11n
163
(K11n
163
)
A knot diagram
1
Linearized knot diagam
6 7 1 7 8 9 11 2 1 8 4
Solving Sequence
4,11
1
3,8
7 5 2 10 9 6
c
11
c
3
c
7
c
4
c
2
c
10
c
9
c
6
c
1
, c
5
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= hb − u, −45168u
15
+ 5735u
14
+ ··· + 12553a − 4016,
u
16
+ 4u
14
+ 13u
12
+ 25u
10
+ 37u
8
+ u
7
+ 39u
6
+ 5u
5
+ 24u
4
+ 7u
3
+ 8u
2
+ 2u + 1i
I
u
2
= h9.55720 × 10
54
u
41
+ 1.20936 × 10
55
u
40
+ ··· + 1.06854 × 10
57
b + 1.17356 × 10
57
,
1.73442 × 10
56
u
41
+ 5.21769 × 10
56
u
40
+ ··· + 1.06854 × 10
57
a + 1.20542 × 10
58
, u
42
+ 3u
41
+ ··· + 36u − 1i
I
u
3
= hb + u, 2u
6
− 4u
5
+ 7u
4
− 6u
3
+ 4u
2
+ a − u − 1, u
7
− 2u
6
+ 4u
5
− 4u
4
+ 4u
3
− 2u
2
+ u − 1i
I
u
4
= h−u
5
+ 2u
4
− 4u
3
+ 5u
2
+ b − 4u + 2, −u
4
+ 2u
3
− 4u
2
+ a + 5u − 3, u
6
− 2u
5
+ 4u
4
− 5u
3
+ 4u
2
− 2u + 1i
* 4 irreducible components of dim
C
= 0, with total 71 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
= hb−u, −45168u
15
+5735u
14
+· · ·+12553a−4016, u
16
+4u
14
+· · ·+2u+1i
(i) Arc colorings
a
4
=
0
u
a
11
=
1
0
a
1
=
1
u
2
a
3
=
u
u
3
+ u
a
8
=
3.59818u
15
− 0.456863u
14
+ ··· + 6.71059u + 0.319924
u
a
7
=
3.59818u
15
− 0.456863u
14
+ ··· + 7.71059u + 0.319924
u
a
5
=
−2.45439u
15
− 4.20816u
14
+ ··· − 29.2987u − 12.3139
1.39951u
15
− 0.238270u
14
+ ··· + 3.68446u − 0.456863
a
2
=
−2.66016u
15
− 2.57118u
14
+ ··· − 20.1125u − 7.64885
0.808412u
15
− 0.199793u
14
+ ··· + 2.76149u − 0.218593
a
10
=
0.456863u
15
+ 1.39951u
14
+ ··· + 6.87644u + 4.59818
−u
2
a
9
=
0.695133u
15
+ 1.99060u
14
+ ··· + 10.1323u + 5.99769
−0.0384769u
15
− 0.336175u
14
+ ··· − 1.42046u − 0.591094
a
6
=
1.01418u
15
− 1.83677u
14
+ ··· − 6.42476u − 4.88361
0.591094u
15
− 0.0384769u
14
+ ··· + 1.92297u − 0.238270
a
6
=
1.01418u
15
− 1.83677u
14
+ ··· − 6.42476u − 4.88361
0.591094u
15
− 0.0384769u
14
+ ··· + 1.92297u − 0.238270
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
31115
12553
u
15
+
20322
12553
u
14
+ ··· −
177549
12553
u −
9899
12553
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
16
− u
15
+ ··· − u + 1
c
2
, c
5
u
16
− u
15
+ ··· + 15u
2
+ 1
c
3
, c
7
, c
10
c
11
u
16
+ 4u
14
+ ··· + 2u + 1
c
4
u
16
− 13u
15
+ ··· − 352u + 64
c
8
u
16
− 13u
15
+ ··· − 36u + 8
c
9
u
16
− 16u
15
+ ··· − 544u + 64
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
16
− 3y
15
+ ··· − 5y + 1
c
2
, c
5
y
16
+ 9y
15
+ ··· + 30y + 1
c
3
, c
7
, c
10
c
11
y
16
+ 8y
15
+ ··· + 12y + 1
c
4
y
16
+ 5y
15
+ ··· + 40448y + 4096
c
8
y
16
− y
15
+ ··· + 496y + 64
c
9
y
16
− 4y
15
+ ··· + 23552y + 4096
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.362872 + 0.921754I
a = 0.762991 − 0.560929I
b = 0.362872 + 0.921754I
3.94475 + 1.12356I 1.32088 + 0.73756I
u = 0.362872 − 0.921754I
a = 0.762991 + 0.560929I
b = 0.362872 − 0.921754I
3.94475 − 1.12356I 1.32088 − 0.73756I
u = −0.067924 + 1.048980I
a = 0.59848 − 1.57127I
b = −0.067924 + 1.048980I
3.11555 + 2.14731I −0.93627 − 3.92704I
u = −0.067924 − 1.048980I
a = 0.59848 + 1.57127I
b = −0.067924 − 1.048980I
3.11555 − 2.14731I −0.93627 + 3.92704I
u = 0.867369 + 0.851352I
a = 0.39653 − 1.47637I
b = 0.867369 + 0.851352I
−4.45687 + 2.76976I −6.60351 − 1.02062I
u = 0.867369 − 0.851352I
a = 0.39653 + 1.47637I
b = 0.867369 − 0.851352I
−4.45687 − 2.76976I −6.60351 + 1.02062I
u = −0.924080 + 0.993395I
a = −0.062325 − 1.181310I
b = −0.924080 + 0.993395I
−2.56347 + 5.89381I −14.0887 − 6.8568I
u = −0.924080 − 0.993395I
a = −0.062325 + 1.181310I
b = −0.924080 − 0.993395I
−2.56347 − 5.89381I −14.0887 + 6.8568I
u = −0.037947 + 0.609427I
a = −4.09907 − 0.73703I
b = −0.037947 + 0.609427I
0.98282 − 4.26271I −0.536037 − 0.693456I
u = −0.037947 − 0.609427I
a = −4.09907 + 0.73703I
b = −0.037947 − 0.609427I
0.98282 + 4.26271I −0.536037 + 0.693456I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.74781 + 1.20294I
a = −0.21869 − 1.80308I
b = −0.74781 + 1.20294I
−0.89621 + 7.24124I −3.27217 − 13.36826I
u = −0.74781 − 1.20294I
a = −0.21869 + 1.80308I
b = −0.74781 − 1.20294I
−0.89621 − 7.24124I −3.27217 + 13.36826I
u = 0.82584 + 1.20295I
a = 0.47696 − 1.60926I
b = 0.82584 + 1.20295I
−2.2047 − 16.1487I −3.69661 + 9.09082I
u = 0.82584 − 1.20295I
a = 0.47696 + 1.60926I
b = 0.82584 − 1.20295I
−2.2047 + 16.1487I −3.69661 − 9.09082I
u = −0.278326 + 0.368111I
a = 1.14513 − 0.86473I
b = −0.278326 + 0.368111I
−0.389238 + 1.281380I −3.68762 − 5.53338I
u = −0.278326 − 0.368111I
a = 1.14513 + 0.86473I
b = −0.278326 − 0.368111I
−0.389238 − 1.281380I −3.68762 + 5.53338I
6
II. I
u
2
=
h9.56×10
54
u
41
+1.21×10
55
u
40
+· · ·+1.07×10
57
b+1.17×10
57
, 1.73×10
56
u
41
+
5.22 × 10
56
u
40
+ · · · + 1.07 × 10
57
a + 1.21 × 10
58
, u
42
+ 3u
41
+ · · · + 36u − 1i
(i) Arc colorings
a
4
=
0
u
a
11
=
1
0
a
1
=
1
u
2
a
3
=
u
u
3
+ u
a
8
=
−0.162317u
41
− 0.488303u
40
+ ··· + 6.42121u − 11.2810
−0.00894419u
41
− 0.0113179u
40
+ ··· − 3.72593u − 1.09829
a
7
=
−0.171261u
41
− 0.499621u
40
+ ··· + 2.69528u − 12.3793
−0.00894419u
41
− 0.0113179u
40
+ ··· − 3.72593u − 1.09829
a
5
=
0.0765764u
41
+ 0.218473u
40
+ ··· − 9.92664u − 3.95597
0.0117602u
41
+ 0.0207404u
40
+ ··· − 5.71991u − 0.217988
a
2
=
0.0458921u
41
+ 0.116885u
40
+ ··· − 1.72493u − 3.74924
−0.00981888u
41
− 0.0511014u
40
+ ··· − 3.81460u − 0.236598
a
10
=
−0.222058u
41
− 0.640758u
40
+ ··· − 2.30612u − 12.3439
0.00407009u
41
− 0.00144471u
40
+ ··· − 7.80288u − 1.22358
a
9
=
−0.234716u
41
− 0.693689u
40
+ ··· − 8.97199u − 13.5929
−0.0134003u
41
− 0.0709336u
40
+ ··· − 7.27710u − 1.23853
a
6
=
0.245729u
41
+ 0.839363u
40
+ ··· + 9.37284u + 4.46731
0.0686483u
41
+ 0.146810u
40
+ ··· − 6.32759u + 0.755792
a
6
=
0.245729u
41
+ 0.839363u
40
+ ··· + 9.37284u + 4.46731
0.0686483u
41
+ 0.146810u
40
+ ··· − 6.32759u + 0.755792
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.445546u
41
+ 1.05637u
40
+ ··· − 7.66940u + 9.51539
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
42
− u
41
+ ··· − 7u − 1
c
2
, c
5
u
42
+ 7u
40
+ ··· + 1895u + 457
c
3
, c
7
, c
10
c
11
u
42
+ 3u
41
+ ··· + 36u − 1
c
4
(u
21
+ 8u
20
+ ··· + 43u + 7)
2
c
8
(u
21
+ 6u
20
+ ··· + 5u + 1)
2
c
9
(u
21
+ 6u
20
+ ··· + 9u + 1)
2
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
42
− y
41
+ ··· − 45y + 1
c
2
, c
5
y
42
+ 14y
41
+ ··· + 2544657y + 208849
c
3
, c
7
, c
10
c
11
y
42
+ 11y
41
+ ··· − 1288y + 1
c
4
(y
21
− 10y
20
+ ··· + 1149y −49)
2
c
8
(y
21
+ 2y
20
+ ··· − 11y −1)
2
c
9
(y
21
− 8y
20
+ ··· + 33y −1)
2
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.885119 + 0.440669I
a = 0.437217 + 0.545665I
b = −0.998691 − 0.783756I
−3.16717 − 1.07030I −12.89268 + 5.67416I
u = −0.885119 − 0.440669I
a = 0.437217 − 0.545665I
b = −0.998691 + 0.783756I
−3.16717 + 1.07030I −12.89268 − 5.67416I
u = −0.221318 + 0.954664I
a = 1.023340 + 0.577719I
b = 0.715301 − 0.650320I
2.51518 + 5.37801I 0.71786 − 8.23406I
u = −0.221318 − 0.954664I
a = 1.023340 − 0.577719I
b = 0.715301 + 0.650320I
2.51518 − 5.37801I 0.71786 + 8.23406I
u = 0.715301 + 0.650320I
a = −1.186310 − 0.108494I
b = −0.221318 − 0.954664I
2.51518 − 5.37801I 0.71786 + 8.23406I
u = 0.715301 − 0.650320I
a = −1.186310 + 0.108494I
b = −0.221318 + 0.954664I
2.51518 + 5.37801I 0.71786 − 8.23406I
u = 0.660616 + 0.665590I
a = 0.142774 + 0.166906I
b = −1.181090 + 0.555383I
−3.87464 − 0.10689I −16.3307 + 2.6685I
u = 0.660616 − 0.665590I
a = 0.142774 − 0.166906I
b = −1.181090 − 0.555383I
−3.87464 + 0.10689I −16.3307 − 2.6685I
u = 0.746526 + 0.760439I
a = 0.567031 − 0.156980I
b = −0.884140 + 0.948082I
−2.33356 + 1.75773I −7.03716 − 6.33959I
u = 0.746526 − 0.760439I
a = 0.567031 + 0.156980I
b = −0.884140 − 0.948082I
−2.33356 − 1.75773I −7.03716 + 6.33959I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.549689 + 0.965680I
a = 1.164290 + 0.499543I
b = −0.011102 − 0.408161I
0.21083 + 2.02252I −3.27794 − 3.16369I
u = −0.549689 − 0.965680I
a = 1.164290 − 0.499543I
b = −0.011102 + 0.408161I
0.21083 − 2.02252I −3.27794 + 3.16369I
u = 0.587817 + 1.024500I
a = −0.44869 + 1.75524I
b = −0.903022 − 0.809434I
−2.75188 − 4.82047I −10.54242 + 4.40996I
u = 0.587817 − 1.024500I
a = −0.44869 − 1.75524I
b = −0.903022 + 0.809434I
−2.75188 + 4.82047I −10.54242 − 4.40996I
u = 0.112117 + 0.790036I
a = 0.80867 − 3.05059I
b = −0.175620 + 1.395210I
5.06212 + 3.17952I 3.66314 + 2.07098I
u = 0.112117 − 0.790036I
a = 0.80867 + 3.05059I
b = −0.175620 − 1.395210I
5.06212 − 3.17952I 3.66314 − 2.07098I
u = 0.716213 + 0.968774I
a = −0.72128 + 1.60893I
b = −0.84147 − 1.24514I
−1.69311 − 7.34221I −7.2251 + 12.7560I
u = 0.716213 − 0.968774I
a = −0.72128 − 1.60893I
b = −0.84147 + 1.24514I
−1.69311 + 7.34221I −7.2251 − 12.7560I
u = −1.20681
a = 0.255916
b = 0.0276533
−2.39902 9.38220
u = −0.903022 + 0.809434I
a = 0.95127 + 1.48619I
b = 0.587817 − 1.024500I
−2.75188 + 4.82047I −10.54242 − 4.40996I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.903022 − 0.809434I
a = 0.95127 − 1.48619I
b = 0.587817 + 1.024500I
−2.75188 − 4.82047I −10.54242 + 4.40996I
u = 0.280918 + 0.724094I
a = −0.42253 + 2.14926I
b = −0.06930 − 1.59935I
4.77684 − 4.89958I −1.86079 + 9.83067I
u = 0.280918 − 0.724094I
a = −0.42253 − 2.14926I
b = −0.06930 + 1.59935I
4.77684 + 4.89958I −1.86079 − 9.83067I
u = 0.819992 + 0.955539I
a = −0.487721 + 0.138368I
b = 1.170640 − 0.603687I
−4.12482 − 9.03603I −5.90532 + 6.27658I
u = 0.819992 − 0.955539I
a = −0.487721 − 0.138368I
b = 1.170640 + 0.603687I
−4.12482 + 9.03603I −5.90532 − 6.27658I
u = −0.998691 + 0.783756I
a = 0.529988 + 0.125234I
b = −0.885119 − 0.440669I
−3.16717 + 1.07030I −12.89268 − 5.67416I
u = −0.998691 − 0.783756I
a = 0.529988 − 0.125234I
b = −0.885119 + 0.440669I
−3.16717 − 1.07030I −12.89268 + 5.67416I
u = −0.884140 + 0.948082I
a = −0.108358 − 0.471345I
b = 0.746526 + 0.760439I
−2.33356 + 1.75773I −7.03716 − 6.33959I
u = −0.884140 − 0.948082I
a = −0.108358 + 0.471345I
b = 0.746526 − 0.760439I
−2.33356 − 1.75773I −7.03716 + 6.33959I
u = −1.181090 + 0.555383I
a = 0.078562 − 0.136872I
b = 0.660616 + 0.665590I
−3.87464 − 0.10689I −16.3307 + 2.6685I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.181090 − 0.555383I
a = 0.078562 + 0.136872I
b = 0.660616 − 0.665590I
−3.87464 + 0.10689I −16.3307 − 2.6685I
u = 1.170640 + 0.603687I
a = −0.236393 + 0.423087I
b = 0.819992 − 0.955539I
−4.12482 + 9.03603I −5.90532 − 6.27658I
u = 1.170640 − 0.603687I
a = −0.236393 − 0.423087I
b = 0.819992 + 0.955539I
−4.12482 − 9.03603I −5.90532 + 6.27658I
u = −0.175620 + 1.395210I
a = −0.01264 − 1.79079I
b = 0.112117 + 0.790036I
5.06212 + 3.17952I 3.66314 + 2.07098I
u = −0.175620 − 1.395210I
a = −0.01264 + 1.79079I
b = 0.112117 − 0.790036I
5.06212 − 3.17952I 3.66314 − 2.07098I
u = −0.84147 + 1.24514I
a = 0.523153 + 1.313150I
b = 0.716213 − 0.968774I
−1.69311 + 7.34221I 0. − 12.75605I
u = −0.84147 − 1.24514I
a = 0.523153 − 1.313150I
b = 0.716213 + 0.968774I
−1.69311 − 7.34221I 0. + 12.75605I
u = −0.011102 + 0.408161I
a = −2.00560 + 2.80444I
b = −0.549689 − 0.965680I
0.21083 − 2.02252I −3.27794 + 3.16369I
u = −0.011102 − 0.408161I
a = −2.00560 − 2.80444I
b = −0.549689 + 0.965680I
0.21083 + 2.02252I −3.27794 − 3.16369I
u = −0.06930 + 1.59935I
a = −0.140568 + 1.053370I
b = 0.280918 − 0.724094I
4.77684 + 4.89958I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.06930 − 1.59935I
a = −0.140568 − 1.053370I
b = 0.280918 + 0.724094I
4.77684 − 4.89958I 0
u = 0.0276533
a = −11.1684
b = −1.20681
−2.39902 9.38220
14
III. I
u
3
= hb + u, 2u
6
− 4u
5
+ 7u
4
− 6u
3
+ 4u
2
+ a − u − 1, u
7
− 2u
6
+ 4u
5
−
4u
4
+ 4u
3
− 2u
2
+ u − 1i
(i) Arc colorings
a
4
=
0
u
a
11
=
1
0
a
1
=
1
u
2
a
3
=
u
u
3
+ u
a
8
=
−2u
6
+ 4u
5
− 7u
4
+ 6u
3
− 4u
2
+ u + 1
−u
a
7
=
−2u
6
+ 4u
5
− 7u
4
+ 6u
3
− 4u
2
+ 1
−u
a
5
=
−2u
5
+ 6u
4
− 11u
3
+ 13u
2
− 11u + 4
u
6
− 2u
5
+ 4u
4
− 4u
3
+ 3u
2
− u
a
2
=
u
6
− 3u
5
+ 7u
4
− 10u
3
+ 10u
2
− 6u + 2
u
6
− 2u
5
+ 3u
4
− 2u
3
+ 2u
2
a
10
=
u
5
− 2u
4
+ 4u
3
− 3u
2
+ 3u − 1
−u
2
a
9
=
u
5
− 3u
4
+ 5u
3
− 5u
2
+ 4u − 2
−u
6
+ u
5
− 2u
4
+ u
3
− 2u
2
a
6
=
−u
5
+ 2u
4
− 4u
3
+ 5u
2
− 5u + 2
u
4
− u
3
+ u
2
a
6
=
−u
5
+ 2u
4
− 4u
3
+ 5u
2
− 5u + 2
u
4
− u
3
+ u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
6
− u
5
+ 2u
4
− 16u
3
+ 11u
2
− 14u − 1
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
7
− u
6
+ u
5
− u
4
+ 3u
3
− u
2
− 1
c
2
, c
5
u
7
− u
6
+ 3u
5
− 5u
4
+ 4u
3
− 5u
2
+ 5u − 1
c
3
, c
10
u
7
+ 2u
6
+ 4u
5
+ 4u
4
+ 4u
3
+ 2u
2
+ u + 1
c
4
u
7
− 6u
6
+ 22u
5
− 53u
4
+ 84u
3
− 80u
2
+ 42u − 9
c
7
, c
11
u
7
− 2u
6
+ 4u
5
− 4u
4
+ 4u
3
− 2u
2
+ u − 1
c
8
u
7
− 2u
6
+ u
5
+ 2u
4
− 2u
3
+ u
2
+ u − 1
c
9
u
7
− u
6
− u
5
+ 2u
4
− 2u
3
− u
2
+ 2u − 1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
7
+ y
6
+ 5y
5
+ 3y
4
+ 5y
3
− 3y
2
− 2y −1
c
2
, c
5
y
7
+ 5y
6
+ 7y
5
− y
4
− 6y
3
+ 5y
2
+ 15y −1
c
3
, c
7
, c
10
c
11
y
7
+ 4y
6
+ 8y
5
+ 10y
4
+ 4y
3
− 4y
2
− 3y −1
c
4
y
7
+ 8y
6
+ 16y
5
+ 11y
4
+ 316y
3
− 298y
2
+ 324y −81
c
8
y
7
− 2y
6
+ 5y
5
− 2y
4
− 2y
3
− y
2
+ 3y −1
c
9
y
7
− 3y
6
+ y
5
+ 2y
4
+ 2y
3
− 5y
2
+ 2y −1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.820970
a = 0.144523
b = −0.820970
−2.80107 −14.6220
u = 0.090842 + 1.238600I
a = −0.38149 + 1.84270I
b = −0.090842 − 1.238600I
6.98186 − 4.35553I 4.40252 + 4.67318I
u = 0.090842 − 1.238600I
a = −0.38149 − 1.84270I
b = −0.090842 + 1.238600I
6.98186 + 4.35553I 4.40252 − 4.67318I
u = 0.780534 + 1.059930I
a = −0.46249 + 1.46757I
b = −0.780534 − 1.059930I
−1.42367 − 6.15520I −4.27125 + 4.83482I
u = 0.780534 − 1.059930I
a = −0.46249 − 1.46757I
b = −0.780534 + 1.059930I
−1.42367 + 6.15520I −4.27125 − 4.83482I
u = −0.281861 + 0.613464I
a = 3.27172 − 0.15712I
b = 0.281861 − 0.613464I
0.77714 + 4.87266I −5.32028 − 10.34979I
u = −0.281861 − 0.613464I
a = 3.27172 + 0.15712I
b = 0.281861 + 0.613464I
0.77714 − 4.87266I −5.32028 + 10.34979I
18
IV. I
u
4
= h−u
5
+ 2u
4
− 4u
3
+ 5u
2
+ b − 4u + 2, −u
4
+ 2u
3
− 4u
2
+ a + 5u −
3, u
6
− 2u
5
+ 4u
4
− 5u
3
+ 4u
2
− 2u + 1i
(i) Arc colorings
a
4
=
0
u
a
11
=
1
0
a
1
=
1
u
2
a
3
=
u
u
3
+ u
a
8
=
u
4
− 2u
3
+ 4u
2
− 5u + 3
u
5
− 2u
4
+ 4u
3
− 5u
2
+ 4u − 2
a
7
=
u
5
− u
4
+ 2u
3
− u
2
− u + 1
u
5
− 2u
4
+ 4u
3
− 5u
2
+ 4u − 2
a
5
=
−u
5
+ 2u
4
− 3u
3
+ 3u
2
− u − 1
u
5
− u
4
+ 2u
3
− u
2
+ 1
a
2
=
−u
5
+ u
4
− 2u
3
+ u
2
+ 2u − 2
u
4
− u
3
+ 3u
2
− 3u + 2
a
10
=
−3u
5
+ 6u
4
− 11u
3
+ 13u
2
− 8u + 2
2u
5
− 3u
4
+ 6u
3
− 6u
2
+ 3u
a
9
=
−2u
5
+ 5u
4
− 9u
3
+ 11u
2
− 8u + 2
2u
5
− 4u
4
+ 7u
3
− 8u
2
+ 4u − 1
a
6
=
−3u
5
+ 6u
4
− 10u
3
+ 12u
2
− 7u
2u
5
− 3u
4
+ 5u
3
− 5u
2
+ 2u + 1
a
6
=
−3u
5
+ 6u
4
− 10u
3
+ 12u
2
− 7u
2u
5
− 3u
4
+ 5u
3
− 5u
2
+ 2u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 3u
5
+ u
4
− 2u
3
+ 6u
2
− 12u + 2
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
6
− 2u
3
+ 4u
2
− 3u + 1
c
2
, c
5
u
6
+ 3u
5
+ 4u
4
+ 4u
3
+ 3u
2
+ u + 1
c
3
, c
10
u
6
+ 2u
5
+ 4u
4
+ 5u
3
+ 4u
2
+ 2u + 1
c
4
, c
8
(u
3
+ u
2
− 1)
2
c
7
, c
11
u
6
− 2u
5
+ 4u
4
− 5u
3
+ 4u
2
− 2u + 1
c
9
(u
3
− u − 1)
2
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
6
+ 8y
4
− 2y
3
+ 4y
2
− y + 1
c
2
, c
5
y
6
− y
5
− 2y
4
+ 4y
3
+ 9y
2
+ 5y + 1
c
3
, c
7
, c
10
c
11
y
6
+ 4y
5
+ 4y
4
+ y
3
+ 4y
2
+ 4y + 1
c
4
, c
8
(y
3
− y
2
+ 2y −1)
2
c
9
(y
3
− 2y
2
+ y −1)
2
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.877439 + 0.479689I
a = 0.215080 − 0.117582I
b = −0.877439 + 0.479689I
−2.90188 −8.25352 + 0.I
u = 0.877439 − 0.479689I
a = 0.215080 + 0.117582I
b = −0.877439 − 0.479689I
−2.90188 −8.25352 + 0.I
u = 0.039862 + 0.693124I
a = 1.22636 − 2.63813I
b = −0.08270 + 1.43799I
4.74081 + 3.77083I −0.87324 − 6.91540I
u = 0.039862 − 0.693124I
a = 1.22636 + 2.63813I
b = −0.08270 − 1.43799I
4.74081 − 3.77083I −0.87324 + 6.91540I
u = 0.08270 + 1.43799I
a = −0.441444 − 1.330990I
b = −0.039862 + 0.693124I
4.74081 − 3.77083I −0.87324 + 6.91540I
u = 0.08270 − 1.43799I
a = −0.441444 + 1.330990I
b = −0.039862 − 0.693124I
4.74081 + 3.77083I −0.87324 − 6.91540I
22
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
(u
6
− 2u
3
+ 4u
2
− 3u + 1)(u
7
− u
6
+ u
5
− u
4
+ 3u
3
− u
2
− 1)
· (u
16
− u
15
+ ··· − u + 1)(u
42
− u
41
+ ··· − 7u − 1)
c
2
, c
5
(u
6
+ 3u
5
+ 4u
4
+ 4u
3
+ 3u
2
+ u + 1)
· (u
7
− u
6
+ ··· + 5u − 1)(u
16
− u
15
+ ··· + 15u
2
+ 1)
· (u
42
+ 7u
40
+ ··· + 1895u + 457)
c
3
, c
10
(u
6
+ 2u
5
+ 4u
4
+ 5u
3
+ 4u
2
+ 2u + 1)
· (u
7
+ 2u
6
+ ··· + u + 1)(u
16
+ 4u
14
+ ··· + 2u + 1)
· (u
42
+ 3u
41
+ ··· + 36u − 1)
c
4
(u
3
+ u
2
− 1)
2
(u
7
− 6u
6
+ 22u
5
− 53u
4
+ 84u
3
− 80u
2
+ 42u − 9)
· (u
16
− 13u
15
+ ··· − 352u + 64)(u
21
+ 8u
20
+ ··· + 43u + 7)
2
c
7
, c
11
(u
6
− 2u
5
+ 4u
4
− 5u
3
+ 4u
2
− 2u + 1)
· (u
7
− 2u
6
+ ··· + u − 1)(u
16
+ 4u
14
+ ··· + 2u + 1)
· (u
42
+ 3u
41
+ ··· + 36u − 1)
c
8
(u
3
+ u
2
− 1)
2
(u
7
− 2u
6
+ u
5
+ 2u
4
− 2u
3
+ u
2
+ u − 1)
· (u
16
− 13u
15
+ ··· − 36u + 8)(u
21
+ 6u
20
+ ··· + 5u + 1)
2
c
9
(u
3
− u − 1)
2
(u
7
− u
6
− u
5
+ 2u
4
− 2u
3
− u
2
+ 2u − 1)
· (u
16
− 16u
15
+ ··· − 544u + 64)(u
21
+ 6u
20
+ ··· + 9u + 1)
2
23
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
(y
6
+ 8y
4
− 2y
3
+ 4y
2
− y + 1)(y
7
+ y
6
+ ··· − 2y −1)
· (y
16
− 3y
15
+ ··· − 5y + 1)(y
42
− y
41
+ ··· − 45y + 1)
c
2
, c
5
(y
6
− y
5
− 2y
4
+ 4y
3
+ 9y
2
+ 5y + 1)
· (y
7
+ 5y
6
+ ··· + 15y −1)(y
16
+ 9y
15
+ ··· + 30y + 1)
· (y
42
+ 14y
41
+ ··· + 2544657y + 208849)
c
3
, c
7
, c
10
c
11
(y
6
+ 4y
5
+ 4y
4
+ y
3
+ 4y
2
+ 4y + 1)
· (y
7
+ 4y
6
+ 8y
5
+ 10y
4
+ 4y
3
− 4y
2
− 3y −1)
· (y
16
+ 8y
15
+ ··· + 12y + 1)(y
42
+ 11y
41
+ ··· − 1288y + 1)
c
4
(y
3
− y
2
+ 2y −1)
2
· (y
7
+ 8y
6
+ 16y
5
+ 11y
4
+ 316y
3
− 298y
2
+ 324y −81)
· (y
16
+ 5y
15
+ ··· + 40448y + 4096)
· (y
21
− 10y
20
+ ··· + 1149y −49)
2
c
8
(y
3
− y
2
+ 2y −1)
2
(y
7
− 2y
6
+ 5y
5
− 2y
4
− 2y
3
− y
2
+ 3y −1)
· (y
16
− y
15
+ ··· + 496y + 64)(y
21
+ 2y
20
+ ··· − 11y −1)
2
c
9
(y
3
− 2y
2
+ y −1)
2
(y
7
− 3y
6
+ y
5
+ 2y
4
+ 2y
3
− 5y
2
+ 2y −1)
· (y
16
− 4y
15
+ ··· + 23552y + 4096)(y
21
− 8y
20
+ ··· + 33y −1)
2
24
