12n
0672
(K12n
0672
)
A knot diagram
1
Linearized knot diagam
4 5 6 2 10 3 11 5 12 8 6 9
Solving Sequence
7,11 3,8
6 4 12 10 5 2 1 9
c
7
c
6
c
3
c
11
c
10
c
5
c
2
c
1
c
9
c
4
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h140432815u
21
− 8970077u
20
+ ··· + 415372544b − 54946683,
2854951501u
21
+ 303304377u
20
+ ··· + 6645960704a − 7253385201, u
22
+ 3u
20
+ ··· + u + 1i
I
u
2
= h−17272682156856u
19
+ 65400234558575u
18
+ ··· + 646621574147963b + 203992951331482,
3.50596 × 10
15
u
19
− 1.00606 × 10
16
u
18
+ ··· + 1.09926 × 10
16
a − 4.23310 × 10
16
, u
20
− 2u
19
+ ··· − 4u + 17i
I
u
3
= hb, −5u
2
+ 4a + 3u − 11, u
3
+ 2u + 1i
I
u
4
= h−243a
4
u + 1435a
3
u + ··· + 487a + 424, a
5
− 4a
4
u − 5a
4
+ 9a
3
u + 2a
3
− 6a
2
+ 6au + 7a − u, u
2
+ 1i
I
u
5
= hb, u
3
+ a + u, u
4
− u
3
+ 2u
2
− 2u + 1i
* 5 irreducible components of dim
C
= 0, with total 59 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
= h1.40 × 10
8
u
21
− 8.97 × 10
6
u
20
+ · · · + 4.15 × 10
8
b − 5.49 × 10
7
, 2.85 ×
10
9
u
21
+ 3.03 × 10
8
u
20
+ · · · + 6.65 × 10
9
a − 7.25 × 10
9
, u
22
+ 3u
20
+ · · · + u + 1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
3
=
−0.429577u
21
− 0.0456374u
20
+ ··· − 2.64683u + 1.09140
−0.338089u
21
+ 0.0215953u
20
+ ··· − 1.82898u + 0.132283
a
8
=
1
−u
2
a
6
=
−0.339086u
21
− 0.230329u
20
+ ··· − 3.30702u + 0.269143
0.141109u
21
− 0.152381u
20
+ ··· − 1.58891u − 0.881521
a
4
=
0.119809u
21
− 0.185566u
20
+ ··· − 4.21378u − 0.352810
−0.0118881u
21
+ 0.0634552u
20
+ ··· + 1.25768u + 0.426641
a
12
=
−0.00781250u
21
− 0.00781250u
20
+ ··· − 1.98438u − 0.992188
0.0156250u
21
+ 0.0156250u
20
+ ··· + 1.96875u − 0.0156250
a
10
=
−u
u
3
+ u
a
5
=
−0.329484u
21
− 0.213284u
20
+ ··· − 3.71828u − 0.0429626
0.169327u
21
− 0.142245u
20
+ ··· − 1.15100u − 0.552370
a
2
=
0.371416u
21
+ 0.116662u
20
+ ··· − 0.554103u + 0.690043
−0.245528u
21
+ 0.287886u
20
+ ··· + 0.564340u + 1.00801
a
1
=
0.0156250u
21
+ 0.0156250u
20
+ ··· + 1.96875u + 0.984375
−0.0312500u
21
− 0.0312500u
20
+ ··· − 1.93750u + 0.0312500
a
9
=
−0.00781250u
21
− 0.00781250u
20
+ ··· − 1.98438u + 0.00781250
0.0156250u
21
+ 0.0156250u
20
+ ··· + 0.968750u − 0.0156250
(ii) Obstruction class = −1
(iii) Cusp Shapes =
63242885225
26583842816
u
21
−
275520283
26583842816
u
20
+ ··· −
34653626479
13291921408
u +
128655382851
26583842816
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
4
u
22
− 4u
21
+ ··· + 225u − 16
c
3
, c
6
u
22
+ 3u
21
+ ··· − 432u + 128
c
5
u
22
+ 6u
21
+ ··· − 12u − 4
c
7
, c
9
, c
10
c
12
u
22
+ 3u
20
+ ··· − u + 1
c
8
, c
11
u
22
− 14u
20
+ ··· − 160u − 32
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
y
22
− 12y
21
+ ··· − 52961y + 256
c
3
, c
6
y
22
− 9y
21
+ ··· − 181504y + 16384
c
5
y
22
+ 4y
21
+ ··· − 56y + 16
c
7
, c
9
, c
10
c
12
y
22
+ 6y
21
+ ··· + 5y + 1
c
8
, c
11
y
22
− 28y
21
+ ··· − 25600y + 1024
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.928587 + 0.449929I
a = 0.444403 + 0.678322I
b = 0.105518 + 0.891648I
0.73454 − 1.42308I 6.61226 − 1.84054I
u = −0.928587 − 0.449929I
a = 0.444403 − 0.678322I
b = 0.105518 − 0.891648I
0.73454 + 1.42308I 6.61226 + 1.84054I
u = 0.805604 + 0.679539I
a = −0.675797 − 0.229153I
b = −0.10006 + 2.03537I
−0.58572 + 5.08842I 2.49387 − 7.97932I
u = 0.805604 − 0.679539I
a = −0.675797 + 0.229153I
b = −0.10006 − 2.03537I
−0.58572 − 5.08842I 2.49387 + 7.97932I
u = 0.016436 + 0.749464I
a = −0.280370 + 0.907991I
b = −0.438482 + 1.324440I
−8.18850 − 4.33155I 5.52961 + 2.50596I
u = 0.016436 − 0.749464I
a = −0.280370 − 0.907991I
b = −0.438482 − 1.324440I
−8.18850 + 4.33155I 5.52961 − 2.50596I
u = −0.722140
a = −3.32146
b = 0.476611
−0.565730 30.7730
u = 0.504021 + 0.445386I
a = 1.24386 − 0.98298I
b = −1.57016 + 0.27263I
−3.04188 + 1.34660I −0.20456 − 4.71267I
u = 0.504021 − 0.445386I
a = 1.24386 + 0.98298I
b = −1.57016 − 0.27263I
−3.04188 − 1.34660I −0.20456 + 4.71267I
u = 0.18886 + 1.40685I
a = 0.0573082 − 0.0995823I
b = −0.186722 − 0.594682I
−11.39190 + 5.29891I −11.9974 − 9.4087I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.18886 − 1.40685I
a = 0.0573082 + 0.0995823I
b = −0.186722 + 0.594682I
−11.39190 − 5.29891I −11.9974 + 9.4087I
u = 1.05891 + 1.05062I
a = −1.049610 + 0.673117I
b = 2.15765 + 0.77847I
6.65098 + 7.24014I 4.89876 − 5.30841I
u = 1.05891 − 1.05062I
a = −1.049610 − 0.673117I
b = 2.15765 − 0.77847I
6.65098 − 7.24014I 4.89876 + 5.30841I
u = −0.82129 + 1.28483I
a = −0.697328 − 0.815294I
b = 1.43657 − 0.80726I
4.44406 − 7.90966I 2.90985 + 4.71284I
u = −0.82129 − 1.28483I
a = −0.697328 + 0.815294I
b = 1.43657 + 0.80726I
4.44406 + 7.90966I 2.90985 − 4.71284I
u = 0.072819 + 0.411896I
a = 1.38341 − 1.45349I
b = 0.042570 − 1.004680I
−1.51746 − 1.42204I 1.40403 + 3.03703I
u = 0.072819 − 0.411896I
a = 1.38341 + 1.45349I
b = 0.042570 + 1.004680I
−1.51746 + 1.42204I 1.40403 − 3.03703I
u = 0.87848 + 1.33285I
a = 0.999157 − 0.834434I
b = −1.68011 − 1.04071I
3.8163 + 15.4146I 2.44451 − 7.76498I
u = 0.87848 − 1.33285I
a = 0.999157 + 0.834434I
b = −1.68011 + 1.04071I
3.8163 − 15.4146I 2.44451 + 7.76498I
u = −1.22340 + 1.04887I
a = 0.809743 + 0.604171I
b = −1.63736 + 0.34201I
6.54087 − 1.13702I 5.32063 − 0.78196I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.22340 − 1.04887I
a = 0.809743 − 0.604171I
b = −1.63736 − 0.34201I
6.54087 + 1.13702I 5.32063 + 0.78196I
u = −0.381582
a = 0.601919
b = 0.264566
0.708401 14.4670
7
II. I
u
2
= h−1.73 × 10
13
u
19
+ 6.54 × 10
13
u
18
+ · · · + 6.47 × 10
14
b + 2.04 ×
10
14
, 3.51 × 10
15
u
19
− 1.01 × 10
16
u
18
+ · · · + 1.10 × 10
16
a − 4.23 ×
10
16
, u
20
− 2u
19
+ · · · − 4u + 17i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
3
=
−0.318939u
19
+ 0.915221u
18
+ ··· − 12.9781u + 3.85087
0.0267122u
19
− 0.101141u
18
+ ··· + 2.78094u − 0.315475
a
8
=
1
−u
2
a
6
=
−0.103485u
19
+ 0.0740278u
18
+ ··· − 8.11622u + 2.12405
0.107851u
19
− 0.263722u
18
+ ··· + 3.65066u − 1.56320
a
4
=
0.0148390u
19
+ 0.231650u
18
+ ··· − 9.04018u + 5.85391
0.0351704u
19
− 0.0375853u
18
+ ··· + 3.45642u + 0.00903128
a
12
=
0.352319u
19
− 1.31815u
18
+ ··· + 3.33066u − 5.70075
0.0984318u
19
− 0.200644u
18
+ ··· + 3.80209u − 1.16277
a
10
=
−u
u
3
+ u
a
5
=
0.0188311u
19
− 0.0566658u
18
+ ··· − 6.85303u + 3.76850
0.107524u
19
− 0.232476u
18
+ ··· + 4.01109u − 1.27070
a
2
=
−0.104445u
19
+ 0.552187u
18
+ ··· − 6.37772u + 4.35674
−0.0495529u
19
+ 0.136649u
18
+ ··· + 0.555470u + 0.796437
a
1
=
−0.0250730u
19
+ 0.177714u
18
+ ··· − 0.967992u + 3.13969
−0.0256385u
19
+ 0.0848373u
18
+ ··· + 0.0314805u + 0.0289650
a
9
=
0.469648u
19
− 0.562887u
18
+ ··· − 7.03901u + 5.29851
−0.00409626u
19
+ 0.110585u
18
+ ··· + 3.78370u + 1.79742
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
141694095517749
646621574147963
u
19
+
11086941637505
646621574147963
u
18
+ ··· −
4773664927135288
646621574147963
u +
1070128990714232
646621574147963
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
4
(u
10
− 3u
9
+ 4u
8
+ u
7
− 6u
6
+ 6u
5
+ u
4
− 2u
3
+ 3u
2
− 2u + 1)
2
c
3
, c
6
(u
10
+ u
9
− 7u
8
− 8u
7
+ 13u
6
+ 14u
5
− 2u
4
+ 2u
3
+ 13u
2
+ 12u + 4)
2
c
5
(u
10
− 2u
9
+ 3u
8
− 2u
7
+ 4u
6
− 3u
5
+ 3u
4
+ 3u
2
− u + 1)
2
c
7
, c
9
, c
10
c
12
u
20
+ 2u
19
+ ··· + 4u + 17
c
8
, c
11
u
20
− 3u
18
+ ··· + 35738u + 11449
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y
10
− y
9
+ 10y
8
− 11y
7
+ 26y
6
− 30y
5
+ y
4
+ 14y
3
+ 3y
2
+ 2y + 1)
2
c
3
, c
6
(y
10
− 15y
9
+ ··· − 40y + 16)
2
c
5
(y
10
+ 2y
9
+ 9y
8
+ 14y
7
+ 28y
6
+ 31y
5
+ 35y
4
+ 20y
3
+ 15y
2
+ 5y + 1)
2
c
7
, c
9
, c
10
c
12
y
20
+ 6y
19
+ ··· + 4064y + 289
c
8
, c
11
y
20
− 6y
19
+ ··· + 896868864y + 131079601
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.155799 + 0.881795I
a = 3.18440 − 1.02398I
b = −0.413972 + 0.524496I
−5.18909 + 0.79591I −0.779599 + 0.811554I
u = 0.155799 − 0.881795I
a = 3.18440 + 1.02398I
b = −0.413972 − 0.524496I
−5.18909 − 0.79591I −0.779599 − 0.811554I
u = 0.074318 + 1.117810I
a = 3.33328 − 3.01725I
b = −0.413972 − 0.524496I
−5.18909 − 0.79591I −0.779599 − 0.811554I
u = 0.074318 − 1.117810I
a = 3.33328 + 3.01725I
b = −0.413972 + 0.524496I
−5.18909 + 0.79591I −0.779599 + 0.811554I
u = 0.922088 + 0.638802I
a = 0.862882 − 0.144749I
b = −0.793271 + 0.121626I
−3.70278 + 2.81207I 4.88002 − 4.64391I
u = 0.922088 − 0.638802I
a = 0.862882 + 0.144749I
b = −0.793271 − 0.121626I
−3.70278 − 2.81207I 4.88002 + 4.64391I
u = 0.027793 + 1.142750I
a = 0.806614 − 0.400008I
b = 0.620250 − 0.748934I
−2.14407 − 1.46073I 6.65931 + 3.28644I
u = 0.027793 − 1.142750I
a = 0.806614 + 0.400008I
b = 0.620250 + 0.748934I
−2.14407 + 1.46073I 6.65931 − 3.28644I
u = −1.218430 + 0.658057I
a = −0.880056 − 0.414251I
b = 1.96899 + 0.18613I
6.57160 + 0.50253I 5.49701 + 0.08773I
u = −1.218430 − 0.658057I
a = −0.880056 + 0.414251I
b = 1.96899 − 0.18613I
6.57160 − 0.50253I 5.49701 − 0.08773I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.03744 + 1.07526I
a = −0.710678 + 0.832607I
b = 1.96899 + 0.18613I
6.57160 + 0.50253I 5.49701 + 0.08773I
u = 1.03744 − 1.07526I
a = −0.710678 − 0.832607I
b = 1.96899 − 0.18613I
6.57160 − 0.50253I 5.49701 − 0.08773I
u = 1.37291 + 0.66267I
a = 0.885501 − 0.517371I
b = −1.88200 + 0.46774I
6.10927 − 7.40677I 4.74326 + 4.41038I
u = 1.37291 − 0.66267I
a = 0.885501 + 0.517371I
b = −1.88200 − 0.46774I
6.10927 + 7.40677I 4.74326 − 4.41038I
u = −0.09604 + 1.52972I
a = −0.0133270 − 0.1369840I
b = −0.793271 − 0.121626I
−3.70278 − 2.81207I 4.88002 + 4.64391I
u = −0.09604 − 1.52972I
a = −0.0133270 + 0.1369840I
b = −0.793271 + 0.121626I
−3.70278 + 2.81207I 4.88002 − 4.64391I
u = −0.138308 + 0.379907I
a = −2.22932 − 2.47499I
b = 0.620250 + 0.748934I
−2.14407 + 1.46073I 6.65931 − 3.28644I
u = −0.138308 − 0.379907I
a = −2.22932 + 2.47499I
b = 0.620250 − 0.748934I
−2.14407 − 1.46073I 6.65931 + 3.28644I
u = −1.13757 + 1.18122I
a = 0.848938 + 0.551739I
b = −1.88200 + 0.46774I
6.10927 − 7.40677I 4.74326 + 4.41038I
u = −1.13757 − 1.18122I
a = 0.848938 − 0.551739I
b = −1.88200 − 0.46774I
6.10927 + 7.40677I 4.74326 − 4.41038I
12
III. I
u
3
= hb, −5u
2
+ 4a + 3u − 11, u
3
+ 2u + 1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
3
=
5
4
u
2
−
3
4
u +
11
4
0
a
8
=
1
−u
2
a
6
=
1
0
a
4
=
5
4
u
2
−
3
4
u +
11
4
0
a
12
=
u
u
a
10
=
−u
−u − 1
a
5
=
u
2
+ u + 1
u
2
+ 2u + 1
a
2
=
1
4
u
2
−
7
4
u +
7
4
−u
2
− 2u − 1
a
1
=
−u
2
− u − 1
−u
2
− 2u − 1
a
9
=
u
2
− u
u
2
− u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
69
16
u
2
+
47
16
u −
7
16
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
3
c
3
, c
6
u
3
c
4
(u + 1)
3
c
5
u
3
+ 3u
2
+ 5u + 2
c
7
, c
9
u
3
+ 2u + 1
c
8
, c
10
, c
11
c
12
u
3
+ 2u − 1
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
3
c
3
, c
6
y
3
c
5
y
3
+ y
2
+ 13y −4
c
7
, c
8
, c
9
c
10
, c
11
, c
12
y
3
+ 4y
2
+ 4y −1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.22670 + 1.46771I
a = −0.048505 − 0.268962I
b = 0
−11.08570 + 5.13794I 9.29669 + 1.44162I
u = 0.22670 − 1.46771I
a = −0.048505 + 0.268962I
b = 0
−11.08570 − 5.13794I 9.29669 − 1.44162I
u = −0.453398
a = 3.34701
b = 0
−0.857735 −2.65590
16
IV. I
u
4
=
h−243a
4
u + 1435a
3
u + · · · + 487a + 424, −4a
4
u + 9a
3
u + · · · − 6a
2
+7a, u
2
+1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
3
=
a
0.335172a
4
u − 1.97931a
3
u + ··· − 0.671724a − 0.584828
a
8
=
1
1
a
6
=
0.104828a
4
u + 0.179310a
3
u + ··· + 0.711724a + 0.664828
−0.00275862a
4
u + 0.668966a
3
u + ··· + 0.307586a − 1.32276
a
4
=
0.377931a
4
u − 1.84828a
3
u + ··· + 0.0606897a − 0.582069
0.0124138a
4
u − 0.710345a
3
u + ··· − 1.68414a + 1.65241
a
12
=
−0.397241a
4
u + 1.93103a
3
u + ··· + 2.69241a − 0.0772414
1
a
10
=
−u
0
a
5
=
0.102069a
4
u + 0.848276a
3
u + ··· + 1.01931a − 0.657931
−0.00275862a
4
u + 0.668966a
3
u + ··· + 0.307586a − 1.32276
a
2
=
−0.263448a
4
u + 1.78621a
3
u + ··· + 0.474483a − 0.223448
0.131034a
4
u + 0.324138a
3
u + ··· + 1.28966a − 2.26897
a
1
=
−1
0
a
9
=
0.0468966a
4
u + 0.827586a
3
u + ··· + 2.57103a + 0.286897
−u
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −
28
725
a
4
u −
104
725
a
4
+
24
145
a
3
u +
172
145
a
3
+
48
725
a
2
u −
3136
725
a
2
−
1156
725
au +
3992
725
a +
2308
725
u −
3856
725
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
2
c
3
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
2
c
4
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
2
c
5
u
10
+ u
8
+ 8u
6
+ 3u
4
+ 3u
2
+ 1
c
6
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
2
c
7
, c
9
, c
10
c
12
(u
2
+ 1)
5
c
8
u
10
+ 2u
9
+ ··· + 96u + 32
c
11
u
10
− 2u
9
+ ··· − 96u + 32
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
2
c
3
, c
6
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
2
c
5
(y
5
+ y
4
+ 8y
3
+ 3y
2
+ 3y + 1)
2
c
7
, c
9
, c
10
c
12
(y + 1)
10
c
8
, c
11
y
10
+ 12y
8
− 592y
6
+ 4096y
4
− 3840y
2
+ 1024
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = −0.361438 − 0.927855I
b = −0.455697 − 1.200150I
−9.16243 + 4.40083I −4.74431 − 3.49859I
u = 1.000000I
a = 0.331455 + 0.820551I
b = 0.339110 − 0.822375I
−3.61897 − 1.53058I −0.51511 + 4.43065I
u = 1.000000I
a = 0.0768928 + 0.0902877I
b = −0.455697 + 1.200150I
−9.16243 − 4.40083I −4.74431 + 3.49859I
u = 1.000000I
a = 1.43128 + 1.79928I
b = 0.339110 + 0.822375I
−3.61897 + 1.53058I −0.51511 − 4.43065I
u = 1.000000I
a = 3.52181 + 2.21774I
b = −0.766826
−5.69095 −1.48114 + 0.I
u = − 1.000000I
a = −0.361438 + 0.927855I
b = −0.455697 + 1.200150I
−9.16243 − 4.40083I −4.74431 + 3.49859I
u = − 1.000000I
a = 0.331455 − 0.820551I
b = 0.339110 + 0.822375I
−3.61897 + 1.53058I −0.51511 − 4.43065I
u = − 1.000000I
a = 0.0768928 − 0.0902877I
b = −0.455697 − 1.200150I
−9.16243 + 4.40083I −4.74431 − 3.49859I
u = − 1.000000I
a = 1.43128 − 1.79928I
b = 0.339110 − 0.822375I
−3.61897 − 1.53058I −0.51511 + 4.43065I
u = − 1.000000I
a = 3.52181 − 2.21774I
b = −0.766826
−5.69095 −1.48114 + 0.I
20
V. I
u
5
= hb, u
3
+ a + u, u
4
− u
3
+ 2u
2
− 2u + 1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
3
=
−u
3
− u
0
a
8
=
1
−u
2
a
6
=
1
0
a
4
=
−u
3
− u
0
a
12
=
u
u
a
10
=
−u
u
3
+ u
a
5
=
−u
3
+ u
2
− 2u + 2
u
3
+ u − 1
a
2
=
−u
2
+ u − 2
−u
3
− u + 1
a
1
=
u
3
− u
2
+ 2u − 2
−u
3
− u + 1
a
9
=
−u
3
− 2u + 1
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
3
− 4u + 3
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
4
c
3
, c
6
u
4
c
4
(u + 1)
4
c
5
(u
2
− u + 1)
2
c
7
, c
9
u
4
− u
3
+ 2u
2
− 2u + 1
c
8
, c
10
, c
11
c
12
u
4
+ u
3
+ 2u
2
+ 2u + 1
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
4
c
3
, c
6
y
4
c
5
(y
2
+ y + 1)
2
c
7
, c
8
, c
9
c
10
, c
11
, c
12
y
4
+ 3y
3
+ 2y
2
+ 1
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.621744 + 0.440597I
a = −0.500000 − 0.866025I
b = 0
−4.93480 + 2.02988I 1.0000 − 3.46410I
u = 0.621744 − 0.440597I
a = −0.500000 + 0.866025I
b = 0
−4.93480 − 2.02988I 1.0000 + 3.46410I
u = −0.121744 + 1.306620I
a = −0.500000 + 0.866025I
b = 0
−4.93480 − 2.02988I 1.00000 + 3.46410I
u = −0.121744 − 1.306620I
a = −0.500000 − 0.866025I
b = 0
−4.93480 + 2.02988I 1.00000 − 3.46410I
24
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
7
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
2
· (u
10
− 3u
9
+ 4u
8
+ u
7
− 6u
6
+ 6u
5
+ u
4
− 2u
3
+ 3u
2
− 2u + 1)
2
· (u
22
− 4u
21
+ ··· + 225u − 16)
c
3
u
7
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
2
· (u
10
+ u
9
− 7u
8
− 8u
7
+ 13u
6
+ 14u
5
− 2u
4
+ 2u
3
+ 13u
2
+ 12u + 4)
2
· (u
22
+ 3u
21
+ ··· − 432u + 128)
c
4
(u + 1)
7
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
2
· (u
10
− 3u
9
+ 4u
8
+ u
7
− 6u
6
+ 6u
5
+ u
4
− 2u
3
+ 3u
2
− 2u + 1)
2
· (u
22
− 4u
21
+ ··· + 225u − 16)
c
5
(u
2
− u + 1)
2
(u
3
+ 3u
2
+ 5u + 2)(u
10
+ u
8
+ 8u
6
+ 3u
4
+ 3u
2
+ 1)
· (u
10
− 2u
9
+ 3u
8
− 2u
7
+ 4u
6
− 3u
5
+ 3u
4
+ 3u
2
− u + 1)
2
· (u
22
+ 6u
21
+ ··· − 12u − 4)
c
6
u
7
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
2
· (u
10
+ u
9
− 7u
8
− 8u
7
+ 13u
6
+ 14u
5
− 2u
4
+ 2u
3
+ 13u
2
+ 12u + 4)
2
· (u
22
+ 3u
21
+ ··· − 432u + 128)
c
7
, c
9
(u
2
+ 1)
5
(u
3
+ 2u + 1)(u
4
− u
3
+ 2u
2
− 2u + 1)
· (u
20
+ 2u
19
+ ··· + 4u + 17)(u
22
+ 3u
20
+ ··· − u + 1)
c
8
(u
3
+ 2u − 1)(u
4
+ u
3
+ 2u
2
+ 2u + 1)(u
10
+ 2u
9
+ ··· + 96u + 32)
· (u
20
− 3u
18
+ ··· + 35738u + 11449)(u
22
− 14u
20
+ ··· − 160u − 32)
c
10
, c
12
(u
2
+ 1)
5
(u
3
+ 2u − 1)(u
4
+ u
3
+ 2u
2
+ 2u + 1)
· (u
20
+ 2u
19
+ ··· + 4u + 17)(u
22
+ 3u
20
+ ··· − u + 1)
c
11
(u
3
+ 2u − 1)(u
4
+ u
3
+ 2u
2
+ 2u + 1)(u
10
− 2u
9
+ ··· − 96u + 32)
· (u
20
− 3u
18
+ ··· + 35738u + 11449)(u
22
− 14u
20
+ ··· − 160u − 32)
25
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
7
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
2
· (y
10
− y
9
+ 10y
8
− 11y
7
+ 26y
6
− 30y
5
+ y
4
+ 14y
3
+ 3y
2
+ 2y + 1)
2
· (y
22
− 12y
21
+ ··· − 52961y + 256)
c
3
, c
6
y
7
(y
5
+ 3y
4
+ ··· − y −1)
2
(y
10
− 15y
9
+ ··· − 40y + 16)
2
· (y
22
− 9y
21
+ ··· − 181504y + 16384)
c
5
(y
2
+ y + 1)
2
(y
3
+ y
2
+ 13y −4)(y
5
+ y
4
+ 8y
3
+ 3y
2
+ 3y + 1)
2
· (y
10
+ 2y
9
+ 9y
8
+ 14y
7
+ 28y
6
+ 31y
5
+ 35y
4
+ 20y
3
+ 15y
2
+ 5y + 1)
2
· (y
22
+ 4y
21
+ ··· − 56y + 16)
c
7
, c
9
, c
10
c
12
(y + 1)
10
(y
3
+ 4y
2
+ 4y −1)(y
4
+ 3y
3
+ 2y
2
+ 1)
· (y
20
+ 6y
19
+ ··· + 4064y + 289)(y
22
+ 6y
21
+ ··· + 5y + 1)
c
8
, c
11
(y
3
+ 4y
2
+ 4y −1)(y
4
+ 3y
3
+ 2y
2
+ 1)
· (y
10
+ 12y
8
− 592y
6
+ 4096y
4
− 3840y
2
+ 1024)
· (y
20
− 6y
19
+ ··· + 896868864y + 131079601)
· (y
22
− 28y
21
+ ··· − 25600y + 1024)
26
