12a
1115
(K12a
1115
)
A knot diagram
1
Linearized knot diagam
4 7 12 9 10 11 3 1 6 5 2 8
Solving Sequence
6,9
10 5 11 7
1,4
2 8 12 3
c
9
c
5
c
10
c
6
c
4
c
1
c
8
c
12
c
3
c
2
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h15u
35
+ 68u
34
+ ··· + 2b − 38, −9u
35
− 36u
34
+ ··· + 4a + 72, u
36
+ 6u
35
+ ··· − 10u − 4i
I
u
2
= h−415484u
5
a
3
+ 374659u
5
a
2
+ ··· + 1141045a + 3493341, u
5
a
3
− u
5
a
2
+ ··· − 62a + 184,
u
6
+ 3u
4
+ u
3
+ 2u
2
+ 2u − 1i
I
u
3
= hu
16
+ u
15
+ ··· + b + 2, −2u
17
− 2u
16
+ ··· + a − 2, u
18
+ u
17
+ ··· + 2u + 1i
I
u
4
= h−352079058u
9
a
3
− 279641663u
9
a
2
+ ··· + 597636419a − 889033224,
2u
9
a
3
+ 3u
9
a
2
+ ··· + 2a + 4, u
10
− u
9
+ 4u
8
− 4u
7
+ 6u
6
− 6u
5
+ 3u
4
− 3u
3
+ 1i
* 4 irreducible components of dim
C
= 0, with total 118 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
= h15u
35
+ 68u
34
+ · · · + 2b − 38, −9u
35
− 36u
34
+ · · · + 4a + 72, u
36
+
6u
35
+ · · · − 10u − 4i
(i) Arc colorings
a
6
=
0
u
a
9
=
1
0
a
10
=
1
−u
2
a
5
=
−u
u
3
+ u
a
11
=
u
2
+ 1
−u
4
− 2u
2
a
7
=
u
5
+ 2u
3
+ u
−u
7
− 3u
5
− 2u
3
+ u
a
1
=
9
4
u
35
+ 9u
34
+ ··· −
79
4
u − 18
−
15
2
u
35
− 34u
34
+ ··· +
41
2
u + 19
a
4
=
−u
3
− 2u
u
3
+ u
a
2
=
49
4
u
35
+ 56u
34
+ ··· −
247
4
u − 66
−
35
2
u
35
− 84u
34
+ ··· +
113
2
u + 49
a
8
=
−4u
35
−
43
2
u
34
+ ··· + 25u +
27
2
5
2
u
35
+ 15u
34
+ ··· −
57
2
u − 18
a
12
=
7
2
u
35
+
33
2
u
34
+ ··· −
43
2
u −
45
2
−
9
2
u
35
− 21u
34
+ ··· +
23
2
u + 14
a
3
=
1
4
u
35
+ 3u
34
+ ··· −
31
4
u − 8
1
2
u
35
+ u
34
+ ··· −
3
2
u + 3
(ii) Obstruction class = −1
(iii) Cusp Shapes = 13u
35
+ 78u
34
+ ··· − 156u − 78
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
u
36
+ 3u
35
+ ··· + 10u − 1
c
2
, c
7
, c
8
c
12
u
36
+ u
35
+ ··· − 4u
2
+ 1
c
3
u
36
+ 36u
35
+ ··· − 851968u − 65536
c
4
, c
6
u
36
+ 6u
35
+ ··· − 3456u − 712
c
5
, c
9
, c
10
u
36
− 6u
35
+ ··· + 10u − 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
36
+ 13y
35
+ ··· − 108y + 1
c
2
, c
7
, c
8
c
12
y
36
− 31y
35
+ ··· − 8y + 1
c
3
y
36
+ 8y
35
+ ··· − 81604378624y + 4294967296
c
4
, c
6
y
36
− 26y
35
+ ··· − 1429120y + 506944
c
5
, c
9
, c
10
y
36
+ 30y
35
+ ··· − 108y + 16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.918601 + 0.135473I
a = −2.16683 − 0.71703I
b = 1.310650 − 0.016930I
11.86120 − 2.65850I 16.0062 + 3.1622I
u = −0.918601 − 0.135473I
a = −2.16683 + 0.71703I
b = 1.310650 + 0.016930I
11.86120 + 2.65850I 16.0062 − 3.1622I
u = −0.886777 + 0.100899I
a = 2.80734 + 0.39802I
b = −1.51502 + 0.47144I
13.5026 − 12.5111I 13.4715 + 6.4902I
u = −0.886777 − 0.100899I
a = 2.80734 − 0.39802I
b = −1.51502 − 0.47144I
13.5026 + 12.5111I 13.4715 − 6.4902I
u = 0.582328 + 0.632591I
a = 1.065630 − 0.902416I
b = −1.302410 + 0.256154I
6.20237 − 3.57524I 13.30271 + 2.91674I
u = 0.582328 − 0.632591I
a = 1.065630 + 0.902416I
b = −1.302410 − 0.256154I
6.20237 + 3.57524I 13.30271 − 2.91674I
u = −0.805953 + 0.027041I
a = −0.345526 + 0.596121I
b = 0.024838 − 0.844400I
3.39332 − 2.17431I 8.53831 + 3.28500I
u = −0.805953 − 0.027041I
a = −0.345526 − 0.596121I
b = 0.024838 + 0.844400I
3.39332 + 2.17431I 8.53831 − 3.28500I
u = 0.642311 + 0.449784I
a = −1.75182 + 0.80743I
b = 1.347300 + 0.355724I
6.72630 + 7.92579I 12.1583 − 8.1491I
u = 0.642311 − 0.449784I
a = −1.75182 − 0.80743I
b = 1.347300 − 0.355724I
6.72630 − 7.92579I 12.1583 + 8.1491I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.501660 + 1.136970I
a = 1.286290 + 0.341993I
b = −1.326480 + 0.043785I
8.78940 − 2.36934I 14.1647 + 0.I
u = −0.501660 − 1.136970I
a = 1.286290 − 0.341993I
b = −1.326480 − 0.043785I
8.78940 + 2.36934I 14.1647 + 0.I
u = −0.452030 + 1.175710I
a = −1.302930 − 0.542898I
b = 1.50606 + 0.43598I
10.20350 + 7.73445I 0
u = −0.452030 − 1.175710I
a = −1.302930 + 0.542898I
b = 1.50606 − 0.43598I
10.20350 − 7.73445I 0
u = −0.084827 + 1.288850I
a = −0.259022 − 0.468223I
b = 0.470070 − 0.345741I
−3.34519 − 1.63537I 0
u = −0.084827 − 1.288850I
a = −0.259022 + 0.468223I
b = 0.470070 + 0.345741I
−3.34519 + 1.63537I 0
u = 0.235443 + 1.273080I
a = −1.35454 + 1.10271I
b = 0.631652 + 0.250784I
−4.21138 + 3.05086I 0
u = 0.235443 − 1.273080I
a = −1.35454 − 1.10271I
b = 0.631652 − 0.250784I
−4.21138 − 3.05086I 0
u = −0.349327 + 1.249240I
a = −0.335653 − 0.135529I
b = −0.108783 − 0.819825I
−0.38230 − 1.98485I 0
u = −0.349327 − 1.249240I
a = −0.335653 + 0.135529I
b = −0.108783 + 0.819825I
−0.38230 + 1.98485I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.071803 + 1.298360I
a = −0.143695 + 1.377620I
b = −0.296292 + 0.618271I
−5.96094 + 1.93016I 0
u = 0.071803 − 1.298360I
a = −0.143695 − 1.377620I
b = −0.296292 − 0.618271I
−5.96094 − 1.93016I 0
u = −0.358553 + 1.289720I
a = 0.899152 + 0.306766I
b = 0.043249 + 0.867682I
−0.71095 − 6.36900I 0
u = −0.358553 − 1.289720I
a = 0.899152 − 0.306766I
b = 0.043249 − 0.867682I
−0.71095 + 6.36900I 0
u = 0.610254
a = 2.40590
b = −0.572689
−0.250744 18.0910
u = −0.399118 + 1.345260I
a = −1.62048 − 1.69722I
b = 1.51341 − 0.49950I
8.9652 − 17.1215I 0
u = −0.399118 − 1.345260I
a = −1.62048 + 1.69722I
b = 1.51341 + 0.49950I
8.9652 + 17.1215I 0
u = 0.18895 + 1.40967I
a = 0.307536 − 1.289560I
b = −1.319040 − 0.457572I
0.76991 + 10.74510I 0
u = 0.18895 − 1.40967I
a = 0.307536 + 1.289560I
b = −1.319040 + 0.457572I
0.76991 − 10.74510I 0
u = −0.41508 + 1.37015I
a = 1.04177 + 1.33272I
b = −1.284840 + 0.058721I
7.13077 − 7.43744I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.41508 − 1.37015I
a = 1.04177 − 1.33272I
b = −1.284840 − 0.058721I
7.13077 + 7.43744I 0
u = 0.09158 + 1.50603I
a = 0.067556 + 0.267829I
b = 1.171500 − 0.194024I
−0.95947 − 1.45291I 0
u = 0.09158 − 1.50603I
a = 0.067556 − 0.267829I
b = 1.171500 + 0.194024I
−0.95947 + 1.45291I 0
u = −0.389978
a = 0.839038
b = −0.338534
0.631815 16.0810
u = 0.249379 + 0.255614I
a = 0.432749 − 1.105430I
b = 0.089749 − 0.497899I
−1.30214 + 0.83943I −2.00109 − 3.97156I
u = 0.249379 − 0.255614I
a = 0.432749 + 1.105430I
b = 0.089749 + 0.497899I
−1.30214 − 0.83943I −2.00109 + 3.97156I
8
II. I
u
2
= h−4.15 × 10
5
a
3
u
5
+ 3.75 × 10
5
a
2
u
5
+ · · · + 1.14 × 10
6
a + 3.49 ×
10
6
, u
5
a
3
− u
5
a
2
+ · · · − 62a + 184, u
6
+ 3u
4
+ u
3
+ 2u
2
+ 2u − 1i
(i) Arc colorings
a
6
=
0
u
a
9
=
1
0
a
10
=
1
−u
2
a
5
=
−u
u
3
+ u
a
11
=
u
2
+ 1
−u
4
− 2u
2
a
7
=
u
5
+ 2u
3
+ u
u
4
+ 2u
2
a
1
=
a
0.126898a
3
u
5
− 0.114429a
2
u
5
+ ··· − 0.348501a − 1.06694
a
4
=
−u
3
− 2u
u
3
+ u
a
2
=
−0.00312508a
3
u
5
+ 0.0678169a
2
u
5
+ ··· + 0.727219a + 1.00927
0.190720a
3
u
5
− 0.341686a
2
u
5
+ ··· + 0.335179a − 1.84361
a
8
=
−0.140638a
3
u
5
− 0.166994a
2
u
5
+ ··· + 0.0966799a − 1.53356
−0.221029a
3
u
5
− 0.473050a
2
u
5
+ ··· − 0.397307a + 1.62574
a
12
=
0.250573a
3
u
5
+ 0.178839a
2
u
5
+ ··· + 0.777234a − 3.90996
0.447730a
3
u
5
− 0.0123159a
2
u
5
+ ··· − 0.381117a + 2.65314
a
3
=
−0.423110a
3
u
5
− 0.178982a
2
u
5
+ ··· − 0.0812311a + 1.15365
0.0741663a
3
u
5
− 0.382732a
2
u
5
+ ··· + 0.0906915a − 1.83998
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
117036
125929
u
5
a
3
−
112360
125929
u
5
a
2
+ ··· +
188412
125929
a +
1819422
125929
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
u
24
− 6u
23
+ ··· − 40u + 13
c
2
, c
7
, c
8
c
12
u
24
− 9u
22
+ ··· − 4u + 1
c
3
(u
2
− u + 1)
12
c
4
, c
6
(u
6
− 3u
5
+ 2u
4
− u
3
+ 5u
2
− 3u − 2)
4
c
5
, c
9
, c
10
(u
6
+ 3u
4
− u
3
+ 2u
2
− 2u − 1)
4
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
24
+ 6y
23
+ ··· + 1260y + 169
c
2
, c
7
, c
8
c
12
y
24
− 18y
23
+ ··· + 108y + 1
c
3
(y
2
+ y + 1)
12
c
4
, c
6
(y
6
− 5y
5
+ 8y
4
− 3y
3
+ 11y
2
− 29y + 4)
4
c
5
, c
9
, c
10
(y
6
+ 6y
5
+ 13y
4
+ 9y
3
− 6y
2
− 8y + 1)
4
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.841864
a = −3.10867 + 0.50234I
b = 1.70590 − 0.70540I
11.46240 − 2.02988I 16.6818 + 3.4641I
u = −0.841864
a = −3.10867 − 0.50234I
b = 1.70590 + 0.70540I
11.46240 + 2.02988I 16.6818 − 3.4641I
u = −0.841864
a = 3.38289 + 0.97731I
b = −1.284970 + 0.023677I
11.46240 + 2.02988I 16.6818 − 3.4641I
u = −0.841864
a = 3.38289 − 0.97731I
b = −1.284970 − 0.023677I
11.46240 − 2.02988I 16.6818 + 3.4641I
u = −0.126468 + 1.352400I
a = −0.275034 − 0.878182I
b = 0.006754 − 1.081960I
−3.42893 − 5.42362I 3.63982 + 6.98172I
u = −0.126468 + 1.352400I
a = −0.756293 − 0.508483I
b = 0.332337 − 0.589055I
−3.42893 − 1.36386I 3.63982 + 0.05352I
u = −0.126468 + 1.352400I
a = 0.402484 − 0.343050I
b = 0.902109 + 0.022381I
−3.42893 − 1.36386I 3.63982 + 0.05352I
u = −0.126468 + 1.352400I
a = −0.28551 + 1.61036I
b = −1.114730 + 0.296237I
−3.42893 − 5.42362I 3.63982 + 6.98172I
u = −0.126468 − 1.352400I
a = −0.275034 + 0.878182I
b = 0.006754 + 1.081960I
−3.42893 + 5.42362I 3.63982 − 6.98172I
u = −0.126468 − 1.352400I
a = −0.756293 + 0.508483I
b = 0.332337 + 0.589055I
−3.42893 + 1.36386I 3.63982 − 0.05352I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.126468 − 1.352400I
a = 0.402484 + 0.343050I
b = 0.902109 − 0.022381I
−3.42893 + 1.36386I 3.63982 − 0.05352I
u = −0.126468 − 1.352400I
a = −0.28551 − 1.61036I
b = −1.114730 − 0.296237I
−3.42893 + 5.42362I 3.63982 − 6.98172I
u = 0.376468 + 1.319680I
a = 1.337000 − 0.149230I
b = −0.322326 − 1.361500I
3.16668 + 10.80330I 8.43784 − 9.36504I
u = 0.376468 + 1.319680I
a = 0.345851 + 0.454309I
b = −0.0385806 + 0.1120340I
3.16668 + 6.74357I 8.43784 − 2.43684I
u = 0.376468 + 1.319680I
a = 1.30610 − 1.33449I
b = −1.292530 − 0.445841I
3.16668 + 6.74357I 8.43784 − 2.43684I
u = 0.376468 + 1.319680I
a = −1.40072 + 2.01996I
b = 1.276970 + 0.375627I
3.16668 + 10.80330I 8.43784 − 9.36504I
u = 0.376468 − 1.319680I
a = 1.337000 + 0.149230I
b = −0.322326 + 1.361500I
3.16668 − 10.80330I 8.43784 + 9.36504I
u = 0.376468 − 1.319680I
a = 0.345851 − 0.454309I
b = −0.0385806 − 0.1120340I
3.16668 − 6.74357I 8.43784 + 2.43684I
u = 0.376468 − 1.319680I
a = 1.30610 + 1.33449I
b = −1.292530 + 0.445841I
3.16668 − 6.74357I 8.43784 + 2.43684I
u = 0.376468 − 1.319680I
a = −1.40072 − 2.01996I
b = 1.276970 − 0.375627I
3.16668 − 10.80330I 8.43784 + 9.36504I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.341865
a = 2.43368 + 1.17121I
b = −1.39615 + 0.48806I
5.51139 − 2.02988I 19.1629 + 3.4641I
u = 0.341865
a = 2.43368 − 1.17121I
b = −1.39615 − 0.48806I
5.51139 + 2.02988I 19.1629 − 3.4641I
u = 0.341865
a = −4.88179 + 3.06904I
b = 1.225210 − 0.191994I
5.51139 − 2.02988I 19.1629 + 3.4641I
u = 0.341865
a = −4.88179 − 3.06904I
b = 1.225210 + 0.191994I
5.51139 + 2.02988I 19.1629 − 3.4641I
14
III.
I
u
3
= hu
16
+u
15
+· · ·+b+2, −2u
17
−2u
16
+· · ·+a−2, u
18
+u
17
+· · ·+2u+1i
(i) Arc colorings
a
6
=
0
u
a
9
=
1
0
a
10
=
1
−u
2
a
5
=
−u
u
3
+ u
a
11
=
u
2
+ 1
−u
4
− 2u
2
a
7
=
u
5
+ 2u
3
+ u
−u
7
− 3u
5
− 2u
3
+ u
a
1
=
2u
17
+ 2u
16
+ ··· + 9u + 2
−u
16
− u
15
+ ··· − 2u − 2
a
4
=
−u
3
− 2u
u
3
+ u
a
2
=
2u
17
+ u
16
+ ··· + 8u + 1
−u
17
− 2u
16
+ ··· − 3u − 2
a
8
=
u
16
− u
15
+ ··· + 10u
2
− 8u
u
17
+ 7u
15
+ ··· + u + 1
a
12
=
−u
17
− u
16
+ ··· − 5u + 2
u
15
+ u
14
+ ··· + 3u + 1
a
3
=
2u
17
+ u
16
+ ··· + 9u + 1
−u
16
− u
15
+ ··· − u − 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −u
16
− u
15
− 7u
14
− 2u
13
− 17u
12
+ 10u
11
− 12u
10
+ 39u
9
+
16u
8
+ 42u
7
+ 27u
6
− 4u
5
+ 2u
4
− 26u
3
− 10u
2
− 4u + 7
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
u
18
+ 3u
17
+ ··· − 3u − 1
c
2
, c
8
u
18
+ u
17
+ ··· − u − 1
c
3
u
18
− 3u
17
+ ··· + 3u − 1
c
4
, c
6
u
18
+ u
17
+ ··· + 7u
2
+ 1
c
5
u
18
− u
17
+ ··· − 2u + 1
c
7
, c
12
u
18
− u
17
+ ··· + u − 1
c
9
, c
10
u
18
+ u
17
+ ··· + 2u + 1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
18
+ 3y
17
+ ··· + 7y + 1
c
2
, c
7
, c
8
c
12
y
18
− 21y
17
+ ··· − 29y + 1
c
3
y
18
+ 7y
17
+ ··· + 3y + 1
c
4
, c
6
y
18
− 11y
17
+ ··· + 14y + 1
c
5
, c
9
, c
10
y
18
+ 17y
17
+ ··· + 8y + 1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.863058
a = −3.08851
b = 1.47146
10.9241 14.9390
u = −0.811794 + 0.086746I
a = −1.66812 − 0.06489I
b = 1.106420 − 0.516453I
8.19254 − 4.11062I 15.0302 + 4.4552I
u = −0.811794 − 0.086746I
a = −1.66812 + 0.06489I
b = 1.106420 + 0.516453I
8.19254 + 4.11062I 15.0302 − 4.4552I
u = −0.037936 + 1.201190I
a = −0.67412 − 1.88976I
b = 1.359340 − 0.368138I
1.99280 − 2.42184I 8.62527 + 0.56589I
u = −0.037936 − 1.201190I
a = −0.67412 + 1.88976I
b = 1.359340 + 0.368138I
1.99280 + 2.42184I 8.62527 − 0.56589I
u = −0.346661 + 1.200250I
a = 0.135968 + 0.447764I
b = −1.186850 − 0.513231I
4.79445 − 0.07036I 11.73338 − 0.07459I
u = −0.346661 − 1.200250I
a = 0.135968 − 0.447764I
b = −1.186850 + 0.513231I
4.79445 + 0.07036I 11.73338 + 0.07459I
u = 0.175966 + 1.280820I
a = −0.806426 + 1.002530I
b = 0.228924 + 0.234817I
−4.68984 + 2.45101I 0.705670 − 1.175054I
u = 0.175966 − 1.280820I
a = −0.806426 − 1.002530I
b = 0.228924 − 0.234817I
−4.68984 − 2.45101I 0.705670 + 1.175054I
u = 0.400557 + 1.266130I
a = 1.79737 − 1.11786I
b = −1.47149 − 0.06981I
6.99702 + 4.52950I 11.21141 − 3.10762I
18
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.400557 − 1.266130I
a = 1.79737 + 1.11786I
b = −1.47149 + 0.06981I
6.99702 − 4.52950I 11.21141 + 3.10762I
u = −0.361990 + 1.332230I
a = 0.81927 + 1.15450I
b = −1.037050 + 0.524649I
3.73552 − 8.34686I 10.33759 + 7.17460I
u = −0.361990 − 1.332230I
a = 0.81927 − 1.15450I
b = −1.037050 − 0.524649I
3.73552 + 8.34686I 10.33759 − 7.17460I
u = −0.04839 + 1.45535I
a = 0.145310 − 0.301991I
b = 1.107200 + 0.202918I
−1.25223 + 1.02332I 5.08940 + 3.59240I
u = −0.04839 − 1.45535I
a = 0.145310 + 0.301991I
b = 1.107200 − 0.202918I
−1.25223 − 1.02332I 5.08940 − 3.59240I
u = 0.507807
a = 1.87659
b = −0.212766
−0.692851 −0.0433770
u = −0.155186 + 0.321559I
a = 0.85670 + 2.76375I
b = −1.235840 − 0.300145I
4.72294 + 1.80776I 7.31942 + 0.02100I
u = −0.155186 − 0.321559I
a = 0.85670 − 2.76375I
b = −1.235840 + 0.300145I
4.72294 − 1.80776I 7.31942 − 0.02100I
19
IV. I
u
4
= h−3.52 × 10
8
a
3
u
9
− 2.80 × 10
8
a
2
u
9
+ · · · + 5.98 × 10
8
a − 8.89 ×
10
8
, 2u
9
a
3
+ 3u
9
a
2
+ · · · + 2a + 4, u
10
− u
9
+ · · · − 3u
3
+ 1i
(i) Arc colorings
a
6
=
0
u
a
9
=
1
0
a
10
=
1
−u
2
a
5
=
−u
u
3
+ u
a
11
=
u
2
+ 1
−u
4
− 2u
2
a
7
=
u
5
+ 2u
3
+ u
−u
7
− 3u
5
− 2u
3
+ u
a
1
=
a
0.394132a
3
u
9
+ 0.313043a
2
u
9
+ ··· − 0.669019a + 0.995221
a
4
=
−u
3
− 2u
u
3
+ u
a
2
=
0.198848a
3
u
9
− 1.61597a
2
u
9
+ ··· + 0.322034a − 4.36671
0.624336a
3
u
9
+ 1.68297a
2
u
9
+ ··· − 0.641178a + 4.12350
a
8
=
−0.139537a
3
u
9
+ 0.126621a
2
u
9
+ ··· − 1.16026a + 0.198975
0.137288a
3
u
9
− 0.949133a
2
u
9
+ ··· + 2.17072a + 0.562076
a
12
=
−0.176443a
3
u
9
− 0.622692a
2
u
9
+ ··· + 2.44767a − 0.594951
0.512002a
3
u
9
+ 0.204390a
2
u
9
+ ··· − 0.220227a + 0.220345
a
3
=
−0.144321a
3
u
9
− 0.0728304a
2
u
9
+ ··· − 4.82417a − 3.30781
−0.228457a
3
u
9
+ 0.463402a
2
u
9
+ ··· + 1.58033a + 2.20288
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
23189728
893302351
u
9
a
3
−
17608364
893302351
u
9
a
2
+ ··· −
2297249516
893302351
a +
5202904734
893302351
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
u
40
− 13u
39
+ ··· − 5772u + 757
c
2
, c
7
, c
8
c
12
u
40
− u
39
+ ··· + 18u
2
+ 1
c
3
(u
2
− u + 1)
20
c
4
, c
6
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
8
c
5
, c
9
, c
10
(u
10
+ u
9
+ 4u
8
+ 4u
7
+ 6u
6
+ 6u
5
+ 3u
4
+ 3u
3
+ 1)
4
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
40
+ 21y
39
+ ··· + 22553644y + 573049
c
2
, c
7
, c
8
c
12
y
40
− 39y
39
+ ··· + 36y + 1
c
3
(y
2
+ y + 1)
20
c
4
, c
6
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
8
c
5
, c
9
, c
10
(y
10
+ 7y
9
+ 20y
8
+ 26y
7
+ 6y
6
− 22y
5
− 19y
4
+ 3y
3
+ 6y
2
+ 1)
4
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.839548 + 0.070481I
a = −0.402562 − 0.505149I
b = −0.0439825 − 0.0696372I
7.51750 + 2.37095I 12.74431 − 0.03448I
u = 0.839548 + 0.070481I
a = −0.87672 − 1.40077I
b = 0.384497 + 1.319600I
7.51750 + 6.43072I 12.7443 − 6.9627I
u = 0.839548 + 0.070481I
a = −2.42644 + 0.17767I
b = 1.336310 + 0.372529I
7.51750 + 2.37095I 12.74431 − 0.03448I
u = 0.839548 + 0.070481I
a = 2.57482 − 0.88548I
b = −1.292970 − 0.351858I
7.51750 + 6.43072I 12.7443 − 6.9627I
u = 0.839548 − 0.070481I
a = −0.402562 + 0.505149I
b = −0.0439825 + 0.0696372I
7.51750 − 2.37095I 12.74431 + 0.03448I
u = 0.839548 − 0.070481I
a = −0.87672 + 1.40077I
b = 0.384497 − 1.319600I
7.51750 − 6.43072I 12.7443 + 6.9627I
u = 0.839548 − 0.070481I
a = −2.42644 − 0.17767I
b = 1.336310 − 0.372529I
7.51750 − 2.37095I 12.74431 + 0.03448I
u = 0.839548 − 0.070481I
a = 2.57482 + 0.88548I
b = −1.292970 + 0.351858I
7.51750 − 6.43072I 12.7443 + 6.9627I
u = 0.090539 + 1.215350I
a = −0.225264 + 0.093412I
b = 1.56209 − 0.31243I
1.97403 − 0.49930I 8.51511 − 0.96655I
u = 0.090539 + 1.215350I
a = 0.66256 + 1.78010I
b = 1.22523 + 0.73772I
1.97403 + 3.56046I 8.51511 − 7.89475I
23
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.090539 + 1.215350I
a = 1.99879 − 0.95641I
b = −1.350730 − 0.169147I
1.97403 + 3.56046I 8.51511 − 7.89475I
u = 0.090539 + 1.215350I
a = −0.39206 − 2.81005I
b = −1.006940 + 0.136833I
1.97403 − 0.49930I 8.51511 − 0.96655I
u = 0.090539 − 1.215350I
a = −0.225264 − 0.093412I
b = 1.56209 + 0.31243I
1.97403 + 0.49930I 8.51511 + 0.96655I
u = 0.090539 − 1.215350I
a = 0.66256 − 1.78010I
b = 1.22523 − 0.73772I
1.97403 − 3.56046I 8.51511 + 7.89475I
u = 0.090539 − 1.215350I
a = 1.99879 + 0.95641I
b = −1.350730 + 0.169147I
1.97403 − 3.56046I 8.51511 + 7.89475I
u = 0.090539 − 1.215350I
a = −0.39206 + 2.81005I
b = −1.006940 − 0.136833I
1.97403 + 0.49930I 8.51511 + 0.96655I
u = 0.383413 + 1.200420I
a = −0.604285 − 0.632212I
b = −0.462034 + 1.251310I
4.04602 − 2.02988I 9.48114 + 3.46410I
u = 0.383413 + 1.200420I
a = 0.478064 − 0.583666I
b = 0.150869 − 0.009153I
4.04602 + 2.02988I 9.48114 − 3.46410I
u = 0.383413 + 1.200420I
a = 1.045730 − 0.689743I
b = −1.382170 + 0.277320I
4.04602 + 2.02988I 9.48114 − 3.46410I
u = 0.383413 + 1.200420I
a = −1.260420 − 0.050726I
b = 1.309920 − 0.319057I
4.04602 − 2.02988I 9.48114 + 3.46410I
24
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.383413 − 1.200420I
a = −0.604285 + 0.632212I
b = −0.462034 − 1.251310I
4.04602 + 2.02988I 9.48114 − 3.46410I
u = 0.383413 − 1.200420I
a = 0.478064 + 0.583666I
b = 0.150869 + 0.009153I
4.04602 − 2.02988I 9.48114 + 3.46410I
u = 0.383413 − 1.200420I
a = 1.045730 + 0.689743I
b = −1.382170 − 0.277320I
4.04602 − 2.02988I 9.48114 + 3.46410I
u = 0.383413 − 1.200420I
a = −1.260420 + 0.050726I
b = 1.309920 + 0.319057I
4.04602 + 2.02988I 9.48114 − 3.46410I
u = −0.383851 + 1.270630I
a = 0.98145 + 1.21602I
b = −1.73426 − 0.65183I
7.51750 − 2.37095I 12.74431 + 0.03448I
u = −0.383851 + 1.270630I
a = −2.23007 − 0.18057I
b = 1.313220 + 0.005597I
7.51750 − 6.43072I 12.7443 + 6.9627I
u = −0.383851 + 1.270630I
a = 1.96754 + 1.53952I
b = −1.67195 + 0.75671I
7.51750 − 6.43072I 12.7443 + 6.9627I
u = −0.383851 + 1.270630I
a = −2.02707 − 2.12285I
b = 1.253450 − 0.039994I
7.51750 − 2.37095I 12.74431 + 0.03448I
u = −0.383851 − 1.270630I
a = 0.98145 − 1.21602I
b = −1.73426 + 0.65183I
7.51750 + 2.37095I 12.74431 − 0.03448I
u = −0.383851 − 1.270630I
a = −2.23007 + 0.18057I
b = 1.313220 − 0.005597I
7.51750 + 6.43072I 12.7443 − 6.9627I
25
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.383851 − 1.270630I
a = 1.96754 − 1.53952I
b = −1.67195 − 0.75671I
7.51750 + 6.43072I 12.7443 − 6.9627I
u = −0.383851 − 1.270630I
a = −2.02707 + 2.12285I
b = 1.253450 + 0.039994I
7.51750 + 2.37095I 12.74431 − 0.03448I
u = −0.429649 + 0.392970I
a = 0.786631 + 0.807814I
b = −1.142270 − 0.034877I
1.97403 + 0.49930I 8.51511 + 0.96655I
u = −0.429649 + 0.392970I
a = 1.29731 − 0.58385I
b = 0.044480 + 0.564141I
1.97403 + 0.49930I 8.51511 + 0.96655I
u = −0.429649 + 0.392970I
a = 0.266316 − 0.274622I
b = −0.176919 + 0.887142I
1.97403 − 3.56046I 8.51511 + 7.89475I
u = −0.429649 + 0.392970I
a = −1.11432 − 1.64211I
b = 1.184170 − 0.201060I
1.97403 − 3.56046I 8.51511 + 7.89475I
u = −0.429649 − 0.392970I
a = 0.786631 − 0.807814I
b = −1.142270 + 0.034877I
1.97403 − 0.49930I 8.51511 − 0.96655I
u = −0.429649 − 0.392970I
a = 1.29731 + 0.58385I
b = 0.044480 − 0.564141I
1.97403 − 0.49930I 8.51511 − 0.96655I
u = −0.429649 − 0.392970I
a = 0.266316 + 0.274622I
b = −0.176919 − 0.887142I
1.97403 + 3.56046I 8.51511 − 7.89475I
u = −0.429649 − 0.392970I
a = −1.11432 + 1.64211I
b = 1.184170 + 0.201060I
1.97403 + 3.56046I 8.51511 − 7.89475I
26
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
11
(u
18
+ 3u
17
+ ··· − 3u − 1)(u
24
− 6u
23
+ ··· − 40u + 13)
· (u
36
+ 3u
35
+ ··· + 10u − 1)(u
40
− 13u
39
+ ··· − 5772u + 757)
c
2
, c
8
(u
18
+ u
17
+ ··· − u − 1)(u
24
− 9u
22
+ ··· − 4u + 1)
· (u
36
+ u
35
+ ··· − 4u
2
+ 1)(u
40
− u
39
+ ··· + 18u
2
+ 1)
c
3
((u
2
− u + 1)
32
)(u
18
− 3u
17
+ ··· + 3u − 1)
· (u
36
+ 36u
35
+ ··· − 851968u − 65536)
c
4
, c
6
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
8
(u
6
− 3u
5
+ 2u
4
− u
3
+ 5u
2
− 3u − 2)
4
· (u
18
+ u
17
+ ··· + 7u
2
+ 1)(u
36
+ 6u
35
+ ··· − 3456u − 712)
c
5
(u
6
+ 3u
4
− u
3
+ 2u
2
− 2u − 1)
4
· (u
10
+ u
9
+ 4u
8
+ 4u
7
+ 6u
6
+ 6u
5
+ 3u
4
+ 3u
3
+ 1)
4
· (u
18
− u
17
+ ··· − 2u + 1)(u
36
− 6u
35
+ ··· + 10u − 4)
c
7
, c
12
(u
18
− u
17
+ ··· + u − 1)(u
24
− 9u
22
+ ··· − 4u + 1)
· (u
36
+ u
35
+ ··· − 4u
2
+ 1)(u
40
− u
39
+ ··· + 18u
2
+ 1)
c
9
, c
10
(u
6
+ 3u
4
− u
3
+ 2u
2
− 2u − 1)
4
· (u
10
+ u
9
+ 4u
8
+ 4u
7
+ 6u
6
+ 6u
5
+ 3u
4
+ 3u
3
+ 1)
4
· (u
18
+ u
17
+ ··· + 2u + 1)(u
36
− 6u
35
+ ··· + 10u − 4)
27
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
11
(y
18
+ 3y
17
+ ··· + 7y + 1)(y
24
+ 6y
23
+ ··· + 1260y + 169)
· (y
36
+ 13y
35
+ ··· − 108y + 1)
· (y
40
+ 21y
39
+ ··· + 22553644y + 573049)
c
2
, c
7
, c
8
c
12
(y
18
− 21y
17
+ ··· − 29y + 1)(y
24
− 18y
23
+ ··· + 108y + 1)
· (y
36
− 31y
35
+ ··· − 8y + 1)(y
40
− 39y
39
+ ··· + 36y + 1)
c
3
((y
2
+ y + 1)
32
)(y
18
+ 7y
17
+ ··· + 3y + 1)
· (y
36
+ 8y
35
+ ··· − 81604378624y + 4294967296)
c
4
, c
6
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
8
· (y
6
− 5y
5
+ 8y
4
− 3y
3
+ 11y
2
− 29y + 4)
4
· (y
18
− 11y
17
+ ··· + 14y + 1)
· (y
36
− 26y
35
+ ··· − 1429120y + 506944)
c
5
, c
9
, c
10
(y
6
+ 6y
5
+ 13y
4
+ 9y
3
− 6y
2
− 8y + 1)
4
· (y
10
+ 7y
9
+ 20y
8
+ 26y
7
+ 6y
6
− 22y
5
− 19y
4
+ 3y
3
+ 6y
2
+ 1)
4
· (y
18
+ 17y
17
+ ··· + 8y + 1)(y
36
+ 30y
35
+ ··· − 108y + 16)
28
