/* 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^16 - 2*x^15 - 5*x^14 + 14*x^13 + 20*x^12 - 29*x^11 - 123*x^10 + 77*x^9 + 285*x^8 - 230*x^7 - 80*x^6 + 103*x^5 - 157*x^4 + 177*x^3 - 24*x^2 - 25*x - 1, 16, 388, [8, 4], 28749978312375390625, [5, 29, 101], [1, a, a^2, a^3, a^4, a^5, a^6, a^7, a^8, a^9, a^10, a^11, 1/5*a^12 - 1/5*a^11 - 1/5*a^10 + 1/5*a^9 - 1/5*a^8 + 1/5*a^7 + 2/5*a^4 - 2/5*a^3 - 2/5*a^2 + 2/5*a + 1/5, 1/5*a^13 - 2/5*a^11 + 1/5*a^7 + 2/5*a^5 + 1/5*a^3 - 2/5*a + 1/5, 1/55*a^14 + 3/55*a^13 - 4/55*a^12 - 4/55*a^11 + 12/55*a^10 - 12/55*a^9 + 23/55*a^8 - 14/55*a^7 - 8/55*a^6 - 19/55*a^5 - 8/55*a^4 - 23/55*a^3 + 27/55*a^2 - 4/55*a - 4/55, 1/39940688485555*a^15 - 224329695619/39940688485555*a^14 + 238047923786/7988137697111*a^13 + 1037262237729/39940688485555*a^12 + 3275071374581/7988137697111*a^11 + 658036001399/3630971680505*a^10 - 995984914568/3630971680505*a^9 + 2570340441211/7988137697111*a^8 - 89852969860/726194336101*a^7 - 4145226179858/39940688485555*a^6 + 296305465455/7988137697111*a^5 + 1280406422858/39940688485555*a^4 - 15408511143472/39940688485555*a^3 + 732777155809/3072360652735*a^2 - 9327629530711/39940688485555*a - 3478936179382/39940688485555], 0, 1, [], 0, [ (871913617)/(5674199245)*a^(15) - (824177207)/(5674199245)*a^(14) - (5327626089)/(5674199245)*a^(13) + (6597254452)/(5674199245)*a^(12) + (25083671482)/(5674199245)*a^(11) + (929366287)/(5674199245)*a^(10) - (21962930511)/(1134839849)*a^(9) - (10224691031)/(1134839849)*a^(8) + (207355733367)/(5674199245)*a^(7) + (34113911386)/(5674199245)*a^(6) - (54282958043)/(5674199245)*a^(5) + (8505744779)/(5674199245)*a^(4) - (23731109145)/(1134839849)*a^(3) + (585254685)/(87295373)*a^(2) + (21255487844)/(5674199245)*a + (4328362828)/(5674199245) , (1651808313253)/(39940688485555)*a^(15) + (837041279352)/(39940688485555)*a^(14) - (1275113808533)/(3630971680505)*a^(13) - (457611481501)/(39940688485555)*a^(12) + (75818884286186)/(39940688485555)*a^(11) + (58118741525302)/(39940688485555)*a^(10) - (253355748538834)/(39940688485555)*a^(9) - (399886605957346)/(39940688485555)*a^(8) + (467225838686432)/(39940688485555)*a^(7) + (735030004106094)/(39940688485555)*a^(6) - (403848333198306)/(39940688485555)*a^(5) - (230926012352852)/(39940688485555)*a^(4) - (12016341975809)/(3630971680505)*a^(3) - (19706828154854)/(3072360652735)*a^(2) + (331284253925847)/(39940688485555)*a + (28034978549246)/(39940688485555) , (1651808313253)/(39940688485555)*a^(15) + (837041279352)/(39940688485555)*a^(14) - (1275113808533)/(3630971680505)*a^(13) - (457611481501)/(39940688485555)*a^(12) + (75818884286186)/(39940688485555)*a^(11) + (58118741525302)/(39940688485555)*a^(10) - (253355748538834)/(39940688485555)*a^(9) - (399886605957346)/(39940688485555)*a^(8) + (467225838686432)/(39940688485555)*a^(7) + (735030004106094)/(39940688485555)*a^(6) - (403848333198306)/(39940688485555)*a^(5) - (230926012352852)/(39940688485555)*a^(4) - (12016341975809)/(3630971680505)*a^(3) - (19706828154854)/(3072360652735)*a^(2) + (371224942411402)/(39940688485555)*a + (67975667034801)/(39940688485555) , (33434213771)/(614472130547)*a^(15) + (1667903461)/(55861102777)*a^(14) - (1361465449826)/(3072360652735)*a^(13) - (147151232489)/(3072360652735)*a^(12) + (7322282793021)/(3072360652735)*a^(11) + (6520011335644)/(3072360652735)*a^(10) - (23679168037474)/(3072360652735)*a^(9) - (41062013469306)/(3072360652735)*a^(8) + (7676274972247)/(614472130547)*a^(7) + (14180693713075)/(614472130547)*a^(6) - (25181372938782)/(3072360652735)*a^(5) - (16532765752163)/(3072360652735)*a^(4) - (15973883056898)/(3072360652735)*a^(3) - (30944317086367)/(3072360652735)*a^(2) + (25654052404654)/(3072360652735)*a + (888445782358)/(614472130547) , (247134177364)/(3630971680505)*a^(15) - (6667490052624)/(39940688485555)*a^(14) - (11912928311937)/(39940688485555)*a^(13) + (9042450698681)/(7988137697111)*a^(12) + (42220362005061)/(39940688485555)*a^(11) - (110997103643937)/(39940688485555)*a^(10) - (321698115832319)/(39940688485555)*a^(9) + (368182268172989)/(39940688485555)*a^(8) + (791552015056356)/(39940688485555)*a^(7) - (944289552902568)/(39940688485555)*a^(6) - (171318373380389)/(39940688485555)*a^(5) + (69769613917363)/(7988137697111)*a^(4) - (503599387192721)/(39940688485555)*a^(3) + (50430249890596)/(3072360652735)*a^(2) - (111585660530302)/(39940688485555)*a - (106008564926662)/(39940688485555) , (1651808313253)/(39940688485555)*a^(15) + (837041279352)/(39940688485555)*a^(14) - (1275113808533)/(3630971680505)*a^(13) - (457611481501)/(39940688485555)*a^(12) + (75818884286186)/(39940688485555)*a^(11) + (58118741525302)/(39940688485555)*a^(10) - (253355748538834)/(39940688485555)*a^(9) - (399886605957346)/(39940688485555)*a^(8) + (467225838686432)/(39940688485555)*a^(7) + (735030004106094)/(39940688485555)*a^(6) - (403848333198306)/(39940688485555)*a^(5) - (230926012352852)/(39940688485555)*a^(4) - (12016341975809)/(3630971680505)*a^(3) - (19706828154854)/(3072360652735)*a^(2) + (331284253925847)/(39940688485555)*a + (67975667034801)/(39940688485555) , (5233376399729)/(39940688485555)*a^(15) - (3018719747086)/(39940688485555)*a^(14) - (7090809053358)/(7988137697111)*a^(13) + (29486243697837)/(39940688485555)*a^(12) + (175194811342084)/(39940688485555)*a^(11) + (9616731364707)/(7988137697111)*a^(10) - (704326895977851)/(39940688485555)*a^(9) - (548393622373461)/(39940688485555)*a^(8) + (1341109934784721)/(39940688485555)*a^(7) + (749231987412783)/(39940688485555)*a^(6) - (129371508761089)/(7988137697111)*a^(5) - (120094931597666)/(39940688485555)*a^(4) - (118190658106401)/(7988137697111)*a^(3) - (9304711047853)/(3072360652735)*a^(2) + (411500332335073)/(39940688485555)*a + (50211198377473)/(39940688485555) , (3581568086476)/(39940688485555)*a^(15) - (3855761026438)/(39940688485555)*a^(14) - (21427793372927)/(39940688485555)*a^(13) + (29943855179338)/(39940688485555)*a^(12) + (99375927055898)/(39940688485555)*a^(11) - (10035084701767)/(39940688485555)*a^(10) - (450971147439017)/(39940688485555)*a^(9) - (29701403283223)/(7988137697111)*a^(8) + (873884096098289)/(39940688485555)*a^(7) + (14201983306689)/(39940688485555)*a^(6) - (243009210607139)/(39940688485555)*a^(5) + (10075552795926)/(3630971680505)*a^(4) - (458773528798106)/(39940688485555)*a^(3) + (10402117107001)/(3072360652735)*a^(2) + (80216078409226)/(39940688485555)*a + (22176219828227)/(39940688485555) , (10468185300919)/(39940688485555)*a^(15) - (3291804240488)/(7988137697111)*a^(14) - (57686788245336)/(39940688485555)*a^(13) + (119458704792919)/(39940688485555)*a^(12) + (22850304254372)/(3630971680505)*a^(11) - (178249073858054)/(39940688485555)*a^(10) - (1324614195313232)/(39940688485555)*a^(9) + (19946438341201)/(3630971680505)*a^(8) + (2878693927838919)/(39940688485555)*a^(7) - (232409309006852)/(7988137697111)*a^(6) - (939436067332582)/(39940688485555)*a^(5) + (481676746119653)/(39940688485555)*a^(4) - (1481870602122054)/(39940688485555)*a^(3) + (9333079168002)/(279305513885)*a^(2) + (30947974117739)/(39940688485555)*a - (64687954365809)/(39940688485555) , (8482769922303)/(39940688485555)*a^(15) - (1040608109494)/(3630971680505)*a^(14) - (47917662299717)/(39940688485555)*a^(13) + (85423706498068)/(39940688485555)*a^(12) + (213956260809347)/(39940688485555)*a^(11) - (17953283428318)/(7988137697111)*a^(10) - (1049749728825862)/(39940688485555)*a^(9) - (38532910548069)/(39940688485555)*a^(8) + (431194755230975)/(7988137697111)*a^(7) - (602520508618493)/(39940688485555)*a^(6) - (598263099109954)/(39940688485555)*a^(5) + (416404870078071)/(39940688485555)*a^(4) - (1223202388808132)/(39940688485555)*a^(3) + (61539947767912)/(3072360652735)*a^(2) + (76429133836213)/(39940688485555)*a - (27498003236016)/(39940688485555) , (8068465755719)/(39940688485555)*a^(15) - (17895287673317)/(39940688485555)*a^(14) - (38027008810866)/(39940688485555)*a^(13) + (11125146579351)/(3630971680505)*a^(12) + (144009039296064)/(39940688485555)*a^(11) - (274801446048372)/(39940688485555)*a^(10) - (977310129135504)/(39940688485555)*a^(9) + (819638933739811)/(39940688485555)*a^(8) + (2301766652744122)/(39940688485555)*a^(7) - (203191894089744)/(3630971680505)*a^(6) - (41014591681642)/(3630971680505)*a^(5) + (851697602462012)/(39940688485555)*a^(4) - (282807891583586)/(7988137697111)*a^(3) + (130259078329903)/(3072360652735)*a^(2) - (37562103886897)/(3630971680505)*a - (133801998469456)/(39940688485555) ], 4442.27803388, [[x^2 - x - 1, 1], [x^4 - x^3 - 3*x^2 + x + 1, 1], [x^4 - 2*x^3 - 4*x^2 + 5*x + 5, 1], [x^4 - x^3 - 28*x^2 + 21*x + 171, 1], [x^8 - 3*x^7 + 2*x^6 + 2*x^5 - 7*x^4 + 11*x^3 - 7*x^2 - x + 1, 2], [x^8 - 2*x^7 - 2*x^6 + 2*x^5 + 5*x^4 + x^3 - 8*x^2 + x + 1, 2], [x^8 - 17*x^6 + 68*x^4 - 37*x^2 + 1, 1]]]