12a
0433
(K12a
0433
)
A knot diagram
1
Linearized knot diagam
3 6 10 8 2 12 5 11 4 9 1 7
Solving Sequence
3,10 4,6
2 1 5 9 11 12 8 7
c
3
c
2
c
1
c
5
c
9
c
10
c
11
c
8
c
7
c
4
, c
6
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−u
41
+ u
40
+ ··· + b + 1, u
42
− u
41
+ ··· + 2a − 2, u
43
− 3u
42
+ ··· + 2u − 2i
I
u
2
= h−83u
30
a + 64u
30
+ ··· − 12a − 29, −2u
30
a + u
30
+ ··· − 2a + 2, u
31
+ u
30
+ ··· − 2u
2
− 1i
I
u
3
= hb + 1, u
3
− 2u
2
+ 2a + u, u
4
+ u
2
+ 2i
I
u
4
= hb − 1, a + u − 1, u
4
+ 1i
I
u
5
= hb + 1, a − u − 1, u
2
+ 1i
I
v
1
= ha, b − 1, v + 1i
* 6 irreducible components of dim
C
= 0, with total 116 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
41
+u
40
+· · ·+b+1, u
42
−u
41
+· · ·+2a−2, u
43
−3u
42
+· · ·+2u−2i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
u
2
a
6
=
−
1
2
u
42
+
1
2
u
41
+ ··· + u + 1
u
41
− u
40
+ ··· + 3u
2
− 1
a
2
=
−
5
2
u
42
+
9
2
u
41
+ ··· + u
2
+ 4u
−u
42
+ 2u
41
+ ··· + 2u − 1
a
1
=
−
7
2
u
42
+
13
2
u
41
+ ··· + 6u − 1
−u
42
+ 2u
41
+ ··· + 2u − 1
a
5
=
u
10
+ u
8
+ 2u
6
+ u
4
+ u
2
+ 1
u
12
+ 2u
10
+ 4u
8
+ 4u
6
+ 3u
4
+ 2u
2
a
9
=
u
u
3
+ u
a
11
=
u
3
u
5
+ u
3
+ u
a
12
=
−
5
2
u
42
+
9
2
u
41
+ ··· + 4u − 1
−u
42
+ 2u
41
+ ··· + 3u − 1
a
8
=
u
5
+ u
u
7
+ u
5
+ 2u
3
+ u
a
7
=
u
15
+ 2u
13
+ 4u
11
+ 4u
9
+ 4u
7
+ 4u
5
+ 2u
3
+ 2u
u
17
+ 3u
15
+ 7u
13
+ 10u
11
+ 11u
9
+ 10u
7
+ 6u
5
+ 4u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −16u
42
+ 34u
41
+ ··· + 22u − 20
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
u
43
+ 17u
42
+ ··· + 16u + 1
c
2
, c
5
, c
6
c
12
u
43
+ u
42
+ ··· − 8u
2
+ 1
c
3
, c
9
u
43
+ 3u
42
+ ··· + 2u + 2
c
4
, c
7
u
43
− 15u
42
+ ··· − 2154u + 158
c
8
, c
10
u
43
− 15u
42
+ ··· + 12u + 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
43
+ 31y
42
+ ··· + 36y −1
c
2
, c
5
, c
6
c
12
y
43
− 17y
42
+ ··· + 16y −1
c
3
, c
9
y
43
+ 15y
42
+ ··· + 12y −4
c
4
, c
7
y
43
+ 27y
42
+ ··· + 268172y −24964
c
8
, c
10
y
43
+ 27y
42
+ ··· + 784y −16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.810305 + 0.610083I
a = −0.872253 − 1.072020I
b = −1.165720 + 0.639728I
−0.67916 + 11.73210I −10.65839 − 6.76823I
u = 0.810305 − 0.610083I
a = −0.872253 + 1.072020I
b = −1.165720 − 0.639728I
−0.67916 − 11.73210I −10.65839 + 6.76823I
u = −0.169320 + 0.970646I
a = 1.076800 + 0.490969I
b = −0.864916 − 0.541410I
1.81117 − 1.96121I −3.54414 + 2.58212I
u = −0.169320 − 0.970646I
a = 1.076800 − 0.490969I
b = −0.864916 + 0.541410I
1.81117 + 1.96121I −3.54414 − 2.58212I
u = −0.404499 + 0.937684I
a = −0.09752 − 2.06018I
b = −1.003290 + 0.619413I
0.64091 + 7.57935I −5.71587 − 9.06778I
u = −0.404499 − 0.937684I
a = −0.09752 + 2.06018I
b = −1.003290 − 0.619413I
0.64091 − 7.57935I −5.71587 + 9.06778I
u = −0.740546 + 0.734320I
a = 0.953869 + 0.031628I
b = 0.638692 + 0.127245I
−3.38498 − 0.54186I −9.64597 + 2.59436I
u = −0.740546 − 0.734320I
a = 0.953869 − 0.031628I
b = 0.638692 − 0.127245I
−3.38498 + 0.54186I −9.64597 − 2.59436I
u = 0.767460 + 0.565351I
a = 0.203752 + 0.596820I
b = −0.551586 − 0.826342I
3.23658 + 0.48012I −5.52727 + 1.98665I
u = 0.767460 − 0.565351I
a = 0.203752 − 0.596820I
b = −0.551586 + 0.826342I
3.23658 − 0.48012I −5.52727 − 1.98665I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.781599 + 0.706193I
a = 1.015530 + 0.059356I
b = 0.943303 + 0.436662I
−4.27279 − 2.51600I −12.07773 + 5.71847I
u = 0.781599 − 0.706193I
a = 1.015530 − 0.059356I
b = 0.943303 − 0.436662I
−4.27279 + 2.51600I −12.07773 − 5.71847I
u = 0.634409 + 0.863030I
a = 0.482681 − 0.289079I
b = −0.073637 + 0.560874I
−0.87271 − 2.47607I −4.48573 + 2.92592I
u = 0.634409 − 0.863030I
a = 0.482681 + 0.289079I
b = −0.073637 − 0.560874I
−0.87271 + 2.47607I −4.48573 − 2.92592I
u = −0.730178 + 0.509618I
a = 0.210279 + 0.671513I
b = −0.659249 − 0.796369I
3.58914 − 2.18174I −5.59185 + 2.68261I
u = −0.730178 − 0.509618I
a = 0.210279 − 0.671513I
b = −0.659249 + 0.796369I
3.58914 + 2.18174I −5.59185 − 2.68261I
u = 0.064317 + 0.887781I
a = 0.245081 + 0.904782I
b = −0.514108 − 0.340137I
1.82719 − 1.38027I −1.41434 + 5.67019I
u = 0.064317 − 0.887781I
a = 0.245081 − 0.904782I
b = −0.514108 + 0.340137I
1.82719 + 1.38027I −1.41434 − 5.67019I
u = −0.019617 + 1.114870I
a = −1.21478 − 1.96630I
b = 0.614989 + 0.851882I
8.98390 − 0.70392I 0.62643 + 2.07043I
u = −0.019617 − 1.114870I
a = −1.21478 + 1.96630I
b = 0.614989 − 0.851882I
8.98390 + 0.70392I 0.62643 − 2.07043I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.070568 + 1.113790I
a = −0.93313 + 2.40704I
b = 1.150350 − 0.663782I
5.52719 + 10.86160I −3.74256 − 7.47837I
u = −0.070568 − 1.113790I
a = −0.93313 − 2.40704I
b = 1.150350 + 0.663782I
5.52719 − 10.86160I −3.74256 + 7.47837I
u = 0.769424 + 0.820046I
a = 1.203010 − 0.319741I
b = 1.082070 − 0.520953I
−6.01940 + 4.69142I −13.7584 − 4.2985I
u = 0.769424 − 0.820046I
a = 1.203010 + 0.319741I
b = 1.082070 + 0.520953I
−6.01940 − 4.69142I −13.7584 + 4.2985I
u = 0.747584 + 0.908886I
a = −1.77260 + 1.30694I
b = −1.099080 − 0.534938I
−5.74879 − 10.41320I −13.1188 + 9.7708I
u = 0.747584 − 0.908886I
a = −1.77260 − 1.30694I
b = −1.099080 + 0.534938I
−5.74879 + 10.41320I −13.1188 − 9.7708I
u = −0.587598 + 1.034130I
a = −0.976042 − 0.394281I
b = 1.109900 + 0.674647I
2.34669 − 4.11995I −6.41118 + 2.08920I
u = −0.587598 − 1.034130I
a = −0.976042 + 0.394281I
b = 1.109900 − 0.674647I
2.34669 + 4.11995I −6.41118 − 2.08920I
u = −0.697004 + 0.966572I
a = −0.886537 − 0.919821I
b = −0.663489 + 0.163610I
−2.67878 + 6.02819I −8.00000 − 8.68993I
u = −0.697004 − 0.966572I
a = −0.886537 + 0.919821I
b = −0.663489 − 0.163610I
−2.67878 − 6.02819I −8.00000 + 8.68993I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.693381 + 0.387489I
a = −0.79741 − 1.27275I
b = −1.120710 + 0.646264I
0.58526 + 8.92556I −9.86563 − 7.36810I
u = −0.693381 − 0.387489I
a = −0.79741 + 1.27275I
b = −1.120710 − 0.646264I
0.58526 − 8.92556I −9.86563 + 7.36810I
u = 0.710991 + 0.990924I
a = −0.093051 + 1.044480I
b = −0.922866 + 0.415678I
−3.40970 − 3.12696I −10.17371 + 0.I
u = 0.710991 − 0.990924I
a = −0.093051 − 1.044480I
b = −0.922866 − 0.415678I
−3.40970 + 3.12696I −10.17371 + 0.I
u = −0.635885 + 1.042150I
a = 0.39218 + 2.01011I
b = 0.683334 − 0.830391I
5.11017 + 7.38861I −3.39621 − 7.50854I
u = −0.635885 − 1.042150I
a = 0.39218 − 2.01011I
b = 0.683334 + 0.830391I
5.11017 − 7.38861I −3.39621 + 7.50854I
u = 0.663748 + 1.042840I
a = −1.50776 + 0.41692I
b = 0.546956 − 0.859893I
4.63845 − 5.90595I −3.49620 + 2.84362I
u = 0.663748 − 1.042840I
a = −1.50776 − 0.41692I
b = 0.546956 + 0.859893I
4.63845 + 5.90595I −3.49620 − 2.84362I
u = 0.692059 + 1.043830I
a = 1.02365 − 2.73608I
b = 1.174490 + 0.646634I
0.6235 − 17.3797I −8.00000 + 11.25544I
u = 0.692059 − 1.043830I
a = 1.02365 + 2.73608I
b = 1.174490 − 0.646634I
0.6235 + 17.3797I −8.00000 − 11.25544I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.580815 + 0.131701I
a = 0.893430 + 0.128520I
b = 0.976159 + 0.538801I
−1.61575 − 4.22948I −11.92293 + 4.59304I
u = −0.580815 − 0.131701I
a = 0.893430 − 0.128520I
b = 0.976159 − 0.538801I
−1.61575 + 4.22948I −11.92293 − 4.59304I
u = 0.375038
a = 0.901679
b = 0.436822
−0.737041 −13.3130
9
II. I
u
2
= h−83u
30
a + 64u
30
+ · · · − 12a − 29, −2u
30
a + u
30
+ · · · − 2a +
2, u
31
+ u
30
+ · · · − 2u
2
− 1i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
u
2
a
6
=
a
1.66000au
30
− 1.28000u
30
+ ··· + 0.240000a + 0.580000
a
2
=
−1.28000au
30
+ 1.74000u
30
+ ··· + 0.580000a − 0.140000
−1.52000au
30
+ 1.66000u
30
+ ··· − 0.780000a − 0.760000
a
1
=
−2.80000au
30
+ 3.40000u
30
+ ··· − 0.200000a − 0.900000
−1.52000au
30
+ 1.66000u
30
+ ··· − 0.780000a − 0.760000
a
5
=
u
10
+ u
8
+ 2u
6
+ u
4
+ u
2
+ 1
u
12
+ 2u
10
+ 4u
8
+ 4u
6
+ 3u
4
+ 2u
2
a
9
=
u
u
3
+ u
a
11
=
u
3
u
5
+ u
3
+ u
a
12
=
1.28000au
30
− 1.74000u
30
+ ··· − 0.580000a + 1.14000
1
a
8
=
u
5
+ u
u
7
+ u
5
+ 2u
3
+ u
a
7
=
u
15
+ 2u
13
+ 4u
11
+ 4u
9
+ 4u
7
+ 4u
5
+ 2u
3
+ 2u
u
17
+ 3u
15
+ 7u
13
+ 10u
11
+ 11u
9
+ 10u
7
+ 6u
5
+ 4u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 4u
30
+ 20u
28
− 4u
27
+ 68u
26
− 20u
25
+ 160u
24
− 64u
23
+ 300u
22
− 144u
21
+ 460u
20
−
252u
19
+ 592u
18
− 364u
17
+ 660u
16
− 436u
15
+ 628u
14
− 452u
13
+ 528u
12
− 396u
11
+
380u
10
− 296u
9
+ 236u
8
− 188u
7
+ 128u
6
− 92u
5
+ 52u
4
− 40u
3
+ 20u
2
− 12u − 6
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
u
62
+ 33u
61
+ ··· + 2505u + 256
c
2
, c
5
, c
6
c
12
u
62
+ u
61
+ ··· + 19u + 16
c
3
, c
9
(u
31
− u
30
+ ··· + 2u
2
+ 1)
2
c
4
, c
7
(u
31
+ 5u
30
+ ··· + 40u + 7)
2
c
8
, c
10
(u
31
− 11u
30
+ ··· − 4u + 1)
2
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
62
− 9y
61
+ ··· + 636463y + 65536
c
2
, c
5
, c
6
c
12
y
62
− 33y
61
+ ··· − 2505y + 256
c
3
, c
9
(y
31
+ 11y
30
+ ··· − 4y −1)
2
c
4
, c
7
(y
31
+ 23y
30
+ ··· − 640y −49)
2
c
8
, c
10
(y
31
+ 19y
30
+ ··· − 8y −1)
2
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.794006 + 0.593785I
a = −0.575606 + 1.111050I
b = −1.060010 − 0.663363I
1.70250 − 6.04082I −7.64635 + 3.16093I
u = −0.794006 + 0.593785I
a = 0.268388 − 0.355056I
b = −0.378076 + 0.912441I
1.70250 − 6.04082I −7.64635 + 3.16093I
u = −0.794006 − 0.593785I
a = −0.575606 − 1.111050I
b = −1.060010 + 0.663363I
1.70250 + 6.04082I −7.64635 − 3.16093I
u = −0.794006 − 0.593785I
a = 0.268388 + 0.355056I
b = −0.378076 − 0.912441I
1.70250 + 6.04082I −7.64635 − 3.16093I
u = 0.752643 + 0.616875I
a = 1.049010 − 0.024204I
b = 1.292420 + 0.176912I
−4.01963 + 2.73446I −11.76690 − 3.38925I
u = 0.752643 + 0.616875I
a = −0.19620 − 1.79030I
b = −0.948917 + 0.478047I
−4.01963 + 2.73446I −11.76690 − 3.38925I
u = 0.752643 − 0.616875I
a = 1.049010 + 0.024204I
b = 1.292420 − 0.176912I
−4.01963 − 2.73446I −11.76690 + 3.38925I
u = 0.752643 − 0.616875I
a = −0.19620 + 1.79030I
b = −0.948917 − 0.478047I
−4.01963 − 2.73446I −11.76690 + 3.38925I
u = 0.307711 + 0.890519I
a = 0.991470 − 0.636002I
b = −0.548491 + 0.670065I
1.93424 − 2.56488I −2.83547 + 4.43258I
u = 0.307711 + 0.890519I
a = 0.06449 + 1.90945I
b = −0.810066 − 0.589243I
1.93424 − 2.56488I −2.83547 + 4.43258I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.307711 − 0.890519I
a = 0.991470 + 0.636002I
b = −0.548491 − 0.670065I
1.93424 + 2.56488I −2.83547 − 4.43258I
u = 0.307711 − 0.890519I
a = 0.06449 − 1.90945I
b = −0.810066 + 0.589243I
1.93424 + 2.56488I −2.83547 − 4.43258I
u = −0.028596 + 1.074730I
a = 1.254810 + 0.086042I
b = −1.300190 − 0.121437I
1.60703 + 1.99617I −4.10076 − 3.62729I
u = −0.028596 + 1.074730I
a = −1.60467 + 2.59295I
b = 0.865196 − 0.489813I
1.60703 + 1.99617I −4.10076 − 3.62729I
u = −0.028596 − 1.074730I
a = 1.254810 − 0.086042I
b = −1.300190 + 0.121437I
1.60703 − 1.99617I −4.10076 + 3.62729I
u = −0.028596 − 1.074730I
a = −1.60467 − 2.59295I
b = 0.865196 + 0.489813I
1.60703 − 1.99617I −4.10076 + 3.62729I
u = −0.730031 + 0.790482I
a = 1.124130 + 0.092019I
b = 0.982872 + 0.347185I
−3.79282 − 0.40298I −11.07070 + 0.52831I
u = −0.730031 + 0.790482I
a = 0.801595 − 0.042941I
b = 0.213919 − 0.536430I
−3.79282 − 0.40298I −11.07070 + 0.52831I
u = −0.730031 − 0.790482I
a = 1.124130 − 0.092019I
b = 0.982872 − 0.347185I
−3.79282 + 0.40298I −11.07070 − 0.52831I
u = −0.730031 − 0.790482I
a = 0.801595 + 0.042941I
b = 0.213919 + 0.536430I
−3.79282 + 0.40298I −11.07070 − 0.52831I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.709633 + 0.857826I
a = 1.50924 + 0.06570I
b = 1.162280 − 0.314153I
−7.28578 − 2.71284I −15.8994 + 3.4466I
u = 0.709633 + 0.857826I
a = −1.89841 + 2.00937I
b = −1.134280 − 0.338014I
−7.28578 − 2.71284I −15.8994 + 3.4466I
u = 0.709633 − 0.857826I
a = 1.50924 − 0.06570I
b = 1.162280 + 0.314153I
−7.28578 + 2.71284I −15.8994 − 3.4466I
u = 0.709633 − 0.857826I
a = −1.89841 − 2.00937I
b = −1.134280 + 0.338014I
−7.28578 + 2.71284I −15.8994 − 3.4466I
u = 0.048600 + 1.113390I
a = −1.10147 + 1.83797I
b = 0.429611 − 0.922254I
7.71400 − 5.04935I −0.87471 + 3.42516I
u = 0.048600 + 1.113390I
a = −1.08873 − 2.37779I
b = 1.032690 + 0.699331I
7.71400 − 5.04935I −0.87471 + 3.42516I
u = 0.048600 − 1.113390I
a = −1.10147 − 1.83797I
b = 0.429611 + 0.922254I
7.71400 + 5.04935I −0.87471 − 3.42516I
u = 0.048600 − 1.113390I
a = −1.08873 + 2.37779I
b = 1.032690 − 0.699331I
7.71400 + 5.04935I −0.87471 − 3.42516I
u = −0.630136 + 0.611565I
a = 0.979082 + 0.056700I
b = 1.231410 + 0.064735I
−3.29780 + 0.92992I −9.59628 − 3.68841I
u = −0.630136 + 0.611565I
a = 0.90502 − 1.81588I
b = −0.766634 + 0.363749I
−3.29780 + 0.92992I −9.59628 − 3.68841I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.630136 − 0.611565I
a = 0.979082 − 0.056700I
b = 1.231410 − 0.064735I
−3.29780 − 0.92992I −9.59628 + 3.68841I
u = −0.630136 − 0.611565I
a = 0.90502 + 1.81588I
b = −0.766634 − 0.363749I
−3.29780 − 0.92992I −9.59628 + 3.68841I
u = −0.711244 + 0.915096I
a = 0.223384 − 0.239937I
b = −0.229078 − 0.626885I
−3.41810 + 5.89464I −10.05487 − 6.44091I
u = −0.711244 + 0.915096I
a = −1.45569 − 1.48316I
b = −1.009990 + 0.409220I
−3.41810 + 5.89464I −10.05487 − 6.44091I
u = −0.711244 − 0.915096I
a = 0.223384 + 0.239937I
b = −0.229078 + 0.626885I
−3.41810 − 5.89464I −10.05487 + 6.44091I
u = −0.711244 − 0.915096I
a = −1.45569 + 1.48316I
b = −1.009990 − 0.409220I
−3.41810 − 5.89464I −10.05487 + 6.44091I
u = 0.696118 + 0.446614I
a = −0.429932 + 1.245830I
b = −0.983943 − 0.673017I
2.60250 − 3.33239I −6.76330 + 3.21859I
u = 0.696118 + 0.446614I
a = 0.375203 − 0.425155I
b = −0.451734 + 0.862793I
2.60250 − 3.33239I −6.76330 + 3.21859I
u = 0.696118 − 0.446614I
a = −0.429932 − 1.245830I
b = −0.983943 + 0.673017I
2.60250 + 3.33239I −6.76330 − 3.21859I
u = 0.696118 − 0.446614I
a = 0.375203 + 0.425155I
b = −0.451734 − 0.862793I
2.60250 + 3.33239I −6.76330 − 3.21859I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.642253 + 1.006370I
a = −0.28971 − 1.62874I
b = −1.280510 + 0.056589I
−2.14842 + 4.14236I −7.79961 − 2.04013I
u = −0.642253 + 1.006370I
a = −1.61379 − 0.81510I
b = 0.751258 + 0.461288I
−2.14842 + 4.14236I −7.79961 − 2.04013I
u = −0.642253 − 1.006370I
a = −0.28971 + 1.62874I
b = −1.280510 − 0.056589I
−2.14842 − 4.14236I −7.79961 + 2.04013I
u = −0.642253 − 1.006370I
a = −1.61379 + 0.81510I
b = 0.751258 − 0.461288I
−2.14842 − 4.14236I −7.79961 + 2.04013I
u = 0.611328 + 1.036450I
a = −1.171880 + 0.475269I
b = 0.974751 − 0.714129I
4.22211 − 1.64856I −3.98491 + 2.12263I
u = 0.611328 + 1.036450I
a = 0.40901 − 1.68159I
b = 0.489978 + 0.891236I
4.22211 − 1.64856I −3.98491 + 2.12263I
u = 0.611328 − 1.036450I
a = −1.171880 − 0.475269I
b = 0.974751 + 0.714129I
4.22211 + 1.64856I −3.98491 − 2.12263I
u = 0.611328 − 1.036450I
a = 0.40901 + 1.68159I
b = 0.489978 − 0.891236I
4.22211 + 1.64856I −3.98491 − 2.12263I
u = 0.673649 + 1.023570I
a = −0.12488 + 1.47943I
b = −1.314250 + 0.172694I
−2.81425 − 8.17190I −9.55732 + 8.00325I
u = 0.673649 + 1.023570I
a = 0.29874 − 3.07399I
b = 0.942920 + 0.509265I
−2.81425 − 8.17190I −9.55732 + 8.00325I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.673649 − 1.023570I
a = −0.12488 − 1.47943I
b = −1.314250 − 0.172694I
−2.81425 + 8.17190I −9.55732 − 8.00325I
u = 0.673649 − 1.023570I
a = 0.29874 + 3.07399I
b = 0.942920 − 0.509265I
−2.81425 + 8.17190I −9.55732 − 8.00325I
u = −0.680810 + 1.043630I
a = −1.54320 − 0.40737I
b = 0.377634 + 0.934666I
3.04348 + 11.60290I −5.65053 − 7.70694I
u = −0.680810 + 1.043630I
a = 0.80613 + 2.68508I
b = 1.073030 − 0.677122I
3.04348 + 11.60290I −5.65053 − 7.70694I
u = −0.680810 − 1.043630I
a = −1.54320 + 0.40737I
b = 0.377634 − 0.934666I
3.04348 − 11.60290I −5.65053 + 7.70694I
u = −0.680810 − 1.043630I
a = 0.80613 − 2.68508I
b = 1.073030 + 0.677122I
3.04348 − 11.60290I −5.65053 + 7.70694I
u = −0.330533 + 0.488116I
a = 1.010390 + 0.142244I
b = 1.168370 + 0.123140I
−3.18273 + 1.02630I −10.18992 − 6.41690I
u = −0.330533 + 0.488116I
a = 0.66597 − 3.17396I
b = −0.903345 + 0.276517I
−3.18273 + 1.02630I −10.18992 − 6.41690I
u = −0.330533 − 0.488116I
a = 1.010390 − 0.142244I
b = 1.168370 − 0.123140I
−3.18273 − 1.02630I −10.18992 + 6.41690I
u = −0.330533 − 0.488116I
a = 0.66597 + 3.17396I
b = −0.903345 − 0.276517I
−3.18273 − 1.02630I −10.18992 + 6.41690I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.495857
a = 0.858117 + 0.046148I
b = 0.631170 + 0.441733I
−0.537061 −10.4180
u = 0.495857
a = 0.858117 − 0.046148I
b = 0.631170 − 0.441733I
−0.537061 −10.4180
19
III. I
u
3
= hb + 1, u
3
− 2u
2
+ 2a + u, u
4
+ u
2
+ 2i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
u
2
a
6
=
−
1
2
u
3
+ u
2
−
1
2
u
−1
a
2
=
−
1
2
u
3
+ u
2
−
1
2
u + 1
−1
a
1
=
−
1
2
u
3
+ u
2
−
1
2
u
−1
a
5
=
−1
0
a
9
=
u
u
3
+ u
a
11
=
u
3
−u
a
12
=
1
2
u
3
+ u
2
−
1
2
u
−u − 1
a
8
=
−u
3
− u
u
a
7
=
−u
3
u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
2
− 12
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
11
c
12
(u − 1)
4
c
2
, c
6
(u + 1)
4
c
3
, c
4
, c
7
c
9
u
4
+ u
2
+ 2
c
8
(u
2
+ u + 2)
2
c
10
(u
2
− u + 2)
2
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
11
, c
12
(y −1)
4
c
3
, c
4
, c
7
c
9
(y
2
+ y + 2)
2
c
8
, c
10
(y
2
+ 3y + 4)
2
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.676097 + 0.978318I
a = −0.021927 + 0.631100I
b = −1.00000
−4.11234 − 5.33349I −14.0000 + 5.2915I
u = 0.676097 − 0.978318I
a = −0.021927 − 0.631100I
b = −1.00000
−4.11234 + 5.33349I −14.0000 − 5.2915I
u = −0.676097 + 0.978318I
a = −0.97807 − 2.01465I
b = −1.00000
−4.11234 + 5.33349I −14.0000 − 5.2915I
u = −0.676097 − 0.978318I
a = −0.97807 + 2.01465I
b = −1.00000
−4.11234 − 5.33349I −14.0000 + 5.2915I
23
IV. I
u
4
= hb − 1, a + u − 1, u
4
+ 1i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
u
2
a
6
=
−u + 1
1
a
2
=
u
−1
a
1
=
u − 1
−1
a
5
=
1
0
a
9
=
u
u
3
+ u
a
11
=
u
3
u
3
a
12
=
u
3
+ u − 1
u
3
− 1
a
8
=
0
u
3
a
7
=
u
3
u
3
(ii) Obstruction class = 1
(iii) Cusp Shapes = −16
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
c
11
(u − 1)
4
c
3
, c
4
, c
7
c
9
u
4
+ 1
c
5
, c
12
(u + 1)
4
c
8
, c
10
(u
2
+ 1)
2
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
11
, c
12
(y −1)
4
c
3
, c
4
, c
7
c
9
(y
2
+ 1)
2
c
8
, c
10
(y + 1)
4
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.707107 + 0.707107I
a = 0.292893 − 0.707107I
b = 1.00000
−4.93480 −16.0000
u = 0.707107 − 0.707107I
a = 0.292893 + 0.707107I
b = 1.00000
−4.93480 −16.0000
u = −0.707107 + 0.707107I
a = 1.70711 − 0.70711I
b = 1.00000
−4.93480 −16.0000
u = −0.707107 − 0.707107I
a = 1.70711 + 0.70711I
b = 1.00000
−4.93480 −16.0000
27
V. I
u
5
= hb + 1, a − u − 1, u
2
+ 1i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
−1
a
6
=
u + 1
−1
a
2
=
u + 2
−1
a
1
=
u + 1
−1
a
5
=
−1
0
a
9
=
u
0
a
11
=
−u
u
a
12
=
1
u − 1
a
8
=
2u
−u
a
7
=
u
−u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8
28
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
10
c
11
, c
12
(u − 1)
2
c
2
, c
6
, c
8
(u + 1)
2
c
3
, c
4
, c
7
c
9
u
2
+ 1
29
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
8
, c
10
c
11
, c
12
(y −1)
2
c
3
, c
4
, c
7
c
9
(y + 1)
2
30
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = 1.00000 + 1.00000I
b = −1.00000
0 −8.00000
u = − 1.000000I
a = 1.00000 − 1.00000I
b = −1.00000
0 −8.00000
31
VI. I
v
1
= ha, b − 1, v + 1i
(i) Arc colorings
a
3
=
1
0
a
10
=
−1
0
a
4
=
1
0
a
6
=
0
1
a
2
=
1
−1
a
1
=
0
−1
a
5
=
1
0
a
9
=
−1
0
a
11
=
−1
0
a
12
=
−1
−1
a
8
=
−1
0
a
7
=
−1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
32
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
c
11
u − 1
c
3
, c
4
, c
7
c
8
, c
9
, c
10
u
c
5
, c
12
u + 1
33
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
11
, c
12
y − 1
c
3
, c
4
, c
7
c
8
, c
9
, c
10
y
34
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −1.00000
a = 0
b = 1.00000
−3.28987 −12.0000
35
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
11
((u − 1)
11
)(u
43
+ 17u
42
+ ··· + 16u + 1)
· (u
62
+ 33u
61
+ ··· + 2505u + 256)
c
2
, c
6
((u − 1)
5
)(u + 1)
6
(u
43
+ u
42
+ ··· − 8u
2
+ 1)(u
62
+ u
61
+ ··· + 19u + 16)
c
3
, c
9
u(u
2
+ 1)(u
4
+ 1)(u
4
+ u
2
+ 2)(u
31
− u
30
+ ··· + 2u
2
+ 1)
2
· (u
43
+ 3u
42
+ ··· + 2u + 2)
c
4
, c
7
u(u
2
+ 1)(u
4
+ 1)(u
4
+ u
2
+ 2)(u
31
+ 5u
30
+ ··· + 40u + 7)
2
· (u
43
− 15u
42
+ ··· − 2154u + 158)
c
5
, c
12
((u − 1)
6
)(u + 1)
5
(u
43
+ u
42
+ ··· − 8u
2
+ 1)(u
62
+ u
61
+ ··· + 19u + 16)
c
8
u(u + 1)
2
(u
2
+ 1)
2
(u
2
+ u + 2)
2
(u
31
− 11u
30
+ ··· − 4u + 1)
2
· (u
43
− 15u
42
+ ··· + 12u + 4)
c
10
u(u − 1)
2
(u
2
+ 1)
2
(u
2
− u + 2)
2
(u
31
− 11u
30
+ ··· − 4u + 1)
2
· (u
43
− 15u
42
+ ··· + 12u + 4)
36
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
11
((y − 1)
11
)(y
43
+ 31y
42
+ ··· + 36y − 1)
· (y
62
− 9y
61
+ ··· + 636463y + 65536)
c
2
, c
5
, c
6
c
12
((y − 1)
11
)(y
43
− 17y
42
+ ··· + 16y − 1)
· (y
62
− 33y
61
+ ··· − 2505y + 256)
c
3
, c
9
y(y + 1)
2
(y
2
+ 1)
2
(y
2
+ y + 2)
2
(y
31
+ 11y
30
+ ··· − 4y − 1)
2
· (y
43
+ 15y
42
+ ··· + 12y − 4)
c
4
, c
7
y(y + 1)
2
(y
2
+ 1)
2
(y
2
+ y + 2)
2
(y
31
+ 23y
30
+ ··· − 640y − 49)
2
· (y
43
+ 27y
42
+ ··· + 268172y − 24964)
c
8
, c
10
y(y − 1)
2
(y + 1)
4
(y
2
+ 3y + 4)
2
(y
31
+ 19y
30
+ ··· − 8y − 1)
2
· (y
43
+ 27y
42
+ ··· + 784y − 16)
37
