12a
0061
(K12a
0061
)
A knot diagram
1
Linearized knot diagam
3 5 7 2 11 8 4 12 1 6 10 9
Solving Sequence
8,12
9 1
4,10
7 3 2 6 11 5
c
8
c
12
c
9
c
7
c
3
c
1
c
6
c
11
c
5
c
2
, c
4
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h9.78678 × 10
34
u
99
+ 6.59298 × 10
35
u
98
+ ··· + 1.09528 × 10
33
b + 7.70863 × 10
34
,
1.13394 × 10
35
u
99
+ 7.80081 × 10
35
u
98
+ ··· + 5.47642 × 10
32
a + 9.43267 × 10
34
, u
100
+ 8u
99
+ ··· − 2u + 1i
I
u
2
= h2a
5
− 2a
4
+ 7a
3
− 5a
2
+ 3b + a − 4, a
6
+ 4a
4
+ a
3
+ 4a
2
+ 1, u − 1i
I
u
3
= hb, −u
2
+ a − u + 1, u
5
+ u
4
− 2u
3
− u
2
+ u − 1i
* 3 irreducible components of dim
C
= 0, with total 111 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
= h9.79 × 10
34
u
99
+ 6.59 × 10
35
u
98
+ · · · + 1.10 × 10
33
b + 7.71 × 10
34
, 1.13 ×
10
35
u
99
+7.80×10
35
u
98
+· · ·+5.48×10
32
a+9.43×10
34
, u
100
+8u
99
+· · ·−2u+1i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
9
=
1
u
2
a
1
=
−u
−u
3
+ u
a
4
=
−207.058u
99
− 1424.44u
98
+ ··· + 486.994u − 172.242
−89.3539u
99
− 601.943u
98
+ ··· + 192.348u − 70.3803
a
10
=
−u
2
+ 1
−u
4
+ 2u
2
a
7
=
70.5297u
99
+ 463.919u
98
+ ··· − 137.456u + 47.4816
154.340u
99
+ 987.870u
98
+ ··· − 227.661u + 90.4459
a
3
=
−173.653u
99
− 1215.48u
98
+ ··· + 437.871u − 154.696
−46.3300u
99
− 355.564u
98
+ ··· + 185.885u − 61.7454
a
2
=
194.960u
99
+ 1330.52u
98
+ ··· − 438.893u + 154.655
135.876u
99
+ 888.170u
98
+ ··· − 235.645u + 90.8592
a
6
=
−83.8108u
99
− 523.951u
98
+ ··· + 90.2049u − 42.9643
154.340u
99
+ 987.870u
98
+ ··· − 227.661u + 90.4459
a
11
=
u
5
− 2u
3
+ u
u
7
− 3u
5
+ 2u
3
+ u
a
5
=
−9.87259u
99
− 93.4878u
98
+ ··· + 64.7923u − 23.7609
155.602u
99
+ 985.103u
98
+ ··· − 207.683u + 85.0368
(ii) Obstruction class = −1
(iii) Cusp Shapes = −10.1896u
99
− 65.6881u
98
+ ··· + 19.6205u − 12.0698
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
100
+ 53u
99
+ ··· + 7u + 1
c
2
, c
4
u
100
− 7u
99
+ ··· + 7u − 1
c
3
, c
7
u
100
− 2u
99
+ ··· + 64u + 32
c
5
, c
10
u
100
− 2u
99
+ ··· + 256u − 64
c
6
u
100
− 36u
99
+ ··· − 27136u + 1024
c
8
, c
9
, c
12
u
100
− 8u
99
+ ··· + 2u + 1
c
11
u
100
+ 42u
99
+ ··· + 49152u + 4096
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
100
− 5y
99
+ ··· − 47y + 1
c
2
, c
4
y
100
− 53y
99
+ ··· − 7y + 1
c
3
, c
7
y
100
− 36y
99
+ ··· − 27136y + 1024
c
5
, c
10
y
100
+ 42y
99
+ ··· + 49152y + 4096
c
6
y
100
+ 48y
99
+ ··· − 43646976y + 1048576
c
8
, c
9
, c
12
y
100
− 88y
99
+ ··· + 50y + 1
c
11
y
100
+ 22y
99
+ ··· + 461373440y + 16777216
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.792365 + 0.583090I
a = −0.108287 − 1.200450I
b = 0.930875 − 0.648990I
−4.34285 − 5.74414I 0
u = 0.792365 − 0.583090I
a = −0.108287 + 1.200450I
b = 0.930875 + 0.648990I
−4.34285 + 5.74414I 0
u = 0.916971 + 0.462976I
a = −0.49303 − 1.44425I
b = 0.631449 − 0.855660I
−4.67169 + 1.91587I 0
u = 0.916971 − 0.462976I
a = −0.49303 + 1.44425I
b = 0.631449 + 0.855660I
−4.67169 − 1.91587I 0
u = 0.854924 + 0.457908I
a = −0.197120 + 0.880397I
b = 0.740168 + 0.665579I
−4.91605 − 0.63546I 0
u = 0.854924 − 0.457908I
a = −0.197120 − 0.880397I
b = 0.740168 − 0.665579I
−4.91605 + 0.63546I 0
u = 0.985240 + 0.468511I
a = −0.090625 − 0.324021I
b = −0.994121 − 0.572049I
−0.62795 + 2.80874I 0
u = 0.985240 − 0.468511I
a = −0.090625 + 0.324021I
b = −0.994121 + 0.572049I
−0.62795 − 2.80874I 0
u = 0.245788 + 0.866914I
a = −0.97785 − 1.13640I
b = 1.096380 − 0.741421I
−1.10857 − 12.68640I 0
u = 0.245788 − 0.866914I
a = −0.97785 + 1.13640I
b = 1.096380 + 0.741421I
−1.10857 + 12.68640I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.10155
a = −3.46719
b = 0.399241
−3.66615 0
u = 0.981965 + 0.530171I
a = 0.362459 + 0.478732I
b = 1.057480 + 0.710417I
−3.35755 + 7.75902I 0
u = 0.981965 − 0.530171I
a = 0.362459 − 0.478732I
b = 1.057480 − 0.710417I
−3.35755 − 7.75902I 0
u = 1.109740 + 0.184312I
a = 0.91419 + 1.42574I
b = 0.008956 + 0.667628I
−2.33193 − 0.86861I 0
u = 1.109740 − 0.184312I
a = 0.91419 − 1.42574I
b = 0.008956 − 0.667628I
−2.33193 + 0.86861I 0
u = 0.366611 + 0.787435I
a = 0.320115 − 0.066003I
b = 0.851525 + 0.600589I
−3.05189 + 0.94281I 0
u = 0.366611 − 0.787435I
a = 0.320115 + 0.066003I
b = 0.851525 − 0.600589I
−3.05189 − 0.94281I 0
u = 0.225159 + 0.838843I
a = 1.14281 + 1.01802I
b = −1.069060 + 0.620828I
1.70469 − 7.47855I 0
u = 0.225159 − 0.838843I
a = 1.14281 − 1.01802I
b = −1.069060 − 0.620828I
1.70469 + 7.47855I 0
u = 0.725807 + 0.461764I
a = 0.402301 + 0.983247I
b = −0.701413 + 0.531818I
−1.60708 − 1.65045I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.725807 − 0.461764I
a = 0.402301 − 0.983247I
b = −0.701413 − 0.531818I
−1.60708 + 1.65045I 0
u = 0.248644 + 0.814575I
a = 0.208663 + 0.177564I
b = 0.626377 + 0.951799I
−2.59413 − 6.47615I 0
u = 0.248644 − 0.814575I
a = 0.208663 − 0.177564I
b = 0.626377 − 0.951799I
−2.59413 + 6.47615I 0
u = 0.261461 + 0.787835I
a = −1.45679 − 1.28675I
b = 0.854513 − 0.596814I
−3.04441 − 3.78909I 0
u = 0.261461 − 0.787835I
a = −1.45679 + 1.28675I
b = 0.854513 + 0.596814I
−3.04441 + 3.78909I 0
u = 1.151430 + 0.362450I
a = 0.074242 + 0.848861I
b = −1.113450 − 0.084513I
1.85816 + 1.15737I 0
u = 1.151430 − 0.362450I
a = 0.074242 − 0.848861I
b = −1.113450 + 0.084513I
1.85816 − 1.15737I 0
u = 0.096928 + 0.785410I
a = 1.335070 + 0.123554I
b = −1.190920 + 0.174139I
5.07427 − 5.31122I 0
u = 0.096928 − 0.785410I
a = 1.335070 − 0.123554I
b = −1.190920 − 0.174139I
5.07427 + 5.31122I 0
u = 0.246130 + 0.725103I
a = −0.0848543 − 0.0498703I
b = −0.415582 − 0.737311I
−0.10772 − 2.32956I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.246130 − 0.725103I
a = −0.0848543 + 0.0498703I
b = −0.415582 + 0.737311I
−0.10772 + 2.32956I 0
u = 0.463614 + 0.601800I
a = 0.012853 + 0.348824I
b = −0.667970 + 0.009377I
−0.89045 − 2.01572I 0. + 5.74366I
u = 0.463614 − 0.601800I
a = 0.012853 − 0.348824I
b = −0.667970 − 0.009377I
−0.89045 + 2.01572I 0. − 5.74366I
u = −1.233550 + 0.137329I
a = −0.191271 + 0.766083I
b = −1.174580 + 0.588727I
−2.36040 − 4.80176I 0
u = −1.233550 − 0.137329I
a = −0.191271 − 0.766083I
b = −1.174580 − 0.588727I
−2.36040 + 4.80176I 0
u = 0.037895 + 0.743132I
a = −1.42538 + 0.35004I
b = 1.181760 + 0.045592I
5.34208 − 0.12901I 4.42196 + 0.I
u = 0.037895 − 0.743132I
a = −1.42538 − 0.35004I
b = 1.181760 − 0.045592I
5.34208 + 0.12901I 4.42196 + 0.I
u = 1.222230 + 0.325361I
a = −0.06233 − 1.43523I
b = 1.128440 − 0.155903I
1.69954 − 3.74158I 0
u = 1.222230 − 0.325361I
a = −0.06233 + 1.43523I
b = 1.128440 + 0.155903I
1.69954 + 3.74158I 0
u = −1.252200 + 0.185808I
a = −0.010517 − 0.443621I
b = 1.172560 − 0.409152I
−0.341204 + 0.562695I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.252200 − 0.185808I
a = −0.010517 + 0.443621I
b = 1.172560 + 0.409152I
−0.341204 − 0.562695I 0
u = 1.287280 + 0.148947I
a = 1.36344 + 0.99627I
b = 0.524112 + 0.620549I
−2.83286 − 0.52713I 0
u = 1.287280 − 0.148947I
a = 1.36344 − 0.99627I
b = 0.524112 − 0.620549I
−2.83286 + 0.52713I 0
u = 1.31120
a = 1.32824
b = 0.620006
−2.89582 0
u = −1.303090 + 0.182442I
a = 0.070720 − 1.309680I
b = −0.360096 − 0.985799I
−5.02002 + 0.85235I 0
u = −1.303090 − 0.182442I
a = 0.070720 + 1.309680I
b = −0.360096 + 0.985799I
−5.02002 − 0.85235I 0
u = −1.293320 + 0.293444I
a = −0.168265 + 0.657605I
b = 1.246390 + 0.043739I
1.19623 + 3.85652I 0
u = −1.293320 − 0.293444I
a = −0.168265 − 0.657605I
b = 1.246390 − 0.043739I
1.19623 − 3.85652I 0
u = 1.324190 + 0.195201I
a = 0.33756 + 2.77633I
b = −0.812746 + 0.636934I
−5.93011 − 1.80289I 0
u = 1.324190 − 0.195201I
a = 0.33756 − 2.77633I
b = −0.812746 − 0.636934I
−5.93011 + 1.80289I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.332070 + 0.204154I
a = 0.957051 + 0.408621I
b = −0.885139 + 0.235664I
−6.07717 + 3.20988I 0
u = −1.332070 − 0.204154I
a = 0.957051 − 0.408621I
b = −0.885139 − 0.235664I
−6.07717 − 3.20988I 0
u = 1.331170 + 0.220010I
a = −1.62138 − 1.30155I
b = −0.642291 − 0.912589I
−5.58043 − 4.45730I 0
u = 1.331170 − 0.220010I
a = −1.62138 + 1.30155I
b = −0.642291 + 0.912589I
−5.58043 + 4.45730I 0
u = −1.333540 + 0.243178I
a = −0.386912 + 1.140080I
b = 0.045137 + 0.949523I
−4.05693 + 5.10453I 0
u = −1.333540 − 0.243178I
a = −0.386912 − 1.140080I
b = 0.045137 − 0.949523I
−4.05693 − 5.10453I 0
u = 1.332280 + 0.250714I
a = 0.00784 − 2.48123I
b = 1.028910 − 0.614240I
−1.40402 − 5.45414I 0
u = 1.332280 − 0.250714I
a = 0.00784 + 2.48123I
b = 1.028910 + 0.614240I
−1.40402 + 5.45414I 0
u = −0.170952 + 0.613820I
a = 1.25570 − 1.69291I
b = −1.093770 − 0.670282I
0.65018 + 7.34518I 0.51895 − 5.45269I
u = −0.170952 − 0.613820I
a = 1.25570 + 1.69291I
b = −1.093770 + 0.670282I
0.65018 − 7.34518I 0.51895 + 5.45269I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.323970 + 0.324415I
a = 0.183042 − 1.129600I
b = −1.247840 − 0.244639I
0.61856 + 9.30284I 0
u = −1.323970 − 0.324415I
a = 0.183042 + 1.129600I
b = −1.247840 + 0.244639I
0.61856 − 9.30284I 0
u = −0.099531 + 0.621357I
a = −1.48635 + 1.42762I
b = 1.060360 + 0.506724I
3.11950 + 2.26469I 3.95815 − 1.35279I
u = −0.099531 − 0.621357I
a = −1.48635 − 1.42762I
b = 1.060360 − 0.506724I
3.11950 − 2.26469I 3.95815 + 1.35279I
u = 0.113794 + 0.615400I
a = 0.185943 + 0.047421I
b = 0.088754 − 0.783282I
0.49975 − 1.97192I 0.59201 + 5.18081I
u = 0.113794 − 0.615400I
a = 0.185943 − 0.047421I
b = 0.088754 + 0.783282I
0.49975 + 1.97192I 0.59201 − 5.18081I
u = 1.377100 + 0.142626I
a = −1.83734 − 0.89104I
b = −0.884984 − 0.635023I
−5.70432 + 3.16921I 0
u = 1.377100 − 0.142626I
a = −1.83734 + 0.89104I
b = −0.884984 + 0.635023I
−5.70432 − 3.16921I 0
u = 1.364170 + 0.252445I
a = −0.18857 + 2.63975I
b = −1.073640 + 0.734262I
−4.22710 − 10.53650I 0
u = 1.364170 − 0.252445I
a = −0.18857 − 2.63975I
b = −1.073640 − 0.734262I
−4.22710 + 10.53650I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.39739 + 0.30031I
a = −0.952776 + 0.849121I
b = −0.476545 + 0.876372I
−5.32452 + 6.07526I 0
u = −1.39739 − 0.30031I
a = −0.952776 − 0.849121I
b = −0.476545 − 0.876372I
−5.32452 − 6.07526I 0
u = −1.40340 + 0.34734I
a = 0.28718 − 2.05993I
b = −1.100920 − 0.667509I
−3.46457 + 11.75370I 0
u = −1.40340 − 0.34734I
a = 0.28718 + 2.05993I
b = −1.100920 + 0.667509I
−3.46457 − 11.75370I 0
u = −1.41011 + 0.31923I
a = −0.63289 + 2.12092I
b = 0.931488 + 0.614497I
−8.35832 + 7.79358I 0
u = −1.41011 − 0.31923I
a = −0.63289 − 2.12092I
b = 0.931488 − 0.614497I
−8.35832 − 7.79358I 0
u = −1.40968 + 0.33237I
a = 1.20654 − 0.93297I
b = 0.655003 − 1.003640I
−7.86542 + 10.61720I 0
u = −1.40968 − 0.33237I
a = 1.20654 + 0.93297I
b = 0.655003 + 1.003640I
−7.86542 − 10.61720I 0
u = −0.070844 + 0.542854I
a = −0.663591 − 0.173609I
b = −0.512497 + 0.878097I
−1.11676 + 1.63882I −1.15180 − 1.38360I
u = −0.070844 − 0.542854I
a = −0.663591 + 0.173609I
b = −0.512497 − 0.878097I
−1.11676 − 1.63882I −1.15180 + 1.38360I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.41825 + 0.35738I
a = −0.19419 + 2.22344I
b = 1.111790 + 0.773357I
−6.3975 + 17.0949I 0
u = −1.41825 − 0.35738I
a = −0.19419 − 2.22344I
b = 1.111790 − 0.773357I
−6.3975 − 17.0949I 0
u = −1.44935 + 0.20132I
a = −0.689559 − 0.441917I
b = −0.595033 − 0.126320I
−7.03499 + 4.85145I 0
u = −1.44935 − 0.20132I
a = −0.689559 + 0.441917I
b = −0.595033 + 0.126320I
−7.03499 − 4.85145I 0
u = −1.47182 + 0.03699I
a = −0.69034 − 1.63645I
b = −0.845947 − 0.756360I
−8.89073 + 2.84281I 0
u = −1.47182 − 0.03699I
a = −0.69034 + 1.63645I
b = −0.845947 + 0.756360I
−8.89073 − 2.84281I 0
u = −1.45081 + 0.29045I
a = 1.203110 − 0.440312I
b = 0.764537 − 0.621264I
−8.88672 + 2.93045I 0
u = −1.45081 − 0.29045I
a = 1.203110 + 0.440312I
b = 0.764537 + 0.621264I
−8.88672 − 2.93045I 0
u = −1.48199 + 0.00967I
a = 0.60989 − 1.90109I
b = 0.811592 − 0.838116I
−12.66580 + 1.42958I 0
u = −1.48199 − 0.00967I
a = 0.60989 + 1.90109I
b = 0.811592 + 0.838116I
−12.66580 − 1.42958I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.51208 + 0.04921I
a = 0.94033 + 1.66888I
b = 0.947379 + 0.764253I
−12.2192 + 7.4080I 0
u = −1.51208 − 0.04921I
a = 0.94033 − 1.66888I
b = 0.947379 − 0.764253I
−12.2192 − 7.4080I 0
u = 0.023033 + 0.467596I
a = 2.55414 − 1.74263I
b = −0.675269 − 0.423151I
−1.65128 − 0.65806I −0.515801 − 1.165772I
u = 0.023033 − 0.467596I
a = 2.55414 + 1.74263I
b = −0.675269 + 0.423151I
−1.65128 + 0.65806I −0.515801 + 1.165772I
u = −0.299051 + 0.324781I
a = −1.50249 − 0.37524I
b = −0.998992 + 0.562705I
−0.44144 − 4.99052I 1.47251 + 5.10258I
u = −0.299051 − 0.324781I
a = −1.50249 + 0.37524I
b = −0.998992 − 0.562705I
−0.44144 + 4.99052I 1.47251 − 5.10258I
u = −0.240767 + 0.153669I
a = 2.02139 + 0.62079I
b = 0.898531 − 0.269343I
1.51367 − 0.61388I 6.21394 + 0.64261I
u = −0.240767 − 0.153669I
a = 2.02139 − 0.62079I
b = 0.898531 + 0.269343I
1.51367 + 0.61388I 6.21394 − 0.64261I
u = 0.065460 + 0.176095I
a = 4.22561 − 2.33746I
b = −0.371284 − 0.481806I
−1.77841 − 0.66560I −4.00156 − 1.15467I
u = 0.065460 − 0.176095I
a = 4.22561 + 2.33746I
b = −0.371284 + 0.481806I
−1.77841 + 0.66560I −4.00156 + 1.15467I
14
II. I
u
2
= h2a
5
− 2a
4
+ 7a
3
− 5a
2
+ 3b + a − 4, a
6
+ 4a
4
+ a
3
+ 4a
2
+ 1, u − 1i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
1
a
9
=
1
1
a
1
=
−1
0
a
4
=
a
−
2
3
a
5
+
2
3
a
4
+ ··· −
1
3
a +
4
3
a
10
=
0
1
a
7
=
2
3
a
5
+
1
3
a
4
+ ··· +
4
3
a +
5
3
2
3
a
5
+
1
3
a
4
+ ··· +
4
3
a +
5
3
a
3
=
1
3
a
5
−
1
3
a
4
+ ··· −
1
3
a −
2
3
−
1
3
a
5
+
1
3
a
4
+ ··· −
5
3
a +
2
3
a
2
=
1
3
a
5
−
1
3
a
4
+ ··· −
1
3
a −
2
3
a
5
+ 3a
3
+ 2a
2
+ a + 1
a
6
=
0
2
3
a
5
+
1
3
a
4
+ ··· +
4
3
a +
5
3
a
11
=
0
1
a
5
=
0
2
3
a
5
+
1
3
a
4
+ ··· +
4
3
a +
5
3
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4a
5
− a
4
− 12a
3
− 8a
2
− 4a − 4
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1
c
2
, c
7
u
6
+ u
5
− u
4
− 2u
3
+ u + 1
c
3
, c
4
u
6
− u
5
− u
4
+ 2u
3
− u + 1
c
5
, c
10
, c
11
u
6
c
6
u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1
c
8
, c
9
(u − 1)
6
c
12
(u + 1)
6
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1
c
2
, c
3
, c
4
c
7
y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1
c
5
, c
10
, c
11
y
6
c
8
, c
9
, c
12
(y − 1)
6
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −0.341164 + 0.940004I
b = −1.073950 + 0.558752I
−1.64493 − 5.69302I −3.10838 + 7.09196I
u = 1.00000
a = −0.341164 − 0.940004I
b = −1.073950 − 0.558752I
−1.64493 + 5.69302I −3.10838 − 7.09196I
u = 1.00000
a = 0.084211 + 0.566250I
b = 1.002190 + 0.295542I
0.245672 + 0.924305I −1.11831 − 1.11590I
u = 1.00000
a = 0.084211 − 0.566250I
b = 1.002190 − 0.295542I
0.245672 − 0.924305I −1.11831 + 1.11590I
u = 1.00000
a = 0.25695 + 1.72779I
b = −0.428243 + 0.664531I
−3.53554 + 0.92430I −5.77331 + 0.83820I
u = 1.00000
a = 0.25695 − 1.72779I
b = −0.428243 − 0.664531I
−3.53554 − 0.92430I −5.77331 − 0.83820I
18
III. I
u
3
= hb, −u
2
+ a − u + 1, u
5
+ u
4
− 2u
3
− u
2
+ u − 1i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
9
=
1
u
2
a
1
=
−u
−u
3
+ u
a
4
=
u
2
+ u − 1
0
a
10
=
−u
2
+ 1
−u
4
+ 2u
2
a
7
=
1
0
a
3
=
u
2
+ u − 1
0
a
2
=
u
2
− 1
−u
3
+ u
a
6
=
1
0
a
11
=
−u
4
+ u
2
+ 1
−u
4
+ 2u
2
a
5
=
u
u
3
− u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −2u
4
− 5u
3
+ 2u
2
+ 8u − 10
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
5
c
3
, c
6
, c
7
u
5
c
4
(u + 1)
5
c
5
u
5
− u
4
+ 2u
3
− u
2
+ u − 1
c
8
, c
9
u
5
+ u
4
− 2u
3
− u
2
+ u − 1
c
10
u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1
c
11
u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1
c
12
u
5
− u
4
− 2u
3
+ u
2
+ u + 1
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y − 1)
5
c
3
, c
6
, c
7
y
5
c
5
, c
10
y
5
+ 3y
4
+ 4y
3
+ y
2
− y − 1
c
8
, c
9
, c
12
y
5
− 5y
4
+ 8y
3
− 3y
2
− y − 1
c
11
y
5
− y
4
+ 8y
3
− 3y
2
+ 3y − 1
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.21774
a = 1.70062
b = 0
−4.04602 −10.7190
u = 0.309916 + 0.549911I
a = −0.896438 + 0.890762I
b = 0
−1.97403 − 1.53058I −6.52924 + 5.40154I
u = 0.309916 − 0.549911I
a = −0.896438 − 0.890762I
b = 0
−1.97403 + 1.53058I −6.52924 − 5.40154I
u = −1.41878 + 0.21917I
a = −0.453870 − 0.402731I
b = 0
−7.51750 + 4.40083I −11.11126 − 1.16747I
u = −1.41878 − 0.21917I
a = −0.453870 + 0.402731I
b = 0
−7.51750 − 4.40083I −11.11126 + 1.16747I
22
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)
5
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
· (u
100
+ 53u
99
+ ··· + 7u + 1)
c
2
((u − 1)
5
)(u
6
+ u
5
+ ··· + u + 1)(u
100
− 7u
99
+ ··· + 7u − 1)
c
3
u
5
(u
6
− u
5
+ ··· − u + 1)(u
100
− 2u
99
+ ··· + 64u + 32)
c
4
((u + 1)
5
)(u
6
− u
5
+ ··· − u + 1)(u
100
− 7u
99
+ ··· + 7u − 1)
c
5
u
6
(u
5
− u
4
+ ··· + u − 1)(u
100
− 2u
99
+ ··· + 256u − 64)
c
6
u
5
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
· (u
100
− 36u
99
+ ··· − 27136u + 1024)
c
7
u
5
(u
6
+ u
5
+ ··· + u + 1)(u
100
− 2u
99
+ ··· + 64u + 32)
c
8
, c
9
((u − 1)
6
)(u
5
+ u
4
+ ··· + u − 1)(u
100
− 8u
99
+ ··· + 2u + 1)
c
10
u
6
(u
5
+ u
4
+ ··· + u + 1)(u
100
− 2u
99
+ ··· + 256u − 64)
c
11
u
6
(u
5
+ 3u
4
+ ··· − u − 1)(u
100
+ 42u
99
+ ··· + 49152u + 4096)
c
12
((u + 1)
6
)(u
5
− u
4
+ ··· + u + 1)(u
100
− 8u
99
+ ··· + 2u + 1)
23
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y − 1)
5
)(y
6
+ y
5
+ ··· + 3y + 1)(y
100
− 5y
99
+ ··· − 47y + 1)
c
2
, c
4
(y − 1)
5
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
· (y
100
− 53y
99
+ ··· − 7y + 1)
c
3
, c
7
y
5
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
· (y
100
− 36y
99
+ ··· − 27136y + 1024)
c
5
, c
10
y
6
(y
5
+ 3y
4
+ ··· − y − 1)(y
100
+ 42y
99
+ ··· + 49152y + 4096)
c
6
y
5
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
· (y
100
+ 48y
99
+ ··· − 43646976y + 1048576)
c
8
, c
9
, c
12
((y − 1)
6
)(y
5
− 5y
4
+ ··· − y − 1)(y
100
− 88y
99
+ ··· + 50y + 1)
c
11
y
6
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y − 1)
· (y
100
+ 22y
99
+ ··· + 461373440y + 16777216)
24
