ 0.000743466u
139
+ ··· + 15.2249u − 1.76281
a
3
=
0.106236u
140
+ 0.508300u
139
+ ··· + 1272.99u − 219.614
−0.00228481u
140
− 0.000604315u
139
+ ··· + 187.057u − 25.4958
a
12
=
u
u
3
+ u
a
7
=
−0.00248641u
140
+ 0.0321432u
139
+ ··· + 722.092u − 104.111
−0.000299686u
140
− 0.00101533u
139
+ ··· + 14.9075u − 1.58172
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.0414932u
140
+ 0.207190u
139
+ ··· + 724.356u − 117.682
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
4(4u
141
− 32u
140
+ ··· + 3141992u − 178832)
c
2
, c
6
u
141
+ u
140
+ ··· + 351u + 55
c
3
4(4u
141
− 8u
140
+ ··· + 6.23445 × 10
8
u + 6.42613 × 10
7
)
c
4
u
141
− 3u
140
+ ··· − 220u + 8
c
5
, c
10
4(4u
141
+ 132u
140
+ ··· + 2.38371 × 10
8
u + 8904704)
c
7
, c
11
u
141
− u
140
+ ··· − 1837u + 121
c
8
u
141
+ 10u
139
+ ··· + 111111u + 8833
c
9
, c
12
u
141
− 4u
140
+ ··· + 17088u + 2439
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
16(16y
141
+ 424y
140
+ ··· − 1.92565 × 10
12
y −3.19809 × 10
10
)
c
2
, c
6
y
141
− 69y
140
+ ··· + 134971y −3025
c
3
16(16y
141
− 152y
140
+ ··· + 1.54486 × 10
17
y −4.12952 × 10
15
)
c
4
y
141
+ 5y
140
+ ··· − 28352y −64
c
5
, c
10
16
· (16y
141
− 1384y
140
+ ··· − 256485850349568y −79293753327616)
c
7
, c
11
y
141
− 85y
140
+ ··· − 1868361y −14641
c
8
y
141
+ 20y
140
+ ··· − 1754905229y −78021889
c
9
, c
12
y
141
+ 96y
140
+ ··· − 196639272y −5948721
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.095449 + 0.996239I
a = −0.24990 + 2.49987I
b = 0.93960 − 2.16853I
3.80151 − 2.20413I 0
u = 0.095449 − 0.996239I
a = −0.24990 − 2.49987I
b = 0.93960 + 2.16853I
3.80151 + 2.20413I 0
u = −0.278400 + 0.967152I
a = 1.09229 − 1.41787I
b = −0.278031 + 0.544892I
−4.33096 + 1.67929I 0
u = −0.278400 − 0.967152I
a = 1.09229 + 1.41787I
b = −0.278031 − 0.544892I
−4.33096 − 1.67929I 0
u = 0.673598 + 0.748269I
a = 0.099029 + 0.593807I
b = −0.432598 + 0.199508I
−1.97243 − 1.27647I 0
u = 0.673598 − 0.748269I
a = 0.099029 − 0.593807I
b = −0.432598 − 0.199508I
−1.97243 + 1.27647I 0
u = 0.223039 + 0.987573I
a = 0.58442 − 2.32933I
b = 0.375446 + 0.667281I
1.30063 + 0.67197I 0
u = 0.223039 − 0.987573I
a = 0.58442 + 2.32933I
b = 0.375446 − 0.667281I
1.30063 − 0.67197I 0
u = −0.861339 + 0.471457I
a = −0.841235 + 0.248130I
b = 1.049060 + 0.677654I
−5.60110 + 1.90491I 0
u = −0.861339 − 0.471457I
a = −0.841235 − 0.248130I
b = 1.049060 − 0.677654I
−5.60110 − 1.90491I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.578248 + 0.849511I
a = 0.16209 + 1.76372I
b = 0.450976 − 0.250429I
−5.57625 + 5.13631I 0
u = −0.578248 − 0.849511I
a = 0.16209 − 1.76372I
b = 0.450976 + 0.250429I
−5.57625 − 5.13631I 0
u = −0.033831 + 1.031260I
a = 2.32764 + 3.12623I
b = 0.367131 − 0.392934I
−0.026952 − 0.379141I 0
u = −0.033831 − 1.031260I
a = 2.32764 − 3.12623I
b = 0.367131 + 0.392934I
−0.026952 + 0.379141I 0
u = 1.016850 + 0.206866I
a = −0.033017 − 0.247268I
b = −0.939675 − 0.380482I
−3.61008 − 3.14065I 0
u = 1.016850 − 0.206866I
a = −0.033017 + 0.247268I
b = −0.939675 + 0.380482I
−3.61008 + 3.14065I 0
u = −0.209952 + 1.035660I
a = −0.31694 − 1.62986I
b = 0.94747 + 1.52081I
−2.20475 + 4.72856I 0
u = −0.209952 − 1.035660I
a = −0.31694 + 1.62986I
b = 0.94747 − 1.52081I
−2.20475 − 4.72856I 0
u = −0.922781 + 0.181538I
a = 0.539393 − 0.043026I
b = −1.098240 − 0.402940I
−8.54223 − 0.85326I 0
u = −0.922781 − 0.181538I
a = 0.539393 + 0.043026I
b = −1.098240 + 0.402940I
−8.54223 + 0.85326I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.675697 + 0.821263I
a = 0.364305 − 0.208869I
b = 1.018160 + 0.063668I
−5.68601 − 0.21782I 0
u = −0.675697 − 0.821263I
a = 0.364305 + 0.208869I
b = 1.018160 − 0.063668I
−5.68601 + 0.21782I 0
u = −0.189768 + 1.050750I
a = 0.73522 + 2.04080I
b = −1.26158 − 1.97879I
0.13706 + 10.32340I 0
u = −0.189768 − 1.050750I
a = 0.73522 − 2.04080I
b = −1.26158 + 1.97879I
0.13706 − 10.32340I 0
u = 0.461850 + 0.966092I
a = 0.286025 + 1.188000I
b = −0.380600 − 0.160610I
−1.52047 − 1.82440I 0
u = 0.461850 − 0.966092I
a = 0.286025 − 1.188000I
b = −0.380600 + 0.160610I
−1.52047 + 1.82440I 0
u = 0.044679 + 1.080780I
a = 2.14087 + 1.72159I
b = −0.0247542 − 0.0353605I
−0.477909 − 0.034324I 0
u = 0.044679 − 1.080780I
a = 2.14087 − 1.72159I
b = −0.0247542 + 0.0353605I
−0.477909 + 0.034324I 0
u = 1.095870 + 0.052456I
a = −0.349762 − 0.256249I
b = 0.940163 − 0.629172I
−1.03152 + 7.37835I 0
u = 1.095870 − 0.052456I
a = −0.349762 + 0.256249I
b = 0.940163 + 0.629172I
−1.03152 − 7.37835I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.019656 + 1.101390I
a = −0.01077 − 1.42051I
b = −0.611209 + 1.110780I
3.11731 − 0.70452I 0
u = −0.019656 − 1.101390I
a = −0.01077 + 1.42051I
b = −0.611209 − 1.110780I
3.11731 + 0.70452I 0
u = −0.489040 + 0.987743I
a = 0.24346 − 1.85055I
b = −0.488190 + 0.283367I
−2.72546 + 11.86230I 0
u = −0.489040 − 0.987743I
a = 0.24346 + 1.85055I
b = −0.488190 − 0.283367I
−2.72546 − 11.86230I 0
u = −0.155070 + 0.883628I
a = −0.0614654 − 0.0052386I
b = 1.60945 − 0.00209I
−3.84260 + 5.33344I 0
u = −0.155070 − 0.883628I
a = −0.0614654 + 0.0052386I
b = 1.60945 + 0.00209I
−3.84260 − 5.33344I 0
u = −0.694327 + 0.555340I
a = −0.417191 + 0.457679I
b = −1.119510 − 0.110845I
−4.04522 − 7.29883I 0
u = −0.694327 − 0.555340I
a = −0.417191 − 0.457679I
b = −1.119510 + 0.110845I
−4.04522 + 7.29883I 0
u = −1.025070 + 0.445390I
a = 0.796456 + 0.041793I
b = −0.857853 − 0.711688I
−7.38816 − 1.30257I 0
u = −1.025070 − 0.445390I
a = 0.796456 − 0.041793I
b = −0.857853 + 0.711688I
−7.38816 + 1.30257I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.038976 + 1.120640I
a = −0.46583 + 1.43064I
b = 1.30233 − 1.15628I
3.62778 + 2.27571I 0
u = 0.038976 − 1.120640I
a = −0.46583 − 1.43064I
b = 1.30233 + 1.15628I
3.62778 − 2.27571I 0
u = 0.791794 + 0.364067I
a = 0.658338 − 0.489197I
b = 0.662326 + 0.952354I
−0.23836 − 8.83833I 0
u = 0.791794 − 0.364067I
a = 0.658338 + 0.489197I
b = 0.662326 − 0.952354I
−0.23836 + 8.83833I 0
u = −0.108520 + 0.864015I
a = −0.304622 + 0.778437I
b = −1.36169 − 0.42386I
−5.07629 + 0.01794I 0
u = −0.108520 − 0.864015I
a = −0.304622 − 0.778437I
b = −1.36169 + 0.42386I
−5.07629 − 0.01794I 0
u = 0.433497 + 1.079400I
a = −0.45407 − 1.46625I
b = 0.541968 + 0.409617I
0.59225 − 6.29271I 0
u = 0.433497 − 1.079400I
a = −0.45407 + 1.46625I
b = 0.541968 − 0.409617I
0.59225 + 6.29271I 0
u = 0.772808 + 0.284016I
a = −0.794886 + 0.073393I
b = −0.655988 − 0.614001I
−2.84985 − 3.74641I 0
u = 0.772808 − 0.284016I
a = −0.794886 − 0.073393I
b = −0.655988 + 0.614001I
−2.84985 + 3.74641I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.116995 + 1.186880I
a = 1.17084 + 1.75963I
b = −1.64443 − 1.68412I
6.13081 − 0.95901I 0
u = 0.116995 − 1.186880I
a = 1.17084 − 1.75963I
b = −1.64443 + 1.68412I
6.13081 + 0.95901I 0
u = 0.762710 + 0.257587I
a = 0.076333 + 0.424199I
b = 1.130040 + 0.010546I
−1.88596 + 1.89489I 0
u = 0.762710 − 0.257587I
a = 0.076333 − 0.424199I
b = 1.130040 − 0.010546I
−1.88596 − 1.89489I 0
u = −0.270954 + 1.170260I
a = 0.170206 + 1.303010I
b = 1.024440 − 0.947296I
2.74652 + 3.73023I 0
u = −0.270954 − 1.170260I
a = 0.170206 − 1.303010I
b = 1.024440 + 0.947296I
2.74652 − 3.73023I 0
u = 1.201760 + 0.060830I
a = −0.1256270 + 0.0200055I
b = 0.420361 − 0.575058I
0.589234 − 0.358253I 0
u = 1.201760 − 0.060830I
a = −0.1256270 − 0.0200055I
b = 0.420361 + 0.575058I
0.589234 + 0.358253I 0
u = 0.821312 + 0.905452I
a = −0.583524 + 0.792567I
b = −0.648764 − 0.500737I
−2.35045 − 4.14937I 0
u = 0.821312 − 0.905452I
a = −0.583524 − 0.792567I
b = −0.648764 + 0.500737I
−2.35045 + 4.14937I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.404991 + 1.154850I
a = 0.630534 − 0.842574I
b = 0.835140 + 0.646297I
5.82172 − 3.79345I 0
u = 0.404991 − 1.154850I
a = 0.630534 + 0.842574I
b = 0.835140 − 0.646297I
5.82172 + 3.79345I 0
u = −0.753077 + 0.180043I
a = −0.365478 + 0.123764I
b = 1.228850 + 0.603117I
−6.46992 − 5.49078I 0
u = −0.753077 − 0.180043I
a = −0.365478 − 0.123764I
b = 1.228850 − 0.603117I
−6.46992 + 5.49078I 0
u = −0.364004 + 1.192990I
a = −0.24811 − 1.48008I
b = −0.98163 + 1.13955I
7.36986 + 7.93251I 0
u = −0.364004 − 1.192990I
a = −0.24811 + 1.48008I
b = −0.98163 − 1.13955I
7.36986 − 7.93251I 0
u = 0.028388 + 1.257480I
a = 0.402500 − 1.176360I
b = −0.810417 + 1.090670I
2.80486 − 1.03172I 0
u = 0.028388 − 1.257480I
a = 0.402500 + 1.176360I
b = −0.810417 − 1.090670I
2.80486 + 1.03172I 0
u = −1.027780 + 0.752205I
a = −0.522991 − 0.578895I
b = −0.167769 + 0.850939I
−0.42952 − 3.99608I 0
u = −1.027780 − 0.752205I
a = −0.522991 + 0.578895I
b = −0.167769 − 0.850939I
−0.42952 + 3.99608I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.239749 + 1.262670I
a = −0.381170 − 1.110580I
b = −0.821813 + 0.811462I
5.66996 − 1.40079I 0
u = −0.239749 − 1.262670I
a = −0.381170 + 1.110580I
b = −0.821813 − 0.811462I
5.66996 + 1.40079I 0
u = −0.424657 + 1.215650I
a = −0.44057 + 1.89762I
b = 1.17671 − 1.30359I
−3.24276 + 9.88118I 0
u = −0.424657 − 1.215650I
a = −0.44057 − 1.89762I
b = 1.17671 + 1.30359I
−3.24276 − 9.88118I 0
u = −1.296020 + 0.062738I
a = 0.266504 − 0.067133I
b = −0.903362 − 0.647003I
−4.4975 − 13.8083I 0
u = −1.296020 − 0.062738I
a = 0.266504 + 0.067133I
b = −0.903362 + 0.647003I
−4.4975 + 13.8083I 0
u = −0.090997 + 0.689676I
a = 0.75731 − 2.87460I
b = 0.15772 + 1.62523I
−1.16476 − 8.75716I −4.00000 + 6.32566I
u = −0.090997 − 0.689676I
a = 0.75731 + 2.87460I
b = 0.15772 − 1.62523I
−1.16476 + 8.75716I −4.00000 − 6.32566I
u = 0.696925 + 1.105420I
a = −0.586808 + 1.100390I
b = 0.021083 − 1.331250I
4.08935 − 3.81621I 0
u = 0.696925 − 1.105420I
a = −0.586808 − 1.100390I
b = 0.021083 + 1.331250I
4.08935 + 3.81621I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.692163 + 0.026852I
a = −0.341080 − 0.457206I
b = −0.467671 − 0.837379I
3.94525 − 4.12110I 2.00476 + 6.03155I
u = −0.692163 − 0.026852I
a = −0.341080 + 0.457206I
b = −0.467671 + 0.837379I
3.94525 + 4.12110I 2.00476 − 6.03155I
u = −0.368285 + 1.256350I
a = 0.492021 + 0.837457I
b = 0.184064 − 0.976095I
7.75006 − 0.16742I 0
u = −0.368285 − 1.256350I
a = 0.492021 − 0.837457I
b = 0.184064 + 0.976095I
7.75006 + 0.16742I 0
u = 0.082752 + 0.682213I
a = 0.25986 − 1.59581I
b = −0.480821 + 0.125817I
2.90833 + 0.54985I 0. − 2.49912I
u = 0.082752 − 0.682213I
a = 0.25986 + 1.59581I
b = −0.480821 − 0.125817I
2.90833 − 0.54985I 0. + 2.49912I
u = −0.572117 + 1.188010I
a = 0.22700 − 1.63667I
b = −1.04827 + 1.41722I
−4.84048 + 7.04288I 0
u = −0.572117 − 1.188010I
a = 0.22700 + 1.63667I
b = −1.04827 − 1.41722I
−4.84048 − 7.04288I 0
u = 0.118677 + 1.315820I
a = −1.165210 + 0.647451I
b = 1.54492 − 0.70662I
3.51125 − 5.42172I 0
u = 0.118677 − 1.315820I
a = −1.165210 − 0.647451I
b = 1.54492 + 0.70662I
3.51125 + 5.42172I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.304472 + 1.288300I
a = −0.273508 − 1.095850I
b = 0.823513 + 0.980253I
3.22138 − 3.22005I 0
u = 0.304472 − 1.288300I
a = −0.273508 + 1.095850I
b = 0.823513 − 0.980253I
3.22138 + 3.22005I 0
u = −0.474912 + 1.258850I
a = 0.52311 − 1.64667I
b = −1.13901 + 1.24021I
−5.10546 + 5.89115I 0
u = −0.474912 − 1.258850I
a = 0.52311 + 1.64667I
b = −1.13901 − 1.24021I
−5.10546 − 5.89115I 0
u = −0.147529 + 0.634432I
a = 0.39125 − 2.89761I
b = −0.332874 + 0.493773I
2.48180 + 0.60490I 1.40848 − 10.75245I
u = −0.147529 − 0.634432I
a = 0.39125 + 2.89761I
b = −0.332874 − 0.493773I
2.48180 − 0.60490I 1.40848 + 10.75245I
u = 0.368719 + 1.312350I
a = 0.25224 − 1.50950I
b = 0.954925 + 1.041100I
4.65207 − 12.80880I 0
u = 0.368719 − 1.312350I
a = 0.25224 + 1.50950I
b = 0.954925 − 1.041100I
4.65207 + 12.80880I 0
u = 0.436981 + 1.293490I
a = −0.070782 + 1.161930I
b = −1.104490 − 0.864456I
1.64150 − 8.12827I 0
u = 0.436981 − 1.293490I
a = −0.070782 − 1.161930I
b = −1.104490 + 0.864456I
1.64150 + 8.12827I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.589650
a = −0.0844322
b = 0.503916
−0.993656 −9.42120
u = −0.72142 + 1.21826I
a = −0.221152 − 1.170240I
b = −0.867133 + 1.102440I
5.18531 + 8.67679I 0
u = −0.72142 − 1.21826I
a = −0.221152 + 1.170240I
b = −0.867133 − 1.102440I
5.18531 − 8.67679I 0
u = −1.42311 + 0.14289I
a = −0.240043 + 0.065262I
b = 0.788948 + 0.535738I
−6.86872 − 6.52858I 0
u = −1.42311 − 0.14289I
a = −0.240043 − 0.065262I
b = 0.788948 − 0.535738I
−6.86872 + 6.52858I 0
u = 0.11954 + 1.43299I
a = 1.26768 + 0.67811I
b = −1.87514 − 0.59266I
3.48668 − 6.32406I 0
u = 0.11954 − 1.43299I
a = 1.26768 − 0.67811I
b = −1.87514 + 0.59266I
3.48668 + 6.32406I 0
u = 0.53069 + 1.34040I
a = 0.305157 + 1.310640I
b = −1.29375 − 1.09616I
0.81939 − 8.57995I 0
u = 0.53069 − 1.34040I
a = 0.305157 − 1.310640I
b = −1.29375 + 1.09616I
0.81939 + 8.57995I 0
u = 0.56155 + 1.33754I
a = −0.27150 − 1.48735I
b = 1.25418 + 1.29637I
2.97127 − 13.23700I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.56155 − 1.33754I
a = −0.27150 + 1.48735I
b = 1.25418 − 1.29637I
2.97127 + 13.23700I 0
u = 0.47650 + 1.37102I
a = 0.273115 + 1.264520I
b = −1.26634 − 0.97467I
1.14752 − 8.38055I 0
u = 0.47650 − 1.37102I
a = 0.273115 − 1.264520I
b = −1.26634 + 0.97467I
1.14752 + 8.38055I 0
u = 0.55306 + 1.35665I
a = 0.016611 − 1.287340I
b = 0.90183 + 1.09110I
4.76509 − 5.67698I 0
u = 0.55306 − 1.35665I
a = 0.016611 + 1.287340I
b = 0.90183 − 1.09110I
4.76509 + 5.67698I 0
u = 0.39319 + 1.42101I
a = −0.249934 + 0.773927I
b = −0.437830 − 0.774382I
5.90469 − 5.99126I 0
u = 0.39319 − 1.42101I
a = −0.249934 − 0.773927I
b = −0.437830 + 0.774382I
5.90469 + 5.99126I 0
u = 0.472360 + 0.148330I
a = 1.071760 + 0.764314I
b = 0.753831 − 0.733289I
−0.91799 − 3.33318I −7.98281 + 6.38975I
u = 0.472360 − 0.148330I
a = 1.071760 − 0.764314I
b = 0.753831 + 0.733289I
−0.91799 + 3.33318I −7.98281 − 6.38975I
u = −0.74301 + 1.30989I
a = 0.247964 + 1.026490I
b = 0.353615 − 1.199870I
1.68452 + 11.14580I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.74301 − 1.30989I
a = 0.247964 − 1.026490I
b = 0.353615 + 1.199870I
1.68452 − 11.14580I 0
u = −0.62087 + 1.38320I
a = 0.17734 − 1.42748I
b = −1.21219 + 1.20921I
−0.3495 + 20.4090I 0
u = −0.62087 − 1.38320I
a = 0.17734 + 1.42748I
b = −1.21219 − 1.20921I
−0.3495 − 20.4090I 0
u = −0.66607 + 1.37632I
a = −0.131806 + 1.283250I
b = 1.16053 − 1.10406I
−2.94876 + 13.56370I 0
u = −0.66607 − 1.37632I
a = −0.131806 − 1.283250I
b = 1.16053 + 1.10406I
−2.94876 − 13.56370I 0
u = 0.350187 + 0.100007I
a = 1.69469 − 1.48006I
b = −0.307860 − 0.494384I
2.93289 + 0.31451I −0.636286 − 0.320969I
u = 0.350187 − 0.100007I
a = 1.69469 + 1.48006I
b = −0.307860 + 0.494384I
2.93289 − 0.31451I −0.636286 + 0.320969I
u = −0.78322 + 1.44536I
a = 0.019178 − 0.755213I
b = −0.436793 + 0.877558I
−2.15491 + 5.33149I 0
u = −0.78322 − 1.44536I
a = 0.019178 + 0.755213I
b = −0.436793 − 0.877558I
−2.15491 − 5.33149I 0
u = 0.238393 + 0.248820I
a = −2.16462 + 0.63875I
b = −0.218505 + 0.787591I
−1.63741 + 0.14479I −8.98491 + 0.24333I
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.238393 − 0.248820I
a = −2.16462 − 0.63875I
b = −0.218505 − 0.787591I
−1.63741 − 0.14479I −8.98491 − 0.24333I
u = −0.293589 + 0.157443I
a = 0.21073 + 1.84452I
b = 0.338272 + 0.531830I
−0.164711 − 1.313570I −2.39050 + 4.68838I
u = −0.293589 − 0.157443I
a = 0.21073 − 1.84452I
b = 0.338272 − 0.531830I
−0.164711 + 1.313570I −2.39050 − 4.68838I
u = 0.96201 + 1.36726I
a = −0.339505 + 0.371102I
b = 0.158786 − 0.662280I
1.59809 + 2.43719I 0
u = 0.96201 − 1.36726I
a = −0.339505 − 0.371102I
b = 0.158786 + 0.662280I
1.59809 − 2.43719I 0
u = 0.40919 + 1.62261I
a = −0.287219 − 0.648808I
b = 0.485277 + 0.700341I
0.38531 − 3.74014I 0
u = 0.40919 − 1.62261I
a = −0.287219 + 0.648808I
b = 0.485277 − 0.700341I
0.38531 + 3.74014I 0
u = 0.082835 + 0.202285I
a = −4.21014 − 4.41810I
b = 0.276785 + 0.589204I
0.89037 − 2.84402I 0.58704 + 10.23878I
u = 0.082835 − 0.202285I
a = −4.21014 + 4.41810I
b = 0.276785 − 0.589204I
0.89037 + 2.84402I 0.58704 − 10.23878I
u = −0.22220 + 2.23712I
a = 0.175325 + 0.048584I
b = 0.0469480 − 0.1227540I
1.76811 − 6.01909I 0
18
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.22220 − 2.23712I
a = 0.175325 − 0.048584I
b = 0.0469480 + 0.1227540I
1.76811 + 6.01909I 0
19
II.
I
u
2
= h7.04×10
51
u
39
−4.76×10
52
u
38
+· · ·+1.87×10
52
b+3.25×10
52
, −9.68×
10
51
u
39
+7.48×10
52
u
38
+· · ·+1.87×10
52
a+1.85×10
53
, u
40
−7u
39
+· · ·−u+1i
(i) Arc colorings
a
1
=
0
u
a
9
=
1
0
a
5
=
0.517346u
39
− 4.00166u
38
+ ··· + 29.0470u − 9.87469
−0.376446u
39
+ 2.54584u
38
+ ··· − 4.50569u − 1.73961
a
10
=
1
u
2
a
11
=
0.746990u
39
− 4.99380u
38
+ ··· − 17.5519u + 12.1534
0.308064u
39
− 2.13174u
38
+ ··· + 6.29908u + 1.96875
a
6
=
1.41085u
39
− 9.18105u
38
+ ··· + 8.37890u + 9.27228
0.164414u
39
− 1.20753u
38
+ ··· + 7.15413u + 0.946038
a
4
=
0.140900u
39
− 1.45582u
38
+ ··· + 24.5413u − 11.6143
−0.376446u
39
+ 2.54584u
38
+ ··· − 4.50569u − 1.73961
a
2
=
−2.19551u
39
+ 15.6904u
38
+ ··· − 62.0796u − 0.779416
−0.198038u
39
+ 1.37113u
38
+ ··· − 10.8428u + 0.718068
a
8
=
0.928856u
39
− 6.92910u
38
+ ··· + 60.1391u − 11.5032
−0.224848u
39
+ 1.41613u
38
+ ··· + 2.57250u − 2.49551
a
3
=
−1.25590u
39
+ 9.04130u
38
+ ··· − 14.3346u − 14.9166
−0.571063u
39
+ 3.89660u
38
+ ··· − 14.5436u − 1.55020
a
12
=
u
u
3
+ u
a
7
=
0.971298u
39
− 7.16873u
38
+ ··· + 61.6895u − 11.7936
−0.141405u
39
+ 0.843708u
38
+ ··· + 4.13793u − 2.84333
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0.761502u
39
− 5.64558u
38
+ ··· + 34.2395u − 13.7197
20
(iv) u-Polynomials at the component
21
Crossings u-Polynomials at each crossing
c
1
u
40
− 12u
39
+ ··· + 10u
2
+ 1
c
2
u
40
− 8u
39
+ ··· − 12u + 1
c
3
u
40
+ 18u
38
+ ··· − 37u + 17
c
4
u
40
− 3u
37
+ ··· + 2u + 1
c
5
u
40
+ 2u
38
+ ··· + 4u + 1
c
6
u
40
+ 8u
39
+ ··· + 12u + 1
c
7
u
40
− 12u
38
+ ··· − 4u + 1
c
8
u
40
− 7u
39
+ ··· − 18u
2
+ 1
c
9
u
40
− 7u
39
+ ··· − u + 1
c
10
u
40
+ 2u
38
+ ··· − 4u + 1
c
11
u
40
− 12u
38
+ ··· + 4u + 1
c
12
u
40
+ 7u
39
+ ··· + u + 1
22
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
40
− 28y
39
+ ··· + 20y + 1
c
2
, c
6
y
40
− 20y
39
+ ··· − 28y + 1
c
3
y
40
+ 36y
39
+ ··· − 1403y + 289
c
4
y
40
− 2y
38
+ ··· + 4y + 1
c
5
, c
10
y
40
+ 4y
39
+ ··· + 6y + 1
c
7
, c
11
y
40
− 24y
39
+ ··· − 36y + 1
c
8
y
40
+ 5y
39
+ ··· − 36y + 1
c
9
, c
12
y
40
+ 29y
39
+ ··· + 99y + 1
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.946242 + 0.349510I
a = −0.805978 + 0.023558I
b = 0.933770 + 0.612301I
−7.51617 − 0.95415I −8.43163 − 6.77725I
u = −0.946242 − 0.349510I
a = −0.805978 − 0.023558I
b = 0.933770 − 0.612301I
−7.51617 + 0.95415I −8.43163 + 6.77725I
u = 0.030719 + 1.023790I
a = −0.39619 + 4.44348I
b = −0.042380 − 0.505633I
−0.221429 + 0.251934I 2.5500 + 14.3415I
u = 0.030719 − 1.023790I
a = −0.39619 − 4.44348I
b = −0.042380 + 0.505633I
−0.221429 − 0.251934I 2.5500 − 14.3415I
u = 0.564372 + 0.790539I
a = 0.992142 − 0.673448I
b = −0.261083 + 0.332273I
0.91210 + 1.80500I −3.21044 − 0.95556I
u = 0.564372 − 0.790539I
a = 0.992142 + 0.673448I
b = −0.261083 − 0.332273I
0.91210 − 1.80500I −3.21044 + 0.95556I
u = −0.387689 + 0.973413I
a = −0.58689 − 2.21445I
b = 0.00553 + 1.62010I
−1.01828 + 10.54540I −4.40885 − 9.72254I
u = −0.387689 − 0.973413I
a = −0.58689 + 2.21445I
b = 0.00553 − 1.62010I
−1.01828 − 10.54540I −4.40885 + 9.72254I
u = −0.663444 + 0.842376I
a = 0.67238 + 1.41264I
b = 0.291967 − 0.854619I
−4.39411 + 4.92275I −7.18399 − 6.96673I
u = −0.663444 − 0.842376I
a = 0.67238 − 1.41264I
b = 0.291967 + 0.854619I
−4.39411 − 4.92275I −7.18399 + 6.96673I
25
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.055620 + 0.366287I
a = −0.189697 − 0.179477I
b = −0.936460 − 0.330534I
−3.99576 − 3.61565I −18.3816 + 10.7652I
u = 1.055620 − 0.366287I
a = −0.189697 + 0.179477I
b = −0.936460 + 0.330534I
−3.99576 + 3.61565I −18.3816 − 10.7652I
u = 0.452170 + 1.084660I
a = 0.40680 − 1.69607I
b = 0.09525 + 1.68813I
3.24706 − 3.50491I −4.00000 + 5.54002I
u = 0.452170 − 1.084660I
a = 0.40680 + 1.69607I
b = 0.09525 − 1.68813I
3.24706 + 3.50491I −4.00000 − 5.54002I
u = 0.148629 + 1.244320I
a = −0.794828 − 0.577364I
b = 1.40506 + 0.27340I
5.24080 − 1.41344I 0. + 4.19264I
u = 0.148629 − 1.244320I
a = −0.794828 + 0.577364I
b = 1.40506 − 0.27340I
5.24080 + 1.41344I 0. − 4.19264I
u = 0.401610 + 1.220670I
a = 0.41750 + 1.41563I
b = −0.87285 − 1.47486I
3.76804 − 0.18785I 0
u = 0.401610 − 1.220670I
a = 0.41750 − 1.41563I
b = −0.87285 + 1.47486I
3.76804 + 0.18785I 0
u = −0.440501 + 0.558188I
a = 0.692735 − 0.930380I
b = 1.039970 − 0.058216I
−6.14307 + 0.98694I −11.27137 − 3.84049I
u = −0.440501 − 0.558188I
a = 0.692735 + 0.930380I
b = 1.039970 + 0.058216I
−6.14307 − 0.98694I −11.27137 + 3.84049I
26
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.424966 + 0.560119I
a = −0.488198 + 0.386585I
b = −0.209886 + 0.523726I
−1.16356 − 1.39520I −3.05172 + 4.03753I
u = 0.424966 − 0.560119I
a = −0.488198 − 0.386585I
b = −0.209886 − 0.523726I
−1.16356 + 1.39520I −3.05172 − 4.03753I
u = −0.494864 + 1.218550I
a = −0.38116 + 1.71946I
b = 1.07649 − 1.41659I
−4.58294 + 6.21882I 0
u = −0.494864 − 1.218550I
a = −0.38116 − 1.71946I
b = 1.07649 + 1.41659I
−4.58294 − 6.21882I 0
u = 0.613241 + 1.185480I
a = 0.243665 − 1.223480I
b = 0.902854 + 1.081210I
5.76751 − 7.92139I 0
u = 0.613241 − 1.185480I
a = 0.243665 + 1.223480I
b = 0.902854 − 1.081210I
5.76751 + 7.92139I 0
u = 0.950498 + 0.949142I
a = −0.484931 + 0.632484I
b = −0.525538 − 0.481617I
−2.03645 − 3.80527I 0
u = 0.950498 − 0.949142I
a = −0.484931 − 0.632484I
b = −0.525538 + 0.481617I
−2.03645 + 3.80527I 0
u = 0.209858 + 1.331430I
a = 0.918312 + 0.308142I
b = −1.53975 − 0.33334I
4.22311 − 4.85234I 0
u = 0.209858 − 1.331430I
a = 0.918312 − 0.308142I
b = −1.53975 + 0.33334I
4.22311 + 4.85234I 0
27
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.44858 + 1.39285I
a = 0.378650 + 1.221020I
b = −1.34970 − 0.94623I
1.37535 − 8.67378I 0
u = 0.44858 − 1.39285I
a = 0.378650 − 1.221020I
b = −1.34970 + 0.94623I
1.37535 + 8.67378I 0
u = −0.022856 + 0.307036I
a = −0.95756 − 3.84593I
b = 0.569691 + 0.151923I
2.29224 − 0.06479I −7.88478 − 2.95573I
u = −0.022856 − 0.307036I
a = −0.95756 + 3.84593I
b = 0.569691 − 0.151923I
2.29224 + 0.06479I −7.88478 + 2.95573I
u = 1.25883 + 1.14060I
a = −0.259034 + 0.200620I
b = 0.147262 − 0.615239I
4.23721 + 1.26029I 0
u = 1.25883 − 1.14060I
a = −0.259034 − 0.200620I
b = 0.147262 + 0.615239I
4.23721 − 1.26029I 0
u = −0.024178 + 0.166635I
a = −4.53771 + 2.88086I
b = −1.262050 − 0.197915I
−4.82914 − 4.69377I −9.21447 + 3.31739I
u = −0.024178 − 0.166635I
a = −4.53771 − 2.88086I
b = −1.262050 + 0.197915I
−4.82914 + 4.69377I −9.21447 − 3.31739I
u = −0.07932 + 2.04703I
a = −0.340021 − 0.029482I
b = 0.531855 − 0.041257I
1.54762 − 5.97634I 0
u = −0.07932 − 2.04703I
a = −0.340021 + 0.029482I
b = 0.531855 + 0.041257I
1.54762 + 5.97634I 0
28
III. I
u
3
= h1.92 × 10
15
u
23
− 1.49 × 10
15
u
22
+ · · · + 6.45 × 10
15
b − 5.92 ×
10
16
, −3.91 × 10
16
u
23
+ 3.28 × 10
16
u
22
+ · · · + 7.10 × 10
16
a + 1.20 ×
10
18
, u
24
+ 6u
22
+ · · · − 35u + 22i
(i) Arc colorings
a
1
=
0
u
a
9
=
1
0
a
5
=
0.550418u
23
− 0.462724u
22
+ ··· + 47.6321u − 16.8535
−0.297399u
23
+ 0.231600u
22
+ ··· − 28.3045u + 9.17993
a
10
=
1
u
2
a
11
=
−0.550418u
23
+ 0.462724u
22
+ ··· − 47.6321u + 17.8535
0.297399u
23
− 0.231600u
22
+ ··· + 28.3045u − 9.17993
a
6
=
1
u
2
a
4
=
0.253019u
23
− 0.231124u
22
+ ··· + 19.3275u − 7.67353
−0.297399u
23
+ 0.231600u
22
+ ··· − 28.3045u + 9.17993
a
2
=
−0.279884u
23
− 0.480690u
22
+ ··· + 15.1249u − 14.8525
0.0570544u
23
+ 0.287597u
22
+ ··· − 17.2953u + 11.3359
a
8
=
−0.232519u
23
− 0.396682u
22
+ ··· + 28.1335u − 16.8365
−0.151039u
23
− 0.149718u
22
+ ··· − 5.79689u − 0.666677
a
3
=
−0.457463u
23
− 0.471451u
22
+ ··· + 8.49636u − 14.0918
0.258109u
23
+ 0.239135u
22
+ ··· − 13.0652u + 11.1327
a
12
=
u
u
3
+ u
a
7
=
−0.157721u
23
− 0.410205u
22
+ ··· + 37.7150u − 19.6197
−0.0934508u
23
− 0.177033u
22
+ ··· + 1.66566u − 3.15234
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
3219464987438840
3225066998988613
u
23
−
5302445282536782
3225066998988613
u
22
+ ···+
333221500168387398
3225066998988613
u −
157691199113955302
3225066998988613
29
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
4
+ u
3
+ u
2
+ 1)
6
c
2
, c
6
u
24
− 6u
22
+ ··· − 11u + 4
c
3
u
24
− 4u
22
+ ··· − 25u + 4
c
4
u
24
+ 2u
22
+ ··· − 7u + 2
c
5
, c
10
(u − 1)
24
c
7
, c
11
u
24
− 2u
22
+ ··· + 5u + 2
c
8
u
24
− 2u
22
+ ··· − 15u + 4
c
9
, c
12
u
24
+ 6u
22
+ ··· + 35u + 22
30
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
4
+ y
3
+ 3y
2
+ 2y + 1)
6
c
2
, c
6
y
24
− 12y
23
+ ··· − 81y + 16
c
3
y
24
− 8y
23
+ ··· + 327y + 16
c
4
y
24
+ 4y
23
+ ··· + 323y + 4
c
5
, c
10
(y −1)
24
c
7
, c
11
y
24
− 4y
23
+ ··· − 29y + 4
c
8
y
24
− 4y
23
+ ··· + 247y + 16
c
9
, c
12
y
24
+ 12y
23
+ ··· + 4539y + 484
31
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.191001 + 0.964913I
a = 0.675439 + 0.382407I
b = −1.46328 − 0.59106I
3.50087 + 1.41510I −2.17326 − 4.90874I
u = −0.191001 − 0.964913I
a = 0.675439 − 0.382407I
b = −1.46328 + 0.59106I
3.50087 − 1.41510I −2.17326 + 4.90874I
u = 0.927562 + 0.073825I
a = −0.030547 − 0.484905I
b = −0.959705 − 0.418739I
−3.50087 − 3.16396I −5.82674 + 2.56480I
u = 0.927562 − 0.073825I
a = −0.030547 + 0.484905I
b = −0.959705 + 0.418739I
−3.50087 + 3.16396I −5.82674 − 2.56480I
u = −0.340095 + 0.864091I
a = −1.15633 + 1.44532I
b = 0.579115 − 0.232353I
−3.50087 − 3.16396I −5.82674 + 2.56480I
u = −0.340095 − 0.864091I
a = −1.15633 − 1.44532I
b = 0.579115 + 0.232353I
−3.50087 + 3.16396I −5.82674 − 2.56480I
u = 0.070799 + 0.921614I
a = −0.43805 − 2.45448I
b = −0.30982 + 2.01530I
3.50087 + 1.41510I −2.17326 − 4.90874I
u = 0.070799 − 0.921614I
a = −0.43805 + 2.45448I
b = −0.30982 − 2.01530I
3.50087 − 1.41510I −2.17326 + 4.90874I
u = 0.985551 + 0.481588I
a = −0.125689 − 0.164530I
b = −0.936751 − 0.240963I
−3.50087 − 3.16396I −5.82674 + 2.56480I
u = 0.985551 − 0.481588I
a = −0.125689 + 0.164530I
b = −0.936751 + 0.240963I
−3.50087 + 3.16396I −5.82674 − 2.56480I
32
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.546299 + 0.953039I
a = 0.58594 − 1.44011I
b = 0.14224 + 1.48836I
3.50087 − 1.41510I −2.17326 + 4.90874I
u = 0.546299 − 0.953039I
a = 0.58594 + 1.44011I
b = 0.14224 − 1.48836I
3.50087 + 1.41510I −2.17326 − 4.90874I
u = −0.513768 + 1.113040I
a = −0.24136 + 1.72443I
b = 1.20751 − 1.40509I
−3.50087 + 3.16396I −5.82674 − 2.56480I
u = −0.513768 − 1.113040I
a = −0.24136 − 1.72443I
b = 1.20751 + 1.40509I
−3.50087 − 3.16396I −5.82674 + 2.56480I
u = −0.052945 + 0.727017I
a = −0.75174 + 2.52693I
b = −0.410238 − 1.270660I
−3.50087 − 3.16396I −5.82674 + 2.56480I
u = −0.052945 − 0.727017I
a = −0.75174 − 2.52693I
b = −0.410238 + 1.270660I
−3.50087 + 3.16396I −5.82674 − 2.56480I
u = 0.205824 + 1.387780I
a = −1.32198 − 0.65925I
b = 1.86665 + 0.48652I
3.50087 − 1.41510I −2.17326 + 4.90874I
u = 0.205824 − 1.387780I
a = −1.32198 + 0.65925I
b = 1.86665 − 0.48652I
3.50087 + 1.41510I −2.17326 − 4.90874I
u = −1.00630 + 1.03348I
a = 0.344521 + 0.739985I
b = 0.520069 − 0.757627I
−3.50087 + 3.16396I −5.82674 − 2.56480I
u = −1.00630 − 1.03348I
a = 0.344521 − 0.739985I
b = 0.520069 + 0.757627I
−3.50087 − 3.16396I −5.82674 + 2.56480I
33
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.67225 + 1.49689I
a = −0.277734 − 0.232694I
b = −0.034888 − 0.142731I
3.50087 + 1.41510I −2.17326 − 4.90874I
u = 0.67225 − 1.49689I
a = −0.277734 + 0.232694I
b = −0.034888 + 0.142731I
3.50087 − 1.41510I −2.17326 + 4.90874I
u = −1.30418 + 1.04259I
a = 0.305721 + 0.224832I
b = −0.200908 − 0.693376I
3.50087 − 1.41510I −2.17326 + 4.90874I
u = −1.30418 − 1.04259I
a = 0.305721 − 0.224832I
b = −0.200908 + 0.693376I
3.50087 + 1.41510I −2.17326 − 4.90874I
34
IV. I
u
4
= h2au + 5b + 4a + 2u − 1, 2a
2
+ au + 2a + 7, u
2
+ 1i
(i) Arc colorings
a
1
=
0
u
a
9
=
1
0
a
5
=
a
−
2
5
au −
4
5
a −
2
5
u +
1
5
a
10
=
1
−1
a
11
=
−
1
10
au −
1
5
a +
7
5
u +
3
10
−u
a
6
=
−
1
5
au +
7
20
a +
1
20
u −
9
10
−
1
5
au −
2
5
a −
1
5
u +
3
5
a
4
=
−
2
5
au +
1
5
a −
2
5
u +
1
5
−
2
5
au −
4
5
a −
2
5
u +
1
5
a
2
=
1
5
au −
1
10
a −
3
10
u +
2
5
−1
a
8
=
−
1
5
au +
1
10
a +
3
10
u +
3
5
1
a
3
=
1
4
a −
1
4
u −
1
2
−
1
5
au −
2
5
a −
1
5
u −
2
5
a
12
=
u
0
a
7
=
−
1
5
au +
1
10
a +
3
10
u −
2
5
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4
35
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
4(4u
4
+ 4u
3
+ 5u
2
+ 2u + 2)
c
2
, c
8
(u + 1)
4
c
3
4(4u
4
+ 12u
3
+ 17u
2
+ 12u + 5)
c
4
u
4
+ 2u
3
+ 5u
2
+ 4u + 8
c
5
4(4u
4
− 3u
2
+ 2u + 2)
c
6
(u − 1)
4
c
7
, c
9
, c
11
c
12
(u
2
+ 1)
2
c
10
4(4u
4
− 3u
2
− 2u + 2)
36
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
16(16y
4
+ 24y
3
+ 25y
2
+ 16y + 4)
c
2
, c
6
, c
8
(y −1)
4
c
3
16(16y
4
− 8y
3
+ 41y
2
+ 26y + 25)
c
4
y
4
+ 6y
3
+ 25y
2
+ 64y + 64
c
5
, c
10
16(16y
4
− 24y
3
+ 25y
2
− 16y + 4)
c
7
, c
9
, c
11
c
12
(y + 1)
4
37
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = −0.43137 + 1.57132I
b = 1.17362 − 1.48451I
4.93480 4.00000
u = 1.000000I
a = −0.56863 − 2.07132I
b = −0.17362 + 1.48451I
4.93480 4.00000
u = − 1.000000I
a = −0.43137 − 1.57132I
b = 1.17362 + 1.48451I
4.93480 4.00000
u = − 1.000000I
a = −0.56863 + 2.07132I
b = −0.17362 − 1.48451I
4.93480 4.00000
38
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
16(u
4
+ u
3
+ u
2
+ 1)
6
(4u
4
+ 4u
3
+ 5u
2
+ 2u + 2)
· (u
40
− 12u
39
+ ··· + 10u
2
+ 1)
· (4u
141
− 32u
140
+ ··· + 3141992u − 178832)
c
2
((u + 1)
4
)(u
24
− 6u
22
+ ··· − 11u + 4)(u
40
− 8u
39
+ ··· − 12u + 1)
· (u
141
+ u
140
+ ··· + 351u + 55)
c
3
16(4u
4
+ 12u
3
+ ··· + 12u + 5)(u
24
− 4u
22
+ ··· − 25u + 4)
· (u
40
+ 18u
38
+ ··· − 37u + 17)
· (4u
141
− 8u
140
+ ··· + 623445392u + 64261303)
c
4
(u
4
+ 2u
3
+ 5u
2
+ 4u + 8)(u
24
+ 2u
22
+ ··· − 7u + 2)
· (u
40
− 3u
37
+ ··· + 2u + 1)(u
141
− 3u
140
+ ··· − 220u + 8)
c
5
16(u − 1)
24
(4u
4
− 3u
2
+ 2u + 2)(u
40
+ 2u
38
+ ··· + 4u + 1)
· (4u
141
+ 132u
140
+ ··· + 238370816u + 8904704)
c
6
((u − 1)
4
)(u
24
− 6u
22
+ ··· − 11u + 4)(u
40
+ 8u
39
+ ··· + 12u + 1)
· (u
141
+ u
140
+ ··· + 351u + 55)
c
7
((u
2
+ 1)
2
)(u
24
− 2u
22
+ ··· + 5u + 2)(u
40
− 12u
38
+ ··· − 4u + 1)
· (u
141
− u
140
+ ··· − 1837u + 121)
c
8
((u + 1)
4
)(u
24
− 2u
22
+ ··· − 15u + 4)(u
40
− 7u
39
+ ··· − 18u
2
+ 1)
· (u
141
+ 10u
139
+ ··· + 111111u + 8833)
c
9
((u
2
+ 1)
2
)(u
24
+ 6u
22
+ ··· + 35u + 22)(u
40
− 7u
39
+ ··· − u + 1)
· (u
141
− 4u
140
+ ··· + 17088u + 2439)
c
10
16(u − 1)
24
(4u
4
− 3u
2
− 2u + 2)(u
40
+ 2u
38
+ ··· − 4u + 1)
· (4u
141
+ 132u
140
+ ··· + 238370816u + 8904704)
c
11
((u
2
+ 1)
2
)(u
24
− 2u
22
+ ··· + 5u + 2)(u
40
− 12u
38
+ ··· + 4u + 1)
· (u
141
− u
140
+ ··· − 1837u + 121)
c
12
((u
2
+ 1)
2
)(u
24
+ 6u
22
+ ··· + 35u + 22)(u
40
+ 7u
39
+ ··· + u + 1)
· (u
141
− 4u
140
+ ··· + 17088u + 2439)
39
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
256(y
4
+ y
3
+ 3y
2
+ 2y + 1)
6
(16y
4
+ 24y
3
+ 25y
2
+ 16y + 4)
· (y
40
− 28y
39
+ ··· + 20y + 1)
· (16y
141
+ 424y
140
+ ··· − 1925653632960y −31980884224)
c
2
, c
6
((y −1)
4
)(y
24
− 12y
23
+ ··· − 81y + 16)(y
40
− 20y
39
+ ··· − 28y + 1)
· (y
141
− 69y
140
+ ··· + 134971y −3025)
c
3
256(16y
4
− 8y
3
+ ··· + 26y + 25)(y
24
− 8y
23
+ ··· + 327y + 16)
· (y
40
+ 36y
39
+ ··· − 1403y + 289)
· (16y
141
− 152y
140
+ ··· + 1.54 × 10
17
y −4.13 × 10
15
)
c
4
(y
4
+ 6y
3
+ 25y
2
+ 64y + 64)(y
24
+ 4y
23
+ ··· + 323y + 4)
· (y
40
− 2y
38
+ ··· + 4y + 1)(y
141
+ 5y
140
+ ··· − 28352y −64)
c
5
, c
10
256(y −1)
24
(16y
4
− 24y
3
+ ··· − 16y + 4)(y
40
+ 4y
39
+ ··· + 6y + 1)
· (16y
141
− 1384y
140
+ ··· − 256485850349568y −79293753327616)
c
7
, c
11
((y + 1)
4
)(y
24
− 4y
23
+ ··· − 29y + 4)(y
40
− 24y
39
+ ··· − 36y + 1)
· (y
141
− 85y
140
+ ··· − 1868361y −14641)
c
8
((y −1)
4
)(y
24
− 4y
23
+ ··· + 247y + 16)(y
40
+ 5y
39
+ ··· − 36y + 1)
· (y
141
+ 20y
140
+ ··· − 1754905229y −78021889)
c
9
, c
12
((y + 1)
4
)(y
24
+ 12y
23
+ ··· + 4539y + 484)
· (y
40
+ 29y
39
+ ··· + 99y + 1)
· (y
141
+ 96y
140
+ ··· − 196639272y −5948721)
40
