12a
0390
(K12a
0390
)
A knot diagram
1
Linearized knot diagam
3 6 9 11 2 10 5 12 1 7 8 4
Solving Sequence
6,10
7
3,11
2 1 5 8 4 9 12
c
6
c
10
c
2
c
1
c
5
c
7
c
4
c
9
c
12
c
3
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h5.37418 × 10
750
u
144
− 4.27866 × 10
751
u
143
+ ··· + 3.05104 × 10
751
b + 1.85665 × 10
755
,
1.01579 × 10
754
u
144
− 8.04515 × 10
754
u
143
+ ··· + 3.45683 × 10
754
a + 3.40763 × 10
758
,
u
145
− 9u
144
+ ··· + 376000u − 36256i
I
u
2
= h−1009040883105882u
27
− 1315626392337378u
26
+ ··· + 68752247482895b − 3458158094392594,
− 901563901956276u
27
− 1137559180351494u
26
+ ··· + 68752247482895a − 2992698774862172,
u
28
+ u
27
+ ··· + 4u − 1i
I
u
3
= hb + 1, 4a
2
+ 6a − u + 4, u
2
− 2i
I
u
4
= h13787a
8
+ 73187b + ··· + 77516a + 215532, a
9
− 5a
7
+ 23a
5
+ 20a
4
− 12a
3
− 10a
2
+ 19a + 11,
u + 1i
I
v
1
= ha, b + 1, v −1i
* 5 irreducible components of dim
C
= 0, with total 187 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
= h5.37 × 10
750
u
144
− 4.28 × 10
751
u
143
+ · · · + 3.05 × 10
751
b + 1.86 ×
10
755
, 1.02 × 10
754
u
144
− 8.05 × 10
754
u
143
+ · · · + 3.46 × 10
754
a + 3.41 ×
10
758
, u
145
− 9u
144
+ · · · + 376000u − 36256i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
7
=
1
u
2
a
3
=
−0.293851u
144
+ 2.32732u
143
+ ··· + 93139.9u − 9857.66
−0.176142u
144
+ 1.40236u
143
+ ··· + 57359.9u − 6085.29
a
11
=
−u
−u
3
+ u
a
2
=
−0.469994u
144
+ 3.72968u
143
+ ··· + 150500.u − 15943.0
−0.176142u
144
+ 1.40236u
143
+ ··· + 57359.9u − 6085.29
a
1
=
−0.0648032u
144
+ 0.499840u
143
+ ··· + 17482.0u − 1820.92
−0.536244u
144
+ 4.22100u
143
+ ··· + 163169.u − 17200.5
a
5
=
−0.158282u
144
+ 1.27149u
143
+ ··· + 54189.4u − 5772.13
0.0630524u
144
− 0.460147u
143
+ ··· − 10118.6u + 963.721
a
8
=
0.274941u
144
− 2.19571u
143
+ ··· − 91792.3u + 9764.90
0.0105693u
144
− 0.0829171u
143
+ ··· − 3248.37u + 345.877
a
4
=
−0.272586u
144
+ 2.14330u
143
+ ··· + 81770.6u − 8595.38
−0.0292223u
144
+ 0.263055u
143
+ ··· + 17159.3u − 1902.46
a
9
=
0.216468u
144
− 1.69100u
143
+ ··· − 61808.0u + 6459.95
−0.0772742u
144
+ 0.598026u
143
+ ··· + 21009.7u − 2186.39
a
12
=
0.00595126u
144
− 0.0196957u
143
+ ··· + 5443.92u − 657.298
−0.0957945u
144
+ 0.751906u
143
+ ··· + 28689.4u − 3022.09
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2.18489u
144
+ 17.3876u
143
+ ··· + 710362.u − 75357.2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
145
+ 60u
144
+ ··· + 69806531u + 3066001
c
2
, c
5
u
145
− 30u
143
+ ··· − 5817u + 1751
c
3
2(2u
145
− 2u
144
+ ··· − 8207989u + 1252007)
c
4
2(2u
145
+ 6u
144
+ ··· − 58u − 1)
c
6
, c
10
u
145
− 9u
144
+ ··· + 376000u − 36256
c
7
u
145
− 10u
144
+ ··· − 13808u + 958
c
8
, c
11
u
145
− u
144
+ ··· − 402u + 9
c
9
u
145
+ 7u
144
+ ··· − 2484u + 124
c
12
u
145
+ 14u
144
+ ··· + 324u + 122
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
145
+ 52y
144
+ ··· − 76219022336469y −9400362132001
c
2
, c
5
y
145
− 60y
144
+ ··· + 69806531y −3066001
c
3
4(4y
145
+ 224y
144
+ ··· − 3.85023 × 10
13
y −1.56752 × 10
12
)
c
4
4(4y
145
+ 80y
144
+ ··· + 1062y −1)
c
6
, c
10
y
145
− 99y
144
+ ··· − 18148659712y −1314497536
c
7
y
145
+ 24y
144
+ ··· − 104405052y −917764
c
8
, c
11
y
145
− 111y
144
+ ··· + 29430y −81
c
9
y
145
− 17y
144
+ ··· + 17645216y −15376
c
12
y
145
− 2y
144
+ ··· − 585788y −14884
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.983060 + 0.090094I
a = 2.13665 + 1.88345I
b = 0.858935 − 0.384607I
1.62861 − 5.53148I 0
u = 0.983060 − 0.090094I
a = 2.13665 − 1.88345I
b = 0.858935 + 0.384607I
1.62861 + 5.53148I 0
u = −0.685449 + 0.758061I
a = 0.427863 + 1.187920I
b = 0.598913 − 0.804263I
5.68349 + 0.09462I 0
u = −0.685449 − 0.758061I
a = 0.427863 − 1.187920I
b = 0.598913 + 0.804263I
5.68349 − 0.09462I 0
u = 0.254251 + 0.937529I
a = 0.89791 + 1.30032I
b = −0.888302 − 0.707889I
6.32851 + 0.10858I 0
u = 0.254251 − 0.937529I
a = 0.89791 − 1.30032I
b = −0.888302 + 0.707889I
6.32851 − 0.10858I 0
u = 0.713038 + 0.747574I
a = −0.790441 + 0.231774I
b = 0.857271 + 0.045849I
1.34056 − 7.92861I 0
u = 0.713038 − 0.747574I
a = −0.790441 − 0.231774I
b = 0.857271 − 0.045849I
1.34056 + 7.92861I 0
u = 0.811575 + 0.514492I
a = 0.53915 + 1.35311I
b = 0.605411 − 0.223383I
1.75716 + 3.74479I 0
u = 0.811575 − 0.514492I
a = 0.53915 − 1.35311I
b = 0.605411 + 0.223383I
1.75716 − 3.74479I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.897025 + 0.529202I
a = −0.331859 − 0.105549I
b = 0.735731 − 0.625405I
4.30487 + 1.12753I 0
u = 0.897025 − 0.529202I
a = −0.331859 + 0.105549I
b = 0.735731 + 0.625405I
4.30487 − 1.12753I 0
u = −0.517746 + 0.906672I
a = −0.545481 − 0.539143I
b = 1.038390 + 0.664944I
4.34586 − 5.42296I 0
u = −0.517746 − 0.906672I
a = −0.545481 + 0.539143I
b = 1.038390 − 0.664944I
4.34586 + 5.42296I 0
u = −1.050360 + 0.161995I
a = 0.51067 + 2.23058I
b = 1.040340 − 0.654724I
−2.96212 + 5.40060I 0
u = −1.050360 − 0.161995I
a = 0.51067 − 2.23058I
b = 1.040340 + 0.654724I
−2.96212 − 5.40060I 0
u = −0.805102 + 0.476131I
a = −0.598161 − 0.563764I
b = 0.356213 + 1.008710I
5.20952 + 4.67407I 0
u = −0.805102 − 0.476131I
a = −0.598161 + 0.563764I
b = 0.356213 − 1.008710I
5.20952 − 4.67407I 0
u = −0.882698 + 0.612745I
a = 1.071400 + 0.504659I
b = −0.768499 − 0.480559I
−0.650607 + 0.239775I 0
u = −0.882698 − 0.612745I
a = 1.071400 − 0.504659I
b = −0.768499 + 0.480559I
−0.650607 − 0.239775I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.072310 + 0.173522I
a = 0.034423 − 0.580747I
b = −0.425481 + 1.312410I
2.71130 + 6.68388I 0
u = −1.072310 − 0.173522I
a = 0.034423 + 0.580747I
b = −0.425481 − 1.312410I
2.71130 − 6.68388I 0
u = 1.082880 + 0.160074I
a = 0.188167 + 0.739468I
b = −0.499543 − 0.904517I
−2.70646 − 3.57717I 0
u = 1.082880 − 0.160074I
a = 0.188167 − 0.739468I
b = −0.499543 + 0.904517I
−2.70646 + 3.57717I 0
u = 0.891059 + 0.068423I
a = −0.285409 − 1.230440I
b = 0.924124 + 0.930627I
5.54059 − 3.39336I 0
u = 0.891059 − 0.068423I
a = −0.285409 + 1.230440I
b = 0.924124 − 0.930627I
5.54059 + 3.39336I 0
u = 0.222169 + 0.852674I
a = −0.642834 + 0.938742I
b = 1.010100 − 0.613224I
1.75366 + 4.60471I 0
u = 0.222169 − 0.852674I
a = −0.642834 − 0.938742I
b = 1.010100 + 0.613224I
1.75366 − 4.60471I 0
u = 1.091750 + 0.259485I
a = 1.028000 − 0.914616I
b = 0.914032 + 0.618678I
3.76788 − 3.76551I 0
u = 1.091750 − 0.259485I
a = 1.028000 + 0.914616I
b = 0.914032 − 0.618678I
3.76788 + 3.76551I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.388134 + 0.782870I
a = 0.386454 − 0.846415I
b = 0.174351 + 0.409736I
2.48869 + 1.37898I 0
u = 0.388134 − 0.782870I
a = 0.386454 + 0.846415I
b = 0.174351 − 0.409736I
2.48869 − 1.37898I 0
u = 1.122820 + 0.087405I
a = −0.609964 + 1.068290I
b = −1.187300 − 0.657079I
−4.77701 − 2.45139I 0
u = 1.122820 − 0.087405I
a = −0.609964 − 1.068290I
b = −1.187300 + 0.657079I
−4.77701 + 2.45139I 0
u = 1.065620 + 0.364968I
a = −0.485814 + 0.394476I
b = 0.367234 − 0.928765I
0.92008 − 3.52870I 0
u = 1.065620 − 0.364968I
a = −0.485814 − 0.394476I
b = 0.367234 + 0.928765I
0.92008 + 3.52870I 0
u = −0.020658 + 1.128840I
a = 0.14589 − 1.41304I
b = −0.614229 + 0.797164I
7.05249 − 7.91380I 0
u = −0.020658 − 1.128840I
a = 0.14589 + 1.41304I
b = −0.614229 − 0.797164I
7.05249 + 7.91380I 0
u = −0.745702 + 0.850929I
a = −0.204447 − 0.338471I
b = 0.784925 + 0.090674I
−2.54065 + 2.41226I 0
u = −0.745702 − 0.850929I
a = −0.204447 + 0.338471I
b = 0.784925 − 0.090674I
−2.54065 − 2.41226I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.140260 + 0.090079I
a = −0.760401 + 0.140342I
b = 0.370111 − 0.802407I
0.41878 − 4.86981I 0
u = 1.140260 − 0.090079I
a = −0.760401 − 0.140342I
b = 0.370111 + 0.802407I
0.41878 + 4.86981I 0
u = −1.16430
a = −0.916535
b = −1.55885
−2.35115 0
u = 0.151303 + 0.819847I
a = −0.33031 − 1.37740I
b = 1.005360 + 0.727730I
6.54392 − 5.53486I 0
u = 0.151303 − 0.819847I
a = −0.33031 + 1.37740I
b = 1.005360 − 0.727730I
6.54392 + 5.53486I 0
u = −1.041960 + 0.548317I
a = 0.53446 + 1.47256I
b = 1.199300 − 0.678298I
2.66277 + 10.75610I 0
u = −1.041960 − 0.548317I
a = 0.53446 − 1.47256I
b = 1.199300 + 0.678298I
2.66277 − 10.75610I 0
u = −1.144180 + 0.280710I
a = −0.52536 − 1.89176I
b = −1.010730 + 0.507563I
−3.26054 + 4.10580I 0
u = −1.144180 − 0.280710I
a = −0.52536 + 1.89176I
b = −1.010730 − 0.507563I
−3.26054 − 4.10580I 0
u = 1.18550
a = −0.763855
b = −1.37910
−5.52230 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.195690 + 0.166098I
a = 0.07704 + 1.68510I
b = −0.885702 − 0.531747I
−3.13450 − 2.17134I 0
u = 1.195690 − 0.166098I
a = 0.07704 − 1.68510I
b = −0.885702 + 0.531747I
−3.13450 + 2.17134I 0
u = 0.147231 + 0.776960I
a = 0.04260 − 2.01983I
b = −0.837232 + 0.751778I
6.51195 + 5.65463I 0
u = 0.147231 − 0.776960I
a = 0.04260 + 2.01983I
b = −0.837232 − 0.751778I
6.51195 − 5.65463I 0
u = 0.401631 + 0.679622I
a = 0.10653 − 1.43292I
b = 0.607703 + 0.710606I
2.97272 − 0.48461I 0
u = 0.401631 − 0.679622I
a = 0.10653 + 1.43292I
b = 0.607703 − 0.710606I
2.97272 + 0.48461I 0
u = 1.191400 + 0.220075I
a = 1.02025 − 1.77251I
b = 1.126050 + 0.612022I
−1.78712 − 10.16790I 0
u = 1.191400 − 0.220075I
a = 1.02025 + 1.77251I
b = 1.126050 − 0.612022I
−1.78712 + 10.16790I 0
u = −0.072552 + 0.782684I
a = −0.349628 + 1.314310I
b = 0.668772 − 0.847851I
7.56826 + 0.30824I 0
u = −0.072552 − 0.782684I
a = −0.349628 − 1.314310I
b = 0.668772 + 0.847851I
7.56826 − 0.30824I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.128570 + 0.485023I
a = −1.04988 − 1.87414I
b = −0.910652 + 0.519441I
−1.11152 + 4.37732I 0
u = −1.128570 − 0.485023I
a = −1.04988 + 1.87414I
b = −0.910652 − 0.519441I
−1.11152 − 4.37732I 0
u = 0.095858 + 1.241060I
a = 0.22271 + 1.49312I
b = −0.674538 − 0.650534I
1.47619 + 2.13178I 0
u = 0.095858 − 1.241060I
a = 0.22271 − 1.49312I
b = −0.674538 + 0.650534I
1.47619 − 2.13178I 0
u = 0.197748 + 1.255820I
a = −0.268541 + 0.928652I
b = 0.954939 − 0.502519I
0.95875 + 4.85612I 0
u = 0.197748 − 1.255820I
a = −0.268541 − 0.928652I
b = 0.954939 + 0.502519I
0.95875 − 4.85612I 0
u = −1.213160 + 0.408995I
a = −0.360762 − 0.243484I
b = 0.400987 + 0.946443I
4.07967 + 4.04266I 0
u = −1.213160 − 0.408995I
a = −0.360762 + 0.243484I
b = 0.400987 − 0.946443I
4.07967 − 4.04266I 0
u = 1.223850 + 0.423966I
a = 0.72684 − 1.43560I
b = 1.159680 + 0.644217I
−1.45588 − 9.25214I 0
u = 1.223850 − 0.423966I
a = 0.72684 + 1.43560I
b = 1.159680 − 0.644217I
−1.45588 + 9.25214I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.667302 + 0.203508I
a = −1.36130 + 1.03136I
b = 0.909212 + 0.467787I
−1.81635 − 3.73460I 0
u = −0.667302 − 0.203508I
a = −1.36130 − 1.03136I
b = 0.909212 − 0.467787I
−1.81635 + 3.73460I 0
u = 0.134120 + 1.295810I
a = 0.426303 + 1.227870I
b = −1.033780 − 0.669869I
5.7731 − 13.4390I 0
u = 0.134120 − 1.295810I
a = 0.426303 − 1.227870I
b = −1.033780 + 0.669869I
5.7731 + 13.4390I 0
u = 1.263880 + 0.347113I
a = −0.435669 − 0.253457I
b = −1.271320 + 0.282733I
−4.64492 − 2.87820I 0
u = 1.263880 − 0.347113I
a = −0.435669 + 0.253457I
b = −1.271320 − 0.282733I
−4.64492 + 2.87820I 0
u = 1.196060 + 0.552992I
a = 0.748770 + 0.074311I
b = −0.754108 + 0.572872I
3.40962 − 5.46166I 0
u = 1.196060 − 0.552992I
a = 0.748770 − 0.074311I
b = −0.754108 − 0.572872I
3.40962 + 5.46166I 0
u = −0.163988 + 0.661489I
a = 1.64018 + 1.79230I
b = −0.962143 − 0.280015I
−0.361799 − 0.690892I 0
u = −0.163988 − 0.661489I
a = 1.64018 − 1.79230I
b = −0.962143 + 0.280015I
−0.361799 + 0.690892I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.113060 + 0.715277I
a = 0.739715 + 1.048430I
b = −0.673595 − 0.730560I
−0.344412 + 1.034890I 0
u = −1.113060 − 0.715277I
a = 0.739715 − 1.048430I
b = −0.673595 + 0.730560I
−0.344412 − 1.034890I 0
u = 1.322570 + 0.039753I
a = −1.117680 + 0.298273I
b = −1.233860 + 0.200738I
−4.69333 − 1.90088I 0
u = 1.322570 − 0.039753I
a = −1.117680 − 0.298273I
b = −1.233860 − 0.200738I
−4.69333 + 1.90088I 0
u = 1.202510 + 0.570331I
a = −0.353545 + 0.664942I
b = 0.189724 − 0.795449I
−0.02933 − 6.64809I 0
u = 1.202510 − 0.570331I
a = −0.353545 − 0.664942I
b = 0.189724 + 0.795449I
−0.02933 + 6.64809I 0
u = 1.286650 + 0.403088I
a = −1.41755 + 1.36786I
b = −0.927742 − 0.564801I
2.85902 − 10.00570I 0
u = 1.286650 − 0.403088I
a = −1.41755 − 1.36786I
b = −0.927742 + 0.564801I
2.85902 + 10.00570I 0
u = −1.354830 + 0.043354I
a = −1.020840 − 0.838053I
b = −0.971571 − 0.166745I
−6.45997 − 0.55941I 0
u = −1.354830 − 0.043354I
a = −1.020840 + 0.838053I
b = −0.971571 + 0.166745I
−6.45997 + 0.55941I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.349680 + 0.132285I
a = −0.208976 − 0.975259I
b = −1.060970 + 0.900995I
0.48168 + 3.59119I 0
u = −1.349680 − 0.132285I
a = −0.208976 + 0.975259I
b = −1.060970 − 0.900995I
0.48168 − 3.59119I 0
u = −1.254560 + 0.522994I
a = −0.213295 − 0.748929I
b = 0.339254 + 0.625085I
−3.15308 + 1.99288I 0
u = −1.254560 − 0.522994I
a = −0.213295 + 0.748929I
b = 0.339254 − 0.625085I
−3.15308 − 1.99288I 0
u = −1.339420 + 0.290116I
a = 0.611052 + 0.186561I
b = 1.365420 − 0.069213I
−4.43721 + 10.90670I 0
u = −1.339420 − 0.290116I
a = 0.611052 − 0.186561I
b = 1.365420 + 0.069213I
−4.43721 − 10.90670I 0
u = −1.36887 + 0.38491I
a = 0.86717 + 1.19426I
b = 1.163830 − 0.669799I
1.77972 + 9.93298I 0
u = −1.36887 − 0.38491I
a = 0.86717 − 1.19426I
b = 1.163830 + 0.669799I
1.77972 − 9.93298I 0
u = 1.39704 + 0.27963I
a = 0.627760 − 0.164251I
b = 1.239420 + 0.027842I
−9.04489 − 6.00167I 0
u = 1.39704 − 0.27963I
a = 0.627760 + 0.164251I
b = 1.239420 − 0.027842I
−9.04489 + 6.00167I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.32420 + 0.54500I
a = 0.549841 − 0.699856I
b = −0.521281 + 0.903568I
−2.43041 − 8.09154I 0
u = 1.32420 − 0.54500I
a = 0.549841 + 0.699856I
b = −0.521281 − 0.903568I
−2.43041 + 8.09154I 0
u = −1.34664 + 0.54674I
a = 0.482093 + 0.630584I
b = −0.497051 − 0.998009I
2.91136 + 13.77410I 0
u = −1.34664 − 0.54674I
a = 0.482093 − 0.630584I
b = −0.497051 + 0.998009I
2.91136 − 13.77410I 0
u = −0.17185 + 1.44841I
a = 0.415405 − 1.294100I
b = −0.972206 + 0.625778I
0.57879 + 7.13312I 0
u = −0.17185 − 1.44841I
a = 0.415405 + 1.294100I
b = −0.972206 − 0.625778I
0.57879 − 7.13312I 0
u = −1.46137 + 0.08407I
a = 0.743164 + 0.017767I
b = 0.922239 + 0.384113I
−4.32335 − 1.52739I 0
u = −1.46137 − 0.08407I
a = 0.743164 − 0.017767I
b = 0.922239 − 0.384113I
−4.32335 + 1.52739I 0
u = 1.36346 + 0.65088I
a = 0.50503 − 1.35961I
b = 1.141390 + 0.550428I
−2.73134 − 11.54070I 0
u = 1.36346 − 0.65088I
a = 0.50503 + 1.35961I
b = 1.141390 − 0.550428I
−2.73134 + 11.54070I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.487823
a = 1.24837
b = −0.700782
−1.20277 −8.62840
u = 0.75895 + 1.31522I
a = −0.207668 − 1.097850I
b = 0.842008 + 0.428077I
1.52746 + 1.15651I 0
u = 0.75895 − 1.31522I
a = −0.207668 + 1.097850I
b = 0.842008 − 0.428077I
1.52746 − 1.15651I 0
u = −1.51612 + 0.19747I
a = −0.467230 + 0.517386I
b = −1.061030 − 0.231239I
−7.20649 − 0.24882I 0
u = −1.51612 − 0.19747I
a = −0.467230 − 0.517386I
b = −1.061030 + 0.231239I
−7.20649 + 0.24882I 0
u = 1.43298 + 0.60208I
a = −0.41885 + 1.50988I
b = −1.112770 − 0.687061I
−4.2403 − 13.9567I 0
u = 1.43298 − 0.60208I
a = −0.41885 − 1.50988I
b = −1.112770 + 0.687061I
−4.2403 + 13.9567I 0
u = −1.53471 + 0.27805I
a = 0.627783 + 0.106824I
b = 0.994398 + 0.023784I
−5.41950 + 0.80147I 0
u = −1.53471 − 0.27805I
a = 0.627783 − 0.106824I
b = 0.994398 − 0.023784I
−5.41950 − 0.80147I 0
u = −1.45073 + 0.58186I
a = −0.49682 − 1.42065I
b = −1.155150 + 0.706026I
0.8594 + 19.9515I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.45073 − 0.58186I
a = −0.49682 + 1.42065I
b = −1.155150 − 0.706026I
0.8594 − 19.9515I 0
u = −0.369267 + 0.229074I
a = 0.132329 − 0.689954I
b = −0.069001 − 0.918620I
4.52436 − 4.78820I 3.35035 + 5.22511I
u = −0.369267 − 0.229074I
a = 0.132329 + 0.689954I
b = −0.069001 + 0.918620I
4.52436 + 4.78820I 3.35035 − 5.22511I
u = −1.32980 + 0.84039I
a = −0.07214 − 1.65888I
b = −1.003170 + 0.673003I
−1.34843 + 6.42495I 0
u = −1.32980 − 0.84039I
a = −0.07214 + 1.65888I
b = −1.003170 − 0.673003I
−1.34843 − 6.42495I 0
u = 1.57692 + 0.08619I
a = 0.675271 + 0.012448I
b = 0.868794 − 0.484131I
−3.40725 + 1.97338I 0
u = 1.57692 − 0.08619I
a = 0.675271 − 0.012448I
b = 0.868794 + 0.484131I
−3.40725 − 1.97338I 0
u = 0.158226 + 0.346808I
a = 6.09653 + 1.83713I
b = −0.879301 + 0.051273I
0.180675 + 0.062235I −5.87156 + 5.71993I
u = 0.158226 − 0.346808I
a = 6.09653 − 1.83713I
b = −0.879301 − 0.051273I
0.180675 − 0.062235I −5.87156 − 5.71993I
u = 1.62271 + 0.13098I
a = 0.190793 + 0.773889I
b = 0.838954 − 0.740978I
3.07691 + 2.80274I 0
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.62271 − 0.13098I
a = 0.190793 − 0.773889I
b = 0.838954 + 0.740978I
3.07691 − 2.80274I 0
u = 0.070868 + 0.354198I
a = 1.67167 + 0.84301I
b = −0.155815 + 0.410239I
−0.08532 + 1.56228I −1.25767 − 3.36895I
u = 0.070868 − 0.354198I
a = 1.67167 − 0.84301I
b = −0.155815 − 0.410239I
−0.08532 − 1.56228I −1.25767 + 3.36895I
u = 0.358412 + 0.036935I
a = −2.95778 − 1.49510I
b = 1.037770 − 0.422808I
1.03754 + 8.53088I −4.62589 − 8.79162I
u = 0.358412 − 0.036935I
a = −2.95778 + 1.49510I
b = 1.037770 + 0.422808I
1.03754 − 8.53088I −4.62589 + 8.79162I
u = −0.203538 + 0.289178I
a = 0.260562 − 0.611319I
b = −1.191550 − 0.212559I
0.013209 + 0.790607I 0.62162 − 9.19646I
u = −0.203538 − 0.289178I
a = 0.260562 + 0.611319I
b = −1.191550 + 0.212559I
0.013209 − 0.790607I 0.62162 + 9.19646I
u = −1.52485 + 0.64530I
a = 0.378961 + 1.243280I
b = 1.057690 − 0.554389I
−5.08456 + 6.57916I 0
u = −1.52485 − 0.64530I
a = 0.378961 − 1.243280I
b = 1.057690 + 0.554389I
−5.08456 − 6.57916I 0
u = 1.43719 + 0.89441I
a = −0.473666 + 1.287330I
b = −0.803562 − 0.521797I
2.59886 + 1.15864I 0
18
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.43719 − 0.89441I
a = −0.473666 − 1.287330I
b = −0.803562 + 0.521797I
2.59886 − 1.15864I 0
u = 0.082280 + 0.192921I
a = 2.84630 + 2.28467I
b = −0.934942 + 0.403937I
−1.98226 + 1.39082I −8.83258 − 3.49235I
u = 0.082280 − 0.192921I
a = 2.84630 − 2.28467I
b = −0.934942 − 0.403937I
−1.98226 − 1.39082I −8.83258 + 3.49235I
u = 1.37697 + 1.17042I
a = 0.320758 − 0.630926I
b = −0.901456 + 0.533961I
2.27029 + 5.43161I 0
u = 1.37697 − 1.17042I
a = 0.320758 + 0.630926I
b = −0.901456 − 0.533961I
2.27029 − 5.43161I 0
19
II.
I
u
2
= h−1.01×10
15
u
27
−1.32×10
15
u
26
+· · ·+6.88×10
13
b−3.46×10
15
, −9.02×
10
14
u
27
−1.14×10
15
u
26
+· · ·+6.88×10
13
a−2.99×10
15
, u
28
+u
27
+· · ·+4u−1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
7
=
1
u
2
a
3
=
13.1132u
27
+ 16.5458u
26
+ ··· − 24.9650u + 43.5287
14.6765u
27
+ 19.1358u
26
+ ··· − 27.8941u + 50.2988
a
11
=
−u
−u
3
+ u
a
2
=
27.7897u
27
+ 35.6815u
26
+ ··· − 52.8591u + 93.8276
14.6765u
27
+ 19.1358u
26
+ ··· − 27.8941u + 50.2988
a
1
=
−7.57904u
27
− 9.80304u
26
+ ··· + 20.7126u − 23.0928
−12.0572u
27
− 15.2717u
26
+ ··· + 27.8680u − 37.5807
a
5
=
−56.6493u
27
− 73.4876u
26
+ ··· + 119.041u − 192.560
−27.0732u
27
− 34.8367u
26
+ ··· + 56.5704u − 91.3875
a
8
=
−1.09896u
27
− 1.15998u
26
+ ··· − 6.19770u − 4.60526
6.01762u
27
+ 7.64526u
26
+ ··· − 15.6610u + 18.6767
a
4
=
−49.7448u
27
− 64.8719u
26
+ ··· + 105.533u − 169.520
−33.4113u
27
− 42.9037u
26
+ ··· + 70.1387u − 112.716
a
9
=
−14.9939u
27
− 19.8047u
26
+ ··· + 38.3727u − 48.2107
−16.5467u
27
− 21.3049u
26
+ ··· + 37.3496u − 52.5440
a
12
=
−4.35504u
27
− 5.87482u
26
+ ··· + 19.4892u − 12.5137
−11.7029u
27
− 15.5955u
26
+ ··· + 33.5141u − 38.5718
(ii) Obstruction class = 1
(iii) Cusp Shapes
=
6612661367678
212855255365
u
27
+
8065415664027
212855255365
u
26
+ ··· −
8238301010007
212855255365
u +
23383603443811
212855255365
20
(iv) u-Polynomials at the component
21
Crossings u-Polynomials at each crossing
c
1
u
28
− 12u
27
+ ··· − 10u + 1
c
2
u
28
+ 4u
27
+ ··· + 4u + 1
c
3
u
28
− 2u
27
+ ··· − 3u
2
− 1
c
4
u
28
− 2u
27
+ ··· − 3u − 1
c
5
u
28
− 4u
27
+ ··· − 4u + 1
c
6
u
28
+ u
27
+ ··· + 4u − 1
c
7
u
28
+ 2u
27
+ ··· + 2u + 1
c
8
u
28
+ u
27
+ ··· + 13u + 1
c
9
u
28
+ u
26
+ ··· + 4u − 1
c
10
u
28
− u
27
+ ··· − 4u − 1
c
11
u
28
− u
27
+ ··· − 13u + 1
c
12
u
28
− 4u
26
+ ··· + 2u
2
+ 1
22
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
28
+ 4y
27
+ ··· + 38y + 1
c
2
, c
5
y
28
− 12y
27
+ ··· − 10y + 1
c
3
y
28
+ 8y
27
+ ··· + 6y + 1
c
4
y
28
− 4y
27
+ ··· − 3y + 1
c
6
, c
10
y
28
− 19y
27
+ ··· − 30y + 1
c
7
y
28
+ 2y
27
+ ··· − 4y + 1
c
8
, c
11
y
28
− 19y
27
+ ··· − 53y + 1
c
9
y
28
+ 2y
27
+ ··· − 12y + 1
c
12
y
28
− 8y
27
+ ··· + 4y + 1
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.999822 + 0.223884I
a = 0.000268 − 0.172722I
b = −0.277398 + 1.070030I
3.24551 + 6.41417I 1.88941 − 5.19504I
u = −0.999822 − 0.223884I
a = 0.000268 + 0.172722I
b = −0.277398 − 1.070030I
3.24551 − 6.41417I 1.88941 + 5.19504I
u = −0.982727 + 0.437950I
a = −1.273480 + 0.548117I
b = 0.457536 + 0.328658I
2.38845 + 6.75835I −2.08112 − 6.86262I
u = −0.982727 − 0.437950I
a = −1.273480 − 0.548117I
b = 0.457536 − 0.328658I
2.38845 − 6.75835I −2.08112 + 6.86262I
u = 0.894648 + 0.621540I
a = −1.11319 + 1.10365I
b = 0.668057 − 0.689490I
0.057006 − 1.227000I 2.27688 + 6.63604I
u = 0.894648 − 0.621540I
a = −1.11319 − 1.10365I
b = 0.668057 + 0.689490I
0.057006 + 1.227000I 2.27688 − 6.63604I
u = 1.127590 + 0.146820I
a = −0.23107 + 1.50081I
b = −0.974742 − 0.632962I
−4.03236 − 2.70646I −9.85359 + 5.60503I
u = 1.127590 − 0.146820I
a = −0.23107 − 1.50081I
b = −0.974742 + 0.632962I
−4.03236 + 2.70646I −9.85359 − 5.60503I
u = −1.15475
a = −0.670156
b = −1.68416
−2.66613 −22.6310
u = 0.736493 + 0.224307I
a = 0.125580 − 1.074830I
b = −0.477371 − 0.343605I
−1.24178 − 2.22670I −5.45139 + 3.88786I
25
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.736493 − 0.224307I
a = 0.125580 + 1.074830I
b = −0.477371 + 0.343605I
−1.24178 + 2.22670I −5.45139 − 3.88786I
u = −1.190620 + 0.388898I
a = 1.12300 + 1.47156I
b = 1.163710 − 0.552680I
−0.26719 + 10.95580I −4.27305 − 10.28671I
u = −1.190620 − 0.388898I
a = 1.12300 − 1.47156I
b = 1.163710 + 0.552680I
−0.26719 − 10.95580I −4.27305 + 10.28671I
u = 1.27179
a = −0.836795
b = −1.14925
−4.79047 −7.02690
u = −0.666716 + 1.139490I
a = −0.468850 − 0.885646I
b = 0.988008 + 0.546985I
1.53526 − 6.10045I −3.53945 + 10.21475I
u = −0.666716 − 1.139490I
a = −0.468850 + 0.885646I
b = 0.988008 − 0.546985I
1.53526 + 6.10045I −3.53945 − 10.21475I
u = 1.147340 + 0.721844I
a = 0.14983 − 1.85012I
b = 1.010510 + 0.654604I
−1.00490 − 6.45415I 2.53221 + 8.73592I
u = 1.147340 − 0.721844I
a = 0.14983 + 1.85012I
b = 1.010510 − 0.654604I
−1.00490 + 6.45415I 2.53221 − 8.73592I
u = −1.218690 + 0.596584I
a = −0.170334 + 0.761916I
b = −0.612405 − 0.648951I
2.76377 − 3.72906I 0.63152 + 6.67791I
u = −1.218690 − 0.596584I
a = −0.170334 − 0.761916I
b = −0.612405 + 0.648951I
2.76377 + 3.72906I 0.63152 − 6.67791I
26
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.48251 + 0.07555I
a = 0.779761 − 0.142593I
b = 0.881043 − 0.427003I
−5.32374 + 1.76278I −10.46211 − 4.48061I
u = 1.48251 − 0.07555I
a = 0.779761 + 0.142593I
b = 0.881043 + 0.427003I
−5.32374 − 1.76278I −10.46211 + 4.48061I
u = −0.95803 + 1.15701I
a = 0.06893 + 1.42563I
b = 0.711490 − 0.511469I
2.48501 − 1.77929I 0. + 7.92881I
u = −0.95803 − 1.15701I
a = 0.06893 − 1.42563I
b = 0.711490 + 0.511469I
2.48501 + 1.77929I 0. − 7.92881I
u = −0.226235 + 0.319298I
a = 0.02045 − 4.49376I
b = −1.035020 + 0.172534I
−0.141659 + 0.143494I −5.65645 + 9.38551I
u = −0.226235 − 0.319298I
a = 0.02045 + 4.49376I
b = −1.035020 − 0.172534I
−0.141659 − 0.143494I −5.65645 − 9.38551I
u = 0.295736 + 0.003714I
a = 1.24258 − 0.73376I
b = 0.913297 − 0.853503I
6.55480 + 3.17014I 4.71921 − 1.90637I
u = 0.295736 − 0.003714I
a = 1.24258 + 0.73376I
b = 0.913297 + 0.853503I
6.55480 − 3.17014I 4.71921 + 1.90637I
27
III. I
u
3
= hb + 1, 4a
2
+ 6a − u + 4, u
2
− 2i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
7
=
1
2
a
3
=
a
−1
a
11
=
−u
−u
a
2
=
a − 1
−1
a
1
=
−1
0
a
5
=
a
−1
a
8
=
2a −
1
2
u + 3
2a + 3
a
4
=
3a + 2
2a + 1
a
9
=
u
u
a
12
=
2a −
3
2
u + 3
2a − u + 3
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8
28
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
8
(u − 1)
4
c
3
2(2u
4
+ 3u
2
− 2u + 1)
c
4
2(2u
4
+ 3u
2
+ 2u + 1)
c
5
, c
11
(u + 1)
4
c
6
, c
9
, c
10
(u
2
− 2)
2
c
7
, c
12
u
4
− 2u
3
+ 5u
2
− 4u + 2
29
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
8
, c
11
(y −1)
4
c
3
, c
4
4(4y
4
+ 12y
3
+ 13y
2
+ 2y + 1)
c
6
, c
9
, c
10
(y −2)
4
c
7
, c
12
y
4
+ 6y
3
+ 13y
2
+ 4y + 4
30
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.41421
a = −0.750000 + 0.289735I
b = −1.00000
−4.93480 −8.00000
u = 1.41421
a = −0.750000 − 0.289735I
b = −1.00000
−4.93480 −8.00000
u = −1.41421
a = −0.750000 + 0.889412I
b = −1.00000
−4.93480 −8.00000
u = −1.41421
a = −0.750000 − 0.889412I
b = −1.00000
−4.93480 −8.00000
31
IV.
I
u
4
= h13787a
8
+73187b+· · ·+77516a+215532, a
9
−5a
7
+· · ·+19a+11, u+1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
−1
a
7
=
1
1
a
3
=
a
−0.188380a
8
+ 0.120076a
7
+ ··· − 1.05915a − 2.94495
a
11
=
1
0
a
2
=
−0.188380a
8
+ 0.120076a
7
+ ··· − 0.0591498a − 2.94495
−0.188380a
8
+ 0.120076a
7
+ ··· − 1.05915a − 2.94495
a
1
=
0.0933226a
8
− 0.217170a
7
+ ··· + 1.61290a − 0.0174075
0.0536981a
8
− 0.0546818a
7
+ ··· − 1.76300a + 1.64152
a
5
=
−0.386216a
8
+ 0.323063a
7
+ ··· − 1.14731a − 4.45680
−0.266140a
8
+ 0.281703a
7
+ ··· − 0.513028a − 3.38462
a
8
=
−0.00571140a
8
+ 0.131007a
7
+ ··· − 0.656250a + 1.76739
0.0913823a
8
− 0.0961100a
7
+ ··· + 0.500007a + 1.72175
a
4
=
−0.120076a
8
+ 0.0413598a
7
+ ··· − 0.634279a − 1.07218
−0.266140a
8
+ 0.281703a
7
+ ··· − 0.513028a − 3.38462
a
9
=
0.101821a
8
− 0.268572a
7
+ ··· + 0.670761a − 0.762185
−0.0933226a
8
+ 0.217170a
7
+ ··· − 1.61290a + 0.0174075
a
12
=
a
−0.188380a
8
+ 0.120076a
7
+ ··· − 1.05915a − 2.94495
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6
32
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
9
+ 6u
8
+ 15u
7
+ 22u
6
+ 23u
5
+ 22u
4
+ 14u
3
+ 8u
2
+ u + 1
c
2
, c
5
, c
12
u
9
+ 2u
8
− u
7
− 2u
6
+ 3u
5
+ 2u
4
− 2u
3
+ u + 1
c
3
, c
8
, c
11
u
9
− u
7
− u
5
+ u + 1
c
4
u
9
− 6u
8
+ 15u
7
− 22u
6
+ 23u
5
− 22u
4
+ 14u
3
− 8u
2
+ u − 1
c
6
, c
10
(u + 1)
9
c
7
u
9
− 3u
7
− 4u
6
+ 9u
5
+ 6u
4
− 10u
3
− 8u
2
+ 9u + 1
c
9
u
9
+ u
7
− 3u
6
+ 7u
5
+ 10u
4
+ 2u
3
− 3u
2
− 3u − 1
33
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
9
− 6y
8
+ 7y
7
− 30y
6
− 113y
5
− 174y
4
− 154y
3
− 80y
2
− 15y −1
c
2
, c
5
, c
12
y
9
− 6y
8
+ 15y
7
− 22y
6
+ 23y
5
− 22y
4
+ 14y
3
− 8y
2
+ y −1
c
3
, c
8
, c
11
y
9
− 2y
8
− y
7
+ 2y
6
+ 3y
5
− 2y
4
− 2y
3
+ y −1
c
6
, c
10
(y −1)
9
c
7
y
9
− 6y
8
+ 27y
7
− 90y
6
+ 207y
5
− 334y
4
+ 366y
3
− 256y
2
+ 97y −1
c
9
y
9
+ 2y
8
+ 15y
7
+ 9y
6
+ 107y
5
− 96y
4
+ 16y
3
− y
2
+ 3y −1
34
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 0.717700 + 0.569615I
b = −0.392479 − 0.478671I
−1.64493 −6.00000
u = −1.00000
a = 0.717700 − 0.569615I
b = −0.392479 + 0.478671I
−1.64493 −6.00000
u = −1.00000
a = −1.165340 + 0.609051I
b = 0.608437 − 0.761790I
−1.64493 −6.00000
u = −1.00000
a = −1.165340 − 0.609051I
b = 0.608437 + 0.761790I
−1.64493 −6.00000
u = −1.00000
a = −0.567461
b = −1.58079
−1.64493 −6.00000
u = −1.00000
a = −1.29626 + 0.86761I
b = −1.288800 − 0.404522I
−1.64493 −6.00000
u = −1.00000
a = −1.29626 − 0.86761I
b = −1.288800 + 0.404522I
−1.64493 −6.00000
u = −1.00000
a = 2.02763 + 1.17368I
b = 0.863232 − 0.454705I
−1.64493 −6.00000
u = −1.00000
a = 2.02763 − 1.17368I
b = 0.863232 + 0.454705I
−1.64493 −6.00000
35
V. I
v
1
= ha, b + 1, v − 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
1
0
a
7
=
1
0
a
3
=
0
−1
a
11
=
1
0
a
2
=
−1
−1
a
1
=
−1
0
a
5
=
0
−1
a
8
=
1
1
a
4
=
1
−1
a
9
=
1
0
a
12
=
0
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
36
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
11
, c
12
u − 1
c
5
, c
7
, c
8
u + 1
c
6
, c
9
, c
10
u
37
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
7
c
8
, c
11
, c
12
y −1
c
6
, c
9
, c
10
y
38
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 1.00000
a = 0
b = −1.00000
0 0
39
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
5
)(u
9
+ 6u
8
+ ··· + u + 1)
· (u
28
− 12u
27
+ ··· − 10u + 1)
· (u
145
+ 60u
144
+ ··· + 69806531u + 3066001)
c
2
(u − 1)
5
(u
9
+ 2u
8
− u
7
− 2u
6
+ 3u
5
+ 2u
4
− 2u
3
+ u + 1)
· (u
28
+ 4u
27
+ ··· + 4u + 1)(u
145
− 30u
143
+ ··· − 5817u + 1751)
c
3
4(u − 1)(2u
4
+ 3u
2
− 2u + 1)(u
9
− u
7
− u
5
+ u + 1)
· (u
28
− 2u
27
+ ··· − 3u
2
− 1)
· (2u
145
− 2u
144
+ ··· − 8207989u + 1252007)
c
4
4(u − 1)(2u
4
+ 3u
2
+ 2u + 1)
· (u
9
− 6u
8
+ 15u
7
− 22u
6
+ 23u
5
− 22u
4
+ 14u
3
− 8u
2
+ u − 1)
· (u
28
− 2u
27
+ ··· − 3u − 1)(2u
145
+ 6u
144
+ ··· − 58u − 1)
c
5
(u + 1)
5
(u
9
+ 2u
8
− u
7
− 2u
6
+ 3u
5
+ 2u
4
− 2u
3
+ u + 1)
· (u
28
− 4u
27
+ ··· − 4u + 1)(u
145
− 30u
143
+ ··· − 5817u + 1751)
c
6
u(u + 1)
9
(u
2
− 2)
2
(u
28
+ u
27
+ ··· + 4u − 1)
· (u
145
− 9u
144
+ ··· + 376000u − 36256)
c
7
(u + 1)(u
4
− 2u
3
+ 5u
2
− 4u + 2)
· (u
9
− 3u
7
− 4u
6
+ 9u
5
+ 6u
4
− 10u
3
− 8u
2
+ 9u + 1)
· (u
28
+ 2u
27
+ ··· + 2u + 1)(u
145
− 10u
144
+ ··· − 13808u + 958)
c
8
((u − 1)
4
)(u + 1)(u
9
− u
7
+ ··· + u + 1)(u
28
+ u
27
+ ··· + 13u + 1)
· (u
145
− u
144
+ ··· − 402u + 9)
c
9
u(u
2
− 2)
2
(u
9
+ u
7
− 3u
6
+ 7u
5
+ 10u
4
+ 2u
3
− 3u
2
− 3u − 1)
· (u
28
+ u
26
+ ··· + 4u − 1)(u
145
+ 7u
144
+ ··· − 2484u + 124)
c
10
u(u + 1)
9
(u
2
− 2)
2
(u
28
− u
27
+ ··· − 4u − 1)
· (u
145
− 9u
144
+ ··· + 376000u − 36256)
c
11
(u − 1)(u + 1)
4
(u
9
− u
7
+ ··· + u + 1)(u
28
− u
27
+ ··· − 13u + 1)
· (u
145
− u
144
+ ··· − 402u + 9)
c
12
(u − 1)(u
4
− 2u
3
+ 5u
2
− 4u + 2)
· (u
9
+ 2u
8
− u
7
− 2u
6
+ 3u
5
+ 2u
4
− 2u
3
+ u + 1)
· (u
28
− 4u
26
+ ··· + 2u
2
+ 1)(u
145
+ 14u
144
+ ··· + 324u + 122)
40
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y −1)
5
· (y
9
− 6y
8
+ 7y
7
− 30y
6
− 113y
5
− 174y
4
− 154y
3
− 80y
2
− 15y −1)
· (y
28
+ 4y
27
+ ··· + 38y + 1)
· (y
145
+ 52y
144
+ ··· − 76219022336469y −9400362132001)
c
2
, c
5
((y −1)
5
)(y
9
− 6y
8
+ ··· + y −1)
· (y
28
− 12y
27
+ ··· − 10y + 1)
· (y
145
− 60y
144
+ ··· + 69806531y −3066001)
c
3
16(y −1)(4y
4
+ 12y
3
+ 13y
2
+ 2y + 1)
· (y
9
− 2y
8
− y
7
+ 2y
6
+ 3y
5
− 2y
4
− 2y
3
+ y −1)
· (y
28
+ 8y
27
+ ··· + 6y + 1)
· (4y
145
+ 224y
144
+ ··· − 38502319412515y −1567521528049)
c
4
16(y −1)(4y
4
+ 12y
3
+ 13y
2
+ 2y + 1)
· (y
9
− 6y
8
+ 7y
7
− 30y
6
− 113y
5
− 174y
4
− 154y
3
− 80y
2
− 15y −1)
· (y
28
− 4y
27
+ ··· − 3y + 1)(4y
145
+ 80y
144
+ ··· + 1062y −1)
c
6
, c
10
y(y −2)
4
(y −1)
9
(y
28
− 19y
27
+ ··· − 30y + 1)
· (y
145
− 99y
144
+ ··· − 18148659712y −1314497536)
c
7
(y −1)(y
4
+ 6y
3
+ 13y
2
+ 4y + 4)
· (y
9
− 6y
8
+ 27y
7
− 90y
6
+ 207y
5
− 334y
4
+ 366y
3
− 256y
2
+ 97y −1)
· (y
28
+ 2y
27
+ ··· − 4y + 1)
· (y
145
+ 24y
144
+ ··· − 104405052y −917764)
c
8
, c
11
(y −1)
5
(y
9
− 2y
8
− y
7
+ 2y
6
+ 3y
5
− 2y
4
− 2y
3
+ y −1)
· (y
28
− 19y
27
+ ··· − 53y + 1)(y
145
− 111y
144
+ ··· + 29430y −81)
c
9
y(y −2)
4
(y
9
+ 2y
8
+ ··· + 3y −1)
· (y
28
+ 2y
27
+ ··· − 12y + 1)
· (y
145
− 17y
144
+ ··· + 17645216y −15376)
c
12
(y −1)(y
4
+ 6y
3
+ 13y
2
+ 4y + 4)
· (y
9
− 6y
8
+ 15y
7
− 22y
6
+ 23y
5
− 22y
4
+ 14y
3
− 8y
2
+ y −1)
· (y
28
− 8y
27
+ ··· + 4y + 1)(y
145
− 2y
144
+ ··· − 585788y −14884)
41
