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Characteristic polynomials of the monodromy of the simple and unimodal singularities
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Polynomials
singularity
$n$ 
$\Delta_f(t)$
$A_1$
1:
t + 1
comment: $f=x^{2}$, with $\mu=1$; $\Delta_f(t)=\Phi_{2}(t)$.
$A_1$
2:
t - 1
comment: $f=x^{2}+y^2$, with $\mu=1$; $\Delta_f(t)=\Phi_{1}(t)$.
$A_1$
3:
t + 1
comment: $f=x^{2}+y^2+z^2$, with $\mu=1$; $\Delta_f(t)=\Phi_{2}(t)$.
$A_2$
1:
t^2 + t + 1
comment: $f=x^{3}$, with $\mu=2$; $\Delta_f(t)=\Phi_{3}(t)$.
$A_2$
2:
t^2 - t + 1
comment: $f=x^{3}+y^2$, with $\mu=2$; $\Delta_f(t)=\Phi_{6}(t)$.
$A_2$
3:
t^2 + t + 1
comment: $f=x^{3}+y^2+z^2$, with $\mu=2$; $\Delta_f(t)=\Phi_{3}(t)$.
$A_3$
1:
t^3 + t^2 + t + 1
comment: $f=x^{4}$, with $\mu=3$; $\Delta_f(t)=\Phi_{2}(t)\,\Phi_{4}(t)$.
$A_3$
2:
t^3 - t^2 + t - 1
comment: $f=x^{4}+y^2$, with $\mu=3$; $\Delta_f(t)=\Phi_{1}(t)\,\Phi_{4}(t)$.
$A_3$
3:
t^3 + t^2 + t + 1
comment: $f=x^{4}+y^2+z^2$, with $\mu=3$; $\Delta_f(t)=\Phi_{2}(t)\,\Phi_{4}(t)$.
$A_4$
1:
t^4 + t^3 + t^2 + t + 1
comment: $f=x^{5}$, with $\mu=4$; $\Delta_f(t)=\Phi_{5}(t)$.
$A_4$
2:
t^4 - t^3 + t^2 - t + 1
comment: $f=x^{5}+y^2$, with $\mu=4$; $\Delta_f(t)=\Phi_{10}(t)$.
$A_4$
3:
t^4 + t^3 + t^2 + t + 1
comment: $f=x^{5}+y^2+z^2$, with $\mu=4$; $\Delta_f(t)=\Phi_{5}(t)$.
$A_5$
1:
t^5 + t^4 + t^3 + t^2 + t + 1
comment: $f=x^{6}$, with $\mu=5$; $\Delta_f(t)=\Phi_{2}(t)\,\Phi_{3}(t)\,\Phi_{6}(t)$.
$A_5$
2:
t^5 - t^4 + t^3 - t^2 + t - 1
comment: $f=x^{6}+y^2$, with $\mu=5$; $\Delta_f(t)=\Phi_{1}(t)\,\Phi_{3}(t)\,\Phi_{6}(t)$.
$A_5$
3:
t^5 + t^4 + t^3 + t^2 + t + 1
comment: $f=x^{6}+y^2+z^2$, with $\mu=5$; $\Delta_f(t)=\Phi_{2}(t)\,\Phi_{3}(t)\,\Phi_{6}(t)$.
$A_6$
1:
t^6 + t^5 + t^4 + t^3 + t^2 + t + 1
comment: $f=x^{7}$, with $\mu=6$; $\Delta_f(t)=\Phi_{7}(t)$.
$A_6$
2:
t^6 - t^5 + t^4 - t^3 + t^2 - t + 1
comment: $f=x^{7}+y^2$, with $\mu=6$; $\Delta_f(t)=\Phi_{14}(t)$.
$A_6$
3:
t^6 + t^5 + t^4 + t^3 + t^2 + t + 1
comment: $f=x^{7}+y^2+z^2$, with $\mu=6$; $\Delta_f(t)=\Phi_{7}(t)$.
$A_7$
1:
t^7 + t^6 + t^5 + t^4 + t^3 + t^2 + t + 1
comment: $f=x^{8}$, with $\mu=7$; $\Delta_f(t)=\Phi_{2}(t)\,\Phi_{4}(t)\,\Phi_{8}(t)$.
$A_7$
2:
t^7 - t^6 + t^5 - t^4 + t^3 - t^2 + t - 1
comment: $f=x^{8}+y^2$, with $\mu=7$; $\Delta_f(t)=\Phi_{1}(t)\,\Phi_{4}(t)\,\Phi_{8}(t)$.
$A_7$
3:
t^7 + t^6 + t^5 + t^4 + t^3 + t^2 + t + 1
comment: $f=x^{8}+y^2+z^2$, with $\mu=7$; $\Delta_f(t)=\Phi_{2}(t)\,\Phi_{4}(t)\,\Phi_{8}(t)$.
$A_8$
1:
t^8 + t^7 + t^6 + t^5 + t^4 + t^3 + t^2 + t + 1
comment: $f=x^{9}$, with $\mu=8$; $\Delta_f(t)=\Phi_{3}(t)\,\Phi_{9}(t)$.
$A_8$
2:
t^8 - t^7 + t^6 - t^5 + t^4 - t^3 + t^2 - t + 1
comment: $f=x^{9}+y^2$, with $\mu=8$; $\Delta_f(t)=\Phi_{6}(t)\,\Phi_{18}(t)$.
$A_8$
3:
t^8 + t^7 + t^6 + t^5 + t^4 + t^3 + t^2 + t + 1
comment: $f=x^{9}+y^2+z^2$, with $\mu=8$; $\Delta_f(t)=\Phi_{3}(t)\,\Phi_{9}(t)$.
$A_9$
1:
t^9 + t^8 + t^7 + t^6 + t^5 + t^4 + t^3 + t^2 + t + 1
comment: $f=x^{10}$, with $\mu=9$; $\Delta_f(t)=\Phi_{2}(t)\,\Phi_{5}(t)\,\Phi_{10}(t)$.
$A_9$
2:
t^9 - t^8 + t^7 - t^6 + t^5 - t^4 + t^3 - t^2 + t - 1
comment: $f=x^{10}+y^2$, with $\mu=9$; $\Delta_f(t)=\Phi_{1}(t)\,\Phi_{5}(t)\,\Phi_{10}(t)$.
$A_9$
3:
t^9 + t^8 + t^7 + t^6 + t^5 + t^4 + t^3 + t^2 + t + 1
comment: $f=x^{10}+y^2+z^2$, with $\mu=9$; $\Delta_f(t)=\Phi_{2}(t)\,\Phi_{5}(t)\,\Phi_{10}(t)$.
$A_{10}$
1:
t^10 + t^9 + t^8 + t^7 + t^6 + t^5 + t^4 + t^3 + t^2 + t + 1
comment: $f=x^{11}$, with $\mu=10$; $\Delta_f(t)=\Phi_{11}(t)$.
$A_{10}$
2:
t^10 - t^9 + t^8 - t^7 + t^6 - t^5 + t^4 - t^3 + t^2 - t + 1
comment: $f=x^{11}+y^2$, with $\mu=10$; $\Delta_f(t)=\Phi_{22}(t)$.
$A_{10}$
3:
t^10 + t^9 + t^8 + t^7 + t^6 + t^5 + t^4 + t^3 + t^2 + t + 1
comment: $f=x^{11}+y^2+z^2$, with $\mu=10$; $\Delta_f(t)=\Phi_{11}(t)$.
$A_{11}$
1:
t^11 + t^10 + t^9 + t^8 + t^7 + t^6 + t^5 + t^4 + t^3 + t^2 + t + 1
comment: $f=x^{12}$, with $\mu=11$; $\Delta_f(t)=\Phi_{2}(t)\,\Phi_{3}(t)\,\Phi_{4}(t)\,\Phi_{6}(t)\,\Phi_{12}(t)$.
$A_{11}$
2:
t^11 - t^10 + t^9 - t^8 + t^7 - t^6 + t^5 - t^4 + t^3 - t^2 + t - 1
comment: $f=x^{12}+y^2$, with $\mu=11$; $\Delta_f(t)=\Phi_{1}(t)\,\Phi_{3}(t)\,\Phi_{4}(t)\,\Phi_{6}(t)\,\Phi_{12}(t)$.
$A_{11}$
3:
t^11 + t^10 + t^9 + t^8 + t^7 + t^6 + t^5 + t^4 + t^3 + t^2 + t + 1
comment: $f=x^{12}+y^2+z^2$, with $\mu=11$; $\Delta_f(t)=\Phi_{2}(t)\,\Phi_{3}(t)\,\Phi_{4}(t)\,\Phi_{6}(t)\,\Phi_{12}(t)$.
$A_{12}$
1:
t^12 + t^11 + t^10 + t^9 + t^8 + t^7 + t^6 + t^5 + t^4 + t^3 + t^2 + t + 1
comment: $f=x^{13}$, with $\mu=12$; $\Delta_f(t)=\Phi_{13}(t)$.
$A_{12}$
2:
t^12 - t^11 + t^10 - t^9 + t^8 - t^7 + t^6 - t^5 + t^4 - t^3 + t^2 - t + 1
comment: $f=x^{13}+y^2$, with $\mu=12$; $\Delta_f(t)=\Phi_{26}(t)$.
$A_{12}$
3:
t^12 + t^11 + t^10 + t^9 + t^8 + t^7 + t^6 + t^5 + t^4 + t^3 + t^2 + t + 1
comment: $f=x^{13}+y^2+z^2$, with $\mu=12$; $\Delta_f(t)=\Phi_{13}(t)$.
$D_4$
2:
t^4 - t^3 - t + 1
comment: $f=x^2y+y^{3}$, with $\mu=4$; $\Delta_f(t)=\Phi_{1}(t)^{2}\,\Phi_{3}(t)$.
$D_4$
3:
t^4 + t^3 + t + 1
comment: $f=x^2y+y^{3}+z^2$, with $\mu=4$; $\Delta_f(t)=\Phi_{2}(t)^{2}\,\Phi_{6}(t)$.
$D_5$
2:
t^5 - t^4 + t - 1
comment: $f=x^2y+y^{4}$, with $\mu=5$; $\Delta_f(t)=\Phi_{1}(t)\,\Phi_{8}(t)$.
$D_5$
3:
t^5 + t^4 + t + 1
comment: $f=x^2y+y^{4}+z^2$, with $\mu=5$; $\Delta_f(t)=\Phi_{2}(t)\,\Phi_{8}(t)$.
$D_6$
2:
t^6 - t^5 - t + 1
comment: $f=x^2y+y^{5}$, with $\mu=6$; $\Delta_f(t)=\Phi_{1}(t)^{2}\,\Phi_{5}(t)$.
$D_6$
3:
t^6 + t^5 + t + 1
comment: $f=x^2y+y^{5}+z^2$, with $\mu=6$; $\Delta_f(t)=\Phi_{2}(t)^{2}\,\Phi_{10}(t)$.
$D_7$
2:
t^7 - t^6 + t - 1
comment: $f=x^2y+y^{6}$, with $\mu=7$; $\Delta_f(t)=\Phi_{1}(t)\,\Phi_{4}(t)\,\Phi_{12}(t)$.
$D_7$
3:
t^7 + t^6 + t + 1
comment: $f=x^2y+y^{6}+z^2$, with $\mu=7$; $\Delta_f(t)=\Phi_{2}(t)\,\Phi_{4}(t)\,\Phi_{12}(t)$.
$D_8$
2:
t^8 - t^7 - t + 1
comment: $f=x^2y+y^{7}$, with $\mu=8$; $\Delta_f(t)=\Phi_{1}(t)^{2}\,\Phi_{7}(t)$.
$D_8$
3:
t^8 + t^7 + t + 1
comment: $f=x^2y+y^{7}+z^2$, with $\mu=8$; $\Delta_f(t)=\Phi_{2}(t)^{2}\,\Phi_{14}(t)$.
$D_9$
2:
t^9 - t^8 + t - 1
comment: $f=x^2y+y^{8}$, with $\mu=9$; $\Delta_f(t)=\Phi_{1}(t)\,\Phi_{16}(t)$.
$D_9$
3:
t^9 + t^8 + t + 1
comment: $f=x^2y+y^{8}+z^2$, with $\mu=9$; $\Delta_f(t)=\Phi_{2}(t)\,\Phi_{16}(t)$.
$D_{10}$
2:
t^10 - t^9 - t + 1
comment: $f=x^2y+y^{9}$, with $\mu=10$; $\Delta_f(t)=\Phi_{1}(t)^{2}\,\Phi_{3}(t)\,\Phi_{9}(t)$.
$D_{10}$
3:
t^10 + t^9 + t + 1
comment: $f=x^2y+y^{9}+z^2$, with $\mu=10$; $\Delta_f(t)=\Phi_{2}(t)^{2}\,\Phi_{6}(t)\,\Phi_{18}(t)$.
$D_{11}$
2:
t^11 - t^10 + t - 1
comment: $f=x^2y+y^{10}$, with $\mu=11$; $\Delta_f(t)=\Phi_{1}(t)\,\Phi_{4}(t)\,\Phi_{20}(t)$.
$D_{11}$
3:
t^11 + t^10 + t + 1
comment: $f=x^2y+y^{10}+z^2$, with $\mu=11$; $\Delta_f(t)=\Phi_{2}(t)\,\Phi_{4}(t)\,\Phi_{20}(t)$.
$D_{12}$
2:
t^12 - t^11 - t + 1
comment: $f=x^2y+y^{11}$, with $\mu=12$; $\Delta_f(t)=\Phi_{1}(t)^{2}\,\Phi_{11}(t)$.
$D_{12}$
3:
t^12 + t^11 + t + 1
comment: $f=x^2y+y^{11}+z^2$, with $\mu=12$; $\Delta_f(t)=\Phi_{2}(t)^{2}\,\Phi_{22}(t)$.
$E_6$
2:
t^6 - t^5 + t^3 - t + 1
comment: $f=x^3+y^4$, with $\mu=6$; $\Delta_f(t)=\Phi_{6}(t)\,\Phi_{12}(t)$.
$E_6$
3:
t^6 + t^5 - t^3 + t + 1
comment: $f=x^3+y^4+z^2$, with $\mu=6$; $\Delta_f(t)=\Phi_{3}(t)\,\Phi_{12}(t)$.
$E_7$
2:
t^7 - t^6 + t^4 - t^3 + t - 1
comment: $f=x^3+xy^3$, with $\mu=7$; $\Delta_f(t)=\Phi_{1}(t)\,\Phi_{9}(t)$.
$E_7$
3:
t^7 + t^6 - t^4 - t^3 + t + 1
comment: $f=x^3+xy^3+z^2$, with $\mu=7$; $\Delta_f(t)=\Phi_{2}(t)\,\Phi_{18}(t)$.
$E_8$
2:
t^8 - t^7 + t^5 - t^4 + t^3 - t + 1
comment: $f=x^3+y^5$, with $\mu=8$; $\Delta_f(t)=\Phi_{15}(t)$.
$E_8$
3:
t^8 + t^7 - t^5 - t^4 - t^3 + t + 1
comment: $f=x^3+y^5+z^2$, with $\mu=8$; $\Delta_f(t)=\Phi_{30}(t)$.
$P_8$
3:
t^8 + t^7 + t^6 - 2*t^5 - 2*t^4 - 2*t^3 + t^2 + t + 1
comment: $f=x^3+y^3+z^3$, with $\mu=8$; $\Delta_f(t)=\Phi_{1}(t)^{2}\,\Phi_{3}(t)^{3}$.
$P_8$
4:
t^8 - t^7 + t^6 + 2*t^5 - 2*t^4 + 2*t^3 + t^2 - t + 1
comment: $f=x^3+y^3+z^3+w^2$, with $\mu=8$; $\Delta_f(t)=\Phi_{2}(t)^{2}\,\Phi_{6}(t)^{3}$.
$X_9$
2:
t^9 - t^8 - 2*t^5 + 2*t^4 + t - 1
comment: $f=x^4+y^4$, with $\mu=9$; $\Delta_f(t)=\Phi_{1}(t)^{3}\,\Phi_{2}(t)^{2}\,\Phi_{4}(t)^{2}$.
$X_9$
3:
t^9 + t^8 - 2*t^5 - 2*t^4 + t + 1
comment: $f=x^4+y^4+z^2$, with $\mu=9$; $\Delta_f(t)=\Phi_{1}(t)^{2}\,\Phi_{2}(t)^{3}\,\Phi_{4}(t)^{2}$.
$J_{10}$
2:
t^10 - t^9 + t^7 - t^6 - t^4 + t^3 - t + 1
comment: $f=x^3+y^6$, with $\mu=10$; $\Delta_f(t)=\Phi_{1}(t)^{2}\,\Phi_{2}(t)^{2}\,\Phi_{3}(t)\,\Phi_{6}(t)^{2}$.
$J_{10}$
3:
t^10 + t^9 - t^7 - t^6 - t^4 - t^3 + t + 1
comment: $f=x^3+y^6+z^2$, with $\mu=10$; $\Delta_f(t)=\Phi_{1}(t)^{2}\,\Phi_{2}(t)^{2}\,\Phi_{3}(t)^{2}\,\Phi_{6}(t)$.
$E_{12}$
2:
t^12 - t^11 + t^9 - t^8 + t^6 - t^4 + t^3 - t + 1
comment: $f=x^3+y^7$, with $\mu=12$; $\Delta_f(t)=\Phi_{21}(t)$.
$E_{12}$
3:
t^12 + t^11 - t^9 - t^8 + t^6 - t^4 - t^3 + t + 1
comment: $f=x^3+y^7+z^2$, with $\mu=12$; $\Delta_f(t)=\Phi_{42}(t)$.
$E_{13}$
2:
t^13 - t^12 + t^10 - t^9 + t^7 - t^6 + t^4 - t^3 + t - 1
comment: $f=x^3+xy^5$, with $\mu=13$; $\Delta_f(t)=\Phi_{1}(t)\,\Phi_{5}(t)\,\Phi_{15}(t)$.
$E_{13}$
3:
t^13 + t^12 - t^10 - t^9 + t^7 + t^6 - t^4 - t^3 + t + 1
comment: $f=x^3+xy^5+z^2$, with $\mu=13$; $\Delta_f(t)=\Phi_{2}(t)\,\Phi_{10}(t)\,\Phi_{30}(t)$.
$E_{14}$
2:
t^14 - t^13 + t^11 - t^10 + t^8 - t^7 + t^6 - t^4 + t^3 - t + 1
comment: $f=x^3+y^8$, with $\mu=14$; $\Delta_f(t)=\Phi_{6}(t)\,\Phi_{12}(t)\,\Phi_{24}(t)$.
$E_{14}$
3:
t^14 + t^13 - t^11 - t^10 + t^8 + t^7 + t^6 - t^4 - t^3 + t + 1
comment: $f=x^3+y^8+z^2$, with $\mu=14$; $\Delta_f(t)=\Phi_{3}(t)\,\Phi_{12}(t)\,\Phi_{24}(t)$.
$Z_{11}$
2:
t^11 - t^10 + t^6 - t^5 + t - 1
comment: $f=x^3y+y^5$, with $\mu=11$; $\Delta_f(t)=\Phi_{1}(t)\,\Phi_{3}(t)\,\Phi_{15}(t)$.
$Z_{11}$
3:
t^11 + t^10 - t^6 - t^5 + t + 1
comment: $f=x^3y+y^5+z^2$, with $\mu=11$; $\Delta_f(t)=\Phi_{2}(t)\,\Phi_{6}(t)\,\Phi_{30}(t)$.
$Z_{12}$
2:
t^12 - t^11 - t + 1
comment: $f=x^3y+xy^4$, with $\mu=12$; $\Delta_f(t)=\Phi_{1}(t)^{2}\,\Phi_{11}(t)$.
$Z_{12}$
3:
t^12 + t^11 + t + 1
comment: $f=x^3y+xy^4+z^2$, with $\mu=12$; $\Delta_f(t)=\Phi_{2}(t)^{2}\,\Phi_{22}(t)$.
$Z_{13}$
2:
t^13 - t^12 + t^7 - t^6 + t - 1
comment: $f=x^3y+y^6$, with $\mu=13$; $\Delta_f(t)=\Phi_{1}(t)\,\Phi_{9}(t)\,\Phi_{18}(t)$.
$Z_{13}$
3:
t^13 + t^12 + t^7 + t^6 + t + 1
comment: $f=x^3y+y^6+z^2$, with $\mu=13$; $\Delta_f(t)=\Phi_{2}(t)\,\Phi_{9}(t)\,\Phi_{18}(t)$.
$W_{12}$
2:
t^12 - t^11 + t^8 - t^6 + t^4 - t + 1
comment: $f=x^4+y^5$, with $\mu=12$; $\Delta_f(t)=\Phi_{10}(t)\,\Phi_{20}(t)$.
$W_{12}$
3:
t^12 + t^11 + t^8 - t^6 + t^4 + t + 1
comment: $f=x^4+y^5+z^2$, with $\mu=12$; $\Delta_f(t)=\Phi_{5}(t)\,\Phi_{20}(t)$.
$W_{13}$
2:
t^13 - t^12 + t^9 - t^8 + t^5 - t^4 + t - 1
comment: $f=x^4+xy^4$, with $\mu=13$; $\Delta_f(t)=\Phi_{1}(t)\,\Phi_{8}(t)\,\Phi_{16}(t)$.
$W_{13}$
3:
t^13 + t^12 + t^9 + t^8 + t^5 + t^4 + t + 1
comment: $f=x^4+xy^4+z^2$, with $\mu=13$; $\Delta_f(t)=\Phi_{2}(t)\,\Phi_{8}(t)\,\Phi_{16}(t)$.
$Q_{10}$
3:
t^10 + t^9 + t^8 - t^6 - t^5 - t^4 + t^2 + t + 1
comment: $f=x^3+y^4+yz^2$, with $\mu=10$; $\Delta_f(t)=\Phi_{3}(t)\,\Phi_{24}(t)$.
$Q_{10}$
4:
t^10 - t^9 + t^8 - t^6 + t^5 - t^4 + t^2 - t + 1
comment: $f=x^3+y^4+yz^2+w^2$, with $\mu=10$; $\Delta_f(t)=\Phi_{6}(t)\,\Phi_{24}(t)$.
$Q_{11}$
3:
t^11 + t^10 + t^9 + t^2 + t + 1
comment: $f=x^3+y^2z+xz^3$, with $\mu=11$; $\Delta_f(t)=\Phi_{2}(t)\,\Phi_{3}(t)\,\Phi_{6}(t)\,\Phi_{18}(t)$.
$Q_{11}$
4:
t^11 - t^10 + t^9 - t^2 + t - 1
comment: $f=x^3+y^2z+xz^3+w^2$, with $\mu=11$; $\Delta_f(t)=\Phi_{1}(t)\,\Phi_{3}(t)\,\Phi_{6}(t)\,\Phi_{9}(t)$.
$Q_{12}$
3:
t^12 + t^11 + t^10 + t^7 + t^6 + t^5 + t^2 + t + 1
comment: $f=x^3+y^5+yz^2$, with $\mu=12$; $\Delta_f(t)=\Phi_{3}(t)^{2}\,\Phi_{15}(t)$.
$Q_{12}$
4:
t^12 - t^11 + t^10 - t^7 + t^6 - t^5 + t^2 - t + 1
comment: $f=x^3+y^5+yz^2+w^2$, with $\mu=12$; $\Delta_f(t)=\Phi_{6}(t)^{2}\,\Phi_{30}(t)$.
$S_{11}$
3:
t^11 + t^10 + t^9 + t^8 + t^3 + t^2 + t + 1
comment: $f=x^4+y^2z+xz^2$, with $\mu=11$; $\Delta_f(t)=\Phi_{2}(t)\,\Phi_{4}(t)\,\Phi_{16}(t)$.
$S_{11}$
4:
t^11 - t^10 + t^9 - t^8 + t^3 - t^2 + t - 1
comment: $f=x^4+y^2z+xz^2+w^2$, with $\mu=11$; $\Delta_f(t)=\Phi_{1}(t)\,\Phi_{4}(t)\,\Phi_{16}(t)$.
$S_{12}$
3:
t^12 + t^11 + t^10 + t^9 + t^8 + t^7 + t^6 + t^5 + t^4 + t^3 + t^2 + t + 1
comment: $f=x^2y+y^2z+xz^3$, with $\mu=12$; $\Delta_f(t)=\Phi_{13}(t)$.
$S_{12}$
4:
t^12 - t^11 + t^10 - t^9 + t^8 - t^7 + t^6 - t^5 + t^4 - t^3 + t^2 - t + 1
comment: $f=x^2y+y^2z+xz^3+w^2$, with $\mu=12$; $\Delta_f(t)=\Phi_{26}(t)$.
$U_{12}$
3:
t^12 + t^11 + t^10 + 2*t^9 + t^8 + t^7 + 2*t^6 + t^5 + t^4 + 2*t^3 + t^2 + t + 1
comment: $f=x^3+y^3+z^4$, with $\mu=12$; $\Delta_f(t)=\Phi_{2}(t)^{2}\,\Phi_{4}(t)^{2}\,\Phi_{6}(t)\,\Phi_{12}(t)$.
$U_{12}$
4:
t^12 - t^11 + t^10 - 2*t^9 + t^8 - t^7 + 2*t^6 - t^5 + t^4 - 2*t^3 + t^2 - t + 1
comment: $f=x^3+y^3+z^4+w^2$, with $\mu=12$; $\Delta_f(t)=\Phi_{1}(t)^{2}\,\Phi_{3}(t)\,\Phi_{4}(t)^{2}\,\Phi_{12}(t)$.
$A_{13}$
1:
t^13 + t^12 + t^11 + t^10 + t^9 + t^8 + t^7 + t^6 + t^5 + t^4 + t^3 + t^2 + t + 1
comment: $f=x^{14}$, with $\mu=13$; $\Delta_f(t)=\Phi_{2}(t)\,\Phi_{7}(t)\,\Phi_{14}(t)$.
$A_{13}$
2:
t^13 - t^12 + t^11 - t^10 + t^9 - t^8 + t^7 - t^6 + t^5 - t^4 + t^3 - t^2 + t - 1
comment: $f=x^{14}+y^2$, with $\mu=13$; $\Delta_f(t)=\Phi_{1}(t)\,\Phi_{7}(t)\,\Phi_{14}(t)$.
$A_{13}$
3:
t^13 + t^12 + t^11 + t^10 + t^9 + t^8 + t^7 + t^6 + t^5 + t^4 + t^3 + t^2 + t + 1
comment: $f=x^{14}+y^2+z^2$, with $\mu=13$; $\Delta_f(t)=\Phi_{2}(t)\,\Phi_{7}(t)\,\Phi_{14}(t)$.
$A_{14}$
1:
t^14 + t^13 + t^12 + t^11 + t^10 + t^9 + t^8 + t^7 + t^6 + t^5 + t^4 + t^3 + t^2 + t + 1
comment: $f=x^{15}$, with $\mu=14$; $\Delta_f(t)=\Phi_{3}(t)\,\Phi_{5}(t)\,\Phi_{15}(t)$.
$A_{14}$
2:
t^14 - t^13 + t^12 - t^11 + t^10 - t^9 + t^8 - t^7 + t^6 - t^5 + t^4 - t^3 + t^2 - t + 1
comment: $f=x^{15}+y^2$, with $\mu=14$; $\Delta_f(t)=\Phi_{6}(t)\,\Phi_{10}(t)\,\Phi_{30}(t)$.
$A_{14}$
3:
t^14 + t^13 + t^12 + t^11 + t^10 + t^9 + t^8 + t^7 + t^6 + t^5 + t^4 + t^3 + t^2 + t + 1
comment: $f=x^{15}+y^2+z^2$, with $\mu=14$; $\Delta_f(t)=\Phi_{3}(t)\,\Phi_{5}(t)\,\Phi_{15}(t)$.
$D_{13}$
2:
t^13 - t^12 + t - 1
comment: $f=x^2y+y^{12}$, with $\mu=13$; $\Delta_f(t)=\Phi_{1}(t)\,\Phi_{8}(t)\,\Phi_{24}(t)$.
$D_{13}$
3:
t^13 + t^12 + t + 1
comment: $f=x^2y+y^{12}+z^2$, with $\mu=13$; $\Delta_f(t)=\Phi_{2}(t)\,\Phi_{8}(t)\,\Phi_{24}(t)$.
$D_{14}$
2:
t^14 - t^13 - t + 1
comment: $f=x^2y+y^{13}$, with $\mu=14$; $\Delta_f(t)=\Phi_{1}(t)^{2}\,\Phi_{13}(t)$.
$D_{14}$
3:
t^14 + t^13 + t + 1
comment: $f=x^2y+y^{13}+z^2$, with $\mu=14$; $\Delta_f(t)=\Phi_{2}(t)^{2}\,\Phi_{26}(t)$.
$T_{2,3,7}$
2:
t^11 - t^10 + t^8 - t^7 + t^4 - t^3 + t - 1
comment: $f=x^{3}+y^{7}+a x^2y^2$ with generic $a$ and $\mu=11$; $\Delta_f(t)=\Phi_{1}(t)\,\Phi_{2}(t)^{2}\,\Phi_{6}(t)\,\Phi_{14}(t)$.
$T_{2,3,7}$
3:
t^11 + t^10 - t^8 - t^7 - t^4 - t^3 + t + 1
comment: $f=x^{3}+y^{7}+a x^2y^2+z^2$ with generic $a$ and $\mu=11$; $\Delta_f(t)=\Phi_{1}(t)^{2}\,\Phi_{2}(t)\,\Phi_{3}(t)\,\Phi_{7}(t)$.
$T_{2,3,8}$
2:
t^12 - t^11 + t^9 - t^8 - t^4 + t^3 - t + 1
comment: $f=x^{3}+y^{8}+a x^2y^2$ with generic $a$ and $\mu=12$; $\Delta_f(t)=\Phi_{1}(t)^{2}\,\Phi_{2}(t)^{2}\,\Phi_{4}(t)\,\Phi_{6}(t)\,\Phi_{8}(t)$.
$T_{2,3,8}$
3:
t^12 + t^11 - t^9 - t^8 - t^4 - t^3 + t + 1
comment: $f=x^{3}+y^{8}+a x^2y^2+z^2$ with generic $a$ and $\mu=12$; $\Delta_f(t)=\Phi_{1}(t)^{2}\,\Phi_{2}(t)^{2}\,\Phi_{3}(t)\,\Phi_{4}(t)\,\Phi_{8}(t)$.
$T_{2,3,9}$
2:
t^13 - t^12 + t^10 - t^9 + t^4 - t^3 + t - 1
comment: $f=x^{3}+y^{9}+a x^2y^2$ with generic $a$ and $\mu=13$; $\Delta_f(t)=\Phi_{1}(t)\,\Phi_{2}(t)^{2}\,\Phi_{6}(t)^{2}\,\Phi_{18}(t)$.
$T_{2,3,9}$
3:
t^13 + t^12 - t^10 - t^9 - t^4 - t^3 + t + 1
comment: $f=x^{3}+y^{9}+a x^2y^2+z^2$ with generic $a$ and $\mu=13$; $\Delta_f(t)=\Phi_{1}(t)^{2}\,\Phi_{2}(t)\,\Phi_{3}(t)^{2}\,\Phi_{9}(t)$.
$T_{2,3,10}$
2:
t^14 - t^13 + t^11 - t^10 - t^4 + t^3 - t + 1
comment: $f=x^{3}+y^{10}+a x^2y^2$ with generic $a$ and $\mu=14$; $\Delta_f(t)=\Phi_{1}(t)^{2}\,\Phi_{2}(t)^{2}\,\Phi_{5}(t)\,\Phi_{6}(t)\,\Phi_{10}(t)$.
$T_{2,3,10}$
3:
t^14 + t^13 - t^11 - t^10 - t^4 - t^3 + t + 1
comment: $f=x^{3}+y^{10}+a x^2y^2+z^2$ with generic $a$ and $\mu=14$; $\Delta_f(t)=\Phi_{1}(t)^{2}\,\Phi_{2}(t)^{2}\,\Phi_{3}(t)\,\Phi_{5}(t)\,\Phi_{10}(t)$.
$T_{2,4,5}$
2:
t^10 - t^9 - t^6 + 2*t^5 - t^4 - t + 1
comment: $f=x^{4}+y^{5}+a x^2y^2$ with generic $a$ and $\mu=10$; $\Delta_f(t)=\Phi_{1}(t)^{2}\,\Phi_{2}(t)^{2}\,\Phi_{4}(t)\,\Phi_{10}(t)$.
$T_{2,4,5}$
3:
t^10 + t^9 - t^6 - 2*t^5 - t^4 + t + 1
comment: $f=x^{4}+y^{5}+a x^2y^2+z^2$ with generic $a$ and $\mu=10$; $\Delta_f(t)=\Phi_{1}(t)^{2}\,\Phi_{2}(t)^{2}\,\Phi_{4}(t)\,\Phi_{5}(t)$.
$T_{2,4,6}$
2:
t^11 - t^10 - t^7 + t^6 - t^5 + t^4 + t - 1
comment: $f=x^{4}+y^{6}+a x^2y^2$ with generic $a$ and $\mu=11$; $\Delta_f(t)=\Phi_{1}(t)^{3}\,\Phi_{2}(t)^{2}\,\Phi_{3}(t)\,\Phi_{4}(t)\,\Phi_{6}(t)$.
$T_{2,4,6}$
3:
t^11 + t^10 - t^7 - t^6 - t^5 - t^4 + t + 1
comment: $f=x^{4}+y^{6}+a x^2y^2+z^2$ with generic $a$ and $\mu=11$; $\Delta_f(t)=\Phi_{1}(t)^{2}\,\Phi_{2}(t)^{3}\,\Phi_{3}(t)\,\Phi_{4}(t)\,\Phi_{6}(t)$.
$T_{2,4,7}$
2:
t^12 - t^11 - t^8 + t^7 + t^5 - t^4 - t + 1
comment: $f=x^{4}+y^{7}+a x^2y^2$ with generic $a$ and $\mu=12$; $\Delta_f(t)=\Phi_{1}(t)^{2}\,\Phi_{2}(t)^{2}\,\Phi_{4}(t)\,\Phi_{14}(t)$.
$T_{2,4,7}$
3:
t^12 + t^11 - t^8 - t^7 - t^5 - t^4 + t + 1
comment: $f=x^{4}+y^{7}+a x^2y^2+z^2$ with generic $a$ and $\mu=12$; $\Delta_f(t)=\Phi_{1}(t)^{2}\,\Phi_{2}(t)^{2}\,\Phi_{4}(t)\,\Phi_{7}(t)$.
$T_{2,4,8}$
2:
t^13 - t^12 - t^9 + t^8 - t^5 + t^4 + t - 1
comment: $f=x^{4}+y^{8}+a x^2y^2$ with generic $a$ and $\mu=13$; $\Delta_f(t)=\Phi_{1}(t)^{3}\,\Phi_{2}(t)^{2}\,\Phi_{4}(t)^{2}\,\Phi_{8}(t)$.
$T_{2,4,8}$
3:
t^13 + t^12 - t^9 - t^8 - t^5 - t^4 + t + 1
comment: $f=x^{4}+y^{8}+a x^2y^2+z^2$ with generic $a$ and $\mu=13$; $\Delta_f(t)=\Phi_{1}(t)^{2}\,\Phi_{2}(t)^{3}\,\Phi_{4}(t)^{2}\,\Phi_{8}(t)$.
$T_{2,4,9}$
2:
t^14 - t^13 - t^10 + t^9 + t^5 - t^4 - t + 1
comment: $f=x^{4}+y^{9}+a x^2y^2$ with generic $a$ and $\mu=14$; $\Delta_f(t)=\Phi_{1}(t)^{2}\,\Phi_{2}(t)^{2}\,\Phi_{4}(t)\,\Phi_{6}(t)\,\Phi_{18}(t)$.
$T_{2,4,9}$
3:
t^14 + t^13 - t^10 - t^9 - t^5 - t^4 + t + 1
comment: $f=x^{4}+y^{9}+a x^2y^2+z^2$ with generic $a$ and $\mu=14$; $\Delta_f(t)=\Phi_{1}(t)^{2}\,\Phi_{2}(t)^{2}\,\Phi_{3}(t)\,\Phi_{4}(t)\,\Phi_{9}(t)$.
$T_{2,5,5}$
2:
t^11 - t^10 + 2*t^6 - 2*t^5 + t - 1
comment: $f=x^{5}+y^{5}+a x^2y^2$ with generic $a$ and $\mu=11$; $\Delta_f(t)=\Phi_{1}(t)\,\Phi_{2}(t)^{2}\,\Phi_{10}(t)^{2}$.
$T_{2,5,5}$
3:
t^11 + t^10 - 2*t^6 - 2*t^5 + t + 1
comment: $f=x^{5}+y^{5}+a x^2y^2+z^2$ with generic $a$ and $\mu=11$; $\Delta_f(t)=\Phi_{1}(t)^{2}\,\Phi_{2}(t)\,\Phi_{5}(t)^{2}$.
$T_{2,5,6}$
2:
t^12 - t^11 + t^7 - 2*t^6 + t^5 - t + 1
comment: $f=x^{5}+y^{6}+a x^2y^2$ with generic $a$ and $\mu=12$; $\Delta_f(t)=\Phi_{1}(t)^{2}\,\Phi_{2}(t)^{2}\,\Phi_{3}(t)\,\Phi_{6}(t)\,\Phi_{10}(t)$.
$T_{2,5,6}$
3:
t^12 + t^11 - t^7 - 2*t^6 - t^5 + t + 1
comment: $f=x^{5}+y^{6}+a x^2y^2+z^2$ with generic $a$ and $\mu=12$; $\Delta_f(t)=\Phi_{1}(t)^{2}\,\Phi_{2}(t)^{2}\,\Phi_{3}(t)\,\Phi_{5}(t)\,\Phi_{6}(t)$.
$T_{2,5,7}$
2:
t^13 - t^12 + t^8 - t^7 + t^6 - t^5 + t - 1
comment: $f=x^{5}+y^{7}+a x^2y^2$ with generic $a$ and $\mu=13$; $\Delta_f(t)=\Phi_{1}(t)\,\Phi_{2}(t)^{2}\,\Phi_{10}(t)\,\Phi_{14}(t)$.
$T_{2,5,7}$
3:
t^13 + t^12 - t^8 - t^7 - t^6 - t^5 + t + 1
comment: $f=x^{5}+y^{7}+a x^2y^2+z^2$ with generic $a$ and $\mu=13$; $\Delta_f(t)=\Phi_{1}(t)^{2}\,\Phi_{2}(t)\,\Phi_{5}(t)\,\Phi_{7}(t)$.
$T_{2,5,8}$
2:
t^14 - t^13 + t^9 - t^8 - t^6 + t^5 - t + 1
comment: $f=x^{5}+y^{8}+a x^2y^2$ with generic $a$ and $\mu=14$; $\Delta_f(t)=\Phi_{1}(t)^{2}\,\Phi_{2}(t)^{2}\,\Phi_{4}(t)\,\Phi_{8}(t)\,\Phi_{10}(t)$.
$T_{2,5,8}$
3:
t^14 + t^13 - t^9 - t^8 - t^6 - t^5 + t + 1
comment: $f=x^{5}+y^{8}+a x^2y^2+z^2$ with generic $a$ and $\mu=14$; $\Delta_f(t)=\Phi_{1}(t)^{2}\,\Phi_{2}(t)^{2}\,\Phi_{4}(t)\,\Phi_{5}(t)\,\Phi_{8}(t)$.
$T_{2,6,6}$
2:
t^13 - t^12 - 2*t^7 + 2*t^6 + t - 1
comment: $f=x^{6}+y^{6}+a x^2y^2$ with generic $a$ and $\mu=13$; $\Delta_f(t)=\Phi_{1}(t)^{3}\,\Phi_{2}(t)^{2}\,\Phi_{3}(t)^{2}\,\Phi_{6}(t)^{2}$.
$T_{2,6,6}$
3:
t^13 + t^12 - 2*t^7 - 2*t^6 + t + 1
comment: $f=x^{6}+y^{6}+a x^2y^2+z^2$ with generic $a$ and $\mu=13$; $\Delta_f(t)=\Phi_{1}(t)^{2}\,\Phi_{2}(t)^{3}\,\Phi_{3}(t)^{2}\,\Phi_{6}(t)^{2}$.
$T_{2,6,7}$
2:
t^14 - t^13 - t^8 + 2*t^7 - t^6 - t + 1
comment: $f=x^{6}+y^{7}+a x^2y^2$ with generic $a$ and $\mu=14$; $\Delta_f(t)=\Phi_{1}(t)^{2}\,\Phi_{2}(t)^{2}\,\Phi_{3}(t)\,\Phi_{6}(t)\,\Phi_{14}(t)$.
$T_{2,6,7}$
3:
t^14 + t^13 - t^8 - 2*t^7 - t^6 + t + 1
comment: $f=x^{6}+y^{7}+a x^2y^2+z^2$ with generic $a$ and $\mu=14$; $\Delta_f(t)=\Phi_{1}(t)^{2}\,\Phi_{2}(t)^{2}\,\Phi_{3}(t)\,\Phi_{6}(t)\,\Phi_{7}(t)$.
$T_{3,3,4}$
3:
t^9 + t^8 + t^7 - t^6 - 2*t^5 - 2*t^4 - t^3 + t^2 + t + 1
comment: $f=x^{3}+y^{3}+z^{4}+axyz$ with generic $a$ and $\mu=9$; $\Delta_f(t)=\Phi_{1}(t)^{2}\,\Phi_{2}(t)\,\Phi_{3}(t)^{2}\,\Phi_{4}(t)$.
$T_{3,3,4}$
4:
t^9 - t^8 + t^7 + t^6 - 2*t^5 + 2*t^4 - t^3 - t^2 + t - 1
comment: $f=x^{3}+y^{3}+z^{4}+axyz+w^2$ with generic $a$ and $\mu=9$; $\Delta_f(t)=\Phi_{1}(t)\,\Phi_{2}(t)^{2}\,\Phi_{4}(t)\,\Phi_{6}(t)^{2}$.
$T_{3,3,5}$
3:
t^10 + t^9 + t^8 - t^7 - t^6 - 2*t^5 - t^4 - t^3 + t^2 + t + 1
comment: $f=x^{3}+y^{3}+z^{5}+axyz$ with generic $a$ and $\mu=10$; $\Delta_f(t)=\Phi_{1}(t)^{2}\,\Phi_{3}(t)^{2}\,\Phi_{5}(t)$.
$T_{3,3,5}$
4:
t^10 - t^9 + t^8 + t^7 - t^6 + 2*t^5 - t^4 + t^3 + t^2 - t + 1
comment: $f=x^{3}+y^{3}+z^{5}+axyz+w^2$ with generic $a$ and $\mu=10$; $\Delta_f(t)=\Phi_{2}(t)^{2}\,\Phi_{6}(t)^{2}\,\Phi_{10}(t)$.
$T_{3,3,6}$
3:
t^11 + t^10 + t^9 - t^8 - t^7 - t^6 - t^5 - t^4 - t^3 + t^2 + t + 1
comment: $f=x^{3}+y^{3}+z^{6}+axyz$ with generic $a$ and $\mu=11$; $\Delta_f(t)=\Phi_{1}(t)^{2}\,\Phi_{2}(t)\,\Phi_{3}(t)^{3}\,\Phi_{6}(t)$.
$T_{3,3,6}$
4:
t^11 - t^10 + t^9 + t^8 - t^7 + t^6 - t^5 + t^4 - t^3 - t^2 + t - 1
comment: $f=x^{3}+y^{3}+z^{6}+axyz+w^2$ with generic $a$ and $\mu=11$; $\Delta_f(t)=\Phi_{1}(t)\,\Phi_{2}(t)^{2}\,\Phi_{3}(t)\,\Phi_{6}(t)^{3}$.
$T_{3,3,7}$
3:
t^12 + t^11 + t^10 - t^9 - t^8 - t^7 - t^5 - t^4 - t^3 + t^2 + t + 1
comment: $f=x^{3}+y^{3}+z^{7}+axyz$ with generic $a$ and $\mu=12$; $\Delta_f(t)=\Phi_{1}(t)^{2}\,\Phi_{3}(t)^{2}\,\Phi_{7}(t)$.
$T_{3,3,7}$
4:
t^12 - t^11 + t^10 + t^9 - t^8 + t^7 + t^5 - t^4 + t^3 + t^2 - t + 1
comment: $f=x^{3}+y^{3}+z^{7}+axyz+w^2$ with generic $a$ and $\mu=12$; $\Delta_f(t)=\Phi_{2}(t)^{2}\,\Phi_{6}(t)^{2}\,\Phi_{14}(t)$.
$T_{3,3,8}$
3:
t^13 + t^12 + t^11 - t^10 - t^9 - t^8 - t^5 - t^4 - t^3 + t^2 + t + 1
comment: $f=x^{3}+y^{3}+z^{8}+axyz$ with generic $a$ and $\mu=13$; $\Delta_f(t)=\Phi_{1}(t)^{2}\,\Phi_{2}(t)\,\Phi_{3}(t)^{2}\,\Phi_{4}(t)\,\Phi_{8}(t)$.
$T_{3,3,8}$
4:
t^13 - t^12 + t^11 + t^10 - t^9 + t^8 - t^5 + t^4 - t^3 - t^2 + t - 1
comment: $f=x^{3}+y^{3}+z^{8}+axyz+w^2$ with generic $a$ and $\mu=13$; $\Delta_f(t)=\Phi_{1}(t)\,\Phi_{2}(t)^{2}\,\Phi_{4}(t)\,\Phi_{6}(t)^{2}\,\Phi_{8}(t)$.
$T_{3,3,9}$
3:
t^14 + t^13 + t^12 - t^11 - t^10 - t^9 - t^5 - t^4 - t^3 + t^2 + t + 1
comment: $f=x^{3}+y^{3}+z^{9}+axyz$ with generic $a$ and $\mu=14$; $\Delta_f(t)=\Phi_{1}(t)^{2}\,\Phi_{3}(t)^{3}\,\Phi_{9}(t)$.
$T_{3,3,9}$
4:
t^14 - t^13 + t^12 + t^11 - t^10 + t^9 + t^5 - t^4 + t^3 + t^2 - t + 1
comment: $f=x^{3}+y^{3}+z^{9}+axyz+w^2$ with generic $a$ and $\mu=14$; $\Delta_f(t)=\Phi_{2}(t)^{2}\,\Phi_{6}(t)^{3}\,\Phi_{18}(t)$.
$T_{3,4,4}$
3:
t^10 + t^9 + t^8 - 2*t^6 - 2*t^5 - 2*t^4 + t^2 + t + 1
comment: $f=x^{3}+y^{4}+z^{4}+axyz$ with generic $a$ and $\mu=10$; $\Delta_f(t)=\Phi_{1}(t)^{2}\,\Phi_{2}(t)^{2}\,\Phi_{3}(t)\,\Phi_{4}(t)^{2}$.
$T_{3,4,4}$
4:
t^10 - t^9 + t^8 - 2*t^6 + 2*t^5 - 2*t^4 + t^2 - t + 1
comment: $f=x^{3}+y^{4}+z^{4}+axyz+w^2$ with generic $a$ and $\mu=10$; $\Delta_f(t)=\Phi_{1}(t)^{2}\,\Phi_{2}(t)^{2}\,\Phi_{4}(t)^{2}\,\Phi_{6}(t)$.
$T_{3,4,5}$
3:
t^11 + t^10 + t^9 - t^7 - 2*t^6 - 2*t^5 - t^4 + t^2 + t + 1
comment: $f=x^{3}+y^{4}+z^{5}+axyz$ with generic $a$ and $\mu=11$; $\Delta_f(t)=\Phi_{1}(t)^{2}\,\Phi_{2}(t)\,\Phi_{3}(t)\,\Phi_{4}(t)\,\Phi_{5}(t)$.
$T_{3,4,5}$
4:
t^11 - t^10 + t^9 - t^7 + 2*t^6 - 2*t^5 + t^4 - t^2 + t - 1
comment: $f=x^{3}+y^{4}+z^{5}+axyz+w^2$ with generic $a$ and $\mu=11$; $\Delta_f(t)=\Phi_{1}(t)\,\Phi_{2}(t)^{2}\,\Phi_{4}(t)\,\Phi_{6}(t)\,\Phi_{10}(t)$.
$T_{3,4,6}$
3:
t^12 + t^11 + t^10 - t^8 - t^7 - 2*t^6 - t^5 - t^4 + t^2 + t + 1
comment: $f=x^{3}+y^{4}+z^{6}+axyz$ with generic $a$ and $\mu=12$; $\Delta_f(t)=\Phi_{1}(t)^{2}\,\Phi_{2}(t)^{2}\,\Phi_{3}(t)^{2}\,\Phi_{4}(t)\,\Phi_{6}(t)$.
$T_{3,4,6}$
4:
t^12 - t^11 + t^10 - t^8 + t^7 - 2*t^6 + t^5 - t^4 + t^2 - t + 1
comment: $f=x^{3}+y^{4}+z^{6}+axyz+w^2$ with generic $a$ and $\mu=12$; $\Delta_f(t)=\Phi_{1}(t)^{2}\,\Phi_{2}(t)^{2}\,\Phi_{3}(t)\,\Phi_{4}(t)\,\Phi_{6}(t)^{2}$.
$T_{3,4,7}$
3:
t^13 + t^12 + t^11 - t^9 - t^8 - t^7 - t^6 - t^5 - t^4 + t^2 + t + 1
comment: $f=x^{3}+y^{4}+z^{7}+axyz$ with generic $a$ and $\mu=13$; $\Delta_f(t)=\Phi_{1}(t)^{2}\,\Phi_{2}(t)\,\Phi_{3}(t)\,\Phi_{4}(t)\,\Phi_{7}(t)$.
$T_{3,4,7}$
4:
t^13 - t^12 + t^11 - t^9 + t^8 - t^7 + t^6 - t^5 + t^4 - t^2 + t - 1
comment: $f=x^{3}+y^{4}+z^{7}+axyz+w^2$ with generic $a$ and $\mu=13$; $\Delta_f(t)=\Phi_{1}(t)\,\Phi_{2}(t)^{2}\,\Phi_{4}(t)\,\Phi_{6}(t)\,\Phi_{14}(t)$.
$T_{3,4,8}$
3:
t^14 + t^13 + t^12 - t^10 - t^9 - t^8 - t^6 - t^5 - t^4 + t^2 + t + 1
comment: $f=x^{3}+y^{4}+z^{8}+axyz$ with generic $a$ and $\mu=14$; $\Delta_f(t)=\Phi_{1}(t)^{2}\,\Phi_{2}(t)^{2}\,\Phi_{3}(t)\,\Phi_{4}(t)^{2}\,\Phi_{8}(t)$.
$T_{3,4,8}$
4:
t^14 - t^13 + t^12 - t^10 + t^9 - t^8 - t^6 + t^5 - t^4 + t^2 - t + 1
comment: $f=x^{3}+y^{4}+z^{8}+axyz+w^2$ with generic $a$ and $\mu=14$; $\Delta_f(t)=\Phi_{1}(t)^{2}\,\Phi_{2}(t)^{2}\,\Phi_{4}(t)^{2}\,\Phi_{6}(t)\,\Phi_{8}(t)$.
$T_{3,5,5}$
3:
t^12 + t^11 + t^10 - 2*t^7 - 2*t^6 - 2*t^5 + t^2 + t + 1
comment: $f=x^{3}+y^{5}+z^{5}+axyz$ with generic $a$ and $\mu=12$; $\Delta_f(t)=\Phi_{1}(t)^{2}\,\Phi_{3}(t)\,\Phi_{5}(t)^{2}$.
$T_{3,5,5}$
4:
t^12 - t^11 + t^10 + 2*t^7 - 2*t^6 + 2*t^5 + t^2 - t + 1
comment: $f=x^{3}+y^{5}+z^{5}+axyz+w^2$ with generic $a$ and $\mu=12$; $\Delta_f(t)=\Phi_{2}(t)^{2}\,\Phi_{6}(t)\,\Phi_{10}(t)^{2}$.
$T_{3,5,6}$
3:
t^13 + t^12 + t^11 - t^8 - 2*t^7 - 2*t^6 - t^5 + t^2 + t + 1
comment: $f=x^{3}+y^{5}+z^{6}+axyz$ with generic $a$ and $\mu=13$; $\Delta_f(t)=\Phi_{1}(t)^{2}\,\Phi_{2}(t)\,\Phi_{3}(t)^{2}\,\Phi_{5}(t)\,\Phi_{6}(t)$.
$T_{3,5,6}$
4:
t^13 - t^12 + t^11 + t^8 - 2*t^7 + 2*t^6 - t^5 - t^2 + t - 1
comment: $f=x^{3}+y^{5}+z^{6}+axyz+w^2$ with generic $a$ and $\mu=13$; $\Delta_f(t)=\Phi_{1}(t)\,\Phi_{2}(t)^{2}\,\Phi_{3}(t)\,\Phi_{6}(t)^{2}\,\Phi_{10}(t)$.
$T_{3,5,7}$
3:
t^14 + t^13 + t^12 - t^9 - t^8 - 2*t^7 - t^6 - t^5 + t^2 + t + 1
comment: $f=x^{3}+y^{5}+z^{7}+axyz$ with generic $a$ and $\mu=14$; $\Delta_f(t)=\Phi_{1}(t)^{2}\,\Phi_{3}(t)\,\Phi_{5}(t)\,\Phi_{7}(t)$.
$T_{3,5,7}$
4:
t^14 - t^13 + t^12 + t^9 - t^8 + 2*t^7 - t^6 + t^5 + t^2 - t + 1
comment: $f=x^{3}+y^{5}+z^{7}+axyz+w^2$ with generic $a$ and $\mu=14$; $\Delta_f(t)=\Phi_{2}(t)^{2}\,\Phi_{6}(t)\,\Phi_{10}(t)\,\Phi_{14}(t)$.
$T_{3,6,6}$
3:
t^14 + t^13 + t^12 - 2*t^8 - 2*t^7 - 2*t^6 + t^2 + t + 1
comment: $f=x^{3}+y^{6}+z^{6}+axyz$ with generic $a$ and $\mu=14$; $\Delta_f(t)=\Phi_{1}(t)^{2}\,\Phi_{2}(t)^{2}\,\Phi_{3}(t)^{3}\,\Phi_{6}(t)^{2}$.
$T_{3,6,6}$
4:
t^14 - t^13 + t^12 - 2*t^8 + 2*t^7 - 2*t^6 + t^2 - t + 1
comment: $f=x^{3}+y^{6}+z^{6}+axyz+w^2$ with generic $a$ and $\mu=14$; $\Delta_f(t)=\Phi_{1}(t)^{2}\,\Phi_{2}(t)^{2}\,\Phi_{3}(t)^{2}\,\Phi_{6}(t)^{3}$.
$T_{4,4,4}$
3:
t^11 + t^10 + t^9 + t^8 - 2*t^7 - 2*t^6 - 2*t^5 - 2*t^4 + t^3 + t^2 + t + 1
comment: $f=x^{4}+y^{4}+z^{4}+axyz$ with generic $a$ and $\mu=11$; $\Delta_f(t)=\Phi_{1}(t)^{2}\,\Phi_{2}(t)^{3}\,\Phi_{4}(t)^{3}$.
$T_{4,4,4}$
4:
t^11 - t^10 + t^9 - t^8 - 2*t^7 + 2*t^6 - 2*t^5 + 2*t^4 + t^3 - t^2 + t - 1
comment: $f=x^{4}+y^{4}+z^{4}+axyz+w^2$ with generic $a$ and $\mu=11$; $\Delta_f(t)=\Phi_{1}(t)^{3}\,\Phi_{2}(t)^{2}\,\Phi_{4}(t)^{3}$.
$T_{4,4,5}$
3:
t^12 + t^11 + t^10 + t^9 - t^8 - 2*t^7 - 2*t^6 - 2*t^5 - t^4 + t^3 + t^2 + t + 1
comment: $f=x^{4}+y^{4}+z^{5}+axyz$ with generic $a$ and $\mu=12$; $\Delta_f(t)=\Phi_{1}(t)^{2}\,\Phi_{2}(t)^{2}\,\Phi_{4}(t)^{2}\,\Phi_{5}(t)$.
$T_{4,4,5}$
4:
t^12 - t^11 + t^10 - t^9 - t^8 + 2*t^7 - 2*t^6 + 2*t^5 - t^4 - t^3 + t^2 - t + 1
comment: $f=x^{4}+y^{4}+z^{5}+axyz+w^2$ with generic $a$ and $\mu=12$; $\Delta_f(t)=\Phi_{1}(t)^{2}\,\Phi_{2}(t)^{2}\,\Phi_{4}(t)^{2}\,\Phi_{10}(t)$.
$T_{4,4,6}$
3:
t^13 + t^12 + t^11 + t^10 - t^9 - t^8 - 2*t^7 - 2*t^6 - t^5 - t^4 + t^3 + t^2 + t + 1
comment: $f=x^{4}+y^{4}+z^{6}+axyz$ with generic $a$ and $\mu=13$; $\Delta_f(t)=\Phi_{1}(t)^{2}\,\Phi_{2}(t)^{3}\,\Phi_{3}(t)\,\Phi_{4}(t)^{2}\,\Phi_{6}(t)$.
$T_{4,4,6}$
4:
t^13 - t^12 + t^11 - t^10 - t^9 + t^8 - 2*t^7 + 2*t^6 - t^5 + t^4 + t^3 - t^2 + t - 1
comment: $f=x^{4}+y^{4}+z^{6}+axyz+w^2$ with generic $a$ and $\mu=13$; $\Delta_f(t)=\Phi_{1}(t)^{3}\,\Phi_{2}(t)^{2}\,\Phi_{3}(t)\,\Phi_{4}(t)^{2}\,\Phi_{6}(t)$.
$T_{4,4,7}$
3:
t^14 + t^13 + t^12 + t^11 - t^10 - t^9 - t^8 - 2*t^7 - t^6 - t^5 - t^4 + t^3 + t^2 + t + 1
comment: $f=x^{4}+y^{4}+z^{7}+axyz$ with generic $a$ and $\mu=14$; $\Delta_f(t)=\Phi_{1}(t)^{2}\,\Phi_{2}(t)^{2}\,\Phi_{4}(t)^{2}\,\Phi_{7}(t)$.
$T_{4,4,7}$
4:
t^14 - t^13 + t^12 - t^11 - t^10 + t^9 - t^8 + 2*t^7 - t^6 + t^5 - t^4 - t^3 + t^2 - t + 1
comment: $f=x^{4}+y^{4}+z^{7}+axyz+w^2$ with generic $a$ and $\mu=14$; $\Delta_f(t)=\Phi_{1}(t)^{2}\,\Phi_{2}(t)^{2}\,\Phi_{4}(t)^{2}\,\Phi_{14}(t)$.
$T_{4,5,5}$
3:
t^13 + t^12 + t^11 + t^10 - 2*t^8 - 2*t^7 - 2*t^6 - 2*t^5 + t^3 + t^2 + t + 1
comment: $f=x^{4}+y^{5}+z^{5}+axyz$ with generic $a$ and $\mu=13$; $\Delta_f(t)=\Phi_{1}(t)^{2}\,\Phi_{2}(t)\,\Phi_{4}(t)\,\Phi_{5}(t)^{2}$.
$T_{4,5,5}$
4:
t^13 - t^12 + t^11 - t^10 + 2*t^8 - 2*t^7 + 2*t^6 - 2*t^5 + t^3 - t^2 + t - 1
comment: $f=x^{4}+y^{5}+z^{5}+axyz+w^2$ with generic $a$ and $\mu=13$; $\Delta_f(t)=\Phi_{1}(t)\,\Phi_{2}(t)^{2}\,\Phi_{4}(t)\,\Phi_{10}(t)^{2}$.
$T_{4,5,6}$
3:
t^14 + t^13 + t^12 + t^11 - t^9 - 2*t^8 - 2*t^7 - 2*t^6 - t^5 + t^3 + t^2 + t + 1
comment: $f=x^{4}+y^{5}+z^{6}+axyz$ with generic $a$ and $\mu=14$; $\Delta_f(t)=\Phi_{1}(t)^{2}\,\Phi_{2}(t)^{2}\,\Phi_{3}(t)\,\Phi_{4}(t)\,\Phi_{5}(t)\,\Phi_{6}(t)$.
$T_{4,5,6}$
4:
t^14 - t^13 + t^12 - t^11 + t^9 - 2*t^8 + 2*t^7 - 2*t^6 + t^5 - t^3 + t^2 - t + 1
comment: $f=x^{4}+y^{5}+z^{6}+axyz+w^2$ with generic $a$ and $\mu=14$; $\Delta_f(t)=\Phi_{1}(t)^{2}\,\Phi_{2}(t)^{2}\,\Phi_{3}(t)\,\Phi_{4}(t)\,\Phi_{6}(t)\,\Phi_{10}(t)$.
$T_{5,5,5}$
3:
t^14 + t^13 + t^12 + t^11 + t^10 - 2*t^9 - 2*t^8 - 2*t^7 - 2*t^6 - 2*t^5 + t^4 + t^3 + t^2 + t + 1
comment: $f=x^{5}+y^{5}+z^{5}+axyz$ with generic $a$ and $\mu=14$; $\Delta_f(t)=\Phi_{1}(t)^{2}\,\Phi_{5}(t)^{3}$.
$T_{5,5,5}$
4:
t^14 - t^13 + t^12 - t^11 + t^10 + 2*t^9 - 2*t^8 + 2*t^7 - 2*t^6 + 2*t^5 + t^4 - t^3 + t^2 - t + 1
comment: $f=x^{5}+y^{5}+z^{5}+axyz+w^2$ with generic $a$ and $\mu=14$; $\Delta_f(t)=\Phi_{2}(t)^{2}\,\Phi_{10}(t)^{3}$.
Definition
$\Delta_f(t)=\det(tI-h_*)\in\mathbb{Z}[t]$ is the characteristic polynomial of the geometric monodromy transformation $h_*$ on the reduced middle homology $\tilde H_{n-1}$ of the Milnor fibre [2] of $f+x_{c+1}^2+\cdots+x_n^2$. Here $c$ is the corank. For the simple, parabolic and exceptional labels, $f$ is the normal form in $c$ variables $x,y,z$ from Arnold's classification [1], with the modulus set to $0$ for the parabolic and exceptional unimodal families. For the hyperbolic family $T_{p,q,r}$, $f$ is the generic member of the family. The normal forms are $A_k:x^{k+1}$; $D_k:x^2y+y^{k-1}$; $E_6:x^3+y^4$; $E_7:x^3+xy^3$; $E_8:x^3+y^5$; $P_8:x^3+y^3+z^3$; $X_9:x^4+y^4$; $J_{10}:x^3+y^6$; $E_{12}:x^3+y^7$; $E_{13}:x^3+xy^5$; $E_{14}:x^3+y^8$; $Z_{11}:x^3y+y^5$; $Z_{12}:x^3y+xy^4$; $Z_{13}:x^3y+y^6$; $W_{12}:x^4+y^5$; $W_{13}:x^4+xy^4$; $Q_{10}:x^3+y^4+yz^2$; $Q_{11}:x^3+y^2z+xz^3$; $Q_{12}:x^3+y^5+yz^2$; $S_{11}:x^4+y^2z+xz^2$; $S_{12}:x^2y+y^2z+xz^3$; $U_{12}:x^3+y^3+z^4$; and $T_{p,q,r}:x^p+y^q+z^r+axyz$ for $1/p+1/q+1/r<1$, with the $p=2$ rows written in the split corank-$2$ form $x^q+y^r+ax^2y^2$.
Parameters
singularity
—   singularity ($A_k$ with $k\geq1$, $D_k$ with $k\geq4$, one of $E_6,E_7,E_8$, one of Arnold's parabolic or exceptional unimodal labels $P_8,X_9,J_{10},E_{12},E_{13},E_{14},Z_{11},Z_{12},Z_{13},W_{12},W_{13},Q_{10},Q_{11},Q_{12},S_{11},S_{12},U_{12}$, or $T_{p,q,r}$ with $2\leq p\leq q\leq r$ and $1/p+1/q+1/r<1$)
$n$
—   number of variables (the number of variables, at least the corank of the singularity)
Formulas
(1)
If $f$ has weighted degree $1$ with weights $w_i$, and $x^a$ runs through a monomial basis of the Milnor algebra $\mathbb{C}[x_1,\ldots,x_c]/(\partial f)$, then the eigenvalues are $\exp\left(-2\pi i\left(\sum_iw_i+\sum_ia_iw_i+\frac{n-c}{2}\right)\right)$, each with multiplicity. The product of $t$ minus these eigenvalues is $\Delta_f(t)$.
(2)
If $\mu$ is the Milnor number, then $\Delta_{f+u^2}(t)=(-1)^\mu\Delta_f(-t)$.
(3)
For the three-variable hyperbolic member $T_{p,q,r}$, $\Delta_{T_{p,q,r}}(t)=(t-1)^2\frac{t^p-1}{t-1}\frac{t^q-1}{t-1}\frac{t^r-1}{t-1}$; the other parity of $n$ follows from the suspension formula.
Comments
(4)
$\mu$ is the Milnor number $\dim_{\mathbb{C}}\mathbb{C}[x_1,\ldots,x_c]/(\partial f)$. The degree of $\Delta_f(t)$ is $\mu$, and $\Phi_k(t)$ is the $k$th cyclotomic polynomial.
References
[1]
V. I. Arnold, S. M. Gusein-Zade and A. N. Varchenko, Singularities of Differentiable Maps, Volume I, Birkhauser, 1985.
[2]
John Milnor, Singular Points of Complex Hypersurfaces, Annals of Mathematics Studies 61, Princeton University Press, 1968.
Links
Similar tables
Bernstein-Sato polynomials of the simple and unimodal singularities —   Malgrange-Kashiwara theory gives the set of monodromy eigenvalues from the roots of the Bernstein-Sato polynomial, without their multiplicities
Poincaré polynomials of the finite Coxeter groups —   for the ADE rows with $n=3$, the monodromy eigenvalues are the eigenvalues of a Coxeter element of the corresponding finite Coxeter group
Alexander polynomials of the prime knots with at most ten crossings —   for an irreducible plane curve singularity ($n=2$), the monodromy polynomial is the Alexander polynomial of its link, a torus knot $T(p,q)$ for $x^p+y^q$: $A_2$, $A_4$, $A_6$, $A_8$, $E_6$ and $E_8$ are the knots $3_1$, $5_1$, $7_1$, $9_1$, $8_{19}$ and $10_{124}$
Data properties
Entries are of type: integral polynomial
How well the digits are known: exact
Table is complete: no (it holds every simple or unimodal singularity with Milnor number $\mu\leq14$: $A_k$ and $D_k$ for $k\leq14$, $E_6,E_7,E_8$, the parabolic $P_8,X_9,J_{10}$, all fourteen exceptional unimodal singularities, and the hyperbolic $T_{p,q,r}$ with $1/p+1/q+1/r<1$ and $p+q+r\leq15$; for each singularity it includes rows representing both parities of $n$, and the suspension formula gives every other $n$)
How they were obtained:

For the weighted-homogeneous rows, the generator computes the rational monodromy exponents from the weights and a monomial basis of the Milnor algebra, forms the product over the corresponding roots of unity exactly in cyclotomic factors, checks that each root order occurs in complete Galois orbits, and returns the expanded polynomial in $\mathbb{Z}[t]$.

more

For the hyperbolic $T_{p,q,r}$ rows, it uses the closed form in the Formulas section and applies the suspension formula to change the parity of $n$. Every row agreed with Singular's spectrum from gmssing.lib after the control $x^2+y^3$, whose monodromy polynomial is $t^2-t+1$; the checks also verify the suspension identity on stored rows and compare the ADE rows with $n=3$ against the Coxeter exponents.



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