Hilbert modular form data - 3.3.1937.1-9.1-d

Formats: - HTML - YAML - JSON - 2024-05-18T23:30:36.468274

• hmf_forms •

  Column	Type
  deg	smallint
  dimension	integer
  disc	bigint
  field_bad_primes	integer[]
  field_label	text
  is_CM	text
  is_base_change	text
  label	text
  label_nsuffix	smallint
  label_suffix	text
  level_bad_primes	integer[]
  level_ideal	text
  level_label	text
  level_norm	integer
  parallel_weight	smallint
  short_label	text
  weight	text

  
  {'deg': 3, 'dimension': 4, 'disc': 1937, 'field_bad_primes': [13, 149], 'field_label': '3.3.1937.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '3.3.1937.1-9.1-d', 'label_nsuffix': 3, 'label_suffix': 'd', 'level_bad_primes': [3], 'level_ideal': '[9, 3, w^2 - 3*w - 2]', 'level_label': '9.1', 'level_norm': 9, 'parallel_weight': 2, 'short_label': '9.1-d', 'weight': '[2, 2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[9, 3, w^2 - 3*w - 2]', 1]], 'hecke_eigenvalues': ['e', '-e^3 - 2*e^2 + 5*e + 5', 'e^3 + 2*e^2 - 6*e - 8', '-e^3 - 3*e^2 + 4*e + 11', -1, '2*e^3 + 6*e^2 - 10*e - 23', '-4*e^3 - 10*e^2 + 23*e + 41', '2*e^3 + 6*e^2 - 10*e - 22', '-e^3 - 2*e^2 + 6*e + 8', '6*e^3 + 15*e^2 - 33*e - 61', '-e^3 - 3*e^2 + 7*e + 14', '4*e^3 + 9*e^2 - 23*e - 35', '-2*e^3 - 5*e^2 + 10*e + 14', '-8*e^3 - 21*e^2 + 47*e + 87', '4*e^3 + 10*e^2 - 25*e - 45', '-7*e^3 - 19*e^2 + 39*e + 68', '-3*e^2 - 3*e + 14', '4*e^3 + 9*e^2 - 22*e - 29', '5*e^3 + 13*e^2 - 31*e - 58', '-10*e^3 - 26*e^2 + 55*e + 102', '-3*e^3 - 8*e^2 + 19*e + 32', '-6*e^3 - 15*e^2 + 35*e + 54', '13*e^3 + 34*e^2 - 70*e - 127', '2*e^2 - 2*e - 16', '-12*e^3 - 33*e^2 + 68*e + 130', '7*e^3 + 18*e^2 - 40*e - 65', '5*e^3 + 14*e^2 - 26*e - 41', '-4*e^3 - 11*e^2 + 20*e + 43', '19*e^3 + 50*e^2 - 101*e - 188', '19*e^3 + 48*e^2 - 108*e - 192', '-4*e^3 - 9*e^2 + 28*e + 46', '4*e^3 + 9*e^2 - 24*e - 26', '-11*e^3 - 30*e^2 + 60*e + 107', '3*e^3 + 13*e^2 - 13*e - 53', '-11*e^3 - 29*e^2 + 56*e + 111', '4*e^3 + 12*e^2 - 22*e - 56', '-7*e^3 - 18*e^2 + 38*e + 58', '8*e^3 + 17*e^2 - 47*e - 62', '-5*e^3 - 16*e^2 + 26*e + 60', '7*e^3 + 19*e^2 - 33*e - 73', '-16*e^3 - 44*e^2 + 90*e + 170', '13*e^3 + 34*e^2 - 77*e - 134', '-8*e^3 - 20*e^2 + 51*e + 81', '8*e^3 + 18*e^2 - 50*e - 75', '11*e^3 + 25*e^2 - 66*e - 114', '-2*e^3 - 4*e^2 + 13*e + 30', '-5*e^3 - 9*e^2 + 31*e + 24', '-7*e^3 - 16*e^2 + 45*e + 76', '-22*e^3 - 57*e^2 + 118*e + 212', '-6*e^3 - 18*e^2 + 29*e + 61', '-6*e^3 - 15*e^2 + 43*e + 64', '9*e^3 + 21*e^2 - 56*e - 87', '-24*e^3 - 66*e^2 + 128*e + 244', '-13*e^3 - 34*e^2 + 72*e + 128', '30*e^3 + 78*e^2 - 166*e - 301', '9*e^3 + 22*e^2 - 56*e - 95', '4*e^2 + e - 36', '19*e^3 + 45*e^2 - 111*e - 189', '3*e^3 + 7*e^2 - 16*e - 22', '12*e^3 + 34*e^2 - 70*e - 145', '-7*e^3 - 16*e^2 + 43*e + 58', '20*e^3 + 51*e^2 - 123*e - 201', '14*e^3 + 34*e^2 - 75*e - 136', '22*e^3 + 52*e^2 - 130*e - 206', '24*e^3 + 60*e^2 - 139*e - 230', '-20*e^3 - 49*e^2 + 110*e + 192', '27*e^3 + 72*e^2 - 157*e - 288', '-23*e^3 - 60*e^2 + 120*e + 232', '9*e^3 + 26*e^2 - 46*e - 89', '14*e^3 + 36*e^2 - 86*e - 152', '7*e^3 + 21*e^2 - 42*e - 107', '16*e^3 + 44*e^2 - 92*e - 169', '15*e^3 + 34*e^2 - 91*e - 137', '15*e^3 + 36*e^2 - 81*e - 125', '-13*e^3 - 28*e^2 + 78*e + 114', '7*e^3 + 14*e^2 - 49*e - 69', '-14*e^3 - 36*e^2 + 84*e + 156', '-4*e^2 + 4', '23*e^3 + 61*e^2 - 121*e - 233', '-3*e^3 - 12*e^2 + 18*e + 69', '-15*e^3 - 34*e^2 + 89*e + 140', 'e^3 + 11*e^2 + 7*e - 36', '3*e - 30', '-10*e^3 - 22*e^2 + 69*e + 84', '14*e^3 + 36*e^2 - 76*e - 146', '-2*e^2 - 8*e - 14', '-20*e^3 - 52*e^2 + 117*e + 208', '15*e^3 + 37*e^2 - 81*e - 138', '-31*e^3 - 78*e^2 + 174*e + 308', '-10*e^3 - 32*e^2 + 47*e + 119', '13*e^3 + 37*e^2 - 69*e - 147', '-22*e^3 - 58*e^2 + 114*e + 215', '-6*e^3 - 13*e^2 + 37*e + 33', '6*e^3 + 10*e^2 - 34*e - 24', '12*e^3 + 26*e^2 - 72*e - 104', 'e^3 + 2*e^2 - 4*e - 26', '-24*e^3 - 58*e^2 + 134*e + 227', '8*e^3 + 20*e^2 - 51*e - 85', '13*e^3 + 29*e^2 - 74*e - 109', '42*e^3 + 106*e^2 - 238*e - 422', '-12*e^3 - 33*e^2 + 62*e + 129', '-e^3 - 7*e^2 + e + 12', '-15*e^3 - 40*e^2 + 78*e + 148', '-e^2 - 9*e + 16', '10*e^3 + 34*e^2 - 50*e - 132', '3*e^2 - 6*e - 31', '-9*e^3 - 23*e^2 + 61*e + 82', '-3*e^3 - 5*e^2 + 23*e + 32', '17*e^3 + 42*e^2 - 92*e - 162', '-5*e^3 - 10*e^2 + 34*e + 25', '-9*e^3 - 20*e^2 + 46*e + 82', '-7*e^3 - 16*e^2 + 45*e + 81', '-3*e^3 - e^2 + 27*e + 9', '-36*e^3 - 91*e^2 + 198*e + 354', '23*e^3 + 60*e^2 - 136*e - 228', '-6*e^3 - 12*e^2 + 39*e + 34', '-45*e^3 - 115*e^2 + 252*e + 447', '-5*e^3 - 9*e^2 + 26*e + 25', '-4*e^3 - 9*e^2 + 17*e + 30', '2*e^3 + 8*e^2 - 20*e - 46', '-44*e^3 - 117*e^2 + 243*e + 450', '8*e^3 + 21*e^2 - 39*e - 70', 'e^3 + 4*e^2 - 9*e + 1', '18*e^3 + 46*e^2 - 96*e - 186', '-22*e^3 - 50*e^2 + 132*e + 194', '5*e^3 + 14*e^2 - 30*e - 86', '-e^3 - 4*e^2 + 2*e + 16', '-16*e^3 - 36*e^2 + 94*e + 120', '29*e^3 + 80*e^2 - 154*e - 294', '-24*e^3 - 62*e^2 + 132*e + 210', '30*e^3 + 75*e^2 - 182*e - 298', '36*e^3 + 91*e^2 - 193*e - 345', '-21*e^3 - 55*e^2 + 108*e + 210', '-34*e^3 - 90*e^2 + 176*e + 334', '32*e^3 + 84*e^2 - 171*e - 307', '13*e^3 + 24*e^2 - 86*e - 100', '-16*e^3 - 38*e^2 + 89*e + 158', '24*e^3 + 66*e^2 - 147*e - 268', '4*e^3 + 15*e^2 - 14*e - 40', '22*e^3 + 56*e^2 - 115*e - 202', '15*e^3 + 44*e^2 - 70*e - 162', '-11*e^3 - 32*e^2 + 51*e + 137', '-22*e^3 - 54*e^2 + 138*e + 212', '-26*e^3 - 63*e^2 + 143*e + 258', '-45*e^3 - 116*e^2 + 259*e + 454', '3*e^3 + 12*e^2 - 14*e - 62', '-22*e^3 - 52*e^2 + 121*e + 197', '26*e^3 + 70*e^2 - 146*e - 247', '15*e^3 + 41*e^2 - 85*e - 156', '9*e^3 + 25*e^2 - 43*e - 84', '12*e - 12', '11*e^3 + 30*e^2 - 71*e - 141', '44*e^3 + 112*e^2 - 239*e - 445', '-15*e^3 - 40*e^2 + 96*e + 172', '-25*e^3 - 65*e^2 + 133*e + 271', '-e^3 + 4*e^2 + 14*e - 13', '4*e^3 + 18*e^2 - 14*e - 90', '-6*e^3 - 24*e^2 + 22*e + 68', '42*e^3 + 111*e^2 - 244*e - 453', '26*e^3 + 69*e^2 - 146*e - 292', '2*e^3 + 9*e^2 - 6*e - 55', '17*e^3 + 48*e^2 - 85*e - 166'], 'hecke_polynomial': 'x^4 + 4*x^3 - 2*x^2 - 18*x - 14', 'label': '3.3.1937.1-9.1-d'}
• hmf_fields •

  Column	Type
  degree	smallint
  discriminant	bigint
  ideals	jsonb
  label	text
  narrow_class_no	smallint
  primes	jsonb

  
  {'degree': 3, 'discriminant': 1937, 'ideals': ['[1, 1, 1]', '[3, 3, -w - 2]', '[5, 5, w + 1]', '[7, 7, w - 3]', '[8, 2, 2]', '[9, 3, w^2 - 3*w - 2]', '[9, 9, w - 1]', '[13, 13, w + 3]', '[13, 13, -w + 2]', '[15, 15, -w + 4]', '[19, 19, -w^2 + 2*w + 4]', '[21, 21, -w^2 + w + 6]', '[23, 23, w^2 - 4*w + 1]', '[24, 6, -2*w - 4]', '[25, 5, w^2 - 2*w - 1]', '[25, 25, -w^2 + 6]', '[27, 3, 3]', '[27, 27, -w^2 - w + 2]', '[31, 31, w^2 - 2*w - 9]', '[35, 35, w^2 - 2*w - 3]', '[37, 37, -w^2 + 3*w + 3]', '[39, 39, w^2 - 4]', '[39, 39, -w^2 + 2*w + 2]', '[40, 10, 2*w + 2]', '[41, 41, w^2 - w - 1]', '[41, 41, w^2 - w - 5]', '[41, 41, w^2 - w - 10]', '[43, 43, -2*w - 3]', '[45, 15, -w^2 + 3*w - 1]', '[45, 45, w^2 - 2*w - 8]', '[47, 47, -w^2 - w + 4]', '[49, 7, -w^2 + 5*w - 5]', '[49, 49, -w - 4]', '[56, 14, 2*w - 6]', '[57, 57, w^2 - 7]', '[59, 59, w^2 - w - 4]', '[59, 59, w^2 - 3]', '[59, 59, w - 5]', '[63, 21, w^2 - 2]', '[63, 63, w^2 - 4*w + 3]', '[64, 4, 4]', '[65, 65, -w^2 + w + 2]', '[65, 65, 2*w^2 - 5*w - 7]', '[67, 67, 2*w^2 - 4*w - 9]', '[69, 69, w^2 - w - 3]', '[72, 6, 2*w^2 - 6*w - 4]', '[72, 18, 2*w - 2]', '[73, 73, 2*w^2 - 3*w - 12]', '[75, 15, -w^2 - 3*w + 1]', '[75, 75, -w^2 + 3*w + 4]', '[79, 79, -3*w^2 + 9*w + 5]', '[81, 9, w^2 - 8]', '[81, 9, -3*w - 6]', '[81, 81, -w^2 + 10]', '[91, 91, w^2 + 3*w + 3]', '[91, 91, w^2 - 9]', '[93, 93, -w^2 + 5*w + 17]', '[95, 95, -2*w + 3]', '[97, 97, 2*w^2 - w - 14]', '[97, 97, 2*w^2 - 2*w - 13]', '[97, 97, -2*w^2 + 5*w + 5]', '[101, 101, w^2 - w - 11]', '[104, 26, 2*w + 6]', '[104, 26, -2*w + 4]', '[105, 105, -w^2 - w + 5]', '[111, 111, -w - 5]', '[115, 115, -2*w^2 + 5*w + 2]', '[117, 39, w^2 - 3*w - 5]', '[117, 39, -w^2 + 3*w + 11]', '[117, 117, -w^2 + 3*w - 2]', '[117, 117, w^2 + 2*w - 3]', '[120, 30, -2*w + 8]', '[123, 123, -2*w^2 - w + 9]', '[123, 123, -2*w^2 + 4*w + 19]', '[123, 123, -2*w^2 - 5*w + 1]', '[125, 5, 5]', '[125, 125, -2*w^2 - 2*w + 5]', '[129, 129, 2*w^2 + 7*w + 6]', '[131, 131, w - 6]', '[133, 133, 3*w + 5]', '[135, 15, 3*w + 3]', '[135, 135, -w^2 + 5*w - 4]', '[139, 139, -2*w^2 + 5*w + 4]', '[141, 141, -w^2 + 4*w + 3]', '[147, 21, -2*w^2 + 3*w + 11]', '[147, 147, 2*w^2 - 5*w - 3]', '[149, 149, -3*w + 11]', '[149, 149, -3*w - 4]', '[152, 38, -2*w^2 + 4*w + 8]', '[155, 155, -3*w - 8]', '[157, 157, w^2 - 3*w - 6]', '[161, 161, w^2 + w + 2]', '[168, 42, -2*w^2 + 2*w + 12]', '[169, 13, w^2 - 4*w + 4]', '[169, 13, -w^2 - w + 6]', '[169, 169, -w^2 + 5*w - 2]', '[171, 57, -w^2 - 3*w + 2]', '[171, 171, 2*w^2 - 6*w - 5]', '[173, 173, w^2 - 5*w + 3]', '[173, 173, -2*w^2 + 5*w + 8]', '[173, 173, 3*w^2 - 5*w - 17]', '[175, 35, -4*w^2 + 13*w + 4]', '[175, 175, 3*w - 2]', '[177, 177, -2*w^2 - 2*w + 7]', '[177, 177, -3*w^2 - 5*w + 5]', '[177, 177, -w^2 + 3*w + 10]', '[179, 179, 2*w^2 - w - 11]', '[179, 179, -3*w^2 + 7*w + 12]', '[179, 179, w^2 - 2*w - 12]', '[181, 181, w^2 + w - 16]', '[184, 46, 2*w^2 - 8*w + 2]', '[185, 185, w^2 - 2*w + 2]', '[189, 21, 3*w - 9]', '[189, 189, w^2 - 3*w - 7]', '[192, 12, -4*w - 8]', '[195, 195, 2*w^2 + 4*w - 3]', '[195, 195, -w^2 + w + 12]', '[199, 199, 2*w^2 - 9]', '[200, 10, 2*w^2 - 4*w - 2]', '[200, 50, -2*w^2 + 12]', '[201, 201, -2*w^2 + w + 16]', '[205, 205, w^2 + 6*w]', '[205, 205, w^2 - 3*w - 9]', '[205, 205, w^2 + 2*w - 4]', '[207, 69, -w^2 + 3*w + 8]', '[207, 207, -2*w^2 - 3*w + 5]', '[211, 211, -w^2 + w - 2]', '[215, 215, -2*w^2 - 5*w - 3]', '[216, 6, 6]', '[216, 54, -2*w^2 - 2*w + 4]', '[217, 217, -4*w^2 + 5*w + 28]', '[219, 219, -3*w^2 + 2*w + 22]', '[225, 15, 7*w^2 - 24*w - 2]', '[225, 45, -2*w^2 + 9*w + 2]', '[225, 75, 2*w^2 - 3*w - 10]', '[225, 225, -2*w - 7]', '[229, 229, -w^2 + 3*w - 3]', '[233, 233, w^2 + w - 7]', '[235, 235, 3*w^2 - 7*w - 10]', '[237, 237, w - 7]', '[243, 9, 3*w^2 - 9*w - 6]', '[243, 27, 3*w - 3]', '[243, 243, 3*w^2 - 2*w - 19]', '[245, 35, 3*w^2 - 8*w - 6]', '[245, 245, -w^2 - 5*w - 4]', '[247, 247, -3*w^2 + 8*w + 9]', '[247, 247, -2*w^2 + 2*w + 11]', '[248, 62, 2*w^2 - 4*w - 18]', '[257, 257, 3*w^2 - 3*w - 20]', '[259, 259, -2*w^2 - 2*w + 3]', '[271, 271, w^2 - 4*w - 13]', '[271, 271, 3*w^2 - 4*w - 19]', '[271, 271, 2*w - 9]', '[273, 273, -2*w^2 + 4*w + 13]', '[273, 273, -3*w^2 + w + 17]', '[277, 277, 3*w^2 - 5*w - 20]', '[279, 93, -w^2 + 14]', '[279, 279, -2*w^2 + w + 10]', '[280, 70, 2*w^2 - 4*w - 6]', '[281, 281, -w^2 - w + 13]', '[283, 283, -3*w + 8]', '[285, 285, 2*w^2 + w - 6]', '[287, 287, -3*w^2 + 10*w + 4]', '[287, 287, -3*w^2 + w + 31]', '[287, 287, -3*w^2 + 6*w + 16]', '[291, 291, -5*w^2 + 26]', '[291, 291, w^2 + w - 8]', '[291, 291, -4*w^2 + w + 24]', '[293, 293, -4*w - 7]', '[295, 295, 2*w^2 + 5*w - 2]', '[295, 295, w^2 - 4*w - 5]', '[295, 295, w^2 + 3*w - 3]', '[296, 74, -2*w^2 + 6*w + 6]', '[299, 299, 2*w^2 + w - 10]', '[299, 299, -3*w + 4]', '[301, 301, -2*w^2 + 3*w + 9]', '[303, 303, -2*w^2 + 5*w + 21]', '[307, 307, w^2 + 2*w - 5]', '[311, 311, 2*w^2 - 4*w - 5]', '[312, 78, 2*w^2 - 8]', '[312, 78, -2*w^2 + 4*w + 4]', '[313, 313, -w^2 - w - 3]', '[315, 105, w^2 - 3*w - 14]', '[315, 315, -2*w^2 + 7*w + 4]', '[317, 317, -3*w^2 + 8*w + 5]', '[320, 20, 4*w + 4]', '[325, 65, 2*w^2 + w - 2]', '[325, 65, 3*w^2 - 11*w - 3]', '[325, 325, -w^2 + 4*w - 5]', '[325, 325, -w^2 + 2*w + 13]', '[328, 82, 2*w^2 - 2*w - 2]', '[328, 82, 2*w^2 - 2*w - 10]', '[328, 82, 2*w^2 - 2*w - 20]', '[329, 329, w^2 - w - 13]', '[331, 331, -w^2 + 2*w - 3]', '[333, 111, -2*w^2 + 13]', '[333, 333, w^2 + 7*w + 10]', '[335, 335, 3*w - 7]', '[337, 337, -w - 7]', '[337, 337, w^2 + w - 9]', '[337, 337, 3*w - 5]', '[343, 7, 7]', '[343, 343, -w^2 - w + 12]', '[344, 86, -4*w - 6]', '[345, 345, w^2 + 4*w - 2]', '[351, 39, 3*w + 9]', '[351, 39, -3*w + 6]', '[351, 351, 4*w + 5]', '[351, 351, 3*w^2 - 5*w - 16]', '[359, 359, 2*w^2 - 4*w - 15]', '[360, 30, -2*w^2 + 6*w - 2]', '[360, 90, 2*w^2 - 4*w - 16]', '[361, 19, 2*w^2 + w - 5]', '[361, 361, -w^2 - 4*w - 6]', '[365, 365, w^2 + w - 10]', '[367, 367, -w^2 - 3]', '[367, 367, 3*w^2 - 11*w + 4]', '[367, 367, -2*w^2 + 9*w - 6]', '[369, 123, 5*w^2 - 18*w - 1]', '[369, 123, w^2 - 6*w + 7]', '[369, 123, -4*w^2 + 9*w + 17]', '[369, 369, -w^2 - w + 11]', '[369, 369, -w^2 + 8*w + 2]', '[369, 369, -w^2 + 4*w + 6]', '[373, 373, 2*w^2 - w - 9]', '[375, 15, 5*w^2 - 15*w - 5]', '[375, 375, w^2 - w + 3]', '[376, 94, -2*w^2 - 2*w + 8]', '[379, 379, 3*w^2 - 5*w - 21]', '[383, 383, w - 8]', '[387, 129, w^2 - 3*w + 4]', '[387, 387, -2*w^2 - w + 3]', '[389, 389, -4*w^2 + 9*w + 15]', '[392, 14, -2*w^2 + 10*w - 10]', '[392, 98, -2*w - 8]', '[393, 393, -w^2 + 4*w + 12]', '[395, 395, 3*w^2 - 10*w + 2]', '[397, 397, 2*w^2 + w - 4]', '[397, 397, -4*w^2 + 13*w + 5]', '[397, 397, -w^2 - 2*w - 4]', '[399, 399, w^2 - 6*w + 2]', '[401, 401, w^2 - 5*w - 4]', '[403, 403, 3*w^2 - 3*w - 19]', '[403, 403, 2*w^2 - 7*w - 26]', '[405, 45, 2*w^2 - 7]', '[405, 45, -3*w + 12]', '[405, 405, -2*w^2 + 2*w + 9]', '[413, 413, -3*w^2 + 7*w + 13]', '[413, 413, w^2 - 8*w + 15]', '[413, 413, -2*w^2 + 5*w + 10]', '[417, 417, w^2 + 2*w - 6]', '[421, 421, 3*w^2 - 4*w - 18]', '[423, 141, 2*w^2 - 3*w - 7]', '[423, 423, -w^2 - 3*w - 5]', '[431, 431, w^2 - 4*w - 16]', '[433, 433, w^2 - 4*w - 7]', '[437, 437, -w^2 - 6*w - 3]', '[439, 439, w^2 + 2*w - 17]', '[441, 21, 4*w^2 - 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19]', '[9971, 767, 3*w^2 + 3*w - 31]', '[9971, 9971, 9*w^2 - 35*w + 9]', '[9971, 9971, -6*w^2 + 21*w + 13]', '[9971, 9971, -3*w^2 + 16*w + 10]', '[9975, 1995, 14*w^2 - 53*w - 9]', '[9975, 9975, w^2 + 3*w + 17]', '[9981, 3327, -5*w^2 + 12*w + 46]', '[9981, 9981, -10*w^2 - 11*w + 30]', '[9983, 9983, 7*w^2 - 6*w - 39]', '[9983, 9983, 2*w^2 + 5*w - 30]', '[9987, 9987, w - 22]', '[9989, 9989, 5*w^2 - 22*w + 21]', '[9989, 9989, -12*w^2 + 33*w + 23]', '[9989, 9989, -14*w^2 + 20*w + 101]', '[9992, 2498, 2*w^2 + 8*w - 12]', '[9995, 9995, -5*w^2 + 23*w + 8]', '[9997, 9997, 11*w^2 + 6*w - 42]', '[9997, 9997, 4*w^2 - 11*w - 33]'], 'label': '3.3.1937.1', 'narrow_class_no': 2, 'primes': ['[3, 3, -w - 2]', '[5, 5, w + 1]', '[7, 7, w - 3]', '[8, 2, 2]', '[9, 3, w^2 - 3*w - 2]', '[13, 13, w + 3]', '[13, 13, -w + 2]', '[19, 19, -w^2 + 2*w + 4]', '[23, 23, w^2 - 4*w + 1]', '[25, 5, w^2 - 2*w - 1]', '[31, 31, w^2 - 2*w - 9]', '[37, 37, -w^2 + 3*w + 3]', '[41, 41, w^2 - w - 1]', '[41, 41, w^2 - w - 5]', '[41, 41, w^2 - w - 10]', '[43, 43, -2*w - 3]', '[47, 47, -w^2 - w + 4]', '[49, 7, -w^2 + 5*w - 5]', '[59, 59, w^2 - w - 4]', '[59, 59, w^2 - 3]', '[59, 59, w - 5]', '[67, 67, 2*w^2 - 4*w - 9]', '[73, 73, 2*w^2 - 3*w - 12]', '[79, 79, -3*w^2 + 9*w + 5]', '[97, 97, 2*w^2 - w - 14]', '[97, 97, 2*w^2 - 2*w - 13]', '[97, 97, -2*w^2 + 5*w + 5]', '[101, 101, w^2 - w - 11]', '[131, 131, w - 6]', '[139, 139, -2*w^2 + 5*w + 4]', '[149, 149, -3*w + 11]', '[149, 149, -3*w - 4]', '[157, 157, w^2 - 3*w - 6]', '[173, 173, w^2 - 5*w + 3]', '[173, 173, -2*w^2 + 5*w + 8]', '[173, 173, 3*w^2 - 5*w - 17]', '[179, 179, 2*w^2 - w - 11]', '[179, 179, -3*w^2 + 7*w + 12]', '[179, 179, w^2 - 2*w - 12]', '[181, 181, w^2 + w - 16]', '[199, 199, 2*w^2 - 9]', '[211, 211, -w^2 + w - 2]', '[229, 229, -w^2 + 3*w - 3]', '[233, 233, w^2 + w - 7]', '[257, 257, 3*w^2 - 3*w - 20]', '[271, 271, w^2 - 4*w - 13]', '[271, 271, 3*w^2 - 4*w - 19]', '[271, 271, 2*w - 9]', '[277, 277, 3*w^2 - 5*w - 20]', '[281, 281, -w^2 - w + 13]', '[283, 283, -3*w + 8]', '[293, 293, -4*w - 7]', '[307, 307, w^2 + 2*w - 5]', '[311, 311, 2*w^2 - 4*w - 5]', '[313, 313, -w^2 - w - 3]', '[317, 317, -3*w^2 + 8*w + 5]', '[331, 331, -w^2 + 2*w - 3]', '[337, 337, -w - 7]', '[337, 337, w^2 + w - 9]', '[337, 337, 3*w - 5]', '[359, 359, 2*w^2 - 4*w - 15]', '[361, 19, 2*w^2 + w - 5]', '[367, 367, -w^2 - 3]', '[367, 367, 3*w^2 - 11*w + 4]', '[367, 367, -2*w^2 + 9*w - 6]', '[373, 373, 2*w^2 - w - 9]', '[379, 379, 3*w^2 - 5*w - 21]', '[383, 383, w - 8]', '[389, 389, -4*w^2 + 9*w + 15]', '[397, 397, 2*w^2 + w - 4]', '[397, 397, -4*w^2 + 13*w + 5]', '[397, 397, -w^2 - 2*w - 4]', '[401, 401, w^2 - 5*w - 4]', '[421, 421, 3*w^2 - 4*w - 18]', '[431, 431, w^2 - 4*w - 16]', '[433, 433, w^2 - 4*w - 7]', '[439, 439, w^2 + 2*w - 17]', '[457, 457, 2*w^2 - 3]', '[457, 457, 4*w - 3]', '[457, 457, 2*w^2 - 3*w - 6]', '[463, 463, 3*w^2 - 12*w + 7]', '[479, 479, w^2 - 6*w + 6]', '[479, 479, -w^2 + 15]', '[479, 479, -6*w^2 + 19*w + 1]', '[487, 487, 2*w^2 - 7*w - 5]', '[487, 487, w^2 + 5*w + 8]', '[487, 487, 3*w^2 - 6*w - 17]', '[491, 491, -4*w + 15]', '[503, 503, 8*w^2 - 25*w - 5]', '[509, 509, 3*w^2 - 12*w + 4]', '[509, 509, -3*w^2 - 5*w + 6]', '[509, 509, w^2 - w - 14]', '[521, 521, -4*w^2 + 10*w + 11]', '[523, 523, 2*w^2 - 7*w + 4]', '[523, 523, 2*w^2 - 2*w - 7]', '[523, 523, -7*w^2 + 22*w + 8]', '[529, 23, 4*w^2 - 14*w + 3]', '[541, 541, w^2 + 4*w - 3]', '[541, 541, -5*w - 9]', '[541, 541, -5*w^2 + 11*w + 20]', '[557, 557, -w^2 + 5*w - 8]', '[563, 563, 2*w^2 - 15]', '[563, 563, -w^2 - 2*w + 20]', '[563, 563, w^2 - 3*w - 15]', '[569, 569, 2*w^2 - w - 5]', '[577, 577, 2*w^2 - 3*w - 21]', '[587, 587, -4*w^2 + 11*w + 6]', '[599, 599, 2*w^2 + 2*w - 9]', '[607, 607, -3*w - 10]', '[613, 613, 4*w^2 - 7*w - 25]', '[631, 631, -3*w^2 + 7*w + 7]', '[641, 641, 3*w^2 - 2*w - 17]', '[641, 641, -3*w^2 + 14*w - 12]', '[641, 641, -5*w^2 + 15*w + 9]', '[643, 643, -5*w - 8]', '[647, 647, 3*w^2 - w - 21]', '[653, 653, w^2 + 7*w + 9]', '[673, 673, -3*w^2 - 2*w + 9]', '[683, 683, 5*w^2 - 17*w + 2]', '[683, 683, 3*w^2 - 6*w - 11]', '[683, 683, 2*w^2 - 7*w - 6]', '[691, 691, w^2 + 3*w + 6]', '[701, 701, 2*w^2 - 5*w - 19]', '[709, 709, -3*w^2 + 9*w + 8]', '[727, 727, 3*w - 13]', '[739, 739, -w - 9]', '[743, 743, 5*w - 3]', '[743, 743, 2*w^2 - 5*w - 13]', '[743, 743, 3*w^2 - 3*w - 17]', '[757, 757, 3*w^2 - 4*w - 16]', '[761, 761, w^2 + 4*w - 4]', '[769, 769, 3*w^2 - w - 15]', '[773, 773, -w^2 + 2*w - 5]', '[787, 787, -2*w^2 + 10*w - 9]', '[797, 797, w^2 - 4*w - 17]', '[811, 811, 6*w^2 - 20*w + 1]', '[811, 811, -w^2 + 4*w - 7]', '[811, 811, 4*w - 9]', '[821, 821, 2*w^2 - 5*w - 14]', '[823, 823, -5*w^2 + 14*w + 8]', '[827, 827, 3*w^2 - w - 22]', '[829, 829, -3*w^2 + 6*w + 10]', '[859, 859, -9*w^2 + 29*w + 2]', '[859, 859, 4*w^2 - 13*w + 2]', '[859, 859, -w^2 + w - 5]', '[863, 863, 2*w^2 + w - 13]', '[877, 877, w^2 + 2*w - 11]', '[881, 881, 2*w^2 - 8*w + 7]', '[883, 883, 3*w^2 + 3*w - 4]', '[907, 907, w^2 + 2*w - 13]', '[929, 929, -3*w - 11]', '[937, 937, w^2 - 5*w - 12]', '[941, 941, 5*w - 4]', '[947, 947, 4*w^2 - 7*w - 20]', '[953, 953, 2*w^2 + 6*w - 3]', '[961, 31, 5*w^2 - 8*w - 29]', '[967, 967, -5*w^2 + 14*w + 7]', '[971, 971, w^2 - 5*w - 10]', '[977, 977, 2*w^2 - 4*w - 23]', '[977, 977, w^2 - 8*w + 17]', '[977, 977, 3*w^2 - 19]', '[991, 991, 3*w^2 - 4*w - 3]']}
• 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[]
  minimal_sibling	numeric[]
  monogenic	smallint
  num_ram	smallint
  r2	smallint
  ramps	numeric[]
  rd	double precision
  regulator	numeric
  subfield_mults	integer[]
  subfields	text[]
  torsion_order	smallint
  used_grh	boolean
  dirichlet_group	bigint[]
  frobs	jsonb
  res	jsonb
  source	text
  subfield_inclusions	smallint[]
  torsion_gen	text
  units	jsonb
  unitsGmodule	jsonb
  unitsType	text
  zk	jsonb

  
  {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-1, -8, -1, 1], 'conductor': 0, 'degree': 3, 'dirichlet_group': [], 'disc_abs': 1937, 'disc_rad': 1937, 'disc_sign': 1, 'frobs': [[2, [[3, 1]]], [3, [[2, 1], [1, 1]]], [5, [[2, 1], [1, 1]]], [7, [[2, 1], [1, 1]]], [11, [[3, 1]]], [13, [0]], [17, [[3, 1]]], [19, [[2, 1], [1, 1]]], [23, [[2, 1], [1, 1]]], [29, [[3, 1]]], [31, [[2, 1], [1, 1]]], [37, [[2, 1], [1, 1]]], [41, [[1, 3]]], [43, [[2, 1], [1, 1]]], [47, [[2, 1], [1, 1]]], [53, [[3, 1]]], [59, [[1, 3]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [3, 3], 'galois_label': '3T2', 'galt': 2, 'grd': 44.01136216933077, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '3.3.1937.1', 'local_algs': ['13.1.0.1', '13.2.1.2', '149.1.0.1', '149.2.1.2'], 'monogenic': 1, 'num_ram': 2, 'r2': 0, 'ramps': [13, 149], 'rd': 12.4655048946, 'regulator': {'__RealLiteral__': 0, 'data': '6.542242836', 'prec': 37}, 'res': {'gal': ['-1937,0,625,0,-50,0,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a \\)', '\\( a^{2} + a - 3 \\)'], 'unitsGmodule': [[3, 1], [5, 1]], 'used_grh': False, 'zk': ['1', 'a', 'a^2']}