Hilbert modular form data - 3.3.1345.1-25.2-a

Formats: - HTML - YAML - JSON - 2024-04-30T07:28:44.945028

• 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': 2, 'disc': 1345, 'field_bad_primes': [5, 269], 'field_label': '3.3.1345.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '3.3.1345.1-25.2-a', 'label_nsuffix': 0, 'label_suffix': 'a', 'level_bad_primes': [5], 'level_ideal': '[25, 5, -w^2 + w + 6]', 'level_label': '25.2', 'level_norm': 25, 'parallel_weight': 2, 'short_label': '25.2-a', 'weight': '[2, 2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[5, 5, w + 2]', -1]], 'hecke_eigenvalues': ['e', 0, '-3/2*e + 2', 3, '3/2*e - 1', '-1/2*e + 2', '-3/2*e + 3', -5, 'e - 2', 'e + 2', '1/2*e - 3', '3/2*e + 3', '-3/2*e - 3', 'e + 3', '2*e + 6', '-e + 10', '-11/2*e + 8', '5/2*e + 3', '2*e - 5', 'e - 2', '-5/2*e + 10', '-5/2*e - 10', '2*e + 3', '-3/2*e + 12', -3, 'e + 13', '-2*e + 7', '-6*e - 1', '-4*e + 7', '13/2*e - 11', 18, '-3*e - 12', '-5*e + 9', '5*e - 6', '5*e - 1', '-5*e - 5', '7*e - 13', '-4*e + 19', '8*e - 1', '-3/2*e - 17', '-8*e + 7', '-15/2*e + 14', '-3/2*e - 1', '2*e - 3', '-5*e + 12', '-e - 2', 'e - 17', '-3/2*e + 9', '-e - 14', '-4*e - 4', '3/2*e - 12', '3*e - 9', '7*e + 7', '-3/2*e + 22', '-11*e + 18', '9/2*e + 17', 'e + 7', '-11*e + 5', '-1/2*e - 7', '1/2*e - 1', '-9/2*e - 5', '-15/2*e + 23', '-9*e + 7', '3*e - 4', '3*e + 16', '7*e - 3', '-6*e + 21', '-4*e - 18', '5/2*e - 2', '7*e + 1', '-7/2*e - 7', '13/2*e - 4', '-7*e + 17', '-4*e + 9', '2*e - 7', '17/2*e - 29', '5/2*e + 7', '-3*e - 5', '5*e + 7', '-e', '-1/2*e - 12', '12*e + 3', '9/2*e + 3', '4*e + 19', '-4*e - 9', '4*e + 19', '7/2*e + 7', '-6*e - 21', '-2*e - 18', '3*e - 15', '19/2*e + 3', 'e - 1', '10*e - 28', '12*e - 12', '-3/2*e + 1', '-2*e + 30', '-1/2*e + 6', '-19/2*e + 5', '-1/2*e + 41', 'e + 38', '-13/2*e - 1', '-3/2*e - 9', '2*e - 4', '-5*e + 14', '-9*e + 16', '-8*e + 37', '-16*e + 5', '15/2*e - 16', '-10*e + 3', '3*e - 3', '-3/2*e - 21', '6*e - 21', '-6*e + 10', '-7/2*e - 25', '16*e - 16', '-9*e - 21', '-7*e + 27', '-15*e + 27', '-35/2*e + 28', '14*e - 6', '2*e - 9', '27/2*e - 9', '6*e - 9', '-3/2*e - 21', '-17/2*e - 14', '-15/2*e + 3', '29/2*e - 27', -21, '13*e', '-3*e - 9', '-3*e + 46', '15/2*e - 3', '5/2*e - 35', '-3/2*e - 41', '9*e - 34', '-17/2*e + 40', '-6*e + 14', '3*e - 15', '7*e - 14', '13/2*e + 9', '6*e - 36', '-5*e - 6', '3/2*e + 9', '-7*e - 3', '9/2*e - 27', '-10*e + 32', '12*e - 18', '39/2*e - 19', '9/2*e', '9/2*e - 9', '-17*e + 25', '5*e - 38', '7/2*e - 36', 'e + 14', '-12*e + 30', '-39/2*e + 10', '-12*e + 35', '-11/2*e - 30', '-15/2*e + 18', '-19/2*e + 40', '11*e - 13', '3/2*e - 12', '13/2*e - 27', '17/2*e + 21', '-14*e + 41', '-13/2*e - 33', '-3*e - 18', '-20*e + 22', 3], 'hecke_polynomial': 'x^2 - 2*x - 4', 'label': '3.3.1345.1-25.2-a'}
• hmf_fields •

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

  
  {'degree': 3, 'discriminant': 1345, 'ideals': ['[1, 1, 1]', '[5, 5, -w - 1]', '[5, 5, w + 2]', '[7, 7, w + 3]', '[7, 7, -w + 2]', '[7, 7, -w + 1]', '[8, 2, 2]', '[13, 13, -w^2 + w + 4]', '[19, 19, -w^2 + 5]', '[23, 23, -w^2 - w + 3]', '[25, 5, w^2 - 2*w - 3]', '[25, 5, -w^2 + w + 6]', '[25, 25, -w^2 - w + 5]', '[27, 3, 3]', '[29, 29, w^2 - w - 3]', '[31, 31, w^2 - w - 8]', '[35, 35, w^2 - w - 7]', '[35, 35, -w^2 + 4]', '[35, 35, -2*w + 1]', '[35, 35, w^2 - w - 2]', '[35, 35, -w^2 - w + 2]', '[35, 35, w - 4]', '[37, 37, -w - 4]', '[40, 10, -2*w - 2]', '[40, 10, 2*w + 4]', '[43, 43, 2*w^2 - 4*w - 3]', '[47, 47, w^2 - 3]', '[49, 7, -w^2 - w + 6]', '[49, 7, w^2 - 3*w + 2]', '[49, 7, -w^2 - 2*w + 3]', '[49, 49, -w^2 + 2]', '[49, 49, -w^2 - w + 9]', '[49, 49, 2*w + 3]', '[53, 53, 2*w^2 - w - 11]', '[56, 14, 2*w + 6]', '[56, 14, -2*w + 4]', '[56, 14, -2*w + 2]', '[59, 59, w^2 - 2*w - 4]', '[64, 4, 4]', '[65, 65, 2*w - 3]', '[65, 65, -w^2 - w + 7]', '[67, 67, w^2 + w - 8]', '[71, 71, w^2 + w - 11]', '[73, 73, -w^2 + 4*w - 2]', '[89, 89, 2*w^2 + w - 12]', '[89, 89, w^2 - 10]', '[89, 89, w - 5]', '[91, 91, w + 5]', '[91, 91, -2*w^2 + 11]', '[91, 91, w^2 + 3*w + 3]', '[95, 95, -2*w^2 - 2*w + 9]', '[95, 95, w^2 + 2*w - 4]', '[97, 97, w^2 - 2*w - 5]', '[101, 101, 2*w^2 - w - 17]', '[103, 103, -2*w^2 - 2*w + 7]', '[104, 26, -2*w^2 + 2*w + 8]', '[109, 109, w^2 - 3*w - 3]', '[115, 115, -2*w^2 + w + 10]', '[115, 115, 2*w^2 - 3*w - 5]', '[125, 5, 5]', '[125, 25, w^2 - 2*w + 2]', '[125, 25, -w^2 + w + 11]', '[125, 125, 2*w^2 + 3*w - 4]', '[127, 127, 2*w^2 + w - 9]', '[133, 133, w^2 - 3*w + 3]', '[133, 133, -w^2 + 2*w + 6]', '[133, 133, -2*w^2 + 2*w + 11]', '[135, 15, -3*w - 3]', '[135, 15, 3*w + 6]', '[137, 137, 2*w^2 + w - 13]', '[137, 137, -2*w^2 + 3*w + 8]', '[137, 137, w^2 - 2*w - 10]', '[139, 139, 2*w - 7]', '[145, 145, w^2 + 2*w - 5]', '[145, 145, -3*w + 2]', '[152, 38, -2*w^2 + 10]', '[155, 155, 2*w + 7]', '[155, 155, w^2 - 3*w - 15]', '[161, 161, 3*w + 4]', '[161, 161, w^2 - w + 2]', '[161, 161, -w^2 + 2*w + 7]', '[163, 163, -3*w - 5]', '[163, 163, 2*w^2 - 3*w - 3]', '[163, 163, 2*w^2 + w - 14]', '[169, 13, -w^2 + 5*w - 5]', '[169, 169, -w^2 + 2*w + 9]', '[173, 173, w - 6]', '[175, 35, w^2 - 2*w - 8]', '[175, 35, -2*w^2 - 3*w + 2]', '[175, 35, -2*w^2 - 3*w + 7]', '[175, 35, w^2 + 3*w - 3]', '[175, 35, -2*w^2 + 2*w + 7]', '[175, 35, w^2 - 2*w - 13]', '[175, 175, w + 6]', '[175, 175, -w^2 + 3*w + 4]', '[175, 175, -w^2 + 11]', '[179, 179, -2*w^2 + 6*w - 3]', '[181, 181, 2*w^2 - w - 9]', '[184, 46, -2*w^2 - 2*w + 6]', '[185, 185, w^2 + 5*w + 4]', '[185, 185, -w^2 - 6*w - 8]', '[189, 21, 3*w + 9]', '[189, 21, -3*w + 6]', '[189, 21, -3*w + 3]', '[193, 193, w^2 + 2*w - 6]', '[193, 193, -w^2 - 2*w - 3]', '[193, 193, w^2 + 2*w - 11]', '[200, 10, 2*w^2 - 4*w - 6]', '[200, 10, -2*w^2 + 2*w + 12]', '[200, 50, -2*w^2 - 2*w + 10]', '[203, 203, 2*w^2 + w - 8]', '[203, 203, 3*w^2 - 6*w - 7]', '[203, 203, 2*w^2 - 5*w - 4]', '[215, 215, 2*w^2 - 7*w + 1]', '[215, 215, 3*w - 4]', '[216, 6, 6]', '[217, 217, 3*w^2 - w - 17]', '[217, 217, 2*w^2 - 4*w - 23]', '[217, 217, 2*w^2 - 9]', '[229, 229, w^2 - 3*w - 13]', '[232, 58, 2*w^2 - 2*w - 6]', '[233, 233, w^2 + 2*w - 7]', '[235, 235, 2*w^2 + 4*w - 5]', '[235, 235, -w^2 - 4*w + 2]', '[241, 241, -w^2 + 2*w - 3]', '[245, 35, -w^2 + 5*w - 4]', '[245, 35, 2*w^2 + 2*w - 5]', '[245, 35, 3*w^2 - 2*w - 15]', '[245, 35, 2*w^2 - 5*w + 2]', '[245, 35, -w^2 + 3*w + 5]', '[245, 35, -w^2 - 2*w + 10]', '[245, 245, 3*w^2 + 2*w - 16]', '[245, 245, 4*w + 3]', '[245, 245, 2*w^2 - w - 8]', '[245, 245, -2*w^2 - 5*w + 3]', '[245, 245, w^2 - w - 12]', '[245, 245, -2*w^2 + 3*w + 9]', '[247, 247, w^2 - 5*w + 2]', '[248, 62, 2*w^2 - 2*w - 16]', '[251, 251, 2*w^2 - 2*w - 13]', '[259, 259, w^2 + 3*w - 4]', '[259, 259, -w^2 - 7*w - 12]', '[259, 259, w^2 + 2*w - 8]', '[263, 263, -w^2 + 3*w - 4]', '[265, 265, -w^2 - 2*w + 9]', '[265, 265, 3*w^2 + w - 20]', '[269, 269, 2*w^2 - 2*w - 5]', '[269, 269, 3*w^2 + w - 26]', '[271, 271, 2*w^2 + w - 7]', '[280, 70, 2*w^2 - 2*w - 14]', '[280, 70, -2*w^2 + 8]', '[280, 70, -4*w + 2]', '[280, 70, 2*w^2 - 2*w - 4]', '[280, 70, -2*w^2 - 2*w + 4]', '[280, 70, 2*w - 8]', '[281, 281, 2*w^2 - 2*w - 15]', '[283, 283, 2*w^2 + 2*w - 3]', '[293, 293, w - 7]', '[295, 295, -w - 7]', '[295, 295, w^2 - w + 3]', '[296, 74, -2*w - 8]', '[299, 299, -w^2 + 12]', '[301, 301, 2*w^2 + 2*w - 11]', '[301, 301, 2*w^2 - w - 7]', '[301, 301, -w^2 - 3]', '[307, 307, -w^2 - 4*w - 6]', '[311, 311, 2*w^2 + 3*w - 8]', '[313, 313, w^2 - 3*w - 6]', '[320, 20, -4*w - 4]', '[320, 20, 4*w + 8]', '[325, 65, -3*w^2 - 2*w + 13]', '[325, 65, 2*w^2 + w - 6]', '[325, 325, -2*w^2 + w + 3]', '[329, 329, 2*w^2 - 4*w - 7]', '[329, 329, 3*w^2 + 4*w - 8]', '[329, 329, w^2 - 4*w - 4]', '[335, 335, -2*w^2 + 7]', '[335, 335, 3*w^2 + w - 15]', '[343, 7, 7]', '[343, 49, -2*w^2 + 5*w + 5]', '[343, 49, -3*w^2 + w + 16]', '[343, 49, -2*w^2 - w + 3]', '[343, 49, -w^2 - w + 13]', '[343, 49, w^2 + 2*w + 4]', '[343, 49, -w^2 + 3*w + 12]', '[343, 343, -3*w + 10]', '[343, 343, -4*w + 9]', '[343, 343, -2*w^2 + w + 6]', '[344, 86, 4*w^2 - 8*w - 6]', '[347, 347, w^2 + 3*w - 5]', '[351, 39, -3*w^2 + 3*w + 12]', '[353, 353, 3*w^2 - 5*w - 6]', '[355, 355, -2*w^2 + 3*w + 10]', '[355, 355, 3*w^2 - 2*w - 21]', '[359, 359, 2*w^2 + w - 5]', '[361, 19, 2*w^2 - w - 4]', '[361, 361, -w^2 - 4*w + 3]', '[365, 365, -3*w^2 + 5*w + 3]', '[365, 365, 2*w^2 - w - 5]', '[367, 367, 4*w^2 - 3*w - 20]', '[367, 367, 2*w^2 + w - 4]', '[367, 367, -w^2 - 3*w - 5]', '[371, 371, 3*w^2 - 4*w - 13]', '[371, 371, 5*w^2 - 31]', '[371, 371, 5*w^2 - 5*w - 24]', '[373, 373, w^2 - 3*w - 7]', '[373, 373, 4*w - 3]', '[373, 373, 3*w^2 - 16]', '[376, 94, 2*w^2 - 6]', '[377, 377, -w^2 + 6*w - 10]', '[379, 379, -w^2 + 4*w - 6]', '[392, 14, -2*w^2 - 2*w + 12]', '[392, 14, 2*w^2 - 6*w + 4]', '[392, 14, -2*w^2 - 4*w + 6]', '[392, 98, -2*w^2 + 4]', '[392, 98, -2*w^2 - 2*w + 18]', '[392, 98, 4*w + 6]', '[397, 397, -3*w^2 + 4*w + 9]', '[397, 397, -3*w - 10]', '[397, 397, 2*w^2 - 5]', '[401, 401, -3*w^2 + 2*w + 14]', '[403, 403, 4*w^2 + w - 30]', '[409, 409, w^2 - w - 13]', '[413, 413, w^2 - 3*w - 11]', '[413, 413, 3*w^2 - 5*w - 5]', '[413, 413, 4*w^2 - 7*w - 9]', '[419, 419, w^2 - 3*w - 8]', '[419, 419, 3*w^2 - 5*w - 4]', '[419, 419, 3*w^2 + 2*w - 17]', '[421, 421, 4*w^2 + w - 22]', '[421, 421, 2*w^2 - w - 19]', '[421, 421, 3*w^2 - 6*w - 8]', '[424, 106, 4*w^2 - 2*w - 22]', '[431, 431, -w^2 + 5*w - 8]', '[433, 433, w^2 + 3*w - 6]', '[437, 437, -w^2 + 3*w + 16]', '[439, 439, -w^2 + 6*w - 7]', '[439, 439, 3*w^2 + 3*w - 14]', '[439, 439, -w^2 - w - 4]', '[445, 445, 2*w^2 - 3*w - 19]', '[445, 445, w^2 - 3*w - 10]', '[445, 445, 5*w^2 + 4*w - 22]', '[445, 445, -w^2 + 3*w + 9]', '[445, 445, -w^2 + 4*w + 5]', '[445, 445, -3*w^2 - 3*w + 10]', '[448, 28, 4*w + 12]', '[448, 28, -4*w + 8]', '[448, 28, -4*w + 4]', '[455, 455, 2*w^2 + 3*w - 9]', '[455, 455, -w^2 - 6*w - 5]', '[455, 455, -3*w^2 + 7*w + 6]', '[455, 455, -w^2 - 2*w + 15]', '[455, 455, -2*w^2 + 5*w - 3]', '[455, 455, -w + 8]', '[457, 457, -w - 8]', '[461, 461, 2*w^2 - 3*w - 11]', '[467, 467, 2*w^2 - 19]', '[467, 467, w^2 - 13]', '[467, 467, 2*w^2 + 2*w - 13]', '[469, 469, w^2 + 3*w - 17]', '[469, 469, 2*w - 9]', '[469, 469, 4*w^2 + 2*w - 23]', '[472, 118, 2*w^2 - 4*w - 8]', '[475, 95, w^2 - w + 4]', '[475, 95, w^2 + 3*w - 13]', '[475, 475, -3*w^2 - 5*w + 3]', '[479, 479, 2*w^2 + w - 20]', '[481, 481, 3*w^2 - w - 15]', '[485, 485, -2*w - 9]', '[485, 485, w^2 + 4]', '[487, 487, 2*w^2 + 2*w - 17]', '[497, 497, w^2 + 6*w - 23]', '[497, 497, 5*w - 12]', '[497, 497, 4*w^2 - w - 32]', '[499, 499, 4*w - 5]', '[505, 505, -w^2 + 4*w + 15]', '[505, 505, 3*w^2 - 5*w - 32]', '[509, 509, 2*w^2 - 5*w - 6]', '[511, 511, -5*w - 4]', '[511, 511, w^2 + 3*w - 7]', '[511, 511, 3*w^2 + 2*w - 12]', '[512, 8, 8]', '[513, 57, -3*w^2 + 15]', '[515, 515, 3*w^2 - 3*w - 11]', '[515, 515, -4*w^2 + w + 23]', '[520, 130, 4*w - 6]', '[520, 130, -2*w^2 - 2*w + 14]', '[521, 521, 4*w^2 - 4*w - 17]', '[529, 23, 3*w^2 - 4*w - 8]', '[529, 529, -3*w^2 + 3*w + 17]', '[536, 134, 2*w^2 + 2*w - 16]', '[541, 541, -w^2 - 4*w - 7]', '[545, 545, -w^2 - 2*w - 5]', '[545, 545, 2*w^2 - w + 2]', '[547, 547, -3*w^2 + 5*w + 11]', '[551, 551, w^2 + w - 14]', '[557, 557, 3*w^2 - 2*w - 13]', '[557, 557, 3*w^2 - 2*w - 27]', '[557, 557, 2*w^2 - 3*w - 12]', '[559, 559, w^2 - 4*w - 6]', '[563, 563, -w^2 + 6*w - 6]', '[568, 142, 2*w^2 + 2*w - 22]', '[569, 569, 2*w^2 + 4*w - 7]', '[571, 571, w^2 + 3*w - 12]', '[575, 115, -3*w^2 - 2*w + 18]', '[575, 115, w^2 + 3*w - 8]', '[575, 575, w^2 - 6*w + 3]', '[584, 146, -2*w^2 + 8*w - 4]', '[587, 587, 2*w^2 - 3*w - 18]', '[589, 589, 6*w^2 + w - 39]', '[593, 593, 3*w^2 - 4*w - 14]', '[601, 601, 2*w^2 + 3*w - 10]', '[611, 611, 3*w - 11]', '[613, 613, 3*w^2 - w - 26]', '[613, 613, 2*w^2 + 5*w - 5]', '[613, 613, 3*w^2 + 2*w - 29]', '[617, 617, -w^2 + 2*w - 5]', '[619, 619, w^2 + 3*w - 9]', '[619, 619, -3*w^2 + 8*w + 5]', '[619, 619, 4*w^2 + 3*w - 17]', '[621, 69, -3*w^2 - 3*w + 9]', '[623, 623, 3*w^2 - 3*w - 29]', '[623, 623, 3*w^2 - 26]', '[623, 623, -w^2 + 7*w - 10]', '[623, 623, 7*w^2 + 5*w - 34]', '[623, 623, w^2 + 3*w - 11]', '[623, 623, w^2 - 2*w - 15]', '[623, 623, w^2 - w - 14]', '[623, 623, -w^2 + 6*w - 5]', '[623, 623, 2*w^2 + 3*w - 21]', '[625, 25, w^2 - 6*w + 4]', '[625, 25, 5*w + 5]', '[625, 25, -5*w - 10]', '[625, 125, 3*w^2 - w - 14]', '[625, 625, -3*w^2 + 4*w + 7]', '[635, 635, 5*w^2 + 7*w - 16]', '[635, 635, -3*w^2 - 6*w + 7]', '[637, 91, -2*w^2 + 3*w + 13]', '[637, 91, -3*w^2 + 4*w + 4]', '[637, 91, -w^2 - 4*w + 5]', '[637, 637, w^2 - 4*w + 7]', '[637, 637, -2*w^2 + 2*w + 21]', '[637, 637, -w^2 - 3*w + 10]', '[643, 643, 3*w^2 + 4*w - 12]', '[653, 653, 4*w^2 - 3*w - 19]', '[659, 659, -3*w^2 - 2*w + 25]', '[659, 659, 3*w^2 - 14]', '[659, 659, 3*w^2 + w - 13]', '[661, 661, -3*w^2 + 3*w + 10]', '[665, 665, -w^2 - w - 5]', '[665, 665, -2*w^2 + w + 20]', '[665, 665, 4*w^2 - 2*w - 21]', '[665, 665, 3*w + 11]', '[665, 665, -w^2 + 4*w + 7]', '[665, 665, w - 9]', '[667, 667, -w - 9]', '[675, 15, 3*w^2 - 6*w - 9]', '[675, 15, -3*w^2 + 3*w + 18]', '[675, 75, -3*w^2 - 3*w + 15]', '[677, 677, -4*w + 13]', '[677, 677, 4*w^2 + w - 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3]', '[53, 53, 2*w^2 - w - 11]', '[59, 59, w^2 - 2*w - 4]', '[67, 67, w^2 + w - 8]', '[71, 71, w^2 + w - 11]', '[73, 73, -w^2 + 4*w - 2]', '[89, 89, 2*w^2 + w - 12]', '[89, 89, w^2 - 10]', '[89, 89, w - 5]', '[97, 97, w^2 - 2*w - 5]', '[101, 101, 2*w^2 - w - 17]', '[103, 103, -2*w^2 - 2*w + 7]', '[109, 109, w^2 - 3*w - 3]', '[127, 127, 2*w^2 + w - 9]', '[137, 137, 2*w^2 + w - 13]', '[137, 137, -2*w^2 + 3*w + 8]', '[137, 137, w^2 - 2*w - 10]', '[139, 139, 2*w - 7]', '[163, 163, -3*w - 5]', '[163, 163, 2*w^2 - 3*w - 3]', '[163, 163, 2*w^2 + w - 14]', '[169, 13, -w^2 + 5*w - 5]', '[173, 173, w - 6]', '[179, 179, -2*w^2 + 6*w - 3]', '[181, 181, 2*w^2 - w - 9]', '[193, 193, w^2 + 2*w - 6]', '[193, 193, -w^2 - 2*w - 3]', '[193, 193, w^2 + 2*w - 11]', '[229, 229, w^2 - 3*w - 13]', '[233, 233, w^2 + 2*w - 7]', '[241, 241, -w^2 + 2*w - 3]', '[251, 251, 2*w^2 - 2*w - 13]', '[263, 263, -w^2 + 3*w - 4]', '[269, 269, 2*w^2 - 2*w - 5]', '[269, 269, 3*w^2 + w - 26]', '[271, 271, 2*w^2 + w - 7]', '[281, 281, 2*w^2 - 2*w - 15]', '[283, 283, 2*w^2 + 2*w - 3]', '[293, 293, w - 7]', '[307, 307, -w^2 - 4*w - 6]', '[311, 311, 2*w^2 + 3*w - 8]', '[313, 313, w^2 - 3*w - 6]', '[347, 347, w^2 + 3*w - 5]', '[353, 353, 3*w^2 - 5*w - 6]', '[359, 359, 2*w^2 + w - 5]', '[361, 19, 2*w^2 - w - 4]', '[367, 367, 4*w^2 - 3*w - 20]', '[367, 367, 2*w^2 + w - 4]', '[367, 367, -w^2 - 3*w - 5]', '[373, 373, w^2 - 3*w - 7]', '[373, 373, 4*w - 3]', '[373, 373, 3*w^2 - 16]', '[379, 379, -w^2 + 4*w - 6]', '[397, 397, -3*w^2 + 4*w + 9]', '[397, 397, -3*w - 10]', '[397, 397, 2*w^2 - 5]', '[401, 401, -3*w^2 + 2*w + 14]', '[409, 409, w^2 - w - 13]', '[419, 419, w^2 - 3*w - 8]', '[419, 419, 3*w^2 - 5*w - 4]', '[419, 419, 3*w^2 + 2*w - 17]', '[421, 421, 4*w^2 + w - 22]', '[421, 421, 2*w^2 - w - 19]', '[421, 421, 3*w^2 - 6*w - 8]', '[431, 431, -w^2 + 5*w - 8]', '[433, 433, w^2 + 3*w - 6]', '[439, 439, -w^2 + 6*w - 7]', '[439, 439, 3*w^2 + 3*w - 14]', '[439, 439, -w^2 - w - 4]', '[457, 457, -w - 8]', '[461, 461, 2*w^2 - 3*w - 11]', '[467, 467, 2*w^2 - 19]', '[467, 467, w^2 - 13]', '[467, 467, 2*w^2 + 2*w - 13]', '[479, 479, 2*w^2 + w - 20]', '[487, 487, 2*w^2 + 2*w - 17]', '[499, 499, 4*w - 5]', '[509, 509, 2*w^2 - 5*w - 6]', '[521, 521, 4*w^2 - 4*w - 17]', '[529, 23, 3*w^2 - 4*w - 8]', '[541, 541, -w^2 - 4*w - 7]', '[547, 547, -3*w^2 + 5*w + 11]', '[557, 557, 3*w^2 - 2*w - 13]', '[557, 557, 3*w^2 - 2*w - 27]', '[557, 557, 2*w^2 - 3*w - 12]', '[563, 563, -w^2 + 6*w - 6]', '[569, 569, 2*w^2 + 4*w - 7]', '[571, 571, w^2 + 3*w - 12]', '[587, 587, 2*w^2 - 3*w - 18]', '[593, 593, 3*w^2 - 4*w - 14]', '[601, 601, 2*w^2 + 3*w - 10]', '[613, 613, 3*w^2 - w - 26]', '[613, 613, 2*w^2 + 5*w - 5]', '[613, 613, 3*w^2 + 2*w - 29]', '[617, 617, -w^2 + 2*w - 5]', '[619, 619, w^2 + 3*w - 9]', '[619, 619, -3*w^2 + 8*w + 5]', '[619, 619, 4*w^2 + 3*w - 17]', '[643, 643, 3*w^2 + 4*w - 12]', '[653, 653, 4*w^2 - 3*w - 19]', '[659, 659, -3*w^2 - 2*w + 25]', '[659, 659, 3*w^2 - 14]', '[659, 659, 3*w^2 + w - 13]', '[661, 661, -3*w^2 + 3*w + 10]', '[677, 677, -4*w + 13]', '[677, 677, 4*w^2 + w - 21]', '[677, 677, 2*w^2 - 3*w - 17]', '[691, 691, w^2 - 5*w - 5]', '[701, 701, -2*w^2 + 9*w - 8]', '[709, 709, -5*w - 6]', '[719, 719, 5*w - 11]', '[727, 727, 4*w^2 - w - 22]', '[739, 739, -2*w^2 + 5*w - 4]', '[743, 743, 2*w^2 + 3*w - 11]', '[757, 757, w^2 - 4*w - 8]', '[757, 757, -5*w - 7]', '[757, 757, w^2 + 2*w - 16]', '[761, 761, 5*w - 4]', '[769, 769, 4*w^2 - 7*w - 7]', '[769, 769, 3*w^2 - w - 13]', '[769, 769, 4*w^2 - 5*w - 18]', '[773, 773, 2*w^2 + 5*w + 5]', '[787, 787, w^2 - 3*w - 17]', '[797, 797, 3*w^2 - 3*w - 19]', '[797, 797, w^2 - 4*w - 13]', '[797, 797, 3*w^2 + 2*w - 24]', '[809, 809, 3*w^2 + 2*w - 20]', '[823, 823, 4*w^2 - 3*w - 25]', '[827, 827, 3*w^2 + 5*w - 10]', '[829, 829, w^2 - 4*w - 9]', '[839, 839, 2*w^2 + 5*w - 6]', '[841, 29, 3*w^2 + 2*w - 10]', '[863, 863, w^2 + 4*w - 20]', '[877, 877, 3*w^2 + 3*w - 7]', '[881, 881, 7*w^2 + w - 42]', '[887, 887, -w^2 + 7*w - 9]', '[907, 907, 3*w^2 - w - 12]', '[911, 911, 3*w^2 - 3*w - 5]', '[919, 919, 5*w^2 - 29]', '[929, 929, w - 10]', '[937, 937, w^2 + 4*w - 15]', '[937, 937, w^2 - 2*w - 16]', '[937, 937, 3*w^2 - w - 27]', '[941, 941, 4*w^2 - 3*w - 18]', '[947, 947, 4*w^2 + w - 20]', '[947, 947, 4*w^2 - 7*w - 13]', '[947, 947, 3*w^2 - 2*w - 28]', '[961, 31, 5*w^2 - 2*w - 28]', '[971, 971, 4*w^2 - 3*w - 26]', '[971, 971, -4*w^2 - 7*w + 3]', '[971, 971, 5*w - 9]', '[977, 977, 5*w^2 - w - 29]', '[983, 983, 2*w^2 + 2*w - 23]', '[991, 991, 2*w^2 + 3*w - 13]', '[997, 997, -w^2 + w - 6]']}
• 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, -7, 0, 1], 'conductor': 0, 'degree': 3, 'dirichlet_group': [], 'disc_abs': 1345, 'disc_rad': 1345, 'disc_sign': 1, 'frobs': [[2, [[3, 1]]], [3, [[3, 1]]], [5, [0]], [7, [[1, 3]]], [11, [[3, 1]]], [13, [[2, 1], [1, 1]]], [17, [[3, 1]]], [19, [[2, 1], [1, 1]]], [23, [[2, 1], [1, 1]]], [29, [[2, 1], [1, 1]]], [31, [[2, 1], [1, 1]]], [37, [[2, 1], [1, 1]]], [41, [[3, 1]]], [43, [[2, 1], [1, 1]]], [47, [[2, 1], [1, 1]]], [53, [[2, 1], [1, 1]]], [59, [[2, 1], [1, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [3, 3], 'galois_label': '3T2', 'galt': 2, 'grd': 36.6742416417845, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '3.3.1345.1', 'local_algs': ['5.1.0.1', '5.2.1.1', 'm269.1.1.0', 'm269.2.1.1'], 'monogenic': 1, 'num_ram': 2, 'r2': 0, 'ramps': [5, 269], 'rd': 11.0384330549, 'regulator': {'__RealLiteral__': 0, 'data': '4.92253081641', 'prec': 44}, 'res': {'gal': ['-1345,0,441,0,-42,0,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a \\)', '\\( a^{2} - 2 a - 2 \\)'], 'unitsGmodule': [[3, 1], [5, 1]], 'used_grh': False, 'zk': ['1', 'a', 'a^2']}