Number field data - 8.2.20079525440000.1

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• nf_fields •

  Column	Type
  class_group	jsonb
  class_number	numeric
  cm	boolean
  coeffs	numeric[]
  conductor	numeric
  degree	smallint
  disc_abs	numeric
  disc_rad	numeric
  disc_sign	smallint
  embeddings_gen_imag	double precision[]
  embeddings_gen_real	double precision[]
  gal_is_abelian	boolean
  gal_is_cyclic	boolean
  gal_is_solvable	boolean
  galois_disc_exponents	numeric[]
  galois_label	text
  galt	integer
  grd	double precision
  index	integer
  inessentialp	integer[]
  is_galois	boolean
  is_minimal_sibling	boolean
  iso_number	smallint
  label	text
  local_algs	text[]
  maximal_cm_subfield	numeric[]
  minimal_sibling	numeric[]
  monogenic	smallint
  narrow_class_group	bigint[]
  narrow_class_number	bigint
  num_ram	smallint
  r2	smallint
  ramps	numeric[]
  rd	double precision
  regulator	numeric
  relative_class_number	numeric
  subfield_mults	integer[]
  subfields	text[]
  torsion_order	smallint
  used_grh	boolean

  
  {'class_group': [2], 'class_number': 2, 'cm': False, 'coeffs': [-706, -114, 713, -245, -63, 46, -5, -3, 1], 'conductor': 0, 'degree': 8, 'disc_abs': 20079525440000, 'disc_rad': 130, 'disc_sign': -1, 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [48, 16, 28], 'galois_label': '8T15', 'galt': 15, 'grd': 59.66648156085613, 'inessentialp': [2, 3], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '8.2.20079525440000.1', 'local_algs': ['2.1.2.3a1.2', '2.1.2.3a1.2', '2.1.2.3a1.1', '2.2.1.0a1.1', '5.4.2.4a1.2', '13.1.8.7a1.4'], 'monogenic': -1, 'narrow_class_group': [4], 'narrow_class_number': 4, 'num_ram': 3, 'r2': 3, 'ramps': [2, 5, 13], 'rd': 46.0091468886, 'regulator': {'__RealLiteral__': 0, 'data': '15102.6295629', 'prec': 44}, 'subfield_mults': [1, 1], 'subfields': ['-16.-1.1', '16.56.2.-1.1'], 'torsion_order': 2, 'used_grh': False}
• nf_fields_extra •

  Column	Type
  dirichlet_group	bigint[]
  frobs	jsonb
  label	text
  res	jsonb
  source	text
  subfield_inclusions	smallint[]
  torsion_gen	text
  torsion_gen_coeffs	numeric[]
  unit_signature_rank	smallint
  units	jsonb
  unitsGmodule	jsonb
  unitsType	text
  units_coeffs	numeric[]
  zk	jsonb

  
  {'dirichlet_group': [], 'frobs': [[2, [0]], [3, [[2, 4]]], [5, [0]], [7, [[4, 2]]], [11, [[8, 1]]], [13, [0]], [17, [[2, 4]]], [19, [[8, 1]]], [23, [[8, 1]]], [29, [[2, 3], [1, 2]]], [31, [[4, 2]]], [37, [[2, 2], [1, 4]]], [41, [[8, 1]]], [43, [[2, 4]]], [47, [[2, 2], [1, 4]]], [53, [[8, 1]]], [59, [[8, 1]]]], 'label': '8.2.20079525440000.1', 'res': {'ae': ['-26,0,-91,0,65,0,-13,0,1'], 'gal': ['57025296,-150317856,345573216,-827927568,1045004364,-559438776,248811196,-445745872,384786135,-111393672,52191680,-45212544,1410033,-1101724,7985786,-911248,1493263,-3240120,1571600,-791232,590274,-220792,84752,-54496,16801,-3744,2432,-624,105,-52,10,0,1'], 'sib': ['11664,-15008,-1344,2400,2884,3136,-1264,-4628,3089,-884,584,-68,-214,84,8,-8,1', '256,0,18432,0,8400,0,1128,0,1120,0,810,0,213,0,24,0,1', '261,9342,4934,-14586,-20428,15700,16752,-5626,-12163,4716,2920,-1530,-200,182,-6,-8,1', '287296,0,314168,0,-25703,0,5094,0,2511,0,-852,0,151,0,-10,0,1']}, 'torsion_gen': '\\( -1 \\)', 'unit_signature_rank': 1, 'units': ['\\( \\frac{1}{2097} a^{7} + \\frac{1}{233} a^{6} - \\frac{130}{2097} a^{5} + \\frac{13}{233} a^{4} + \\frac{149}{233} a^{3} - \\frac{3026}{2097} a^{2} + \\frac{50}{2097} a + \\frac{3049}{2097} \\)', '\\( \\frac{29}{1398} a^{7} + \\frac{14}{699} a^{6} - \\frac{275}{1398} a^{5} - \\frac{335}{1398} a^{4} + \\frac{74}{233} a^{3} + \\frac{495}{466} a^{2} + \\frac{2123}{699} a - \\frac{1612}{233} \\)', '\\( \\frac{21071}{33552} a^{7} - \\frac{6355}{8388} a^{6} - \\frac{161551}{33552} a^{5} + \\frac{74009}{3728} a^{4} - \\frac{13891}{5592} a^{3} - \\frac{5526457}{33552} a^{2} + \\frac{95975}{699} a + \\frac{3717593}{16776} \\)', '\\( \\frac{341}{11184} a^{7} - \\frac{3931}{8388} a^{6} - \\frac{26975}{33552} a^{5} + \\frac{10969}{3728} a^{4} - \\frac{48979}{5592} a^{3} - \\frac{320051}{11184} a^{2} + \\frac{146987}{2097} a + \\frac{1332505}{16776} \\)'], 'zk': ['1', 'a', 'a^2', 'a^3', '1/3*a^4 + 1/3*a^3 + 1/3*a - 1/3', '1/3*a^5 - 1/3*a^3 + 1/3*a^2 + 1/3*a + 1/3', '1/18*a^6 - 1/18*a^5 + 1/6*a^3 - 1/6*a^2 + 2/9*a - 1/9', '1/33552*a^7 + 59/2796*a^6 - 3625/33552*a^5 - 427/11184*a^4 - 2689/5592*a^3 - 7919/33552*a^2 + 440/2097*a + 1175/16776']}