Irrationalities and their p-modular reductions

Common Irrationalities in Characteristic 31

C1  =  X + 28
C2  =  X2 + 29X + 3
C4  =  X4 + 3X2 + 16X + 3
C5  =  X5 + 7X + 28


ξ f Cn
b5 18 C1
b5∗ 12 C1
b7 20X + 26 C2
b7∗∗ 11X + 4 C2
b11 21 C1
b11∗∗ 9 C1
b13 14X + 1 C2
b13∗ 17X + 29 C2
b15 13 C1
b15∗∗ 17 C1
b17 26X + 20 C2
b17∗ 5X + 10 C2
b21 3X + 12 C2
b21∗ 28X + 18 C2
b23 23 C1
b23∗∗ 7 C1
b27 14 C1
b27∗∗ 16 C1
b33 19 C1
b33∗ 11 C1
b37 10X + 5 C2
b37∗ 21X + 25 C2
b39 X + 14 C2
b39∗∗ 30X + 16 C2
b95 16X + 30 C2
b95∗∗ 15X C2
c19 19 C1
c19∗2 15 C1
c19∗4 27 C1
c37 9 C1
c37∗2 29 C1
c37∗3 23 C1
i 4X + 27 C2
i2 30X + 1 C2
i3 20 C1
i5 24X + 7 C2
i6 26 C1
i7 9X + 22 C2
i11 12 C1
i14 21X + 10 C2
i15 27 C1
i19 26X + 5 C2
i26 25 C1
i35 23X + 8 C2
k56 26 C1
k56∗3 5 C1
k56∗5 18 C1
k56∗15 13 C1
r2 23 C1
r3 13X + 18 C2
r5 6 C1
r6 20X + 11 C2
r7 10 C1
r10 14 C1
r17 21X + 10 C2
s51 23X3 + 25X2 + 11X + 27 C4
s51∗5 27X3 + 16X2 + 29X + 15 C4
s51∗11 7X3 + 22X2 + 8X + 1 C4
s51∗19 5X3 + 30X2 + 14X + 20 C4
u63 23X + 11 C2
u63∗5 2X + 30 C2
u63∗11 10X + 17 C2
u63∗13 21X + 6 C2
u63∗23 29X + 3 C2
u63∗31 8X + 26 C2
w25 20X4 + 28X3 + 24X2 + X + 19 C5
w25∗2 10X4 + 14X3 + 26X2 + 22X + 25 C5
w25∗3 18X4 + 4X3 + 19X2 + 22X + 14 C5
w25∗6 4X4 + 19X3 + 3X2 + 12X + 10 C5
w25∗9 10X4 + 28X3 + 21X2 + 5X + 25 C5
w41 2X4 + 14X3 + 30X2 + 19 C5
w41∗2 13X4 + X3 + 26X2 + 3X C5
w41∗3 10X4 + 29X3 + 8X2 + X + 17 C5
w41∗4 X4 + 20X3 + 14X2 + 26X + 1 C5
w41∗6 4X4 + 20X3 + 9X2 + 14X + 2 C5
w41∗7 4X4 + 28X3 + 23X2 + 2 C5
w41∗8 18X4 + 29X3 + 28X + 28 C5
w41∗11 3X4 + 6X3 + 25X2 + 19X + 15 C5
w41∗12 10X4 + 10X3 + 28X2 + 28X + 17 C5
w41∗16 28X4 + 29X3 + 23X2 + 5X + 22 C5
y11 5X4 + 30X3 + 2X2 + 27X + 3 C5
y11∗2 22X4 + 30X3 + 6X2 + 6X + 30 C5
y11∗3 9X4 + 10X3 + 4X2 + 13 C5
y11∗4 2X4 + 5X3 + 21X2 + 11X + 11 C5
y11∗5 24X4 + 18X3 + 29X2 + 18X + 4 C5
y15 16 C1
y15∗2 6 C1
y15∗4 3 C1
y15∗7 7 C1
y16 26 C1
y16∗3 14 C1
y16∗5 17 C1
y16∗7 5 C1
y20 6X + 25 C2
y20∗3 15X + 16 C2
y20∗7 16X + 15 C2
y20∗9 25X + 6 C2
y32 20 C1
y32∗3 4 C1
y32∗5 22 C1
y32∗7 10 C1
y32∗9 21 C1
y32∗11 9 C1
y32∗13 27 C1
y32∗15 11 C1
y33 14X3 + 17X2 + 10X + 4 C5
y33∗2 11X4 + 18X3 + 11X2 + 2X + 16 C5
y33∗4 8X4 + 9X3 + 15X + 24 C5
y33∗5 17X4 + 30X3 + 19X2 + 17X + 17 C5
y33∗7 30X4 + 4X3 + 2X2 + 29X + 3 C5
y33∗8 20X4 + 19X3 + 28X2 + 27X + 23 C5
y33∗10 29X4 + 12X3 + 24X2 + 10X + 16 C5
y33∗13 11X4 + 3X3 + 16X2 + 29X + 2 C5
y33∗14 6X4 + 13X3 + X2 + 8X + 5 C5
y33∗16 23X4 + 2X3 + 6X2 + 8X + 15 C5
y60 7X + 24 C2
y60∗7 27X + 4 C2
y60∗11 23X + 8 C2
y60∗13 10X + 21 C2
y60∗17 21X + 10 C2
y60∗19 8X + 23 C2
y60∗23 4X + 27 C2
y60∗29 24X + 7 C2
y64 19X + 12 C2
y64∗3 20X + 11 C2
y64∗5 9X + 22 C2
y64∗7 5X + 26 C2
y64∗9 29X + 2 C2
y64∗11 17X + 14 C2
y64∗13 X + 30 C2
y64∗15 3X + 28 C2
y64∗17 28X + 3 C2
y64∗19 30X + 1 C2
y64∗21 14X + 17 C2
y64∗23 2X + 29 C2
y64∗25 26X + 5 C2
y64∗27 22X + 9 C2
y64∗29 11X + 20 C2
y64∗31 12X + 19 C2
y'24 10X + 3 C2
y'24∗7 21X + 23 C2
y'24∗13 21X + 28 C2
y'24∗19 10X + 8 C2
z3 25 C1
z3∗∗ 5 C1




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