Hilbert modular form data - 4.4.2304.1-576.1-a

Formats: - HTML - YAML - JSON - 2026-06-23T18:13:06.338325

• 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': 1, 'disc': 2304, 'field_bad_primes': [2, 3], 'field_label': '4.4.2304.1', 'is_CM': 'no', 'is_base_change': 'yes', 'label': '4.4.2304.1-576.1-a', 'label_nsuffix': 0, 'label_suffix': 'a', 'level_bad_primes': [2, 3], 'level_ideal': '[576, 12, 2*w^3 - 10*w]', 'level_label': '576.1', 'level_norm': 576, 'parallel_weight': 2, 'short_label': '576.1-a', 'weight': '[2, 2, 2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[2,2,w^3-4*w+1]', -1], ['[9,3,-w^2+2]', -1]], 'hecke_eigenvalues': [0, 1, -8, 8, -8, 8, 10, 10, 8, -8, 8, -8, 2, 2, -8, 8, -8, 8, -6, -6, -6, -6, 2, 2, 2, 2, -6, -6, 0, 0, 0, 0, 10, 10, -16, -16, 16, 16, 18, 18, 18, 18, 0, 0, 0, 0, 2, 2, 2, 2, 16, 16, -16, -16, -30, -30, 32, -32, 32, -32, -22, -22, -22, -22, 2, 2, 2, 2, -24, 24, -24, 24, -22, -22, 16, 16, -16, -16, 26, 26, 26, 26, 24, 24, -24, -24, -14, -14, -14, -14, 10, 10, 10, 10, 8, 8, -8, -8, -24, 24, -24, 24, 18, 18, 18, 18, -24, -24, 24, 24, -22, -22, -22, -22, -24, 24, -24, 24, 34, 34, 34, 34, -24, -24, 24, 24, 16, 16, -16, -16, -46, -46, -46, -46, 24, -24, 24, -24, -6, -6, 16, 16, -16, -16, 48, -48, 48, -48, 0, 0, 0, 0, -22, -22, -22, -22, -46, -46, 16, 16, -16, -16], 'hecke_polynomial': 'x', 'label': '4.4.2304.1-576.1-a'}
• hmf_fields •

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

  
  {'degree': 4, 'discriminant': 2304, 'ideals': ['[1, 1, 1]', '[2, 2, w^3 - 4*w + 1]', '[4, 2, w^3 - 3*w]', '[8, 2, w^3 - w^2 - 3*w + 3]', '[9, 3, -w^2 + 2]', '[16, 2, 2]', '[18, 6, 2*w^3 - w^2 - 7*w + 2]', '[23, 23, w^3 - w^2 - 4*w + 1]', '[23, 23, w^2 - w - 3]', '[23, 23, -w^2 - w + 3]', '[23, 23, -w^3 - w^2 + 4*w + 1]', '[25, 5, w^3 - 5*w + 1]', '[25, 5, w^3 - 5*w - 1]', '[32, 4, 2*w^3 - 8*w + 2]', '[36, 6, w^3 - 5*w]', '[46, 46, w + 3]', '[46, 46, w^3 - 4*w + 3]', '[46, 46, w^3 - 4*w - 3]', '[46, 46, w - 3]', '[47, 47, -3*w^3 + 2*w^2 + 12*w - 8]', '[47, 47, -2*w^3 - w^2 + 6*w]', '[47, 47, 2*w^3 - w^2 - 6*w]', '[47, 47, w^2 + w - 5]', '[49, 7, 2*w^3 - 6*w - 1]', '[49, 7, -2*w^3 + 6*w - 1]', '[50, 10, -w^2 + w + 4]', '[50, 10, -w^2 - w + 4]', '[64, 4, 2*w^3 - 6*w]', '[71, 71, 2*w^3 - w^2 - 7*w + 1]', '[71, 71, 3*w^3 - w^2 - 11*w + 2]', '[71, 71, 4*w^3 - 2*w^2 - 14*w + 5]', '[71, 71, -3*w^3 + 2*w^2 + 10*w - 4]', '[72, 6, w^3 - w^2 - 5*w + 5]', '[73, 73, -w^3 - 2*w^2 + 3*w + 5]', '[73, 73, -w^3 + 2*w^2 + 3*w - 3]', '[73, 73, w^3 + 2*w^2 - 3*w - 3]', '[73, 73, w^3 - 2*w^2 - 3*w + 5]', '[81, 3, 3]', '[92, 46, -w^2 - 2*w + 3]', '[92, 46, -2*w^3 - w^2 + 8*w + 1]', '[92, 46, 2*w^3 - w^2 - 8*w + 1]', '[92, 46, w^2 - 2*w - 3]', '[94, 94, -w^3 + 2*w^2 + 4*w - 5]', '[94, 94, 2*w^3 - 3*w^2 - 5*w + 6]', '[94, 94, -2*w^3 + w^2 + 7*w - 6]', '[94, 94, w^3 + 2*w^2 - 4*w - 5]', '[97, 97, 2*w^2 + w - 4]', '[97, 97, w^3 + 2*w^2 - 4*w - 4]', '[97, 97, -w^3 + 2*w^2 + 4*w - 4]', '[97, 97, 2*w^2 - w - 4]', '[98, 14, w^3 - 2*w^2 - 2*w + 5]', '[98, 14, -3*w^3 + 2*w^2 + 10*w - 7]', '[100, 10, -w^3 - 2*w^2 + 3*w + 4]', '[100, 10, w^3 - 2*w^2 - 3*w + 4]', '[121, 11, 2*w^3 - 5*w]', '[121, 11, 3*w^3 - 10*w]', '[128, 4, 2*w^3 - 2*w^2 - 6*w + 6]', '[142, 142, 2*w^3 - 9*w + 1]', '[142, 142, -w^3 + 6*w - 1]', '[142, 142, w^3 - 6*w - 1]', '[142, 142, 2*w^3 - 9*w - 1]', '[144, 6, -2*w^2 + 4]', '[146, 146, 4*w^3 - w^2 - 15*w + 2]', '[146, 146, -2*w^3 + w^2 + 7*w]', '[146, 146, -4*w^3 + 3*w^2 + 13*w - 6]', '[146, 146, 6*w^3 - 3*w^2 - 21*w + 8]', '[162, 6, 3*w^3 - 12*w + 3]', '[167, 167, -2*w^3 + 3*w^2 + 5*w - 7]', '[167, 167, -2*w^3 - w^2 + 10*w - 2]', '[167, 167, 3*w^3 - 11*w + 3]', '[167, 167, 3*w^3 - 2*w^2 - 10*w + 8]', '[169, 13, 2*w^3 - 9*w]', '[169, 13, w^3 - 6*w]', '[184, 46, 3*w^3 + w^2 - 9*w - 1]', '[184, 46, -3*w^3 - w^2 + 9*w + 3]', '[184, 46, 3*w^3 - w^2 - 9*w + 3]', '[184, 46, -3*w^3 + w^2 + 9*w - 1]', '[188, 94, -6*w^3 + 3*w^2 + 22*w - 9]', '[188, 94, -w^3 + w - 4]', '[188, 94, -w^3 + w + 4]', '[188, 94, -4*w^3 + w^2 + 14*w - 1]', '[191, 191, w^2 - 2*w - 4]', '[191, 191, 2*w^3 + w^2 - 8*w]', '[191, 191, -2*w^3 + w^2 + 8*w]', '[191, 191, w^2 + 2*w - 4]', '[193, 193, -w - 4]', '[193, 193, -w^3 + 4*w - 4]', '[193, 193, w^3 - 4*w - 4]', '[193, 193, w - 4]', '[194, 194, -5*w^3 + 3*w^2 + 18*w - 8]', '[194, 194, -4*w^3 + 2*w^2 + 13*w - 3]', '[194, 194, -4*w^3 + 2*w^2 + 15*w - 5]', '[194, 194, -3*w^3 + w^2 + 10*w]', '[196, 14, -w^3 + 3*w - 4]', '[196, 14, -w^3 + 3*w + 4]', '[200, 10, 3*w^3 - w^2 - 11*w + 1]', '[200, 10, 3*w^3 + w^2 - 11*w - 1]', '[207, 69, 2*w^3 + w^2 - 7*w + 1]', '[207, 69, w^3 + w^2 - 2*w - 5]', '[207, 69, w^3 - w^2 - 2*w + 5]', '[207, 69, -2*w^3 + w^2 + 7*w + 1]', '[225, 15, 3*w^3 - w^2 - 9*w + 2]', '[225, 15, 3*w^3 + w^2 - 9*w - 2]', '[239, 239, 4*w^3 - 3*w^2 - 16*w + 12]', '[239, 239, -5*w^3 + w^2 + 19*w - 6]', '[239, 239, 4*w^3 - 16*w + 3]', '[239, 239, w^3 - 2*w^2 - 5*w + 9]', '[241, 241, 2*w^3 + w^2 - 10*w - 4]', '[241, 241, 2*w^3 - w^2 - 10*w]', '[241, 241, -2*w^3 - w^2 + 10*w]', '[241, 241, -2*w^3 + w^2 + 10*w - 4]', '[242, 22, 2*w^3 - 2*w^2 - 5*w + 5]', '[242, 22, 3*w^3 - 3*w^2 - 10*w + 10]', '[256, 4, 4]', '[263, 263, -2*w^3 + 2*w^2 + 6*w - 7]', '[263, 263, -4*w^3 + 3*w^2 + 13*w - 9]', '[263, 263, -w^3 + 2*w^2 + 2*w - 6]', '[263, 263, -3*w^3 + 3*w^2 + 9*w - 8]', '[284, 142, -w^2 - 2*w + 5]', '[284, 142, w^3 - 2*w^2 - 5*w + 8]', '[284, 142, 3*w^3 - 2*w^2 - 13*w + 10]', '[284, 142, -2*w^3 + w^2 + 10*w - 7]', '[288, 12, 4*w^3 - 2*w^2 - 14*w + 4]', '[289, 17, 3*w^3 - 9*w + 1]', '[289, 17, -3*w^3 + 9*w + 1]', '[292, 146, 3*w^3 - 13*w - 2]', '[292, 146, -w^3 + 7*w - 2]', '[292, 146, -w^3 + 7*w + 2]', '[292, 146, 3*w^3 - 13*w + 2]', '[311, 311, 2*w^3 + w^2 - 8*w + 2]', '[311, 311, -w^2 - 2*w + 6]', '[311, 311, 3*w^3 - 2*w^2 - 13*w + 9]', '[311, 311, -2*w^3 + w^2 + 8*w + 2]', '[313, 313, -w^3 - w^2 + 4*w - 3]', '[313, 313, w^2 - w - 7]', '[313, 313, w^2 + w - 7]', '[313, 313, w^3 - w^2 - 4*w - 3]', '[324, 6, 3*w^3 - 9*w]', '[334, 334, -3*w^3 + w^2 + 8*w]', '[334, 334, -w^3 + 2*w - 5]', '[334, 334, w^3 - 2*w - 5]', '[334, 334, 3*w^3 + w^2 - 8*w]', '[337, 337, 3*w^3 - 8*w - 2]', '[337, 337, -4*w^3 + 13*w - 2]', '[337, 337, 4*w^3 - 13*w - 2]', '[337, 337, 3*w^3 - 8*w + 2]', '[338, 26, w^3 - w^2 - 6*w + 6]', '[338, 26, 2*w^3 - 2*w^2 - 9*w + 9]', '[359, 359, w^3 + 2*w^2 - 6*w - 6]', '[359, 359, -2*w^3 + 2*w^2 + 9*w - 2]', '[359, 359, 2*w^3 + 2*w^2 - 9*w - 2]', '[359, 359, -w^3 + 2*w^2 + 6*w - 6]', '[361, 19, -w^3 + 5*w - 5]', '[361, 19, w^3 - 5*w - 5]', '[368, 46, 2*w^3 - 2*w^2 - 8*w + 2]', '[368, 46, 2*w^2 - 2*w - 6]', '[368, 46, -2*w^2 - 2*w + 6]', '[368, 46, -2*w^3 - 2*w^2 + 8*w + 2]', '[376, 94, -3*w^3 + w^2 + 13*w - 3]', '[376, 94, -5*w^3 + w^2 + 17*w - 5]', '[376, 94, 3*w^3 + w^2 - 15*w + 3]', '[376, 94, -3*w^3 - w^2 + 13*w + 3]', '[382, 382, -4*w^3 + w^2 + 13*w - 2]', '[382, 382, -2*w^3 + 3*w^2 + 7*w - 8]', '[382, 382, 2*w^3 - w^2 - 9*w + 8]', '[382, 382, -4*w^3 + w^2 + 17*w - 6]', '[383, 383, -w^3 + w^2 - 3]', '[383, 383, 4*w^3 + w^2 - 15*w - 1]', '[383, 383, -4*w^3 + w^2 + 15*w - 1]', '[383, 383, w^3 + w^2 - 3]', '[386, 386, -3*w^3 - w^2 + 12*w]', '[386, 386, -4*w^3 + 17*w - 5]', '[386, 386, -4*w^3 + 15*w - 3]', '[386, 386, -5*w^3 + w^2 + 20*w - 8]', '[388, 194, -2*w^3 + w^2 + 10*w - 1]', '[388, 194, -2*w^3 - w^2 + 10*w + 3]', '[388, 194, -2*w^3 + w^2 + 10*w - 3]', '[388, 194, -2*w^3 - w^2 + 10*w + 1]', '[392, 14, -5*w^3 + w^2 + 19*w - 7]', '[392, 14, 3*w^3 + w^2 - 13*w + 1]', '[400, 10, 2*w^3 - 10*w + 2]', '[400, 10, 2*w^3 - 10*w - 2]', '[409, 409, 3*w^3 + w^2 - 8*w - 1]', '[409, 409, 4*w^3 - w^2 - 13*w + 3]', '[409, 409, 4*w^3 + w^2 - 13*w - 3]', '[409, 409, -3*w^3 + w^2 + 8*w - 1]', '[414, 138, -w^3 - 3*w^2 + 2*w + 6]', '[414, 138, 2*w^3 - 3*w^2 - 7*w + 6]', '[414, 138, 2*w^3 + 3*w^2 - 7*w - 6]', '[414, 138, -w^3 + 3*w^2 + 2*w - 6]', '[423, 141, -6*w^3 + 4*w^2 + 21*w - 14]', '[423, 141, -2*w^3 + 2*w^2 + 10*w - 1]', '[423, 141, 2*w^3 + 2*w^2 - 10*w - 1]', '[423, 141, -w^3 + 3*w^2 + 2*w - 9]', '[431, 431, -3*w^3 - 2*w^2 + 11*w + 3]', '[431, 431, -w^3 + 2*w^2 + w - 5]', '[431, 431, w^3 + 2*w^2 - w - 5]', '[431, 431, 3*w^3 - 2*w^2 - 11*w + 3]', '[433, 433, 3*w^3 - 13*w + 1]', '[433, 433, w^3 + w^2 - 4*w - 7]', '[433, 433, -w^3 + w^2 + 4*w - 7]', '[433, 433, 3*w^3 - 13*w - 1]', '[441, 21, 2*w^3 + w^2 - 10*w - 2]', '[441, 21, -2*w^3 + w^2 + 10*w - 2]', '[450, 30, w^3 - 2*w^2 - 2*w + 7]', '[450, 30, -w^3 - 2*w^2 + 2*w + 7]', '[457, 457, 2*w^3 - 9*w - 6]', '[457, 457, w^3 - 6*w - 6]', '[457, 457, -w^3 + 6*w - 6]', '[457, 457, -2*w^3 + 9*w - 6]', '[478, 478, w^3 - 3*w^2 - 4*w + 8]', '[478, 478, -4*w^3 + 13*w - 1]', '[478, 478, -4*w^3 + 13*w + 1]', '[478, 478, -w^3 - 3*w^2 + 4*w + 8]', '[479, 479, -2*w^3 + w^2 + 4*w - 4]', '[479, 479, 4*w^3 + w^2 - 14*w]', '[479, 479, -4*w^3 + w^2 + 14*w]', '[479, 479, 2*w^3 + w^2 - 4*w - 4]', '[482, 482, -2*w^3 + w^2 + 11*w - 10]', '[482, 482, -6*w^3 + 3*w^2 + 25*w - 14]', '[482, 482, 2*w^3 + w^2 - 5*w - 6]', '[482, 482, 2*w^3 - 3*w^2 - 9*w + 10]', '[484, 22, w^2 + 3]', '[484, 22, -w^2 + 7]', '[503, 503, -3*w^3 - 2*w^2 + 10*w + 2]', '[503, 503, 2*w^3 + 2*w^2 - 5*w - 6]', '[503, 503, -2*w^3 + 2*w^2 + 5*w - 6]', '[503, 503, 3*w^3 - 2*w^2 - 10*w + 2]', '[512, 8, 4*w^3 - 16*w + 4]', '[526, 526, -w - 5]', '[526, 526, -w^3 + 4*w - 5]', '[526, 526, w^3 - 4*w - 5]', '[526, 526, w - 5]', '[529, 23, -2*w^3 + 10*w + 1]', '[529, 23, -2*w^3 + 10*w - 1]', '[529, 23, -3*w^3 + 8*w]', '[529, 23, -4*w^3 + 13*w]', '[529, 23, w^3 - 3*w + 5]', '[529, 23, -w^3 + 3*w + 5]', '[529, 529, -w^3 - 3*w^2 + 4*w + 5]', '[529, 529, -3*w^2 + w + 7]', '[529, 529, -3*w^2 - w + 7]', '[529, 529, w^3 - 3*w^2 - 4*w + 5]', '[568, 142, -w^3 - 3*w^2 + 3*w + 5]', '[568, 142, -w^3 - 3*w^2 + 3*w + 7]', '[568, 142, w^3 - 3*w^2 - 3*w + 7]', '[568, 142, -w^3 + 3*w^2 + 3*w - 5]', '[575, 115, 3*w^3 - 2*w^2 - 8*w + 6]', '[575, 115, w^3 + 4]', '[575, 115, -4*w^3 + 15*w + 4]', '[575, 115, -4*w^3 + 2*w^2 + 13*w - 2]', '[575, 115, 4*w^3 + 2*w^2 - 13*w - 2]', '[575, 115, 4*w^3 - 15*w + 4]', '[575, 115, 3*w^3 + 2*w^2 - 8*w - 6]', '[575, 115, w^3 - 4]', '[576, 12, 2*w^3 - 10*w]', '[577, 577, 3*w^3 + w^2 - 11*w - 8]', '[577, 577, -w^3 + w^2 + 6*w - 9]', '[577, 577, -4*w^3 + 4*w^2 + 15*w - 12]', '[577, 577, -4*w^3 + w^2 + 12*w]', '[578, 34, 2*w^3 - 3*w^2 - 5*w + 8]', '[578, 34, 4*w^3 - 3*w^2 - 13*w + 10]', '[584, 146, w^3 - 3*w^2 - 5*w + 11]', '[584, 146, -3*w^3 + w^2 + 15*w - 9]', '[584, 146, w^3 + w^2 - w - 5]', '[584, 146, 5*w^3 - 3*w^2 - 21*w + 15]', '[599, 599, 2*w^3 + 2*w^2 - 8*w - 1]', '[599, 599, 2*w^2 - 2*w - 7]', '[599, 599, 2*w^2 + 2*w - 7]', '[599, 599, -2*w^3 + 2*w^2 + 8*w - 1]', '[601, 601, -w^3 + 3*w^2 + 4*w - 7]', '[601, 601, 3*w^2 - w - 5]', '[601, 601, 3*w^2 + w - 5]', '[601, 601, w^3 + 3*w^2 - 4*w - 7]', '[622, 622, 4*w^3 - w^2 - 17*w + 10]', '[622, 622, -w^3 - 3*w^2 + 4*w + 6]', '[622, 622, w^3 - 3*w^2 - 4*w + 6]', '[622, 622, 3*w^2 - w - 6]', '[625, 5, 5]', '[625, 25, w^3 - 3*w^2 - 3*w + 6]', '[625, 25, -w^3 - 3*w^2 + 3*w + 6]', '[626, 626, -7*w^3 + w^2 + 28*w - 8]', '[626, 626, -2*w^3 - 2*w^2 + 9*w + 1]', '[626, 626, -4*w^3 + 17*w - 7]', '[626, 626, -7*w^3 + w^2 + 26*w - 6]', '[639, 213, 3*w^3 + w^2 - 12*w + 1]', '[639, 213, 5*w^3 - 19*w + 3]', '[639, 213, 6*w^3 - w^2 - 24*w + 8]', '[639, 213, -4*w^3 + 17*w - 6]', '[647, 647, -6*w^3 + 3*w^2 + 21*w - 7]', '[647, 647, -5*w^3 + 3*w^2 + 17*w - 6]', '[647, 647, 4*w^3 - 2*w^2 - 14*w + 3]', '[647, 647, 5*w^3 - 2*w^2 - 18*w + 4]', '[648, 6, 3*w^3 - 3*w^2 - 9*w + 9]', '[657, 219, -w^3 - w^2 + 5*w + 8]', '[657, 219, -w^3 - w^2 + 5*w - 4]', '[657, 219, w^3 - w^2 - 5*w - 4]', '[657, 219, w^3 - w^2 - 5*w + 8]', '[668, 334, -4*w^3 - w^2 + 18*w - 3]', '[668, 334, -3*w^3 + 4*w^2 + 7*w - 8]', '[668, 334, 3*w^3 - 2*w^2 - 9*w + 8]', '[668, 334, -6*w^3 + w^2 + 22*w - 7]', '[673, 673, -5*w^3 + 2*w^2 + 16*w - 6]', '[673, 673, 3*w^3 - w^2 - 14*w + 5]', '[673, 673, -3*w^3 - w^2 + 14*w + 5]', '[673, 673, 5*w^3 + 2*w^2 - 16*w - 6]', '[674, 674, 2*w^3 - 4*w^2 - 5*w + 11]', '[674, 674, -5*w^3 + 3*w^2 + 16*w - 10]', '[674, 674, w^3 - 3*w^2 + 6]', '[674, 674, -6*w^3 + 4*w^2 + 21*w - 15]', '[676, 26, -3*w^2 + 5]', '[676, 26, -3*w^2 + 7]', '[718, 718, -5*w^3 + w^2 + 16*w]', '[718, 718, -3*w + 7]', '[718, 718, -4*w^3 + 4*w^2 + 15*w - 11]', '[718, 718, -7*w^3 + 3*w^2 + 28*w - 12]', '[719, 719, 3*w^3 - w^2 - 13*w - 2]', '[719, 719, 6*w^3 - w^2 - 23*w + 7]', '[719, 719, -5*w^3 + 20*w - 4]', '[719, 719, -3*w^3 - w^2 + 13*w - 2]', '[722, 38, -6*w^3 + w^2 + 25*w - 10]', '[722, 38, -4*w^3 - w^2 + 15*w]', '[729, 9, -3*w^2 + 6]', '[736, 92, 2*w + 6]', '[736, 92, 2*w^3 - 8*w + 6]', '[736, 92, 2*w^3 - 8*w - 6]', '[736, 92, 2*w - 6]', '[743, 743, -3*w^3 + w^2 + 11*w + 2]', '[743, 743, w^3 + w^2 - w - 6]', '[743, 743, -w^3 + w^2 + w - 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14]', '[1847, 1847, -3*w^3 + 6*w^2 + 9*w - 19]', '[1847, 1847, -10*w^3 + 7*w^2 + 36*w - 26]', '[1847, 1847, 6*w^3 - 2*w^2 - 20*w + 1]', '[1849, 43, -w^3 + 5*w - 7]', '[1849, 43, w^3 - 5*w - 7]', '[1863, 69, 3*w^3 - 3*w^2 - 12*w + 3]', '[1863, 69, 3*w^2 - 3*w - 9]', '[1863, 69, -3*w^2 - 3*w + 9]', '[1863, 69, -3*w^3 - 3*w^2 + 12*w + 3]', '[1871, 1871, 4*w^3 + w^2 - 15*w + 3]', '[1871, 1871, -w^3 + w^2 - 7]', '[1871, 1871, w^3 + w^2 - 7]', '[1871, 1871, -4*w^3 + w^2 + 15*w + 3]', '[1873, 1873, -3*w^3 - 5*w^2 + 11*w + 8]', '[1873, 1873, 4*w^3 + 2*w^2 - 19*w - 8]', '[1873, 1873, 8*w + 3]', '[1873, 1873, 3*w^3 - 2*w^2 - 16*w]', '[1874, 1874, 7*w^3 - 5*w^2 - 28*w + 20]', '[1874, 1874, 2*w^3 - 2*w^2 - 11*w + 9]', '[1874, 1874, 5*w - 7]', '[1874, 1874, -w^3 + 3*w^2 + 6*w - 14]', '[1912, 478, 5*w^3 - w^2 - 21*w + 3]', '[1912, 478, -w^3 + w^2 + 3*w - 9]', '[1912, 478, w^3 + w^2 - 3*w - 9]', '[1912, 478, 5*w^3 + w^2 - 21*w - 3]', '[1916, 958, -3*w^3 - 2*w^2 + 11*w - 2]', '[1916, 958, w^3 - 2*w^2 - w + 10]', '[1916, 958, w^3 + 2*w^2 - w - 10]', '[1916, 958, -3*w^3 + 2*w^2 + 11*w + 2]', '[1922, 62, 3*w^3 - 4*w^2 - 8*w + 11]', '[1922, 62, 5*w^3 - 4*w^2 - 16*w + 13]', '[1928, 482, -5*w^3 + w^2 + 17*w + 3]', '[1928, 482, 7*w^3 - 3*w^2 - 27*w + 7]', '[1928, 482, -9*w^3 + 5*w^2 + 29*w - 9]', '[1928, 482, -11*w^3 + 7*w^2 + 39*w - 19]', '[1936, 22, 4*w^3 - 10*w]', '[1936, 22, 6*w^3 - 20*w]', '[1966, 1966, -7*w^3 + w^2 + 30*w - 10]', '[1966, 1966, -4*w^2 + w + 9]', '[1966, 1966, 6*w^3 - 2*w^2 - 25*w + 15]', '[1966, 1966, -7*w^3 + w^2 + 24*w - 4]', '[1993, 1993, -w^3 + w^2 + 4*w - 9]', '[1993, 1993, 5*w^3 - 21*w - 1]', '[1993, 1993, 5*w^3 - 21*w + 1]', '[1993, 1993, w^3 + w^2 - 4*w - 9]', '[2012, 1006, w^2 - 4*w - 7]', '[2012, 1006, -4*w^3 + w^2 + 16*w + 3]', '[2012, 1006, -4*w^3 - w^2 + 16*w - 3]', '[2012, 1006, -w^2 - 4*w + 7]', '[2017, 2017, w^3 + 4*w^2 - 3*w - 7]', '[2017, 2017, -w^3 + 4*w^2 + 3*w - 9]', '[2017, 2017, w^3 + 4*w^2 - 3*w - 9]', '[2017, 2017, -w^3 + 4*w^2 + 3*w - 7]', '[2018, 2018, 2*w^3 - 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3*w^2 - 18*w + 5]', '[2087, 2087, -2*w^3 + 3*w^2 + 3*w - 7]', '[2089, 2089, -8*w^3 + 2*w^2 + 26*w - 1]', '[2089, 2089, -7*w^3 - 2*w^2 + 29*w + 3]', '[2089, 2089, 7*w^3 - 2*w^2 - 29*w + 3]', '[2089, 2089, 11*w^3 - 5*w^2 - 43*w + 18]', '[2104, 526, -5*w^3 - w^2 + 15*w + 1]', '[2104, 526, -5*w^3 + w^2 + 15*w - 3]', '[2104, 526, -5*w^3 - w^2 + 15*w + 3]', '[2104, 526, -5*w^3 + w^2 + 15*w - 1]', '[2111, 2111, -5*w^3 + 2*w^2 + 20*w - 2]', '[2111, 2111, 2*w^2 + 5*w - 6]', '[2111, 2111, 2*w^2 - 5*w - 6]', '[2111, 2111, 5*w^3 + 2*w^2 - 20*w - 2]', '[2113, 2113, 4*w^2 + w - 8]', '[2113, 2113, w^3 + 4*w^2 - 4*w - 8]', '[2113, 2113, -w^3 + 4*w^2 + 4*w - 8]', '[2113, 2113, 4*w^2 - w - 8]', '[2116, 46, -w^3 + 4*w^2 + 3*w - 8]', '[2116, 46, w^3 + 4*w^2 - 3*w - 8]', '[2116, 46, -w^2 - 5]', '[2116, 46, w^2 - 9]', '[2116, 46, 5*w^3 - 15*w - 2]', '[2116, 46, 5*w^3 - 15*w + 2]', '[2116, 1058, 2*w^3 + w^2 - 12*w - 3]', '[2116, 1058, 4*w^3 + w^2 - 18*w - 1]', '[2116, 1058, 4*w^3 - w^2 - 18*w + 1]', '[2116, 1058, 2*w^3 - w^2 - 12*w + 3]', '[2137, 2137, -3*w^3 + 2*w^2 + 13*w - 13]', '[2137, 2137, 5*w^3 - w^2 - 22*w + 7]', '[2137, 2137, -6*w^3 + 2*w^2 + 19*w - 4]', '[2137, 2137, -4*w^3 + 5*w^2 + 14*w - 14]', '[2151, 717, 5*w^3 + 3*w^2 - 16*w - 3]', '[2151, 717, -9*w^3 + 4*w^2 + 33*w - 11]', '[2151, 717, -8*w^3 + 3*w^2 + 28*w - 6]', '[2151, 717, 3*w^3 - 5*w^2 - 9*w + 16]', '[2161, 2161, -3*w^3 - w^2 + 15*w + 4]', '[2161, 2161, 3*w^3 - w^2 - 15*w]', '[2161, 2161, 3*w^3 + w^2 - 15*w]', '[2161, 2161, 3*w^3 - w^2 - 15*w + 4]', '[2162, 2162, -5*w^3 + 3*w^2 + 16*w - 14]', '[2162, 2162, -6*w^3 + w^2 + 19*w + 6]', '[2162, 2162, 6*w^3 + 5*w^2 - 17*w - 6]', '[2162, 2162, 6*w^3 - 21*w - 7]', '[2162, 2162, w^3 - 3*w^2 - 6*w + 12]', '[2162, 2162, -4*w^3 - 2*w^2 + 15*w + 1]', '[2162, 2162, -7*w^3 + 5*w^2 + 18*w - 2]', '[2162, 2162, 5*w^3 + w^2 - 18*w + 2]', '[2162, 2162, 5*w^3 - w^2 - 18*w - 2]', '[2162, 2162, -7*w^3 - 5*w^2 + 18*w + 2]', '[2162, 2162, 4*w^3 - 2*w^2 - 15*w + 1]', '[2162, 2162, w^3 + 3*w^2 - 6*w - 12]', '[2162, 2162, -6*w^3 + 21*w - 7]', '[2162, 2162, 6*w^3 - 5*w^2 - 17*w + 6]', '[2162, 2162, -6*w^3 - w^2 + 19*w - 6]', '[2162, 2162, -5*w^3 - 3*w^2 + 16*w + 14]', '[2169, 723, -6*w^3 - 2*w^2 + 18*w + 7]', '[2169, 723, 6*w^3 + 2*w^2 - 18*w - 1]', '[2169, 723, -6*w^3 + 2*w^2 + 18*w - 1]', '[2169, 723, -6*w^3 + 2*w^2 + 18*w - 7]', '[2178, 66, w^3 - w^2 - 8*w + 8]', '[2178, 66, 4*w^3 - 4*w^2 - 17*w + 17]', '[2206, 2206, 6*w^3 - 6*w^2 - 19*w + 13]', '[2206, 2206, -7*w^3 + w^2 + 28*w - 4]', '[2206, 2206, -11*w^3 + 5*w^2 + 38*w - 14]', '[2206, 2206, w - 7]', '[2207, 2207, 5*w^3 + 2*w^2 - 21*w - 1]', '[2207, 2207, -w^3 + 4*w^2 - 10]', '[2207, 2207, -8*w^3 + 5*w^2 + 27*w - 17]', '[2207, 2207, -10*w^3 + 3*w^2 + 38*w - 16]', '[2209, 47, 5*w^3 - w^2 - 15*w + 2]', '[2209, 47, 5*w^3 + w^2 - 15*w - 2]', '[2209, 47, 4*w^2 - 7]', '[2209, 47, 4*w^2 - 9]', '[2209, 47, -w^3 + 3*w - 7]', '[2209, 47, w^3 - 3*w - 7]', '[2209, 2209, -2*w^3 - w^2 + 12*w]', '[2209, 2209, 4*w^3 - w^2 - 18*w + 4]', '[2209, 2209, -4*w^3 - w^2 + 18*w + 4]', '[2209, 2209, 2*w^3 - w^2 - 12*w]', '[2231, 2231, 3*w^3 - 2*w^2 - 13*w - 1]', '[2231, 2231, -3*w^3 - w^2 + 7*w + 10]', '[2231, 2231, -3*w^3 - 3*w^2 + 11*w + 2]', '[2231, 2231, -5*w^3 - 2*w^2 + 15*w + 11]', '[2231, 2231, -w^3 + 3*w^2 + w - 10]', '[2231, 2231, 5*w^3 - 2*w^2 - 15*w - 3]', '[2231, 2231, w^3 + 2*w^2 - 7*w - 9]', '[2231, 2231, 5*w^3 - w^2 - 17*w - 6]', '[2231, 2231, -5*w^3 - w^2 + 17*w - 6]', '[2231, 2231, w^3 - 2*w^2 - 7*w + 9]', '[2231, 2231, -5*w^3 - 2*w^2 + 15*w - 3]', '[2231, 2231, -w^3 - 3*w^2 + w + 10]', '[2231, 2231, -5*w^3 + 2*w^2 + 15*w - 11]', '[2231, 2231, 3*w^3 - 3*w^2 - 11*w + 2]', '[2231, 2231, -3*w^3 + w^2 + 7*w - 10]', '[2231, 2231, -3*w^3 - 2*w^2 + 13*w - 1]', '[2254, 322, 6*w^3 + 2*w^2 - 19*w - 5]', '[2254, 322, -6*w^3 - 2*w^2 + 17*w - 1]', '[2254, 322, -7*w^3 + 2*w^2 + 22*w - 9]', '[2254, 322, 5*w^3 - 2*w^2 - 14*w + 3]', '[2254, 322, -7*w^3 - 2*w^2 + 22*w + 9]', '[2254, 322, 5*w^3 + 2*w^2 - 14*w - 3]', '[2254, 322, 6*w^3 - 2*w^2 - 19*w + 5]', '[2254, 322, -6*w^3 + 2*w^2 + 17*w + 1]', '[2258, 2258, 2*w^2 + 3*w - 11]', '[2258, 2258, 3*w^3 - 3*w^2 - 14*w + 12]', '[2258, 2258, -w^3 + w^2 + 8*w - 10]', '[2258, 2258, 6*w^3 - 4*w^2 - 25*w + 17]', '[2272, 284, 4*w^3 - 18*w + 2]', '[2272, 284, -2*w^3 + 12*w - 2]', '[2272, 284, 2*w^3 - 12*w - 2]', '[2272, 284, 4*w^3 - 18*w - 2]', '[2281, 2281, 9*w^3 - 4*w^2 - 34*w + 20]', '[2281, 2281, 4*w^3 + 2*w^2 - 20*w + 1]', '[2281, 2281, -9*w^3 + 3*w^2 + 31*w - 12]', '[2281, 2281, -5*w^2 + 3*w + 11]', '[2300, 230, 4*w^3 + 3*w^2 - 12*w - 1]', '[2300, 230, 4*w^3 + w^2 - 16*w + 5]', '[2300, 230, 4*w^3 + 3*w^2 - 12*w - 11]', '[2300, 230, w^2 + 4*w - 9]', '[2300, 230, 4*w^3 - 3*w^2 - 12*w + 11]', '[2300, 230, -w^2 + 4*w + 9]', '[2300, 230, -4*w^3 + 3*w^2 + 12*w - 1]', '[2300, 230, -4*w^3 + w^2 + 16*w + 5]', '[2302, 2302, 2*w^3 - w^2 - 9*w + 10]', '[2302, 2302, -6*w^3 + w^2 + 25*w - 6]', '[2302, 2302, -8*w^3 + 3*w^2 + 27*w - 8]', '[2302, 2302, -4*w^3 + 5*w^2 + 13*w - 12]', '[2303, 329, 3*w^3 + 3*w^2 - 7*w - 8]', '[2303, 329, 4*w^3 - w^2 - 16*w - 4]', '[2303, 329, -5*w^3 - 3*w^2 + 17*w + 4]', '[2303, 329, w^2 - 4*w - 8]', '[2303, 329, 5*w^3 - 3*w^2 - 17*w + 4]', '[2303, 329, w^2 + 4*w - 8]', '[2303, 329, 4*w^3 + w^2 - 16*w + 4]', '[2303, 329, -3*w^3 + 3*w^2 + 7*w - 8]', '[2304, 12, -4*w^2 + 8]', '[2306, 2306, -5*w^3 - w^2 + 20*w - 2]', '[2306, 2306, -6*w^3 + 25*w - 7]', '[2306, 2306, -6*w^3 + 23*w - 5]', '[2306, 2306, -7*w^3 + w^2 + 28*w - 10]', '[2308, 1154, 7*w^3 - 6*w^2 - 25*w + 16]', '[2308, 1154, -8*w^3 + 3*w^2 + 26*w - 5]', '[2308, 1154, -8*w^3 + 3*w^2 + 32*w - 11]', '[2308, 1154, -7*w^3 + 2*w^2 + 23*w - 8]', '[2312, 34, 7*w^3 - w^2 - 27*w + 9]', '[2312, 34, 5*w^3 + w^2 - 21*w + 3]', '[2336, 292, 8*w^3 - 2*w^2 - 30*w + 4]', '[2336, 292, -4*w^3 + 2*w^2 + 14*w]', '[2336, 292, -8*w^3 + 6*w^2 + 26*w - 12]', '[2336, 292, 12*w^3 - 6*w^2 - 42*w + 16]', '[2350, 470, -6*w^3 - w^2 + 19*w]', '[2350, 470, -8*w^3 + 3*w^2 + 27*w - 10]', '[2350, 470, 7*w^3 - 2*w^2 - 22*w + 1]', '[2350, 470, 5*w^3 + 2*w^2 - 22*w - 3]', '[2350, 470, -7*w^3 - 2*w^2 + 22*w + 1]', '[2350, 470, -5*w^3 + 2*w^2 + 22*w - 3]', '[2350, 470, -6*w^3 + w^2 + 19*w]', '[2350, 470, -8*w^3 - 3*w^2 + 27*w + 10]', '[2351, 2351, 4*w^3 - 3*w^2 - 16*w + 4]', '[2351, 2351, 3*w^2 + 4*w - 8]', '[2351, 2351, 3*w^2 - 4*w - 8]', '[2351, 2351, -4*w^3 - 3*w^2 + 16*w + 4]', '[2367, 789, -2*w^3 + 3*w^2 + 10*w - 12]', '[2367, 789, -5*w^3 + 3*w^2 + 22*w - 15]', '[2367, 789, 2*w^2 + 3*w - 10]', '[2367, 789, -3*w^3 + 2*w^2 + 15*w - 13]', '[2377, 2377, 4*w^3 - w^2 - 18*w + 2]', '[2377, 2377, -2*w^3 - w^2 + 12*w + 2]', '[2377, 2377, 2*w^3 - w^2 - 12*w + 2]', '[2377, 2377, -4*w^3 - w^2 + 18*w + 2]', '[2396, 1198, w^3 - 2*w^2 + w + 6]', '[2396, 1198, -5*w^3 - 2*w^2 + 19*w + 2]', '[2396, 1198, -5*w^3 + 2*w^2 + 19*w - 2]', '[2396, 1198, w^3 + 2*w^2 + w - 6]', '[2399, 2399, 7*w^3 - 25*w - 5]', '[2399, 2399, 5*w^3 - 3*w^2 - 20*w + 5]', '[2399, 2399, -5*w^3 - 3*w^2 + 20*w + 5]', '[2399, 2399, -7*w^3 + 25*w - 5]', '[2401, 7, 7]', '[2401, 49, -5*w^3 + 15*w - 1]', '[2401, 49, 5*w^3 - 15*w - 1]', '[2402, 2402, 2*w^3 - 4*w^2 - 3*w + 9]', '[2402, 2402, -7*w^3 + 5*w^2 + 24*w - 18]', '[2402, 2402, 3*w^3 - 5*w^2 - 8*w + 14]', '[2402, 2402, -6*w^3 + 4*w^2 + 19*w - 13]', '[2404, 1202, -4*w^3 + w^2 + 18*w - 3]', '[2404, 1202, -2*w^3 - w^2 + 12*w + 1]', '[2404, 1202, -2*w^3 + w^2 + 12*w - 1]', '[2404, 1202, -4*w^3 - w^2 + 18*w + 3]', '[2423, 2423, -4*w^3 - w^2 + 17*w - 5]', '[2423, 2423, -w^3 + w^2 + 8*w - 9]', '[2423, 2423, w^3 + w^2 - 8*w - 9]', '[2423, 2423, 4*w^3 - w^2 - 17*w - 5]', '[2425, 485, -6*w^3 - 3*w^2 + 17*w + 3]', '[2425, 485, -6*w^3 + w^2 + 19*w - 5]', '[2425, 485, -7*w^3 - 3*w^2 + 22*w + 9]', '[2425, 485, -5*w^3 + w^2 + 14*w + 1]', '[2425, 485, -7*w^3 + 3*w^2 + 22*w - 9]', '[2425, 485, -5*w^3 - w^2 + 14*w - 1]', '[2425, 485, -6*w^3 + 3*w^2 + 17*w - 3]', '[2425, 485, -6*w^3 - w^2 + 19*w + 5]', '[2446, 2446, -5*w^2 + 3*w + 6]', '[2446, 2446, 5*w^3 - 14*w - 3]', '[2446, 2446, -5*w^3 + 14*w - 3]', '[2446, 2446, -4*w^3 - w^2 + 19*w - 10]', '[2447, 2447, -7*w^3 + 4*w^2 + 25*w - 9]', '[2447, 2447, 8*w^3 - 4*w^2 - 29*w + 10]', '[2447, 2447, -7*w^3 + 3*w^2 + 24*w - 5]', '[2447, 2447, 6*w^3 - 3*w^2 - 20*w + 4]', '[2450, 70, -6*w^3 + 3*w^2 + 23*w - 6]', '[2450, 70, 6*w^3 - w^2 - 21*w - 2]', '[2450, 70, -6*w^3 - w^2 + 21*w - 2]', '[2450, 70, 6*w^3 + 3*w^2 - 23*w - 6]', '[2473, 2473, -11*w^3 + 4*w^2 + 39*w - 13]', '[2473, 2473, -8*w^3 + 2*w^2 + 32*w - 9]', '[2473, 2473, -9*w^3 + 3*w^2 + 31*w - 8]', '[2473, 2473, -8*w^3 + w^2 + 32*w - 6]', '[2488, 622, 9*w^3 - 5*w^2 - 29*w + 13]', '[2488, 622, 3*w^3 + w^2 - 15*w - 3]', '[2488, 622, 3*w^3 - w^2 - 15*w + 3]', '[2488, 622, -3*w^3 - w^2 + 15*w + 1]', '[2498, 2498, 5*w^3 - 2*w^2 - 16*w - 1]', '[2498, 2498, 4*w^3 - 2*w^2 - 11*w + 9]', '[2498, 2498, -4*w^3 - 2*w^2 + 11*w + 9]', '[2498, 2498, -5*w^3 - 2*w^2 + 16*w - 1]', '[2500, 10, 5*w^3 - 15*w]', '[2500, 50, 3*w^3 - 15*w - 2]', '[2500, 50, 3*w^3 - 15*w + 2]', '[2504, 626, -7*w^3 + 5*w^2 + 21*w - 13]', '[2504, 626, -5*w^3 + 5*w^2 + 17*w - 19]', '[2504, 626, -7*w^3 + 7*w^2 + 23*w - 21]', '[2504, 626, -w^3 + 3*w^2 - w - 7]', '[2521, 2521, -3*w^3 + 5*w^2 + 9*w - 8]', '[2521, 2521, -3*w^3 - 5*w^2 + 9*w + 12]', '[2521, 2521, 3*w^3 - 5*w^2 - 9*w + 12]', '[2521, 2521, 3*w^3 + 5*w^2 - 9*w - 8]', '[2543, 2543, 5*w^3 + w^2 - 19*w + 2]', '[2543, 2543, 6*w^3 + w^2 - 23*w + 1]', '[2543, 2543, -6*w^3 + w^2 + 23*w + 1]', '[2543, 2543, -5*w^3 + w^2 + 19*w + 2]', '[2556, 426, 2*w^3 - 3*w^2 - 4*w + 9]', '[2556, 426, 3*w^3 - 4*w^2 - 9*w + 14]', '[2556, 426, 7*w^3 - 6*w^2 - 23*w + 18]', '[2556, 426, -6*w^3 + 5*w^2 + 18*w - 13]', '[2588, 1294, -4*w^3 + 3*w^2 + 18*w - 15]', '[2588, 1294, -3*w^3 + 2*w^2 + 15*w - 12]', '[2588, 1294, w^3 - 2*w^2 - 7*w + 10]', '[2588, 1294, 2*w^3 - 3*w^2 - 10*w + 13]', '[2591, 2591, -8*w^3 + 4*w^2 + 28*w - 9]', '[2591, 2591, 6*w^3 + 3*w^2 - 21*w - 5]', '[2591, 2591, -6*w^3 + 3*w^2 + 21*w - 5]', '[2591, 2591, 7*w^3 - 3*w^2 - 25*w + 6]', '[2592, 12, 6*w^3 - 24*w + 6]', '[2593, 2593, -2*w^2 + w - 4]', '[2593, 2593, w^3 + 2*w^2 - 4*w - 12]', '[2593, 2593, -w^3 + 2*w^2 + 4*w - 12]', '[2593, 2593, -2*w^2 - w - 4]', '[2594, 2594, -10*w^3 + 3*w^2 + 37*w - 8]', '[2594, 2594, 2*w^3 - 4*w^2 - 5*w + 13]', '[2594, 2594, -8*w^3 + 6*w^2 + 27*w - 19]', '[2594, 2594, -12*w^3 + 5*w^2 + 43*w - 14]', '[2601, 51, 3*w^3 - w^2 - 15*w + 2]', '[2601, 51, 3*w^3 + w^2 - 15*w - 2]', '[2617, 2617, 6*w^3 - w^2 - 18*w - 2]', '[2617, 2617, 6*w^3 + w^2 - 18*w - 6]', '[2617, 2617, -6*w^3 + w^2 + 18*w - 6]', '[2617, 2617, -6*w^3 - w^2 + 18*w - 2]', '[2628, 438, 7*w^3 + 2*w^2 - 23*w - 4]', '[2628, 438, -5*w^3 + 2*w^2 + 13*w - 4]', '[2628, 438, -5*w^3 - 2*w^2 + 13*w + 4]', '[2628, 438, 7*w^3 - 2*w^2 - 23*w + 4]', '[2638, 2638, -w^3 - w^2 + 2*w + 10]', '[2638, 2638, -6*w^3 + 2*w^2 + 25*w - 7]', '[2638, 2638, -8*w^3 + 4*w^2 + 25*w - 7]', '[2638, 2638, -9*w^3 + 7*w^2 + 32*w - 20]', '[2642, 2642, 3*w^2 - 3*w - 10]', '[2642, 2642, -2*w^3 + 3*w^2 + 5*w - 12]', '[2642, 2642, 8*w^3 - 7*w^2 - 25*w + 18]', '[2642, 2642, -10*w^3 + 7*w^2 + 33*w - 20]', '[2663, 2663, 3*w^3 + 2*w^2 - 13*w + 3]', '[2663, 2663, -w^3 + 2*w^2 + 7*w - 11]', '[2663, 2663, w^3 + 2*w^2 - 7*w - 11]', '[2663, 2663, -3*w^3 + 2*w^2 + 13*w + 3]', '[2672, 334, -4*w^3 + 6*w^2 + 10*w - 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20]', '[5234, 5234, 4*w^3 - 7*w^2 - 9*w + 16]', '[5234, 5234, -12*w^3 + 7*w^2 + 41*w - 24]', '[5256, 438, 3*w^3 - 5*w^2 - 9*w + 19]', '[5256, 438, -9*w^3 + 7*w^2 + 27*w - 17]', '[5256, 438, -w^3 + 3*w^2 - w - 9]', '[5256, 438, 11*w^3 - 9*w^2 - 37*w + 27]', '[5276, 2638, -2*w^3 - 3*w^2 + 12*w + 11]', '[5276, 2638, -4*w^3 - 3*w^2 + 18*w + 1]', '[5276, 2638, -4*w^3 + 3*w^2 + 18*w - 1]', '[5276, 2638, -2*w^3 + 3*w^2 + 12*w - 11]', '[5279, 5279, 6*w^3 - 4*w^2 - 24*w + 7]', '[5279, 5279, 5*w^3 - 2*w^2 - 17*w - 3]', '[5279, 5279, -5*w^3 - 2*w^2 + 17*w - 3]', '[5279, 5279, 6*w^3 + 4*w^2 - 24*w - 7]', '[5281, 5281, 2*w^3 - 8*w - 9]', '[5281, 5281, 2*w - 9]', '[5281, 5281, -2*w - 9]', '[5281, 5281, -2*w^3 + 8*w - 9]', '[5284, 2642, 3*w^3 - 13*w - 10]', '[5284, 2642, w^3 - 7*w + 10]', '[5284, 2642, w^3 - 7*w - 10]', '[5284, 2642, -3*w^3 + 13*w - 10]', '[5303, 5303, 7*w^3 + 2*w^2 - 25*w - 1]', '[5303, 5303, -7*w^3 - 3*w^2 + 26*w + 5]', '[5303, 5303, 7*w^3 - 3*w^2 - 26*w + 5]', '[5303, 5303, -7*w^3 + 2*w^2 + 25*w - 1]', '[5326, 5326, 6*w^3 - w^2 - 27*w + 16]', '[5326, 5326, -12*w^3 + 3*w^2 + 49*w - 18]', '[5326, 5326, -10*w^3 + w^2 + 35*w - 4]', '[5326, 5326, 5*w^2 - w - 10]', '[5329, 73, -w^3 + 5*w^2 + 3*w - 10]', '[5329, 73, w^3 + 5*w^2 - 3*w - 10]', '[5329, 73, 3*w^3 - 16*w]', '[5329, 73, -3*w^2 - 4]', '[5329, 73, 7*w^3 - 21*w + 5]', '[5329, 73, 7*w^3 - 21*w - 5]', '[5329, 5329, -6*w^3 - w^2 + 17*w - 1]', '[5329, 5329, 7*w^3 - w^2 - 22*w + 5]', '[5329, 5329, -7*w^3 - w^2 + 22*w + 5]', '[5329, 5329, 6*w^3 - w^2 - 17*w - 1]', '[5344, 668, -6*w^3 + 2*w^2 + 16*w]', '[5344, 668, -2*w^3 + 4*w - 10]', '[5344, 668, 2*w^3 - 4*w - 10]', '[5344, 668, 6*w^3 + 2*w^2 - 16*w]', '[5351, 5351, 3*w^2 - 5*w - 9]', '[5351, 5351, 5*w^3 - 3*w^2 - 20*w + 3]', '[5351, 5351, -5*w^3 - 3*w^2 + 20*w + 3]', '[5351, 5351, 3*w^2 + 5*w - 9]', '[5374, 5374, -6*w^3 + w^2 + 17*w - 4]', '[5374, 5374, 7*w^3 + w^2 - 22*w]', '[5374, 5374, -7*w^3 + w^2 + 22*w]', '[5374, 5374, 6*w^3 + w^2 - 17*w - 4]', '[5378, 5378, 3*w^3 + w^2 - 6*w - 10]', '[5378, 5378, -9*w^3 + 6*w^2 + 28*w - 17]', '[5378, 5378, w^3 - 4*w^2 + 2*w + 9]', '[5378, 5378, 9*w^3 - 5*w^2 - 38*w + 22]', '[5384, 1346, -15*w^3 + 5*w^2 + 59*w - 27]', '[5384, 1346, 15*w^3 - 9*w^2 - 53*w + 25]', '[5384, 1346, -7*w^3 + w^2 + 25*w + 3]', '[5384, 1346, 7*w^3 + 3*w^2 - 27*w - 5]', '[5391, 1797, 4*w^3 - 3*w^2 - 14*w]', '[5391, 1797, 2*w^3 + 3*w^2 - 4*w - 12]', '[5391, 1797, -2*w^3 + 3*w^2 + 4*w - 12]', '[5391, 1797, -4*w^3 - 3*w^2 + 14*w]', '[5392, 674, 6*w^3 - 16*w - 4]', '[5392, 674, -8*w^3 + 26*w - 4]', '[5392, 674, 8*w^3 - 26*w - 4]', '[5392, 674, -6*w^3 + 16*w - 4]', '[5399, 5399, -w^3 + 4*w^2 + w - 15]', '[5399, 5399, -3*w^3 - 4*w^2 + 11*w + 1]', '[5399, 5399, 3*w^3 - 4*w^2 - 11*w + 1]', '[5399, 5399, w^3 + 4*w^2 - w - 15]', '[5408, 52, 2*w^3 - 2*w^2 - 12*w + 12]', '[5408, 52, 4*w^3 - 4*w^2 - 18*w + 18]', '[5409, 1803, -2*w^3 + w^2 + 7*w - 11]', '[5409, 1803, w^3 - w^2 - 2*w - 7]', '[5409, 1803, -w^3 - w^2 + 2*w - 7]', '[5409, 1803, 2*w^3 + w^2 - 7*w - 11]', '[5422, 5422, -6*w^3 + 17*w - 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13]', '[5543, 5543, -7*w^3 - w^2 + 28*w - 3]', '[5543, 5543, -4*w^3 + 5*w^2 + 9*w - 11]', '[5543, 5543, 4*w^3 + 5*w^2 - 9*w - 11]', '[5543, 5543, -7*w^3 + w^2 + 28*w + 3]', '[5543, 5543, -8*w^3 - 3*w^2 + 23*w + 13]', '[5543, 5543, 9*w^3 + w^2 - 32*w - 13]', '[5543, 5543, -w^2 - 7*w + 7]', '[5543, 5543, 7*w^3 - 5*w^2 - 24*w + 9]', '[5543, 5543, 9*w^3 + 3*w^2 - 28*w + 1]', '[5543, 5543, -4*w^3 + w^2 + 7*w + 9]', '[5566, 506, 9*w^3 + 2*w^2 - 30*w - 3]', '[5566, 506, 6*w^3 + 3*w^2 - 15*w - 2]', '[5566, 506, 9*w^3 - 3*w^2 - 30*w + 10]', '[5566, 506, 6*w^3 - 2*w^2 - 15*w + 5]', '[5566, 506, -9*w^3 - 3*w^2 + 30*w + 10]', '[5566, 506, -6*w^3 - 2*w^2 + 15*w + 5]', '[5566, 506, -9*w^3 + 2*w^2 + 30*w - 3]', '[5566, 506, -6*w^3 + 3*w^2 + 15*w - 2]', '[5569, 5569, 3*w^3 + w^2 - 11*w + 8]', '[5569, 5569, -w^3 + w^2 + w - 12]', '[5569, 5569, w^3 + w^2 - w - 12]', '[5569, 5569, -3*w^3 + w^2 + 11*w + 8]', '[5591, 5591, -2*w^2 + 10*w + 7]', '[5591, 5591, -5*w^3 - 2*w^2 + 19*w - 7]', '[5591, 5591, 5*w^3 - 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2*w - 10]', '[9913, 9913, -5*w^3 + 18*w + 12]', '[9913, 9913, 10*w^3 + 2*w^2 - 33*w - 10]', '[9913, 9913, -2*w^3 + 6*w^2 + 7*w - 14]', '[9913, 9913, -2*w^3 + 3*w - 12]', '[9913, 9913, -3*w^3 + 18*w - 4]', '[9913, 9913, -7*w^3 - 2*w^2 + 18*w - 2]', '[9927, 3309, 4*w^3 + 3*w^2 - 17*w + 3]', '[9927, 3309, w^3 + 3*w^2 - 8*w - 15]', '[9927, 3309, -w^3 + 3*w^2 + 8*w - 15]', '[9927, 3309, -4*w^3 + 3*w^2 + 17*w + 3]', '[9934, 9934, -2*w^3 - 6*w^2 + 7*w + 11]', '[9934, 9934, -7*w^3 + 2*w^2 + 30*w - 19]', '[9934, 9934, w^3 - 6*w^2 - 2*w + 13]', '[9934, 9934, 2*w^3 - 6*w^2 - 7*w + 11]', '[9938, 9938, 2*w^3 - 4*w^2 - 3*w + 13]', '[9938, 9938, 5*w^3 - 4*w^2 - 18*w + 3]', '[9938, 9938, -5*w^3 - 4*w^2 + 18*w + 3]', '[9938, 9938, -10*w^3 + 8*w^2 + 31*w - 21]', '[9952, 1244, 8*w^3 - 2*w^2 - 34*w + 20]', '[9952, 1244, -2*w^3 - 6*w^2 + 8*w + 12]', '[9952, 1244, 2*w^3 - 6*w^2 - 8*w + 12]', '[9952, 1244, 6*w^2 - 2*w - 12]', '[9959, 9959, 6*w^3 + 3*w^2 - 24*w - 2]', '[9959, 9959, 10*w^3 + 2*w^2 - 35*w]', '[9959, 9959, 10*w^3 - 37*w + 6]', '[9959, 9959, 2*w^3 - 6*w^2 - 4*w + 19]', '[9959, 9959, 3*w^3 - 2*w^2 - 6*w + 12]', '[9959, 9959, 5*w^3 - 4*w^2 - 14*w + 14]', '[9959, 9959, -4*w^3 + 6*w^2 + 18*w - 21]', '[9959, 9959, -8*w^3 + 5*w^2 + 30*w - 10]', '[9959, 9959, 8*w^3 + 5*w^2 - 30*w - 10]', '[9959, 9959, -4*w^3 - 6*w^2 + 18*w + 21]', '[9959, 9959, 5*w^3 + 4*w^2 - 14*w - 14]', '[9959, 9959, 3*w^3 + 2*w^2 - 6*w - 12]', '[9959, 9959, 2*w^3 + 6*w^2 - 4*w - 19]', '[9959, 9959, -10*w^3 + 37*w + 6]', '[9959, 9959, -10*w^3 + 2*w^2 + 35*w]', '[9959, 9959, -6*w^3 + 3*w^2 + 24*w - 2]', '[9986, 9986, -4*w^3 + 8*w^2 + 13*w - 31]', '[9986, 9986, 6*w^3 - 4*w^2 - 17*w - 3]', '[9986, 9986, 12*w^3 - 10*w^2 - 41*w + 21]', '[9986, 9986, -8*w^3 - 3*w^2 + 31*w + 4]', '[9992, 2498, 7*w^3 - w^2 - 25*w - 7]', '[9992, 2498, -3*w^3 + w^2 + 5*w - 11]', '[9992, 2498, -3*w^3 - w^2 + 5*w + 11]', '[9992, 2498, 7*w^3 + w^2 - 25*w + 7]', '[10000, 10, 10]', '[10000, 50, 2*w^3 - 6*w^2 - 6*w + 12]', '[10000, 50, -2*w^3 - 6*w^2 + 6*w + 12]'], 'label': '4.4.2304.1', 'narrow_class_no': 2, 'primes': ['[2, 2, w^3 - 4*w + 1]', '[9, 3, -w^2 + 2]', '[23, 23, w^3 - w^2 - 4*w + 1]', '[23, 23, w^2 - w - 3]', '[23, 23, -w^2 - w + 3]', '[23, 23, -w^3 - w^2 + 4*w + 1]', '[25, 5, w^3 - 5*w + 1]', '[25, 5, w^3 - 5*w - 1]', '[47, 47, -3*w^3 + 2*w^2 + 12*w - 8]', '[47, 47, -2*w^3 - w^2 + 6*w]', '[47, 47, 2*w^3 - w^2 - 6*w]', '[47, 47, w^2 + w - 5]', '[49, 7, 2*w^3 - 6*w - 1]', '[49, 7, -2*w^3 + 6*w - 1]', '[71, 71, 2*w^3 - w^2 - 7*w + 1]', '[71, 71, 3*w^3 - w^2 - 11*w + 2]', '[71, 71, 4*w^3 - 2*w^2 - 14*w + 5]', '[71, 71, -3*w^3 + 2*w^2 + 10*w - 4]', '[73, 73, -w^3 - 2*w^2 + 3*w + 5]', '[73, 73, -w^3 + 2*w^2 + 3*w - 3]', '[73, 73, w^3 + 2*w^2 - 3*w - 3]', '[73, 73, w^3 - 2*w^2 - 3*w + 5]', '[97, 97, 2*w^2 + w - 4]', '[97, 97, w^3 + 2*w^2 - 4*w - 4]', '[97, 97, -w^3 + 2*w^2 + 4*w - 4]', '[97, 97, 2*w^2 - w - 4]', '[121, 11, 2*w^3 - 5*w]', '[121, 11, 3*w^3 - 10*w]', '[167, 167, -2*w^3 + 3*w^2 + 5*w - 7]', '[167, 167, -2*w^3 - w^2 + 10*w - 2]', '[167, 167, 3*w^3 - 11*w + 3]', '[167, 167, 3*w^3 - 2*w^2 - 10*w + 8]', '[169, 13, 2*w^3 - 9*w]', '[169, 13, w^3 - 6*w]', '[191, 191, w^2 - 2*w - 4]', '[191, 191, 2*w^3 + w^2 - 8*w]', '[191, 191, -2*w^3 + w^2 + 8*w]', '[191, 191, w^2 + 2*w - 4]', '[193, 193, -w - 4]', '[193, 193, -w^3 + 4*w - 4]', '[193, 193, w^3 - 4*w - 4]', '[193, 193, w - 4]', '[239, 239, 4*w^3 - 3*w^2 - 16*w + 12]', '[239, 239, -5*w^3 + w^2 + 19*w - 6]', '[239, 239, 4*w^3 - 16*w + 3]', '[239, 239, w^3 - 2*w^2 - 5*w + 9]', '[241, 241, 2*w^3 + w^2 - 10*w - 4]', '[241, 241, 2*w^3 - w^2 - 10*w]', '[241, 241, -2*w^3 - w^2 + 10*w]', '[241, 241, -2*w^3 + w^2 + 10*w - 4]', '[263, 263, -2*w^3 + 2*w^2 + 6*w - 7]', '[263, 263, -4*w^3 + 3*w^2 + 13*w - 9]', '[263, 263, -w^3 + 2*w^2 + 2*w - 6]', '[263, 263, -3*w^3 + 3*w^2 + 9*w - 8]', '[289, 17, 3*w^3 - 9*w + 1]', '[289, 17, -3*w^3 + 9*w + 1]', '[311, 311, 2*w^3 + w^2 - 8*w + 2]', '[311, 311, -w^2 - 2*w + 6]', '[311, 311, 3*w^3 - 2*w^2 - 13*w + 9]', '[311, 311, -2*w^3 + w^2 + 8*w + 2]', '[313, 313, -w^3 - w^2 + 4*w - 3]', '[313, 313, w^2 - w - 7]', '[313, 313, w^2 + w - 7]', '[313, 313, w^3 - w^2 - 4*w - 3]', '[337, 337, 3*w^3 - 8*w - 2]', '[337, 337, -4*w^3 + 13*w - 2]', '[337, 337, 4*w^3 - 13*w - 2]', '[337, 337, 3*w^3 - 8*w + 2]', '[359, 359, w^3 + 2*w^2 - 6*w - 6]', '[359, 359, -2*w^3 + 2*w^2 + 9*w - 2]', '[359, 359, 2*w^3 + 2*w^2 - 9*w - 2]', '[359, 359, -w^3 + 2*w^2 + 6*w - 6]', '[361, 19, -w^3 + 5*w - 5]', '[361, 19, w^3 - 5*w - 5]', '[383, 383, -w^3 + w^2 - 3]', '[383, 383, 4*w^3 + w^2 - 15*w - 1]', '[383, 383, -4*w^3 + w^2 + 15*w - 1]', '[383, 383, w^3 + w^2 - 3]', '[409, 409, 3*w^3 + w^2 - 8*w - 1]', '[409, 409, 4*w^3 - w^2 - 13*w + 3]', '[409, 409, 4*w^3 + w^2 - 13*w - 3]', '[409, 409, -3*w^3 + w^2 + 8*w - 1]', '[431, 431, -3*w^3 - 2*w^2 + 11*w + 3]', '[431, 431, -w^3 + 2*w^2 + w - 5]', '[431, 431, w^3 + 2*w^2 - w - 5]', '[431, 431, 3*w^3 - 2*w^2 - 11*w + 3]', '[433, 433, 3*w^3 - 13*w + 1]', '[433, 433, w^3 + w^2 - 4*w - 7]', '[433, 433, -w^3 + w^2 + 4*w - 7]', '[433, 433, 3*w^3 - 13*w - 1]', '[457, 457, 2*w^3 - 9*w - 6]', '[457, 457, w^3 - 6*w - 6]', '[457, 457, -w^3 + 6*w - 6]', '[457, 457, -2*w^3 + 9*w - 6]', '[479, 479, -2*w^3 + w^2 + 4*w - 4]', '[479, 479, 4*w^3 + w^2 - 14*w]', '[479, 479, -4*w^3 + w^2 + 14*w]', '[479, 479, 2*w^3 + w^2 - 4*w - 4]', '[503, 503, -3*w^3 - 2*w^2 + 10*w + 2]', '[503, 503, 2*w^3 + 2*w^2 - 5*w - 6]', '[503, 503, -2*w^3 + 2*w^2 + 5*w - 6]', '[503, 503, 3*w^3 - 2*w^2 - 10*w + 2]', '[577, 577, 3*w^3 + w^2 - 11*w - 8]', '[577, 577, -w^3 + w^2 + 6*w - 9]', '[577, 577, -4*w^3 + 4*w^2 + 15*w - 12]', '[577, 577, -4*w^3 + w^2 + 12*w]', '[599, 599, 2*w^3 + 2*w^2 - 8*w - 1]', '[599, 599, 2*w^2 - 2*w - 7]', '[599, 599, 2*w^2 + 2*w - 7]', '[599, 599, -2*w^3 + 2*w^2 + 8*w - 1]', '[601, 601, -w^3 + 3*w^2 + 4*w - 7]', '[601, 601, 3*w^2 - w - 5]', '[601, 601, 3*w^2 + w - 5]', '[601, 601, w^3 + 3*w^2 - 4*w - 7]', '[647, 647, -6*w^3 + 3*w^2 + 21*w - 7]', '[647, 647, -5*w^3 + 3*w^2 + 17*w - 6]', '[647, 647, 4*w^3 - 2*w^2 - 14*w + 3]', '[647, 647, 5*w^3 - 2*w^2 - 18*w + 4]', '[673, 673, -5*w^3 + 2*w^2 + 16*w - 6]', '[673, 673, 3*w^3 - w^2 - 14*w + 5]', '[673, 673, -3*w^3 - w^2 + 14*w + 5]', '[673, 673, 5*w^3 + 2*w^2 - 16*w - 6]', '[719, 719, 3*w^3 - w^2 - 13*w - 2]', '[719, 719, 6*w^3 - w^2 - 23*w + 7]', '[719, 719, -5*w^3 + 20*w - 4]', '[719, 719, -3*w^3 - w^2 + 13*w - 2]', '[743, 743, -3*w^3 + w^2 + 11*w + 2]', '[743, 743, w^3 + w^2 - w - 6]', '[743, 743, -w^3 + w^2 + w - 6]', '[743, 743, 3*w^3 + w^2 - 11*w + 2]', '[769, 769, -4*w^3 + 17*w - 2]', '[769, 769, -2*w^3 + w^2 + 8*w - 8]', '[769, 769, 2*w^3 + w^2 - 8*w - 8]', '[769, 769, 4*w^3 - 17*w - 2]', '[839, 839, w^3 + 3*w^2 - 6*w - 9]', '[839, 839, -4*w^3 - 2*w^2 + 16*w + 3]', '[839, 839, 4*w^3 - 2*w^2 - 16*w + 3]', '[839, 839, -w^3 + 3*w^2 + 6*w - 9]', '[841, 29, -4*w^3 + w^2 + 12*w - 2]', '[841, 29, 4*w^3 + w^2 - 12*w - 2]', '[863, 863, 2*w^2 + 3*w - 6]', '[863, 863, 3*w^3 - 2*w^2 - 12*w + 2]', '[863, 863, 3*w^3 + 2*w^2 - 12*w - 2]', '[863, 863, 2*w^2 - 3*w - 6]', '[887, 887, w^3 + 2*w^2 - 6*w - 8]', '[887, 887, 2*w^2 - 2*w - 9]', '[887, 887, 2*w^2 + 2*w - 9]', '[887, 887, -w^3 + 2*w^2 + 6*w - 8]', '[911, 911, -3*w^3 - 3*w^2 + 11*w + 4]', '[911, 911, w^3 + 3*w^2 - w - 8]', '[911, 911, -w^3 + 3*w^2 + w - 8]', '[911, 911, 3*w^3 - 3*w^2 - 11*w + 4]', '[937, 937, -w^3 - w^2 + 8*w + 1]', '[937, 937, 4*w^3 - w^2 - 17*w + 3]', '[937, 937, -4*w^3 - w^2 + 17*w + 3]', '[937, 937, w^3 - w^2 - 8*w + 1]', '[961, 31, -4*w^3 + 12*w - 1]', '[961, 31, 4*w^3 - 12*w - 1]', '[983, 983, w^2 + 3*w - 7]', '[983, 983, 3*w^3 - w^2 - 12*w - 3]', '[983, 983, 3*w^3 + w^2 - 12*w + 3]', '[983, 983, w^2 - 3*w - 7]']}
• 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[]
  maxp	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
  unit_signature_rank	smallint
  used_grh	boolean

  
  {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, 0, -4, 0, 1], 'conductor': 24, 'degree': 4, 'disc_abs': 2304, 'disc_rad': 6, 'disc_sign': 1, 'gal_is_abelian': True, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [8, 2], 'galois_label': '4T2', 'galt': 2, 'grd': 6.928203230275509, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '4.4.2304.1', 'local_algs': ['2.1.4.8b1.6', '3.2.2.2a1.2'], 'maxp': 3, 'monogenic': 1, 'narrow_class_group': [2], 'narrow_class_number': 2, 'num_ram': 2, 'r2': 0, 'ramps': [2, 3], 'rd': 6.92820323028, 'regulator': {'__RealLiteral__': 0, 'data': '2.66089858019', 'prec': 44}, 'subfield_mults': [1, 1, 1], 'subfields': ['-3.0.1', '-6.0.1', '-2.0.1'], 'torsion_order': 2, 'unit_signature_rank': 3, 'used_grh': False}