12n
0213
(K12n
0213
)
A knot diagram
1
Linearized knot diagam
3 5 7 2 11 9 3 12 6 1 7 10
Solving Sequence
3,7 8,12
9 6 11 5 2 1 4 10
c
7
c
8
c
6
c
11
c
5
c
2
c
1
c
4
c
10
c
3
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−4.59949 × 10
269
u
80
+ 6.86481 × 10
269
u
79
+ ··· + 5.51786 × 10
269
b + 2.33003 × 10
272
,
− 2.46814 × 10
269
u
80
+ 3.35212 × 10
269
u
79
+ ··· + 1.10357 × 10
270
a + 1.23485 × 10
272
,
u
81
− 2u
80
+ ··· + 128u + 256i
I
u
2
= hb, −9u
4
+ 4u
3
− 3u
2
+ 17a + 18u − 1, u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1i
I
v
1
= ha, −941v
7
− 2551v
6
− 1791v
5
+ 6184v
4
+ 16309v
3
− 15249v
2
+ 887b − 4192v + 1842,
v
8
+ 2v
7
− 8v
5
− 13v
4
+ 28v
3
− 7v
2
− 3v + 1i
* 3 irreducible components of dim
C
= 0, with total 94 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−4.60 × 10
269
u
80
+ 6.86 × 10
269
u
79
+ · · · + 5.52 × 10
269
b + 2.33 ×
10
272
, −2.47 × 10
269
u
80
+ 3.35 × 10
269
u
79
+ · · · + 1.10 × 10
270
a + 1.23 ×
10
272
, u
81
− 2u
80
+ · · · + 128u + 256i
(i) Arc colorings
a
3
=
0
u
a
7
=
1
0
a
8
=
1
−u
2
a
12
=
0.223650u
80
− 0.303752u
79
+ ··· − 220.646u − 111.896
0.833564u
80
− 1.24411u
79
+ ··· − 1041.50u − 422.270
a
9
=
0.0640486u
80
− 0.0983033u
79
+ ··· − 107.977u − 39.3161
−0.588758u
80
+ 0.829945u
79
+ ··· + 564.671u + 265.326
a
6
=
−0.0674337u
80
+ 0.135096u
79
+ ··· + 187.141u + 50.7879
0.563979u
80
− 0.802383u
79
+ ··· − 556.962u − 256.795
a
11
=
1.05721u
80
− 1.54786u
79
+ ··· − 1262.14u − 534.166
0.833564u
80
− 1.24411u
79
+ ··· − 1041.50u − 422.270
a
5
=
0.314943u
80
− 0.447399u
79
+ ··· − 386.680u − 179.586
0.697460u
80
− 1.02573u
79
+ ··· − 848.797u − 360.306
a
2
=
0.382518u
80
− 0.578331u
79
+ ··· − 462.117u − 180.720
0.697460u
80
− 1.02573u
79
+ ··· − 848.797u − 360.306
a
1
=
0.382518u
80
− 0.578331u
79
+ ··· − 462.117u − 180.720
0.598651u
80
− 0.876596u
79
+ ··· − 726.974u − 312.510
a
4
=
u
u
a
10
=
0.412932u
80
− 0.594022u
79
+ ··· − 454.675u − 197.166
−0.598651u
80
+ 0.876596u
79
+ ··· + 726.974u + 312.510
(ii) Obstruction class = −1
(iii) Cusp Shapes = −1.57477u
80
+ 2.25832u
79
+ ··· + 1490.53u + 646.531
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
81
+ 36u
80
+ ··· + 29u + 1
c
2
, c
4
u
81
− 10u
80
+ ··· − 13u + 1
c
3
, c
7
u
81
− 2u
80
+ ··· + 128u + 256
c
5
17(17u
81
− 14u
80
+ ··· − 259698u + 23437)
c
6
, c
9
u
81
− 3u
80
+ ··· + 3u − 1
c
8
17(17u
81
− 148u
80
+ ··· − 626508u − 174339)
c
10
, c
12
u
81
− 7u
80
+ ··· + 339u − 289
c
11
u
81
− 2u
80
+ ··· − 32096u + 9248
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
81
+ 28y
80
+ ··· + 6913y −1
c
2
, c
4
y
81
− 36y
80
+ ··· + 29y −1
c
3
, c
7
y
81
− 48y
80
+ ··· + 2080768y −65536
c
5
289(289y
81
+ 19082y
80
+ ··· − 6.59115 × 10
9
y −5.49293 × 10
8
)
c
6
, c
9
y
81
+ 45y
80
+ ··· + 5y −1
c
8
289(289y
81
− 4428y
80
+ ··· − 1.69694 × 10
11
y −3.03941 × 10
10
)
c
10
, c
12
y
81
− 43y
80
+ ··· + 4014687y −83521
c
11
y
81
+ 30y
80
+ ··· − 1164952064y −85525504
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.917288 + 0.136182I
a = −1.80406 − 1.65669I
b = 0.466096 + 1.065420I
1.75099 − 2.26560I 0
u = 0.917288 − 0.136182I
a = −1.80406 + 1.65669I
b = 0.466096 − 1.065420I
1.75099 + 2.26560I 0
u = 0.120668 + 1.075100I
a = 0.110583 − 0.334996I
b = −0.63907 − 1.32827I
3.50365 − 4.45577I 0
u = 0.120668 − 1.075100I
a = 0.110583 + 0.334996I
b = −0.63907 + 1.32827I
3.50365 + 4.45577I 0
u = −1.065120 + 0.201662I
a = 0.13685 − 1.63080I
b = 0.90356 + 1.59497I
−0.801342 − 0.587804I 0
u = −1.065120 − 0.201662I
a = 0.13685 + 1.63080I
b = 0.90356 − 1.59497I
−0.801342 + 0.587804I 0
u = 1.102270 + 0.086046I
a = 0.731098 + 0.138738I
b = −1.77507 + 0.10621I
2.29933 + 2.90155I 0
u = 1.102270 − 0.086046I
a = 0.731098 − 0.138738I
b = −1.77507 − 0.10621I
2.29933 − 2.90155I 0
u = 0.377849 + 1.055930I
a = −0.042987 + 0.341087I
b = −0.154093 + 1.058040I
2.93287 − 0.15502I 0
u = 0.377849 − 1.055930I
a = −0.042987 − 0.341087I
b = −0.154093 − 1.058040I
2.93287 + 0.15502I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.124380 + 0.061386I
a = 0.045693 − 0.667032I
b = 1.263870 + 0.473188I
0.245536 − 0.603566I 0
u = −1.124380 − 0.061386I
a = 0.045693 + 0.667032I
b = 1.263870 − 0.473188I
0.245536 + 0.603566I 0
u = 1.109070 + 0.299410I
a = −0.44786 − 1.55704I
b = 0.27630 + 1.76877I
−1.06769 + 4.07791I 0
u = 1.109070 − 0.299410I
a = −0.44786 + 1.55704I
b = 0.27630 − 1.76877I
−1.06769 − 4.07791I 0
u = −0.304908 + 0.772829I
a = 1.70493 − 1.90308I
b = 1.263410 + 0.370125I
−1.76648 + 3.44608I −11.81203 − 6.71131I
u = −0.304908 − 0.772829I
a = 1.70493 + 1.90308I
b = 1.263410 − 0.370125I
−1.76648 − 3.44608I −11.81203 + 6.71131I
u = 0.037140 + 0.801194I
a = 0.424195 + 0.072722I
b = 0.321351 − 0.451413I
−0.644523 + 1.154210I −7.22358 − 5.30161I
u = 0.037140 − 0.801194I
a = 0.424195 − 0.072722I
b = 0.321351 + 0.451413I
−0.644523 − 1.154210I −7.22358 + 5.30161I
u = 1.181860 + 0.365384I
a = −0.322573 − 0.695076I
b = 1.16061 + 1.01997I
−0.44702 + 4.44359I 0
u = 1.181860 − 0.365384I
a = −0.322573 + 0.695076I
b = 1.16061 − 1.01997I
−0.44702 − 4.44359I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.305807 + 1.214000I
a = 0.138866 + 0.073449I
b = −0.076313 − 0.714540I
−1.00073 + 1.10337I 0
u = 0.305807 − 1.214000I
a = 0.138866 − 0.073449I
b = −0.076313 + 0.714540I
−1.00073 − 1.10337I 0
u = 1.259720 + 0.183479I
a = 0.42270 − 1.68355I
b = −0.647775 + 1.125350I
−0.57249 + 7.40525I 0
u = 1.259720 − 0.183479I
a = 0.42270 + 1.68355I
b = −0.647775 − 1.125350I
−0.57249 − 7.40525I 0
u = 1.271440 + 0.091622I
a = −1.26707 + 0.81502I
b = −0.635645 + 0.052930I
3.70065 + 2.46096I 0
u = 1.271440 − 0.091622I
a = −1.26707 − 0.81502I
b = −0.635645 − 0.052930I
3.70065 − 2.46096I 0
u = −1.207870 + 0.444621I
a = 0.756760 + 0.229343I
b = −2.00837 + 0.41189I
1.14509 − 8.06770I 0
u = −1.207870 − 0.444621I
a = 0.756760 − 0.229343I
b = −2.00837 − 0.41189I
1.14509 + 8.06770I 0
u = −0.031998 + 0.705333I
a = 2.25763 + 3.03351I
b = 0.595287 − 0.236308I
−0.856013 − 0.572838I −9.77883 − 6.76958I
u = −0.031998 − 0.705333I
a = 2.25763 − 3.03351I
b = 0.595287 + 0.236308I
−0.856013 + 0.572838I −9.77883 + 6.76958I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.254380 + 0.379088I
a = 0.073419 − 0.993964I
b = 0.322122 + 0.778979I
−3.62852 − 1.44404I 0
u = −1.254380 − 0.379088I
a = 0.073419 + 0.993964I
b = 0.322122 − 0.778979I
−3.62852 + 1.44404I 0
u = −1.290060 + 0.297853I
a = −2.40362 + 0.15222I
b = −0.496430 + 0.171022I
3.27537 − 3.11183I 0
u = −1.290060 − 0.297853I
a = −2.40362 − 0.15222I
b = −0.496430 − 0.171022I
3.27537 + 3.11183I 0
u = −0.430170 + 1.261980I
a = 0.0208238 − 0.0730675I
b = 0.075154 + 0.342675I
−7.39266 − 4.46618I 0
u = −0.430170 − 1.261980I
a = 0.0208238 + 0.0730675I
b = 0.075154 − 0.342675I
−7.39266 + 4.46618I 0
u = 0.003874 + 1.341760I
a = −0.051217 + 0.133529I
b = 0.462332 − 1.087250I
1.57086 + 4.63500I 0
u = 0.003874 − 1.341760I
a = −0.051217 − 0.133529I
b = 0.462332 + 1.087250I
1.57086 − 4.63500I 0
u = 0.359544 + 1.313050I
a = −0.0563961 − 0.1200560I
b = 0.74899 + 1.24410I
0.87722 − 10.39950I 0
u = 0.359544 − 1.313050I
a = −0.0563961 + 0.1200560I
b = 0.74899 − 1.24410I
0.87722 + 10.39950I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.384620 + 0.499680I
a = −3.36808 − 2.21393I
b = −0.093782 + 0.930633I
−3.35669 − 0.78678I −13.41061 − 2.25803I
u = 0.384620 − 0.499680I
a = −3.36808 + 2.21393I
b = −0.093782 − 0.930633I
−3.35669 + 0.78678I −13.41061 + 2.25803I
u = 0.264306 + 0.568630I
a = −3.33735 − 2.02034I
b = −0.391309 + 0.555476I
−3.28994 − 0.66311I −15.7713 − 6.3444I
u = 0.264306 − 0.568630I
a = −3.33735 + 2.02034I
b = −0.391309 − 0.555476I
−3.28994 + 0.66311I −15.7713 + 6.3444I
u = −0.470622 + 1.297750I
a = 0.1152940 − 0.0121795I
b = −0.480849 + 0.922837I
−2.44609 + 4.54883I 0
u = −0.470622 − 1.297750I
a = 0.1152940 + 0.0121795I
b = −0.480849 − 0.922837I
−2.44609 − 4.54883I 0
u = −0.563976 + 0.252821I
a = 3.87049 − 0.67399I
b = −0.924450 + 0.521315I
−2.51389 − 1.66198I −7.48365 + 7.67369I
u = −0.563976 − 0.252821I
a = 3.87049 + 0.67399I
b = −0.924450 − 0.521315I
−2.51389 + 1.66198I −7.48365 − 7.67369I
u = −1.314700 + 0.516481I
a = −0.700496 + 0.794611I
b = −0.170363 − 1.259370I
7.93642 − 0.74689I 0
u = −1.314700 − 0.516481I
a = −0.700496 − 0.794611I
b = −0.170363 + 1.259370I
7.93642 + 0.74689I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.41962 + 0.28061I
a = −0.08835 − 1.53474I
b = 0.68305 + 1.74784I
9.06005 − 4.28051I 0
u = −1.41962 − 0.28061I
a = −0.08835 + 1.53474I
b = 0.68305 − 1.74784I
9.06005 + 4.28051I 0
u = 0.536208 + 0.020154I
a = 0.381909 + 0.660403I
b = −0.990257 + 0.466409I
1.74024 + 2.57808I −1.64614 − 3.99127I
u = 0.536208 − 0.020154I
a = 0.381909 − 0.660403I
b = −0.990257 − 0.466409I
1.74024 − 2.57808I −1.64614 + 3.99127I
u = 1.26179 + 0.74689I
a = −0.568701 − 0.625869I
b = −0.446841 + 1.027050I
5.50142 + 6.66477I 0
u = 1.26179 − 0.74689I
a = −0.568701 + 0.625869I
b = −0.446841 − 1.027050I
5.50142 − 6.66477I 0
u = 1.45648 + 0.17045I
a = −0.014130 − 1.109200I
b = −0.486362 + 1.176390I
5.13729 + 0.14448I 0
u = 1.45648 − 0.17045I
a = −0.014130 + 1.109200I
b = −0.486362 − 1.176390I
5.13729 − 0.14448I 0
u = −1.38541 + 0.48962I
a = −0.222539 + 1.164460I
b = −0.863918 − 1.085180I
3.90532 − 6.32227I 0
u = −1.38541 − 0.48962I
a = −0.222539 − 1.164460I
b = −0.863918 + 1.085180I
3.90532 + 6.32227I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.36979 + 0.56225I
a = 0.32140 + 1.55951I
b = 1.00900 − 1.78065I
7.48247 + 10.42400I 0
u = 1.36979 − 0.56225I
a = 0.32140 − 1.55951I
b = 1.00900 + 1.78065I
7.48247 − 10.42400I 0
u = 0.510766 + 0.040571I
a = −0.0448621 − 0.1105510I
b = 1.130170 + 0.637260I
−3.66273 − 6.35091I 0.98592 + 2.27880I
u = 0.510766 − 0.040571I
a = −0.0448621 + 0.1105510I
b = 1.130170 − 0.637260I
−3.66273 + 6.35091I 0.98592 − 2.27880I
u = −0.488226
a = 0.0864842
b = −1.20413
−7.82560 −1.06680
u = −0.460537
a = 2.90679
b = −0.378026
−2.10956 0.570870
u = 1.43085 + 0.59706I
a = 0.225520 + 1.054550I
b = 0.617156 − 1.185330I
2.95577 + 5.59636I 0
u = 1.43085 − 0.59706I
a = 0.225520 − 1.054550I
b = 0.617156 + 1.185330I
2.95577 − 5.59636I 0
u = −1.34748 + 0.77249I
a = 0.341891 − 1.108690I
b = 0.88792 + 1.14316I
0.44420 − 11.92600I 0
u = −1.34748 − 0.77249I
a = 0.341891 + 1.108690I
b = 0.88792 − 1.14316I
0.44420 + 11.92600I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.37337 + 0.74737I
a = −0.47636 − 1.44039I
b = −1.00899 + 1.43140I
4.1305 + 17.6948I 0
u = 1.37337 − 0.74737I
a = −0.47636 + 1.44039I
b = −1.00899 − 1.43140I
4.1305 − 17.6948I 0
u = −1.47814 + 0.54713I
a = −0.19095 + 1.42666I
b = −0.82247 − 1.43998I
6.48435 − 11.27690I 0
u = −1.47814 − 0.54713I
a = −0.19095 − 1.42666I
b = −0.82247 + 1.43998I
6.48435 + 11.27690I 0
u = 1.52599 + 0.50100I
a = 0.477540 + 0.885654I
b = 0.108340 − 1.030180I
6.76050 + 2.10600I 0
u = 1.52599 − 0.50100I
a = 0.477540 − 0.885654I
b = 0.108340 + 1.030180I
6.76050 − 2.10600I 0
u = −1.60879 + 0.22946I
a = 0.417558 − 1.009620I
b = −0.125923 + 1.213300I
8.03820 + 4.62100I 0
u = −1.60879 − 0.22946I
a = 0.417558 + 1.009620I
b = −0.125923 − 1.213300I
8.03820 − 4.62100I 0
u = −0.218066 + 0.304864I
a = 0.49252 + 3.66787I
b = 0.425595 − 0.658071I
−0.977641 − 0.985323I −3.19724 − 0.04207I
u = −0.218066 − 0.304864I
a = 0.49252 − 3.66787I
b = 0.425595 + 0.658071I
−0.977641 + 0.985323I −3.19724 + 0.04207I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.341255
a = 1.06309
b = 0.618121
−0.986770 −9.94130
13
II. I
u
2
= hb, −9u
4
+ 4u
3
− 3u
2
+ 17a + 18u − 1, u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1i
(i) Arc colorings
a
3
=
0
u
a
7
=
1
0
a
8
=
1
−u
2
a
12
=
0.529412u
4
− 0.235294u
3
+ ··· − 1.05882u + 0.0588235
0
a
9
=
0.131488u
4
− 0.463668u
3
+ ··· − 0.910035u + 1.14533
−u
2
a
6
=
0.0622837u
4
+ 0.148789u
3
+ ··· + 0.463668u + 1.59516
−u
4
a
11
=
0.529412u
4
− 0.235294u
3
+ ··· − 1.05882u + 0.0588235
0
a
5
=
u
2
+ 1
−u
4
a
2
=
−u
4
− u
2
− 1
−u
4
a
1
=
−u
4
− u
2
− 1
−u
4
+ u
3
+ u
2
+ 1
a
4
=
u
u
a
10
=
1.52941u
4
− 0.235294u
3
+ ··· − 1.05882u + 1.05882
u
4
− u
3
− u
2
− 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
1429
289
u
4
−
3783
289
u
3
−
1128
289
u
2
−
3092
289
u −
5595
289
14
(iv) u-Polynomials at the component
15
Crossings u-Polynomials at each crossing
c
1
u
5
− 5u
4
+ 8u
3
− 3u
2
− u − 1
c
2
u
5
+ u
4
− 2u
3
− u
2
+ u − 1
c
3
u
5
− u
4
+ 2u
3
− u
2
+ u − 1
c
4
u
5
− u
4
− 2u
3
+ u
2
+ u + 1
c
5
17(17u
5
+ 32u
4
+ 18u
3
− u
2
− 4u − 1)
c
6
u
5
− 3u
4
+ 4u
3
− u
2
− u + 1
c
7
u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1
c
8
17(17u
5
− 42u
4
+ 43u
3
− 22u
2
+ 6u − 1)
c
9
u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1
c
10
(u − 1)
5
c
11
u
5
c
12
(u + 1)
5
16
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
5
− 9y
4
+ 32y
3
− 35y
2
− 5y −1
c
2
, c
4
y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1
c
3
, c
7
y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1
c
5
289(289y
5
− 412y
4
+ 252y
3
− 81y
2
+ 14y −1)
c
6
, c
9
y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1
c
8
289(289y
5
− 302y
4
+ 205y
3
− 52y
2
− 8y −1)
c
10
, c
12
(y −1)
5
c
11
y
5
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.339110 + 0.822375I
a = −0.244471 − 1.039700I
b = 0
−1.97403 + 1.53058I −12.32109 − 4.31295I
u = 0.339110 − 0.822375I
a = −0.244471 + 1.039700I
b = 0
−1.97403 − 1.53058I −12.32109 + 4.31295I
u = −0.766826
a = 1.26368
b = 0
−4.04602 −9.25800
u = −0.455697 + 1.200150I
a = 0.053809 + 0.194708I
b = 0
−7.51750 − 4.40083I −35.8077 − 9.0642I
u = −0.455697 − 1.200150I
a = 0.053809 − 0.194708I
b = 0
−7.51750 + 4.40083I −35.8077 + 9.0642I
19
III. I
v
1
= ha, −941v
7
− 2551v
6
+ · · · + 887b + 1842, v
8
+ 2v
7
− 8v
5
− 13v
4
+
28v
3
− 7v
2
− 3v + 1i
(i) Arc colorings
a
3
=
v
0
a
7
=
1
0
a
8
=
1
0
a
12
=
0
1.06088v
7
+ 2.87599v
6
+ ··· + 4.72604v − 2.07666
a
9
=
1
1.62683v
7
+ 3.57497v
6
+ ··· + 1.17926v − 3.82638
a
6
=
−1.62683v
7
− 3.57497v
6
+ ··· − 1.17926v + 4.82638
−2.38219v
7
− 5.33258v
6
+ ··· + 1.21984v + 6.70349
a
11
=
1.06088v
7
+ 2.87599v
6
+ ··· + 4.72604v − 2.07666
1.06088v
7
+ 2.87599v
6
+ ··· + 4.72604v − 2.07666
a
5
=
−0.244645v
7
− 0.242390v
6
+ ··· + 4.60090v + 1.12289
−v
7
− 2v
6
+ 8v
4
+ 13v
3
− 28v
2
+ 7v + 3
a
2
=
0.244645v
7
+ 0.242390v
6
+ ··· − 3.60090v − 1.12289
v
7
+ 2v
6
− 8v
4
− 13v
3
+ 28v
2
− 7v − 3
a
1
=
0.244645v
7
+ 0.242390v
6
+ ··· − 4.60090v − 1.12289
v
7
+ 2v
6
− 8v
4
− 13v
3
+ 28v
2
− 7v − 3
a
4
=
v
0
a
10
=
0.755355v
7
+ 1.75761v
6
+ ··· − 2.39910v − 1.87711
v
7
+ 2v
6
− 8v
4
− 13v
3
+ 28v
2
− 7v − 3
(ii) Obstruction class = 1
(iii) Cusp Shapes
=
7569
887
v
7
+
17105
887
v
6
+
3122
887
v
5
−
63760
887
v
4
−
119185
887
v
3
+
185558
887
v
2
+
17829
887
v −
42646
887
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
8
c
3
, c
7
u
8
c
4
(u + 1)
8
c
5
, c
10
u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1
c
6
u
8
− 3u
7
+ 7u
6
− 10u
5
+ 11u
4
− 10u
3
+ 6u
2
− 4u + 1
c
8
u
8
− u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1
c
9
u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1
c
11
u
8
+ u
7
− u
6
− 2u
5
+ u
4
+ 2u
3
− 2u − 1
c
12
u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y − 1)
8
c
3
, c
7
y
8
c
5
, c
10
, c
12
y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1
c
6
, c
9
y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1
c
8
, c
11
y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 1.230330 + 0.083902I
a = 0
b = −0.855237 + 0.665892I
0.51448 + 2.57849I −10.43522 − 3.68514I
v = 1.230330 − 0.083902I
a = 0
b = −0.855237 − 0.665892I
0.51448 − 2.57849I −10.43522 + 3.68514I
v = 0.370895 + 0.073482I
a = 0
b = 1.031810 + 0.655470I
−4.02461 − 6.44354I −20.0271 + 7.9066I
v = 0.370895 − 0.073482I
a = 0
b = 1.031810 − 0.655470I
−4.02461 + 6.44354I −20.0271 − 7.9066I
v = −0.337834
a = 0
b = −1.09818
−8.14766 −26.7400
v = −1.21928 + 2.03110I
a = 0
b = 0.570868 + 0.730671I
−2.68559 + 1.13123I −8.69271 + 4.28492I
v = −1.21928 − 2.03110I
a = 0
b = 0.570868 − 0.730671I
−2.68559 − 1.13123I −8.69271 − 4.28492I
v = −2.42604
a = 0
b = 0.603304
−2.48997 −21.9500
23
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
8
)(u
5
− 5u
4
+ ··· − u − 1)(u
81
+ 36u
80
+ ··· + 29u + 1)
c
2
((u − 1)
8
)(u
5
+ u
4
+ ··· + u − 1)(u
81
− 10u
80
+ ··· − 13u + 1)
c
3
u
8
(u
5
− u
4
+ ··· + u − 1)(u
81
− 2u
80
+ ··· + 128u + 256)
c
4
((u + 1)
8
)(u
5
− u
4
+ ··· + u + 1)(u
81
− 10u
80
+ ··· − 13u + 1)
c
5
289(17u
5
+ 32u
4
+ 18u
3
− u
2
− 4u − 1)
· (u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1)
· (17u
81
− 14u
80
+ ··· − 259698u + 23437)
c
6
(u
5
− 3u
4
+ 4u
3
− u
2
− u + 1)
· (u
8
− 3u
7
+ 7u
6
− 10u
5
+ 11u
4
− 10u
3
+ 6u
2
− 4u + 1)
· (u
81
− 3u
80
+ ··· + 3u − 1)
c
7
u
8
(u
5
+ u
4
+ ··· + u + 1)(u
81
− 2u
80
+ ··· + 128u + 256)
c
8
289(17u
5
− 42u
4
+ 43u
3
− 22u
2
+ 6u − 1)
· (u
8
− u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1)
· (17u
81
− 148u
80
+ ··· − 626508u − 174339)
c
9
(u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1)
· (u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1)
· (u
81
− 3u
80
+ ··· + 3u − 1)
c
10
(u − 1)
5
(u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1)
· (u
81
− 7u
80
+ ··· + 339u − 289)
c
11
u
5
(u
8
+ u
7
− u
6
− 2u
5
+ u
4
+ 2u
3
− 2u − 1)
· (u
81
− 2u
80
+ ··· − 32096u + 9248)
c
12
(u + 1)
5
(u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1)
· (u
81
− 7u
80
+ ··· + 339u − 289)
24
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y − 1)
8
(y
5
− 9y
4
+ 32y
3
− 35y
2
− 5y − 1)
· (y
81
+ 28y
80
+ ··· + 6913y − 1)
c
2
, c
4
((y − 1)
8
)(y
5
− 5y
4
+ ··· − y − 1)(y
81
− 36y
80
+ ··· + 29y − 1)
c
3
, c
7
y
8
(y
5
+ 3y
4
+ ··· − y − 1)(y
81
− 48y
80
+ ··· + 2080768y − 65536)
c
5
83521(289y
5
− 412y
4
+ 252y
3
− 81y
2
+ 14y − 1)
· (y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1)
· (289y
81
+ 19082y
80
+ ··· − 6591150616y − 549292969)
c
6
, c
9
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y − 1)
· (y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1)
· (y
81
+ 45y
80
+ ··· + 5y − 1)
c
8
83521(289y
5
− 302y
4
+ 205y
3
− 52y
2
− 8y − 1)
· (y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1)
· (289y
81
− 4428y
80
+ ··· − 169694389746y − 30394086921)
c
10
, c
12
(y − 1)
5
(y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1)
· (y
81
− 43y
80
+ ··· + 4014687y − 83521)
c
11
y
5
(y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1)
· (y
81
+ 30y
80
+ ··· − 1164952064y − 85525504)
25
