Hilbert modular form data - 3.3.316.1-128.7-b

Formats: - HTML - YAML - JSON - 2025-11-26T12:24:48.744890

• hmf_forms •

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

  
  {'deg': 3, 'dimension': 1, 'disc': 316, 'field_bad_primes': [2, 79], 'field_label': '3.3.316.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '3.3.316.1-128.7-b', 'label_nsuffix': 1, 'label_suffix': 'b', 'level_bad_primes': [2], 'level_ideal': '[128, 64, -3*w^2 - w + 6]', 'level_label': '128.7', 'level_norm': 128, 'parallel_weight': 2, 'short_label': '128.7-b', 'weight': '[2, 2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[2, 2, -w]', 1], ['[2, 2, w - 1]', -1]], 'hecke_eigenvalues': [-1, 0, 0, -2, 0, 4, 8, -2, 4, -6, 6, -8, 12, 4, 6, 2, -12, 6, -10, -6, 12, -8, -4, 18, -2, 6, -14, 0, -6, -10, 20, 14, 20, 4, -18, -8, -10, 26, 22, -14, 10, -16, 8, 16, 20, 24, 20, -28, 6, -26, -4, 2, -14, -30, 24, -16, 20, 12, 12, -2, 22, 0, 20, -28, 28, -4, -8, 6, -10, 10, 20, -20, 16, 16, 24, 2, 2, 22, -4, -22, -12, -30, 6, -40, 32, -12, 24, 4, -2, 18, 12, -20, -40, 36, 18, 6, -16, 2, 24, -36, -42, 6, 42, -4, -34, -16, 10, -38, -24, -12, 0, -4, -10, 14, -24, 30, -38, -12, -8, -2, -14, -2, 48, -48, 42, 26, 42, 14, 6, -26, -6, -52, 2, -8, 10, 54, 6, 4, 40, -20, -30, -40, 22, 22, 4, 46, 46, 2, 14, 12, 24, -12, 52, -34, 42, 18, -30, 18, 36, -8, -28, -34, -32, -48, 34, 36, -4, 24, 6, 58, 38], 'hecke_polynomial': 'x', 'label': '3.3.316.1-128.7-b'}
• hmf_fields •

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

  
  {'degree': 3, 'discriminant': 316, 'ideals': ['[1, 1, 1]', '[2, 2, -w]', '[2, 2, w - 1]', '[4, 2, w^2 - 4]', '[4, 2, w^2 - w - 4]', '[4, 4, w + 1]', '[8, 2, 2]', '[8, 4, -w^2 + 2]', '[8, 4, -w^2 + w + 2]', '[8, 8, w^2 - 1]', '[11, 11, w^2 - w - 1]', '[16, 4, -2*w]', '[16, 4, -w^2 + 2*w + 2]', '[16, 4, 2*w - 2]', '[16, 8, w^2 - w - 6]', '[16, 16, 2*w^2 - w - 7]', '[17, 17, -w^2 - w + 3]', '[19, 19, w^2 - w + 1]', '[22, 22, w + 3]', '[22, 22, 2*w^2 - w - 10]', '[23, 23, 2*w - 3]', '[27, 3, 3]', '[29, 29, 2*w + 1]', '[31, 31, 2*w^2 - 2*w - 9]', '[32, 4, 2*w^2 - 8]', '[32, 4, 2*w^2 - 2*w - 8]', '[32, 8, -w^2 + 2*w - 2]', '[32, 8, 2*w + 2]', '[32, 16, -w^2 - w + 4]', '[32, 32, -w^2 + 2*w + 3]', '[34, 34, -w^2 - 1]', '[34, 34, -w + 4]', '[37, 37, 2*w^2 - 2*w - 5]', '[38, 38, -w^2 + 7]', '[38, 38, -2*w^2 + w + 6]', '[41, 41, 2*w^2 - 9]', '[43, 43, w^2 + w - 5]', '[43, 43, -3*w^2 + w + 15]', '[43, 43, -2*w^2 + 2*w + 11]', '[44, 22, -w^2 + 2*w + 4]', '[44, 22, -w^2 - w + 6]', '[44, 44, w^2 + 2*w - 3]', '[46, 46, -2*w^2 - w + 6]', '[46, 46, -w^2 + 2*w + 5]', '[53, 53, w^2 - w - 7]', '[54, 6, -3*w]', '[54, 6, 3*w - 3]', '[58, 58, 2*w^2 - w - 1]', '[58, 58, -2*w^2 + 3*w + 2]', '[61, 61, 4*w^2 - 2*w - 15]', '[62, 62, w + 4]', '[62, 62, -2*w^2 + w + 5]', '[64, 4, 4]', '[64, 8, 3*w^2 - 2*w - 10]', '[64, 8, -2*w^2 + 4]', '[64, 8, -2*w^2 + 2*w + 4]', '[64, 16, 2*w^2 - 2]', '[64, 32, -w^2 + w - 2]', '[64, 64, 2*w^2 - 3*w - 1]', '[67, 67, -5*w^2 + 3*w + 23]', '[68, 34, 3*w^2 - w - 10]', '[68, 34, w^2 - 4*w]', '[68, 68, 2*w^2 - w - 11]', '[73, 73, 2*w^2 - 3]', '[73, 73, -3*w^2 - w + 7]', '[73, 73, -6*w^2 + 4*w + 25]', '[74, 74, -3*w^2 + 2*w + 15]', '[74, 74, -3*w + 4]', '[76, 38, w^2 - 3*w - 2]', '[76, 38, w^2 + 2*w - 4]', '[76, 76, 3*w - 5]', '[79, 79, w^2 - 5*w + 1]', '[79, 79, 3*w^2 - 3*w - 11]', '[82, 82, -2*w^2 + w + 4]', '[82, 82, -w + 5]', '[83, 83, 2*w^2 - 2*w - 3]', '[86, 86, -2*w^2 + w + 2]', '[86, 86, w^2 + 2*w - 9]', '[86, 86, -3*w - 4]', '[86, 86, w^2 - 2*w + 3]', '[86, 86, 2*w^2 - 3*w - 6]', '[86, 86, 2*w^2 + w - 7]', '[88, 22, 2*w^2 - 2*w - 2]', '[88, 44, -w^2 + 3*w - 4]', '[88, 44, -w^2 - 2]', '[88, 88, 4*w^2 - w - 17]', '[92, 46, -w^2 - w - 2]', '[92, 46, -w^2 + 8]', '[92, 92, 2*w^2 - w - 3]', '[106, 106, 3*w + 2]', '[106, 106, -w^2 - 2*w + 5]', '[108, 6, 3*w^2 - 12]', '[108, 6, 3*w^2 - 3*w - 12]', '[108, 12, 3*w + 3]', '[109, 109, w^2 - 3*w - 3]', '[113, 113, 3*w^2 - 3*w - 13]', '[116, 58, w^2 - w - 8]', '[116, 58, 3*w^2 - 8]', '[116, 116, 3*w^2 - 2*w - 9]', '[121, 11, 3*w^2 - w - 9]', '[121, 121, -w^2 + 3*w + 7]', '[122, 122, -2*w^2 + 3*w + 7]', '[122, 122, -2*w^2 - w + 8]', '[124, 62, -w^2 - 2*w + 8]', '[124, 62, w^2 + 3*w - 4]', '[124, 124, w^2 - 4*w - 1]', '[125, 5, -5]', '[128, 8, -4*w]', '[128, 8, -2*w^2 + 4*w + 4]', '[128, 8, 4*w - 4]', '[128, 16, -w^2 - 2*w + 6]', '[128, 16, 2*w^2 - 2*w - 12]', '[128, 32, 4*w^2 - 2*w - 14]', '[128, 64, -3*w^2 - w + 6]', '[128, 128, w + 5]', '[131, 131, -6*w^2 + 2*w + 25]', '[134, 134, 2*w^2 - 3*w - 10]', '[134, 134, 3*w^2 - 13]', '[136, 34, -2*w^2 - 2*w + 6]', '[136, 68, -w^2 + 3*w + 4]', '[136, 68, 3*w^2 - 14]', '[136, 136, -w^2 - 2*w + 7]', '[137, 137, -w^2 + w - 3]', '[146, 146, 5*w - 1]', '[146, 146, 4*w^2 + 5*w - 6]', '[146, 146, 2*w^2 - w - 12]', '[146, 146, -2*w^2 - 5*w + 4]', '[146, 146, -w^2 - 4*w - 1]', '[146, 146, 4*w^2 - 3*w - 13]', '[148, 74, w^2 - 3*w - 6]', '[148, 74, -5*w^2 + 4*w + 20]', '[148, 148, 2*w^2 + w - 9]', '[149, 149, 2*w - 7]', '[151, 151, w^2 - 3*w - 5]', '[152, 38, 2*w^2 - 2*w + 2]', '[152, 76, -3*w^2 - w + 10]', '[152, 76, -w^2 + 4*w - 6]', '[152, 152, -2*w^2 + 3*w + 9]', '[157, 157, 3*w^2 - 3*w - 7]', '[158, 158, 2*w^2 + w - 10]', '[158, 158, -3*w^2 + 4*w + 5]', '[158, 158, -2*w^2 - 3*w + 5]', '[158, 158, -w + 6]', '[163, 163, 2*w^2 - 13]', '[164, 82, -7*w^2 + 4*w + 32]', '[164, 82, -9*w^2 + 5*w + 36]', '[164, 164, 4*w^2 - w - 13]', '[166, 166, -2*w^2 + 7*w - 1]', '[166, 166, -5*w + 4]', '[167, 167, -4*w + 5]', '[172, 86, -3*w^2 + 2*w + 16]', '[172, 86, -5*w^2 + 3*w + 18]', '[172, 86, -3*w^2 + 5*w + 2]', '[172, 86, w^2 - 2*w + 4]', '[172, 86, 3*w^2 - 2*w - 8]', '[172, 86, -3*w^2 - w + 4]', '[172, 172, -5*w^2 + 4*w + 21]', '[172, 172, 3*w^2 - 7]', '[172, 172, w^2 + 3]', '[173, 173, -7*w^2 + 3*w + 27]', '[176, 44, 2*w + 6]', '[176, 44, 5*w^2 - 2*w - 18]', '[176, 44, 4*w^2 - 2*w - 20]', '[176, 88, -3*w^2 + w + 8]', '[176, 176, -w^2 + 9]', '[179, 179, 4*w^2 - 4*w - 11]', '[181, 181, 4*w^2 - 15]', '[181, 181, w^2 - 3*w + 5]', '[181, 181, w^2 + 3*w - 5]', '[184, 46, 4*w - 6]', '[184, 92, w^2 - 4*w - 2]', '[184, 92, 3*w^2 - 7*w - 2]', '[184, 184, 3*w + 7]', '[187, 187, -4*w - 1]', '[193, 193, 2*w^2 - 4*w - 5]', '[197, 197, 2*w^2 + 2*w - 7]', '[209, 209, 3*w^2 + 3*w - 7]', '[211, 211, 4*w^2 - 2*w - 13]', '[211, 211, -7*w^2 + 5*w + 29]', '[211, 211, w^2 - w - 9]', '[212, 106, -7*w^2 + 5*w + 30]', '[212, 106, -7*w^2 + 2*w + 28]', '[212, 212, w^2 - 4*w - 9]', '[216, 6, 6]', '[216, 12, -3*w^2 + 6]', '[216, 12, -3*w^2 + 3*w + 6]', '[216, 24, 3*w^2 - 3]', '[218, 218, -3*w^2 + 4*w + 1]', '[218, 218, 2*w^2 - w + 2]', '[223, 223, 5*w^2 - w - 23]', '[226, 226, w + 6]', '[226, 226, -3*w^2 + 2*w + 7]', '[227, 227, -3*w^2 + 3*w + 17]', '[227, 227, 3*w^2 - w - 7]', '[227, 227, 3*w^2 + w - 11]', '[229, 229, 5*w^2 - w - 21]', '[232, 58, 4*w + 2]', '[232, 116, -w^2 - 3*w + 6]', '[232, 116, 3*w^2 - 4*w - 10]', '[232, 232, -2*w^2 + 5*w + 3]', '[233, 233, 3*w^2 - 5*w - 7]', '[239, 239, -w^2 + 7*w - 5]', '[242, 22, -2*w^2 - 3*w + 6]', '[242, 22, -w^2 + 4*w + 3]', '[242, 242, 3*w^2 - 5]', '[242, 242, -4*w^2 + 3*w + 12]', '[244, 122, -w^2 + w - 4]', '[244, 122, -w^2 - 2*w + 12]', '[244, 244, 3*w^2 - 4*w - 3]', '[248, 62, 4*w^2 - 4*w - 18]', '[248, 124, 3*w^2 - 4*w - 2]', '[248, 124, 5*w^2 - w - 22]', '[248, 248, -3*w^2 - 2*w + 9]', '[250, 10, 5*w]', '[250, 10, -5*w + 5]', '[253, 253, -2*w^2 + 2*w + 13]', '[256, 8, 4*w^2 - 16]', '[256, 8, 4*w^2 - 4*w - 16]', '[256, 16, -2*w^2 + 4*w - 4]', '[256, 16, 3*w^2 - 2*w - 2]', '[256, 16, 4*w + 4]', '[256, 32, -2*w^2 - 2*w + 8]', '[256, 64, -2*w^2 + 4*w + 6]', '[256, 128, -w^2 - 3*w + 10]', '[256, 256, w^2 + 4*w - 5]', '[257, 257, -4*w - 3]', '[257, 257, w^2 - 5*w - 1]', '[257, 257, -3*w^2 + w + 17]', '[262, 262, 4*w^2 - w - 12]', '[262, 262, 2*w^2 - w - 13]', '[263, 263, 3*w^2 - 3*w - 5]', '[268, 134, 5*w^2 - 4*w - 16]', '[268, 134, -3*w^2 + w + 6]', '[268, 268, -w + 7]', '[271, 271, 4*w^2 - 4*w - 17]', '[271, 271, 3*w^2 - w - 3]', '[271, 271, w^2 + 3*w - 7]', '[272, 68, -2*w^2 - 2]', '[272, 68, -3*w^2 + 2*w + 6]', '[272, 68, -2*w + 8]', '[272, 136, 3*w^2 - 3*w - 2]', '[272, 272, -2*w^2 + 5*w - 5]', '[274, 274, 7*w - 2]', '[274, 274, w^2 - 8*w + 5]', '[283, 283, 6*w - 1]', '[289, 17, w^2 + 3*w - 9]', '[289, 289, 5*w^2 - 3*w - 17]', '[292, 146, -3*w^2 - w + 12]', '[292, 146, -w^2 + 4*w + 8]', '[292, 146, 3*w^2 - 6*w - 20]', '[292, 146, 7*w^2 - w - 26]', '[292, 146, -w^2 - 3*w + 8]', '[292, 146, -w^2 + 4*w + 4]', '[292, 292, 4*w^2 + 5*w - 7]', '[292, 292, -7*w^2 - 6*w + 13]', '[292, 292, -8*w^2 + 5*w + 37]', '[293, 293, 3*w^2 - w - 5]', '[296, 74, 4*w^2 - 4*w - 10]', '[296, 148, -3*w^2 + w + 4]', '[296, 148, w^2 - 10]', '[296, 296, w^2 - 2*w + 5]', '[297, 33, 3*w^2 - 3*w - 3]', '[298, 298, -5*w^2 + 2*w + 17]', '[298, 298, -2*w^2 + 7*w]', '[302, 302, 2*w^2 + w + 2]', '[302, 302, -3*w^2 + 2*w + 3]', '[304, 76, -2*w^2 + 14]', '[304, 76, -w^2 + 2*w + 10]', '[304, 76, -4*w^2 + 2*w + 12]', '[304, 152, -w^2 - w - 4]', '[304, 304, 3*w^2 - 2*w - 5]', '[307, 307, 2*w^2 + 2*w - 9]', '[307, 307, -2*w^2 + 2*w - 3]', '[307, 307, 4*w^2 - 17]', '[311, 311, w^2 + w - 11]', '[311, 311, 2*w^2 - 4*w - 7]', '[311, 311, -2*w^2 - 2*w + 13]', '[313, 313, -2*w - 7]', '[313, 313, 4*w^2 - 19]', '[313, 313, -5*w^2 - w + 13]', '[314, 314, -3*w^2 + 8*w + 1]', '[314, 314, -5*w + 6]', '[316, 158, w^2 - 3*w + 6]', '[316, 158, -3*w^2 + 2*w + 4]', '[316, 158, -w^2 + 7*w - 6]', '[316, 158, w^2 - 8*w + 12]', '[316, 316, 4*w^2 - 11*w + 1]', '[316, 316, -3*w^2 - 1]', '[319, 319, w^2 + 5*w - 5]', '[323, 323, 3*w^2 - 7*w - 3]', '[326, 326, -2*w^2 + 5*w + 4]', '[326, 326, -5*w + 9]', '[328, 82, 4*w^2 - 18]', '[328, 164, 3*w^2 - 4*w - 14]', '[328, 164, 5*w^2 - 5*w - 18]', '[328, 328, -w^2 + 4*w + 5]', '[331, 331, 2*w^2 - 4*w - 11]', '[331, 331, 6*w^2 - 4*w - 21]', '[331, 331, -4*w^2 + 2*w + 21]', '[332, 166, -3*w^2 + 4*w + 12]', '[332, 166, -3*w^2 - w + 16]', '[332, 332, 2*w^2 + 3*w - 7]', '[334, 334, -6*w^2 + 5*w + 24]', '[334, 334, w^2 - 4*w - 7]', '[341, 341, -3*w^2 - w + 13]', '[343, 7, -7]', '[344, 86, 2*w^2 + 2*w - 10]', '[344, 86, -6*w^2 + 2*w + 30]', '[344, 86, -4*w^2 + 4*w + 22]', '[344, 172, w^2 - 4*w - 6]', '[344, 172, w^2 - w - 10]', '[344, 172, -w^2 - 4*w + 6]', '[344, 172, 3*w^2 - 5*w - 8]', '[344, 172, -7*w^2 + 4*w + 26]', '[344, 172, -7*w^2 + 3*w + 26]', '[344, 344, 4*w^2 - 3*w - 11]', '[344, 344, 5*w + 1]', '[344, 344, 5*w^2 + 2*w - 11]', '[346, 346, 4*w^2 + w - 14]', '[346, 346, 3*w^2 - 4*w - 13]', '[347, 347, -2*w^2 + 8*w - 1]', '[349, 349, w^2 - 7*w + 1]', '[352, 44, -2*w^2 + 4*w + 8]', '[352, 44, -2*w^2 - 2*w + 12]', '[352, 88, 2*w^2 + 4*w - 6]', '[352, 88, -3*w^2 - 2*w + 10]', '[352, 176, w^2 - 5*w - 2]', '[352, 352, 5*w - 7]', '[353, 353, -6*w^2 + 2*w + 21]', '[358, 358, -5*w + 8]', '[358, 358, -4*w^2 + 9*w + 3]', '[361, 19, -5*w^2 + 3*w + 25]', '[361, 361, 2*w^2 + 2*w - 11]', '[362, 362, w + 7]', '[362, 362, 4*w^2 - w - 11]', '[362, 362, -4*w^2 + w + 2]', '[362, 362, -4*w^2 - w + 8]', '[362, 362, 2*w^2 - 9*w + 2]', '[362, 362, 3*w^2 - 4*w + 3]', '[367, 367, 3*w^2 + w - 15]', '[368, 92, -4*w^2 - 2*w + 12]', '[368, 92, 7*w^2 - 2*w - 30]', '[368, 92, -2*w^2 + 4*w + 10]', '[368, 184, -3*w^2 - w + 14]', '[368, 368, 3*w^2 + 4*w - 7]', '[373, 373, 2*w^2 - 4*w - 9]', '[374, 374, 6*w^2 - 5*w - 25]', '[374, 374, 4*w^2 - 7*w - 2]', '[383, 383, -9*w^2 + 3*w + 37]', '[386, 386, -4*w^2 + 7*w + 1]', '[386, 386, 2*w^2 - 3*w + 4]', '[391, 391, -w^2 + w - 5]', '[394, 394, -4*w^2 - w + 4]', '[394, 394, 2*w^2 - w + 3]', '[401, 401, 4*w^2 - 2*w - 11]', '[407, 407, -8*w^2 + 6*w + 35]', '[409, 409, 4*w^2 - 4*w - 9]', '[418, 418, 4*w^2 - 5*w - 7]', '[418, 418, w - 8]', '[422, 422, -2*w^2 - 3*w + 8]', '[422, 422, 5*w^2 - 4*w - 15]', '[422, 422, -w^2 - 4*w + 7]', '[422, 422, -2*w^2 + 5*w + 5]', '[422, 422, 2*w^2 - w - 14]', '[422, 422, 5*w + 2]', '[424, 106, 2*w^2 - 2*w - 14]', '[424, 212, 5*w^2 - 14]', '[424, 212, 5*w^2 - 3*w - 16]', '[424, 424, -4*w^2 - w + 7]', '[431, 431, -5*w^2 + 5*w + 19]', '[432, 12, -6*w]', '[432, 12, -3*w^2 + 6*w + 6]', '[432, 12, 6*w - 6]', '[432, 24, 3*w^2 - 3*w - 18]', '[432, 48, 6*w^2 - 3*w - 21]', '[436, 218, -3*w^2 + w + 18]', '[436, 218, -5*w^2 + 2*w + 16]', '[436, 436, -w^2 - 2*w - 5]', '[437, 437, 4*w^2 - 9]', '[439, 439, 2*w - 9]', '[443, 443, w^2 - 5*w - 3]', '[443, 443, 5*w^2 - 5*w - 23]', '[443, 443, 3*w^2 - 5*w - 17]', '[446, 446, -w^2 - 2*w + 13]', '[446, 446, -4*w^2 + 3*w + 10]', '[449, 449, -4*w^2 + 4*w + 1]', '[451, 451, -3*w^2 + 5*w + 9]', '[452, 226, -w^2 - 6*w]', '[452, 226, w^2 + 5*w - 6]', '[452, 452, 3*w^2 - 4*w - 19]', '[454, 454, -5*w - 6]', '[454, 454, -2*w^2 - 5*w + 6]', '[454, 454, w^2 + 5]', '[454, 454, 3*w^2 + 2*w - 11]', '[454, 454, -w^2 + 6*w + 1]', '[454, 454, -4*w^2 - w + 6]', '[458, 458, -w^2 + 11]', '[458, 458, -4*w^2 + w + 10]', '[459, 51, -3*w^2 - 3*w + 9]', '[461, 461, 5*w^2 - 7*w - 9]', '[464, 116, 4*w^2 - 2*w - 2]', '[464, 116, w^2 - 2*w + 6]', '[464, 116, -4*w^2 + 6*w + 4]', '[464, 232, w^2 - 5*w - 10]', '[464, 464, 4*w^2 + w - 15]', '[466, 466, 2*w^2 - 5*w + 6]', '[466, 466, -6*w^2 + w + 25]', '[467, 467, 5*w^2 + w - 17]', '[473, 473, -2*w^2 + 6*w + 3]', '[473, 473, 6*w^2 - 6*w - 17]', '[473, 473, 5*w^2 - w - 15]', '[478, 478, -4*w^2 + 5*w + 14]', '[478, 478, -5*w - 3]', '[479, 479, 2*w^2 + 4*w - 7]', '[484, 22, -9*w^2 + 3*w + 38]', '[484, 22, -7*w^2 + 6*w + 32]', '[484, 44, 5*w^2 + 2*w - 15]', '[484, 242, 3*w^2 - 7*w - 4]', '[484, 242, w^2 + 4*w - 8]', '[484, 484, 7*w - 1]', '[487, 487, 5*w^2 - 5*w - 13]', '[488, 122, 8*w^2 - 4*w - 30]', '[488, 244, 7*w^2 - 3*w - 34]', '[488, 244, 3*w^2 - 8*w - 2]', '[488, 488, -w^2 + 2*w + 11]', '[493, 493, 2*w^2 - 15]', '[496, 124, 2*w + 8]', '[496, 124, -5*w^2 - 2*w + 10]', '[496, 124, -4*w^2 + 2*w + 10]', '[496, 248, -w^2 - 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29]', '[1892, 1892, 9*w^2 + 4*w - 25]', '[1894, 1894, 10*w^2 - 7*w]', '[1894, 1894, 6*w^2 - 15*w + 10]', '[1894, 1894, -6*w^2 + 3*w + 4]', '[1894, 1894, -10*w^2 + 17*w - 7]', '[1894, 1894, -6*w^2 - w + 27]', '[1894, 1894, 4*w^2 - 7*w + 7]', '[1901, 1901, 8*w^2 - 8*w - 21]', '[1901, 1901, 9*w^2 + w - 31]', '[1901, 1901, w^2 - 13*w + 3]', '[1903, 1903, 6*w^2 - 4*w - 33]', '[1907, 1907, -3*w^2 - w - 5]', '[1909, 1909, -6*w^2 + 16*w + 1]', '[1912, 478, 2*w^2 - 14*w + 10]', '[1912, 956, -w^2 + 12*w - 2]', '[1912, 956, -3*w^2 + 3*w + 22]', '[1912, 1912, -8*w^2 + 5*w + 25]', '[1913, 1913, -4*w - 13]', '[1916, 958, -w^2 + 4*w + 16]', '[1916, 958, -7*w^2 + 3*w + 20]', '[1916, 1916, 8*w^2 + 5*w - 11]', '[1921, 1921, 10*w^2 - 2*w - 33]', '[1922, 62, 6*w^2 + w - 28]', '[1922, 62, 8*w^2 - 9*w - 27]', '[1922, 1922, 7*w^2 - 12*w - 5]', '[1922, 1922, -2*w^2 + 5*w - 10]', '[1931, 1931, -10*w^2 + 2*w + 45]', '[1931, 1931, w^2 + 7*w - 15]', '[1931, 1931, 6*w^2 - 6*w - 11]', '[1933, 1933, 3*w^2 - 7*w - 13]', '[1934, 1934, 2*w^2 + 11*w - 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27]', '[9974, 9974, 10*w^2 - 7*w - 20]', '[9976, 2494, -4*w^2 + 16*w + 38]', '[9976, 2494, 10*w^2 - 2*w - 18]', '[9976, 2494, -14*w^2 + 14*w + 54]', '[9976, 4988, -15*w^2 - w + 54]', '[9976, 4988, -15*w^2 + 12*w + 46]', '[9976, 4988, -13*w^2 - w + 68]', '[9976, 4988, -11*w^2 + 10]', '[9976, 4988, -w^2 + 3*w - 20]', '[9976, 4988, -13*w^2 + 54]', '[9976, 9976, -12*w^2 + 13*w + 53]', '[9976, 9976, 6*w^2 + 7*w - 27]', '[9976, 9976, 11*w^2 - 14*w - 17]', '[9977, 9977, -13*w^2 - 5*w + 25]', '[9983, 9983, -31*w^2 + 15*w + 141]', '[9988, 4994, 15*w^2 - 4*w - 48]', '[9988, 4994, 9*w^2 - 5*w - 52]', '[9988, 4994, -23*w^2 + 7*w + 96]', '[9988, 4994, -17*w^2 + 16*w + 80]', '[9988, 4994, 9*w^2 - 13*w - 32]', '[9988, 4994, 9*w^2 + 4*w - 36]', '[9988, 9988, 4*w^2 + 9*w + 13]', '[9988, 9988, 14*w^2 + 7*w - 39]', '[9988, 9988, 2*w^2 + 15*w + 5]', '[9994, 9994, 14*w^2 - 15*w - 35]', '[9994, 9994, 4*w^2 + w - 36]', '[9998, 9998, 20*w^2 + 11*w - 12]', '[9998, 9998, -14*w^2 + 3*w - 1]'], 'label': '3.3.316.1', 'narrow_class_no': 1, 'primes': ['[2, 2, -w]', '[2, 2, w - 1]', '[11, 11, w^2 - w - 1]', '[17, 17, -w^2 - w + 3]', '[19, 19, w^2 - w + 1]', '[23, 23, 2*w - 3]', '[27, 3, 3]', '[29, 29, 2*w + 1]', '[31, 31, 2*w^2 - 2*w - 9]', '[37, 37, 2*w^2 - 2*w - 5]', '[41, 41, 2*w^2 - 9]', '[43, 43, w^2 + w - 5]', '[43, 43, -3*w^2 + w + 15]', '[43, 43, -2*w^2 + 2*w + 11]', '[53, 53, w^2 - w - 7]', '[61, 61, 4*w^2 - 2*w - 15]', '[67, 67, -5*w^2 + 3*w + 23]', '[73, 73, 2*w^2 - 3]', '[73, 73, -3*w^2 - w + 7]', '[73, 73, -6*w^2 + 4*w + 25]', '[79, 79, w^2 - 5*w + 1]', '[79, 79, 3*w^2 - 3*w - 11]', '[83, 83, 2*w^2 - 2*w - 3]', '[109, 109, w^2 - 3*w - 3]', '[113, 113, 3*w^2 - 3*w - 13]', '[121, 11, 3*w^2 - w - 9]', '[125, 5, -5]', '[131, 131, -6*w^2 + 2*w + 25]', '[137, 137, -w^2 + w - 3]', '[149, 149, 2*w - 7]', '[151, 151, w^2 - 3*w - 5]', '[157, 157, 3*w^2 - 3*w - 7]', '[163, 163, 2*w^2 - 13]', '[167, 167, -4*w + 5]', '[173, 173, -7*w^2 + 3*w + 27]', '[179, 179, 4*w^2 - 4*w - 11]', '[181, 181, 4*w^2 - 15]', '[181, 181, w^2 - 3*w + 5]', '[181, 181, w^2 + 3*w - 5]', '[193, 193, 2*w^2 - 4*w - 5]', '[197, 197, 2*w^2 + 2*w - 7]', '[211, 211, 4*w^2 - 2*w - 13]', '[211, 211, -7*w^2 + 5*w + 29]', '[211, 211, w^2 - w - 9]', '[223, 223, 5*w^2 - w - 23]', '[227, 227, -3*w^2 + 3*w + 17]', '[227, 227, 3*w^2 - w - 7]', '[227, 227, 3*w^2 + w - 11]', '[229, 229, 5*w^2 - w - 21]', '[233, 233, 3*w^2 - 5*w - 7]', '[239, 239, -w^2 + 7*w - 5]', '[257, 257, -4*w - 3]', '[257, 257, w^2 - 5*w - 1]', '[257, 257, -3*w^2 + w + 17]', '[263, 263, 3*w^2 - 3*w - 5]', '[271, 271, 4*w^2 - 4*w - 17]', '[271, 271, 3*w^2 - w - 3]', '[271, 271, w^2 + 3*w - 7]', '[283, 283, 6*w - 1]', '[289, 17, w^2 + 3*w - 9]', '[293, 293, 3*w^2 - w - 5]', '[307, 307, 2*w^2 + 2*w - 9]', '[307, 307, -2*w^2 + 2*w - 3]', '[307, 307, 4*w^2 - 17]', '[311, 311, w^2 + w - 11]', '[311, 311, 2*w^2 - 4*w - 7]', '[311, 311, -2*w^2 - 2*w + 13]', '[313, 313, -2*w - 7]', '[313, 313, 4*w^2 - 19]', '[313, 313, -5*w^2 - w + 13]', '[331, 331, 2*w^2 - 4*w - 11]', '[331, 331, 6*w^2 - 4*w - 21]', '[331, 331, -4*w^2 + 2*w + 21]', '[343, 7, -7]', '[347, 347, -2*w^2 + 8*w - 1]', '[349, 349, w^2 - 7*w + 1]', '[353, 353, -6*w^2 + 2*w + 21]', '[361, 19, -5*w^2 + 3*w + 25]', '[367, 367, 3*w^2 + w - 15]', '[373, 373, 2*w^2 - 4*w - 9]', '[383, 383, -9*w^2 + 3*w + 37]', '[401, 401, 4*w^2 - 2*w - 11]', '[409, 409, 4*w^2 - 4*w - 9]', '[431, 431, -5*w^2 + 5*w + 19]', '[439, 439, 2*w - 9]', '[443, 443, w^2 - 5*w - 3]', '[443, 443, 5*w^2 - 5*w - 23]', '[443, 443, 3*w^2 - 5*w - 17]', '[449, 449, -4*w^2 + 4*w + 1]', '[461, 461, 5*w^2 - 7*w - 9]', '[467, 467, 5*w^2 + w - 17]', '[479, 479, 2*w^2 + 4*w - 7]', '[487, 487, 5*w^2 - 5*w - 13]', '[499, 499, -w^2 + 3*w - 7]', '[509, 509, -7*w^2 + w + 27]', '[521, 521, w^2 - w - 11]', '[523, 523, 4*w^2 - 6*w - 11]', '[529, 23, 4*w^2 + 2*w - 13]', '[547, 547, -11*w^2 + 5*w + 43]', '[563, 563, 4*w^2 - 7]', '[569, 569, -6*w - 1]', '[569, 569, 4*w^2 - 5]', '[569, 569, w^2 - 5*w - 9]', '[571, 571, 5*w^2 - 3*w - 15]', '[577, 577, w^2 + 5*w - 7]', '[599, 599, 4*w^2 - 4*w - 7]', '[601, 601, -12*w^2 + 8*w + 51]', '[613, 613, 4*w^2 + 1]', '[643, 643, 6*w^2 - 2*w - 31]', '[647, 647, 2*w^2 - 2*w - 15]', '[647, 647, 4*w^2 - 4*w - 23]', '[647, 647, w^2 - 5*w - 7]', '[661, 661, -8*w^2 + 6*w + 39]', '[673, 673, 3*w^2 - 5*w - 15]', '[683, 683, -w^2 + 9*w - 7]', '[701, 701, 4*w^2 - 4*w - 5]', '[709, 709, 4*w^2 - 2*w - 7]', '[719, 719, 3*w^2 - 5*w - 13]', '[727, 727, w^2 - 7*w - 1]', '[733, 733, 2*w^2 + 4*w - 9]', '[733, 733, 3*w^2 + 3*w - 11]', '[733, 733, w^2 + w - 13]', '[743, 743, 2*w^2 - 6*w - 5]', '[751, 751, 6*w^2 - 2*w - 19]', '[761, 761, -12*w^2 + 6*w + 47]', '[761, 761, 3*w^2 - 5*w - 21]', '[761, 761, 2*w^2 + 6*w - 7]', '[769, 769, -6*w^2 + 6*w + 23]', '[773, 773, -2*w^2 + 2*w - 5]', '[773, 773, -13*w^2 + 5*w + 57]', '[773, 773, -11*w^2 + 7*w + 51]', '[787, 787, 5*w^2 - w - 13]', '[797, 797, -2*w^2 + 8*w - 11]', '[811, 811, -5*w^2 + 5*w + 1]', '[821, 821, -7*w^2 + 3*w + 35]', '[821, 821, -4*w^2 + 2*w + 23]', '[821, 821, 5*w^2 + w - 19]', '[823, 823, w^2 + 5*w - 13]', '[823, 823, -12*w^2 + 4*w + 49]', '[823, 823, -7*w^2 + w + 29]', '[829, 829, -w^2 + w - 7]', '[839, 839, 4*w^2 + 2*w - 15]', '[841, 29, 4*w^2 - 6*w - 13]', '[853, 853, 7*w^2 - 7*w - 25]', '[863, 863, 7*w^2 - 5*w - 35]', '[877, 877, -6*w - 5]', '[877, 877, w^2 + 5*w - 11]', '[877, 877, 5*w^2 - 3*w - 13]', '[881, 881, w^2 - 3*w - 13]', '[887, 887, -9*w^2 + 5*w + 33]', '[907, 907, w^2 - 9*w + 1]', '[911, 911, -6*w^2 + 6*w + 25]', '[919, 919, 5*w^2 - 3*w - 27]', '[929, 929, 2*w - 11]', '[937, 937, -7*w^2 + w + 31]', '[941, 941, -6*w^2 + 4*w + 31]', '[941, 941, -8*w^2 + 2*w + 27]', '[941, 941, 3*w^2 + 5*w - 9]', '[947, 947, -10*w + 7]', '[947, 947, 2*w^2 + 8*w - 7]', '[947, 947, 2*w^2 + 4*w - 11]', '[961, 31, -14*w^2 + 8*w + 55]', '[967, 967, -w^2 - w - 7]', '[971, 971, -10*w^2 + 8*w + 39]', '[977, 977, -10*w^2 + 6*w + 37]', '[983, 983, 3*w^2 + 3*w - 13]', '[983, 983, -4*w - 11]', '[983, 983, -10*w^2 + 4*w + 37]', '[997, 997, w^2 + 9*w - 7]', '[997, 997, 5*w^2 - 7*w - 27]', '[997, 997, 6*w^2 - 8*w - 11]']}
• 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': [2, -4, -1, 1], 'conductor': 0, 'degree': 3, 'dirichlet_group': [], 'disc_abs': 316, 'disc_rad': 158, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[3, 1]]], [5, [[3, 1]]], [7, [[3, 1]]], [11, [[2, 1], [1, 1]]], [13, [[3, 1]]], [17, [[2, 1], [1, 1]]], [19, [[2, 1], [1, 1]]], [23, [[2, 1], [1, 1]]], [29, [[2, 1], [1, 1]]], [31, [[2, 1], [1, 1]]], [37, [[2, 1], [1, 1]]], [41, [[2, 1], [1, 1]]], [43, [[1, 3]]], [47, [[3, 1]]], [53, [[2, 1], [1, 1]]], [59, [[3, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [6, 3], 'galois_label': '3T2', 'galt': 2, 'grd': 17.776388834631177, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '3.3.316.1', 'local_algs': ['2.1.1.0a1.1', '2.1.2.2a1.1', '79.1.1.0a1.1', '79.1.2.1a1.2'], 'monogenic': 1, 'narrow_class_group': [], 'narrow_class_number': 1, 'num_ram': 2, 'r2': 0, 'ramps': [2, 79], 'rd': 6.81128460769, 'regulator': {'__RealLiteral__': 0, 'data': '3.91345849211', 'prec': 44}, 'res': {'gal': ['8,-8,-34,54,-17,-2,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a^{2} - a - 3 \\)', '\\( a^{2} - a - 5 \\)'], 'unitsGmodule': [[3, 1], [5, 1]], 'used_grh': False, 'zk': ['1', 'a', 'a^2']}