Hilbert modular form data - 4.4.1957.1-81.1-c

Formats: - HTML - YAML - JSON - 2025-12-21T16:18:00.379443

• 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': 4, 'dimension': 2, 'disc': 1957, 'field_bad_primes': [19, 103], 'field_label': '4.4.1957.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '4.4.1957.1-81.1-c', 'label_nsuffix': 2, 'label_suffix': 'c', 'level_bad_primes': [3], 'level_ideal': '[81, 3, 3]', 'level_label': '81.1', 'level_norm': 81, 'parallel_weight': 2, 'short_label': '81.1-c', 'weight': '[2, 2, 2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[3, 3, -w^3 + 3*w + 1]', 1], ['[27, 3, -2*w^3 + w^2 + 6*w - 1]', 1]], 'hecke_eigenvalues': [-1, 'e', 4, 'e + 3', -6, -1, '-e', '-e - 1', '-e + 3', 'e - 3', 6, -6, 0, '2*e + 4', '-2*e - 4', '-e + 5', 'e + 4', 0, '-e + 8', '-e + 3', '2*e - 2', '-2*e - 4', '-3*e + 2', 'e - 12', '-2*e - 4', 0, '-3*e - 2', '-e + 9', '-2*e - 4', '-4*e + 4', '3*e + 5', 6, '-3*e + 8', 'e - 9', '-3*e + 5', '-3*e - 2', 6, '-e + 11', -6, '-2*e - 4', '-e - 18', '-e - 16', 'e + 12', '-5*e + 4', '2*e - 8', '2*e + 10', '2*e - 20', '-2*e + 14', 24, '4*e', 'e + 10', '-4*e + 14', '3*e - 1', 24, '2*e - 14', '3*e - 1', -12, -12, '-e + 3', '-5*e + 6', '5*e - 3', '-e - 16', '2*e - 2', '4*e - 10', '2*e - 14', '-6*e + 6', '-2*e + 8', '-4*e - 2', '3*e + 20', '-e - 22', 'e - 17', 'e - 18', '4*e + 14', '2*e - 26', 30, 22, '-3*e + 10', -30, 'e + 9', '3*e - 20', '2*e + 4', 12, '-3*e + 20', '-4*e - 14', '4*e + 20', '4*e - 10', '3*e + 5', '3*e - 16', '4*e + 2', 6, '-2*e - 22', 24, '-3*e - 5', 'e + 34', '3*e + 19', '4*e + 4', '6*e', 'e + 3', '5*e + 5', '-2*e - 22', '2*e - 14', '4*e - 16', '5*e', -20, '-7*e - 6', '-4*e + 10', -12, '4*e - 16', 36, -2, 'e - 5', '8*e - 2', '-8*e - 4', '-3*e + 22', '2*e - 8', '-4*e + 16', 28, '-5*e - 12', '-e - 22', '-5*e + 6', 18, '-2*e - 28', '-6*e + 6', '-4*e + 10', '-2*e - 22', '-2*e - 28', '6*e - 6', 24, '-e', '-7*e + 5', '5*e - 12', 14, '8*e + 10', '-2*e + 2', '-5*e - 27', 'e - 17', '3*e - 13', -12, 30, '-6*e + 24', '6*e - 12', '4*e - 16', '7*e - 20', -30, '-6*e + 12', -6, '-2*e + 32', 'e + 49', '-e + 15', '-2*e + 32', '2*e + 10', '8*e - 10', '-e + 5', '-6*e + 24', '2*e + 16', '-2*e + 20', '-4*e - 8', '3*e + 29', 'e - 17', -6, '-2*e + 8', '-2*e - 16', '-4*e + 8', '-3*e + 19'], 'hecke_polynomial': 'x^2 - x - 21', 'label': '4.4.1957.1-81.1-c'}
• hmf_fields •

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

  
  {'degree': 4, 'discriminant': 1957, 'ideals': ['[1, 1, 1]', '[3, 3, -w^3 + 3*w + 1]', '[7, 7, -w^2 + 2]', '[9, 9, w^3 - w^2 - 3*w]', '[16, 2, 2]', '[19, 19, -w^3 + w^2 + 4*w]', '[21, 21, -w^3 + w^2 + 2*w - 2]', '[23, 23, w^3 + w^2 - 4*w - 2]', '[27, 3, -2*w^3 + w^2 + 6*w - 1]', '[27, 27, w^3 - 2*w - 2]', '[31, 31, -w^3 + 5*w]', '[37, 37, -w^3 + 5*w + 1]', '[43, 43, w^2 + w - 3]', '[43, 43, -w^2 + 2*w + 3]', '[47, 47, -w^3 + w^2 + 2*w + 2]', '[47, 47, 3*w^3 - w^2 - 10*w - 2]', '[48, 6, -2*w^3 + 6*w + 2]', '[49, 49, w + 3]', '[53, 53, -w^3 + w^2 + 2*w - 3]', '[57, 57, -w^3 + 2*w^2 + 3*w - 4]', '[59, 59, -2*w^3 + w^2 + 8*w + 1]', '[59, 59, w^3 - 2*w^2 - 3*w + 3]', '[61, 61, -w^3 + w^2 + w - 2]', '[63, 63, w^3 + w^2 - 4*w - 1]', '[67, 67, 2*w^3 - 5*w - 2]', '[69, 69, -w^3 + 3*w + 4]', '[71, 71, 2*w^2 - w - 3]', '[73, 73, 2*w^2 - w - 5]', '[73, 73, w^3 - 2*w^2 - 2*w + 5]', '[81, 3, 3]', '[81, 81, 2*w^3 - 5*w]', '[83, 83, w^3 + w^2 - 6*w - 3]', '[89, 89, w^3 + w^2 - 4*w]', '[93, 93, -2*w^2 + w + 4]', '[97, 97, 2*w^3 - 9*w]', '[97, 97, 3*w^3 - 10*w - 3]', '[101, 101, w^3 + 2*w^2 - 4*w - 6]', '[101, 101, w^3 - 6*w + 1]', '[103, 103, -2*w^3 - w^2 + 8*w + 3]', '[111, 111, w^3 + w^2 - 5*w]', '[112, 14, -2*w^2 + 4]', '[127, 127, 2*w^3 - 9*w - 3]', '[129, 129, 2*w^3 - w^2 - 8*w - 2]', '[129, 129, -w^3 + w^2 + 6*w]', '[131, 131, -w^3 + w^2 + 3*w - 5]', '[133, 133, -2*w^3 - w^2 + 6*w + 1]', '[137, 137, w^3 - 6*w - 2]', '[139, 139, w^3 - 3*w + 3]', '[141, 141, -3*w^3 + w^2 + 8*w + 3]', '[141, 141, 3*w^3 + w^2 - 10*w - 9]', '[144, 18, 2*w^3 - 2*w^2 - 6*w]', '[147, 147, w^2 + 2*w - 3]', '[149, 149, -w^3 + 2*w^2 + w - 4]', '[151, 151, -3*w^3 + w^2 + 11*w + 2]', '[157, 157, -w^3 + 2*w^2 + 2*w - 7]', '[157, 157, w^3 + w^2 - 2*w - 4]', '[159, 159, -2*w^3 - 2*w^2 + 7*w + 9]', '[161, 161, -2*w^3 + 9*w + 1]', '[163, 163, w^3 - 6*w]', '[171, 171, 2*w^3 - 9*w - 2]', '[173, 173, 2*w^3 - w^2 - 9*w]', '[177, 177, -2*w^3 - 2*w^2 + 6*w + 7]', '[177, 177, -w^3 + 6*w + 1]', '[181, 181, -w^3 - w^2 + 7*w]', '[183, 183, w^3 + 2*w^2 - 4*w - 2]', '[189, 21, -2*w^3 + w^2 + 9*w - 1]', '[189, 189, -w + 4]', '[197, 197, -w - 4]', '[197, 197, -2*w^3 + 3*w^2 + 6*w - 5]', '[199, 199, -3*w^3 + w^2 + 9*w + 1]', '[199, 199, -2*w^3 + 2*w^2 + 9*w - 5]', '[201, 201, 2*w^3 - w^2 - 8*w - 5]', '[207, 207, -3*w^3 + 2*w^2 + 11*w - 1]', '[211, 211, -w^3 + 2*w^2 + 5*w - 5]', '[213, 213, w^3 + w^2 - 7*w - 4]', '[217, 217, -3*w^3 + w^2 + 9*w]', '[219, 219, -3*w^3 - w^2 + 12*w + 4]', '[219, 219, 3*w^3 + w^2 - 13*w - 6]', '[229, 229, 2*w^3 + w^2 - 8*w - 2]', '[239, 239, 3*w^3 - w^2 - 12*w - 3]', '[243, 9, -3*w^3 + 9*w + 3]', '[243, 243, 2*w^3 - 2*w^2 - 5*w + 5]', '[249, 249, 2*w^3 + 3*w^2 - 9*w - 8]', '[251, 251, -2*w^3 + 2*w^2 + 7*w]', '[251, 251, 4*w^3 - 13*w - 2]', '[256, 4, 4]', '[257, 257, -2*w^3 + 3*w^2 + 5*w - 7]', '[259, 259, -3*w^3 + 9*w + 2]', '[267, 267, -w^3 + w^2 - 3]', '[279, 279, -3*w^3 + 10*w - 1]', '[281, 281, -3*w^3 + 3*w^2 + 11*w - 3]', '[283, 283, w^3 + 2*w^2 - 3*w - 8]', '[283, 283, 2*w^3 + w^2 - 6*w - 7]', '[289, 17, -w^3 - 2*w^2 + 4*w + 1]', '[289, 17, 4*w^3 - 15*w - 2]', '[291, 291, -3*w^2 + 2*w + 7]', '[291, 291, 3*w^3 + w^2 - 12*w - 10]', '[293, 293, 3*w^3 - 11*w]', '[301, 301, -w^3 + 3*w^2 + 2*w - 6]', '[301, 301, -w^3 - 2*w^2 + 6*w + 2]', '[303, 303, 4*w^3 + w^2 - 17*w - 9]', '[303, 303, -w^3 + 3*w^2 + 2*w - 4]', '[304, 38, -2*w^3 + 2*w^2 + 8*w]', '[309, 309, -2*w^3 - 2*w^2 + 10*w + 9]', '[311, 311, -4*w^3 + w^2 + 13*w]', '[313, 313, 2*w^3 + w^2 - 10*w - 3]', '[317, 317, 3*w^3 - w^2 - 8*w + 1]', '[317, 317, 3*w^3 - 2*w^2 - 9*w - 2]', '[329, 329, -3*w^2 + 2*w + 5]', '[329, 329, 4*w^3 + w^2 - 16*w - 5]', '[331, 331, 2*w^3 - 10*w + 1]', '[333, 333, -w^3 + 2*w^2 - 4]', '[336, 42, -2*w^3 + 2*w^2 + 4*w - 4]', '[337, 337, -2*w^3 + 2*w^2 + 5*w - 6]', '[337, 337, 3*w^3 - 8*w - 3]', '[343, 7, -w^3 + 3*w^2 + 2*w - 5]', '[343, 343, w^3 + w^2 - 7*w - 3]', '[347, 347, -3*w^3 + w^2 + 11*w + 4]', '[347, 347, w^3 - 7*w + 1]', '[347, 347, -2*w^3 - w^2 + 10*w + 4]', '[347, 347, 3*w^2 - w - 4]', '[353, 353, 3*w^3 - 2*w^2 - 7*w + 4]', '[353, 353, -4*w^3 + w^2 + 13*w + 1]', '[361, 19, -w^3 + 3*w^2 + 4*w - 5]', '[361, 19, 3*w^2 - 2*w - 6]', '[367, 367, 4*w^3 - 2*w^2 - 15*w]', '[368, 46, 2*w^3 + 2*w^2 - 8*w - 4]', '[371, 371, -5*w^3 + 18*w + 3]', '[373, 373, -w^3 - w^2 + 7*w + 2]', '[373, 373, -3*w^3 + w^2 + 8*w + 1]', '[381, 381, 3*w^3 + 3*w^2 - 11*w - 10]', '[383, 383, -2*w^3 - w^2 + 7*w]', '[387, 387, -3*w^3 + w^2 + 8*w]', '[387, 387, -w^3 + 2*w^2 + 5*w - 6]', '[393, 393, 4*w^3 - 13*w - 3]', '[399, 399, -w^3 + w^2 + 3*w - 6]', '[401, 401, -w^3 + 4*w - 4]', '[401, 401, 3*w^3 - 13*w - 4]', '[409, 409, -w^3 + 3*w^2 + 3*w - 6]', '[409, 409, 3*w^3 - 2*w^2 - 11*w]', '[411, 411, 2*w^3 + 3*w^2 - 7*w - 7]', '[413, 413, -4*w^3 - w^2 + 13*w + 3]', '[413, 413, w^3 - 3*w + 4]', '[417, 417, 3*w^3 - 8*w - 1]', '[419, 419, -4*w^3 + 14*w + 1]', '[421, 421, 4*w^3 - 13*w - 4]', '[421, 421, w^3 + 2*w^2 - 6*w - 10]', '[423, 423, 4*w^3 - 5*w^2 - 8*w]', '[423, 423, -2*w^3 + w^2 + 4*w + 6]', '[427, 427, w^3 + w^2 - 3]', '[431, 431, w^2 - w - 7]', '[431, 431, -3*w^3 + 12*w - 1]', '[432, 6, -4*w^3 + 2*w^2 + 12*w - 2]', '[432, 54, 2*w^3 - 4*w - 4]', '[437, 437, -w^2 - 2*w + 5]', '[439, 439, 3*w^3 - 11*w + 1]', '[441, 441, 2*w^3 - 2*w^2 - 8*w - 1]', '[443, 443, 2*w^3 + 2*w^2 - 11*w - 9]', '[443, 443, -4*w^3 + 3*w^2 + 13*w - 2]', '[447, 447, 2*w^3 + 2*w^2 - 9*w - 4]', '[449, 449, 3*w^3 + w^2 - 10*w - 2]', '[453, 453, 3*w^3 + 2*w^2 - 10*w - 10]', '[457, 457, -3*w^3 + 3*w^2 + 10*w - 2]', '[457, 457, w^3 + w^2 - 2*w - 7]', '[461, 461, 2*w^3 - w^2 - 10*w + 2]', '[467, 467, -2*w^3 + 3*w^2 + 6*w - 11]', '[469, 469, w^3 - 8*w - 4]', '[471, 471, 5*w^3 + w^2 - 18*w - 6]', '[471, 471, 3*w^3 - w^2 - 12*w - 5]', '[477, 477, w^2 - 7]', '[479, 479, 3*w^3 + w^2 - 12*w - 3]', '[479, 479, -w^3 + 2*w^2 + w - 6]', '[483, 483, -w^3 - 3*w^2 + 5*w + 8]', '[487, 487, 3*w^2 - 7]', '[487, 487, -w^3 - 3*w^2 + 5*w + 7]', '[487, 487, -w^3 + w^2 - 4]', '[487, 487, 3*w^3 - 13*w - 3]', '[489, 489, 3*w^2 - w - 5]', '[491, 491, 3*w^3 - 3*w^2 - 9*w + 1]', '[496, 62, -2*w^3 + 10*w]', '[497, 497, w^3 - w^2 - 4*w - 4]', '[499, 499, -2*w^3 - 3*w^2 + 6*w + 10]', '[499, 499, 2*w^3 - 10*w - 3]', '[509, 509, -3*w^2 + w + 7]', '[509, 509, 2*w^3 - w^2 - 10*w - 1]', '[511, 511, -2*w^2 - w + 8]', '[511, 511, w^3 + w^2 - 4*w - 8]', '[513, 57, w^3 - 2*w^2 - 6*w + 5]', '[513, 513, -2*w^3 - w^2 + 9*w]', '[519, 519, w^3 + 3*w^2 - 3*w - 7]', '[521, 521, w - 5]', '[529, 529, -3*w^3 + 4*w^2 + 10*w - 7]', '[531, 531, -w - 5]', '[531, 531, -w^3 - 3*w^2 + 4*w + 6]', '[541, 541, 3*w^2 - 5]', '[543, 543, w^3 - 4*w^2 + 6]', '[547, 547, 3*w^2 - w - 6]', '[547, 547, -w^3 + 2*w^2 + 5*w - 7]', '[549, 549, w^3 - 2*w^2 + 3*w + 1]', '[557, 557, 2*w^3 - w^2 - 6*w + 6]', '[557, 557, -3*w^3 - w^2 + 9*w]', '[563, 563, -w^3 + 4*w^2 + 3*w - 11]', '[567, 21, -3*w^2 + 6]', '[567, 567, -4*w^3 + w^2 + 12*w + 3]', '[569, 569, 3*w^3 - 12*w + 2]', '[577, 577, 2*w^3 + w^2 - 5*w - 6]', '[577, 577, 3*w^3 - w^2 - 13*w + 1]', '[581, 581, 4*w^3 - 12*w - 5]', '[587, 587, 2*w^3 - w^2 - 10*w + 1]', '[589, 589, 2*w^3 - 2*w^2 - 4*w + 5]', '[591, 591, 4*w^3 + w^2 - 12*w - 5]', '[591, 591, 2*w^3 - 10*w - 1]', '[592, 74, -2*w^3 + 10*w + 2]', '[597, 597, -2*w^3 + 7*w + 7]', '[597, 597, 3*w^3 - 3*w^2 - 11*w + 2]', '[599, 599, w^3 - w^2 - 3*w - 4]', '[603, 603, -3*w^3 + w^2 + 5*w + 3]', '[613, 613, -w^3 + 2*w^2 + 5*w - 8]', '[617, 617, 3*w^3 - 2*w^2 - 10*w - 2]', '[617, 617, 3*w^3 - w^2 - 13*w]', '[619, 619, w^3 - 2*w^2 - 4*w - 3]', '[621, 69, -w^3 + 2*w^2 - 5]', '[621, 621, -w^3 - 2*w^2 + 2*w + 7]', '[623, 623, 2*w^3 - 3*w^2 - 8*w + 1]', '[625, 5, -5]', '[631, 631, -4*w^3 + 2*w^2 + 14*w + 1]', '[633, 633, 3*w^3 - 2*w^2 - 12*w - 1]', '[639, 639, -4*w^2 + 4*w + 3]', '[643, 643, 5*w^3 - 16*w - 2]', '[647, 647, 3*w^3 - 2*w^2 - 11*w - 1]', '[651, 651, -w^3 + 4*w + 6]', '[657, 657, 2*w^3 + w^2 - 11*w - 1]', '[657, 657, -2*w^3 - 2*w^2 + 10*w + 3]', '[659, 659, 2*w^3 - 3*w^2 - 7*w]', '[659, 659, 4*w^3 - 2*w^2 - 11*w - 1]', '[677, 677, -5*w^3 + 2*w^2 + 16*w - 2]', '[677, 677, -5*w^3 + 3*w^2 + 15*w - 2]', '[679, 679, 4*w^3 - 17*w - 6]', '[679, 679, -5*w^3 + 2*w^2 + 16*w]', '[683, 683, -4*w^3 + 3*w^2 + 12*w]', '[687, 687, w^3 + 2*w^2 - 7*w - 8]', '[688, 86, 2*w^2 + 2*w - 6]', '[688, 86, -2*w^2 + 4*w + 6]', '[703, 703, w^3 - w^2 + 5]', '[707, 707, 2*w^3 + w^2 - 9*w - 10]', '[707, 707, 4*w^3 - 2*w^2 - 11*w + 2]', '[713, 713, 2*w^3 - 4*w - 5]', '[717, 717, 4*w^3 + 3*w^2 - 13*w - 12]', '[719, 719, w^3 - 4*w^2 - 2*w + 4]', '[719, 719, w^3 + w^2 - w - 5]', '[721, 721, -4*w^3 + w^2 + 15*w + 5]', '[729, 9, 4*w^3 - 2*w^2 - 15*w - 1]', '[729, 27, 3*w^3 - 3*w^2 - 9*w]', '[729, 729, -3*w^3 - w^2 + 11*w + 2]', '[733, 733, 3*w^3 + w^2 - 10*w - 1]', '[733, 733, 5*w^3 - 3*w^2 - 15*w + 3]', '[739, 739, 5*w^3 - 3*w^2 - 18*w + 2]', '[747, 747, w^3 - 4*w^2 + 3*w + 6]', '[752, 94, -2*w^3 + 2*w^2 + 4*w + 4]', '[752, 94, 6*w^3 - 2*w^2 - 20*w - 4]', '[753, 753, 2*w^3 + w^2 - 10*w - 11]', '[753, 753, -2*w^3 - w^2 + 4*w + 5]', '[757, 757, 4*w^2 - 3*w - 9]', '[768, 12, -4*w^3 + 12*w + 4]', '[771, 771, 4*w^3 + w^2 - 16*w - 4]', '[773, 773, -4*w^3 + w^2 + 12*w + 1]', '[773, 773, w^3 + 3*w^2 - 6*w - 3]', '[777, 777, 3*w^3 - 3*w^2 - 10*w + 1]', '[784, 98, 2*w + 6]', '[787, 787, 2*w^3 + 2*w^2 - 9*w - 3]', '[787, 787, -2*w^3 + 4*w^2 + 5*w - 6]', '[801, 801, 2*w^3 - 5*w^2 - 4*w + 4]', '[811, 811, -w^3 + 3*w^2 - 7]', '[817, 817, -3*w^3 - w^2 + 14*w + 4]', '[817, 817, 4*w^3 - 3*w^2 - 13*w + 1]', '[821, 821, 4*w^3 - 2*w^2 - 13*w - 3]', '[821, 821, w^3 + w - 3]', '[821, 821, -w^3 + 4*w^2 + w - 5]', '[821, 821, -w^3 + 4*w^2 + 2*w - 10]', '[827, 827, -3*w^3 - w^2 + 14*w + 6]', '[829, 829, w^3 - w^2 - 7*w + 5]', '[837, 93, 4*w^3 + w^2 - 15*w - 4]', '[837, 837, w^3 - w^2 + 6]', '[843, 843, -2*w^2 - 3*w + 5]', '[848, 106, -2*w^3 + 2*w^2 + 4*w - 6]', '[849, 849, 6*w^3 - 23*w - 10]', '[849, 849, 6*w^3 - 22*w - 11]', '[851, 851, w^3 - 4*w^2 - w + 8]', '[857, 857, w^3 - w^2 - 5*w - 5]', '[857, 857, 2*w^3 + w^2 - 11*w - 5]', '[867, 51, 2*w^3 + 3*w^2 - 10*w - 13]', '[867, 51, w^3 - w^2 + 2*w + 4]', '[873, 873, -2*w^3 - w^2 + 5*w + 7]', '[873, 873, -3*w^3 + 5*w^2 + 5*w - 7]', '[879, 879, 2*w^2 - 3*w - 8]', '[881, 881, -3*w^3 - 2*w^2 + 13*w + 5]', '[881, 881, -2*w^3 + 4*w^2 + 7*w - 8]', '[889, 889, 5*w^3 + w^2 - 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8*w - 9]', '[1603, 1603, 4*w^3 - 2*w^2 - 15*w - 3]', '[1607, 1607, 3*w^3 - 4*w^2 - 9*w]', '[1607, 1607, 3*w^3 - 4*w^2 - 11*w + 2]', '[1613, 1613, -6*w^3 + 21*w + 2]', '[1616, 202, 2*w^3 + 4*w^2 - 8*w - 12]', '[1616, 202, 2*w^3 - 12*w + 2]', '[1621, 1621, -3*w^3 + 5*w^2 + 9*w - 10]', '[1623, 1623, 2*w^3 - 12*w - 5]', '[1627, 1627, -3*w^3 + w^2 + 10*w - 7]', '[1627, 1627, -4*w^3 - 2*w^2 + 13*w + 4]', '[1629, 1629, -5*w^3 + 8*w^2 + 7*w - 7]', '[1633, 1633, -4*w^3 + 3*w^2 + 13*w + 5]', '[1641, 1641, 5*w^3 - 2*w^2 - 18*w - 3]', '[1641, 1641, 3*w^3 + w^2 - 15*w - 7]', '[1643, 1643, 3*w^3 - 5*w^2 - 8*w + 14]', '[1647, 183, 2*w^3 + 2*w^2 - 9*w + 1]', '[1647, 1647, w^3 - 6*w^2 + 5]', '[1648, 206, -4*w^3 - 2*w^2 + 16*w + 6]', '[1657, 1657, -3*w^3 + 5*w^2 + 11*w - 8]', '[1663, 1663, 2*w^3 + 3*w^2 - 9*w - 4]', '[1663, 1663, 3*w^3 - 5*w^2 - 9*w + 7]', '[1671, 1671, w^3 + 2*w + 6]', '[1671, 1671, -5*w^3 + 15*w + 2]', '[1673, 1673, 6*w^3 + 2*w^2 - 20*w - 7]', '[1679, 1679, -6*w^3 + w^2 + 21*w + 9]', '[1679, 1679, 6*w^3 - w^2 - 19*w - 6]', '[1689, 1689, 7*w^3 - 28*w - 9]', '[1691, 1691, -w^3 + 5*w^2 + 5*w - 5]', '[1693, 1693, -2*w^3 - 3*w^2 + 11*w + 4]', '[1697, 1697, 4*w^2 - w - 7]', '[1699, 1699, 2*w^3 + 4*w^2 - 7*w - 9]', '[1701, 63, -3*w^3 + 3*w^2 + 6*w - 6]', '[1701, 1701, w^3 - 3*w^2 - 6*w + 8]', '[1707, 1707, -2*w^3 + 3*w^2 + 3*w - 7]', '[1721, 1721, 5*w^3 - 2*w^2 - 19*w - 3]', '[1721, 1721, -4*w^3 + 3*w^2 + 13*w + 1]', '[1723, 1723, 2*w^3 - 5*w^2 - 4*w + 6]', '[1731, 1731, 5*w^3 - w^2 - 19*w - 9]', '[1731, 1731, 4*w^2 - w - 9]', '[1733, 1733, w^3 - 9*w + 1]', '[1733, 1733, 4*w^3 - 3*w^2 - 14*w]', '[1739, 1739, w^3 + 5*w^2 - 8*w - 15]', '[1739, 1739, -w^3 - 3*w^2 + 10*w + 5]', '[1743, 1743, -4*w^3 + 4*w^2 + 11*w + 1]', '[1747, 1747, w^3 - 4*w^2 + 11]', '[1753, 1753, 2*w^3 - 9*w - 9]', '[1757, 1757, -3*w^3 - 2*w^2 + 10*w + 2]', '[1757, 1757, 5*w^3 - 2*w^2 - 22*w - 4]', '[1761, 1761, 4*w^2 - 7]', '[1767, 1767, -3*w^3 - 2*w^2 + 11*w + 3]', '[1773, 1773, -2*w^3 - 2*w^2 + 11*w - 1]', '[1773, 1773, -3*w^3 + 3*w^2 + 11*w + 1]', '[1776, 222, 2*w^3 + 2*w^2 - 10*w]', '[1789, 1789, w^3 - 9*w - 3]', '[1789, 1789, -5*w^3 + 21*w + 3]', '[1791, 1791, 2*w^3 - w^2 - 2*w - 5]', '[1791, 1791, w^3 + 2*w^2 - 6]', '[1792, 28, -4*w^2 + 8]', '[1797, 1797, 5*w^3 - 14*w - 6]', '[1799, 1799, -w^3 + 3*w^2 + 5*w - 11]', '[1801, 1801, 5*w^3 - 2*w^2 - 13*w + 3]', '[1801, 1801, 4*w^2 - w - 8]', '[1809, 201, w^3 - 2*w^2 - 3*w - 4]', '[1809, 1809, -4*w^3 + 4*w^2 + 13*w + 5]', '[1811, 1811, 2*w^3 - 2*w^2 - 6*w - 5]', '[1811, 1811, 2*w^3 + 4*w^2 - 8*w - 11]', '[1811, 1811, 6*w^3 - w^2 - 19*w]', '[1811, 1811, -3*w^3 + 4*w^2 + 10*w - 1]', '[1813, 1813, -4*w^3 + 3*w^2 + 10*w - 7]', '[1829, 1829, 2*w^3 - 3*w^2 - 4*w + 10]', '[1829, 1829, 2*w^3 + 2*w^2 - 5*w - 9]', '[1831, 1831, -2*w^3 + 5*w^2 + 4*w - 9]', '[1831, 1831, -w^3 + w^2 - w - 7]', '[1839, 1839, 6*w^3 - 2*w^2 - 21*w - 4]', '[1843, 1843, 3*w^3 - 4*w^2 - 7*w + 9]', '[1843, 1843, 2*w^3 + 3*w^2 - 5*w - 10]', '[1847, 1847, w^3 - w^2 - 9*w + 1]', '[1847, 1847, -5*w^3 + w^2 + 15*w + 3]', '[1849, 43, -3*w^3 + 5*w^2 + 9*w - 9]', '[1849, 43, w^3 + 4*w^2 - 4*w - 8]', '[1849, 1849, -5*w^3 - w^2 + 18*w + 4]', '[1849, 1849, 5*w^3 - 3*w^2 - 13*w]', '[1851, 1851, 4*w^3 + w^2 - 11*w - 9]', '[1851, 1851, w^3 + 4*w^2 - 4*w - 10]', '[1857, 1857, 5*w^3 + w^2 - 12*w - 6]', '[1863, 69, 3*w^3 + 3*w^2 - 12*w - 6]', '[1863, 1863, -w^3 + 4*w - 6]', '[1867, 1867, 2*w^3 + w^2 - 4*w - 7]', '[1869, 1869, -5*w^3 + 3*w^2 + 11*w - 3]', '[1871, 1871, -w^3 + w^2 + w - 9]', '[1873, 1873, 5*w^3 + w^2 - 17*w - 3]', '[1875, 15, 5*w^3 - 15*w - 5]', '[1879, 1879, -w^3 + 3*w - 6]', '[1889, 1889, -4*w^3 - w^2 + 18*w + 6]', '[1891, 1891, 4*w^3 - 5*w^2 - 11*w + 2]', '[1893, 1893, -3*w^3 - 2*w^2 + 9*w + 11]', '[1899, 1899, 3*w^3 + 3*w^2 - 8*w - 10]', '[1907, 1907, 2*w^3 - 2*w^2 - 5*w - 5]', '[1907, 1907, -2*w^3 - w^2 + 12*w + 1]', '[1909, 1909, -6*w^3 + 17*w + 11]', '[1917, 213, w^3 + w^2 - 9*w - 1]', '[1917, 1917, w^3 - 4*w^2 + 5*w + 7]', '[1919, 1919, 5*w^3 + 2*w^2 - 17*w - 6]', '[1919, 1919, -4*w^3 + 3*w^2 + 9*w - 6]', '[1929, 1929, 2*w^3 + w^2 - 11*w - 13]', '[1931, 1931, w^3 + w^2 - 9*w - 3]', '[1941, 1941, 3*w^3 + 2*w^2 - 8*w - 9]', '[1949, 1949, w^3 + w^2 - 5*w - 10]', '[1949, 1949, 4*w^2 - 5*w - 10]', '[1951, 1951, 3*w^3 + w^2 - 8*w - 9]', '[1951, 1951, 5*w^3 - 15*w - 3]', '[1953, 1953, w^3 + w - 5]', '[1957, 1957, -w^3 - 4*w^2 + 4*w + 9]', '[1961, 1961, -4*w^2 + 3*w + 15]', '[1967, 1967, -5*w^3 + 16*w - 3]', '[1971, 219, 5*w^3 - w^2 - 21*w + 1]', '[1971, 219, -7*w^3 + 2*w^2 + 27*w - 5]', '[1971, 1971, 5*w^2 - 4*w - 10]', '[1971, 1971, -w^3 - 4*w^2 + 9*w + 11]', '[1977, 1977, 3*w^3 - w^2 - 9*w - 8]', '[1977, 1977, 3*w^3 + w^2 - 5*w - 5]', '[1979, 1979, -4*w^3 - w^2 + 13*w]', '[1981, 1981, w^3 + 3*w^2 - 7*w - 14]', '[1981, 1981, 2*w^3 + 3*w^2 - 11*w - 13]', '[1987, 1987, -5*w^3 + 4*w^2 + 18*w - 3]', '[1987, 1987, -6*w^3 + 2*w^2 + 19*w - 1]', '[1987, 1987, -w^3 + 3*w^2 + 7*w - 7]', '[1987, 1987, w^3 + w^2 - 6]', '[1993, 1993, -3*w^3 + 3*w^2 + 7*w - 8]', '[1997, 1997, -6*w^3 + 3*w^2 + 22*w]', '[2011, 2011, -w^3 + 5*w^2 + w - 12]', '[2011, 2011, 5*w^3 - 2*w^2 - 17*w - 5]', '[2021, 2021, 5*w^3 + 4*w^2 - 24*w - 13]', '[2021, 2021, 2*w^3 - 3*w - 6]', '[2021, 2021, w^3 - 6*w^2 + 6*w + 9]', '[2021, 2021, -8*w^3 + 2*w^2 + 27*w + 4]', '[2023, 119, 7*w^3 - 2*w^2 - 26*w - 4]', '[2023, 119, -2*w^3 + 4*w^2 + 9*w]', '[2027, 2027, 3*w^3 - 3*w^2 - 12*w - 1]', '[2029, 2029, 3*w^3 + w^2 - 15*w - 3]', '[2029, 2029, 4*w^3 - 4*w^2 - 11*w + 10]', '[2031, 2031, -w^2 + w + 9]', '[2031, 2031, -w^3 + 2*w + 8]', '[2032, 254, 4*w^3 - 18*w - 6]', '[2037, 2037, 7*w^3 - 6*w^2 - 21*w + 5]', '[2037, 2037, -4*w^3 - w^2 + 15*w + 2]', '[2039, 2039, 4*w^3 - w^2 - 18*w - 4]', '[2047, 2047, -w^3 + 3*w^2 + 3*w + 3]', '[2049, 2049, -3*w^3 + 7*w + 8]', '[2051, 2051, 5*w^3 - 3*w^2 - 19*w]', '[2061, 2061, w^3 - 5*w^2 + 7]', '[2064, 258, 4*w^3 - 2*w^2 - 16*w - 4]', '[2064, 258, -2*w^3 + 2*w^2 + 12*w]', '[2077, 2077, 5*w^2 - 3*w - 7]', '[2081, 2081, 4*w^3 + w^2 - 16*w - 2]', '[2081, 2081, 2*w^2 + 3*w - 7]', '[2081, 2081, -3*w^3 + 2*w^2 + 5*w - 5]', '[2081, 2081, -w^3 + 2*w^2 - 2*w - 6]', '[2087, 2087, -5*w^3 + 17*w - 1]', '[2087, 2087, -5*w^3 + 21*w + 4]', '[2089, 2089, 5*w^3 - 5*w^2 - 15*w + 13]', '[2089, 2089, -6*w^3 + 19*w + 3]', '[2096, 262, -2*w^3 + 2*w^2 + 6*w - 10]', '[2107, 2107, -4*w^3 + 3*w^2 + 13*w + 2]', '[2107, 2107, w^2 - 9]', '[2109, 2109, 6*w^3 - 2*w^2 - 19*w]', '[2111, 2111, -5*w^3 + 3*w^2 + 16*w + 2]', '[2121, 2121, -w^3 - 2*w^2 + w + 8]', '[2121, 2121, -6*w^3 + 7*w^2 + 17*w - 6]', '[2128, 266, -4*w^3 - 2*w^2 + 12*w + 2]', '[2129, 2129, 2*w^3 + w^2 - 8*w - 11]', '[2129, 2129, 5*w^3 - 18*w]', '[2139, 2139, 5*w^3 - w^2 - 14*w + 1]', '[2141, 2141, -4*w^3 - w^2 + 13*w - 3]', '[2141, 2141, 3*w^3 + 2*w^2 - 12*w - 3]', '[2151, 2151, -w^3 + 5*w + 8]', '[2153, 2153, -7*w^3 + 2*w^2 + 23*w - 1]', '[2157, 2157, -w^2 + 7*w + 3]', '[2157, 2157, 4*w^3 - 2*w^2 - 15*w - 5]', '[2161, 2161, -w^3 + 2*w^2 - w - 7]', '[2163, 2163, 5*w^3 - 2*w^2 - 14*w - 1]', '[2177, 2177, -5*w^3 + 2*w^2 + 21*w + 1]', '[2183, 2183, -5*w^3 + 2*w^2 + 14*w - 1]', '[2183, 2183, -2*w^2 + 4*w + 11]', '[2187, 9, -6*w^3 + 3*w^2 + 18*w - 3]', '[2187, 81, 3*w^3 - 6*w - 6]', '[2187, 2187, 2*w^3 - 12*w + 1]', '[2191, 2191, 6*w^3 - w^2 - 19*w - 5]', '[2192, 274, 2*w^3 - 12*w - 4]', '[2199, 2199, w^2 - 5*w - 8]', '[2199, 2199, w - 7]', '[2201, 2201, 5*w^3 - 3*w^2 - 12*w - 1]', '[2207, 2207, -2*w^3 + 5*w^2 + 7*w - 11]', '[2209, 47, 4*w^3 + w^2 - 14*w - 1]', '[2209, 47, 3*w^3 + 2*w^2 - 13*w - 3]', '[2209, 2209, 6*w^3 - 3*w^2 - 18*w + 1]', '[2209, 2209, -5*w^3 + w^2 + 14*w + 4]', '[2213, 2213, -w - 7]', '[2217, 2217, w^3 + 3*w^2 - 2*w - 11]', '[2219, 2219, 3*w^3 + 3*w^2 - 13*w - 6]', '[2219, 2219, -2*w^3 + 2*w^2 + 12*w - 1]', '[2221, 2221, 3*w^3 - 3*w^2 - 14*w - 2]', '[2224, 278, 2*w^3 - 6*w + 6]', '[2231, 2231, 3*w^3 - 7*w - 9]', '[2231, 2231, -4*w^3 - 3*w^2 + 19*w + 16]', '[2239, 2239, 2*w^3 - 6*w - 9]', '[2239, 2239, 5*w^3 + w^2 - 19*w - 4]', '[2239, 2239, -3*w^3 - 4*w^2 + 8*w + 12]', '[2239, 2239, 5*w^3 - 2*w^2 - 18*w - 4]', '[2241, 249, -w^3 + 5*w^2 - 8]', '[2241, 2241, -2*w^3 - 6*w^2 + 13*w + 10]', '[2256, 282, -6*w^3 + 2*w^2 + 16*w + 6]', '[2256, 282, 6*w^3 + 2*w^2 - 20*w - 18]', '[2257, 2257, 3*w^3 - 4*w^2 - 10*w]', '[2259, 2259, w^3 - 3*w^2 - w - 3]', '[2259, 2259, -w^3 - 3*w^2 + w + 9]', '[2263, 2263, 7*w^3 - 3*w^2 - 22*w - 1]', '[2263, 2263, -8*w^3 + 5*w^2 + 26*w - 3]', '[2271, 2271, 5*w^3 + 3*w^2 - 23*w - 12]', '[2273, 2273, -2*w^3 - w^2 + 12*w + 4]', '[2273, 2273, -5*w^3 + 2*w^2 + 14*w]', '[2279, 2279, 9*w^3 - 2*w^2 - 31*w - 1]', '[2279, 2279, -6*w^3 - w^2 + 25*w + 10]', '[2281, 2281, w^2 + 4*w - 6]', '[2281, 2281, -2*w^3 + w^2 + 8*w - 8]', '[2281, 2281, 3*w^3 - 15*w - 5]', '[2281, 2281, -4*w^3 - 2*w^2 + 15*w + 5]', '[2287, 2287, -2*w^3 + 7*w - 6]', '[2287, 2287, -w^3 + 3*w^2 - 10]', '[2293, 2293, -w^3 + 3*w^2 - 2*w - 7]', '[2297, 2297, -w^3 + 2*w^2 + 7*w - 7]', '[2297, 2297, w^3 + 5*w^2 - 4*w - 15]', '[2303, 2303, -2*w^3 + w^2 + 7*w + 7]', '[2303, 2303, 8*w^3 - w^2 - 29*w - 9]', '[2304, 36, 4*w^3 - 4*w^2 - 12*w]', '[2309, 2309, 4*w^3 - 3*w^2 - 14*w - 1]', '[2313, 2313, -3*w^3 - w^2 + 16*w]', '[2317, 2317, 6*w^3 - 3*w^2 - 18*w + 2]', '[2319, 2319, 3*w^2 - 7*w - 8]', '[2319, 2319, -2*w^3 + 8*w + 9]', '[2323, 2323, -2*w^3 + w^2 + w + 4]', '[2323, 2323, -7*w^3 + 27*w + 14]', '[2331, 2331, 2*w^3 + w^2 - 3*w - 6]', '[2339, 2339, 5*w^3 - 19*w]', '[2351, 2351, 2*w^3 + 3*w^2 - 9*w - 3]', '[2352, 294, 2*w^2 + 4*w - 6]', '[2357, 2357, -6*w^3 + 4*w^2 + 18*w + 1]', '[2359, 2359, 2*w^3 - 13*w - 6]', '[2359, 2359, -w^3 + 4*w^2 + 6*w - 10]', '[2361, 2361, w^3 + 3*w^2 - 9*w - 10]', '[2361, 2361, 2*w^3 + w^2 - 12*w - 3]', '[2369, 2369, 5*w^3 - 18*w - 13]', '[2371, 2371, -2*w^3 + 2*w^2 + 3*w - 8]', '[2371, 2371, 3*w^3 + 2*w^2 - 11*w - 2]', '[2381, 2381, -2*w^3 + w - 6]', '[2381, 2381, -2*w^3 + 5*w^2 + 5*w - 10]', '[2383, 2383, -2*w^3 + 3*w^2 + 3*w - 8]', '[2383, 2383, w^3 - w^2 - 5*w + 9]', '[2384, 298, -2*w^3 + 4*w^2 + 2*w - 8]', '[2389, 2389, -3*w^3 - w^2 + 8*w - 5]', '[2393, 2393, 3*w^3 - 3*w^2 - 12*w - 2]', '[2401, 7, 7]', '[2401, 2401, -4*w^3 - w^2 + 17*w + 1]', '[2403, 267, -5*w^3 + 4*w^2 + 12*w - 7]', '[2403, 2403, w^3 - 2*w^2 + 5*w + 2]', '[2413, 2413, w^2 - 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6*w^2 - 15*w]', '[9549, 9549, -w^3 - 2*w^2 - w + 10]', '[9549, 9549, 2*w^3 - 7*w^2 - 4*w + 9]', '[9551, 9551, -5*w^3 + 6*w^2 + 13*w - 15]', '[9552, 1194, -4*w^3 + 14*w + 14]', '[9552, 1194, 6*w^3 - 6*w^2 - 22*w + 4]', '[9561, 9561, 4*w^3 + 6*w^2 - 21*w - 22]', '[9561, 9561, 2*w^3 + 6*w^2 - 7*w - 13]', '[9563, 9563, -8*w^3 + 3*w^2 + 24*w - 2]', '[9563, 9563, 7*w^3 - 5*w^2 - 16*w + 9]', '[9569, 9569, 9*w^3 - 2*w^2 - 28*w + 2]', '[9569, 9569, 5*w^3 - 26*w - 13]', '[9573, 9573, -3*w^3 - 7*w^2 + 15*w + 16]', '[9577, 9577, w^3 - w^2 - 10*w + 9]', '[9577, 9577, -2*w^3 + w^2 + 5*w - 11]', '[9579, 9579, -9*w^3 + 2*w^2 + 31*w + 12]', '[9583, 9583, -2*w^3 - 6*w^2 + 7*w + 14]', '[9584, 1198, 2*w^3 - 2*w^2 - 6*w - 8]', '[9587, 9587, -w^3 + 3*w^2 - 2*w - 14]', '[9591, 9591, w - 10]', '[9593, 9593, 3*w^3 + w^2 - 11*w - 15]', '[9597, 9597, 4*w^3 - 8*w^2 - 9*w + 13]', '[9597, 9597, 3*w^3 - w^2 - 19*w + 5]', '[9611, 9611, -w - 10]', '[9613, 9613, w^3 + 6*w^2 - 5*w - 13]', '[9613, 9613, 3*w^2 + 4*w - 11]', '[9617, 9617, -5*w^3 + 8*w^2 + 15*w - 16]', '[9617, 9617, -3*w^3 + 3*w^2 + 5*w - 12]', '[9619, 9619, -10*w^3 + 3*w^2 + 33*w]', '[9619, 9619, -4*w^3 + 5*w^2 + 8*w - 11]', '[9621, 9621, -2*w^3 + 6*w^2 - 13]', '[9621, 9621, -w^3 + 2*w + 11]', '[9623, 9623, 3*w^2 - 6*w - 13]', '[9623, 9623, -9*w^3 + 3*w^2 + 28*w + 4]', '[9627, 9627, 7*w^3 + 2*w^2 - 19*w - 14]', '[9629, 9629, -5*w^3 - 3*w^2 + 22*w + 6]', '[9629, 9629, 9*w^3 - 4*w^2 - 28*w + 3]', '[9631, 9631, -7*w^3 + 28*w - 1]', '[9637, 9637, 3*w^3 + w^2 - 14*w - 16]', '[9641, 9641, 5*w^3 - 8*w^2 - 16*w + 17]', '[9648, 1206, -6*w^3 + 2*w^2 + 10*w + 6]', '[9651, 9651, -5*w^3 - 7*w^2 + 22*w + 23]', '[9651, 9651, -8*w^3 - 6*w^2 + 33*w + 20]', '[9653, 9653, -3*w^3 + 7*w^2 + 11*w - 13]', '[9653, 9653, -w^2 - 7*w - 12]', '[9661, 9661, 4*w^3 - 20*w - 3]', '[9671, 9671, 6*w^3 + 2*w^2 - 21*w - 4]', '[9671, 9671, -3*w^3 + 2*w - 9]', '[9677, 9677, -4*w^3 + 7*w^2 + 8*w - 15]', '[9681, 9681, -8*w^3 + 9*w^2 + 26*w - 9]', '[9683, 9683, -5*w^3 - 4*w^2 + 25*w + 21]', '[9683, 9683, -13*w^3 - 4*w^2 + 45*w + 24]', '[9687, 9687, 7*w^3 + 5*w^2 - 24*w - 24]', '[9687, 9687, w^3 + 6*w^2 - 4*w - 12]', '[9689, 9689, 4*w^3 - 21*w - 8]', '[9689, 9689, -2*w^3 + 7*w^2 + 7*w - 16]', '[9697, 9697, 6*w^3 - 2*w^2 - 27*w - 5]', '[9699, 9699, 6*w^3 - 13*w - 2]', '[9703, 9703, 2*w^3 - w^2 - 2*w - 12]', '[9709, 9709, -9*w^3 + 2*w^2 + 29*w + 1]', '[9709, 9709, 7*w^3 - 3*w^2 - 27*w - 5]', '[9719, 9719, 2*w^3 + w^2 - 5*w - 15]', '[9727, 9727, -3*w^3 + 3*w^2 + 5*w - 13]', '[9729, 9729, -7*w^3 + 5*w^2 + 22*w + 1]', '[9729, 9729, -w^3 + 5*w^2 + 4*w - 23]', '[9739, 9739, -8*w^3 + 3*w^2 + 23*w - 4]', '[9739, 9739, 5*w^3 - w^2 - 23*w]', '[9747, 57, 7*w^3 - 5*w^2 - 30*w + 8]', '[9747, 57, 4*w^3 + w^2 - 21*w - 1]', '[9747, 513, 3*w^3 - 7*w^2 - 9*w + 10]', '[9747, 513, 2*w^3 - 2*w^2 + w + 8]', '[9749, 9749, 4*w^3 - 2*w^2 - 20*w + 1]', '[9751, 9751, -4*w^3 + 7*w^2 + 20*w - 13]', '[9751, 9751, -8*w^3 + 25*w + 6]', '[9753, 9753, -w^3 - w^2 + 12*w + 2]', '[9753, 9753, -5*w^3 - 2*w^2 + 10*w + 9]', '[9769, 9769, 7*w^3 - 25*w + 1]', '[9771, 9771, 4*w^3 - 4*w^2 - 19*w - 5]', '[9771, 9771, -7*w^3 - 3*w^2 + 22*w + 6]', '[9777, 9777, -w^3 + 5*w + 11]', '[9777, 9777, -w^3 + 7*w^2 - w - 11]', '[9781, 9781, 6*w^3 + w^2 - 22*w - 1]', '[9781, 9781, 3*w^3 + w^2 - 5*w - 9]', '[9781, 9781, w^3 + 4*w^2 + w - 11]', '[9781, 9781, 7*w^3 - 19*w - 7]', '[9787, 9787, -10*w^3 + 5*w^2 + 31*w - 1]', '[9787, 9787, -8*w^3 - 2*w^2 + 30*w + 9]', '[9791, 9791, 9*w^3 - 32*w - 3]', '[9791, 9791, 7*w^3 - 5*w^2 - 28*w + 1]', '[9797, 9797, 9*w^3 - 4*w^2 - 30*w - 4]', '[9797, 9797, -6*w^3 + 6*w^2 + 20*w - 3]', '[9797, 9797, -3*w^3 + 7*w^2 + 8*w - 13]', '[9797, 9797, -2*w^3 + 7*w^2 + 3*w - 12]', '[9807, 9807, 9*w^3 - 8*w^2 - 28*w + 21]', '[9808, 1226, -2*w^3 + 4*w^2 + 10*w - 16]', '[9811, 9811, w^3 + 6*w^2 - 4*w - 13]', '[9813, 9813, -3*w^3 + 2*w^2 + 2*w - 7]', '[9819, 9819, -w^3 + 2*w^2 + 8*w + 9]', '[9819, 9819, -6*w^3 + 12*w^2 + 8*w - 11]', '[9821, 9821, 6*w^3 - 6*w^2 - 18*w + 1]', '[9827, 9827, -3*w^3 + 8*w^2 - 12]', '[9827, 9827, 5*w^3 - 8*w^2 - 15*w + 11]', '[9829, 9829, 3*w^3 + w^2 - 18*w]', '[9829, 9829, -6*w^3 + 5*w^2 + 19*w + 1]', '[9833, 9833, 6*w^3 + 3*w^2 - 20*w - 6]', '[9837, 9837, 2*w^3 + 2*w^2 - 7]', '[9837, 9837, w^3 - 5*w^2 + 3*w + 13]', '[9839, 9839, 3*w^3 - w^2 - 3*w - 7]', '[9839, 9839, 5*w^3 - 8*w^2 - 14*w + 12]', '[9847, 9847, -5*w^3 + w^2 + 23*w + 3]', '[9847, 9847, 8*w^3 - w^2 - 23*w - 9]', '[9849, 9849, -3*w^3 + 6*w^2 + 13*w + 2]', '[9851, 9851, -2*w^3 + 4*w^2 + 11*w - 12]', '[9861, 9861, -11*w^3 + 4*w^2 + 36*w - 5]', '[9863, 9863, 10*w^3 - 3*w^2 - 38*w - 6]', '[9863, 9863, 3*w^3 + 5*w^2 - 9*w - 19]', '[9863, 9863, w^3 - 12*w - 2]', '[9863, 9863, -w^3 + 7*w^2 + 4*w - 8]', '[9869, 9869, -w^3 + 7*w^2 + 3*w - 8]', '[9871, 9871, -7*w^3 + 5*w^2 + 21*w + 3]', '[9872, 1234, 6*w^3 - 4*w^2 - 20*w - 4]', '[9872, 1234, 6*w^3 - 2*w^2 - 26*w]', '[9879, 9879, 5*w^2 - 6*w + 4]', '[9887, 9887, -8*w^3 + 3*w^2 + 24*w + 1]', '[9887, 9887, 4*w^3 + w^2 - 10*w - 14]', '[9891, 9891, -2*w^3 + 15*w + 5]', '[9891, 9891, -9*w^3 + w^2 + 29*w + 3]', '[9897, 9897, 8*w^3 + 4*w^2 - 36*w - 21]', '[9899, 9899, 6*w^3 - 5*w^2 - 21*w + 1]', '[9904, 1238, 2*w^3 - 4*w^2 - 8*w - 6]', '[9909, 1101, -7*w^3 + 8*w^2 + 27*w - 20]', '[9909, 9909, -8*w^3 + 25*w + 7]', '[9913, 9913, 2*w^3 - w^2 - 5*w - 10]', '[9913, 9913, -8*w^3 - 4*w^2 + 29*w + 14]', '[9917, 9917, w^3 + w^2 + 2*w - 9]', '[9917, 9917, -5*w^3 + 8*w^2 + 14*w - 13]', '[9921, 9921, 5*w^3 - w^2 - 24*w - 7]', '[9921, 9921, 2*w^3 + w^2 - 16*w - 14]', '[9927, 9927, -4*w^2 + 11*w + 2]', '[9927, 9927, 4*w^3 + 2*w^2 - 21*w - 6]', '[9929, 9929, 6*w^3 + w^2 - 21*w]', '[9936, 138, -2*w^3 + 4*w^2 - 10]', '[9936, 1242, -2*w^3 - 4*w^2 + 4*w + 14]', '[9939, 9939, -2*w^3 - 5*w^2 + 15*w + 16]', '[9943, 9943, -3*w^3 + 5*w^2 + 4*w - 11]', '[9949, 9949, 3*w^3 + 2*w^2 - 18*w - 4]', '[9949, 9949, -8*w^3 + 4*w^2 + 23*w - 3]', '[9957, 9957, -w^3 - 6*w^2 + 10*w + 18]', '[9957, 9957, 6*w^3 - 3*w^2 - 22*w - 8]', '[9961, 9961, w^3 + 7*w^2 - 4*w - 20]', '[9961, 9961, 7*w^3 - 20*w - 4]', '[9968, 1246, 4*w^3 - 6*w^2 - 16*w + 2]', '[9973, 9973, 7*w^3 + 2*w^2 - 28*w - 7]', '[9973, 9973, 7*w^3 - 6*w^2 - 21*w + 1]', '[9983, 9983, -2*w^3 + 2*w^2 + 6*w - 13]', '[9987, 9987, 7*w^3 - w^2 - 20*w - 4]', '[9989, 9989, 2*w^3 + 7*w^2 - 9*w - 22]', '[9991, 9991, -4*w^3 + 4*w^2 + 9*w - 13]', '[9991, 9991, 6*w^3 - 27*w - 1]', '[9993, 9993, -w^3 + 7*w + 12]', '[9993, 9993, -3*w^3 + 2*w^2 + 3*w - 8]', '[10000, 10, -10]'], 'label': '4.4.1957.1', 'narrow_class_no': 1, 'primes': ['[3, 3, -w^3 + 3*w + 1]', '[7, 7, -w^2 + 2]', '[16, 2, 2]', '[19, 19, -w^3 + w^2 + 4*w]', '[23, 23, w^3 + w^2 - 4*w - 2]', '[27, 3, -2*w^3 + w^2 + 6*w - 1]', '[31, 31, -w^3 + 5*w]', '[37, 37, -w^3 + 5*w + 1]', '[43, 43, w^2 + w - 3]', '[43, 43, -w^2 + 2*w + 3]', '[47, 47, -w^3 + w^2 + 2*w + 2]', '[47, 47, 3*w^3 - w^2 - 10*w - 2]', '[53, 53, -w^3 + w^2 + 2*w - 3]', '[59, 59, -2*w^3 + w^2 + 8*w + 1]', '[59, 59, w^3 - 2*w^2 - 3*w + 3]', '[61, 61, -w^3 + w^2 + w - 2]', '[67, 67, 2*w^3 - 5*w - 2]', '[71, 71, 2*w^2 - w - 3]', '[73, 73, 2*w^2 - w - 5]', '[73, 73, w^3 - 2*w^2 - 2*w + 5]', '[83, 83, w^3 + w^2 - 6*w - 3]', '[89, 89, w^3 + w^2 - 4*w]', '[97, 97, 2*w^3 - 9*w]', '[97, 97, 3*w^3 - 10*w - 3]', '[101, 101, w^3 + 2*w^2 - 4*w - 6]', '[101, 101, w^3 - 6*w + 1]', '[103, 103, -2*w^3 - w^2 + 8*w + 3]', '[127, 127, 2*w^3 - 9*w - 3]', '[131, 131, -w^3 + w^2 + 3*w - 5]', '[137, 137, w^3 - 6*w - 2]', '[139, 139, w^3 - 3*w + 3]', '[149, 149, -w^3 + 2*w^2 + w - 4]', '[151, 151, -3*w^3 + w^2 + 11*w + 2]', '[157, 157, -w^3 + 2*w^2 + 2*w - 7]', '[157, 157, w^3 + w^2 - 2*w - 4]', '[163, 163, w^3 - 6*w]', '[173, 173, 2*w^3 - w^2 - 9*w]', '[181, 181, -w^3 - w^2 + 7*w]', '[197, 197, -w - 4]', '[197, 197, -2*w^3 + 3*w^2 + 6*w - 5]', '[199, 199, -3*w^3 + w^2 + 9*w + 1]', '[199, 199, -2*w^3 + 2*w^2 + 9*w - 5]', '[211, 211, -w^3 + 2*w^2 + 5*w - 5]', '[229, 229, 2*w^3 + w^2 - 8*w - 2]', '[239, 239, 3*w^3 - w^2 - 12*w - 3]', '[251, 251, -2*w^3 + 2*w^2 + 7*w]', '[251, 251, 4*w^3 - 13*w - 2]', '[257, 257, -2*w^3 + 3*w^2 + 5*w - 7]', '[281, 281, -3*w^3 + 3*w^2 + 11*w - 3]', '[283, 283, w^3 + 2*w^2 - 3*w - 8]', '[283, 283, 2*w^3 + w^2 - 6*w - 7]', '[289, 17, -w^3 - 2*w^2 + 4*w + 1]', '[289, 17, 4*w^3 - 15*w - 2]', '[293, 293, 3*w^3 - 11*w]', '[311, 311, -4*w^3 + w^2 + 13*w]', '[313, 313, 2*w^3 + w^2 - 10*w - 3]', '[317, 317, 3*w^3 - w^2 - 8*w + 1]', '[317, 317, 3*w^3 - 2*w^2 - 9*w - 2]', '[331, 331, 2*w^3 - 10*w + 1]', '[337, 337, -2*w^3 + 2*w^2 + 5*w - 6]', '[337, 337, 3*w^3 - 8*w - 3]', '[343, 7, -w^3 + 3*w^2 + 2*w - 5]', '[347, 347, -3*w^3 + w^2 + 11*w + 4]', '[347, 347, w^3 - 7*w + 1]', '[347, 347, -2*w^3 - w^2 + 10*w + 4]', '[347, 347, 3*w^2 - w - 4]', '[353, 353, 3*w^3 - 2*w^2 - 7*w + 4]', '[353, 353, -4*w^3 + w^2 + 13*w + 1]', '[361, 19, -w^3 + 3*w^2 + 4*w - 5]', '[367, 367, 4*w^3 - 2*w^2 - 15*w]', '[373, 373, -w^3 - w^2 + 7*w + 2]', '[373, 373, -3*w^3 + w^2 + 8*w + 1]', '[383, 383, -2*w^3 - w^2 + 7*w]', '[401, 401, -w^3 + 4*w - 4]', '[401, 401, 3*w^3 - 13*w - 4]', '[409, 409, -w^3 + 3*w^2 + 3*w - 6]', '[409, 409, 3*w^3 - 2*w^2 - 11*w]', '[419, 419, -4*w^3 + 14*w + 1]', '[421, 421, 4*w^3 - 13*w - 4]', '[421, 421, w^3 + 2*w^2 - 6*w - 10]', '[431, 431, w^2 - w - 7]', '[431, 431, -3*w^3 + 12*w - 1]', '[439, 439, 3*w^3 - 11*w + 1]', '[443, 443, 2*w^3 + 2*w^2 - 11*w - 9]', '[443, 443, -4*w^3 + 3*w^2 + 13*w - 2]', '[449, 449, 3*w^3 + w^2 - 10*w - 2]', '[457, 457, -3*w^3 + 3*w^2 + 10*w - 2]', '[457, 457, w^3 + w^2 - 2*w - 7]', '[461, 461, 2*w^3 - w^2 - 10*w + 2]', '[467, 467, -2*w^3 + 3*w^2 + 6*w - 11]', '[479, 479, 3*w^3 + w^2 - 12*w - 3]', '[479, 479, -w^3 + 2*w^2 + w - 6]', '[487, 487, 3*w^2 - 7]', '[487, 487, -w^3 - 3*w^2 + 5*w + 7]', '[487, 487, -w^3 + w^2 - 4]', '[487, 487, 3*w^3 - 13*w - 3]', '[491, 491, 3*w^3 - 3*w^2 - 9*w + 1]', '[499, 499, -2*w^3 - 3*w^2 + 6*w + 10]', '[499, 499, 2*w^3 - 10*w - 3]', '[509, 509, -3*w^2 + w + 7]', '[509, 509, 2*w^3 - w^2 - 10*w - 1]', '[521, 521, w - 5]', '[541, 541, 3*w^2 - 5]', '[547, 547, 3*w^2 - w - 6]', '[547, 547, -w^3 + 2*w^2 + 5*w - 7]', '[557, 557, 2*w^3 - w^2 - 6*w + 6]', '[557, 557, -3*w^3 - w^2 + 9*w]', '[563, 563, -w^3 + 4*w^2 + 3*w - 11]', '[569, 569, 3*w^3 - 12*w + 2]', '[577, 577, 2*w^3 + w^2 - 5*w - 6]', '[577, 577, 3*w^3 - w^2 - 13*w + 1]', '[587, 587, 2*w^3 - w^2 - 10*w + 1]', '[599, 599, w^3 - w^2 - 3*w - 4]', '[613, 613, -w^3 + 2*w^2 + 5*w - 8]', '[617, 617, 3*w^3 - 2*w^2 - 10*w - 2]', '[617, 617, 3*w^3 - w^2 - 13*w]', '[619, 619, w^3 - 2*w^2 - 4*w - 3]', '[625, 5, -5]', '[631, 631, -4*w^3 + 2*w^2 + 14*w + 1]', '[643, 643, 5*w^3 - 16*w - 2]', '[647, 647, 3*w^3 - 2*w^2 - 11*w - 1]', '[659, 659, 2*w^3 - 3*w^2 - 7*w]', '[659, 659, 4*w^3 - 2*w^2 - 11*w - 1]', '[677, 677, -5*w^3 + 2*w^2 + 16*w - 2]', '[677, 677, -5*w^3 + 3*w^2 + 15*w - 2]', '[683, 683, -4*w^3 + 3*w^2 + 12*w]', '[719, 719, w^3 - 4*w^2 - 2*w + 4]', '[719, 719, w^3 + w^2 - w - 5]', '[733, 733, 3*w^3 + w^2 - 10*w - 1]', '[733, 733, 5*w^3 - 3*w^2 - 15*w + 3]', '[739, 739, 5*w^3 - 3*w^2 - 18*w + 2]', '[757, 757, 4*w^2 - 3*w - 9]', '[773, 773, -4*w^3 + w^2 + 12*w + 1]', '[773, 773, w^3 + 3*w^2 - 6*w - 3]', '[787, 787, 2*w^3 + 2*w^2 - 9*w - 3]', '[787, 787, -2*w^3 + 4*w^2 + 5*w - 6]', '[811, 811, -w^3 + 3*w^2 - 7]', '[821, 821, 4*w^3 - 2*w^2 - 13*w - 3]', '[821, 821, w^3 + w - 3]', '[821, 821, -w^3 + 4*w^2 + w - 5]', '[821, 821, -w^3 + 4*w^2 + 2*w - 10]', '[827, 827, -3*w^3 - w^2 + 14*w + 6]', '[829, 829, w^3 - w^2 - 7*w + 5]', '[857, 857, w^3 - w^2 - 5*w - 5]', '[857, 857, 2*w^3 + w^2 - 11*w - 5]', '[881, 881, -3*w^3 - 2*w^2 + 13*w + 5]', '[881, 881, -2*w^3 + 4*w^2 + 7*w - 8]', '[907, 907, w^3 + 2*w^2 - w - 6]', '[907, 907, -4*w^3 + w^2 + 11*w + 3]', '[911, 911, -4*w^3 - w^2 + 13*w + 2]', '[929, 929, -w^3 + w^2 + 3*w - 7]', '[937, 937, -w^3 + 4*w - 5]', '[937, 937, -4*w^2 + 3*w + 8]', '[941, 941, 5*w^3 - 19*w - 2]', '[941, 941, 3*w^3 - 14*w - 5]', '[947, 947, 3*w^3 - 2*w^2 - 12*w - 2]', '[947, 947, -4*w^3 + w^2 + 11*w - 1]', '[967, 967, -2*w^3 - 2*w^2 + 7*w + 1]', '[967, 967, -w^3 + 2*w^2 - 6]', '[971, 971, -2*w^3 + 4*w^2 + 7*w - 7]', '[977, 977, w^3 + w^2 - 8*w - 2]', '[977, 977, w^3 - 4*w^2 - w + 6]', '[991, 991, 3*w^3 - 14*w]', '[991, 991, -3*w^3 + 3*w^2 + 11*w - 1]']}
• 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
  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, -1, -4, 0, 1], 'conductor': 0, 'degree': 4, 'dirichlet_group': [], 'disc_abs': 1957, 'disc_rad': 1957, 'disc_sign': 1, 'frobs': [[2, [[4, 1]]], [3, [[3, 1], [1, 1]]], [5, [[4, 1]]], [7, [[3, 1], [1, 1]]], [11, [[4, 1]]], [13, [[4, 1]]], [17, [[2, 2]]], [19, [0]], [23, [[3, 1], [1, 1]]], [29, [[4, 1]]], [31, [[3, 1], [1, 1]]], [37, [[3, 1], [1, 1]]], [41, [[4, 1]]], [43, [[2, 1], [1, 2]]], [47, [[2, 1], [1, 2]]], [53, [[3, 1], [1, 1]]], [59, [[2, 1], [1, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [12, 12], 'galois_label': '4T5', 'galt': 5, 'grd': 44.23799272118933, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '4.4.1957.1', 'local_algs': ['19.1.2.1a1.2', '19.2.1.0a1.1', '103.2.1.0a1.1', '103.1.2.1a1.1'], 'monogenic': 1, 'narrow_class_group': [], 'narrow_class_number': 1, 'num_ram': 2, 'r2': 0, 'ramps': [19, 103], 'rd': 6.65116476425, 'regulator': {'__RealLiteral__': 0, 'data': '1.91836302339', 'prec': 44}, 'res': {'gal': ['-432,-15768,-87720,-100180,319541,679643,-400845,-1504030,168250,1798485,51374,-1334261,-59554,642831,3022,-200528,11205,38921,-4546,-4338,734,236,-50,-4,1'], 'sib': ['-10,-77,56,41,-18,-3,1', '1,-3,-5,15,-6,-2,1', '1,8,-1,-77,42,155,-90,-121,64,37,-17,-3,1', '100,0,-937,0,2261,0,-1714,0,391,0,-34,0,1', '11943,-3791,-5955,952,1007,-34,-56,0,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a^{3} - 4 a - 1 \\)', '\\( a + 1 \\)', '\\( a^{3} - 3 a \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3']}