Number field data - 16.0.166101760110563345913601.2

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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': [10], 'class_number': 10, 'cm': False, 'coeffs': [2448, 8568, 10208, 3912, 4393, -2374, 2820, -2361, 1614, -460, 317, -118, 6, 15, 4, -4, 1], 'conductor': 0, 'degree': 16, 'disc_abs': 166101760110563345913601, 'disc_rad': 799, 'disc_sign': 1, 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [8, 8], 'galois_label': '16T13', 'galt': 13, 'grd': 28.26658805020514, 'inessentialp': [2, 3], 'is_galois': True, 'is_minimal_sibling': False, 'iso_number': 2, 'label': '16.0.166101760110563345913601.2', 'local_algs': ['17.1.2.1a1.1', '17.1.2.1a1.1', '17.1.2.1a1.1', '17.1.2.1a1.1', '17.1.2.1a1.1', '17.1.2.1a1.1', '17.1.2.1a1.1', '17.1.2.1a1.1', '47.1.2.1a1.1', '47.1.2.1a1.1', '47.1.2.1a1.1', '47.1.2.1a1.1', '47.1.2.1a1.1', '47.1.2.1a1.1', '47.1.2.1a1.1', '47.1.2.1a1.1'], 'maximal_cm_subfield': [256, 0, 15, 0, 1], 'minimal_sibling': [19, -27, 6, 23, -15, 1, 2, -1, 1], 'monogenic': -1, 'narrow_class_group': [10], 'narrow_class_number': 10, 'num_ram': 2, 'r2': 8, 'ramps': [17, 47], 'rd': 28.2665880502, 'regulator': {'__RealLiteral__': 0, 'data': '25496.198852', 'prec': 40}, 'subfield_mults': [1, 1, 1, 1, 2, 2, 1, 4, 4], 'subfields': ['200.-1.1', '-4.-1.1', '12.-1.1', '256.0.15.0.1', '-1.-8.9.-2.1', '1.1.10.-1.1', '752.-1504.1400.-784.247.-30.-1.0.1', '19.-27.6.23.-15.1.2.-1.1', '51.-25.50.-23.29.-9.8.-1.1'], 'torsion_order': 2, 'used_grh': True}
• 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, [[4, 4]]], [3, [[2, 8]]], [5, [[8, 2]]], [7, [[2, 8]]], [11, [[8, 2]]], [13, [[2, 8]]], [17, [0]], [19, [[2, 8]]], [23, [[8, 2]]], [29, [[8, 2]]], [31, [[8, 2]]], [37, [[2, 8]]], [41, [[8, 2]]], [43, [[2, 8]]], [47, [0]], [53, [[2, 8]]], [59, [[4, 4]]]], 'label': '16.0.166101760110563345913601.2', 'res': {'sib': ['19,-27,6,23,-15,1,2,-1,1', '51,-25,50,-23,29,-9,8,-1,1']}, 'torsion_gen': '\\( -1 \\)', 'unit_signature_rank': 0, 'units': ['\\( \\frac{5389143671017339217}{170979210470541587587452} a^{15} - \\frac{34672680005992623149}{170979210470541587587452} a^{14} + \\frac{271008000830050525}{770176623741178322466} a^{13} + \\frac{123284130867144516083}{170979210470541587587452} a^{12} - \\frac{33711131463735928309}{18997690052282398620828} a^{11} - \\frac{535493599522946138693}{85489605235270793793726} a^{10} + \\frac{3889033786427922975235}{170979210470541587587452} a^{9} - \\frac{3184895446911698030509}{170979210470541587587452} a^{8} + \\frac{1662528426233578746428}{42744802617635396896863} a^{7} - \\frac{26177359589011946429099}{170979210470541587587452} a^{6} + \\frac{22082556624381272641441}{170979210470541587587452} a^{5} + \\frac{2272863127445087274478}{14248267539211798965621} a^{4} + \\frac{32685638188988134355695}{170979210470541587587452} a^{3} - \\frac{12187358547605267545199}{56993070156847195862484} a^{2} - \\frac{223093740319210834991}{558755589773011724142} a + \\frac{6341840528339836893}{93125931628835287357} \\)', '\\( \\frac{48369350781127955}{568037244088178031852} a^{15} - \\frac{2021720910639371635}{3976260708617246222964} a^{14} + \\frac{25229367283473446}{26866626409575987993} a^{13} + \\frac{337688280264816883}{233897688742190954292} a^{12} - \\frac{18349497271560238271}{3976260708617246222964} a^{11} - \\frac{10286266463408285170}{994065177154311555741} a^{10} + \\frac{231091960358399235083}{3976260708617246222964} a^{9} - \\frac{348601460246647794407}{3976260708617246222964} a^{8} + \\frac{8277069982345687365}{73634457566986041166} a^{7} - \\frac{955731998979666138403}{3976260708617246222964} a^{6} + \\frac{424998858510915342557}{1325420236205748740988} a^{5} + \\frac{233362801904384787991}{1988130354308623111482} a^{4} - \\frac{175393492086427551383}{568037244088178031852} a^{3} - \\frac{378507681649450554787}{3976260708617246222964} a^{2} + \\frac{468140420426703487}{6497158020616415397} a + \\frac{8605754849468700829}{6497158020616415397} \\)', '\\( \\frac{3059021719474486468}{14248267539211798965621} a^{15} - \\frac{147887459824172141015}{170979210470541587587452} a^{14} + \\frac{139859832482405917}{330075695889076423914} a^{13} + \\frac{26857554068889147358}{4749422513070599655207} a^{12} - \\frac{576255174139128271205}{170979210470541587587452} a^{11} - \\frac{142374145060293940333}{4749422513070599655207} a^{10} + \\frac{6732136547187945315383}{85489605235270793793726} a^{9} - \\frac{8737113662511072562015}{170979210470541587587452} a^{8} + \\frac{9812783342408890276397}{85489605235270793793726} a^{7} - \\frac{1021719295768237696471}{12212800747895827684818} a^{6} - \\frac{62613270922499342176177}{170979210470541587587452} a^{5} + \\frac{113538316355993814803269}{85489605235270793793726} a^{4} - \\frac{43488933027653541111659}{28496535078423597931242} a^{3} + \\frac{60830719936430644101551}{24425601495791655369636} a^{2} + \\frac{344754845922695246231}{558755589773011724142} a + \\frac{3182316326983198453}{279377794886505862071} \\)', '\\( \\frac{702622880077331785}{56993070156847195862484} a^{15} + \\frac{166358736709802508}{1583140837690199885069} a^{14} - \\frac{294756906200313035}{770176623741178322466} a^{13} - \\frac{19274105554525941869}{56993070156847195862484} a^{12} + \\frac{131388746451809223863}{28496535078423597931242} a^{11} + \\frac{29103497945109734605}{14248267539211798965621} a^{10} - \\frac{25305804287950689401}{1117511179546023448284} a^{9} + \\frac{80231991454952390836}{4749422513070599655207} a^{8} + \\frac{1005231550372309157636}{14248267539211798965621} a^{7} + \\frac{298874167939028091927}{6332563350760799540276} a^{6} - \\frac{33747425680933338053}{2035466791315971280803} a^{5} - \\frac{6830328890304726310396}{14248267539211798965621} a^{4} + \\frac{47356459903068909441089}{56993070156847195862484} a^{3} + \\frac{5853859836140403258020}{14248267539211798965621} a^{2} + \\frac{574914800715898694921}{558755589773011724142} a + \\frac{18696969628711154316}{93125931628835287357} \\)', '\\( \\frac{1167919956616181539}{6705067077276140689704} a^{15} - \\frac{625242473247916093}{1676266769319035172426} a^{14} - \\frac{5641742684722355}{5033834142099204722} a^{13} + \\frac{40646373750279693877}{6705067077276140689704} a^{12} + \\frac{4637747437491290315}{1117511179546023448284} a^{11} - \\frac{95850588650840228281}{3352533538638070344852} a^{10} + \\frac{112529194115644711247}{6705067077276140689704} a^{9} + \\frac{22842074406125665309}{239466681331290738918} a^{8} - \\frac{119996652834554831695}{3352533538638070344852} a^{7} + \\frac{1886484018965983583861}{6705067077276140689704} a^{6} - \\frac{1604795812356768007255}{1676266769319035172426} a^{5} + \\frac{270912095632667826691}{159644454220860492612} a^{4} - \\frac{5881266598401268161085}{6705067077276140689704} a^{3} + \\frac{168621009238369046090}{93125931628835287357} a^{2} + \\frac{37978330797701275069}{13303704518405041051} a + \\frac{113976280908751064404}{93125931628835287357} \\)', '\\( \\frac{53947984055894579}{568037244088178031852} a^{15} - \\frac{1307022086684815411}{3976260708617246222964} a^{14} + \\frac{2520824127081206}{26866626409575987993} a^{13} + \\frac{7649685844766034659}{3976260708617246222964} a^{12} + \\frac{3221513608883056993}{3976260708617246222964} a^{11} - \\frac{11400501631402069279}{994065177154311555741} a^{10} + \\frac{97790039175418740971}{3976260708617246222964} a^{9} - \\frac{92985344745317407415}{3976260708617246222964} a^{8} + \\frac{6705041241413928409}{73634457566986041166} a^{7} - \\frac{289004023577083709179}{3976260708617246222964} a^{6} + \\frac{35285680416063429185}{1325420236205748740988} a^{5} + \\frac{248227449914448086011}{1988130354308623111482} a^{4} - \\frac{60017975974077018071}{568037244088178031852} a^{3} + \\frac{2948468998886816645501}{3976260708617246222964} a^{2} + \\frac{1621110179277733429}{2165719340205471799} a + \\frac{6940382268833623690}{6497158020616415397} \\)', '\\( \\frac{293149877006839205}{1356977860877314187202} a^{15} - \\frac{20819892292966175609}{24425601495791655369636} a^{14} + \\frac{2214812612872526053}{2310529871223534967398} a^{13} + \\frac{4920929859208461701}{1676266769319035172426} a^{12} + \\frac{254182290076448162719}{170979210470541587587452} a^{11} - \\frac{337240473062741548672}{14248267539211798965621} a^{10} + \\frac{3051981127257956588110}{42744802617635396896863} a^{9} - \\frac{18314355521349333814591}{170979210470541587587452} a^{8} + \\frac{31422057755988439285061}{85489605235270793793726} a^{7} - \\frac{22419779556046722828455}{42744802617635396896863} a^{6} + \\frac{128298371232065962736567}{170979210470541587587452} a^{5} - \\frac{56196463510170015358727}{85489605235270793793726} a^{4} + \\frac{5886350893413186633770}{4749422513070599655207} a^{3} + \\frac{61793579798455671374057}{170979210470541587587452} a^{2} + \\frac{410169472639734618023}{186251863257670574714} a + \\frac{312626050078591535812}{279377794886505862071} \\)'], 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', '1/3*a^8 - 1/3*a^7 + 1/3*a^6 - 1/3*a^5 + 1/3*a^4 - 1/3*a^3 + 1/3*a^2 - 1/3*a', '1/3*a^9 - 1/3*a', '1/3*a^10 - 1/3*a^2', '1/3*a^11 - 1/3*a^3', '1/21*a^12 + 1/7*a^10 - 1/7*a^9 + 1/7*a^8 + 1/7*a^7 - 1/7*a^6 - 2/7*a^5 - 1/21*a^4 - 1/7*a^2 - 2/7*a + 2/7', '1/42*a^13 - 2/21*a^11 - 1/14*a^10 - 2/21*a^9 - 2/21*a^8 - 17/42*a^7 + 4/21*a^6 + 1/7*a^5 - 1/6*a^4 - 5/21*a^3 + 4/21*a^2 - 1/42*a', '1/12852*a^14 - 22/3213*a^13 - 1/1071*a^12 + 1147/12852*a^11 + 17/126*a^10 + 263/6426*a^9 + 605/12852*a^8 - 1499/3213*a^7 - 505/6426*a^6 - 6241/12852*a^5 - 1096/3213*a^4 - 1/14*a^3 - 835/12852*a^2 + 1/21*a - 2/21', '1/341958420941083175174904*a^15 + 1158000470252821123/56993070156847195862484*a^14 - 17756938038279349981/2310529871223534967398*a^13 - 5023662135941811290633/341958420941083175174904*a^12 - 3367948612100121423067/42744802617635396896863*a^11 - 10887227512069868189221/170979210470541587587452*a^10 - 463607041132966764295/37995380104564797241656*a^9 + 9419766270793172164723/56993070156847195862484*a^8 - 46522686423373749418685/170979210470541587587452*a^7 - 2865822335855207978975/6705067077276140689704*a^6 - 5027847963849906012115/24425601495791655369636*a^5 + 75024191621151657677077/170979210470541587587452*a^4 - 132815607763620815528083/341958420941083175174904*a^3 + 68070631551445772387959/170979210470541587587452*a^2 - 114885739708574052928/279377794886505862071*a - 99404019747569416300/279377794886505862071']}