12a
1079
(K12a
1079
)
A knot diagram
1
Linearized knot diagam
4 7 10 11 9 12 3 6 1 2 5 8
Solving Sequence
3,10 4,7
8 2 11 5 1 9 12 6
c
3
c
7
c
2
c
10
c
4
c
1
c
9
c
12
c
6
c
5
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.45606 × 10
1797
u
172
+ 4.28745 × 10
1797
u
171
+ ··· + 9.44770 × 10
1797
b 2.86748 × 10
1798
,
1.34169 × 10
1798
u
172
3.67073 × 10
1798
u
171
+ ··· + 1.57462 × 10
1798
a + 2.75924 × 10
1799
,
u
173
3u
172
+ ··· + 74u 5i
I
u
2
= h−6.40598 × 10
90
u
40
1.88911 × 10
91
u
39
+ ··· + 3.54564 × 10
91
b + 6.32745 × 10
91
,
3.86971 × 10
90
u
40
+ 1.37761 × 10
91
u
39
+ ··· + 5.06521 × 10
90
a + 2.20586 × 10
90
, u
41
+ 4u
40
+ ··· + 8u + 1i
I
v
1
= ha, b 1, v 1i
* 3 irreducible components of dim
C
= 0, with total 215 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−1.46 × 10
1797
u
172
+ 4.29 × 10
1797
u
171
+ · · · + 9.45 × 10
1797
b
2.87 × 10
1798
, 1.34 × 10
1798
u
172
3.67 × 10
1798
u
171
+ · · · + 1.57 × 10
1798
a +
2.76 × 10
1799
, u
173
3u
172
+ · · · + 74u 5i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
u
2
a
7
=
0.852074u
172
+ 2.33119u
171
+ ··· + 192.061u 17.5233
0.154118u
172
0.453809u
171
+ ··· 43.4524u + 3.03511
a
8
=
0.697956u
172
+ 1.87738u
171
+ ··· + 148.609u 14.4882
0.154118u
172
0.453809u
171
+ ··· 43.4524u + 3.03511
a
2
=
0.880846u
172
2.41344u
171
+ ··· 189.358u + 15.3554
0.0527602u
172
0.167734u
171
+ ··· 44.7616u + 7.47187
a
11
=
0.659939u
172
1.79682u
171
+ ··· 125.453u + 10.8685
0.150489u
172
0.412764u
171
+ ··· 33.4644u + 2.15245
a
5
=
1.66068u
172
4.55348u
171
+ ··· 348.176u + 32.1923
0.0936094u
172
+ 0.255286u
171
+ ··· + 20.9243u 1.12248
a
1
=
0.990881u
172
2.73865u
171
+ ··· 246.669u + 23.9728
0.0504515u
172
0.161358u
171
+ ··· 44.9493u + 7.44738
a
9
=
1.14343u
172
3.12968u
171
+ ··· 248.351u + 22.1620
0.204142u
172
0.568632u
171
+ ··· 60.6632u + 6.72298
a
12
=
0.911362u
172
+ 2.49693u
171
+ ··· + 192.888u 16.1126
0.100738u
172
+ 0.274420u
171
+ ··· + 21.0835u 2.10841
a
6
=
0.642395u
172
1.78447u
171
+ ··· 137.745u + 12.1505
0.0117123u
172
0.00281222u
171
+ ··· 14.1390u + 1.15428
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4.49529u
172
13.8680u
171
+ ··· 2310.57u + 192.724
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
173
19u
172
+ ··· + 21313u 34383
c
2
, c
7
u
173
2u
172
+ ··· 128u 57
c
3
u
173
3u
172
+ ··· + 74u 5
c
4
, c
11
u
173
8u
172
+ ··· 475086499u 26150301
c
5
, c
8
u
173
5u
172
+ ··· 39097u + 5255
c
6
u
173
2u
172
+ ··· 127187u 8237
c
9
u
173
5u
172
+ ··· 11110439275u 2018788719
c
10
u
173
u
172
+ ··· 195900u 10457
c
12
u
173
+ 8u
172
+ ··· + 109558u 21897
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
173
51y
172
+ ··· + 66157887691y 1182190689
c
2
, c
7
y
173
84y
172
+ ··· + 141898y 3249
c
3
y
173
+ 57y
172
+ ··· + 226y 25
c
4
, c
11
y
173
98y
172
+ ··· + 14008959254796871y 683838242390601
c
5
, c
8
y
173
+ 93y
172
+ ··· 1610278131y 27615025
c
6
y
173
10y
172
+ ··· + 2537115305y 67848169
c
9
y
173
55y
172
+ ··· 3.85 × 10
19
y 4.08 × 10
18
c
10
y
173
+ 53y
172
+ ··· + 582535008y 109348849
c
12
y
173
40y
172
+ ··· 18126440756y 479478609
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.771804 + 0.616839I
a = 0.39746 1.58134I
b = 0.575916 + 0.329596I
0.73868 6.06646I 0
u = 0.771804 0.616839I
a = 0.39746 + 1.58134I
b = 0.575916 0.329596I
0.73868 + 6.06646I 0
u = 0.327529 + 0.959841I
a = 0.909180 + 0.473505I
b = 0.521248 0.478347I
4.82456 3.09167I 0
u = 0.327529 0.959841I
a = 0.909180 0.473505I
b = 0.521248 + 0.478347I
4.82456 + 3.09167I 0
u = 0.893032 + 0.512926I
a = 1.87164 0.35247I
b = 1.195920 0.317103I
3.46692 4.24825I 0
u = 0.893032 0.512926I
a = 1.87164 + 0.35247I
b = 1.195920 + 0.317103I
3.46692 + 4.24825I 0
u = 0.884605 + 0.378784I
a = 1.85819 0.14668I
b = 1.265240 + 0.030420I
7.57089 1.71431I 0
u = 0.884605 0.378784I
a = 1.85819 + 0.14668I
b = 1.265240 0.030420I
7.57089 + 1.71431I 0
u = 1.020480 + 0.191153I
a = 2.22668 0.53281I
b = 1.060020 + 0.469899I
2.47628 + 9.71556I 0
u = 1.020480 0.191153I
a = 2.22668 + 0.53281I
b = 1.060020 0.469899I
2.47628 9.71556I 0
5
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.310676 + 0.909070I
a = 1.13471 0.91152I
b = 0.769375 0.374994I
1.35686 + 2.59200I 0
u = 0.310676 0.909070I
a = 1.13471 + 0.91152I
b = 0.769375 + 0.374994I
1.35686 2.59200I 0
u = 0.209331 + 0.932459I
a = 0.515968 + 0.653908I
b = 0.891224 + 0.338281I
1.01217 + 3.12518I 0
u = 0.209331 0.932459I
a = 0.515968 0.653908I
b = 0.891224 0.338281I
1.01217 3.12518I 0
u = 0.903470 + 0.153525I
a = 0.089516 + 0.427393I
b = 0.150812 + 0.347980I
1.85433 + 1.23746I 0
u = 0.903470 0.153525I
a = 0.089516 0.427393I
b = 0.150812 0.347980I
1.85433 1.23746I 0
u = 0.534516 + 0.943325I
a = 0.253784 + 0.163165I
b = 0.143471 0.644994I
5.23731 5.69130I 0
u = 0.534516 0.943325I
a = 0.253784 0.163165I
b = 0.143471 + 0.644994I
5.23731 + 5.69130I 0
u = 0.847467 + 0.694335I
a = 1.130120 0.548135I
b = 1.074320 0.683913I
2.13377 + 3.30366I 0
u = 0.847467 0.694335I
a = 1.130120 + 0.548135I
b = 1.074320 + 0.683913I
2.13377 3.30366I 0
6
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.059570 + 0.295085I
a = 1.94245 + 0.11465I
b = 1.155320 + 0.440201I
6.18080 6.34984I 0
u = 1.059570 0.295085I
a = 1.94245 0.11465I
b = 1.155320 0.440201I
6.18080 + 6.34984I 0
u = 1.057830 + 0.417082I
a = 1.365150 + 0.034155I
b = 1.59091 + 0.12319I
4.45701 9.89476I 0
u = 1.057830 0.417082I
a = 1.365150 0.034155I
b = 1.59091 0.12319I
4.45701 + 9.89476I 0
u = 0.115228 + 0.839112I
a = 1.67477 + 0.38358I
b = 1.149070 + 0.528934I
4.12366 3.97170I 0
u = 0.115228 0.839112I
a = 1.67477 0.38358I
b = 1.149070 0.528934I
4.12366 + 3.97170I 0
u = 0.274378 + 0.797674I
a = 0.885026 0.966071I
b = 0.954736 0.435772I
2.53247 + 7.27988I 0
u = 0.274378 0.797674I
a = 0.885026 + 0.966071I
b = 0.954736 + 0.435772I
2.53247 7.27988I 0
u = 0.811488 + 0.839964I
a = 1.57035 + 1.08983I
b = 0.245624 + 0.756593I
7.44936 0.53307I 0
u = 0.811488 0.839964I
a = 1.57035 1.08983I
b = 0.245624 0.756593I
7.44936 + 0.53307I 0
7
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.595608 + 1.013850I
a = 0.169753 + 0.015600I
b = 0.001884 + 0.755426I
5.25176 2.86179I 0
u = 0.595608 1.013850I
a = 0.169753 0.015600I
b = 0.001884 0.755426I
5.25176 + 2.86179I 0
u = 0.485744 + 0.665646I
a = 1.006990 0.543825I
b = 1.25260 0.86382I
0.02523 + 12.00230I 0
u = 0.485744 0.665646I
a = 1.006990 + 0.543825I
b = 1.25260 + 0.86382I
0.02523 12.00230I 0
u = 0.288924 + 0.768932I
a = 1.45194 + 0.66827I
b = 0.568154 0.388478I
4.58612 2.13205I 0
u = 0.288924 0.768932I
a = 1.45194 0.66827I
b = 0.568154 + 0.388478I
4.58612 + 2.13205I 0
u = 0.090615 + 0.816399I
a = 1.34471 + 1.06956I
b = 0.693540 + 0.393354I
3.40908 + 3.07298I 0
u = 0.090615 0.816399I
a = 1.34471 1.06956I
b = 0.693540 0.393354I
3.40908 3.07298I 0
u = 0.656834 + 0.456210I
a = 2.44343 0.66596I
b = 0.020467 0.688172I
3.03193 + 6.49857I 0
u = 0.656834 0.456210I
a = 2.44343 + 0.66596I
b = 0.020467 + 0.688172I
3.03193 6.49857I 0
8
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.573018 + 0.543113I
a = 1.036760 + 0.596641I
b = 1.14168 + 0.89708I
2.74658 + 6.71616I 0
u = 0.573018 0.543113I
a = 1.036760 0.596641I
b = 1.14168 0.89708I
2.74658 6.71616I 0
u = 1.050190 + 0.606462I
a = 1.38501 0.32197I
b = 1.53027 0.37409I
2.82769 3.81698I 0
u = 1.050190 0.606462I
a = 1.38501 + 0.32197I
b = 1.53027 + 0.37409I
2.82769 + 3.81698I 0
u = 0.620347 + 1.051040I
a = 0.111676 + 0.732193I
b = 1.253110 0.353916I
0.75493 2.23733I 0
u = 0.620347 1.051040I
a = 0.111676 0.732193I
b = 1.253110 + 0.353916I
0.75493 + 2.23733I 0
u = 0.798891 + 0.934167I
a = 1.73060 0.88718I
b = 1.085620 0.539353I
4.08066 + 7.63216I 0
u = 0.798891 0.934167I
a = 1.73060 + 0.88718I
b = 1.085620 + 0.539353I
4.08066 7.63216I 0
u = 0.436532 + 0.635112I
a = 1.38475 1.10083I
b = 1.237080 0.610945I
3.24345 7.96682I 0
u = 0.436532 0.635112I
a = 1.38475 + 1.10083I
b = 1.237080 + 0.610945I
3.24345 + 7.96682I 0
9
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.476347 + 1.142860I
a = 0.248989 + 0.082084I
b = 0.371624 0.514992I
6.14067 3.17595I 0
u = 0.476347 1.142860I
a = 0.248989 0.082084I
b = 0.371624 + 0.514992I
6.14067 + 3.17595I 0
u = 1.201370 + 0.302411I
a = 1.301830 + 0.096557I
b = 1.261640 + 0.068574I
3.90299 + 0.46319I 0
u = 1.201370 0.302411I
a = 1.301830 0.096557I
b = 1.261640 0.068574I
3.90299 0.46319I 0
u = 0.790408 + 0.974551I
a = 0.222631 + 0.218548I
b = 0.570108 0.583458I
1.39173 + 3.03834I 0
u = 0.790408 0.974551I
a = 0.222631 0.218548I
b = 0.570108 + 0.583458I
1.39173 3.03834I 0
u = 0.652253 + 0.358586I
a = 0.351804 0.584101I
b = 0.082947 + 0.626679I
3.14829 + 2.27443I 0
u = 0.652253 0.358586I
a = 0.351804 + 0.584101I
b = 0.082947 0.626679I
3.14829 2.27443I 0
u = 1.090420 + 0.641267I
a = 1.28188 0.96977I
b = 0.951554 0.253556I
0.79136 + 3.29959I 0
u = 1.090420 0.641267I
a = 1.28188 + 0.96977I
b = 0.951554 + 0.253556I
0.79136 3.29959I 0
10
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.192030 + 0.440347I
a = 1.231700 0.113799I
b = 1.301890 0.116928I
7.48423 + 5.34721I 0
u = 1.192030 0.440347I
a = 1.231700 + 0.113799I
b = 1.301890 + 0.116928I
7.48423 5.34721I 0
u = 0.781611 + 1.011340I
a = 0.088109 + 0.454713I
b = 0.965838 0.735415I
1.33379 + 2.59811I 0
u = 0.781611 1.011340I
a = 0.088109 0.454713I
b = 0.965838 + 0.735415I
1.33379 2.59811I 0
u = 0.898132 + 0.938994I
a = 0.113394 + 0.229786I
b = 0.300953 + 0.965635I
2.29687 3.81092I 0
u = 0.898132 0.938994I
a = 0.113394 0.229786I
b = 0.300953 0.965635I
2.29687 + 3.81092I 0
u = 0.202556 + 0.666398I
a = 1.48907 2.53927I
b = 1.144620 0.491821I
0.04009 10.77620I 0
u = 0.202556 0.666398I
a = 1.48907 + 2.53927I
b = 1.144620 + 0.491821I
0.04009 + 10.77620I 0
u = 0.582427 + 1.198980I
a = 0.1062270 + 0.0814320I
b = 0.307299 + 0.661890I
5.39810 6.59757I 0
u = 0.582427 1.198980I
a = 0.1062270 0.0814320I
b = 0.307299 0.661890I
5.39810 + 6.59757I 0
11
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.595071 + 0.293276I
a = 0.960088 0.059502I
b = 1.157920 0.699124I
2.76594 0.82042I 0
u = 0.595071 0.293276I
a = 0.960088 + 0.059502I
b = 1.157920 + 0.699124I
2.76594 + 0.82042I 0
u = 0.197798 + 0.632612I
a = 0.298551 + 0.201969I
b = 0.140312 0.490544I
0.251995 + 1.167390I 0
u = 0.197798 0.632612I
a = 0.298551 0.201969I
b = 0.140312 + 0.490544I
0.251995 1.167390I 0
u = 1.176470 + 0.663942I
a = 1.026570 0.199156I
b = 1.038940 0.525323I
3.18652 1.20243I 0
u = 1.176470 0.663942I
a = 1.026570 + 0.199156I
b = 1.038940 + 0.525323I
3.18652 + 1.20243I 0
u = 0.489322 + 0.424466I
a = 3.61572 1.51104I
b = 1.041160 0.486793I
2.98959 + 5.99414I 0
u = 0.489322 0.424466I
a = 3.61572 + 1.51104I
b = 1.041160 + 0.486793I
2.98959 5.99414I 0
u = 0.553755 + 0.311828I
a = 0.086698 + 0.147270I
b = 0.00775 1.58504I
2.77098 3.15696I 0
u = 0.553755 0.311828I
a = 0.086698 0.147270I
b = 0.00775 + 1.58504I
2.77098 + 3.15696I 0
12
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.051630 + 0.871791I
a = 1.47913 0.77264I
b = 0.396452 0.582440I
3.81059 7.12042I 0
u = 1.051630 0.871791I
a = 1.47913 + 0.77264I
b = 0.396452 + 0.582440I
3.81059 + 7.12042I 0
u = 1.339450 + 0.272311I
a = 1.305310 0.185779I
b = 1.224180 0.120179I
7.83078 4.10815I 0
u = 1.339450 0.272311I
a = 1.305310 + 0.185779I
b = 1.224180 + 0.120179I
7.83078 + 4.10815I 0
u = 0.260548 + 1.346570I
a = 0.372320 + 0.129068I
b = 0.383847 0.198499I
5.78719 3.27740I 0
u = 0.260548 1.346570I
a = 0.372320 0.129068I
b = 0.383847 + 0.198499I
5.78719 + 3.27740I 0
u = 0.540444 + 0.236092I
a = 1.76684 1.87855I
b = 1.064290 0.461952I
6.03952 1.30060I 0
u = 0.540444 0.236092I
a = 1.76684 + 1.87855I
b = 1.064290 + 0.461952I
6.03952 + 1.30060I 0
u = 1.00260 + 0.99784I
a = 0.0479860 + 0.0683654I
b = 0.463303 1.175820I
3.9091 + 14.3052I 0
u = 1.00260 0.99784I
a = 0.0479860 0.0683654I
b = 0.463303 + 1.175820I
3.9091 14.3052I 0
13
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.380777 + 0.433816I
a = 1.39771 + 1.44587I
b = 1.141210 + 0.620104I
1.18248 3.63276I 0
u = 0.380777 0.433816I
a = 1.39771 1.44587I
b = 1.141210 0.620104I
1.18248 + 3.63276I 0
u = 1.02110 + 0.99823I
a = 0.0181824 0.0903520I
b = 0.565972 + 1.238050I
7.12079 + 7.64482I 0
u = 1.02110 0.99823I
a = 0.0181824 + 0.0903520I
b = 0.565972 1.238050I
7.12079 7.64482I 0
u = 0.221479 + 0.524398I
a = 0.420856 0.196728I
b = 0.073568 1.045510I
0.32442 + 2.05901I 0
u = 0.221479 0.524398I
a = 0.420856 + 0.196728I
b = 0.073568 + 1.045510I
0.32442 2.05901I 0
u = 0.94557 + 1.07962I
a = 0.069344 0.261082I
b = 0.341921 0.882790I
1.76439 8.64944I 0
u = 0.94557 1.07962I
a = 0.069344 + 0.261082I
b = 0.341921 + 0.882790I
1.76439 + 8.64944I 0
u = 0.01118 + 1.43980I
a = 0.077941 0.361287I
b = 1.150280 0.237849I
0.01971 + 4.42792I 0
u = 0.01118 1.43980I
a = 0.077941 + 0.361287I
b = 1.150280 + 0.237849I
0.01971 4.42792I 0
14
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.89322 + 1.14294I
a = 1.42783 + 0.82370I
b = 1.110460 + 0.566366I
3.14263 + 11.42110I 0
u = 0.89322 1.14294I
a = 1.42783 0.82370I
b = 1.110460 0.566366I
3.14263 11.42110I 0
u = 1.01855 + 1.06509I
a = 1.34401 0.89192I
b = 1.079310 0.862048I
1.61273 9.07333I 0
u = 1.01855 1.06509I
a = 1.34401 + 0.89192I
b = 1.079310 + 0.862048I
1.61273 + 9.07333I 0
u = 1.07007 + 1.01607I
a = 0.222969 0.283585I
b = 0.588593 0.899615I
1.93016 + 1.77297I 0
u = 1.07007 1.01607I
a = 0.222969 + 0.283585I
b = 0.588593 + 0.899615I
1.93016 1.77297I 0
u = 0.59580 + 1.36183I
a = 0.330826 + 0.187193I
b = 0.412461 0.047465I
5.08049 6.03903I 0
u = 0.59580 1.36183I
a = 0.330826 0.187193I
b = 0.412461 + 0.047465I
5.08049 + 6.03903I 0
u = 1.25785 + 0.80648I
a = 1.60637 0.35517I
b = 0.929722 0.430484I
2.25673 6.96320I 0
u = 1.25785 0.80648I
a = 1.60637 + 0.35517I
b = 0.929722 + 0.430484I
2.25673 + 6.96320I 0
15
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.68933 + 1.33561I
a = 1.32515 1.00348I
b = 0.845483 0.389760I
2.07173 0.49277I 0
u = 0.68933 1.33561I
a = 1.32515 + 1.00348I
b = 0.845483 + 0.389760I
2.07173 + 0.49277I 0
u = 0.026810 + 0.492713I
a = 1.094720 + 0.033699I
b = 1.46826 + 0.52395I
1.06608 + 2.76062I 21.2259 6.9158I
u = 0.026810 0.492713I
a = 1.094720 0.033699I
b = 1.46826 0.52395I
1.06608 2.76062I 21.2259 + 6.9158I
u = 0.29341 + 1.47990I
a = 0.39388 + 1.47257I
b = 0.00064 + 1.43127I
7.83616 0.90984I 0
u = 0.29341 1.47990I
a = 0.39388 1.47257I
b = 0.00064 1.43127I
7.83616 + 0.90984I 0
u = 0.219019 + 0.426393I
a = 1.36079 2.17280I
b = 0.390412 + 0.560000I
0.15969 6.71976I 4.00000 + 5.95672I
u = 0.219019 0.426393I
a = 1.36079 + 2.17280I
b = 0.390412 0.560000I
0.15969 + 6.71976I 4.00000 5.95672I
u = 1.26696 + 0.87132I
a = 1.55381 0.28865I
b = 1.136610 0.482113I
2.21266 + 9.70416I 0
u = 1.26696 0.87132I
a = 1.55381 + 0.28865I
b = 1.136610 + 0.482113I
2.21266 9.70416I 0
16
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.70912 + 1.39026I
a = 0.529659 0.194908I
b = 0.858036 0.602660I
1.25833 + 1.46506I 0
u = 0.70912 1.39026I
a = 0.529659 + 0.194908I
b = 0.858036 + 0.602660I
1.25833 1.46506I 0
u = 0.74538 + 1.37969I
a = 0.779922 0.083463I
b = 0.690066 + 0.410656I
3.45403 + 0.99244I 0
u = 0.74538 1.37969I
a = 0.779922 + 0.083463I
b = 0.690066 0.410656I
3.45403 0.99244I 0
u = 0.270858 + 0.299713I
a = 0.42510 3.44166I
b = 1.120710 0.431374I
2.61891 2.60527I 2.19979 + 2.42977I
u = 0.270858 0.299713I
a = 0.42510 + 3.44166I
b = 1.120710 + 0.431374I
2.61891 + 2.60527I 2.19979 2.42977I
u = 1.19735 + 1.05685I
a = 1.40190 + 0.42418I
b = 1.165460 + 0.514043I
2.14917 + 7.43905I 0
u = 1.19735 1.05685I
a = 1.40190 0.42418I
b = 1.165460 0.514043I
2.14917 7.43905I 0
u = 0.131695 + 0.359172I
a = 1.94861 + 4.86669I
b = 0.998265 + 0.422503I
2.40329 + 0.40749I 11.27009 + 0.81722I
u = 0.131695 0.359172I
a = 1.94861 4.86669I
b = 0.998265 0.422503I
2.40329 0.40749I 11.27009 0.81722I
17
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.14275 + 1.14857I
a = 1.24104 + 0.69121I
b = 1.23896 + 0.77805I
4.8409 14.7640I 0
u = 1.14275 1.14857I
a = 1.24104 0.69121I
b = 1.23896 0.77805I
4.8409 + 14.7640I 0
u = 0.61057 + 1.50821I
a = 0.412925 + 0.132575I
b = 0.797914 + 0.364812I
1.292400 + 0.235559I 0
u = 0.61057 1.50821I
a = 0.412925 0.132575I
b = 0.797914 0.364812I
1.292400 0.235559I 0
u = 0.360748 + 0.057808I
a = 1.81412 2.11052I
b = 0.322395 1.000550I
5.45575 3.27553I 11.12246 + 3.81811I
u = 0.360748 0.057808I
a = 1.81412 + 2.11052I
b = 0.322395 + 1.000550I
5.45575 + 3.27553I 11.12246 3.81811I
u = 1.18500 + 1.16023I
a = 1.252350 0.647899I
b = 1.23895 0.73568I
1.4041 21.0729I 0
u = 1.18500 1.16023I
a = 1.252350 + 0.647899I
b = 1.23895 + 0.73568I
1.4041 + 21.0729I 0
u = 0.229098 + 0.236735I
a = 4.67353 10.02870I
b = 0.417238 0.056129I
3.21981 6.95231I 16.0662 + 21.3010I
u = 0.229098 0.236735I
a = 4.67353 + 10.02870I
b = 0.417238 + 0.056129I
3.21981 + 6.95231I 16.0662 21.3010I
18
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.281786 + 0.164554I
a = 1.57933 3.60160I
b = 0.632665 0.429307I
1.61418 3.63737I 3.03644 + 2.05493I
u = 0.281786 0.164554I
a = 1.57933 + 3.60160I
b = 0.632665 + 0.429307I
1.61418 + 3.63737I 3.03644 2.05493I
u = 1.23998 + 1.15184I
a = 1.36064 + 0.54329I
b = 0.915621 + 0.418635I
0.85773 3.62337I 0
u = 1.23998 1.15184I
a = 1.36064 0.54329I
b = 0.915621 0.418635I
0.85773 + 3.62337I 0
u = 0.199861 + 0.231647I
a = 0.95907 + 3.00855I
b = 0.666540 + 0.257986I
1.46465 0.07572I 7.82957 0.25967I
u = 0.199861 0.231647I
a = 0.95907 3.00855I
b = 0.666540 0.257986I
1.46465 + 0.07572I 7.82957 + 0.25967I
u = 0.275213
a = 14.8178
b = 0.369430
7.33542 36.0940
u = 1.23400 + 1.22259I
a = 1.144000 + 0.603249I
b = 1.173050 + 0.611089I
0.34581 + 9.42252I 0
u = 1.23400 1.22259I
a = 1.144000 0.603249I
b = 1.173050 0.611089I
0.34581 9.42252I 0
u = 1.44536 + 0.98520I
a = 1.143970 + 0.261724I
b = 0.985011 + 0.449323I
2.45138 4.64512I 0
19
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.44536 0.98520I
a = 1.143970 0.261724I
b = 0.985011 0.449323I
2.45138 + 4.64512I 0
u = 0.233347 + 0.056878I
a = 1.75864 1.41813I
b = 1.47296 0.43619I
1.73590 + 0.84771I 10.7047 12.7164I
u = 0.233347 0.056878I
a = 1.75864 + 1.41813I
b = 1.47296 + 0.43619I
1.73590 0.84771I 10.7047 + 12.7164I
u = 0.161708 + 0.164950I
a = 0.039432 + 1.336790I
b = 0.675722 + 1.129920I
0.73454 2.34093I 14.3158 10.9429I
u = 0.161708 0.164950I
a = 0.039432 1.336790I
b = 0.675722 1.129920I
0.73454 + 2.34093I 14.3158 + 10.9429I
u = 1.35566 + 1.14725I
a = 1.062650 0.562680I
b = 1.188430 0.669605I
3.94810 + 4.36162I 0
u = 1.35566 1.14725I
a = 1.062650 + 0.562680I
b = 1.188430 + 0.669605I
3.94810 4.36162I 0
u = 1.24947 + 1.32010I
a = 1.115280 0.657489I
b = 1.153690 0.615821I
4.1843 + 14.1413I 0
u = 1.24947 1.32010I
a = 1.115280 + 0.657489I
b = 1.153690 + 0.615821I
4.1843 14.1413I 0
u = 0.106054 + 0.137180I
a = 1.140470 + 0.701562I
b = 1.77806 + 0.75687I
1.12029 2.35732I 83.1331 68.1270I
20
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.106054 0.137180I
a = 1.140470 0.701562I
b = 1.77806 0.75687I
1.12029 + 2.35732I 83.1331 + 68.1270I
u = 1.14349 + 1.49257I
a = 0.534176 0.051240I
b = 1.108580 + 0.603272I
5.13750 + 5.70484I 0
u = 1.14349 1.49257I
a = 0.534176 + 0.051240I
b = 1.108580 0.603272I
5.13750 5.70484I 0
u = 0.31408 + 1.87481I
a = 0.390747 0.437455I
b = 0.902258 0.415976I
2.29988 2.89024I 0
u = 0.31408 1.87481I
a = 0.390747 + 0.437455I
b = 0.902258 + 0.415976I
2.29988 + 2.89024I 0
u = 0.75156 + 1.82392I
a = 0.751552 + 0.609069I
b = 0.866179 + 0.410595I
0.24995 + 1.88241I 0
u = 0.75156 1.82392I
a = 0.751552 0.609069I
b = 0.866179 0.410595I
0.24995 1.88241I 0
u = 1.19249 + 1.58454I
a = 0.611465 + 0.027573I
b = 1.080280 0.550315I
1.83842 + 11.72340I 0
u = 1.19249 1.58454I
a = 0.611465 0.027573I
b = 1.080280 + 0.550315I
1.83842 11.72340I 0
u = 1.75154 + 2.17674I
a = 0.876531 + 0.580572I
b = 0.900051 + 0.459766I
0.24409 + 1.89759I 0
21
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.75154 2.17674I
a = 0.876531 0.580572I
b = 0.900051 0.459766I
0.24409 1.89759I 0
u = 0.57403 + 3.27869I
a = 0.820454 + 0.602706I
b = 0.862689 + 0.484557I
0.35740 1.98173I 0
u = 0.57403 3.27869I
a = 0.820454 0.602706I
b = 0.862689 0.484557I
0.35740 + 1.98173I 0
22
II.
I
u
2
= h−6.41×10
90
u
40
1.89×10
91
u
39
+· · ·+3.55×10
91
b+6.33×10
91
, 3.87×
10
90
u
40
+1.38×10
91
u
39
+· · ·+5.07×10
90
a+2.21×10
90
, u
41
+4u
40
+· · ·+8u+1i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
u
2
a
7
=
0.763979u
40
2.71975u
39
+ ··· 5.05847u 0.435494
0.180672u
40
+ 0.532797u
39
+ ··· 4.35985u 1.78457
a
8
=
0.583308u
40
2.18695u
39
+ ··· 9.41832u 2.22006
0.180672u
40
+ 0.532797u
39
+ ··· 4.35985u 1.78457
a
2
=
0.493136u
40
+ 1.80281u
39
+ ··· + 12.0580u + 1.94930
0.250054u
40
0.726703u
39
+ ··· 5.18045u + 1.23710
a
11
=
0.322186u
40
1.29954u
39
+ ··· 7.71395u 0.780577
0.184764u
40
0.784460u
39
+ ··· 3.72762u 1.41781
a
5
=
0.0449115u
40
0.0648536u
39
+ ··· + 2.25221u + 1.15905
0.205611u
40
+ 0.654268u
39
+ ··· + 1.96948u + 1.24059
a
1
=
0.236336u
40
+ 1.09068u
39
+ ··· + 7.74230u + 3.35613
0.0930975u
40
0.110825u
39
+ ··· 2.91670u + 1.55217
a
9
=
0.0446578u
40
0.498544u
39
+ ··· 6.20282u 2.11052
0.497668u
40
+ 1.54471u
39
+ ··· + 4.22623u 0.242844
a
12
=
0.462813u
40
+ 1.75922u
39
+ ··· + 3.27199u + 1.22909
0.394878u
40
+ 1.51216u
39
+ ··· + 3.93208u + 0.327294
a
6
=
0.504817u
40
1.91641u
39
+ ··· 15.4310u 2.78430
0.000614494u
40
0.162058u
39
+ ··· 11.4524u 2.27283
(ii) Obstruction class = 1
(iii) Cusp Shapes = 13.0566u
40
+ 48.8251u
39
+ ··· + 201.006u + 16.0619
23
(iv) u-Polynomials at the component
24
Crossings u-Polynomials at each crossing
c
1
u
41
+ 3u
40
+ ··· + 5u 1
c
2
u
41
+ 2u
40
+ ··· 2u 1
c
3
u
41
+ 4u
40
+ ··· + 8u + 1
c
4
u
41
+ 2u
40
+ ··· + 3u + 1
c
5
u
41
6u
40
+ ··· + 11u 1
c
6
u
41
2u
40
+ ··· + 7u + 3
c
7
u
41
2u
40
+ ··· 2u + 1
c
8
u
41
+ 6u
40
+ ··· + 11u + 1
c
9
u
41
+ 9u
40
+ ··· 245u + 43
c
10
u
41
u
40
+ ··· + 8u + 3
c
11
u
41
2u
40
+ ··· + 3u 1
c
12
u
41
+ 12u
40
+ ··· + 4u 1
25
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
41
23y
40
+ ··· 7y 1
c
2
, c
7
y
41
24y
40
+ ··· + 36y 1
c
3
y
41
+ 54y
40
+ ··· 8y 1
c
4
, c
11
y
41
+ 2y
40
+ ··· 7y 1
c
5
, c
8
y
41
+ 18y
40
+ ··· + 3y 1
c
6
y
41
18y
40
+ ··· + 103y 9
c
9
y
41
15y
40
+ ··· 22879y 1849
c
10
y
41
+ 29y
40
+ ··· + 10y 9
c
12
y
41
60y
40
+ ··· 90y 1
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 0.519600 + 0.823390I
a = 0.0318540 + 0.1215280I
b = 0.110011 0.971361I
6.04012 4.89441I 11.09334 + 5.96160I
u = 0.519600 0.823390I
a = 0.0318540 0.1215280I
b = 0.110011 + 0.971361I
6.04012 + 4.89441I 11.09334 5.96160I
u = 0.772150 + 0.693935I
a = 0.55916 + 1.49440I
b = 0.653551 0.031455I
2.49865 + 4.82480I 1.83523 6.56334I
u = 0.772150 0.693935I
a = 0.55916 1.49440I
b = 0.653551 + 0.031455I
2.49865 4.82480I 1.83523 + 6.56334I
u = 1.015940 + 0.264045I
a = 1.72247 + 0.15437I
b = 1.213780 0.349939I
5.27050 6.60777I 1.14612 + 7.13667I
u = 1.015940 0.264045I
a = 1.72247 0.15437I
b = 1.213780 + 0.349939I
5.27050 + 6.60777I 1.14612 7.13667I
u = 0.480498 + 1.027800I
a = 0.586486 0.354862I
b = 1.143530 + 0.531702I
1.30291 3.55768I 0. + 8.05240I
u = 0.480498 1.027800I
a = 0.586486 + 0.354862I
b = 1.143530 0.531702I
1.30291 + 3.55768I 0. 8.05240I
u = 0.469234 + 1.072390I
a = 0.401538 0.802477I
b = 0.708390 0.334626I
1.13294 + 2.10954I 0
u = 0.469234 1.072390I
a = 0.401538 + 0.802477I
b = 0.708390 + 0.334626I
1.13294 2.10954I 0
28
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 0.504496 + 1.128020I
a = 0.207932 0.955157I
b = 0.986973 0.168446I
1.58158 + 2.40548I 0
u = 0.504496 1.128020I
a = 0.207932 + 0.955157I
b = 0.986973 + 0.168446I
1.58158 2.40548I 0
u = 0.943541 + 0.800725I
a = 1.93770 + 0.80821I
b = 0.926275 + 0.625409I
0.49123 + 8.62241I 0
u = 0.943541 0.800725I
a = 1.93770 0.80821I
b = 0.926275 0.625409I
0.49123 8.62241I 0
u = 0.357671 + 0.664380I
a = 0.216331 + 1.152770I
b = 1.030350 0.532868I
3.50335 4.79038I 7.79216 + 6.10738I
u = 0.357671 0.664380I
a = 0.216331 1.152770I
b = 1.030350 + 0.532868I
3.50335 + 4.79038I 7.79216 6.10738I
u = 1.016030 + 0.730073I
a = 1.33137 + 0.56401I
b = 1.278120 + 0.482304I
4.31949 3.19355I 0
u = 1.016030 0.730073I
a = 1.33137 0.56401I
b = 1.278120 0.482304I
4.31949 + 3.19355I 0
u = 0.517413 + 0.339003I
a = 4.32461 + 4.16229I
b = 0.501613 + 0.075923I
3.08412 + 6.77173I 5.97918 + 6.92597I
u = 0.517413 0.339003I
a = 4.32461 4.16229I
b = 0.501613 0.075923I
3.08412 6.77173I 5.97918 6.92597I
29
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 0.276811 + 1.383390I
a = 0.181152 + 0.130077I
b = 0.562952 0.117650I
5.48768 3.32991I 0
u = 0.276811 1.383390I
a = 0.181152 0.130077I
b = 0.562952 + 0.117650I
5.48768 + 3.32991I 0
u = 0.062511 + 0.580723I
a = 1.41604 + 0.62470I
b = 1.144100 + 0.563700I
0.51284 10.42480I 0.95607 + 6.35463I
u = 0.062511 0.580723I
a = 1.41604 0.62470I
b = 1.144100 0.563700I
0.51284 + 10.42480I 0.95607 6.35463I
u = 0.516059
a = 8.29925
b = 0.489380
7.17877 15.7260
u = 1.13916 + 0.95101I
a = 1.54955 0.39851I
b = 1.150930 0.463429I
2.33097 + 8.99690I 0
u = 1.13916 0.95101I
a = 1.54955 + 0.39851I
b = 1.150930 + 0.463429I
2.33097 8.99690I 0
u = 0.123958 + 0.494638I
a = 0.364094 0.165052I
b = 0.910340 0.866875I
0.94903 + 2.39411I 13.74629 + 1.16223I
u = 0.123958 0.494638I
a = 0.364094 + 0.165052I
b = 0.910340 + 0.866875I
0.94903 2.39411I 13.74629 1.16223I
u = 0.60218 + 1.40181I
a = 0.218172 + 0.059029I
b = 0.554629 0.175083I
4.94655 5.78713I 0
30
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 0.60218 1.40181I
a = 0.218172 0.059029I
b = 0.554629 + 0.175083I
4.94655 + 5.78713I 0
u = 0.30783 + 1.52146I
a = 0.38770 1.41936I
b = 0.03360 1.46924I
7.79328 + 0.94674I 0
u = 0.30783 1.52146I
a = 0.38770 + 1.41936I
b = 0.03360 + 1.46924I
7.79328 0.94674I 0
u = 0.66068 + 1.46546I
a = 0.369780 + 0.579023I
b = 0.575124 + 0.605255I
1.32502 1.67201I 0
u = 0.66068 1.46546I
a = 0.369780 0.579023I
b = 0.575124 0.605255I
1.32502 + 1.67201I 0
u = 0.180377 + 0.302366I
a = 1.54419 + 0.56583I
b = 1.55407 0.03581I
1.96969 + 0.91814I 12.3799 21.2139I
u = 0.180377 0.302366I
a = 1.54419 0.56583I
b = 1.55407 + 0.03581I
1.96969 0.91814I 12.3799 + 21.2139I
u = 0.229299 + 0.141620I
a = 0.665819 0.638353I
b = 1.53827 + 0.31304I
1.08601 2.43088I 15.0321 + 21.2118I
u = 0.229299 0.141620I
a = 0.665819 + 0.638353I
b = 1.53827 0.31304I
1.08601 + 2.43088I 15.0321 21.2118I
u = 1.74223 + 4.59191I
a = 0.869509 0.530183I
b = 0.875674 0.480957I
0.18980 1.95729I 0
31
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 1.74223 4.59191I
a = 0.869509 + 0.530183I
b = 0.875674 + 0.480957I
0.18980 + 1.95729I 0
32
III. I
v
1
= ha, b 1, v 1i
(i) Arc colorings
a
3
=
1
0
a
10
=
1
0
a
4
=
1
0
a
7
=
0
1
a
8
=
1
1
a
2
=
1
1
a
11
=
0
1
a
5
=
1
1
a
1
=
2
1
a
9
=
1
1
a
12
=
1
0
a
6
=
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
u 1
c
2
, c
4
, c
6
c
7
, c
9
, c
10
c
11
, c
12
u + 1
c
3
, c
5
, c
8
u
34
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
6
, c
7
, c
9
c
10
, c
11
, c
12
y 1
c
3
, c
5
, c
8
y
35
(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
36
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u 1)(u
41
+ 3u
40
+ ··· + 5u 1)
· (u
173
19u
172
+ ··· + 21313u 34383)
c
2
(u + 1)(u
41
+ 2u
40
+ ··· 2u 1)(u
173
2u
172
+ ··· 128u 57)
c
3
u(u
41
+ 4u
40
+ ··· + 8u + 1)(u
173
3u
172
+ ··· + 74u 5)
c
4
(u + 1)(u
41
+ 2u
40
+ ··· + 3u + 1)
· (u
173
8u
172
+ ··· 475086499u 26150301)
c
5
u(u
41
6u
40
+ ··· + 11u 1)(u
173
5u
172
+ ··· 39097u + 5255)
c
6
(u + 1)(u
41
2u
40
+ ··· + 7u + 3)(u
173
2u
172
+ ··· 127187u 8237)
c
7
(u + 1)(u
41
2u
40
+ ··· 2u + 1)(u
173
2u
172
+ ··· 128u 57)
c
8
u(u
41
+ 6u
40
+ ··· + 11u + 1)(u
173
5u
172
+ ··· 39097u + 5255)
c
9
(u + 1)(u
41
+ 9u
40
+ ··· 245u + 43)
· (u
173
5u
172
+ ··· 11110439275u 2018788719)
c
10
(u + 1)(u
41
u
40
+ ··· + 8u + 3)(u
173
u
172
+ ··· 195900u 10457)
c
11
(u + 1)(u
41
2u
40
+ ··· + 3u 1)
· (u
173
8u
172
+ ··· 475086499u 26150301)
c
12
(u + 1)(u
41
+ 12u
40
+ ··· + 4u 1)
· (u
173
+ 8u
172
+ ··· + 109558u 21897)
37
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y 1)(y
41
23y
40
+ ··· 7y 1)
· (y
173
51y
172
+ ··· + 66157887691y 1182190689)
c
2
, c
7
(y 1)(y
41
24y
40
+ ··· + 36y 1)
· (y
173
84y
172
+ ··· + 141898y 3249)
c
3
y(y
41
+ 54y
40
+ ··· 8y 1)(y
173
+ 57y
172
+ ··· + 226y 25)
c
4
, c
11
(y 1)(y
41
+ 2y
40
+ ··· 7y 1)
· (y
173
98y
172
+ ··· + 14008959254796871y 683838242390601)
c
5
, c
8
y(y
41
+ 18y
40
+ ··· + 3y 1)
· (y
173
+ 93y
172
+ ··· 1610278131y 27615025)
c
6
(y 1)(y
41
18y
40
+ ··· + 103y 9)
· (y
173
10y
172
+ ··· + 2537115305y 67848169)
c
9
(y 1)(y
41
15y
40
+ ··· 22879y 1849)
· (y
173
55y
172
+ ··· 3.85 × 10
19
y 4.08 × 10
18
)
c
10
(y 1)(y
41
+ 29y
40
+ ··· + 10y 9)
· (y
173
+ 53y
172
+ ··· + 582535008y 109348849)
c
12
(y 1)(y
41
60y
40
+ ··· 90y 1)
· (y
173
40y
172
+ ··· 18126440756y 479478609)
38