12n
0666
(K12n
0666
)
A knot diagram
1
Linearized knot diagam
4 5 6 8 9 11 12 2 3 6 7 8
Solving Sequence
8,12 1,5
4 2 9 7 11 6 3 10
c
12
c
4
c
1
c
8
c
7
c
11
c
6
c
3
c
9
c
2
, c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−u
15
+ 6u
13
+ ··· + b − 4, −5u
15
− 4u
14
+ ··· + 3a − 13, u
16
+ 2u
15
+ ··· − 13u + 3i
I
u
2
= h−u
13
a + u
13
+ ··· − a + 1, −u
13
a − 2u
13
+ ··· + a + 7,
u
14
− u
13
− 7u
12
+ 5u
11
+ 19u
10
− 4u
9
− 26u
8
− 13u
7
+ 17u
6
+ 21u
5
+ u
4
− 4u
3
− 6u
2
− 3u − 1i
I
u
3
= hu
6
− 4u
4
+ 2u
3
+ 4u
2
+ b − 3u + 1, −u
5
− u
4
+ 4u
3
+ 2u
2
+ a − 5u − 1,
u
7
+ 2u
6
− 3u
5
− 6u
4
+ 3u
3
+ 5u
2
+ 1i
I
u
4
= hb − 1, a
2
+ a + u − 2, u
2
− u − 1i
I
u
5
= hb − 1, a, u + 1i
I
u
6
= h−u
2
+ b + 2, −u
2
+ 3a − 2u + 1, u
3
+ 2u
2
− u − 3i
I
u
7
= hb, a − 1, u − 1i
I
u
8
= hb + 1, a − 1, u − 1i
I
v
1
= ha, b − 1, v + 1i
* 9 irreducible components of dim
C
= 0, with total 62 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−u
15
+6u
13
+· · ·+b−4, −5u
15
−4u
14
+· · ·+3a−13, u
16
+2u
15
+· · ·−13u+3i
(i) Arc colorings
a
8
=
0
u
a
12
=
1
0
a
1
=
1
u
2
a
5
=
5
3
u
15
+
4
3
u
14
+ ··· − 18u +
13
3
u
15
− 6u
13
+ ··· − 18u + 4
a
4
=
5
3
u
15
+
4
3
u
14
+ ··· − 18u +
13
3
5u
15
+ 3u
14
+ ··· − 49u + 10
a
2
=
2
3
u
15
−
2
3
u
14
+ ··· − 13u +
10
3
3u
15
+ u
14
+ ··· − 35u + 7
a
9
=
1
3
u
15
−
4
3
u
14
+ ··· − 20u +
11
3
u
15
− u
14
+ ··· − 24u + 5
a
7
=
u
u
a
11
=
−u
2
+ 1
−u
2
a
6
=
−u
3
+ 2u
−u
3
+ u
a
3
=
2
3
u
15
−
2
3
u
14
+ ··· + 6u −
5
3
2u
15
+ u
14
+ ··· − 8u + 1
a
10
=
−u
4
+ 3u
2
− 1
−u
4
+ 2u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 5u
15
+ 4u
14
−36u
13
−14u
12
+ 103u
11
−32u
10
−158u
9
+ 170u
8
+
88u
7
− 217u
6
+ 91u
5
+ 87u
4
− 95u
3
+ 35u
2
+ 10u − 18
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
16
+ u
15
+ ··· + 13u + 1
c
2
u
16
+ 10u
15
+ ··· − 5u − 3
c
4
, c
9
u
16
− 5u
15
+ ··· − 17u + 5
c
5
, c
8
u
16
+ 2u
15
+ ··· − 2u − 1
c
6
, c
7
, c
10
c
11
, c
12
u
16
− 2u
15
+ ··· + 13u + 3
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
16
+ 13y
15
+ ··· − 49y + 1
c
2
y
16
− 4y
14
+ ··· + 113y + 9
c
4
, c
9
y
16
− 11y
15
+ ··· − 199y + 25
c
5
, c
8
y
16
− 10y
15
+ ··· − 18y + 1
c
6
, c
7
, c
10
c
11
, c
12
y
16
− 16y
15
+ ··· − 43y + 9
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.548500 + 0.853725I
a = 0.30836 − 1.43712I
b = −0.66590 − 1.54507I
5.38391 − 10.31740I −5.41022 + 7.34778I
u = 0.548500 − 0.853725I
a = 0.30836 + 1.43712I
b = −0.66590 + 1.54507I
5.38391 + 10.31740I −5.41022 − 7.34778I
u = 0.578322 + 0.876148I
a = −0.869193 + 0.857447I
b = −0.18633 + 1.46072I
5.31272 + 4.64447I −4.44340 − 2.64217I
u = 0.578322 − 0.876148I
a = −0.869193 − 0.857447I
b = −0.18633 − 1.46072I
5.31272 − 4.64447I −4.44340 + 2.64217I
u = 0.217481 + 0.592732I
a = 0.47227 + 1.50811I
b = 0.203575 + 0.996171I
0.50766 − 2.36838I −7.45824 + 4.04010I
u = 0.217481 − 0.592732I
a = 0.47227 − 1.50811I
b = 0.203575 − 0.996171I
0.50766 + 2.36838I −7.45824 − 4.04010I
u = 1.39667
a = −1.16562
b = 1.59448
−6.42671 −13.8540
u = −1.384810 + 0.218261I
a = −0.413538 − 0.720270I
b = 0.78536 − 1.50062I
−4.59888 + 5.31561I −16.0697 − 5.0195I
u = −1.384810 − 0.218261I
a = −0.413538 + 0.720270I
b = 0.78536 + 1.50062I
−4.59888 − 5.31561I −16.0697 + 5.0195I
u = −1.48477 + 0.03326I
a = 0.374186 + 0.661888I
b = 0.159333 + 0.652088I
−7.28530 − 0.33372I −13.77762 + 1.31768I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.48477 − 0.03326I
a = 0.374186 − 0.661888I
b = 0.159333 − 0.652088I
−7.28530 + 0.33372I −13.77762 − 1.31768I
u = 0.471433 + 0.149281I
a = 1.189440 + 0.539880I
b = 0.190619 − 0.017488I
−0.951255 − 0.232345I −11.11372 + 2.61454I
u = 0.471433 − 0.149281I
a = 1.189440 − 0.539880I
b = 0.190619 + 0.017488I
−0.951255 + 0.232345I −11.11372 − 2.61454I
u = −1.54560 + 0.31071I
a = 0.806991 + 0.667934I
b = −1.09400 + 1.47232I
−1.4014 + 14.5984I −9.03391 − 7.72929I
u = −1.54560 − 0.31071I
a = 0.806991 − 0.667934I
b = −1.09400 − 1.47232I
−1.4014 − 14.5984I −9.03391 + 7.72929I
u = 1.80224
a = −0.238089
b = 0.620201
−15.4721 −27.5320
6
II.
I
u
2
= h−u
13
a+u
13
+· · ·−a+1, −u
13
a−2u
13
+· · ·+a+7, u
14
−u
13
+· · ·−3u−1i
(i) Arc colorings
a
8
=
0
u
a
12
=
1
0
a
1
=
1
u
2
a
5
=
a
u
13
a − u
13
+ ··· + a − 1
a
4
=
a
u
13
a − u
13
+ ··· + a − 1
a
2
=
2u
13
a − u
12
a + ··· + a − 2
2u
13
− 14u
11
+ ··· − u − 1
a
9
=
−u
13
a + u
13
+ ··· + u + 2
−u
13
a + u
13
+ ··· + 8u + 3
a
7
=
u
u
a
11
=
−u
2
+ 1
−u
2
a
6
=
−u
3
+ 2u
−u
3
+ u
a
3
=
u
13
a − u
12
+ ··· + 2a − 2
u
13
a − u
12
+ ··· + a − 1
a
10
=
−u
4
+ 3u
2
− 1
−u
4
+ 2u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 11u
13
− 10u
12
− 72u
11
+ 49u
10
+ 176u
9
− 43u
8
− 211u
7
− 87u
6
+
135u
5
+ 125u
4
− 27u
3
− 12u
2
− 25u − 14
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
28
− 4u
27
+ ··· + 82u − 11
c
2
(u
14
− 6u
13
+ ··· − 10u + 4)
2
c
4
, c
9
u
28
− 2u
27
+ ··· − 264u + 24
c
5
, c
8
u
28
− u
27
+ ··· − 11u − 1
c
6
, c
7
, c
10
c
11
, c
12
(u
14
+ u
13
+ ··· + 3u − 1)
2
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
28
+ 24y
27
+ ··· + 3132y + 121
c
2
(y
14
− 4y
13
+ ··· − 188y + 16)
2
c
4
, c
9
y
28
− 18y
27
+ ··· − 12000y + 576
c
5
, c
8
y
28
+ y
27
+ ··· − 47y + 1
c
6
, c
7
, c
10
c
11
, c
12
(y
14
− 15y
13
+ ··· + 3y + 1)
2
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.543841 + 0.788845I
a = −0.786499 − 1.127240I
b = −0.15757 − 1.50904I
6.74935 + 2.61367I −3.08817 − 3.10085I
u = −0.543841 + 0.788845I
a = 0.59080 + 1.44573I
b = −0.57036 + 1.40275I
6.74935 + 2.61367I −3.08817 − 3.10085I
u = −0.543841 − 0.788845I
a = −0.786499 + 1.127240I
b = −0.15757 + 1.50904I
6.74935 − 2.61367I −3.08817 + 3.10085I
u = −0.543841 − 0.788845I
a = 0.59080 − 1.44573I
b = −0.57036 − 1.40275I
6.74935 − 2.61367I −3.08817 + 3.10085I
u = 1.10803
a = 0.948288
b = −0.313019
−1.64992 −5.91590
u = 1.10803
a = 0.875781
b = −0.967676
−1.64992 −5.91590
u = −1.315420 + 0.077239I
a = −1.053540 − 0.890197I
b = 0.734783 − 1.046780I
−2.09644 + 4.46056I −6.21772 − 5.02110I
u = −1.315420 + 0.077239I
a = 0.461982 − 0.077443I
b = −1.17028 − 1.69999I
−2.09644 + 4.46056I −6.21772 − 5.02110I
u = −1.315420 − 0.077239I
a = −1.053540 + 0.890197I
b = 0.734783 + 1.046780I
−2.09644 − 4.46056I −6.21772 + 5.02110I
u = −1.315420 − 0.077239I
a = 0.461982 + 0.077443I
b = −1.17028 + 1.69999I
−2.09644 − 4.46056I −6.21772 + 5.02110I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.45797 + 0.12777I
a = −0.697357 + 0.508441I
b = 1.08158 + 1.81362I
−5.60858 − 6.11443I −13.6408 + 6.9717I
u = 1.45797 + 0.12777I
a = −0.139548 − 1.280800I
b = −0.085041 − 0.349273I
−5.60858 − 6.11443I −13.6408 + 6.9717I
u = 1.45797 − 0.12777I
a = −0.697357 − 0.508441I
b = 1.08158 − 1.81362I
−5.60858 + 6.11443I −13.6408 − 6.9717I
u = 1.45797 − 0.12777I
a = −0.139548 + 1.280800I
b = −0.085041 + 0.349273I
−5.60858 + 6.11443I −13.6408 − 6.9717I
u = −0.019410 + 0.530789I
a = −0.270655 + 0.346124I
b = −1.106740 + 0.564246I
1.71604 − 2.54798I −1.07278 + 1.43352I
u = −0.019410 + 0.530789I
a = 1.01173 + 2.29513I
b = 0.289802 + 1.068640I
1.71604 − 2.54798I −1.07278 + 1.43352I
u = −0.019410 − 0.530789I
a = −0.270655 − 0.346124I
b = −1.106740 − 0.564246I
1.71604 + 2.54798I −1.07278 − 1.43352I
u = −0.019410 − 0.530789I
a = 1.01173 − 2.29513I
b = 0.289802 − 1.068640I
1.71604 + 2.54798I −1.07278 − 1.43352I
u = −0.357381 + 0.324231I
a = −0.75149 − 2.13461I
b = 0.39490 − 1.51758I
0.35035 + 4.37070I −10.2424 − 10.7977I
u = −0.357381 + 0.324231I
a = −1.29088 + 2.35828I
b = −0.049630 − 0.292724I
0.35035 + 4.37070I −10.2424 − 10.7977I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.357381 − 0.324231I
a = −0.75149 + 2.13461I
b = 0.39490 + 1.51758I
0.35035 − 4.37070I −10.2424 + 10.7977I
u = −0.357381 − 0.324231I
a = −1.29088 − 2.35828I
b = −0.049630 + 0.292724I
0.35035 − 4.37070I −10.2424 + 10.7977I
u = 1.54231 + 0.28303I
a = 0.901435 − 0.599841I
b = −0.93554 − 1.19334I
−0.04950 − 6.56214I −6.38364 + 4.80522I
u = 1.54231 + 0.28303I
a = −0.669860 + 0.302514I
b = 0.29812 + 1.50281I
−0.04950 − 6.56214I −6.38364 + 4.80522I
u = 1.54231 − 0.28303I
a = 0.901435 + 0.599841I
b = −0.93554 + 1.19334I
−0.04950 + 6.56214I −6.38364 − 4.80522I
u = 1.54231 − 0.28303I
a = −0.669860 − 0.302514I
b = 0.29812 − 1.50281I
−0.04950 + 6.56214I −6.38364 − 4.80522I
u = −1.63650
a = 1.21145
b = −0.967540
−10.3421 10.2070
u = −1.63650
a = 0.352250
b = 0.800198
−10.3421 10.2070
12
III. I
u
3
= hu
6
− 4u
4
+ 2u
3
+ 4u
2
+ b − 3u + 1, −u
5
− u
4
+ 4u
3
+ 2u
2
+ a −
5u − 1, u
7
+ 2u
6
− 3u
5
− 6u
4
+ 3u
3
+ 5u
2
+ 1i
(i) Arc colorings
a
8
=
0
u
a
12
=
1
0
a
1
=
1
u
2
a
5
=
u
5
+ u
4
− 4u
3
− 2u
2
+ 5u + 1
−u
6
+ 4u
4
− 2u
3
− 4u
2
+ 3u − 1
a
4
=
u
5
+ u
4
− 4u
3
− 2u
2
+ 5u + 1
−2u
6
− u
5
+ 8u
4
− 8u
2
+ 3u − 2
a
2
=
u
6
+ u
5
− 4u
4
− 3u
3
+ 5u
2
+ 3u − 1
−u
5
+ 3u
3
− u − 1
a
9
=
u
2
− 2
−u
6
− u
5
+ 4u
4
+ 2u
3
− 4u
2
− u − 1
a
7
=
u
u
a
11
=
−u
2
+ 1
−u
2
a
6
=
−u
3
+ 2u
−u
3
+ u
a
3
=
u
5
+ u
4
− 4u
3
− 2u
2
+ 5u + 2
−u
3
+ 2u
a
10
=
u
4
− 3u
2
+ 1
u
4
− 2u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −3u
6
+ u
5
+ 15u
4
− 12u
3
− 20u
2
+ 17u − 7
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
7
+ u
6
+ 4u
5
+ 5u
4
+ 7u
3
+ 6u
2
+ 4u + 1
c
2
u
7
+ 8u
6
+ 31u
5
+ 75u
4
+ 122u
3
+ 133u
2
+ 90u + 29
c
4
, c
9
u
7
− u
6
+ u
4
+ u
3
− 2u
2
+ 1
c
5
, c
8
u
7
− 2u
5
− u
4
+ u
3
− u − 1
c
6
, c
7
u
7
− 2u
6
− 3u
5
+ 6u
4
+ 3u
3
− 5u
2
− 1
c
10
, c
11
, c
12
u
7
+ 2u
6
− 3u
5
− 6u
4
+ 3u
3
+ 5u
2
+ 1
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
7
+ 7y
6
+ 20y
5
+ 27y
4
+ 19y
3
+ 10y
2
+ 4y −1
c
2
y
7
− 2y
6
+ 5y
5
− 9y
4
+ 50y
3
− 79y
2
+ 386y −841
c
4
, c
9
y
7
− y
6
+ 4y
5
− 5y
4
+ 7y
3
− 6y
2
+ 4y −1
c
5
, c
8
y
7
− 4y
6
+ 6y
5
− 7y
4
+ 5y
3
− 4y
2
+ y −1
c
6
, c
7
, c
10
c
11
, c
12
y
7
− 10y
6
+ 39y
5
− 74y
4
+ 65y
3
− 13y
2
− 10y −1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.278170 + 0.302690I
a = 0.690513 + 0.118128I
b = −0.587538 − 0.609722I
−3.01119 + 1.09708I −11.40523 − 3.58425I
u = 1.278170 − 0.302690I
a = 0.690513 − 0.118128I
b = −0.587538 + 0.609722I
−3.01119 − 1.09708I −11.40523 + 3.58425I
u = −1.399450 + 0.156175I
a = −0.465734 − 0.770245I
b = 0.41431 − 1.55213I
−3.71133 + 5.67264I −7.64975 − 7.54460I
u = −1.399450 − 0.156175I
a = −0.465734 + 0.770245I
b = 0.41431 + 1.55213I
−3.71133 − 5.67264I −7.64975 + 7.54460I
u = 0.037900 + 0.397504I
a = 1.60254 + 2.17123I
b = −0.126346 + 1.154250I
1.16830 − 3.69824I −2.64032 + 6.74904I
u = 0.037900 − 0.397504I
a = 1.60254 − 2.17123I
b = −0.126346 − 1.154250I
1.16830 + 3.69824I −2.64032 − 6.74904I
u = −1.83325
a = 0.345358
b = −0.400851
−15.2105 3.39060
16
IV. I
u
4
= hb − 1, a
2
+ a + u − 2, u
2
− u − 1i
(i) Arc colorings
a
8
=
0
u
a
12
=
1
0
a
1
=
1
u + 1
a
5
=
a
1
a
4
=
a
au + a + 1
a
2
=
a + 1
au + a + u + 2
a
9
=
−au − 2u + 1
−3au − a − 3u − 1
a
7
=
u
u
a
11
=
−u
−u − 1
a
6
=
−1
−u − 1
a
3
=
a + 1
au + a + u + 2
a
10
=
0
u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −7u − 22
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
(u − 1)
4
c
2
u
4
c
4
, c
5
, c
8
c
9
u
4
+ u
3
− 3u
2
− u + 1
c
6
, c
7
(u
2
+ u − 1)
2
c
10
, c
11
, c
12
(u
2
− u − 1)
2
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
(y −1)
4
c
2
y
4
c
4
, c
5
, c
8
c
9
y
4
− 7y
3
+ 13y
2
− 7y + 1
c
6
, c
7
, c
10
c
11
, c
12
(y
2
− 3y + 1)
2
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.618034
a = 1.19353
b = 1.00000
−2.63189 −17.6740
u = −0.618034
a = −2.19353
b = 1.00000
−2.63189 −17.6740
u = 1.61803
a = −1.29496
b = 1.00000
−10.5276 −33.3260
u = 1.61803
a = 0.294963
b = 1.00000
−10.5276 −33.3260
20
V. I
u
5
= hb − 1, a, u + 1i
(i) Arc colorings
a
8
=
0
−1
a
12
=
1
0
a
1
=
1
1
a
5
=
0
1
a
4
=
0
1
a
2
=
1
2
a
9
=
1
1
a
7
=
−1
−1
a
11
=
0
−1
a
6
=
−1
0
a
3
=
1
1
a
10
=
1
1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −18
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
u + 1
c
4
, c
9
u
c
5
, c
6
, c
7
c
8
, c
10
, c
11
c
12
u − 1
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
5
, c
6
, c
7
c
8
, c
10
, c
11
c
12
y −1
c
4
, c
9
y
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 0
b = 1.00000
−4.93480 −18.0000
24
VI. I
u
6
= h−u
2
+ b + 2, −u
2
+ 3a − 2u + 1, u
3
+ 2u
2
− u − 3i
(i) Arc colorings
a
8
=
0
u
a
12
=
1
0
a
1
=
1
u
2
a
5
=
1
3
u
2
+
2
3
u −
1
3
u
2
− 2
a
4
=
1
3
u
2
+
2
3
u −
1
3
u
2
+ u − 2
a
2
=
−
2
3
u
2
−
1
3
u +
5
3
1
a
9
=
−
4
3
u
2
−
2
3
u +
7
3
−u
2
+ 2
a
7
=
u
u
a
11
=
−u
2
+ 1
−u
2
a
6
=
2u
2
+ u − 3
2u
2
− 3
a
3
=
−
2
3
u
2
−
1
3
u +
8
3
−2u
2
− u + 4
a
10
=
−2u
2
− u + 5
−3u
2
− u + 6
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
3
+ u − 1
c
2
u
3
+ 2u
2
− u − 3
c
4
, c
9
(u + 1)
3
c
5
, c
8
u
3
− 2u
2
+ u + 1
c
6
, c
7
, c
10
c
11
, c
12
u
3
− 2u
2
− u + 3
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
3
+ 2y
2
+ y −1
c
2
, c
6
, c
7
c
10
, c
11
, c
12
y
3
− 6y
2
+ 13y −9
c
4
, c
9
(y −1)
3
c
5
, c
8
y
3
− 2y
2
+ 5y −1
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 1.14790
a = 0.871157
b = −0.682328
−1.64493 −6.00000
u = −1.57395 + 0.36899I
a = −0.602245 − 0.141188I
b = 0.341164 − 1.161540I
−1.64493 −6.00000
u = −1.57395 − 0.36899I
a = −0.602245 + 0.141188I
b = 0.341164 + 1.161540I
−1.64493 −6.00000
28
VII. I
u
7
= hb, a − 1, u − 1i
(i) Arc colorings
a
8
=
0
1
a
12
=
1
0
a
1
=
1
1
a
5
=
1
0
a
4
=
1
1
a
2
=
1
1
a
9
=
−1
0
a
7
=
1
1
a
11
=
0
−1
a
6
=
1
0
a
3
=
2
1
a
10
=
1
1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6
29
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
c
2
, c
3
u − 1
c
4
, c
6
, c
7
c
8
, c
9
, c
10
c
11
, c
12
u + 1
30
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
c
2
, c
3
, c
4
c
6
, c
7
, c
8
c
9
, c
10
, c
11
c
12
y − 1
31
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 1.00000
b = 0
−1.64493 −6.00000
32
VIII. I
u
8
= hb + 1, a − 1, u − 1i
(i) Arc colorings
a
8
=
0
1
a
12
=
1
0
a
1
=
1
1
a
5
=
1
−1
a
4
=
1
0
a
2
=
0
1
a
9
=
0
1
a
7
=
1
1
a
11
=
0
−1
a
6
=
1
0
a
3
=
1
0
a
10
=
1
1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6
33
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
u − 1
c
3
, c
8
u
c
4
, c
5
, c
6
c
7
, c
9
, c
10
c
11
, c
12
u + 1
34
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
6
, c
7
c
9
, c
10
, c
11
c
12
y − 1
c
3
, c
8
y
35
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
8
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 1.00000
b = −1.00000
−1.64493 −6.00000
36
IX. I
v
1
= ha, b − 1, v + 1i
(i) Arc colorings
a
8
=
−1
0
a
12
=
1
0
a
1
=
1
0
a
5
=
0
1
a
4
=
−1
1
a
2
=
0
1
a
9
=
−1
−1
a
7
=
−1
0
a
11
=
1
0
a
6
=
−1
0
a
3
=
0
1
a
10
=
−1
0
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6
37
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
5
, c
8
, c
9
u + 1
c
2
, c
6
, c
7
c
10
, c
11
, c
12
u
38
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
5
, c
8
, c
9
y − 1
c
2
, c
6
, c
7
c
10
, c
11
, c
12
y
39
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −1.00000
a = 0
b = 1.00000
−1.64493 −6.00000
40
X. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
3
u(u − 1)
5
(u + 1)
2
(u
3
+ u − 1)(u
7
+ u
6
+ ··· + 4u + 1)
· (u
16
+ u
15
+ ··· + 13u + 1)(u
28
− 4u
27
+ ··· + 82u − 11)
c
2
u
5
(u − 1)
2
(u + 1)(u
3
+ 2u
2
− u − 3)
· (u
7
+ 8u
6
+ 31u
5
+ 75u
4
+ 122u
3
+ 133u
2
+ 90u + 29)
· ((u
14
− 6u
13
+ ··· − 10u + 4)
2
)(u
16
+ 10u
15
+ ··· − 5u − 3)
c
4
, c
9
u(u + 1)
6
(u
4
+ u
3
− 3u
2
− u + 1)(u
7
− u
6
+ u
4
+ u
3
− 2u
2
+ 1)
· (u
16
− 5u
15
+ ··· − 17u + 5)(u
28
− 2u
27
+ ··· − 264u + 24)
c
5
, c
8
u(u − 1)(u + 1)
2
(u
3
− 2u
2
+ u + 1)(u
4
+ u
3
− 3u
2
− u + 1)
· (u
7
− 2u
5
− u
4
+ u
3
− u − 1)(u
16
+ 2u
15
+ ··· − 2u − 1)
· (u
28
− u
27
+ ··· − 11u − 1)
c
6
, c
7
u(u − 1)(u + 1)
2
(u
2
+ u − 1)
2
(u
3
− 2u
2
− u + 3)
· (u
7
− 2u
6
+ ··· − 5u
2
− 1)(u
14
+ u
13
+ ··· + 3u − 1)
2
· (u
16
− 2u
15
+ ··· + 13u + 3)
c
10
, c
11
, c
12
u(u − 1)(u + 1)
2
(u
2
− u − 1)
2
(u
3
− 2u
2
− u + 3)
· (u
7
+ 2u
6
+ ··· + 5u
2
+ 1)(u
14
+ u
13
+ ··· + 3u − 1)
2
· (u
16
− 2u
15
+ ··· + 13u + 3)
41
XI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
3
y(y − 1)
7
(y
3
+ 2y
2
+ y − 1)
· (y
7
+ 7y
6
+ 20y
5
+ 27y
4
+ 19y
3
+ 10y
2
+ 4y − 1)
· (y
16
+ 13y
15
+ ··· − 49y + 1)(y
28
+ 24y
27
+ ··· + 3132y + 121)
c
2
y
5
(y − 1)
3
(y
3
− 6y
2
+ 13y − 9)
· (y
7
− 2y
6
+ 5y
5
− 9y
4
+ 50y
3
− 79y
2
+ 386y − 841)
· ((y
14
− 4y
13
+ ··· − 188y + 16)
2
)(y
16
− 4y
14
+ ··· + 113y + 9)
c
4
, c
9
y(y − 1)
6
(y
4
− 7y
3
+ 13y
2
− 7y + 1)
· (y
7
− y
6
+ 4y
5
− 5y
4
+ 7y
3
− 6y
2
+ 4y − 1)
· (y
16
− 11y
15
+ ··· − 199y + 25)(y
28
− 18y
27
+ ··· − 12000y + 576)
c
5
, c
8
y(y − 1)
3
(y
3
− 2y
2
+ 5y − 1)(y
4
− 7y
3
+ 13y
2
− 7y + 1)
· (y
7
− 4y
6
+ ··· + y − 1)(y
16
− 10y
15
+ ··· − 18y + 1)
· (y
28
+ y
27
+ ··· − 47y + 1)
c
6
, c
7
, c
10
c
11
, c
12
y(y − 1)
3
(y
2
− 3y + 1)
2
(y
3
− 6y
2
+ 13y − 9)
· (y
7
− 10y
6
+ 39y
5
− 74y
4
+ 65y
3
− 13y
2
− 10y − 1)
· ((y
14
− 15y
13
+ ··· + 3y + 1)
2
)(y
16
− 16y
15
+ ··· − 43y + 9)
42
