// time = 1.68 seconds

data[526]:=[*
<526, 1, 2, [ 1, -1 ], 0, [
<2, x^2 + 2*x + 1>,
<3, x^2 - 8>,
<5, x^2 - 6*x + 7>,
<7, x^2 - 4*x - 4>,
<11, x^2>,
<13, x^2 + 4*x + 4>,
<17, x^2 - 6*x + 9>,
<19, x^2 - 4*x - 28>
]>,
<526, 2, 4, [ 1, 1 ], 1, [
<2, x^4 + 4*x^3 + 6*x^2 + 4*x + 1>,
<3, x^4 - x^3 - 4*x^2 + 2*x + 3>,
<5, x^4 + 5*x^3 + 4*x^2 - 8*x - 9>,
<7, x^4 + x^3 - 12*x^2 + 12*x + 1>,
<11, x^4 + 8*x^3 + 11*x^2 - 42*x - 89>,
<13, x^4 - 6*x^2 - x + 7>,
<17, x^4 + 9*x^3 + 18*x^2 - 22*x - 59>,
<19, x^4 + 6*x^3 - 21*x^2 - 106*x + 93>
]>,
<526, 3, 4, [ -1, -1 ], 1, [
<2, x^4 - 4*x^3 + 6*x^2 - 4*x + 1>,
<3, x^4 + 5*x^3 + 6*x^2 - 1>,
<5, x^4 + 7*x^3 + 10*x^2 - 16*x - 31>,
<7, x^4 + 5*x^3 - 10*x^2 - 50*x - 25>,
<11, x^4 + 8*x^3 - 5*x^2 - 154*x - 281>,
<13, x^4 + 12*x^3 + 48*x^2 + 77*x + 41>,
<17, x^4 + 5*x^3 - 26*x^2 - 50*x + 149>,
<19, x^4 + 12*x^3 + 13*x^2 - 268*x - 779>
]>,
<526, 4, 5, [ 1, -1 ], 0, [
<2, x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1>,
<3, x^5 + 3*x^4 - 4*x^3 - 10*x^2 + 7*x + 4>,
<5, x^5 - x^4 - 12*x^3 + 12*x^2 + 21*x - 8>,
<7, x^5 + 7*x^4 - 90*x^2 - 181*x - 56>,
<11, x^5 - 8*x^4 - 9*x^3 + 166*x^2 - 209*x - 92>,
<13, x^5 - 2*x^4 - 54*x^3 + 67*x^2 + 561*x + 394>,
<17, x^5 - 9*x^4 - 32*x^3 + 466*x^2 - 823*x - 1042>,
<19, x^5 + 2*x^4 - 33*x^3 - 72*x^2 - 13*x + 2>
]>,
<526, 5, 6, [ -1, 1 ], 0, [
<2, x^6 - 6*x^5 + 15*x^4 - 20*x^3 + 15*x^2 - 6*x + 1>,
<3, x^6 - 3*x^5 - 6*x^4 + 20*x^3 + 3*x^2 - 32*x + 16>,
<5, x^6 - 5*x^5 + x^4 + 21*x^3 - 11*x^2 - 22*x - 1>,
<7, x^6 - 5*x^5 - 2*x^4 + 24*x^3 - 19*x^2 - 4*x + 4>,
<11, x^6 - 4*x^5 - 9*x^4 + 50*x^3 - 17*x^2 - 96*x + 64>,
<13, x^6 - 36*x^4 - 27*x^3 + 309*x^2 + 376*x - 124>,
<17, x^6 - x^5 - 39*x^4 + 67*x^3 + 367*x^2 - 932*x + 421>,
<19, x^6 - 6*x^5 - 19*x^4 + 80*x^3 - 17*x^2 - 104*x + 64>
]>
*];