12n
0209
(K12n
0209
)
A knot diagram
1
Linearized knot diagam
3 5 7 2 10 12 3 11 1 7 9 6
Solving Sequence
8,11
9
3,12
7 4 6 1 10 5 2
c
8
c
11
c
7
c
3
c
6
c
12
c
10
c
5
c
2
c
1
, c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−5.23422 × 10
225
u
80
− 3.14728 × 10
226
u
79
+ ··· + 7.26097 × 10
226
b − 1.56109 × 10
228
,
1.52450 × 10
227
u
80
+ 8.16205 × 10
227
u
79
+ ··· + 1.04921 × 10
229
a + 3.18901 × 10
229
,
u
81
+ 7u
80
+ ··· + 339u + 289i
I
u
2
= hb, u
7
+ 2u
6
− 2u
5
− 4u
4
+ 2u
3
+ 2u
2
+ a + 2, u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1i
I
u
3
= h17a
4
− 21a
3
− 14a
2
+ 2b − 10a − 2, 17a
5
− 21a
4
− 14a
3
− 10a
2
− 3a − 1, u − 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−5.23 × 10
225
u
80
− 3.15 × 10
226
u
79
+ · · · + 7.26 × 10
226
b − 1.56 ×
10
228
, 1.52 × 10
227
u
80
+ 8.16 × 10
227
u
79
+ · · · + 1.05 × 10
229
a + 3.19 ×
10
229
, u
81
+ 7u
80
+ · · · + 339u + 289i
(i) Arc colorings
a
8
=
1
0
a
11
=
0
u
a
9
=
1
u
2
a
3
=
−0.0145300u
80
− 0.0777923u
79
+ ··· − 22.8342u − 3.03944
0.0720871u
80
+ 0.433451u
79
+ ··· + 3.99323u + 21.4997
a
12
=
−u
−u
3
+ u
a
7
=
0.0147005u
80
+ 0.0809008u
79
+ ··· − 2.31377u − 2.09026
0.0156887u
80
+ 0.119395u
79
+ ··· + 8.42077u + 7.01956
a
4
=
−0.0746670u
80
− 0.405647u
79
+ ··· − 44.6010u − 7.58701
−0.113401u
80
− 0.763523u
79
+ ··· − 3.60335u − 48.0310
a
6
=
0.0281304u
80
+ 0.170708u
79
+ ··· − 0.344505u + 3.51186
−0.00165030u
80
+ 0.00828984u
79
+ ··· + 3.99497u + 2.63202
a
1
=
0.0351087u
80
+ 0.201342u
79
+ ··· + 5.20848u + 5.81452
0.0238883u
80
+ 0.167706u
79
+ ··· + 0.366478u + 11.4771
a
10
=
−0.00904290u
80
− 0.0356816u
79
+ ··· − 5.40973u + 0.0932125
−0.0291714u
80
− 0.166685u
79
+ ··· − 3.26701u − 5.74492
a
5
=
−0.0232151u
80
− 0.118816u
79
+ ··· − 8.79210u − 5.37544
−0.0263971u
80
− 0.159410u
79
+ ··· + 3.72966u − 8.15827
a
2
=
−0.0129986u
80
− 0.114755u
79
+ ··· − 18.9004u − 15.8345
0.121360u
80
+ 0.725051u
79
+ ··· + 18.3566u + 28.5476
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.172208u
80
− 0.999000u
79
+ ··· − 8.43774u − 31.9194
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
u
81
− 2u
80
+ ··· − 32096u + 9248
c
6
, c
12
u
81
− 3u
80
+ ··· + 3u − 1
c
8
, c
11
u
81
− 7u
80
+ ··· + 339u − 289
c
9
17(17u
81
− 148u
80
+ ··· − 626508u − 174339)
c
10
17(17u
81
− 14u
80
+ ··· − 259698u + 23437)
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
y
81
+ 30y
80
+ ··· − 1164952064y −85525504
c
6
, c
12
y
81
+ 45y
80
+ ··· + 5y −1
c
8
, c
11
y
81
− 43y
80
+ ··· + 4014687y −83521
c
9
289(289y
81
− 4428y
80
+ ··· − 1.69694 × 10
11
y −3.03941 × 10
10
)
c
10
289(289y
81
+ 19082y
80
+ ··· − 6.59115 × 10
9
y −5.49293 × 10
8
)
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.917000 + 0.360308I
a = −1.078270 + 0.779634I
b = 1.254380 + 0.379088I
−3.62852 + 1.44404I 0
u = −0.917000 − 0.360308I
a = −1.078270 − 0.779634I
b = 1.254380 − 0.379088I
−3.62852 − 1.44404I 0
u = −0.111889 + 0.977557I
a = −1.355590 + 0.347160I
b = 1.38541 − 0.48962I
3.90532 − 6.32227I 0
u = −0.111889 − 0.977557I
a = −1.355590 − 0.347160I
b = 1.38541 + 0.48962I
3.90532 + 6.32227I 0
u = −0.940232 + 0.031195I
a = −0.010189 + 0.505506I
b = 0.430170 + 1.261980I
−7.39266 + 4.46618I 14.6599 − 16.9007I
u = −0.940232 − 0.031195I
a = −0.010189 − 0.505506I
b = 0.430170 − 1.261980I
−7.39266 − 4.46618I 14.6599 + 16.9007I
u = −0.371472 + 0.861519I
a = 1.261110 − 0.601092I
b = −1.45648 + 0.17045I
5.13729 − 0.14448I 0
u = −0.371472 − 0.861519I
a = 1.261110 + 0.601092I
b = −1.45648 − 0.17045I
5.13729 + 0.14448I 0
u = −0.800962 + 0.697533I
a = −0.975358 + 0.428485I
b = 1.60879 − 0.22946I
8.03820 + 4.62100I 0
u = −0.800962 − 0.697533I
a = −0.975358 − 0.428485I
b = 1.60879 + 0.22946I
8.03820 − 4.62100I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.342134 + 1.013250I
a = 0.746244 − 0.080296I
b = −0.120668 − 1.075100I
3.50365 − 4.45577I 0
u = −0.342134 − 1.013250I
a = 0.746244 + 0.080296I
b = −0.120668 + 1.075100I
3.50365 + 4.45577I 0
u = 0.892514 + 0.209012I
a = 1.48162 + 1.11275I
b = 0.031998 − 0.705333I
−0.856013 − 0.572838I 0
u = 0.892514 − 0.209012I
a = 1.48162 − 1.11275I
b = 0.031998 + 0.705333I
−0.856013 + 0.572838I 0
u = 0.895635 + 0.122019I
a = −1.93397 − 4.12821I
b = 1.290060 − 0.297853I
3.27537 − 3.11183I −8.00000 − 6.68590I
u = 0.895635 − 0.122019I
a = −1.93397 + 4.12821I
b = 1.290060 + 0.297853I
3.27537 + 3.11183I −8.00000 + 6.68590I
u = −0.839636 + 0.720962I
a = −0.96974 + 1.18828I
b = 1.314700 + 0.516481I
7.93642 + 0.74689I 0
u = −0.839636 − 0.720962I
a = −0.96974 − 1.18828I
b = 1.314700 − 0.516481I
7.93642 − 0.74689I 0
u = 1.105450 + 0.164736I
a = 0.28372 − 1.70100I
b = −0.264306 − 0.568630I
−3.28994 − 0.66311I 0
u = 1.105450 − 0.164736I
a = 0.28372 + 1.70100I
b = −0.264306 + 0.568630I
−3.28994 + 0.66311I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.020470 + 0.465233I
a = 0.350709 − 0.283567I
b = 0.470622 − 1.297750I
−2.44609 + 4.54883I 0
u = −1.020470 − 0.465233I
a = 0.350709 + 0.283567I
b = 0.470622 + 1.297750I
−2.44609 − 4.54883I 0
u = −1.000620 + 0.534124I
a = 0.72960 − 1.23645I
b = −1.26179 − 0.74689I
5.50142 + 6.66477I 0
u = −1.000620 − 0.534124I
a = 0.72960 + 1.23645I
b = −1.26179 + 0.74689I
5.50142 − 6.66477I 0
u = −0.555993 + 0.653154I
a = −0.902306 + 0.309346I
b = −0.377849 + 1.055930I
2.93287 + 0.15502I −5.05413 − 1.86046I
u = −0.555993 − 0.653154I
a = −0.902306 − 0.309346I
b = −0.377849 − 1.055930I
2.93287 − 0.15502I −5.05413 + 1.86046I
u = 1.046410 + 0.466176I
a = −3.05815 − 0.66577I
b = 0.563976 − 0.252821I
−2.51389 − 1.66198I 0
u = 1.046410 − 0.466176I
a = −3.05815 + 0.66577I
b = 0.563976 + 0.252821I
−2.51389 + 1.66198I 0
u = −0.337368 + 0.781993I
a = 2.07028 − 1.19509I
b = −0.917288 − 0.136182I
1.75099 − 2.26560I −3.42990 + 1.10505I
u = −0.337368 − 0.781993I
a = 2.07028 + 1.19509I
b = −0.917288 + 0.136182I
1.75099 + 2.26560I −3.42990 − 1.10505I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.582612 + 0.616671I
a = 0.778140 − 0.416338I
b = −1.52599 + 0.50100I
6.76050 − 2.10600I −3.77694 − 1.06020I
u = −0.582612 − 0.616671I
a = 0.778140 + 0.416338I
b = −1.52599 − 0.50100I
6.76050 + 2.10600I −3.77694 + 1.06020I
u = −1.013890 + 0.572439I
a = 0.396514 − 0.225881I
b = −0.003874 − 1.341760I
1.57086 + 4.63500I 0
u = −1.013890 − 0.572439I
a = 0.396514 + 0.225881I
b = −0.003874 + 1.341760I
1.57086 − 4.63500I 0
u = 1.152030 + 0.190177I
a = −0.407337 + 0.569974I
b = 0.218066 − 0.304864I
−0.977641 − 0.985323I 0
u = 1.152030 − 0.190177I
a = −0.407337 − 0.569974I
b = 0.218066 + 0.304864I
−0.977641 + 0.985323I 0
u = 0.971105 + 0.694183I
a = −0.589638 + 0.317515I
b = 0.304908 + 0.772829I
−1.76648 − 3.44608I 0
u = 0.971105 − 0.694183I
a = −0.589638 − 0.317515I
b = 0.304908 − 0.772829I
−1.76648 + 3.44608I 0
u = 0.303060 + 0.732514I
a = 0.632497 − 0.637842I
b = −0.536208 + 0.020154I
1.74024 − 2.57808I −1.64614 + 3.99127I
u = 0.303060 − 0.732514I
a = 0.632497 + 0.637842I
b = −0.536208 − 0.020154I
1.74024 + 2.57808I −1.64614 − 3.99127I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.035680 + 0.682829I
a = −0.796823 − 0.654771I
b = 1.124380 + 0.061386I
0.245536 + 0.603566I 0
u = 1.035680 − 0.682829I
a = −0.796823 + 0.654771I
b = 1.124380 − 0.061386I
0.245536 − 0.603566I 0
u = −0.702589 + 0.265855I
a = −0.411201 + 0.605874I
b = −0.305807 + 1.214000I
−1.00073 − 1.10337I −4.49607 − 0.18743I
u = −0.702589 − 0.265855I
a = −0.411201 − 0.605874I
b = −0.305807 − 1.214000I
−1.00073 + 1.10337I −4.49607 + 0.18743I
u = −1.130500 + 0.585115I
a = 1.40224 − 0.57524I
b = −1.259720 − 0.183479I
−0.57249 + 7.40525I 0
u = −1.130500 − 0.585115I
a = 1.40224 + 0.57524I
b = −1.259720 + 0.183479I
−0.57249 − 7.40525I 0
u = −1.116140 + 0.622717I
a = 0.992749 − 0.874868I
b = −1.43085 − 0.59706I
2.95577 + 5.59636I 0
u = −1.116140 − 0.622717I
a = 0.992749 + 0.874868I
b = −1.43085 + 0.59706I
2.95577 − 5.59636I 0
u = 0.702392 + 0.146750I
a = 2.32167 + 2.92316I
b = −1.271440 − 0.091622I
3.70065 + 2.46096I −6.55380 − 6.04709I
u = 0.702392 − 0.146750I
a = 2.32167 − 2.92316I
b = −1.271440 + 0.091622I
3.70065 − 2.46096I −6.55380 + 6.04709I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.291990 + 0.043575I
a = 1.44776 − 1.57835I
b = −0.384620 − 0.499680I
−3.35669 − 0.78678I 0
u = 1.291990 − 0.043575I
a = 1.44776 + 1.57835I
b = −0.384620 + 0.499680I
−3.35669 + 0.78678I 0
u = −0.471330 + 1.253510I
a = −1.260940 + 0.410905I
b = 1.41962 − 0.28061I
9.06005 − 4.28051I 0
u = −0.471330 − 1.253510I
a = −1.260940 − 0.410905I
b = 1.41962 + 0.28061I
9.06005 + 4.28051I 0
u = 0.787166 + 1.096680I
a = 1.126360 + 0.105606I
b = −1.102270 + 0.086046I
2.29933 − 2.90155I 0
u = 0.787166 − 1.096680I
a = 1.126360 − 0.105606I
b = −1.102270 − 0.086046I
2.29933 + 2.90155I 0
u = −1.196940 + 0.647328I
a = −0.358449 + 0.094835I
b = −0.359544 + 1.313050I
0.87722 + 10.39950I 0
u = −1.196940 − 0.647328I
a = −0.358449 − 0.094835I
b = −0.359544 − 1.313050I
0.87722 − 10.39950I 0
u = 0.617289
a = −0.857589
b = 0.341255
−0.986770 −9.94130
u = −1.268250 + 0.582299I
a = −0.955708 + 0.972461I
b = 1.34748 + 0.77249I
0.44420 + 11.92600I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.268250 − 0.582299I
a = −0.955708 − 0.972461I
b = 1.34748 − 0.77249I
0.44420 − 11.92600I 0
u = −1.38442 + 0.30949I
a = −0.1103470 − 0.0721860I
b = −0.510766 + 0.040571I
−3.66273 + 6.35091I 0
u = −1.38442 − 0.30949I
a = −0.1103470 + 0.0721860I
b = −0.510766 − 0.040571I
−3.66273 − 6.35091I 0
u = −0.32443 + 1.38328I
a = 1.191390 − 0.162158I
b = −1.36979 + 0.56225I
7.48247 − 10.42400I 0
u = −0.32443 − 1.38328I
a = 1.191390 + 0.162158I
b = −1.36979 − 0.56225I
7.48247 + 10.42400I 0
u = −1.42131
a = 0.106801
b = 0.488226
−7.82560 0
u = −1.25444 + 0.74996I
a = −1.14964 + 0.82641I
b = 1.47814 + 0.54713I
6.48435 + 11.27690I 0
u = −1.25444 − 0.74996I
a = −1.14964 − 0.82641I
b = 1.47814 − 0.54713I
6.48435 − 11.27690I 0
u = 1.34051 + 0.58473I
a = 0.691710 + 0.826704I
b = −1.181860 + 0.365384I
−0.44702 − 4.44359I 0
u = 1.34051 − 0.58473I
a = 0.691710 − 0.826704I
b = −1.181860 − 0.365384I
−0.44702 + 4.44359I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.35336 + 0.72876I
a = 1.11496 − 0.96787I
b = −1.37337 − 0.74737I
4.1305 + 17.6948I 0
u = −1.35336 − 0.72876I
a = 1.11496 + 0.96787I
b = −1.37337 + 0.74737I
4.1305 − 17.6948I 0
u = 1.11420 + 1.11195I
a = −1.120210 − 0.444761I
b = 1.207870 − 0.444621I
1.14509 − 8.06770I 0
u = 1.11420 − 1.11195I
a = −1.120210 + 0.444761I
b = 1.207870 + 0.444621I
1.14509 + 8.06770I 0
u = 1.61987 + 0.43109I
a = −0.221127 − 0.151444I
b = 1.065120 + 0.201662I
−0.801342 + 0.587804I 0
u = 1.61987 − 0.43109I
a = −0.221127 + 0.151444I
b = 1.065120 − 0.201662I
−0.801342 − 0.587804I 0
u = 1.69004 + 0.12943I
a = 0.194604 + 0.340687I
b = −1.109070 + 0.299410I
−1.06769 − 4.07791I 0
u = 1.69004 − 0.12943I
a = 0.194604 − 0.340687I
b = −1.109070 − 0.299410I
−1.06769 + 4.07791I 0
u = −0.082384 + 0.274939I
a = −1.95414 + 0.28616I
b = −0.037140 + 0.801194I
−0.644523 − 1.154210I −7.22358 + 5.30161I
u = −0.082384 − 0.274939I
a = −1.95414 − 0.28616I
b = −0.037140 − 0.801194I
−0.644523 + 1.154210I −7.22358 − 5.30161I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.146017
a = −7.23453
b = 0.460537
−2.10956 0.570870
13
II.
I
u
2
= hb, u
7
+2u
6
−2u
5
−4u
4
+2u
3
+2u
2
+a+2, u
8
+u
7
−3u
6
−2u
5
+3u
4
+2u−1i
(i) Arc colorings
a
8
=
1
0
a
11
=
0
u
a
9
=
1
u
2
a
3
=
−u
7
− 2u
6
+ 2u
5
+ 4u
4
− 2u
3
− 2u
2
− 2
0
a
12
=
−u
−u
3
+ u
a
7
=
1
0
a
4
=
−u
7
− 2u
6
+ 2u
5
+ 4u
4
− 2u
3
− 2u
2
− 2
0
a
6
=
−u
4
+ u
2
+ 1
−u
6
+ 2u
4
− u
2
a
1
=
−u
7
+ 2u
5
− 2u
−u
7
+ u
6
+ 2u
5
− 3u
4
+ 2u
2
− 2u + 1
a
10
=
u
u
a
5
=
u
7
− 2u
5
+ 2u
u
7
− u
6
− 2u
5
+ 3u
4
− 2u
2
+ 2u − 1
a
2
=
−2u
7
− 2u
6
+ 4u
5
+ 4u
4
− 2u
3
− 2u
2
− 2u − 2
−u
7
+ u
6
+ 2u
5
− 3u
4
+ 2u
2
− 2u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −u
7
− 9u
6
− u
5
+ 22u
4
− 3u
3
− 12u
2
+ 13u − 26
14
(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
9
u
8
− u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 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
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1
c
10
, c
11
u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1
c
12
u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1
15
(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
9
y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1
c
6
, c
12
y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1
c
8
, c
10
, c
11
y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.180120 + 0.268597I
a = −1.21928 − 2.03110I
b = 0
−2.68559 − 1.13123I −8.69271 − 4.28492I
u = 1.180120 − 0.268597I
a = −1.21928 + 2.03110I
b = 0
−2.68559 + 1.13123I −8.69271 + 4.28492I
u = 0.108090 + 0.747508I
a = 1.230330 − 0.083902I
b = 0
0.51448 − 2.57849I −10.43522 + 3.68514I
u = 0.108090 − 0.747508I
a = 1.230330 + 0.083902I
b = 0
0.51448 + 2.57849I −10.43522 − 3.68514I
u = −1.37100
a = −0.337834
b = 0
−8.14766 −26.7400
u = −1.334530 + 0.318930I
a = 0.370895 − 0.073482I
b = 0
−4.02461 + 6.44354I −20.0271 − 7.9066I
u = −1.334530 − 0.318930I
a = 0.370895 + 0.073482I
b = 0
−4.02461 − 6.44354I −20.0271 + 7.9066I
u = 0.463640
a = −2.42604
b = 0
−2.48997 −21.9500
17
III.
I
u
3
= h17a
4
−21a
3
−14a
2
+2b−10a−2, 17a
5
−21a
4
−14a
3
−10a
2
−3a−1, u−1i
(i) Arc colorings
a
8
=
1
0
a
11
=
0
1
a
9
=
1
1
a
3
=
a
−
17
2
a
4
+
21
2
a
3
+ 7a
2
+ 5a + 1
a
12
=
−1
0
a
7
=
−
1
2
a +
1
2
−
17
4
a
4
+
19
2
a
3
+ ··· − a −
3
2
a
4
=
−
17
4
a
4
+
21
4
a
3
+ ··· +
15
4
a +
3
4
51
8
a
4
−
63
8
a
3
−
59
8
a
2
−
9
8
a
a
6
=
−
17
4
a
4
+
19
2
a
3
+ ··· −
3
2
a − 1
−
17
4
a
4
+
19
2
a
3
+ ··· − a −
3
2
a
1
=
51
16
a
4
+
11
8
a
3
+ ··· −
47
8
a −
39
16
−1.06250a
4
+ 8.75000a
3
+ ··· − 5.25000a − 2.06250
a
10
=
1
4
a
2
−
1
2
a +
1
4
−
17
4
a
4
+
59
8
a
3
+ ··· +
5
8
a +
3
8
a
5
=
−
17
4
a
4
+
19
2
a
3
+ ··· −
3
2
a − 1
−
17
4
a
4
+
19
2
a
3
+ ··· − a −
3
2
a
2
=
17
4
a
3
−
21
4
a
2
−
13
4
a −
7
4
−11.6875a
4
+ 17.6250a
3
+ ··· + 1.87500a − 0.562500
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
1479
16
a
4
+
1075
8
a
3
+
295
4
a
2
+
37
8
a −
341
16
18
(iv) u-Polynomials at the component
19
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
u
5
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
(u − 1)
5
c
9
17(17u
5
− 42u
4
+ 43u
3
− 22u
2
+ 6u − 1)
c
10
17(17u
5
+ 32u
4
+ 18u
3
− u
2
− 4u − 1)
c
11
(u + 1)
5
c
12
u
5
− 3u
4
+ 4u
3
− u
2
− u + 1
20
21
(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
y
5
c
6
, c
12
y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1
c
8
, c
11
(y −1)
5
c
9
289(289y
5
− 302y
4
+ 205y
3
− 52y
2
− 8y −1)
c
10
289(289y
5
− 412y
4
+ 252y
3
− 81y
2
+ 14y −1)
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −0.303936 + 0.297874I
b = 0.339110 + 0.822375I
−1.97403 + 1.53058I −12.32109 − 4.31295I
u = 1.00000
a = −0.303936 − 0.297874I
b = 0.339110 − 0.822375I
−1.97403 − 1.53058I −12.32109 + 4.31295I
u = 1.00000
a = −0.015358 + 0.416047I
b = −0.455697 + 1.200150I
−7.51750 − 4.40083I −35.8077 − 9.0642I
u = 1.00000
a = −0.015358 − 0.416047I
b = −0.455697 − 1.200150I
−7.51750 + 4.40083I −35.8077 + 9.0642I
u = 1.00000
a = 1.87388
b = −0.766826
−4.04602 −9.25800
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
u
5
(u
8
− u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1)
· (u
81
− 2u
80
+ ··· − 32096u + 9248)
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
(u − 1)
5
(u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1)
· (u
81
− 7u
80
+ ··· + 339u − 289)
c
9
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
10
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
11
(u + 1)
5
(u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1)
· (u
81
− 7u
80
+ ··· + 339u − 289)
c
12
(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)
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
y
5
(y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1)
· (y
81
+ 30y
80
+ ··· − 1164952064y −85525504)
c
6
, c
12
(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
, c
11
(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
9
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
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)
25
