Hilbert modular form data - 4.4.4913.1-47.2-c

Formats: - HTML - YAML - JSON - 2024-05-04T21:42:13.979497

• 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': 4913, 'field_bad_primes': [17], 'field_label': '4.4.4913.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '4.4.4913.1-47.2-c', 'label_nsuffix': 2, 'label_suffix': 'c', 'level_bad_primes': [47], 'level_ideal': '[47,47,-w^3 + 2*w^2 + 5*w - 5]', 'level_label': '47.2', 'level_norm': 47, 'parallel_weight': 2, 'short_label': '47.2-c', 'weight': '[2, 2, 2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[47,47,-w^3 + 2*w^2 + 5*w - 5]', 1]], 'hecke_eigenvalues': [1, 1, -6, 2, 2, 2, 2, 0, -1, 8, 8, -4, -4, 4, -4, 2, 6, -2, 6, 14, 10, -6, 18, 18, 0, 16, -8, 16, 6, -2, -2, -2, -10, 22, -10, 6, -2, 14, 14, -2, -8, 8, -16, -8, -16, 0, 24, -24, 12, 28, -12, -20, 24, -8, -8, 16, -10, 22, -10, -26, 20, -4, -4, -20, -14, 2, -14, 18, 10, 26, 26, 10, -38, 34, 10, -6, -22, -22, -38, 26, -22, 2, -20, -28, -28, -12, 32, 8, -40, 0, -2, 30, 30, -2, 12, -20, -36, -20, -6, 10, -38, 34, -2, 38, -18, -34, 0, 16, -16, 0, 22, -10, 6, 6, -14, -32, 0, -8, 0, 20, 36, -12, -44, 42, 2, -22, -6, -8, -32, -8, 24, 30, -34, 30, -18, -42, -34, 14, 6, -34, -34, -2, 30, -24, -56, -32, -32, -28, 36, -12, 28, -48, 40, -40, -40, 30, 54, -42, -42], 'hecke_polynomial': 'x', 'label': '4.4.4913.1-47.2-c'}
• hmf_fields •

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

  
  {'degree': 4, 'discriminant': 4913, 'ideals': ['[1, 1, 1]', '[4, 2, -1/2*w^3 + 3*w + 5/2]', '[4, 2, w^3 - w^2 - 6*w]', '[13, 13, -1/2*w^3 + w^2 + 3*w - 1/2]', '[13, 13, 1/2*w^3 - w^2 - 3*w + 7/2]', '[13, 13, -1/2*w^3 + 4*w - 1/2]', '[13, 13, -1/2*w^3 + 4*w + 5/2]', '[16, 2, 2]', '[16, 4, w^3 - w^2 - 5*w]', '[16, 4, w^3 - w^2 - 5*w + 1]', '[17, 17, 1/2*w^3 - w^2 - w + 3/2]', '[47, 47, -w^2 + 2]', '[47, 47, -w^3 + 2*w^2 + 5*w - 5]', '[47, 47, -3/2*w^3 + w^2 + 10*w + 3/2]', '[47, 47, -1/2*w^3 + 5*w - 1/2]', '[52, 26, -w^3 + 2*w^2 + 5*w - 4]', '[52, 26, -w^3 + w^2 + 7*w - 2]', '[52, 26, w^2 - w - 4]', '[52, 26, w^3 - w^2 - 7*w]', '[52, 26, -w^2 + w + 2]', '[52, 26, -3/2*w^3 + w^2 + 10*w + 1/2]', '[52, 26, -w^2 + 3]', '[52, 26, 1/2*w^3 - 5*w - 1/2]', '[64, 4, -w^3 + 6*w + 5]', '[64, 4, 2*w^3 - 2*w^2 - 12*w]', '[64, 8, w^3 - w^2 - 5*w + 4]', '[64, 8, -w^3 + w^2 + 5*w + 3]', '[67, 67, 3/2*w^3 - 2*w^2 - 8*w + 3/2]', '[67, 67, 1/2*w^3 - 2*w - 5/2]', '[67, 67, -1/2*w^3 + w^2 + w - 5/2]', '[67, 67, -3/2*w^3 + w^2 + 9*w - 1/2]', '[68, 34, -w^2 + w + 3]', '[68, 34, w^3 - w^2 - 7*w + 1]', '[81, 3, -3]', '[89, 89, w^2 - 2*w - 4]', '[89, 89, 3/2*w^3 - 2*w^2 - 9*w + 3/2]', '[89, 89, -1/2*w^3 + w^2 + 4*w - 7/2]', '[89, 89, -w^3 + 7*w + 1]', '[101, 101, -1/2*w^3 + 3*w - 5/2]', '[101, 101, -1/2*w^3 + w^2 + 2*w - 11/2]', '[101, 101, -w^3 + w^2 + 6*w + 3]', '[101, 101, w - 4]', '[103, 103, 3/2*w^3 - 3*w^2 - 7*w + 7/2]', '[103, 103, -w^2 + 8]', '[103, 103, -1/2*w^3 - w^2 + 3*w + 11/2]', '[103, 103, -1/2*w^3 - w^2 + 3*w + 13/2]', '[137, 137, 1/2*w^3 - 2*w - 7/2]', '[137, 137, -1/2*w^3 + w^2 + w - 7/2]', '[137, 137, 3/2*w^3 - 2*w^2 - 8*w + 1/2]', '[137, 137, -3/2*w^3 + w^2 + 9*w - 3/2]', '[149, 149, 3/2*w^3 - 9*w - 13/2]', '[149, 149, 7/2*w^3 - 3*w^2 - 21*w - 3/2]', '[149, 149, 2*w^3 - 2*w^2 - 12*w - 1]', '[149, 149, -w^2 + 6]', '[157, 157, -5/2*w^3 + 3*w^2 + 13*w - 9/2]', '[157, 157, -2*w^3 + 3*w^2 + 12*w - 4]', '[157, 157, 1/2*w^3 - 2*w^2 - 2*w + 15/2]', '[157, 157, 5/2*w^3 - 2*w^2 - 14*w - 3/2]', '[169, 13, -5/2*w^3 + 2*w^2 + 14*w + 1/2]', '[169, 13, 3/2*w^3 - w^2 - 7*w - 1/2]', '[169, 13, -3/2*w^3 + 2*w^2 + 6*w - 3/2]', '[169, 13, 5/2*w^3 - 3*w^2 - 13*w + 7/2]', '[169, 13, -2*w^3 + 2*w^2 + 10*w + 1]', '[169, 13, -2*w^3 + 2*w^2 + 10*w - 3]', '[169, 169, 3/2*w^3 - 2*w^2 - 10*w + 5/2]', '[169, 169, -1/2*w^3 - w^2 + 5*w + 7/2]', '[169, 169, 3/2*w^3 - 2*w^2 - 10*w + 7/2]', '[169, 169, -1/2*w^3 - w^2 + 5*w + 9/2]', '[188, 94, 2*w^3 - 3*w^2 - 11*w + 4]', '[188, 94, 1/2*w^3 - w^2 - 4*w + 9/2]', '[188, 94, -3/2*w^3 + 2*w^2 + 9*w - 1/2]', '[188, 94, w^2 - 3*w - 3]', '[188, 94, w^2 + w - 4]', '[188, 94, -2*w^3 + w^2 + 13*w + 1]', '[188, 94, -w^3 + 7*w]', '[188, 94, w^2 - 2*w - 5]', '[191, 191, 3/2*w^3 - 2*w^2 - 8*w - 1/2]', '[191, 191, -3/2*w^3 + w^2 + 9*w - 5/2]', '[191, 191, 1/2*w^3 - 2*w - 9/2]', '[191, 191, -1/2*w^3 + w^2 + w - 9/2]', '[208, 26, -w^3 + 2*w^2 + 6*w - 1]', '[208, 26, w^3 - 2*w^2 - 6*w + 7]', '[208, 26, -w^3 + 8*w - 1]', '[208, 26, -w^3 + 8*w + 5]', '[208, 52, -w^3 + 9*w]', '[208, 52, 1/2*w^3 - w - 5/2]', '[208, 52, -w^3 + 2*w^2 + 3*w - 4]', '[208, 52, 5/2*w^3 - 3*w^2 - 14*w + 5/2]', '[208, 52, 2*w^3 - w^2 - 12*w - 1]', '[208, 52, -3/2*w^3 + 3*w^2 + 8*w - 15/2]', '[208, 52, 2*w^3 - w^2 - 14*w - 3]', '[208, 52, 1/2*w^3 - 2*w^2 - 3*w + 7/2]', '[221, 221, w + 4]', '[221, 221, -w^3 + w^2 + 6*w - 5]', '[221, 221, 1/2*w^3 - 3*w - 11/2]', '[221, 221, -1/2*w^3 + w^2 + 2*w + 5/2]', '[239, 239, -5/2*w^3 + 2*w^2 + 16*w + 1/2]', '[239, 239, 2*w^3 - 13*w - 8]', '[239, 239, -7/2*w^3 + 3*w^2 + 20*w - 1/2]', '[239, 239, -1/2*w^3 + 4*w + 11/2]', '[251, 251, -5/2*w^3 + 3*w^2 + 13*w - 1/2]', '[251, 251, -2*w^3 + w^2 + 14*w + 2]', '[251, 251, 3/2*w^3 - w^2 - 7*w - 7/2]', '[251, 251, -w^3 + 9*w + 1]', '[256, 4, 4]', '[256, 8, 2*w^3 - 2*w^2 - 10*w]', '[256, 8, 2*w^3 - 2*w^2 - 10*w + 2]', '[256, 16, -w^3 + w^2 + 5*w + 4]', '[256, 16, w^3 - w^2 - 5*w + 5]', '[268, 134, -3*w^3 + 2*w^2 + 17*w + 2]', '[268, 134, 7/2*w^3 - 3*w^2 - 20*w - 1/2]', '[268, 134, w^3 + w^2 - 7*w - 9]', '[268, 134, -w^2 + w + 8]', '[268, 134, 2*w^3 - w^2 - 13*w - 7]', '[268, 134, 1/2*w^3 + w^2 - 4*w - 11/2]', '[268, 134, -4*w^3 + 3*w^2 + 25*w + 3]', '[268, 134, -2*w^3 + 2*w^2 + 13*w - 1]', '[271, 271, -w^3 + 7*w - 1]', '[271, 271, -3/2*w^3 + 2*w^2 + 9*w + 1/2]', '[271, 271, w^2 - 2*w - 6]', '[271, 271, -1/2*w^3 + w^2 + 4*w - 11/2]', '[272, 34, w^3 - 2*w^2 - 2*w + 3]', '[272, 68, 1/2*w^3 + w^2 - 6*w + 1/2]', '[272, 68, w^3 - 2*w^2 - 7*w]', '[289, 17, 2*w^3 - 2*w^2 - 10*w + 1]', '[293, 293, -1/2*w^3 + 2*w^2 + 2*w - 13/2]', '[293, 293, -3/2*w^3 + w^2 + 11*w - 3/2]', '[293, 293, -1/2*w^3 + 2*w^2 + 2*w - 7/2]', '[293, 293, -3/2*w^3 + w^2 + 11*w + 3/2]', '[307, 307, w^3 - w^2 - 8*w + 1]', '[307, 307, 2*w^3 - 2*w^2 - 13*w + 2]', '[307, 307, -1/2*w^3 + 2*w^2 + w - 9/2]', '[307, 307, -1/2*w^3 - w^2 + 4*w + 9/2]', '[324, 6, 3/2*w^3 - 9*w - 15/2]', '[324, 6, -3*w^3 + 3*w^2 + 18*w]', '[353, 353, -3/2*w^3 + 2*w^2 + 8*w - 15/2]', '[353, 353, 11/2*w^3 - 4*w^2 - 34*w - 7/2]', '[353, 353, 6*w^3 - 4*w^2 - 36*w - 7]', '[353, 353, 9/2*w^3 - 3*w^2 - 26*w - 5/2]', '[356, 178, -w^2 + 2*w + 9]', '[356, 178, 5/2*w^3 - 17*w - 21/2]', '[356, 178, 4*w^3 - 3*w^2 - 23*w - 1]', '[356, 178, -1/2*w^3 + w^2 + 2*w - 13/2]', '[356, 178, -4*w^3 + 3*w^2 + 25*w + 2]', '[356, 178, -3*w^3 + 3*w^2 + 16*w - 4]', '[356, 178, 7/2*w^3 - 2*w^2 - 23*w - 11/2]', '[356, 178, -2*w^3 + 13*w + 7]', '[361, 19, 1/2*w^3 + w^2 - 3*w - 15/2]', '[361, 19, -2*w^3 + 2*w^2 + 10*w - 7]', '[373, 373, -1/2*w^3 + 2*w^2 + 2*w - 9/2]', '[373, 373, -3/2*w^3 + w^2 + 11*w + 1/2]', '[373, 373, -1/2*w^3 + 2*w^2 + 2*w - 11/2]', '[373, 373, 3/2*w^3 - w^2 - 11*w + 1/2]', '[404, 202, -5*w^3 + 5*w^2 + 30*w - 2]', '[404, 202, -4*w^3 + 4*w^2 + 23*w - 1]', '[404, 202, w^2 + w - 5]', '[404, 202, 3/2*w^3 + w^2 - 10*w - 25/2]', '[404, 202, -9/2*w^3 + 2*w^2 + 27*w + 21/2]', '[404, 202, -2*w^3 + 3*w^2 + 12*w - 3]', '[404, 202, 4*w^3 - 3*w^2 - 25*w - 6]', '[404, 202, 3/2*w^3 - 9*w - 19/2]', '[409, 409, 2*w^3 - 3*w^2 - 10*w + 2]', '[409, 409, -w^3 + 5*w + 5]', '[409, 409, -1/2*w^3 + w^2 - 7/2]', '[409, 409, 5/2*w^3 - 2*w^2 - 15*w + 5/2]', '[412, 206, 2*w^3 - 2*w^2 - 11*w + 7]', '[412, 206, 8*w^3 - 7*w^2 - 47*w]', '[412, 206, 5/2*w^3 - 3*w^2 - 12*w + 9/2]', '[412, 206, -7/2*w^3 + 23*w + 39/2]', '[412, 206, w^3 - w^2 - 3*w + 5]', '[412, 206, 2*w^3 - w^2 - 11*w + 1]', '[412, 206, 5/2*w^3 - 2*w^2 - 13*w + 3/2]', '[412, 206, w^3 - w^2 - 4*w + 6]', '[421, 421, -2*w^3 + w^2 + 12*w]', '[421, 421, 5/2*w^3 - 3*w^2 - 14*w + 3/2]', '[421, 421, -w^3 + 2*w^2 + 3*w - 5]', '[421, 421, 1/2*w^3 - w - 7/2]', '[443, 443, 5/2*w^3 - 3*w^2 - 15*w + 3/2]', '[443, 443, 1/2*w^3 - w^2 - 5*w + 9/2]', '[443, 443, -1/2*w^3 + 2*w^2 - 13/2]', '[443, 443, -3/2*w^3 + 10*w + 3/2]', '[463, 463, 4*w^3 - 4*w^2 - 22*w + 5]', '[463, 463, 3*w^3 - 4*w^2 - 14*w + 2]', '[463, 463, -5/2*w^3 + 2*w^2 + 14*w - 7/2]', '[463, 463, 3/2*w^3 - w^2 - 7*w - 9/2]', '[509, 509, -7/2*w^3 + 2*w^2 + 20*w + 3/2]', '[509, 509, 5/2*w^3 - w^2 - 16*w - 5/2]', '[509, 509, -5/2*w^3 + 4*w^2 + 10*w - 13/2]', '[509, 509, 9/2*w^3 - 5*w^2 - 25*w + 7/2]', '[523, 523, 3*w^3 - 3*w^2 - 16*w + 3]', '[523, 523, 2*w^3 - 2*w^2 - 9*w + 2]', '[523, 523, 5/2*w^3 - 3*w^2 - 12*w + 3/2]', '[523, 523, -5/2*w^3 + 2*w^2 + 13*w + 3/2]', '[548, 274, -w^3 + 7*w + 8]', '[548, 274, 5/2*w^3 - w^2 - 16*w - 19/2]', '[548, 274, w^3 + w^2 - 7*w - 8]', '[548, 274, 4*w^3 - 3*w^2 - 23*w - 3]', '[548, 274, -4*w^3 + 3*w^2 + 23*w + 2]', '[548, 274, -3*w^3 + 3*w^2 + 19*w - 1]', '[548, 274, -7/2*w^3 + 3*w^2 + 22*w + 1/2]', '[548, 274, 2*w^2 - w - 9]', '[557, 557, 3*w^3 - 3*w^2 - 16*w + 1]', '[557, 557, 5/2*w^3 - 2*w^2 - 13*w + 1/2]', '[557, 557, -2*w^3 + 2*w^2 + 9*w]', '[557, 557, -5/2*w^3 + 3*w^2 + 12*w - 7/2]', '[577, 577, -w^3 - w^2 + 6*w + 9]', '[577, 577, 7/2*w^3 - 3*w^2 - 21*w - 7/2]', '[577, 577, 1/2*w^3 - 2*w^2 - 3*w + 17/2]', '[577, 577, -5/2*w^3 + 3*w^2 + 13*w - 19/2]', '[596, 298, -w - 5]', '[596, 298, -5/2*w^3 + 2*w^2 + 13*w + 1/2]', '[596, 298, 3*w^3 - 3*w^2 - 16*w + 2]', '[596, 298, w^3 - w^2 - 6*w + 6]', '[596, 298, -1/2*w^3 + 3*w + 13/2]', '[596, 298, -1/2*w^3 + w^2 + 2*w + 7/2]', '[596, 298, 5/2*w^3 - 3*w^2 - 12*w + 5/2]', '[596, 298, 2*w^3 - 2*w^2 - 9*w + 1]', '[599, 599, -4*w^3 + 4*w^2 + 22*w - 1]', '[599, 599, w^3 + w^2 - 8*w - 7]', '[599, 599, -5/2*w^3 + 3*w^2 + 16*w - 11/2]', '[599, 599, 3/2*w^3 - w^2 - 7*w - 13/2]', '[611, 611, -3/2*w^3 + 3*w^2 + 6*w - 17/2]', '[611, 611, 3*w^3 - 2*w^2 - 18*w]', '[611, 611, w^3 - 4*w - 4]', '[611, 611, -3/2*w^3 + w^2 + 7*w + 11/2]', '[611, 611, 3*w^3 - 4*w^2 - 16*w + 4]', '[611, 611, -5/2*w^3 + 3*w^2 + 13*w + 3/2]', '[611, 611, -1/2*w^3 + 2*w^2 + 4*w - 13/2]', '[611, 611, 5/2*w^3 - 2*w^2 - 14*w + 9/2]', '[611, 611, w^3 - 2*w^2 - 2*w + 4]', '[611, 611, -3/2*w^3 + 9*w + 1/2]', '[611, 611, -3*w + 4]', '[611, 611, -5/2*w^3 + w^2 + 17*w + 3/2]', '[611, 611, -3*w^3 + 3*w^2 + 18*w + 1]', '[611, 611, 3/2*w^3 - 2*w^2 - 6*w + 13/2]', '[611, 611, -5/2*w^3 + 4*w^2 + 14*w - 11/2]', '[611, 611, -1/2*w^3 - w^2 + 7*w + 9/2]', '[613, 613, w^3 - 5*w - 9]', '[613, 613, -2*w^3 + 3*w^2 + 10*w + 2]', '[613, 613, -1/2*w^3 + w^2 - 15/2]', '[613, 613, -5/2*w^3 + 2*w^2 + 15*w - 13/2]', '[625, 5, -5]', '[628, 314, -2*w^3 + 4*w^2 + 11*w - 13]', '[628, 314, -2*w^3 + 3*w^2 + 9*w - 12]', '[628, 314, -9/2*w^3 + 5*w^2 + 26*w - 9/2]', '[628, 314, -9/2*w^3 + 4*w^2 + 25*w - 7/2]', '[628, 314, -4*w^3 + 4*w^2 + 21*w - 7]', '[628, 314, 5/2*w^3 - 2*w^2 - 15*w + 7/2]', '[628, 314, 2*w^3 - 3*w^2 - 9*w + 8]', '[628, 314, -3/2*w^3 + 2*w^2 + 7*w - 17/2]', '[647, 647, 2*w^3 - 3*w^2 - 8*w + 6]', '[647, 647, -3*w^3 + 2*w^2 + 17*w - 1]', '[647, 647, 3/2*w^3 - w^2 - 6*w - 7/2]', '[647, 647, -7/2*w^3 + 4*w^2 + 19*w - 3/2]', '[659, 659, w^3 + w^2 - 6*w - 5]', '[659, 659, -2*w^3 + 4*w^2 + 9*w - 8]', '[659, 659, -7/2*w^3 + 3*w^2 + 22*w - 1/2]', '[659, 659, 1/2*w^3 - 7*w + 1/2]', '[676, 26, 2*w^3 - w^2 - 13*w + 1]', '[676, 26, -5/2*w^3 + 3*w^2 + 14*w - 1/2]', '[676, 26, 1/2*w^3 - w - 9/2]', '[676, 26, -w^2 + 3*w + 5]', '[676, 26, -3*w^3 + 3*w^2 + 15*w + 2]', '[676, 26, -w^3 + w^2 + 5*w - 6]', '[676, 26, -2*w^3 + 3*w^2 + 11*w - 2]', '[676, 26, w^3 - 2*w^2 - 3*w + 6]', '[676, 26, -3*w^3 + 3*w^2 + 15*w - 5]', '[676, 26, w^3 - w^2 - 5*w - 5]', '[676, 26, w^2 + w - 6]', '[676, 26, 2*w^3 - w^2 - 12*w + 1]', '[676, 338, -2*w^3 + w^2 + 10*w + 5]', '[676, 338, 3/2*w^3 - 2*w^2 - 5*w + 9/2]', '[676, 338, 3/2*w^3 - 2*w^2 - 11*w + 5/2]', '[676, 338, 7/2*w^3 - 3*w^2 - 20*w + 7/2]', '[676, 338, 5/2*w^3 - 3*w^2 - 16*w + 9/2]', '[676, 338, -w^3 - w^2 + 8*w + 6]', '[676, 338, 3*w^3 - 4*w^2 - 15*w + 2]', '[676, 338, -2*w^2 + 3*w + 5]', '[701, 701, 3*w^3 - 2*w^2 - 18*w - 8]', '[701, 701, 7/2*w^3 - 3*w^2 - 21*w - 9/2]', '[701, 701, -1/2*w^3 - 2*w^2 + 3*w + 19/2]', '[701, 701, 15/2*w^3 - 5*w^2 - 45*w - 19/2]', '[727, 727, 2*w^3 - 3*w^2 - 12*w + 2]', '[727, 727, w^3 - 2*w^2 - 7*w + 7]', '[727, 727, 1/2*w^3 + w^2 - 6*w - 13/2]', '[727, 727, 3/2*w^3 - 11*w - 1/2]', '[752, 94, -2*w^2 + 4]', '[752, 94, -2*w^3 + 4*w^2 + 10*w - 10]', '[752, 94, -3*w^3 + 2*w^2 + 20*w + 3]', '[752, 94, -w^3 + 10*w - 1]', '[752, 188, -w^3 + w^2 + 3*w + 5]', '[752, 188, w^3 - w^2 - 9*w]', '[752, 188, -3*w^3 + 3*w^2 + 19*w - 4]', '[752, 188, -2*w^3 + w^2 + 11*w - 3]', '[752, 188, -3*w^3 + 3*w^2 + 17*w + 3]', '[752, 188, -2*w^3 + 3*w^2 + 9*w - 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2]', '[1172, 586, 3/2*w^3 + w^2 - 12*w - 29/2]', '[1172, 586, -3*w^3 + 2*w^2 + 17*w - 2]', '[1172, 586, -9/2*w^3 + 3*w^2 + 28*w + 3/2]', '[1172, 586, 3*w^3 - w^2 - 21*w - 11]', '[1172, 586, 2*w^2 - 3*w - 11]', '[1172, 586, w^2 - 3*w - 7]', '[1172, 586, -6*w^3 + 3*w^2 + 37*w + 9]', '[1223, 1223, 5*w^3 - 6*w^2 - 29*w + 7]', '[1223, 1223, -5/2*w^3 + 4*w^2 + 11*w - 1/2]', '[1223, 1223, 5/2*w^3 - w^2 - 14*w - 17/2]', '[1223, 1223, -4*w^3 + 4*w^2 + 23*w - 8]', '[1228, 614, 7/2*w^3 - 2*w^2 - 21*w - 3/2]', '[1228, 614, 11/2*w^3 - 4*w^2 - 33*w - 3/2]', '[1228, 614, 5*w^3 - 3*w^2 - 30*w - 4]', '[1228, 614, w^3 + w^2 - 9*w - 10]', '[1228, 614, -w^2 + 3*w + 8]', '[1228, 614, -2*w^2 + 3*w + 13]', '[1228, 614, -4*w^3 + 3*w^2 + 24*w - 1]', '[1228, 614, -7/2*w^3 + w^2 + 24*w + 25/2]', '[1237, 1237, 3*w^3 - 2*w^2 - 15*w - 3]', '[1237, 1237, -w^2 + 2*w + 10]', '[1237, 1237, 7/2*w^3 - 4*w^2 - 18*w - 5/2]', '[1237, 1237, 9/2*w^3 - 3*w^2 - 29*w - 9/2]', '[1259, 1259, 4*w^3 - 6*w^2 - 19*w + 6]', '[1259, 1259, -3*w^3 + w^2 + 16*w + 7]', '[1259, 1259, -3*w^3 + w^2 + 22*w + 3]', '[1259, 1259, -3/2*w^3 + 2*w^2 + 3*w - 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2]', '[2027, 2027, 3/2*w^3 - 4*w^2 - 8*w + 21/2]', '[2027, 2027, 7/2*w^3 - w^2 - 22*w - 31/2]', '[2027, 2027, 13/2*w^3 - 4*w^2 - 38*w - 19/2]', '[2036, 1018, 5*w^3 - 31*w - 20]', '[2036, 1018, -10*w^3 + 7*w^2 + 63*w + 13]', '[2036, 1018, -4*w^3 + 5*w^2 + 25*w - 10]', '[2036, 1018, 17/2*w^3 - 5*w^2 - 54*w - 27/2]', '[2036, 1018, -w^3 - 3*w^2 + 9*w + 25]', '[2036, 1018, -5/2*w^3 + 5*w^2 + 12*w - 21/2]', '[2036, 1018, -5*w^3 + w^2 + 32*w + 16]', '[2036, 1018, 11*w^3 - 9*w^2 - 65*w - 4]', '[2039, 2039, 13/2*w^3 - 3*w^2 - 41*w - 21/2]', '[2039, 2039, 7*w^3 - 4*w^2 - 44*w - 8]', '[2039, 2039, 6*w^3 - 5*w^2 - 34*w + 4]', '[2039, 2039, -9/2*w^3 + 4*w^2 + 25*w - 13/2]', '[2041, 2041, 3/2*w^3 - 3*w^2 - 11*w + 17/2]', '[2041, 2041, 5/2*w^3 - w^2 - 10*w + 15/2]', '[2041, 2041, 5/2*w^3 - 3*w^2 - 18*w + 15/2]', '[2041, 2041, -9*w^3 + 12*w^2 + 50*w - 22]', '[2041, 2041, -17/2*w^3 + 10*w^2 + 46*w - 39/2]', '[2041, 2041, -11/2*w^3 + 8*w^2 + 30*w - 27/2]', '[2041, 2041, 7/2*w^3 - 5*w^2 - 21*w + 11/2]', '[2041, 2041, 7/2*w^3 - 6*w^2 - 15*w + 23/2]', '[2041, 2041, 5/2*w^3 - 5*w^2 - 13*w + 21/2]', '[2041, 2041, -1/2*w^3 + 3*w^2 + 3*w - 15/2]', '[2041, 2041, -5*w^3 + 6*w^2 + 28*w - 6]', '[2041, 2041, -4*w^3 + 3*w^2 + 24*w - 2]', '[2041, 2041, -7/2*w^3 + 4*w^2 + 23*w - 3/2]', '[2041, 2041, 7/2*w^3 - 2*w^2 - 14*w + 11/2]', '[2041, 2041, 5/2*w^3 - 4*w^2 - 13*w + 5/2]', '[2041, 2041, -13/2*w^3 + 8*w^2 + 35*w - 41/2]', '[2053, 2053, 7/2*w^3 - 2*w^2 - 21*w - 1/2]', '[2053, 2053, 4*w^3 - 5*w^2 - 22*w + 4]', '[2053, 2053, -3/2*w^3 + 3*w^2 + 4*w - 13/2]', '[2053, 2053, w^3 - 3*w - 5]', '[2087, 2087, -1/2*w^3 + 2*w^2 - 2*w - 11/2]', '[2087, 2087, -7/2*w^3 + 5*w^2 + 19*w - 11/2]', '[2087, 2087, 7/2*w^3 - 2*w^2 - 22*w - 1/2]', '[2087, 2087, 1/2*w^3 + w^2 - w - 13/2]', '[2092, 1046, -3*w^2 + w + 16]', '[2092, 1046, -2*w^2 - w + 9]', '[2092, 1046, 13/2*w^3 - 6*w^2 - 39*w - 1/2]', '[2092, 1046, 7/2*w^3 - 4*w^2 - 21*w + 1/2]', '[2092, 1046, 11/2*w^3 - 5*w^2 - 32*w - 5/2]', '[2092, 1046, -7*w^3 + 5*w^2 + 43*w + 10]', '[2092, 1046, -w^3 - w^2 + 6*w + 12]', '[2092, 1046, 4*w^3 - w^2 - 24*w - 13]', '[2129, 2129, -3*w^3 + 3*w^2 + 20*w - 1]', '[2129, 2129, -1/2*w^3 + 3*w^2 - 19/2]', '[2129, 2129, -2*w^3 + 2*w^2 + 15*w - 4]', '[2129, 2129, 1/2*w^3 + 2*w^2 - 5*w - 11/2]', '[2141, 2141, -2*w^3 + 2*w^2 + 15*w]', '[2141, 2141, -1/2*w^3 + 3*w^2 - 11/2]', '[2141, 2141, -3*w^3 + 3*w^2 + 20*w - 5]', '[2141, 2141, 1/2*w^3 + 2*w^2 - 5*w - 19/2]', '[2143, 2143, 4*w^3 - 5*w^2 - 26*w + 12]', '[2143, 2143, 3/2*w^3 + 2*w^2 - 13*w - 29/2]', '[2143, 2143, 1/2*w^3 + 3*w^2 - 8*w - 9/2]', '[2143, 2143, -3*w^3 + 4*w^2 + 21*w - 1]', '[2192, 274, w^3 - 4*w - 7]', '[2192, 274, -w^3 + 2*w^2 + 2*w - 7]', '[2192, 274, 3*w^3 - 4*w^2 - 16*w + 1]', '[2192, 274, -3*w^3 + 2*w^2 + 18*w - 3]', '[2192, 548, -w^2 - 2*w + 7]', '[2192, 548, -7/2*w^3 + 4*w^2 + 19*w + 3/2]', '[2192, 548, -5/2*w^3 + w^2 + 16*w - 1/2]', '[2192, 548, -3/2*w^3 + w^2 + 6*w + 13/2]', '[2192, 548, -3*w^3 + 4*w^2 + 17*w - 2]', '[2192, 548, -3*w^3 + 2*w^2 + 17*w - 4]', '[2192, 548, -1/2*w^3 + 2*w^2 - w - 15/2]', '[2192, 548, -2*w^3 + 3*w^2 + 8*w - 9]', '[2197, 13, -9/2*w^3 + 5*w^2 + 25*w - 3/2]', '[2197, 13, -7/2*w^3 + 2*w^2 + 20*w - 1/2]', '[2197, 13, 5/2*w^3 - 4*w^2 - 10*w + 17/2]', '[2197, 13, -3/2*w^3 + w^2 + 5*w + 9/2]', '[2197, 169, 7/2*w^3 - 3*w^2 - 21*w + 13/2]', '[2197, 169, 2*w^3 - w^2 - 16*w + 2]', '[2197, 169, -w^3 + 2*w^2 + 8*w - 8]', '[2197, 169, 3*w^3 - 4*w^2 - 18*w + 2]', '[2197, 169, -1/2*w^3 + w^2 - w - 13/2]', '[2197, 169, -3*w^3 + 2*w^2 + 21*w + 3]', '[2197, 169, -2*w^2 + 4*w + 9]', '[2197, 169, 3/2*w^3 - 4*w^2 - 7*w + 23/2]', '[2197, 169, 3/2*w^3 - 8*w - 19/2]', '[2197, 169, 5/2*w^3 - 4*w^2 - 12*w + 1/2]', '[2197, 169, -1/2*w^3 + 3*w^2 + 2*w - 11/2]', '[2197, 169, -2*w^3 + 14*w + 1]', '[2197, 2197, -4*w^3 + 4*w^2 + 21*w - 4]', '[2197, 2197, 3*w^3 - 3*w^2 - 14*w + 3]', '[2197, 2197, -7/2*w^3 + 4*w^2 + 17*w - 3/2]', '[2197, 2197, 7/2*w^3 - 3*w^2 - 18*w - 3/2]', '[2209, 47, 7/2*w^3 - 3*w^2 - 23*w - 1/2]', '[2209, 47, -3/2*w^3 + 4*w^2 + 6*w - 21/2]', '[2209, 47, -3/2*w^3 + w^2 + 13*w - 5/2]', '[2209, 47, -1/2*w^3 - 2*w^2 + 4*w + 11/2]', '[2209, 47, -2*w^3 + 2*w^2 + 10*w + 7]', '[2209, 47, -2*w^3 + 2*w^2 + 10*w - 9]', '[2209, 2209, 5/2*w^3 - 4*w^2 - 16*w + 5/2]', '[2209, 2209, -3/2*w^3 - w^2 + 13*w + 21/2]', '[2209, 2209, 3/2*w^3 + w^2 - 13*w - 3/2]', '[2209, 2209, 5/2*w^3 - 4*w^2 - 16*w + 23/2]', '[2228, 1114, -2*w^3 - w^2 + 13*w + 16]', '[2228, 1114, -2*w^3 - w^2 + 12*w + 13]', '[2228, 1114, 15/2*w^3 - 6*w^2 - 45*w - 11/2]', '[2228, 1114, 6*w^3 - 5*w^2 - 37*w - 5]', '[2228, 1114, -w^3 + 3*w^2 + 6*w - 12]', '[2228, 1114, -9/2*w^3 + 4*w^2 + 27*w + 9/2]', '[2228, 1114, 2*w^3 - 11*w - 9]', '[2228, 1114, -9/2*w^3 + 5*w^2 + 26*w - 5/2]', '[2243, 2243, -9/2*w^3 + 4*w^2 + 26*w - 11/2]', '[2243, 2243, 6*w^3 - 4*w^2 - 35*w - 2]', '[2243, 2243, 15/2*w^3 - 5*w^2 - 46*w - 11/2]', '[2243, 2243, 9/2*w^3 - 2*w^2 - 28*w - 11/2]', '[2308, 1154, 7/2*w^3 - 3*w^2 - 18*w + 3/2]', '[2308, 1154, 12*w^3 - 7*w^2 - 73*w - 19]', '[2308, 1154, -7*w^3 + 9*w^2 + 41*w - 13]', '[2308, 1154, 7/2*w^3 - 4*w^2 - 17*w + 9/2]', '[2308, 1154, w^3 - w^2 - 4*w + 8]', '[2308, 1154, -7*w^3 + 3*w^2 + 45*w + 21]', '[2308, 1154, 2*w^3 - 2*w^2 - 11*w + 9]', '[2308, 1154, -2*w^3 + 5*w^2 + 11*w - 17]', '[2311, 2311, -15/2*w^3 + 4*w^2 + 47*w + 21/2]', '[2311, 2311, -11/2*w^3 + 5*w^2 + 31*w - 13/2]', '[2311, 2311, -5*w^3 + 4*w^2 + 28*w - 4]', '[2311, 2311, 6*w^3 - 3*w^2 - 38*w - 8]', '[2329, 2329, -1/2*w^3 - w^2 + 5*w - 9/2]', '[2329, 2329, -w^3 + 4*w^2 + w - 5]', '[2329, 2329, 1/2*w^3 + w^2 - 10*w + 3/2]', '[2329, 2329, -3*w^3 + 4*w^2 + 12*w - 4]', '[2333, 2333, -1/2*w^3 + 3*w^2 + w - 21/2]', '[2333, 2333, -5/2*w^3 + 2*w^2 + 18*w + 3/2]', '[2333, 2333, -5/2*w^3 + 2*w^2 + 18*w - 7/2]', '[2333, 2333, -1/2*w^3 + 3*w^2 + w - 11/2]', '[2347, 2347, -7/2*w^3 + 3*w^2 + 23*w - 5/2]', '[2347, 2347, 3/2*w^3 - 4*w^2 - 6*w + 15/2]', '[2347, 2347, -3/2*w^3 + w^2 + 13*w + 1/2]', '[2347, 2347, 1/2*w^3 + 2*w^2 - 4*w - 17/2]', '[2381, 2381, 11/2*w^3 - 5*w^2 - 30*w - 7/2]', '[2381, 2381, 9/2*w^3 - 6*w^2 - 28*w + 25/2]', '[2381, 2381, -5/2*w^3 + 4*w^2 + 18*w - 7/2]', '[2381, 2381, 5/2*w^3 + w^2 - 19*w - 25/2]', '[2384, 298, 3*w^3 - 18*w - 13]', '[2384, 298, 7*w^3 - 6*w^2 - 42*w - 3]', '[2384, 298, 4*w^3 - 4*w^2 - 24*w - 2]', '[2384, 298, -2*w^2 + 12]', '[2384, 596, -5*w^3 + 4*w^2 + 27*w + 6]', '[2384, 596, -13/2*w^3 + 5*w^2 + 40*w + 15/2]', '[2384, 596, -w^3 - 2*w^2 + 7*w + 16]', '[2384, 596, 4*w^3 - 5*w^2 - 18*w - 1]', '[2384, 596, 11/2*w^3 - 6*w^2 - 29*w + 21/2]', '[2384, 596, 7/2*w^3 - 3*w^2 - 16*w + 11/2]', '[2384, 596, 5*w^3 - 5*w^2 - 29*w]', '[2384, 596, -w^3 - w^2 + 5*w + 9]', '[2393, 2393, 3/2*w^3 - 4*w^2 - 7*w + 15/2]', '[2393, 2393, -1/2*w^3 + 3*w^2 + 2*w - 19/2]', '[2393, 2393, -3*w^3 + 2*w^2 + 21*w - 1]', '[2393, 2393, -2*w^3 + w^2 + 16*w + 2]', '[2396, 1198, -21/2*w^3 + 8*w^2 + 63*w + 17/2]', '[2396, 1198, -3*w^3 + 5*w^2 + 14*w - 16]', '[2396, 1198, -8*w^3 + 6*w^2 + 47*w + 7]', '[2396, 1198, 13/2*w^3 - 2*w^2 - 43*w - 41/2]', '[2396, 1198, -11/2*w^3 + 5*w^2 + 32*w - 11/2]', '[2396, 1198, 13/2*w^3 - 3*w^2 - 40*w - 39/2]', '[2396, 1198, 3*w^3 + w^2 - 20*w - 22]', '[2396, 1198, -8*w^3 + 5*w^2 + 49*w + 8]', '[2401, 7, -7]', '[2444, 1222, -w - 7]', '[2444, 1222, -7/2*w^3 + 3*w^2 + 18*w + 1/2]', '[2444, 1222, 1/2*w^3 - 3*w^2 + 13/2]', '[2444, 1222, -1/2*w^3 + 3*w^2 - 17/2]', '[2444, 1222, 7/2*w^3 - 5*w^2 - 20*w + 11/2]', '[2444, 1222, -3*w^3 + 5*w^2 + 18*w - 6]', '[2444, 1222, -4*w^3 + 4*w^2 + 23*w + 3]', '[2444, 1222, -w^3 + w^2 + 6*w - 8]', '[2444, 1222, -1/2*w^3 - 2*w^2 + 5*w + 13/2]', '[2444, 1222, -4*w^3 + 3*w^2 + 21*w + 4]', '[2444, 1222, -3*w^3 + 3*w^2 + 14*w - 2]', '[2444, 1222, w^3 - w^2 - 2*w - 6]', '[2444, 1222, -1/2*w^3 + 2*w^2 + 5*w - 15/2]', '[2444, 1222, 4*w^3 - 5*w^2 - 19*w + 2]', '[2444, 1222, -3*w^3 + 3*w^2 + 13*w - 4]', '[2444, 1222, 5/2*w^3 - 19*w - 5/2]', '[2444, 1222, 2*w^3 - 2*w^2 - 15*w + 3]', '[2444, 1222, -3*w^3 + 3*w^2 + 20*w - 4]', '[2444, 1222, -1/2*w^3 - 2*w^2 + 5*w + 17/2]', '[2444, 1222, -7/2*w^3 + 4*w^2 + 17*w - 5/2]', '[2444, 1222, 2*w^3 - 4*w^2 - 13*w + 11]', '[2444, 1222, -1/2*w^3 + 3*w + 17/2]', '[2444, 1222, 2*w^3 - 2*w^2 - 15*w + 1]', '[2444, 1222, -5/2*w^3 + 4*w^2 + 11*w - 23/2]', '[2444, 1222, -2*w^2 + 5*w + 7]', '[2444, 1222, 1/2*w^3 - w^2 - 2*w - 11/2]', '[2444, 1222, 3*w^3 - 3*w^2 - 20*w + 2]', '[2444, 1222, 4*w^3 - 4*w^2 - 21*w + 3]', '[2444, 1222, -3/2*w^3 - w^2 + 14*w + 17/2]', '[2444, 1222, -5*w^3 + 5*w^2 + 27*w - 6]', '[2444, 1222, 5/2*w^3 - w^2 - 14*w + 5/2]', '[2444, 1222, 3*w^3 - w^2 - 20*w - 2]', '[2447, 2447, 9/2*w^3 - 6*w^2 - 24*w + 13/2]', '[2447, 2447, 3/2*w^3 - 6*w - 11/2]', '[2447, 2447, -3/2*w^3 + 3*w^2 + 3*w - 11/2]', '[2447, 2447, -9/2*w^3 + 3*w^2 + 27*w + 1/2]', '[2452, 1226, -10*w^3 + 8*w^2 + 59*w + 5]', '[2452, 1226, 13/2*w^3 - 2*w^2 - 41*w - 49/2]', '[2452, 1226, 4*w^3 - 3*w^2 - 25*w - 10]', '[2452, 1226, -7*w^3 + 7*w^2 + 44*w]', '[2452, 1226, -13/2*w^3 + 4*w^2 + 37*w + 21/2]', '[2452, 1226, 7/2*w^3 + w^2 - 22*w - 37/2]', '[2452, 1226, -4*w^3 + 5*w^2 + 25*w - 9]', '[2452, 1226, -4*w^3 + 7*w^2 + 22*w - 15]', '[2483, 2483, -3*w^3 + 6*w^2 + 16*w - 16]', '[2483, 2483, -11/2*w^3 + 7*w^2 + 33*w - 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5]', '[5303, 5303, 7/2*w^3 - 5*w^2 - 22*w + 5/2]', '[5303, 5303, w^3 + 2*w^2 - 11*w - 13]', '[5303, 5303, 2*w^3 + w^2 - 16*w - 2]', '[5303, 5303, 5/2*w^3 - 4*w^2 - 17*w + 25/2]', '[5308, 2654, 2*w^3 - w^2 - 11*w - 12]', '[5308, 2654, -13/2*w^3 + 6*w^2 + 35*w + 9/2]', '[5308, 2654, -9*w^3 + 4*w^2 + 59*w + 24]', '[5308, 2654, 14*w^3 - 7*w^2 - 87*w - 25]', '[5308, 2654, 31/2*w^3 - 8*w^2 - 97*w - 71/2]', '[5308, 2654, -14*w^3 + 8*w^2 + 85*w + 23]', '[5308, 2654, -10*w^3 + 11*w^2 + 59*w - 13]', '[5308, 2654, -6*w^3 + 11*w^2 + 32*w - 31]', '[5317, 5317, 7/2*w^3 - 2*w^2 - 25*w - 5/2]', '[5317, 5317, -5/2*w^3 + w^2 + 20*w + 1/2]', '[5317, 5317, 7/2*w^3 - 5*w^2 - 13*w + 5/2]', '[5317, 5317, 13/2*w^3 - 8*w^2 - 34*w + 23/2]', '[5317, 5317, -w^3 + w^2 + 8*w - 11]', '[5317, 5317, -1/2*w^3 - w^2 + 4*w - 11/2]', '[5317, 5317, -11/2*w^3 + w^2 + 35*w + 31/2]', '[5317, 5317, 2*w^3 - 2*w^2 - 13*w - 8]', '[5317, 5317, 1/2*w^3 - 2*w^2 - w + 29/2]', '[5317, 5317, -2*w^3 + 5*w^2 + 10*w - 12]', '[5317, 5317, 13/2*w^3 - 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7/2]', '[409, 409, 5/2*w^3 - 2*w^2 - 15*w + 5/2]', '[421, 421, -2*w^3 + w^2 + 12*w]', '[421, 421, 5/2*w^3 - 3*w^2 - 14*w + 3/2]', '[421, 421, -w^3 + 2*w^2 + 3*w - 5]', '[421, 421, 1/2*w^3 - w - 7/2]', '[443, 443, 5/2*w^3 - 3*w^2 - 15*w + 3/2]', '[443, 443, 1/2*w^3 - w^2 - 5*w + 9/2]', '[443, 443, -1/2*w^3 + 2*w^2 - 13/2]', '[443, 443, -3/2*w^3 + 10*w + 3/2]', '[463, 463, 4*w^3 - 4*w^2 - 22*w + 5]', '[463, 463, 3*w^3 - 4*w^2 - 14*w + 2]', '[463, 463, -5/2*w^3 + 2*w^2 + 14*w - 7/2]', '[463, 463, 3/2*w^3 - w^2 - 7*w - 9/2]', '[509, 509, -7/2*w^3 + 2*w^2 + 20*w + 3/2]', '[509, 509, 5/2*w^3 - w^2 - 16*w - 5/2]', '[509, 509, -5/2*w^3 + 4*w^2 + 10*w - 13/2]', '[509, 509, 9/2*w^3 - 5*w^2 - 25*w + 7/2]', '[523, 523, 3*w^3 - 3*w^2 - 16*w + 3]', '[523, 523, 2*w^3 - 2*w^2 - 9*w + 2]', '[523, 523, 5/2*w^3 - 3*w^2 - 12*w + 3/2]', '[523, 523, -5/2*w^3 + 2*w^2 + 13*w + 3/2]', '[557, 557, 3*w^3 - 3*w^2 - 16*w + 1]', '[557, 557, 5/2*w^3 - 2*w^2 - 13*w + 1/2]', '[557, 557, -2*w^3 + 2*w^2 + 9*w]', '[557, 557, -5/2*w^3 + 3*w^2 + 12*w - 7/2]', '[577, 577, -w^3 - w^2 + 6*w + 9]', '[577, 577, 7/2*w^3 - 3*w^2 - 21*w - 7/2]', '[577, 577, 1/2*w^3 - 2*w^2 - 3*w + 17/2]', '[577, 577, -5/2*w^3 + 3*w^2 + 13*w - 19/2]', '[599, 599, -4*w^3 + 4*w^2 + 22*w - 1]', '[599, 599, w^3 + w^2 - 8*w - 7]', '[599, 599, -5/2*w^3 + 3*w^2 + 16*w - 11/2]', '[599, 599, 3/2*w^3 - w^2 - 7*w - 13/2]', '[613, 613, w^3 - 5*w - 9]', '[613, 613, -2*w^3 + 3*w^2 + 10*w + 2]', '[613, 613, -1/2*w^3 + w^2 - 15/2]', '[613, 613, -5/2*w^3 + 2*w^2 + 15*w - 13/2]', '[625, 5, -5]', '[647, 647, 2*w^3 - 3*w^2 - 8*w + 6]', '[647, 647, -3*w^3 + 2*w^2 + 17*w - 1]', '[647, 647, 3/2*w^3 - w^2 - 6*w - 7/2]', '[647, 647, -7/2*w^3 + 4*w^2 + 19*w - 3/2]', '[659, 659, w^3 + w^2 - 6*w - 5]', '[659, 659, -2*w^3 + 4*w^2 + 9*w - 8]', '[659, 659, -7/2*w^3 + 3*w^2 + 22*w - 1/2]', '[659, 659, 1/2*w^3 - 7*w + 1/2]', '[701, 701, 3*w^3 - 2*w^2 - 18*w - 8]', '[701, 701, 7/2*w^3 - 3*w^2 - 21*w - 9/2]', '[701, 701, -1/2*w^3 - 2*w^2 + 3*w + 19/2]', '[701, 701, 15/2*w^3 - 5*w^2 - 45*w - 19/2]', '[727, 727, 2*w^3 - 3*w^2 - 12*w + 2]', '[727, 727, w^3 - 2*w^2 - 7*w + 7]', '[727, 727, 1/2*w^3 + w^2 - 6*w - 13/2]', '[727, 727, 3/2*w^3 - 11*w - 1/2]', '[761, 761, 3*w^3 - 4*w^2 - 18*w + 4]', '[761, 761, -w^3 + 2*w^2 + 8*w - 6]', '[761, 761, 2*w^2 - 4*w - 7]', '[761, 761, -2*w^3 + 14*w + 3]', '[769, 769, 5/2*w^3 - 3*w^2 - 15*w + 1/2]', '[769, 769, -1/2*w^3 + w^2 + 5*w - 11/2]', '[769, 769, 3/2*w^3 - 10*w - 1/2]', '[769, 769, -1/2*w^3 + 2*w^2 - 15/2]', '[829, 829, 7/2*w^3 - 4*w^2 - 20*w + 5/2]', '[829, 829, -5/2*w^3 + 4*w^2 + 12*w - 7/2]', '[829, 829, 7/2*w^3 - 3*w^2 - 21*w + 7/2]', '[829, 829, 3/2*w^3 - 3*w^2 - 5*w + 13/2]', '[863, 863, 3*w^3 - 2*w^2 - 19*w + 1]', '[863, 863, w^2 - 4*w - 4]', '[863, 863, -5/2*w^3 + 4*w^2 + 13*w - 9/2]', '[863, 863, 1/2*w^3 + w^2 - 2*w - 13/2]', '[883, 883, -4*w^3 + 4*w^2 + 22*w - 3]', '[883, 883, 3*w^3 - 2*w^2 - 16*w - 2]', '[883, 883, -3*w^3 + 4*w^2 + 14*w - 4]', '[883, 883, 2*w^3 - 2*w^2 - 8*w + 1]', '[919, 919, 1/2*w^3 - w - 11/2]', '[919, 919, -5/2*w^3 + 3*w^2 + 14*w + 1/2]', '[919, 919, w^3 - 2*w^2 - 3*w + 7]', '[919, 919, -2*w^3 + w^2 + 12*w - 2]', '[953, 953, 7/2*w^3 - 3*w^2 - 19*w + 3/2]', '[953, 953, 5/2*w^3 - 2*w^2 - 12*w - 3/2]', '[953, 953, 7/2*w^3 - 4*w^2 - 18*w + 5/2]', '[953, 953, -5/2*w^3 + 3*w^2 + 11*w - 7/2]']}
• 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, 1, -6, -1, 1], 'conductor': 17, 'degree': 4, 'dirichlet_group': [16, 1, 4, 13], 'disc_abs': 4913, 'disc_rad': 17, 'disc_sign': 1, 'frobs': [[2, [[2, 2]]], [3, [[4, 1]]], [5, [[4, 1]]], [7, [[4, 1]]], [11, [[4, 1]]], [13, [[1, 4]]], [17, [0]], [19, [[2, 2]]], [23, [[4, 1]]], [29, [[4, 1]]], [31, [[4, 1]]], [37, [[4, 1]]], [41, [[4, 1]]], [43, [[2, 2]]], [47, [[1, 4]]], [53, [[2, 2]]], [59, [[2, 2]]]], 'gal_is_abelian': True, 'gal_is_cyclic': True, 'gal_is_solvable': True, 'galois_disc_exponents': [3], 'galois_label': '4T1', 'galt': 1, 'grd': 8.37214402859269, 'index': 2, 'inessentialp': [2], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '4.4.4913.1', 'local_algs': ['17.4.3.1'], 'monogenic': -1, 'num_ram': 1, 'r2': 0, 'ramps': [17], 'rd': 8.37214402859, 'regulator': {'__RealLiteral__': 0, 'data': '3.46198873228', 'prec': 44}, 'res': {}, 'subfield_mults': [1], 'subfields': ['-4.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1}{2} a^{3} - 3 a - \\frac{3}{2} \\)', '\\( a \\)', '\\( \\frac{1}{2} a^{3} - a^{2} - 3 a + \\frac{5}{2} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', '1/2*a^3 - 1/2']}