12n
0177
(K12n
0177
)
A knot diagram
1
Linearized knot diagam
3 5 8 2 9 11 3 6 5 12 7 10
Solving Sequence
6,11 3,7
8 4 9 12 5 2 10 1
c
6
c
7
c
3
c
8
c
11
c
5
c
2
c
10
c
12
c
1
, c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h5.55413 × 10
18
u
43
− 1.55873 × 10
20
u
42
+ ··· + 7.63795 × 10
20
b + 1.57862 × 10
18
,
− 5.19595 × 10
20
u
43
− 8.80516 × 10
20
u
42
+ ··· + 7.63795 × 10
20
a + 1.42510 × 10
21
, u
44
+ 2u
43
+ ··· + u − 1i
I
u
2
= hu
3
− u
2
+ b + 1, u
4
− u
2
+ a + 2u + 1, u
5
− u
4
+ u
2
+ u − 1i
* 2 irreducible components of dim
C
= 0, with total 49 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
= h5.55×10
18
u
43
−1.56×10
20
u
42
+· · ·+7.64×10
20
b+1.58×10
18
, −5.20×
10
20
u
43
−8.81×10
20
u
42
+· · ·+7.64×10
20
a+1.43×10
21
, u
44
+2u
43
+· · ·+u−1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
3
=
0.680281u
43
+ 1.15282u
42
+ ··· + 2.62761u − 1.86582
−0.00727175u
43
+ 0.204078u
42
+ ··· + 1.80199u − 0.00206682
a
7
=
1
u
2
a
8
=
0.380377u
43
+ 0.278454u
42
+ ··· − 1.47705u + 0.357193
0.725562u
43
+ 1.09260u
42
+ ··· + 2.20628u − 1.03029
a
4
=
0.157495u
43
+ 0.219673u
42
+ ··· + 2.88571u − 1.49128
−0.100370u
43
+ 0.294432u
42
+ ··· + 2.99466u − 0.234008
a
9
=
−0.345186u
43
− 0.814150u
42
+ ··· − 3.68333u + 1.38748
0.725562u
43
+ 1.09260u
42
+ ··· + 2.20628u − 1.03029
a
12
=
−u
−u
3
+ u
a
5
=
−0.727339u
43
− 1.22924u
42
+ ··· + 0.506371u + 1.13240
−0.0878881u
43
− 0.762349u
42
+ ··· − 1.82252u + 0.614206
a
2
=
0.141633u
43
− 0.0701701u
42
+ ··· + 2.62190u − 1.14094
−0.0770011u
43
− 0.0103397u
42
+ ··· + 2.58613u − 0.141084
a
10
=
u
3
u
5
− u
3
+ u
a
1
=
−u
5
− u
−u
7
+ u
5
− 2u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes =
2222195580300966085542
763794622492335702017
u
43
+
3198001597405456212425
763794622492335702017
u
42
+ ··· −
5752714676140583930170
763794622492335702017
u −
8762178869972642405852
763794622492335702017
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
44
+ 46u
43
+ ··· + 113u + 1
c
2
, c
4
u
44
− 6u
43
+ ··· − u − 1
c
3
, c
7
u
44
− u
43
+ ··· + 416u + 32
c
5
, c
8
, c
9
u
44
− 2u
43
+ ··· − u − 1
c
6
, c
11
u
44
− 2u
43
+ ··· − u − 1
c
10
, c
12
u
44
+ 18u
43
+ ··· + 7u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
44
− 90y
43
+ ··· − 1337y + 1
c
2
, c
4
y
44
− 46y
43
+ ··· − 113y + 1
c
3
, c
7
y
44
− 33y
43
+ ··· − 42496y + 1024
c
5
, c
8
, c
9
y
44
+ 30y
43
+ ··· − 7y + 1
c
6
, c
11
y
44
− 18y
43
+ ··· − 7y + 1
c
10
, c
12
y
44
+ 18y
43
+ ··· − 7y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.932256 + 0.333118I
a = 2.11928 + 0.73637I
b = 1.213880 + 0.113209I
−3.19612 + 1.16436I −18.0367 − 4.2407I
u = −0.932256 − 0.333118I
a = 2.11928 − 0.73637I
b = 1.213880 − 0.113209I
−3.19612 − 1.16436I −18.0367 + 4.2407I
u = −0.811966 + 0.606824I
a = −0.214198 − 0.517770I
b = −0.639085 − 0.323465I
1.69246 + 2.33995I −6.03512 − 4.58901I
u = −0.811966 − 0.606824I
a = −0.214198 + 0.517770I
b = −0.639085 + 0.323465I
1.69246 − 2.33995I −6.03512 + 4.58901I
u = 0.832515 + 0.488298I
a = −8.47385 − 3.13565I
b = −1.08225 − 8.34772I
0.05907 − 2.03841I −80.5474 − 19.3778I
u = 0.832515 − 0.488298I
a = −8.47385 + 3.13565I
b = −1.08225 + 8.34772I
0.05907 + 2.03841I −80.5474 + 19.3778I
u = −0.462434 + 0.927925I
a = 0.0471309 + 0.1087380I
b = 1.40403 + 0.74743I
−2.93440 − 8.69141I −10.66822 + 4.32970I
u = −0.462434 − 0.927925I
a = 0.0471309 − 0.1087380I
b = 1.40403 − 0.74743I
−2.93440 + 8.69141I −10.66822 − 4.32970I
u = 0.934426 + 0.187999I
a = −2.13830 + 1.36144I
b = −0.759161 + 0.468019I
−1.48992 + 2.07213I −15.1717 − 3.4409I
u = 0.934426 − 0.187999I
a = −2.13830 − 1.36144I
b = −0.759161 − 0.468019I
−1.48992 − 2.07213I −15.1717 + 3.4409I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.482142 + 0.949428I
a = −0.0877578 − 0.0008070I
b = −1.354460 + 0.278382I
−6.98988 + 2.57441I −14.1642 − 0.9556I
u = 0.482142 − 0.949428I
a = −0.0877578 + 0.0008070I
b = −1.354460 − 0.278382I
−6.98988 − 2.57441I −14.1642 + 0.9556I
u = −0.996393 + 0.394966I
a = 1.48606 − 0.29444I
b = 0.886377 + 0.223778I
−3.65397 + 1.39656I −17.3361 − 0.7595I
u = −0.996393 − 0.394966I
a = 1.48606 + 0.29444I
b = 0.886377 − 0.223778I
−3.65397 − 1.39656I −17.3361 + 0.7595I
u = −0.940835 + 0.551460I
a = −0.76026 − 1.52020I
b = −1.52495 − 0.13898I
1.36697 + 2.08215I −9.41465 − 2.27806I
u = −0.940835 − 0.551460I
a = −0.76026 + 1.52020I
b = −1.52495 + 0.13898I
1.36697 − 2.08215I −9.41465 + 2.27806I
u = −0.519753 + 0.965172I
a = 0.0449987 − 0.1105440I
b = 1.073030 − 0.166548I
−2.51155 + 3.63795I −12.71077 − 3.32802I
u = −0.519753 − 0.965172I
a = 0.0449987 + 0.1105440I
b = 1.073030 + 0.166548I
−2.51155 − 3.63795I −12.71077 + 3.32802I
u = 1.025600 + 0.460789I
a = −0.04638 − 1.42837I
b = 0.097152 + 0.226092I
−3.18176 − 4.85577I −16.2664 + 7.5137I
u = 1.025600 − 0.460789I
a = −0.04638 + 1.42837I
b = 0.097152 − 0.226092I
−3.18176 + 4.85577I −16.2664 − 7.5137I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.005340 + 0.543119I
a = 1.45241 − 1.16375I
b = 1.010000 + 0.655687I
−1.71867 − 4.49690I −15.4552 + 5.1685I
u = 1.005340 − 0.543119I
a = 1.45241 + 1.16375I
b = 1.010000 − 0.655687I
−1.71867 + 4.49690I −15.4552 − 5.1685I
u = −1.042980 + 0.576491I
a = −2.06544 − 1.02569I
b = −1.108870 + 0.723364I
0.96122 + 8.18685I −10.86677 − 8.84051I
u = −1.042980 − 0.576491I
a = −2.06544 + 1.02569I
b = −1.108870 − 0.723364I
0.96122 − 8.18685I −10.86677 + 8.84051I
u = −0.484164 + 0.645863I
a = −0.335926 + 0.386406I
b = −0.946963 − 0.737557I
2.57983 − 3.38804I −7.14865 + 3.85146I
u = −0.484164 − 0.645863I
a = −0.335926 − 0.386406I
b = −0.946963 + 0.737557I
2.57983 + 3.38804I −7.14865 − 3.85146I
u = 0.572656 + 0.492792I
a = −0.479357 + 0.261809I
b = 0.622384 − 0.489340I
−0.415071 + 0.135386I −12.51812 − 0.53462I
u = 0.572656 − 0.492792I
a = −0.479357 − 0.261809I
b = 0.622384 + 0.489340I
−0.415071 − 0.135386I −12.51812 + 0.53462I
u = 1.272740 + 0.019314I
a = 1.88935 − 0.59100I
b = 1.50663 − 0.34571I
−9.39659 + 6.06487I −16.0679 − 3.3672I
u = 1.272740 − 0.019314I
a = 1.88935 + 0.59100I
b = 1.50663 + 0.34571I
−9.39659 − 6.06487I −16.0679 + 3.3672I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.27574
a = −2.04286
b = −1.59279
−13.6601 −18.7020
u = 0.928890 + 0.877784I
a = 0.288927 + 0.058403I
b = −0.0255637 − 0.0518981I
9.64608 − 3.25423I 3.42401 + 0.I
u = 0.928890 − 0.877784I
a = 0.288927 − 0.058403I
b = −0.0255637 + 0.0518981I
9.64608 + 3.25423I 3.42401 + 0.I
u = −1.140930 + 0.668019I
a = 1.78965 + 0.99216I
b = 1.58220 − 0.85694I
−5.0177 + 14.5388I −12.0000 − 8.1006I
u = −1.140930 − 0.668019I
a = 1.78965 − 0.99216I
b = 1.58220 + 0.85694I
−5.0177 − 14.5388I −12.0000 + 8.1006I
u = 1.147110 + 0.679799I
a = −1.30957 + 1.19970I
b = −1.45466 − 0.44146I
−9.05324 − 8.53642I −12.00000 + 5.03243I
u = 1.147110 − 0.679799I
a = −1.30957 − 1.19970I
b = −1.45466 + 0.44146I
−9.05324 + 8.53642I −12.00000 − 5.03243I
u = −0.454054 + 0.487305I
a = −0.035389 − 0.728908I
b = −0.876425 + 0.512471I
2.46066 + 2.02868I −5.66385 − 3.37535I
u = −0.454054 − 0.487305I
a = −0.035389 + 0.728908I
b = −0.876425 − 0.512471I
2.46066 − 2.02868I −5.66385 + 3.37535I
u = −1.152990 + 0.700059I
a = 0.682516 + 1.130440I
b = 1.087850 − 0.088161I
−4.49244 + 2.47578I −12.00000 + 0.I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.152990 − 0.700059I
a = 0.682516 − 1.130440I
b = 1.087850 + 0.088161I
−4.49244 − 2.47578I −12.00000 + 0.I
u = 0.435796
a = −0.661080
b = 0.319506
−0.646256 −15.3650
u = 0.157314 + 0.396862I
a = −0.50192 + 2.61945I
b = 0.425511 + 0.468538I
−1.15253 + 1.27543I −10.53847 − 1.56080I
u = 0.157314 − 0.396862I
a = −0.50192 − 2.61945I
b = 0.425511 − 0.468538I
−1.15253 − 1.27543I −10.53847 + 1.56080I
9
II. I
u
2
= hu
3
− u
2
+ b + 1, u
4
− u
2
+ a + 2u + 1, u
5
− u
4
+ u
2
+ u − 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
3
=
−u
4
+ u
2
− 2u − 1
−u
3
+ u
2
− 1
a
7
=
1
u
2
a
8
=
1
u
2
a
4
=
−u
4
+ u
2
− 2u − 1
−u
3
+ u
2
− 1
a
9
=
−u
2
+ 1
u
2
a
12
=
−u
−u
3
+ u
a
5
=
u
4
− u
2
+ 1
−u
4
a
2
=
−2u
4
+ 2u
2
− 2u − 2
u
4
− u
3
+ u
2
− 1
a
10
=
u
3
u
4
− u
3
− u
2
+ 1
a
1
=
−u
4
+ u
2
− 1
u
4
(ii) Obstruction class = 1
(iii) Cusp Shapes = u
4
− u
3
+ 6u
2
− 4u − 15
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
5
c
3
, c
7
u
5
c
4
(u + 1)
5
c
5
, c
10
u
5
− u
4
+ 4u
3
− 3u
2
+ 3u − 1
c
6
u
5
− u
4
+ u
2
+ u − 1
c
8
, c
9
, c
12
u
5
+ u
4
+ 4u
3
+ 3u
2
+ 3u + 1
c
11
u
5
+ u
4
− u
2
+ u + 1
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
5
c
3
, c
7
y
5
c
5
, c
8
, c
9
c
10
, c
12
y
5
+ 7y
4
+ 16y
3
+ 13y
2
+ 3y −1
c
6
, c
11
y
5
− y
4
+ 4y
3
− 3y
2
+ 3y −1
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.758138 + 0.584034I
a = 1.47956 − 1.63976I
b = −1.10636 − 1.69341I
0.17487 + 2.21397I −11.6350 − 8.8712I
u = −0.758138 − 0.584034I
a = 1.47956 + 1.63976I
b = −1.10636 + 1.69341I
0.17487 − 2.21397I −11.6350 + 8.8712I
u = 0.935538 + 0.903908I
a = 0.044146 − 0.313338I
b = 0.532511 + 0.056433I
9.31336 − 3.33174I −19.7758 + 5.0940I
u = 0.935538 − 0.903908I
a = 0.044146 + 0.313338I
b = 0.532511 − 0.056433I
9.31336 + 3.33174I −19.7758 − 5.0940I
u = 0.645200
a = −2.04741
b = −0.852303
−2.52712 −15.1780
13
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
5
)(u
44
+ 46u
43
+ ··· + 113u + 1)
c
2
((u − 1)
5
)(u
44
− 6u
43
+ ··· − u − 1)
c
3
, c
7
u
5
(u
44
− u
43
+ ··· + 416u + 32)
c
4
((u + 1)
5
)(u
44
− 6u
43
+ ··· − u − 1)
c
5
(u
5
− u
4
+ 4u
3
− 3u
2
+ 3u − 1)(u
44
− 2u
43
+ ··· − u − 1)
c
6
(u
5
− u
4
+ u
2
+ u − 1)(u
44
− 2u
43
+ ··· − u − 1)
c
8
, c
9
(u
5
+ u
4
+ 4u
3
+ 3u
2
+ 3u + 1)(u
44
− 2u
43
+ ··· − u − 1)
c
10
(u
5
− u
4
+ 4u
3
− 3u
2
+ 3u − 1)(u
44
+ 18u
43
+ ··· + 7u + 1)
c
11
(u
5
+ u
4
− u
2
+ u + 1)(u
44
− 2u
43
+ ··· − u − 1)
c
12
(u
5
+ u
4
+ 4u
3
+ 3u
2
+ 3u + 1)(u
44
+ 18u
43
+ ··· + 7u + 1)
14
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
5
)(y
44
− 90y
43
+ ··· − 1337y + 1)
c
2
, c
4
((y −1)
5
)(y
44
− 46y
43
+ ··· − 113y + 1)
c
3
, c
7
y
5
(y
44
− 33y
43
+ ··· − 42496y + 1024)
c
5
, c
8
, c
9
(y
5
+ 7y
4
+ 16y
3
+ 13y
2
+ 3y −1)(y
44
+ 30y
43
+ ··· − 7y + 1)
c
6
, c
11
(y
5
− y
4
+ 4y
3
− 3y
2
+ 3y −1)(y
44
− 18y
43
+ ··· − 7y + 1)
c
10
, c
12
(y
5
+ 7y
4
+ 16y
3
+ 13y
2
+ 3y −1)(y
44
+ 18y
43
+ ··· − 7y + 1)
15
