12a
0891
(K12a
0891
)
A knot diagram
1
Linearized knot diagam
4 6 7 1 11 10 5 12 2 3 8 9
Solving Sequence
6,10 3,7
4 11 2 1 5 8 9 12
c
6
c
3
c
10
c
2
c
1
c
5
c
7
c
9
c
12
c
4
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h3.11585 × 10
1116
u
152
+ 1.63261 × 10
1116
u
151
+ ··· + 7.00851 × 10
1115
b − 6.18169 × 10
1116
,
3.79481 × 10
1116
u
152
+ 2.05132 × 10
1116
u
151
+ ··· + 7.00851 × 10
1115
a − 9.83526 × 10
1116
,
u
153
+ u
152
+ ··· − 3u − 1i
I
u
2
= h−2.36234 × 10
27
u
30
− 5.41386 × 10
27
u
29
+ ··· + 6.33336 × 10
27
b − 9.12988 × 10
27
,
2.80253 × 10
27
u
30
+ 5.27117 × 10
27
u
29
+ ··· + 6.33336 × 10
27
a + 1.02266 × 10
28
, u
31
+ 3u
30
+ ··· + u + 1i
I
u
3
= hb, −u
5
+ 2u
4
+ 4u
3
− 9u
2
+ 4a + 13u − 5, u
6
− 3u
5
+ 2u
4
− 3u
3
− 2u
2
− 2u − 1i
* 3 irreducible components of dim
C
= 0, with total 190 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
= h3.12 × 10
1116
u
152
+ 1.63 × 10
1116
u
151
+ · · · + 7.01 × 10
1115
b − 6.18 ×
10
1116
, 3.79 × 10
1116
u
152
+ 2.05 × 10
1116
u
151
+ · · · + 7.01 × 10
1115
a − 9.84 ×
10
1116
, u
153
+ u
152
+ · · · − 3u − 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
3
=
−5.41457u
152
− 2.92690u
151
+ ··· − 14.9314u + 14.0333
−4.44582u
152
− 2.32946u
151
+ ··· + 5.48619u + 8.82027
a
7
=
1
u
2
a
4
=
−2.16296u
152
− 1.21387u
151
+ ··· − 18.3691u + 7.70073
−3.81062u
152
− 1.86944u
151
+ ··· + 4.12205u + 7.28169
a
11
=
1.57210u
152
+ 1.32824u
151
+ ··· + 44.1822u − 6.53834
−1.94193u
152
− 0.485705u
151
+ ··· + 6.20185u + 1.74833
a
2
=
−0.968757u
152
− 0.597437u
151
+ ··· − 20.4176u + 5.21305
−4.44582u
152
− 2.32946u
151
+ ··· + 5.48619u + 8.82027
a
1
=
1.66932u
152
+ 0.497431u
151
+ ··· − 23.0859u + 2.01272
−2.13293u
152
− 1.01455u
151
+ ··· − 1.93762u + 4.02211
a
5
=
−3.61369u
152
− 1.21232u
151
+ ··· − 22.2380u + 11.3427
−3.40152u
152
− 1.28917u
151
+ ··· + 1.85705u + 5.98673
a
8
=
−5.90920u
152
− 3.75096u
151
+ ··· − 12.6563u + 14.0426
4.60273u
152
+ 1.50922u
151
+ ··· − 11.8883u − 5.78819
a
9
=
−0.342166u
152
+ 0.639353u
151
+ ··· + 48.2398u − 2.78180
3.85620u
152
+ 1.17459u
151
+ ··· − 8.25942u − 5.50487
a
12
=
2.29977u
152
+ 1.43257u
151
+ ··· + 9.44943u − 1.68228
5.25264u
152
+ 1.44816u
151
+ ··· − 12.5949u − 7.66935
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.951754u
152
− 2.70912u
151
+ ··· − 13.7606u + 0.254180
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
153
+ 6u
152
+ ··· − 839u − 307
c
2
u
153
− 8u
152
+ ··· − 1344u − 64
c
3
u
153
− u
152
+ ··· + 615240u − 163556
c
5
u
153
+ 42u
151
+ ··· − 56802438868u − 10797888812
c
6
u
153
+ u
152
+ ··· − 3u − 1
c
7
u
153
+ 5u
152
+ ··· − 2075740u − 194200
c
8
, c
11
, c
12
u
153
− 77u
151
+ ··· + 13u − 1
c
9
u
153
− 33u
151
+ ··· + 680974452u − 75062943
c
10
u
153
+ 4u
152
+ ··· + 17u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
153
+ 92y
152
+ ··· − 3754947y −94249
c
2
y
153
+ 44y
152
+ ··· + 1161216y −4096
c
3
y
153
− 21y
152
+ ··· + 1454894069632y −26750565136
c
5
y
153
+ 84y
152
+ ··· − 5.53 × 10
21
y −1.17 × 10
20
c
6
y
153
− 21y
152
+ ··· + 73y −1
c
7
y
153
− 47y
152
+ ··· + 2201363212400y −37713640000
c
8
, c
11
, c
12
y
153
− 154y
152
+ ··· + y −1
c
9
y
153
− 66y
152
+ ··· + 487511585631586602y −5634445411821249
c
10
y
153
+ 24y
152
+ ··· − 555y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.973353 + 0.148533I
a = −1.04719 + 1.41780I
b = −0.417717 + 0.750536I
−8.58768 − 7.55812I 0
u = 0.973353 − 0.148533I
a = −1.04719 − 1.41780I
b = −0.417717 − 0.750536I
−8.58768 + 7.55812I 0
u = 0.867373 + 0.453722I
a = 0.149660 − 0.797153I
b = 1.20531 − 1.58661I
−9.06733 − 5.39501I 0
u = 0.867373 − 0.453722I
a = 0.149660 + 0.797153I
b = 1.20531 + 1.58661I
−9.06733 + 5.39501I 0
u = −0.972730
a = 0.518545
b = −0.217110
−1.29206 0
u = 0.781124 + 0.577758I
a = 0.08294 − 1.58923I
b = 0.95531 − 1.16559I
1.27140 − 4.48962I 0
u = 0.781124 − 0.577758I
a = 0.08294 + 1.58923I
b = 0.95531 + 1.16559I
1.27140 + 4.48962I 0
u = −0.826284 + 0.494731I
a = 0.21183 + 1.66604I
b = 0.97788 + 1.47738I
−3.47461 + 5.28528I 0
u = −0.826284 − 0.494731I
a = 0.21183 − 1.66604I
b = 0.97788 − 1.47738I
−3.47461 − 5.28528I 0
u = 0.619722 + 0.736392I
a = 0.004500 − 0.337299I
b = 1.30690 − 0.66973I
−2.45600 − 5.85568I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.619722 − 0.736392I
a = 0.004500 + 0.337299I
b = 1.30690 + 0.66973I
−2.45600 + 5.85568I 0
u = −0.329800 + 0.898354I
a = 0.249134 − 1.285850I
b = −0.0813293 + 0.0031954I
2.99162 + 2.89965I 0
u = −0.329800 − 0.898354I
a = 0.249134 + 1.285850I
b = −0.0813293 − 0.0031954I
2.99162 − 2.89965I 0
u = 0.356418 + 0.985409I
a = 0.434742 + 1.241200I
b = −0.443127 − 0.087929I
−2.26925 − 3.85824I 0
u = 0.356418 − 0.985409I
a = 0.434742 − 1.241200I
b = −0.443127 + 0.087929I
−2.26925 + 3.85824I 0
u = 1.05005
a = −0.0880587
b = −1.15611
−6.56914 0
u = −0.393235 + 0.857642I
a = −1.06688 + 1.48421I
b = 0.901301 + 0.488346I
2.61679 + 6.43034I 0
u = −0.393235 − 0.857642I
a = −1.06688 − 1.48421I
b = 0.901301 − 0.488346I
2.61679 − 6.43034I 0
u = −0.895296 + 0.589714I
a = 0.310160 + 1.325900I
b = 1.19061 + 0.94394I
−2.74813 + 3.64489I 0
u = −0.895296 − 0.589714I
a = 0.310160 − 1.325900I
b = 1.19061 − 0.94394I
−2.74813 − 3.64489I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.795571 + 0.473574I
a = 1.59964 − 0.10837I
b = 0.066361 + 0.614898I
−9.04738 + 1.18227I 0
u = 0.795571 − 0.473574I
a = 1.59964 + 0.10837I
b = 0.066361 − 0.614898I
−9.04738 − 1.18227I 0
u = −0.812516 + 0.439182I
a = −0.245879 + 0.500905I
b = −0.893866 + 0.708689I
−2.09655 + 0.26711I 0
u = −0.812516 − 0.439182I
a = −0.245879 − 0.500905I
b = −0.893866 − 0.708689I
−2.09655 − 0.26711I 0
u = −0.421496 + 0.992141I
a = 0.068442 + 0.960075I
b = 0.23495 + 1.81386I
0.86232 + 2.51923I 0
u = −0.421496 − 0.992141I
a = 0.068442 − 0.960075I
b = 0.23495 − 1.81386I
0.86232 − 2.51923I 0
u = −0.061438 + 0.902325I
a = 0.075783 − 1.027940I
b = −0.44341 − 1.89241I
2.02051 + 4.84345I 0
u = −0.061438 − 0.902325I
a = 0.075783 + 1.027940I
b = −0.44341 + 1.89241I
2.02051 − 4.84345I 0
u = −0.833519 + 0.344884I
a = 0.143031 + 0.852046I
b = 0.97507 + 1.20612I
−1.60976 + 3.75013I 0
u = −0.833519 − 0.344884I
a = 0.143031 − 0.852046I
b = 0.97507 − 1.20612I
−1.60976 − 3.75013I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.201392 + 0.878936I
a = 0.25333 + 1.48149I
b = 0.156786 − 0.309665I
−1.19863 − 2.66458I 0
u = 0.201392 − 0.878936I
a = 0.25333 − 1.48149I
b = 0.156786 + 0.309665I
−1.19863 + 2.66458I 0
u = −0.527832 + 0.993727I
a = 0.082403 − 1.023070I
b = −0.468349 − 0.777321I
3.84410 + 4.00937I 0
u = −0.527832 − 0.993727I
a = 0.082403 + 1.023070I
b = −0.468349 + 0.777321I
3.84410 − 4.00937I 0
u = 0.497291 + 1.036640I
a = 0.088921 + 0.906155I
b = −0.791615 + 0.502372I
5.64479 + 0.25144I 0
u = 0.497291 − 1.036640I
a = 0.088921 − 0.906155I
b = −0.791615 − 0.502372I
5.64479 − 0.25144I 0
u = 0.405116 + 1.080960I
a = −1.01082 − 1.00751I
b = 1.188840 − 0.415562I
−3.17421 − 9.26039I 0
u = 0.405116 − 1.080960I
a = −1.01082 + 1.00751I
b = 1.188840 + 0.415562I
−3.17421 + 9.26039I 0
u = −0.781644 + 0.300193I
a = 1.77937 − 0.79388I
b = −0.060681 − 0.552079I
−1.49841 + 1.51843I 0
u = −0.781644 − 0.300193I
a = 1.77937 + 0.79388I
b = −0.060681 + 0.552079I
−1.49841 − 1.51843I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.554491 + 1.042730I
a = 0.239454 − 0.192604I
b = 0.335302 − 1.053270I
−0.18119 + 2.07511I 0
u = −0.554491 − 1.042730I
a = 0.239454 + 0.192604I
b = 0.335302 + 1.053270I
−0.18119 − 2.07511I 0
u = −0.773515 + 0.268831I
a = −0.80494 − 2.04805I
b = −0.341865 − 0.645055I
−2.80427 + 3.49940I 0
u = −0.773515 − 0.268831I
a = −0.80494 + 2.04805I
b = −0.341865 + 0.645055I
−2.80427 − 3.49940I 0
u = 1.100940 + 0.450679I
a = −0.293571 − 0.397214I
b = −1.07149 − 0.97058I
−7.11145 + 0.23787I 0
u = 1.100940 − 0.450679I
a = −0.293571 + 0.397214I
b = −1.07149 + 0.97058I
−7.11145 − 0.23787I 0
u = 0.318683 + 0.730046I
a = 0.055493 + 1.093020I
b = −1.07179 + 1.87224I
−5.05861 − 10.12750I 0
u = 0.318683 − 0.730046I
a = 0.055493 − 1.093020I
b = −1.07179 − 1.87224I
−5.05861 + 10.12750I 0
u = −0.504370 + 1.100750I
a = 0.055033 − 0.790183I
b = −0.930533 − 0.292260I
0.11426 − 3.67355I 0
u = −0.504370 − 1.100750I
a = 0.055033 + 0.790183I
b = −0.930533 + 0.292260I
0.11426 + 3.67355I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.683605 + 0.383090I
a = 0.835310 − 0.266566I
b = −0.083301 − 0.373260I
−1.220670 + 0.364289I 0
u = −0.683605 − 0.383090I
a = 0.835310 + 0.266566I
b = −0.083301 + 0.373260I
−1.220670 − 0.364289I 0
u = −0.186368 + 0.743142I
a = 0.0714649 − 0.0048705I
b = 1.17367 + 0.86749I
2.17358 + 2.56779I 0
u = −0.186368 − 0.743142I
a = 0.0714649 + 0.0048705I
b = 1.17367 − 0.86749I
2.17358 − 2.56779I 0
u = −0.702889 + 0.206928I
a = 0.43730 + 1.59440I
b = −0.08565 + 1.60880I
−6.00659 + 5.00728I 0
u = −0.702889 − 0.206928I
a = 0.43730 − 1.59440I
b = −0.08565 − 1.60880I
−6.00659 − 5.00728I 0
u = 1.157010 + 0.567669I
a = 0.348684 − 0.730841I
b = 0.820526 − 0.685310I
0.56887 − 2.07115I 0
u = 1.157010 − 0.567669I
a = 0.348684 + 0.730841I
b = 0.820526 + 0.685310I
0.56887 + 2.07115I 0
u = 0.631950 + 0.294444I
a = 2.70218 + 0.77459I
b = −0.157887 + 0.567601I
−0.58566 − 6.76292I 0
u = 0.631950 − 0.294444I
a = 2.70218 − 0.77459I
b = −0.157887 − 0.567601I
−0.58566 + 6.76292I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.626657 + 0.252019I
a = 0.33296 + 1.82587I
b = 1.020000 + 0.826234I
−3.12725 + 3.37507I 0
u = −0.626657 − 0.252019I
a = 0.33296 − 1.82587I
b = 1.020000 − 0.826234I
−3.12725 − 3.37507I 0
u = −0.571915 + 0.353443I
a = 3.04284 − 0.26347I
b = −0.224004 − 0.635965I
−6.93504 + 10.92390I 0
u = −0.571915 − 0.353443I
a = 3.04284 + 0.26347I
b = −0.224004 + 0.635965I
−6.93504 − 10.92390I 0
u = −1.065600 + 0.804520I
a = −0.032315 + 0.873196I
b = 0.94789 + 1.10004I
−1.78649 + 4.39191I 0
u = −1.065600 − 0.804520I
a = −0.032315 − 0.873196I
b = 0.94789 − 1.10004I
−1.78649 − 4.39191I 0
u = −0.647944 + 0.052897I
a = −2.15693 + 2.10454I
b = −0.026201 + 0.892423I
−10.90870 + 3.66614I −22.9081 + 0.I
u = −0.647944 − 0.052897I
a = −2.15693 − 2.10454I
b = −0.026201 − 0.892423I
−10.90870 − 3.66614I −22.9081 + 0.I
u = 0.576304 + 0.297865I
a = −0.74284 − 1.53036I
b = 0.924640 − 0.897404I
0.05784 − 3.70712I 0
u = 0.576304 − 0.297865I
a = −0.74284 + 1.53036I
b = 0.924640 + 0.897404I
0.05784 + 3.70712I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.618264 + 0.173096I
a = 0.135414 − 0.910542I
b = 1.70579 − 1.69790I
−7.29185 + 10.11150I −18.4720 − 11.8238I
u = −0.618264 − 0.173096I
a = 0.135414 + 0.910542I
b = 1.70579 + 1.69790I
−7.29185 − 10.11150I −18.4720 + 11.8238I
u = −1.36448
a = 0.660395
b = 0.785262
−2.86005 0
u = 0.614991 + 0.133702I
a = 0.818152 − 1.102080I
b = 0.633098 − 0.666609I
0.75866 − 1.62813I 0. + 3.46469I
u = 0.614991 − 0.133702I
a = 0.818152 + 1.102080I
b = 0.633098 + 0.666609I
0.75866 + 1.62813I 0. − 3.46469I
u = 0.358121 + 0.510471I
a = −0.61433 − 2.94445I
b = 0.383855 − 0.598168I
0.98655 − 3.25875I −6.00000 + 8.72783I
u = 0.358121 − 0.510471I
a = −0.61433 + 2.94445I
b = 0.383855 + 0.598168I
0.98655 + 3.25875I −6.00000 − 8.72783I
u = 1.067710 + 0.878468I
a = −0.007537 + 1.111750I
b = −0.555437 + 1.288330I
−9.31337 − 0.97833I 0
u = 1.067710 − 0.878468I
a = −0.007537 − 1.111750I
b = −0.555437 − 1.288330I
−9.31337 + 0.97833I 0
u = −0.561932 + 0.251908I
a = −1.26889 + 2.08348I
b = 0.818448 + 1.013020I
−5.29787 + 5.09826I −17.0685 − 4.6385I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.561932 − 0.251908I
a = −1.26889 − 2.08348I
b = 0.818448 − 1.013020I
−5.29787 − 5.09826I −17.0685 + 4.6385I
u = 0.591740 + 0.092087I
a = −1.74551 + 2.70376I
b = −0.093513 + 0.651902I
−3.81956 + 1.02043I −21.3279 + 0.I
u = 0.591740 − 0.092087I
a = −1.74551 − 2.70376I
b = −0.093513 − 0.651902I
−3.81956 − 1.02043I −21.3279 + 0.I
u = −0.589450 + 0.094016I
a = 0.083379 − 1.326010I
b = −1.39304 − 1.69778I
−10.65620 − 3.00835I −21.4885 + 0.I
u = −0.589450 − 0.094016I
a = 0.083379 + 1.326010I
b = −1.39304 + 1.69778I
−10.65620 + 3.00835I −21.4885 + 0.I
u = −1.092710 + 0.888260I
a = −0.007131 − 1.110860I
b = −0.727077 − 1.100620I
−3.44388 + 5.41506I 0
u = −1.092710 − 0.888260I
a = −0.007131 + 1.110860I
b = −0.727077 + 1.100620I
−3.44388 − 5.41506I 0
u = 1.19233 + 0.77344I
a = −0.228171 − 0.547479I
b = −0.232851 − 1.309320I
−8.26908 − 0.39568I 0
u = 1.19233 − 0.77344I
a = −0.228171 + 0.547479I
b = −0.232851 + 1.309320I
−8.26908 + 0.39568I 0
u = 0.476415 + 0.302223I
a = 0.045115 + 0.855413I
b = 1.79211 + 0.99841I
0.16950 − 6.61987I −9.2353 + 17.8026I
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.476415 − 0.302223I
a = 0.045115 − 0.855413I
b = 1.79211 − 0.99841I
0.16950 + 6.61987I −9.2353 − 17.8026I
u = −0.316116 + 0.461533I
a = −0.681920 − 0.916688I
b = 1.013040 + 0.132992I
1.73851 + 2.42009I 0. − 4.60534I
u = −0.316116 − 0.461533I
a = −0.681920 + 0.916688I
b = 1.013040 − 0.132992I
1.73851 − 2.42009I 0. + 4.60534I
u = −1.06891 + 0.97466I
a = −0.174523 + 0.372134I
b = −0.245761 + 0.682455I
−2.25355 + 0.65421I 0
u = −1.06891 − 0.97466I
a = −0.174523 − 0.372134I
b = −0.245761 − 0.682455I
−2.25355 − 0.65421I 0
u = 1.12825 + 0.90766I
a = −0.036226 + 1.071980I
b = −0.96360 + 1.15229I
−4.46458 − 9.83926I 0
u = 1.12825 − 0.90766I
a = −0.036226 − 1.071980I
b = −0.96360 − 1.15229I
−4.46458 + 9.83926I 0
u = −1.15321 + 0.88708I
a = −0.073268 − 1.097130I
b = −1.06186 − 1.27564I
−11.3463 + 12.7687I 0
u = −1.15321 − 0.88708I
a = −0.073268 + 1.097130I
b = −1.06186 + 1.27564I
−11.3463 − 12.7687I 0
u = 1.05683 + 1.00112I
a = −0.049387 − 0.910129I
b = 0.77650 − 1.48829I
−10.39940 − 5.61779I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.05683 − 1.00112I
a = −0.049387 + 0.910129I
b = 0.77650 + 1.48829I
−10.39940 + 5.61779I 0
u = 0.95068 + 1.10742I
a = 0.323524 + 1.009420I
b = −1.133040 + 0.823103I
−5.46544 − 7.07487I 0
u = 0.95068 − 1.10742I
a = 0.323524 − 1.009420I
b = −1.133040 − 0.823103I
−5.46544 + 7.07487I 0
u = 0.536184 + 0.052296I
a = −0.007625 − 1.229430I
b = −1.26962 − 1.20723I
−3.63573 − 1.60579I −22.7303 + 5.1459I
u = 0.536184 − 0.052296I
a = −0.007625 + 1.229430I
b = −1.26962 + 1.20723I
−3.63573 + 1.60579I −22.7303 − 5.1459I
u = 0.478861 + 0.215780I
a = 1.25793 − 1.91727I
b = −0.191534 − 1.031660I
0.37950 − 3.31559I −10.26010 + 5.38518I
u = 0.478861 − 0.215780I
a = 1.25793 + 1.91727I
b = −0.191534 + 1.031660I
0.37950 + 3.31559I −10.26010 − 5.38518I
u = 1.25844 + 0.86415I
a = −0.091391 − 0.703587I
b = 1.09013 − 1.47933I
−9.53310 − 5.23260I 0
u = 1.25844 − 0.86415I
a = −0.091391 + 0.703587I
b = 1.09013 + 1.47933I
−9.53310 + 5.23260I 0
u = 0.89120 + 1.24075I
a = −0.630088 − 0.355012I
b = 0.161487 − 0.678566I
−8.21739 − 6.33398I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.89120 − 1.24075I
a = −0.630088 + 0.355012I
b = 0.161487 + 0.678566I
−8.21739 + 6.33398I 0
u = −1.10869 + 1.09769I
a = −0.036521 + 0.965954I
b = 0.86176 + 1.26947I
−1.81927 + 9.63095I 0
u = −1.10869 − 1.09769I
a = −0.036521 − 0.965954I
b = 0.86176 − 1.26947I
−1.81927 − 9.63095I 0
u = −1.06175 + 1.15974I
a = 0.290403 − 0.840480I
b = −1.08709 − 1.01208I
−1.49054 + 7.19197I 0
u = −1.06175 − 1.15974I
a = 0.290403 + 0.840480I
b = −1.08709 + 1.01208I
−1.49054 − 7.19197I 0
u = 1.13779 + 1.09225I
a = −0.042477 − 0.992088I
b = 1.00425 − 1.23198I
−1.2912 − 15.5289I 0
u = 1.13779 − 1.09225I
a = −0.042477 + 0.992088I
b = 1.00425 + 1.23198I
−1.2912 + 15.5289I 0
u = −1.14942 + 1.08768I
a = −0.055049 + 1.009640I
b = 1.10393 + 1.26113I
−7.9772 + 19.9447I 0
u = −1.14942 − 1.08768I
a = −0.055049 − 1.009640I
b = 1.10393 − 1.26113I
−7.9772 − 19.9447I 0
u = 1.11113 + 1.14601I
a = 0.479886 + 0.280342I
b = −0.259706 + 0.850399I
−10.09360 − 2.21771I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.11113 − 1.14601I
a = 0.479886 − 0.280342I
b = −0.259706 − 0.850399I
−10.09360 + 2.21771I 0
u = 1.24925 + 1.04928I
a = 0.239713 + 0.375516I
b = −0.286619 + 1.375030I
−9.02603 − 3.61548I 0
u = 1.24925 − 1.04928I
a = 0.239713 − 0.375516I
b = −0.286619 − 1.375030I
−9.02603 + 3.61548I 0
u = 1.07701 + 1.23112I
a = 0.377474 + 0.763941I
b = −1.13228 + 1.15916I
−6.91946 − 7.80523I 0
u = 1.07701 − 1.23112I
a = 0.377474 − 0.763941I
b = −1.13228 − 1.15916I
−6.91946 + 7.80523I 0
u = −1.30125 + 1.00999I
a = −0.202491 − 0.697920I
b = −1.024790 − 0.646544I
−2.56372 + 11.41290I 0
u = −1.30125 − 1.00999I
a = −0.202491 + 0.697920I
b = −1.024790 + 0.646544I
−2.56372 − 11.41290I 0
u = 1.45511 + 0.80587I
a = 0.292213 − 0.411474I
b = 0.330378 − 0.065657I
−4.17694 + 0.30246I 0
u = 1.45511 − 0.80587I
a = 0.292213 + 0.411474I
b = 0.330378 + 0.065657I
−4.17694 − 0.30246I 0
u = −1.06587 + 1.30478I
a = −0.379495 + 0.362333I
b = 0.114193 + 0.535816I
−2.26278 + 2.34342I 0
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.06587 − 1.30478I
a = −0.379495 − 0.362333I
b = 0.114193 − 0.535816I
−2.26278 − 2.34342I 0
u = −0.289524 + 0.100770I
a = 2.96083 + 0.20418I
b = −1.001940 + 0.804715I
1.025480 − 0.968502I −2.36472 + 3.34628I
u = −0.289524 − 0.100770I
a = 2.96083 − 0.20418I
b = −1.001940 − 0.804715I
1.025480 + 0.968502I −2.36472 − 3.34628I
u = −1.36120 + 1.02781I
a = 0.379701 − 0.329178I
b = −0.035259 − 0.715957I
−2.09831 − 1.10294I 0
u = −1.36120 − 1.02781I
a = 0.379701 + 0.329178I
b = −0.035259 + 0.715957I
−2.09831 + 1.10294I 0
u = −0.80929 + 1.51889I
a = −0.405060 − 0.031931I
b = −0.266928 + 0.636597I
−9.69135 − 4.97953I 0
u = −0.80929 − 1.51889I
a = −0.405060 + 0.031931I
b = −0.266928 − 0.636597I
−9.69135 + 4.97953I 0
u = 1.34044 + 1.10344I
a = −0.122135 + 0.555960I
b = −0.807948 + 0.639284I
2.50722 − 7.96117I 0
u = 1.34044 − 1.10344I
a = −0.122135 − 0.555960I
b = −0.807948 − 0.639284I
2.50722 + 7.96117I 0
u = 0.187746 + 0.122088I
a = 4.43901 + 1.18428I
b = −1.356580 − 0.326759I
−5.10483 + 4.76476I −7.44455 − 4.46642I
18
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.187746 − 0.122088I
a = 4.43901 − 1.18428I
b = −1.356580 + 0.326759I
−5.10483 − 4.76476I −7.44455 + 4.46642I
u = −1.29587 + 1.27074I
a = 0.008655 − 0.407001I
b = −0.496314 − 0.725702I
0.24511 + 3.81066I 0
u = −1.29587 − 1.27074I
a = 0.008655 + 0.407001I
b = −0.496314 + 0.725702I
0.24511 − 3.81066I 0
u = 0.056866 + 0.150925I
a = −3.83042 + 6.90509I
b = 0.628596 − 0.105902I
−2.39803 − 0.01397I −2.00851 + 2.65727I
u = 0.056866 − 0.150925I
a = −3.83042 − 6.90509I
b = 0.628596 + 0.105902I
−2.39803 + 0.01397I −2.00851 − 2.65727I
u = −0.149088
a = 7.52486
b = 0.665030
−2.39363 −2.62210
u = 0.94658 + 1.59540I
a = −0.300283 − 0.083545I
b = −0.145120 − 0.478624I
−2.99299 + 1.96639I 0
u = 0.94658 − 1.59540I
a = −0.300283 + 0.083545I
b = −0.145120 + 0.478624I
−2.99299 − 1.96639I 0
u = 1.43162 + 1.20495I
a = 0.343652 + 0.233077I
b = 0.138295 + 0.734497I
−1.29300 + 6.73093I 0
u = 1.43162 − 1.20495I
a = 0.343652 − 0.233077I
b = 0.138295 − 0.734497I
−1.29300 − 6.73093I 0
19
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.37369 + 1.27851I
a = 0.376751 − 0.181168I
b = 0.260544 − 0.826280I
−7.82294 − 11.13260I 0
u = −1.37369 − 1.27851I
a = 0.376751 + 0.181168I
b = 0.260544 + 0.826280I
−7.82294 + 11.13260I 0
u = −2.48372
a = 0.154048
b = 0.248855
−2.71118 0
20
II.
I
u
2
= h−2.36×10
27
u
30
−5.41×10
27
u
29
+· · ·+6.33×10
27
b−9.13×10
27
, 2.80×
10
27
u
30
+5.27×10
27
u
29
+· · ·+6.33×10
27
a+1.02×10
28
, u
31
+3u
30
+· · ·+u+1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
3
=
−0.442503u
30
− 0.832287u
29
+ ··· + 0.854181u − 1.61472
0.373000u
30
+ 0.854816u
29
+ ··· − 0.819135u + 1.44155
a
7
=
1
u
2
a
4
=
−1.00947u
30
− 2.01249u
29
+ ··· + 1.62060u − 3.55149
0.264498u
30
+ 0.550822u
29
+ ··· − 0.772876u + 0.920843
a
11
=
−0.665272u
30
− 1.64435u
29
+ ··· − 0.422080u − 0.519358
0.262068u
30
+ 0.732446u
29
+ ··· + 0.700639u + 0.579730
a
2
=
−0.815504u
30
− 1.68710u
29
+ ··· + 1.67332u − 3.05627
0.373000u
30
+ 0.854816u
29
+ ··· − 0.819135u + 1.44155
a
1
=
0.635054u
30
+ 1.36529u
29
+ ··· − 1.34272u − 1.41463
−0.00560930u
30
− 0.192096u
29
+ ··· + 1.03985u + 1.19647
a
5
=
−0.147229u
30
− 0.752163u
29
+ ··· + 0.100229u + 1.63891
−0.183834u
30
− 0.354776u
29
+ ··· + 0.629452u − 1.61687
a
8
=
−0.948483u
30
− 1.68044u
29
+ ··· − 0.0391048u − 2.54698
0.183506u
30
− 0.178960u
29
+ ··· − 1.10173u + 0.791313
a
9
=
−1.73143u
30
− 4.64811u
29
+ ··· + 0.453351u − 2.58303
0.804088u
30
+ 2.27132u
29
+ ··· + 0.423930u + 1.48394
a
12
=
0.605226u
30
+ 2.13079u
29
+ ··· + 0.857480u − 0.859614
−0.184452u
30
− 0.894715u
29
+ ··· − 1.17730u + 0.569531
(ii) Obstruction class = 1
(iii) Cusp Shapes = 2.87355u
30
+ 5.85554u
29
+ ··· − 6.06330u − 2.88256
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
31
− 7u
30
+ ··· − 7u + 1
c
2
u
31
+ 3u
30
+ ··· + 615u + 161
c
3
u
31
+ 2u
30
+ ··· + 20u − 4
c
4
u
31
+ 7u
30
+ ··· − 7u − 1
c
5
u
31
+ 12u
29
+ ··· − 16u + 4
c
6
u
31
+ 3u
30
+ ··· + u + 1
c
7
u
31
+ 6u
30
+ ··· + 84u + 8
c
8
u
31
+ 7u
30
+ ··· − 9u − 1
c
9
u
31
− u
30
+ ··· + 20u − 1
c
10
u
31
− u
30
+ ··· + u − 1
c
11
, c
12
u
31
− 7u
30
+ ··· − 9u + 1
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
31
+ 29y
30
+ ··· − 13y −1
c
2
y
31
+ 23y
30
+ ··· − 51001y −25921
c
3
y
31
+ 16y
30
+ ··· + 144y −16
c
5
y
31
+ 24y
30
+ ··· − 288y −16
c
6
y
31
− 5y
30
+ ··· + 7y −1
c
7
y
31
− 14y
30
+ ··· + 1168y −64
c
8
, c
11
, c
12
y
31
− 33y
30
+ ··· + 41y −1
c
9
y
31
− 13y
30
+ ··· + 204y −1
c
10
y
31
+ 13y
30
+ ··· − 13y −1
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.435850 + 0.889653I
a = −0.122174 + 0.893643I
b = −0.25983 + 1.84756I
1.31548 − 2.73347I 2.62255 + 7.17529I
u = 0.435850 − 0.889653I
a = −0.122174 − 0.893643I
b = −0.25983 − 1.84756I
1.31548 + 2.73347I 2.62255 − 7.17529I
u = 0.717549 + 0.581853I
a = −0.03702 − 1.62500I
b = 0.84656 − 1.16725I
1.06721 − 4.54532I −17.8905 + 15.7633I
u = 0.717549 − 0.581853I
a = −0.03702 + 1.62500I
b = 0.84656 + 1.16725I
1.06721 + 4.54532I −17.8905 − 15.7633I
u = −0.775605 + 0.493053I
a = 0.27102 + 1.89032I
b = 0.97150 + 1.08876I
−2.96200 + 4.47410I −6.22995 − 7.87974I
u = −0.775605 − 0.493053I
a = 0.27102 − 1.89032I
b = 0.97150 − 1.08876I
−2.96200 − 4.47410I −6.22995 + 7.87974I
u = −0.046189 + 0.898752I
a = −0.630400 + 0.203952I
b = −0.406193 − 0.425088I
−2.62871 − 1.35120I −12.31193 + 1.21875I
u = −0.046189 − 0.898752I
a = −0.630400 − 0.203952I
b = −0.406193 + 0.425088I
−2.62871 + 1.35120I −12.31193 − 1.21875I
u = 0.873346 + 0.207088I
a = −0.376535 − 1.035570I
b = 0.555658 − 0.526320I
−0.30275 − 1.96468I −7.79171 + 3.88920I
u = 0.873346 − 0.207088I
a = −0.376535 + 1.035570I
b = 0.555658 + 0.526320I
−0.30275 + 1.96468I −7.79171 − 3.88920I
24
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.280256 + 0.843804I
a = −0.172257 − 1.089940I
b = 0.54886 − 1.60421I
2.10850 − 3.89705I −2.69296 + 4.84858I
u = 0.280256 − 0.843804I
a = −0.172257 + 1.089940I
b = 0.54886 + 1.60421I
2.10850 + 3.89705I −2.69296 − 4.84858I
u = −0.624294 + 0.520327I
a = −0.60319 + 1.66211I
b = 0.83238 + 1.27903I
−4.59216 + 5.54035I −9.32097 − 9.86500I
u = −0.624294 − 0.520327I
a = −0.60319 − 1.66211I
b = 0.83238 − 1.27903I
−4.59216 − 5.54035I −9.32097 + 9.86500I
u = −0.235809 + 0.703779I
a = −1.014930 − 0.196430I
b = −0.200096 + 1.060140I
−9.64770 + 3.50955I −12.88121 − 2.67575I
u = −0.235809 − 0.703779I
a = −1.014930 + 0.196430I
b = −0.200096 − 1.060140I
−9.64770 − 3.50955I −12.88121 + 2.67575I
u = 1.156780 + 0.759666I
a = −0.180295 − 0.494447I
b = −0.108064 − 0.740346I
−2.14392 − 1.28172I −11.74862 + 4.27913I
u = 1.156780 − 0.759666I
a = −0.180295 + 0.494447I
b = −0.108064 + 0.740346I
−2.14392 + 1.28172I −11.74862 − 4.27913I
u = −0.539178 + 0.083354I
a = −0.511789 − 1.183050I
b = 0.927039 + 0.447466I
0.28797 − 5.93567I −6.16337 + 5.12675I
u = −0.539178 − 0.083354I
a = −0.511789 + 1.183050I
b = 0.927039 − 0.447466I
0.28797 + 5.93567I −6.16337 − 5.12675I
25
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.21600 + 0.82992I
a = −0.335850 + 0.468428I
b = 0.227613 + 1.232470I
−9.28423 + 3.03654I −14.3326 + 1.1980I
u = −1.21600 − 0.82992I
a = −0.335850 − 0.468428I
b = 0.227613 − 1.232470I
−9.28423 − 3.03654I −14.3326 − 1.1980I
u = 0.454238 + 0.253472I
a = −0.68706 + 1.27199I
b = 0.466669 − 1.082130I
−6.52285 + 9.77818I −8.78752 − 5.56489I
u = 0.454238 − 0.253472I
a = −0.68706 − 1.27199I
b = 0.466669 + 1.082130I
−6.52285 − 9.77818I −8.78752 + 5.56489I
u = −0.97971 + 1.11771I
a = 0.356501 − 0.939296I
b = −1.102100 − 0.750132I
−5.14619 + 8.57314I −9.16347 − 9.22741I
u = −0.97971 − 1.11771I
a = 0.356501 + 0.939296I
b = −1.102100 + 0.750132I
−5.14619 − 8.57314I −9.16347 + 9.22741I
u = −1.20054 + 0.97745I
a = 0.091162 − 0.704143I
b = −1.02028 − 1.53716I
−9.06090 + 5.57309I −5.52526 − 8.61845I
u = −1.20054 − 0.97745I
a = 0.091162 + 0.704143I
b = −1.02028 + 1.53716I
−9.06090 − 5.57309I −5.52526 + 8.61845I
u = 1.07667 + 1.12485I
a = 0.225814 + 0.863721I
b = −0.98634 + 1.03639I
−1.44404 − 6.76467I −6.69848 − 0.75343I
u = 1.07667 − 1.12485I
a = 0.225814 − 0.863721I
b = −0.98634 − 1.03639I
−1.44404 + 6.76467I −6.69848 + 0.75343I
26
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.75473
a = 0.453988
b = 0.413212
−4.07334 8.83190
27
III.
I
u
3
= hb, −u
5
+2u
4
+4u
3
−9u
2
+4a+13u−5, u
6
−3u
5
+2u
4
−3u
3
−2u
2
−2u−1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
3
=
1
4
u
5
−
1
2
u
4
+ ··· −
13
4
u +
5
4
0
a
7
=
1
u
2
a
4
=
−
1
2
u
5
+ 2u
4
+ ··· −
5
2
u +
3
2
1
4
u
5
−
1
2
u
4
+ ··· −
1
4
u +
1
4
a
11
=
3u
5
−
21
2
u
4
+ ··· − 3u −
5
2
u
a
2
=
1
4
u
5
−
1
2
u
4
+ ··· −
13
4
u +
5
4
0
a
1
=
5
4
u
5
−
9
2
u
4
+ ··· −
9
4
u +
5
4
−
1
2
u
5
+
3
2
u
4
−
1
2
u
3
+
1
2
u
a
5
=
−
3
2
u
5
+
9
2
u
4
+ ··· +
7
2
u + 4
u
2
a
8
=
−
5
4
u
5
+
9
2
u
4
+ ··· +
9
4
u −
5
4
1
2
u
5
−
3
2
u
4
+
1
2
u
3
−
1
2
u
a
9
=
3u
5
−
21
2
u
4
+ ··· − 3u −
5
2
u
a
12
=
17
4
u
5
− 15u
4
+ ··· −
21
4
u −
5
4
−
1
2
u
5
+
3
2
u
4
−
1
2
u
3
+
3
2
u
(ii) Obstruction class = 1
(iii) Cusp Shapes =
21
4
u
5
− 21u
4
+
45
2
u
3
−
113
4
u
2
+
11
4
u −
53
4
28
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
3
− u
2
+ 2u − 1)
2
c
2
u
6
c
3
(u
3
+ u
2
− 1)
2
c
4
, c
7
(u
3
+ u
2
+ 2u + 1)
2
c
5
, c
6
u
6
− 3u
5
+ 2u
4
− 3u
3
− 2u
2
− 2u − 1
c
8
(u − 1)
6
c
9
, c
10
u
6
− 3u
4
− 2u
3
+ 6u
2
− 2u − 1
c
11
, c
12
(u + 1)
6
29
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
7
(y
3
+ 3y
2
+ 2y −1)
2
c
2
y
6
c
3
(y
3
− y
2
+ 2y −1)
2
c
5
, c
6
y
6
− 5y
5
− 18y
4
− 31y
3
− 12y
2
+ 1
c
8
, c
11
, c
12
(y −1)
6
c
9
, c
10
y
6
− 6y
5
+ 21y
4
− 42y
3
+ 34y
2
− 16y + 1
30
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.527087 + 1.198340I
a = 0.025633 + 0.671082I
b = 0
1.37919 − 2.82812I −3.82976 + 3.11418I
u = 0.527087 − 1.198340I
a = 0.025633 − 0.671082I
b = 0
1.37919 + 2.82812I −3.82976 − 3.11418I
u = −0.189446 + 0.636059I
a = 0.74217 − 2.50548I
b = 0
1.37919 + 2.82812I −0.640805 + 0.659759I
u = −0.189446 − 0.636059I
a = 0.74217 + 2.50548I
b = 0
1.37919 − 2.82812I −0.640805 − 0.659759I
u = −0.473427
a = 3.36799
b = 0
−2.75839 −24.4510
u = 2.79815
a = 0.0964131
b = 0
−2.75839 −120.610
31
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
3
− u
2
+ 2u − 1)
2
)(u
31
− 7u
30
+ ··· − 7u + 1)
· (u
153
+ 6u
152
+ ··· − 839u − 307)
c
2
u
6
(u
31
+ 3u
30
+ ··· + 615u + 161)(u
153
− 8u
152
+ ··· − 1344u − 64)
c
3
((u
3
+ u
2
− 1)
2
)(u
31
+ 2u
30
+ ··· + 20u − 4)
· (u
153
− u
152
+ ··· + 615240u − 163556)
c
4
((u
3
+ u
2
+ 2u + 1)
2
)(u
31
+ 7u
30
+ ··· − 7u − 1)
· (u
153
+ 6u
152
+ ··· − 839u − 307)
c
5
(u
6
− 3u
5
+ ··· − 2u − 1)(u
31
+ 12u
29
+ ··· − 16u + 4)
· (u
153
+ 42u
151
+ ··· − 56802438868u − 10797888812)
c
6
(u
6
− 3u
5
+ ··· − 2u − 1)(u
31
+ 3u
30
+ ··· + u + 1)
· (u
153
+ u
152
+ ··· − 3u − 1)
c
7
((u
3
+ u
2
+ 2u + 1)
2
)(u
31
+ 6u
30
+ ··· + 84u + 8)
· (u
153
+ 5u
152
+ ··· − 2075740u − 194200)
c
8
((u − 1)
6
)(u
31
+ 7u
30
+ ··· − 9u − 1)(u
153
− 77u
151
+ ··· + 13u − 1)
c
9
(u
6
− 3u
4
− 2u
3
+ 6u
2
− 2u − 1)(u
31
− u
30
+ ··· + 20u − 1)
· (u
153
− 33u
151
+ ··· + 680974452u − 75062943)
c
10
(u
6
− 3u
4
− 2u
3
+ 6u
2
− 2u − 1)(u
31
− u
30
+ ··· + u − 1)
· (u
153
+ 4u
152
+ ··· + 17u + 1)
c
11
, c
12
((u + 1)
6
)(u
31
− 7u
30
+ ··· − 9u + 1)(u
153
− 77u
151
+ ··· + 13u − 1)
32
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y
3
+ 3y
2
+ 2y −1)
2
)(y
31
+ 29y
30
+ ··· − 13y −1)
· (y
153
+ 92y
152
+ ··· − 3754947y −94249)
c
2
y
6
(y
31
+ 23y
30
+ ··· − 51001y −25921)
· (y
153
+ 44y
152
+ ··· + 1161216y −4096)
c
3
((y
3
− y
2
+ 2y −1)
2
)(y
31
+ 16y
30
+ ··· + 144y −16)
· (y
153
− 21y
152
+ ··· + 1454894069632y −26750565136)
c
5
(y
6
− 5y
5
− 18y
4
− 31y
3
− 12y
2
+ 1)(y
31
+ 24y
30
+ ··· − 288y −16)
· (y
153
+ 84y
152
+ ··· − 5.53 × 10
21
y −1.17 × 10
20
)
c
6
(y
6
− 5y
5
− 18y
4
− 31y
3
− 12y
2
+ 1)(y
31
− 5y
30
+ ··· + 7y −1)
· (y
153
− 21y
152
+ ··· + 73y −1)
c
7
((y
3
+ 3y
2
+ 2y −1)
2
)(y
31
− 14y
30
+ ··· + 1168y −64)
· (y
153
− 47y
152
+ ··· + 2201363212400y −37713640000)
c
8
, c
11
, c
12
((y −1)
6
)(y
31
− 33y
30
+ ··· + 41y −1)(y
153
− 154y
152
+ ··· + y −1)
c
9
(y
6
− 6y
5
+ 21y
4
− 42y
3
+ 34y
2
− 16y + 1)
· (y
31
− 13y
30
+ ··· + 204y −1)
· (y
153
− 66y
152
+ ··· + 487511585631586602y −5634445411821249)
c
10
(y
6
− 6y
5
+ ··· − 16y + 1)(y
31
+ 13y
30
+ ··· − 13y −1)
· (y
153
+ 24y
152
+ ··· − 555y −1)
33
