/* Data is in the following format
   Note, if the class group has not been computed, it, the class number, the fundamental units, regulator and whether grh was assumed are all 0.
[polynomial,
degree,
t-number of Galois group,
signature [r,s],
discriminant,
list of ramifying primes,
integral basis as polynomials in a,
1 if it is a cm field otherwise 0,
class number,
class group structure,
1 if grh was assumed and 0 if not,
fundamental units,
regulator,
list of subfields each as a pair [polynomial, number of subfields isomorphic to one defined by this polynomial]
]
*/

[x^31 - 4*x - 4, 31, 12, [1, 15], -17443590486413448385781876351835033630345588173537542144, [2, 29161973, 14898732471895043, 37391233052164359356929], [1, a, a^2, a^3, a^4, a^5, a^6, a^7, a^8, a^9, a^10, a^11, a^12, a^13, a^14, a^15, 1/2*a^16, 1/2*a^17, 1/2*a^18, 1/2*a^19, 1/2*a^20, 1/2*a^21, 1/2*a^22, 1/2*a^23, 1/2*a^24, 1/2*a^25, 1/2*a^26, 1/2*a^27, 1/2*a^28, 1/2*a^29, 1/2*a^30], 0, 1, [], 1, [ (1)/(2)*a^(30) - (1)/(2)*a^(29) + (1)/(2)*a^(28) - (1)/(2)*a^(27) + (1)/(2)*a^(26) - (1)/(2)*a^(25) + (1)/(2)*a^(24) - (1)/(2)*a^(23) + (1)/(2)*a^(22) - (1)/(2)*a^(21) + (1)/(2)*a^(20) - (1)/(2)*a^(19) + (1)/(2)*a^(18) - (1)/(2)*a^(17) + (1)/(2)*a^(16) - 1 , (1)/(2)*a^(30) - (1)/(2)*a^(29) + (1)/(2)*a^(28) - (1)/(2)*a^(27) + (1)/(2)*a^(26) - (1)/(2)*a^(25) + (1)/(2)*a^(24) - (1)/(2)*a^(23) + (1)/(2)*a^(22) - (1)/(2)*a^(21) + (1)/(2)*a^(20) - (1)/(2)*a^(19) + (1)/(2)*a^(18) - (1)/(2)*a^(17) + (1)/(2)*a^(16) - 3 , (1)/(2)*a^(16) + a^(8) + 1 , a^(30) - a^(29) + a^(28) - a^(27) + a^(26) - a^(25) + (1)/(2)*a^(24) - (1)/(2)*a^(23) + (1)/(2)*a^(22) - (1)/(2)*a^(21) + (1)/(2)*a^(20) - (1)/(2)*a^(19) - 5 , (1)/(2)*a^(21) - a - 1 , (1)/(2)*a^(28) + (1)/(2)*a^(24) - (1)/(2)*a^(21) + (1)/(2)*a^(20) - a^(17) - a^(13) - a^(12) - a^(9) - a^(8) + a^(6) - a^(5) - a^(4) + 2*a^(2) + a - 1 , (1)/(2)*a^(30) - (1)/(2)*a^(29) + (1)/(2)*a^(28) - (1)/(2)*a^(27) + (1)/(2)*a^(26) + (1)/(2)*a^(24) + (1)/(2)*a^(23) + (1)/(2)*a^(21) - (1)/(2)*a^(20) + (1)/(2)*a^(19) + (1)/(2)*a^(17) + (1)/(2)*a^(16) - a^(13) - a^(12) - a^(11) - a^(10) - a^(8) - 2*a^(6) - a^(5) - 2*a^(4) - a^(3) - 1 , a^(28) + a^(26) + (1)/(2)*a^(24) - (1)/(2)*a^(22) - a^(20) - (1)/(2)*a^(19) - a^(18) - (1)/(2)*a^(17) - (1)/(2)*a^(16) + a^(14) + a^(13) + 2*a^(12) + a^(11) + 2*a^(10) - 2*a^(6) - a^(5) - 3*a^(4) - 2*a^(3) - 3*a^(2) - 2*a + 1 , (7)/(2)*a^(30) - (5)/(2)*a^(29) + 2*a^(28) - (5)/(2)*a^(27) + (5)/(2)*a^(26) - 2*a^(25) + a^(24) - (3)/(2)*a^(23) + 2*a^(22) - a^(21) + (1)/(2)*a^(20) - (1)/(2)*a^(19) + (3)/(2)*a^(18) - a^(17) - a^(16) + a^(14) - a^(13) - a^(12) + 2*a^(11) + a^(10) - a^(9) - a^(8) + 2*a^(7) - a^(6) - 2*a^(5) - a^(4) + 3*a^(3) - a^(2) - a - 13 , (1)/(2)*a^(30) + a^(28) - a^(27) + (1)/(2)*a^(26) - a^(25) + a^(24) - (3)/(2)*a^(23) + a^(22) - (1)/(2)*a^(21) + 2*a^(20) - a^(19) + (1)/(2)*a^(18) - (3)/(2)*a^(17) + (3)/(2)*a^(16) - a^(15) + a^(14) - a^(13) + 2*a^(12) - a^(11) - a^(10) - 3*a^(9) + a^(8) + a^(7) + 2*a^(6) - a^(5) + a^(4) - 3*a - 3 , (11)/(2)*a^(30) - (7)/(2)*a^(29) + a^(28) + a^(27) - (3)/(2)*a^(26) - a^(25) + 5*a^(24) - 8*a^(23) + (17)/(2)*a^(22) - (13)/(2)*a^(21) + 4*a^(20) - a^(19) - 2*a^(18) + 4*a^(17) - (5)/(2)*a^(16) - 2*a^(15) + 7*a^(14) - 10*a^(13) + 8*a^(12) - 4*a^(11) + 3*a^(9) - 6*a^(8) + 7*a^(7) - 3*a^(6) - 4*a^(5) + 11*a^(4) - 11*a^(3) + 6*a^(2) - 27 , (1)/(2)*a^(30) - (1)/(2)*a^(29) + (1)/(2)*a^(27) + (1)/(2)*a^(26) - a^(25) + (1)/(2)*a^(24) + a^(23) - (3)/(2)*a^(21) + (1)/(2)*a^(19) - a^(18) - (1)/(2)*a^(17) + (3)/(2)*a^(16) + a^(15) - a^(14) - a^(13) + a^(12) - a^(10) + 2*a^(8) + a^(7) - a^(6) + a^(4) - a^(3) - 4*a^(2) - a + 1 , a^(30) - (3)/(2)*a^(29) + (3)/(2)*a^(28) - a^(27) + a^(26) - (1)/(2)*a^(24) + (3)/(2)*a^(23) - 2*a^(22) + a^(21) - (1)/(2)*a^(20) - (3)/(2)*a^(19) + (3)/(2)*a^(18) - a^(17) + a^(16) + a^(15) + a^(13) - 2*a^(12) + a^(11) - 3*a^(10) + a^(8) - a^(7) + 3*a^(6) + a^(5) - 4*a - 3 , (1)/(2)*a^(30) - a^(29) + (1)/(2)*a^(28) - (1)/(2)*a^(27) + a^(26) + (1)/(2)*a^(25) + a^(24) - a^(22) - (1)/(2)*a^(21) - (3)/(2)*a^(20) + (1)/(2)*a^(19) + a^(17) + a^(15) + a^(13) - a^(11) - 2*a^(10) - 2*a^(9) + a^(7) + 4*a^(6) + 2*a^(5) + a^(4) - a^(3) - 2*a^(2) - 2*a - 3 , 2*a^(30) - 3*a^(29) + (3)/(2)*a^(28) + (1)/(2)*a^(27) - (5)/(2)*a^(26) + (5)/(2)*a^(25) - (3)/(2)*a^(24) - (5)/(2)*a^(23) + (7)/(2)*a^(22) - 3*a^(21) - a^(20) + (5)/(2)*a^(19) - 4*a^(18) + 2*a^(17) + (3)/(2)*a^(16) - 5*a^(15) + 4*a^(14) - 4*a^(12) + 4*a^(11) - 4*a^(10) - 2*a^(9) + 5*a^(8) - 8*a^(7) + 3*a^(5) - 7*a^(4) + 4*a^(3) - a^(2) - 7*a + 1 ], 2698409433385651.0, []]