12a
1143
(K12a
1143
)
A knot diagram
1
Linearized knot diagam
4 8 9 11 10 12 3 2 6 1 7 5
Solving Sequence
5,10 1,6
11 4 2 9 3 8 12 7
c
5
c
10
c
4
c
1
c
9
c
3
c
8
c
12
c
6
c
2
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.26077 × 10
467
u
123
+ 4.32011 × 10
467
u
122
+ ··· + 2.45681 × 10
468
b + 2.19615 × 10
470
,
9.69556 × 10
471
u
123
− 1.56547 × 10
472
u
122
+ ··· + 3.26731 × 10
472
a + 4.84843 × 10
474
,
u
124
− 2u
123
+ ··· − 5614u + 1364i
I
u
2
= h−u
21
− u
20
+ ··· + b − 2u, −10u
21
− 10u
20
+ ··· + a + 1, u
22
+ u
21
+ ··· + 11u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 146 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−1.26 × 10
467
u
123
+ 4.32 × 10
467
u
122
+ · · · + 2.46 × 10
468
b + 2.20 ×
10
470
, 9.70 × 10
471
u
123
− 1.57 × 10
472
u
122
+ · · · + 3.27 × 10
472
a + 4.85 ×
10
474
, u
124
− 2u
123
+ · · · − 5614u + 1364i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
1
=
−0.296744u
123
+ 0.479132u
122
+ ··· + 78.4664u − 148.392
0.0513172u
123
− 0.175842u
122
+ ··· + 506.859u − 89.3903
a
6
=
1
u
2
a
11
=
0.263856u
123
− 0.445950u
122
+ ··· + 418.848u − 27.0755
0.107261u
123
− 0.307184u
122
+ ··· + 677.350u − 134.544
a
4
=
0.0329429u
123
+ 0.00314808u
122
+ ··· + 13.4976u − 5.87222
−0.112479u
123
+ 0.430289u
122
+ ··· − 1616.41u + 354.133
a
2
=
0.226699u
123
− 0.407802u
122
+ ··· + 447.589u − 58.3829
0.0544174u
123
− 0.110292u
122
+ ··· + 117.960u − 7.49864
a
9
=
u
u
3
+ u
a
3
=
0.165608u
123
− 0.460201u
122
+ ··· + 1639.89u − 362.844
−0.122116u
123
+ 0.393698u
122
+ ··· − 1282.66u + 267.260
a
8
=
−0.0804638u
123
− 0.0954324u
122
+ ··· + 889.846u − 304.518
0.112857u
123
− 0.223252u
122
+ ··· + 280.121u − 14.1022
a
12
=
−0.348061u
123
+ 0.654974u
122
+ ··· − 428.392u − 59.0017
0.0513172u
123
− 0.175842u
122
+ ··· + 506.859u − 89.3903
a
7
=
0.164071u
123
− 0.393500u
122
+ ··· + 615.316u − 105.535
−0.0882862u
123
+ 0.0113354u
122
+ ··· + 806.973u − 229.648
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.298290u
123
+ 0.622766u
122
+ ··· − 296.136u − 18.3046
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
124
− 25u
123
+ ··· − 112353915u + 5993827
c
2
, c
7
, c
8
u
124
− u
123
+ ··· − 25u + 7
c
3
u
124
+ u
123
+ ··· − 130387u + 20503
c
4
u
124
− 3u
122
+ ··· + 161u + 13
c
5
, c
9
u
124
+ 2u
123
+ ··· + 5614u + 1364
c
6
, c
11
u
124
+ u
123
+ ··· + 23u
2
+ 1
c
10
u
124
+ 15u
123
+ ··· + 55987u + 6721
c
12
u
124
− 7u
123
+ ··· + 4u + 5
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
124
+ 63y
123
+ ··· + 431798753106101y + 35925962105929
c
2
, c
7
, c
8
y
124
+ 115y
123
+ ··· − 611y + 49
c
3
y
124
+ 21y
123
+ ··· + 4053965961y + 420373009
c
4
y
124
− 6y
123
+ ··· − 1091y + 169
c
5
, c
9
y
124
+ 84y
123
+ ··· + 69263508y + 1860496
c
6
, c
11
y
124
+ 75y
123
+ ··· + 46y + 1
c
10
y
124
− 39y
123
+ ··· + 13491579y + 45171841
c
12
y
124
− 9y
123
+ ··· + 764y + 25
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.429038 + 0.902009I
a = 1.68525 − 0.38916I
b = −0.311918 − 0.444710I
−1.32425 + 6.17844I 0
u = −0.429038 − 0.902009I
a = 1.68525 + 0.38916I
b = −0.311918 + 0.444710I
−1.32425 − 6.17844I 0
u = 0.462532 + 0.888982I
a = −1.76445 − 0.60323I
b = 0.303288 − 0.490179I
4.02276 − 9.56251I 0
u = 0.462532 − 0.888982I
a = −1.76445 + 0.60323I
b = 0.303288 + 0.490179I
4.02276 + 9.56251I 0
u = −0.700036 + 0.709979I
a = 0.229510 + 0.746472I
b = 0.124354 + 0.576117I
3.94855 + 2.83097I 0
u = −0.700036 − 0.709979I
a = 0.229510 − 0.746472I
b = 0.124354 − 0.576117I
3.94855 − 2.83097I 0
u = 0.981319 + 0.236471I
a = −0.783751 − 0.565134I
b = −0.617900 − 0.966488I
−2.59935 + 5.08228I 0
u = 0.981319 − 0.236471I
a = −0.783751 + 0.565134I
b = −0.617900 + 0.966488I
−2.59935 − 5.08228I 0
u = 0.086681 + 0.973158I
a = −0.00243 + 1.90093I
b = 0.030909 + 1.238560I
2.62831 − 4.26746I 0
u = 0.086681 − 0.973158I
a = −0.00243 − 1.90093I
b = 0.030909 − 1.238560I
2.62831 + 4.26746I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.095969 + 1.021210I
a = 0.220373 − 0.630602I
b = −1.72011 − 1.08206I
2.69663 − 0.68082I 0
u = 0.095969 − 1.021210I
a = 0.220373 + 0.630602I
b = −1.72011 + 1.08206I
2.69663 + 0.68082I 0
u = 0.370950 + 0.971281I
a = −1.241830 − 0.070439I
b = 0.371399 − 0.335424I
0.09413 − 2.84309I 0
u = 0.370950 − 0.971281I
a = −1.241830 + 0.070439I
b = 0.371399 + 0.335424I
0.09413 + 2.84309I 0
u = 0.313151 + 0.906275I
a = −1.54848 + 0.35133I
b = 0.262555 − 0.312852I
0.11097 − 3.14486I 0
u = 0.313151 − 0.906275I
a = −1.54848 − 0.35133I
b = 0.262555 + 0.312852I
0.11097 + 3.14486I 0
u = −0.164015 + 1.040220I
a = −0.054409 − 0.616648I
b = 1.58232 − 1.32724I
1.24453 + 5.17092I 0
u = −0.164015 − 1.040220I
a = −0.054409 + 0.616648I
b = 1.58232 + 1.32724I
1.24453 − 5.17092I 0
u = −0.212093 + 0.914220I
a = 1.20372 + 0.90772I
b = −0.201605 − 0.220439I
−2.33446 + 0.04536I 0
u = −0.212093 − 0.914220I
a = 1.20372 − 0.90772I
b = −0.201605 + 0.220439I
−2.33446 − 0.04536I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.804822 + 0.421468I
a = −0.378791 − 1.325140I
b = −0.884556 − 0.459821I
5.66189 + 7.24435I 0
u = −0.804822 − 0.421468I
a = −0.378791 + 1.325140I
b = −0.884556 + 0.459821I
5.66189 − 7.24435I 0
u = 0.198160 + 1.075310I
a = −0.017029 − 0.668357I
b = −1.45606 − 1.33338I
6.92773 − 9.08534I 0
u = 0.198160 − 1.075310I
a = −0.017029 + 0.668357I
b = −1.45606 + 1.33338I
6.92773 + 9.08534I 0
u = 0.148724 + 0.891560I
a = −1.00500 + 1.31466I
b = 0.137345 − 0.196084I
2.53652 + 3.22819I 0
u = 0.148724 − 0.891560I
a = −1.00500 − 1.31466I
b = 0.137345 + 0.196084I
2.53652 − 3.22819I 0
u = −0.086394 + 0.891345I
a = 0.01279 + 1.90669I
b = −0.028215 + 1.210280I
−2.79053 + 1.40664I 0
u = −0.086394 − 0.891345I
a = 0.01279 − 1.90669I
b = −0.028215 − 1.210280I
−2.79053 − 1.40664I 0
u = 0.022631 + 0.891353I
a = 0.678765 − 0.708120I
b = −1.63314 − 0.40873I
2.07163 + 0.00309I 0
u = 0.022631 − 0.891353I
a = 0.678765 + 0.708120I
b = −1.63314 + 0.40873I
2.07163 − 0.00309I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.585165 + 0.655216I
a = −0.02505 + 1.56182I
b = 0.197316 + 1.012240I
3.36567 + 5.34298I 0
u = 0.585165 − 0.655216I
a = −0.02505 − 1.56182I
b = 0.197316 − 1.012240I
3.36567 − 5.34298I 0
u = −0.500010 + 1.005970I
a = 1.076970 − 0.838445I
b = −0.498140 − 0.541028I
5.50091 + 1.31479I 0
u = −0.500010 − 1.005970I
a = 1.076970 + 0.838445I
b = −0.498140 + 0.541028I
5.50091 − 1.31479I 0
u = −0.027819 + 1.125170I
a = −0.189806 − 0.869996I
b = 1.39218 − 1.00783I
9.87166 − 0.88998I 0
u = −0.027819 − 1.125170I
a = −0.189806 + 0.869996I
b = 1.39218 + 1.00783I
9.87166 + 0.88998I 0
u = 0.484087 + 1.046120I
a = −0.532918 − 0.890610I
b = 0.761211 − 0.508120I
0.82050 − 3.27711I 0
u = 0.484087 − 1.046120I
a = −0.532918 + 0.890610I
b = 0.761211 + 0.508120I
0.82050 + 3.27711I 0
u = −0.805587 + 0.255045I
a = 0.835929 − 0.540608I
b = 0.560971 − 1.075010I
−6.01541 − 1.74622I 0
u = −0.805587 − 0.255045I
a = 0.835929 + 0.540608I
b = 0.560971 + 1.075010I
−6.01541 + 1.74622I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.272926 + 0.770151I
a = −0.07991 + 1.85151I
b = 0.077707 + 1.153040I
−0.494017 + 0.400897I 0
u = 0.272926 − 0.770151I
a = −0.07991 − 1.85151I
b = 0.077707 − 1.153040I
−0.494017 − 0.400897I 0
u = 0.875095 + 0.798824I
a = 0.258542 − 1.033790I
b = 0.992694 − 0.413905I
6.18916 + 1.08773I 0
u = 0.875095 − 0.798824I
a = 0.258542 + 1.033790I
b = 0.992694 + 0.413905I
6.18916 − 1.08773I 0
u = 1.184150 + 0.060077I
a = −0.724908 − 0.563543I
b = −0.598421 − 0.796681I
−1.57972 + 4.09540I 0
u = 1.184150 − 0.060077I
a = −0.724908 + 0.563543I
b = −0.598421 + 0.796681I
−1.57972 − 4.09540I 0
u = −0.781131 + 0.900945I
a = −0.140088 − 0.946832I
b = −0.977580 − 0.378701I
0.91229 + 1.62358I 0
u = −0.781131 − 0.900945I
a = −0.140088 + 0.946832I
b = −0.977580 + 0.378701I
0.91229 − 1.62358I 0
u = −0.514731 + 0.616656I
a = 0.13083 + 1.57981I
b = −0.132112 + 1.014200I
−2.11748 − 2.25181I 0
u = −0.514731 − 0.616656I
a = 0.13083 − 1.57981I
b = −0.132112 − 1.014200I
−2.11748 + 2.25181I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.443758 + 1.113810I
a = 0.535403 − 1.156400I
b = −0.809563 − 0.717437I
4.63131 + 5.69550I 0
u = −0.443758 − 1.113810I
a = 0.535403 + 1.156400I
b = −0.809563 + 0.717437I
4.63131 − 5.69550I 0
u = −0.650787 + 0.458753I
a = −0.116154 + 1.229630I
b = −0.265439 + 0.755719I
3.97357 + 3.16961I 0
u = −0.650787 − 0.458753I
a = −0.116154 − 1.229630I
b = −0.265439 − 0.755719I
3.97357 − 3.16961I 0
u = 0.375770 + 1.178470I
a = 0.401548 + 0.683189I
b = −1.40008 + 1.27787I
0.72861 − 2.29224I 0
u = 0.375770 − 1.178470I
a = 0.401548 − 0.683189I
b = −1.40008 − 1.27787I
0.72861 + 2.29224I 0
u = 0.660459 + 0.349683I
a = 0.40515 − 1.46038I
b = 0.838795 − 0.404745I
0.27121 − 4.07907I 0
u = 0.660459 − 0.349683I
a = 0.40515 + 1.46038I
b = 0.838795 + 0.404745I
0.27121 + 4.07907I 0
u = −1.263940 + 0.063468I
a = 0.681095 + 0.548580I
b = 0.566060 + 0.715758I
4.84240 + 1.94421I 0
u = −1.263940 − 0.063468I
a = 0.681095 − 0.548580I
b = 0.566060 − 0.715758I
4.84240 − 1.94421I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.259080 + 0.136328I
a = 0.738363 − 0.540497I
b = 0.662306 − 0.785058I
−2.53324 − 8.07258I 0
u = −1.259080 − 0.136328I
a = 0.738363 + 0.540497I
b = 0.662306 + 0.785058I
−2.53324 + 8.07258I 0
u = −0.320939 + 1.233930I
a = 0.350226 − 1.229280I
b = −0.957171 − 0.893803I
5.42700 + 3.81877I 0
u = −0.320939 − 1.233930I
a = 0.350226 + 1.229280I
b = −0.957171 + 0.893803I
5.42700 − 3.81877I 0
u = 0.556229 + 0.441771I
a = −0.414046 + 1.292080I
b = −0.021503 + 0.905843I
−1.44502 − 0.93498I 0. + 4.22793I
u = 0.556229 − 0.441771I
a = −0.414046 − 1.292080I
b = −0.021503 − 0.905843I
−1.44502 + 0.93498I 0. − 4.22793I
u = −0.460116 + 1.205690I
a = −0.389158 + 0.823343I
b = 1.31109 + 1.18753I
−3.01169 + 6.43216I 0
u = −0.460116 − 1.205690I
a = −0.389158 − 0.823343I
b = 1.31109 − 1.18753I
−3.01169 − 6.43216I 0
u = 0.622901 + 0.331989I
a = −0.877964 − 0.412394I
b = −0.530054 − 1.225180I
−1.98271 − 1.58289I −6.10488 + 2.48235I
u = 0.622901 − 0.331989I
a = −0.877964 + 0.412394I
b = −0.530054 + 1.225180I
−1.98271 + 1.58289I −6.10488 − 2.48235I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.007556 + 0.697885I
a = −1.18651 − 1.10695I
b = 1.297920 − 0.129233I
−0.07084 − 3.87346I −2.00000 + 3.83412I
u = 0.007556 − 0.697885I
a = −1.18651 + 1.10695I
b = 1.297920 + 0.129233I
−0.07084 + 3.87346I −2.00000 − 3.83412I
u = 0.277441 + 1.276370I
a = −0.290324 − 1.231730I
b = 0.993460 − 0.946714I
11.76340 − 1.43261I 0
u = 0.277441 − 1.276370I
a = −0.290324 + 1.231730I
b = 0.993460 + 0.946714I
11.76340 + 1.43261I 0
u = 0.368108 + 1.260320I
a = −0.370276 − 1.281850I
b = 0.902550 − 0.916519I
4.70148 − 7.74112I 0
u = 0.368108 − 1.260320I
a = −0.370276 + 1.281850I
b = 0.902550 + 0.916519I
4.70148 + 7.74112I 0
u = 1.317750 + 0.145363I
a = −0.739652 − 0.526848I
b = −0.686263 − 0.758316I
3.16742 + 11.59570I 0
u = 1.317750 − 0.145363I
a = −0.739652 + 0.526848I
b = −0.686263 + 0.758316I
3.16742 − 11.59570I 0
u = −0.376776 + 1.291150I
a = 0.354574 − 1.313210I
b = −0.891912 − 0.948404I
10.4608 + 11.1461I 0
u = −0.376776 − 1.291150I
a = 0.354574 + 1.313210I
b = −0.891912 + 0.948404I
10.4608 − 11.1461I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.524787 + 1.243110I
a = 0.342414 + 0.924406I
b = −1.25693 + 1.15170I
0.61612 − 10.46510I 0
u = 0.524787 − 1.243110I
a = 0.342414 − 0.924406I
b = −1.25693 − 1.15170I
0.61612 + 10.46510I 0
u = −0.384048 + 1.299600I
a = 0.143405 − 0.019199I
b = −0.704801 − 0.004449I
5.01205 + 2.43417I 0
u = −0.384048 − 1.299600I
a = 0.143405 + 0.019199I
b = −0.704801 + 0.004449I
5.01205 − 2.43417I 0
u = 0.078120 + 1.358980I
a = 0.036327 + 0.505445I
b = −0.41338 + 1.66529I
4.22892 − 2.38024I 0
u = 0.078120 − 1.358980I
a = 0.036327 − 0.505445I
b = −0.41338 − 1.66529I
4.22892 + 2.38024I 0
u = −0.619910 + 0.031832I
a = −0.600655 + 1.206700I
b = −0.582431 + 0.448450I
1.68669 − 1.74339I −1.63098 + 4.10289I
u = −0.619910 − 0.031832I
a = −0.600655 − 1.206700I
b = −0.582431 − 0.448450I
1.68669 + 1.74339I −1.63098 − 4.10289I
u = 0.841258 + 1.098000I
a = 0.218330 − 0.717943I
b = 1.014160 − 0.304108I
3.50862 − 3.52331I 0
u = 0.841258 − 1.098000I
a = 0.218330 + 0.717943I
b = 1.014160 + 0.304108I
3.50862 + 3.52331I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.494120 + 0.303968I
a = 0.311730 + 0.937039I
b = 0.292452 + 0.485896I
−1.098610 − 0.581768I −7.07223 + 1.77255I
u = 0.494120 − 0.303968I
a = 0.311730 − 0.937039I
b = 0.292452 − 0.485896I
−1.098610 + 0.581768I −7.07223 − 1.77255I
u = 0.032606 + 0.567236I
a = 1.76400 − 1.43740I
b = −1.159970 − 0.006433I
5.16188 + 7.48943I 3.17866 − 3.66859I
u = 0.032606 − 0.567236I
a = 1.76400 + 1.43740I
b = −1.159970 + 0.006433I
5.16188 − 7.48943I 3.17866 + 3.66859I
u = −0.17927 + 1.44242I
a = −0.022651 + 0.593242I
b = 0.74742 + 1.29047I
11.01550 + 5.42605I 0
u = −0.17927 − 1.44242I
a = −0.022651 − 0.593242I
b = 0.74742 − 1.29047I
11.01550 − 5.42605I 0
u = 0.58095 + 1.34867I
a = 0.202222 + 1.000290I
b = −1.19889 + 1.13701I
2.45556 − 10.22880I 0
u = 0.58095 − 1.34867I
a = 0.202222 − 1.000290I
b = −1.19889 − 1.13701I
2.45556 + 10.22880I 0
u = −0.05846 + 1.48456I
a = 0.029784 + 0.470756I
b = 0.374264 + 0.598156I
4.31761 − 2.04256I 0
u = −0.05846 − 1.48456I
a = 0.029784 − 0.470756I
b = 0.374264 − 0.598156I
4.31761 + 2.04256I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.68990 + 1.31887I
a = 0.161766 − 0.386469I
b = 0.970188 − 0.140538I
2.41585 − 1.90654I 0
u = 0.68990 − 1.31887I
a = 0.161766 + 0.386469I
b = 0.970188 + 0.140538I
2.41585 + 1.90654I 0
u = −0.61893 + 1.35399I
a = −0.193399 + 1.046750I
b = 1.19720 + 1.12548I
1.3424 + 14.5629I 0
u = −0.61893 − 1.35399I
a = −0.193399 − 1.046750I
b = 1.19720 − 1.12548I
1.3424 − 14.5629I 0
u = −0.55138 + 1.39704I
a = −0.144196 + 0.964221I
b = 1.17922 + 1.14302I
9.44295 + 8.14107I 0
u = −0.55138 − 1.39704I
a = −0.144196 − 0.964221I
b = 1.17922 − 1.14302I
9.44295 − 8.14107I 0
u = 0.63721 + 1.37032I
a = 0.171878 + 1.067290I
b = −1.19325 + 1.12131I
7.0861 − 18.3127I 0
u = 0.63721 − 1.37032I
a = 0.171878 − 1.067290I
b = −1.19325 − 1.12131I
7.0861 + 18.3127I 0
u = −0.79995 + 1.28963I
a = −0.254587 − 0.492084I
b = −1.030060 − 0.192373I
2.04419 + 5.21190I 0
u = −0.79995 − 1.28963I
a = −0.254587 + 0.492084I
b = −1.030060 + 0.192373I
2.04419 − 5.21190I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.02842 + 1.52838I
a = −0.068403 + 0.471779I
b = −0.542764 + 0.674113I
10.43590 + 5.24037I 0
u = 0.02842 − 1.52838I
a = −0.068403 − 0.471779I
b = −0.542764 − 0.674113I
10.43590 − 5.24037I 0
u = 0.17949 + 1.53829I
a = −0.029573 + 0.477876I
b = −0.183723 + 0.535048I
4.37166 − 2.10439I 0
u = 0.17949 − 1.53829I
a = −0.029573 − 0.477876I
b = −0.183723 − 0.535048I
4.37166 + 2.10439I 0
u = −0.70469 + 1.39938I
a = −0.240422 − 0.321828I
b = −1.009830 − 0.093936I
8.13178 − 0.72885I 0
u = −0.70469 − 1.39938I
a = −0.240422 + 0.321828I
b = −1.009830 + 0.093936I
8.13178 + 0.72885I 0
u = 0.83522 + 1.33470I
a = 0.314352 − 0.469320I
b = 1.063130 − 0.177636I
7.64868 − 8.28578I 0
u = 0.83522 − 1.33470I
a = 0.314352 + 0.469320I
b = 1.063130 + 0.177636I
7.64868 + 8.28578I 0
u = −0.369196 + 0.183259I
a = −1.11240 − 1.95462I
b = −0.747649 − 0.207144I
1.35199 + 0.88919I 3.39091 − 0.08903I
u = −0.369196 − 0.183259I
a = −1.11240 + 1.95462I
b = −0.747649 + 0.207144I
1.35199 − 0.88919I 3.39091 + 0.08903I
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.24460 + 1.69324I
a = 0.038762 + 0.455089I
b = 0.109759 + 0.495776I
10.60140 + 5.23335I 0
u = −0.24460 − 1.69324I
a = 0.038762 − 0.455089I
b = 0.109759 − 0.495776I
10.60140 − 5.23335I 0
u = 0.141668 + 0.204783I
a = 0.94653 − 4.87240I
b = 0.831213 − 0.064363I
7.11783 + 0.87669I 8.03399 − 1.15662I
u = 0.141668 − 0.204783I
a = 0.94653 + 4.87240I
b = 0.831213 + 0.064363I
7.11783 − 0.87669I 8.03399 + 1.15662I
17
II. I
u
2
=
h−u
21
−u
20
+· · ·+b−2u, −10u
21
−10u
20
+· · ·+a+1 , u
22
+u
21
+· · ·+11u
2
+1i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
1
=
10u
21
+ 10u
20
+ ··· + 58u − 1
u
21
+ u
20
+ ··· + 9u
3
+ 2u
a
6
=
1
u
2
a
11
=
−48u
21
− 47u
20
+ ··· − 202u + 11
−u
21
− u
20
+ ··· − u
2
− 10u
a
4
=
−10u
21
− 49u
20
+ ··· − 59u − 153
−u
20
− u
19
+ ··· − u − 9
a
2
=
−211u
21
− 172u
20
+ ··· − 571u + 153
−29u
21
− 28u
20
+ ··· − 103u + 9
a
9
=
u
u
3
+ u
a
3
=
−11u
21
− 57u
20
+ ··· − 68u − 183
−u
21
− 8u
20
+ ··· − 9u − 32
a
8
=
308u
21
+ 377u
20
+ ··· + 850u + 148
79u
21
+ 116u
20
+ ··· + 226u + 79
a
12
=
9u
21
+ 9u
20
+ ··· + 56u − 1
u
21
+ u
20
+ ··· + 9u
3
+ 2u
a
7
=
u
21
+ 10u
20
+ ··· + 12u + 57
u
20
+ u
19
+ ··· + 10u
2
+ 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 19u
21
+ 19u
20
+ 162u
19
+ 120u
18
+ 591u
17
+ 309u
16
+ 1272u
15
+
391u
14
+ 1757u
13
+ 124u
12
+ 1428u
11
− 538u
10
+ 434u
9
− 1057u
8
− 536u
7
− 1012u
6
−
720u
5
− 583u
4
− 430u
3
− 187u
2
− 91u − 33
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
22
+ 6u
21
+ ··· + 4u + 1
c
2
u
22
+ 11u
20
+ ··· − 2u + 1
c
3
u
22
+ 2u
20
+ ··· − 3u
2
+ 1
c
4
u
22
+ u
21
+ ··· − 2u + 1
c
5
u
22
+ u
21
+ ··· + 11u
2
+ 1
c
6
u
22
+ 11u
20
+ ··· − u + 1
c
7
, c
8
u
22
+ 11u
20
+ ··· + 2u + 1
c
9
u
22
− u
21
+ ··· + 11u
2
+ 1
c
10
u
22
− 6u
20
+ ··· + 10u + 1
c
11
u
22
+ 11u
20
+ ··· + u + 1
c
12
u
22
+ 2u
21
+ ··· − u + 1
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
22
+ 10y
21
+ ··· + 10y + 1
c
2
, c
7
, c
8
y
22
+ 22y
21
+ ··· − 6y + 1
c
3
y
22
+ 4y
21
+ ··· − 6y + 1
c
4
y
22
− 3y
21
+ ··· − 2y + 1
c
5
, c
9
y
22
+ 19y
21
+ ··· + 22y + 1
c
6
, c
11
y
22
+ 22y
21
+ ··· + 19y + 1
c
10
y
22
− 12y
21
+ ··· − 8y + 1
c
12
y
22
− 2y
21
+ ··· − 3y + 1
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.340337 + 1.001630I
a = −0.398638 − 0.426371I
b = 1.51038 − 0.24981I
1.87630 − 1.59707I 1.15780 + 3.70396I
u = 0.340337 − 1.001630I
a = −0.398638 + 0.426371I
b = 1.51038 + 0.24981I
1.87630 + 1.59707I 1.15780 − 3.70396I
u = −0.419510 + 0.842237I
a = 0.706205 − 0.731152I
b = −1.102950 + 0.134654I
−0.26177 + 5.19653I −3.06421 − 8.10176I
u = −0.419510 − 0.842237I
a = 0.706205 + 0.731152I
b = −1.102950 − 0.134654I
−0.26177 − 5.19653I −3.06421 + 8.10176I
u = −0.677823 + 0.845900I
a = 0.128108 − 1.065530I
b = −0.789050 − 0.079226I
6.63530 + 0.42922I 4.90333 − 3.13326I
u = −0.677823 − 0.845900I
a = 0.128108 + 1.065530I
b = −0.789050 + 0.079226I
6.63530 − 0.42922I 4.90333 + 3.13326I
u = 0.451026 + 0.770459I
a = −0.839247 − 0.992023I
b = 0.948079 + 0.182922I
5.01746 − 8.71032I 2.25837 + 8.31806I
u = 0.451026 − 0.770459I
a = −0.839247 + 0.992023I
b = 0.948079 − 0.182922I
5.01746 + 8.71032I 2.25837 − 8.31806I
u = 0.644739 + 0.990832I
a = −0.136257 − 0.805367I
b = 0.848966 − 0.216285I
1.34285 − 2.47156I −0.11229 + 3.24313I
u = 0.644739 − 0.990832I
a = −0.136257 + 0.805367I
b = 0.848966 + 0.216285I
1.34285 + 2.47156I −0.11229 − 3.24313I
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.066527 + 0.668555I
a = −0.81933 + 1.67139I
b = 0.302997 + 1.150940I
−0.41425 − 1.43318I −0.97365 + 4.31956I
u = 0.066527 − 0.668555I
a = −0.81933 − 1.67139I
b = 0.302997 − 1.150940I
−0.41425 + 1.43318I −0.97365 − 4.31956I
u = −0.033510 + 0.622115I
a = 0.57836 + 2.47870I
b = −0.122784 + 1.004720I
−3.46211 − 0.94572I −11.35490 + 0.43033I
u = −0.033510 − 0.622115I
a = 0.57836 − 2.47870I
b = −0.122784 − 1.004720I
−3.46211 + 0.94572I −11.35490 − 0.43033I
u = −0.774968 + 1.158860I
a = −0.036843 − 0.668688I
b = −0.692821 − 0.332086I
4.94732 + 3.59571I 6.06414 − 7.04675I
u = −0.774968 − 1.158860I
a = −0.036843 + 0.668688I
b = −0.692821 + 0.332086I
4.94732 − 3.59571I 6.06414 + 7.04675I
u = 0.031403 + 0.593218I
a = −0.66469 + 3.02925I
b = 0.100511 + 0.908168I
1.52935 + 3.79602I −5.69472 − 2.78460I
u = 0.031403 − 0.593218I
a = −0.66469 − 3.02925I
b = 0.100511 − 0.908168I
1.52935 − 3.79602I −5.69472 + 2.78460I
u = 0.12665 + 1.48894I
a = −0.018753 − 0.376762I
b = 0.258428 − 1.158700I
3.78359 − 2.27838I −8.74297 + 3.33558I
u = 0.12665 − 1.48894I
a = −0.018753 + 0.376762I
b = 0.258428 + 1.158700I
3.78359 + 2.27838I −8.74297 − 3.33558I
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.25487 + 1.67606I
a = 0.001094 − 0.398599I
b = −0.261755 − 0.832709I
10.25970 + 5.43299I −6.44089 − 7.39131I
u = −0.25487 − 1.67606I
a = 0.001094 + 0.398599I
b = −0.261755 + 0.832709I
10.25970 − 5.43299I −6.44089 + 7.39131I
23
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
22
+ 6u
21
+ ··· + 4u + 1)
· (u
124
− 25u
123
+ ··· − 112353915u + 5993827)
c
2
(u
22
+ 11u
20
+ ··· − 2u + 1)(u
124
− u
123
+ ··· − 25u + 7)
c
3
(u
22
+ 2u
20
+ ··· − 3u
2
+ 1)(u
124
+ u
123
+ ··· − 130387u + 20503)
c
4
(u
22
+ u
21
+ ··· − 2u + 1)(u
124
− 3u
122
+ ··· + 161u + 13)
c
5
(u
22
+ u
21
+ ··· + 11u
2
+ 1)(u
124
+ 2u
123
+ ··· + 5614u + 1364)
c
6
(u
22
+ 11u
20
+ ··· − u + 1)(u
124
+ u
123
+ ··· + 23u
2
+ 1)
c
7
, c
8
(u
22
+ 11u
20
+ ··· + 2u + 1)(u
124
− u
123
+ ··· − 25u + 7)
c
9
(u
22
− u
21
+ ··· + 11u
2
+ 1)(u
124
+ 2u
123
+ ··· + 5614u + 1364)
c
10
(u
22
− 6u
20
+ ··· + 10u + 1)(u
124
+ 15u
123
+ ··· + 55987u + 6721)
c
11
(u
22
+ 11u
20
+ ··· + u + 1)(u
124
+ u
123
+ ··· + 23u
2
+ 1)
c
12
(u
22
+ 2u
21
+ ··· − u + 1)(u
124
− 7u
123
+ ··· + 4u + 5)
24
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
22
+ 10y
21
+ ··· + 10y + 1)
· (y
124
+ 63y
123
+ ··· + 431798753106101y + 35925962105929)
c
2
, c
7
, c
8
(y
22
+ 22y
21
+ ··· − 6y + 1)(y
124
+ 115y
123
+ ··· − 611y + 49)
c
3
(y
22
+ 4y
21
+ ··· − 6y + 1)
· (y
124
+ 21y
123
+ ··· + 4053965961y + 420373009)
c
4
(y
22
− 3y
21
+ ··· − 2y + 1)(y
124
− 6y
123
+ ··· − 1091y + 169)
c
5
, c
9
(y
22
+ 19y
21
+ ··· + 22y + 1)
· (y
124
+ 84y
123
+ ··· + 69263508y + 1860496)
c
6
, c
11
(y
22
+ 22y
21
+ ··· + 19y + 1)(y
124
+ 75y
123
+ ··· + 46y + 1)
c
10
(y
22
− 12y
21
+ ··· − 8y + 1)
· (y
124
− 39y
123
+ ··· + 13491579y + 45171841)
c
12
(y
22
− 2y
21
+ ··· − 3y + 1)(y
124
− 9y
123
+ ··· + 764y + 25)
25
