Hilbert modular form data - 3.3.1901.1-4.2-a

Formats: - HTML - YAML - JSON - 2026-02-23T05:45:22.745802

• 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': 1901, 'field_bad_primes': [1901], 'field_label': '3.3.1901.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '3.3.1901.1-4.2-a', 'label_nsuffix': 0, 'label_suffix': 'a', 'level_bad_primes': [2], 'level_ideal': '[4, 4, -w]', 'level_label': '4.2', 'level_norm': 4, 'parallel_weight': 2, 'short_label': '4.2-a', 'weight': '[2, 2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[2, 2, w + 2]', -1]], 'hecke_eigenvalues': [0, 0, 1, 1, 3, -1, -3, 3, 4, -6, 10, 2, 2, 5, 10, 11, -12, -1, 11, 2, -10, 1, -18, 1, 1, 6, 18, -16, -1, 19, -9, 14, 16, -8, 9, -6, 7, -10, 18, -1, 8, 16, 24, 18, 10, 26, 1, 26, 23, -6, 10, 25, -7, 7, 22, -13, -21, -19, 18, -22, -14, -31, -25, -18, -6, -2, -29, 19, -4, -34, -2, 4, 6, 0, 16, -34, 27, 39, 20, -28, 30, -2, 1, 5, -4, 30, -5, 10, -19, -27, 26, -6, -38, -12, 8, 16, -16, -32, -14, 20, 5, -34, -22, 5, 2, 10, 28, 25, 16, 39, -10, 14, -12, -6, 23, -18, -13, 10, -24, -46, 32, 28, -22, -29, 19, -6, -5, -33, -20, 33, -19, 18, 21, 34, 31, 20, -26, -22, -14, -28, -10, -3, 1, 26, -22, -32, -18, -23, 25, 10, 42, 27, 51, -58, -38, -26, -2, -22, 50, -54, -39, -18, -7, -5, 18, -34, -12, 48, 0, -21, 18, -44], 'hecke_polynomial': 'x', 'label': '3.3.1901.1-4.2-a'}
• hmf_fields •

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

  
  {'degree': 3, 'discriminant': 1901, 'ideals': ['[1, 1, 1]', '[2, 2, w + 2]', '[3, 3, w + 1]', '[4, 2, -w^2 + 3*w + 3]', '[4, 4, -w]', '[6, 6, w^2 - 2*w - 6]', '[8, 2, 2]', '[8, 8, w - 4]', '[9, 3, -w^2 + 2*w + 7]', '[9, 9, w^2 - 2*w - 9]', '[12, 6, w^2 - 3*w - 1]', '[12, 12, w^2 - w - 8]', '[13, 13, w + 3]', '[13, 13, -w + 3]', '[13, 13, -w + 1]', '[16, 4, 2*w + 4]', '[16, 4, -w^2 + w + 9]', '[16, 16, w^2 - 2*w - 8]', '[17, 17, -w^2 - 2*w + 1]', '[18, 6, -w^2 + 2*w + 10]', '[18, 18, w - 2]', '[23, 23, w^2 - 2*w - 5]', '[24, 6, 2*w + 2]', '[24, 24, w^2 - 3*w - 4]', '[26, 26, -w^2 + w + 6]', '[26, 26, -w^2 - w + 2]', '[26, 26, -w^2 + 2*w + 2]', '[27, 3, 3]', '[27, 27, -2*w - 5]', '[31, 31, 2*w + 3]', '[31, 31, -2*w^2 + 3*w + 15]', '[31, 31, 3*w + 7]', '[32, 4, -2*w^2 + 6*w + 6]', '[32, 8, -2*w]', '[32, 32, -w^2 + 4*w]', '[34, 34, 2*w^2 - 3*w - 18]', '[36, 6, w^2 + w - 1]', '[36, 12, -w^2 + 2*w + 4]', '[36, 18, w^2 - w - 11]', '[36, 36, w^2 - 4]', '[37, 37, 3*w^2 - 4*w - 27]', '[39, 39, -w^2 + 2*w + 3]', '[39, 39, 2*w - 7]', '[39, 39, -w^2 + 1]', '[41, 41, -2*w^2 + 7*w + 1]', '[46, 46, w^2 - 6]', '[48, 12, -w^2 + w + 5]', '[48, 12, 2*w^2 - 4*w - 12]', '[48, 48, -w - 4]', '[51, 51, w - 5]', '[52, 26, -w^2 + 3*w + 5]', '[52, 26, -3*w^2 + 5*w + 25]', '[52, 26, -w^2 + 3*w + 11]', '[52, 52, w^2 - w]', '[52, 52, -w^2 - 3*w]', '[52, 52, w^2 - 3*w]', '[54, 6, 3*w + 6]', '[54, 54, w^2 - w - 2]', '[59, 59, w^2 - 3]', '[61, 61, 4*w^2 - 12*w - 11]', '[62, 62, w^2 - 5*w - 2]', '[62, 62, -3*w^2 + 3*w + 22]', '[62, 62, -w^2 + 2]', '[64, 4, 4]', '[64, 8, -w^2 - 3*w - 3]', '[64, 16, 2*w - 8]', '[64, 64, w^2 - w - 4]', '[68, 34, -w^2 + w + 3]', '[68, 68, 2*w^2 - 5*w - 8]', '[69, 69, 2*w - 1]', '[71, 71, w^2 - 2*w - 11]', '[72, 6, -2*w^2 + 4*w + 14]', '[72, 18, 2*w^2 - 4*w - 18]', '[72, 24, -w^2 - w + 4]', '[72, 72, -w^2 + 2*w]', '[74, 74, 5*w^2 - 8*w - 42]', '[78, 78, -w^2 - 2*w + 2]', '[78, 78, 2*w^2 - 3*w - 14]', '[78, 78, 2*w^2 - 5*w - 10]', '[81, 9, 2*w^2 - 7*w - 5]', '[81, 9, 3*w + 3]', '[81, 81, -w^2 + 13]', '[82, 82, w^2 - 3*w - 6]', '[92, 46, -3*w^2 + 11*w + 1]', '[92, 92, w^2 - 4*w - 4]', '[93, 93, -w^2 + 7]', '[93, 93, 3*w^2 - 8*w - 11]', '[93, 93, 2*w^2 - 2*w - 19]', '[96, 12, 2*w^2 - 6*w - 2]', '[96, 24, 2*w^2 - 2*w - 16]', '[96, 96, 2*w^2 - 5*w - 4]', '[97, 97, 3*w + 5]', '[101, 101, 2*w^2 - 6*w - 7]', '[102, 102, w^2 - 3*w - 10]', '[103, 103, 2*w^2 - 3*w - 19]', '[104, 26, 2*w + 6]', '[104, 26, -2*w + 6]', '[104, 26, -2*w + 2]', '[104, 104, -w^2 + 5*w - 4]', '[104, 104, 3*w + 4]', '[104, 104, w^2 - w - 12]', '[107, 107, -3*w^2 + 10*w + 3]', '[108, 6, -3*w^2 + 9*w + 9]', '[108, 12, -3*w]', '[108, 54, w^2 - 3*w - 7]', '[108, 108, -3*w^2 + 7*w + 16]', '[109, 109, -w - 5]', '[109, 109, 5*w^2 - 8*w - 41]', '[109, 109, 2*w^2 - 2*w - 21]', '[111, 111, 2*w^2 - 4*w - 15]', '[113, 113, -4*w - 3]', '[117, 39, -2*w^2 + 4*w + 17]', '[117, 39, -w^2 - 4*w - 5]', '[117, 39, -2*w^2 + 4*w + 11]', '[117, 117, 2*w^2 - 5*w - 7]', '[117, 117, 2*w^2 - 2*w - 13]', '[117, 117, -4*w - 1]', '[118, 118, 3*w^2 + 6*w - 2]', '[122, 122, w - 6]', '[123, 123, 3*w^2 - 10*w - 7]', '[124, 62, w^2 - 3*w + 1]', '[124, 62, -w^2 - 5*w - 5]', '[124, 62, -w^2 + 3*w + 9]', '[124, 124, 4*w^2 - 5*w - 32]', '[124, 124, -w^2 + 3*w + 8]', '[124, 124, 3*w^2 - 6*w - 20]', '[125, 5, -5]', '[127, 127, 2*w^2 - 2*w - 17]', '[128, 8, 4*w + 8]', '[128, 8, -2*w^2 + 2*w + 18]', '[128, 32, 2*w^2 - 4*w - 16]', '[128, 128, -3*w^2 + 9*w + 4]', '[131, 131, 2*w - 3]', '[136, 34, -2*w^2 - 4*w + 2]', '[136, 136, w^2 - 8]', '[137, 137, 2*w^2 - 5*w - 5]', '[137, 137, w^2 - 4*w - 13]', '[137, 137, 2*w - 5]', '[138, 138, -w^2 - w + 18]', '[139, 139, 2*w^2 - 3*w - 13]', '[142, 142, w^2 - 6*w - 18]', '[144, 12, -2*w^2 + 4*w + 20]', '[144, 12, -w^2 + 5*w + 1]', '[144, 36, -w^2 - 3*w + 1]', '[144, 36, 2*w - 4]', '[144, 48, -w^2 + 5*w + 4]', '[144, 144, -w^2 - 5*w - 4]', '[148, 74, -w^2 - w + 5]', '[148, 148, w^2 - 12]', '[151, 151, 2*w^2 - 9]', '[153, 51, -2*w^2 + w + 11]', '[153, 153, w^2 - 4*w - 5]', '[156, 78, -w^2 + 3*w + 13]', '[156, 78, w^2 - w + 1]', '[156, 78, 3*w^2 - 11*w - 5]', '[156, 156, -2*w^2 + 7*w]', '[156, 156, w^2 - 2*w - 12]', '[156, 156, 3*w^2 - 4*w - 28]', '[162, 18, -w^2 - w - 2]', '[162, 18, 3*w^2 - 6*w - 18]', '[162, 162, -3*w^2 + 4*w + 22]', '[163, 163, 2*w^2 - 5*w - 11]', '[164, 82, 3*w^2 - 5*w - 21]', '[164, 164, -3*w - 8]', '[169, 13, w^2 - 4*w + 3]', '[169, 13, -w^2 + 9]', '[169, 13, -w^2 - 2*w + 3]', '[169, 169, 2*w^2 + 3*w - 1]', '[169, 169, w^2 - 2*w + 1]', '[169, 169, 2*w^2 - 8*w - 3]', '[173, 173, -2*w^2 + 8*w - 1]', '[177, 177, 2*w^2 + 6*w + 1]', '[179, 179, w^2 - 15]', '[181, 181, -w^2 + 11]', '[183, 183, -4*w^2 + 13*w + 5]', '[184, 46, 2*w^2 - 4*w - 10]', '[184, 184, -5*w^2 + 12*w + 24]', '[186, 186, -3*w^2 - 2*w + 10]', '[186, 186, w^2 - 10]', '[186, 186, 4*w^2 - 5*w - 30]', '[191, 191, 3*w - 1]', '[192, 12, 4*w + 4]', '[192, 24, w^2 - 5*w + 3]', '[192, 48, 2*w^2 - 6*w - 8]', '[192, 192, w^2 + 4*w]', '[193, 193, -6*w^2 + 16*w + 23]', '[194, 194, 5*w^2 - 8*w - 38]', '[197, 197, 2*w^2 - 8*w + 3]', '[199, 199, 4*w^2 - 5*w - 35]', '[202, 202, -w - 6]', '[204, 102, 5*w^2 - 7*w - 39]', '[204, 204, -w^2 + 5*w]', '[206, 206, 3*w^2 - 8*w - 10]', '[207, 69, 2*w^2 - w - 23]', '[207, 207, -4*w^2 + 5*w + 33]', '[208, 52, -3*w^2 + 3*w + 23]', '[208, 52, -2*w^2 + 2*w + 12]', '[208, 52, -2*w^2 - 2*w + 4]', '[208, 52, -2*w^2 + 4*w + 4]', '[208, 52, 3*w^2 - 11*w - 7]', '[208, 52, -w^2 + w + 13]', '[208, 208, 4*w^2 - 7*w - 28]', '[208, 208, 2*w^2 - 5*w - 20]', '[208, 208, 2*w^2 - 3*w - 12]', '[211, 211, 2*w - 9]', '[213, 213, -4*w - 7]', '[214, 214, w^2 - 4*w - 6]', '[216, 6, 6]', '[216, 24, 3*w - 12]', '[216, 54, -4*w - 10]', '[216, 216, -2*w^2 + 3*w + 20]', '[218, 218, 4*w^2 - 7*w - 34]', '[218, 218, -w^2 - 7*w - 10]', '[218, 218, 3*w - 10]', '[221, 221, 4*w^2 - 9*w - 21]', '[221, 221, 4*w^2 - 7*w - 31]', '[221, 221, 2*w + 7]', '[222, 222, 2*w^2 - 5*w - 22]', '[223, 223, 3*w^2 - 8*w - 13]', '[226, 226, -3*w^2 + 7*w + 14]', '[227, 227, 3*w^2 + 2*w - 11]', '[227, 227, w^2 - 4*w - 15]', '[227, 227, w - 7]', '[229, 229, -4*w^2 + 15*w - 1]', '[234, 78, -4*w^2 + 5*w + 34]', '[234, 78, -2*w^2 + w + 14]', '[234, 78, w^2 - 5*w + 2]', '[234, 234, w^2 + w - 6]', '[234, 234, -w^2 + 5*w - 6]', '[234, 234, -w^2 + 3*w - 2]', '[236, 118, -w^2 + 5*w - 1]', '[236, 236, -w^2 - 6*w - 4]', '[239, 239, -4*w - 5]', '[243, 9, -3*w^2 + 6*w + 21]', '[243, 27, 3*w^2 - 6*w - 27]', '[243, 243, -2*w^2 + 4*w + 9]', '[244, 122, 3*w^2 - 3*w - 29]', '[244, 244, w^2 - 4*w - 12]', '[246, 246, -w^2 - 2]', '[248, 62, 4*w + 6]', '[248, 62, -4*w^2 + 6*w + 30]', '[248, 62, 6*w + 14]', '[248, 248, 5*w + 12]', '[248, 248, 3*w^2 - 5*w - 28]', '[248, 248, 2*w^2 - 5*w - 12]', '[250, 10, -5*w - 10]', '[254, 254, 4*w^2 - 3*w - 26]', '[256, 8, -4*w^2 + 12*w + 12]', '[256, 16, -4*w]', '[256, 16, w^2 - 5*w - 5]', '[256, 64, -2*w^2 + 8*w]', '[256, 256, -5*w - 4]', '[257, 257, 2*w^2 + w - 9]', '[262, 262, 2*w^2 + w - 6]', '[263, 263, -w^2 - 6*w - 7]', '[269, 269, w^2 - 4*w - 7]', '[272, 68, 4*w^2 - 6*w - 36]', '[272, 68, 3*w^2 - 11*w - 3]', '[272, 272, 3*w^2 - 10*w - 8]', '[274, 274, 2*w^2 - w - 10]', '[274, 274, w^2 + 3*w - 2]', '[274, 274, 3*w - 2]', '[276, 138, 5*w^2 - 15*w - 11]', '[276, 276, -4*w^2 + 7*w + 32]', '[277, 277, 4*w^2 - 7*w - 33]', '[278, 278, 3*w^2 - w - 18]', '[279, 93, -w^2 + 2*w + 13]', '[279, 93, 2*w^2 - 4*w - 5]', '[279, 93, -4*w^2 + 8*w + 37]', '[279, 279, -2*w^2 - 2*w + 3]', '[279, 279, -2*w^2 + 8*w + 1]', '[279, 279, 2*w^2 - 3*w - 11]', '[281, 281, 6*w^2 - 17*w - 19]', '[281, 281, 3*w^2 - 8*w - 9]', '[281, 281, -5*w - 1]', '[284, 142, 3*w^2 - 7*w - 17]', '[284, 284, w^2 + 2*w - 4]', '[288, 12, 2*w^2 + 2*w - 2]', '[288, 24, -2*w^2 + 4*w + 8]', '[288, 36, 2*w^2 - 2*w - 22]', '[288, 72, 2*w^2 - 8]', '[288, 96, 2*w^2 + 5*w + 4]', '[288, 288, -3*w^2 + 5*w + 20]', '[289, 17, -2*w^2 + 9*w - 5]', '[289, 289, 3*w^2 - 4*w - 21]', '[291, 291, 4*w^2 - 10*w - 17]', '[293, 293, -3*w^2 + 8*w + 7]', '[293, 293, 2*w^2 + 5*w - 1]', '[293, 293, 6*w^2 - 10*w - 47]', '[296, 74, 6*w^2 - 8*w - 54]', '[296, 296, 3*w^2 - 3*w - 20]', '[299, 299, 2*w^2 - 6*w - 9]', '[299, 299, 2*w^2 - 2*w - 11]', '[299, 299, 4*w^2 - 10*w - 19]', '[302, 302, -w^2 + w - 2]', '[303, 303, -2*w^2 + 5*w + 1]', '[306, 102, w^2 - 2*w + 2]', '[306, 306, -w^2 - 4*w - 6]', '[307, 307, 2*w^2 - 2*w - 3]', '[309, 309, w^2 - 4*w - 11]', '[312, 78, -2*w^2 + 4*w + 6]', '[312, 78, 4*w - 14]', '[312, 78, -2*w^2 + 2]', '[312, 312, w^2 - 4*w - 8]', '[312, 312, 3*w^2 - 8*w - 8]', '[312, 312, 5*w^2 - 9*w - 44]', '[313, 313, 2*w^2 - 4*w - 7]', '[317, 317, 3*w^2 - 6*w - 17]', '[317, 317, 2*w^2 - 7*w - 7]', '[317, 317, 2*w^2 + 2*w - 7]', '[321, 321, 4*w^2 - 14*w - 9]', '[324, 18, w^2 + w - 7]', '[324, 18, 3*w^2 - 9*w - 3]', '[324, 36, -w^2 - w + 16]', '[324, 36, 3*w^2 - 3*w - 24]', '[324, 162, -w^2 - w - 3]', '[324, 324, w^2 - 4*w + 4]', '[326, 326, w^2 - 3*w - 14]', '[327, 327, 2*w^2 - 5*w - 13]', '[327, 327, 2*w^2 - 4*w - 21]', '[327, 327, -w^2 - 6*w - 5]', '[328, 82, -4*w^2 + 14*w + 2]', '[328, 328, 2*w^2 - 3*w - 4]', '[331, 331, 2*w^2 + 7*w + 7]', '[333, 111, 2*w^2 - 7*w + 1]', '[333, 333, -w - 7]', '[337, 337, w^2 - 4*w - 9]', '[337, 337, 3*w^2 - 4*w - 29]', '[337, 337, w^2 - 6*w - 5]', '[338, 26, -4*w^2 + 13*w + 10]', '[338, 26, -2*w^2 + 9*w + 6]', '[338, 26, -w^2 + 4*w + 10]', '[338, 338, -3*w^2 + 6*w + 22]', '[338, 338, w^2 + 6*w + 6]', '[338, 338, -2*w^2 - w + 2]', '[339, 339, -9*w^2 + 28*w + 19]', '[343, 7, -7]', '[346, 346, 2*w^2 - 3*w - 10]', '[347, 347, 2*w^2 + 4*w - 3]', '[349, 349, 2*w^2 - w - 25]', '[351, 39, 3*w + 9]', '[351, 39, -3*w + 9]', '[351, 39, -3*w + 3]', '[351, 351, -w^2 + 6*w + 1]', '[351, 351, 2*w^2 - w - 15]', '[351, 351, 2*w^2 + 3*w - 5]', '[354, 354, -w^2 + w + 14]', '[358, 358, 3*w^2 - 6*w - 26]', '[359, 359, -2*w^2 - w + 5]', '[362, 362, -3*w^2 + 2*w + 18]', '[366, 366, w^2 - 5*w - 6]', '[368, 92, 5*w^2 - 9*w - 37]', '[368, 92, 2*w^2 - 12]', '[368, 368, -3*w^2 + 3*w + 28]', '[369, 123, -w^2 - 4*w + 1]', '[369, 369, -4*w^2 + 8*w + 27]', '[372, 186, -3*w^2 + 7*w + 13]', '[372, 186, -w^2 + 7*w + 5]', '[372, 186, w^2 + 3*w + 5]', '[372, 372, w^2 + 2*w + 4]', '[372, 372, 3*w^2 - w - 16]', '[372, 372, w - 8]', '[375, 15, -5*w - 5]', '[379, 379, 4*w^2 - 9*w - 23]', '[379, 379, -5*w^2 + 18*w + 3]', '[379, 379, 2*w^2 - 3*w - 21]', '[381, 381, 2*w^2 - w - 9]', '[382, 382, 3*w^2 + 5*w - 2]', '[383, 383, -w^2 + 6*w - 7]', '[384, 24, -2*w^2 + 2*w + 10]', '[384, 24, 4*w^2 - 8*w - 24]', '[384, 96, -2*w - 8]', '[384, 384, -w^2 + 16]', '[386, 386, 2*w^2 - w - 22]', '[388, 194, w^2 - 3*w + 3]', '[388, 388, 7*w^2 - 9*w - 56]', '[391, 391, -5*w - 9]', '[393, 393, 2*w^2 - w - 3]', '[394, 394, -2*w^2 + 5*w + 14]', '[397, 397, 2*w^2 - 7]', '[398, 398, 7*w^2 - 9*w - 54]', '[401, 401, 9*w^2 - 28*w - 21]', '[403, 403, -3*w^2 + 2*w + 21]', '[403, 403, 4*w^2 + 7*w - 5]', '[403, 403, -3*w^2 - 4*w + 7]', '[403, 403, 3*w^2 - 2*w - 33]', '[403, 403, -3*w^2 + 6*w + 23]', '[403, 403, -2*w^2 + 3*w + 9]', '[403, 403, -4*w + 1]', '[403, 403, -2*w^2 - w + 3]', '[403, 403, -5*w^2 + 6*w + 37]', '[404, 202, 3*w^2 - 3*w - 25]', '[404, 404, -w^2 - 8*w - 12]', '[408, 102, 2*w - 10]', '[408, 408, 2*w^2 + w - 4]', '[411, 411, -w^2 + 8*w + 3]', '[411, 411, -6*w^2 + 11*w + 41]', '[411, 411, 2*w^2 - 3*w - 5]', '[412, 206, -3*w^2 - 7*w + 1]', '[412, 412, w^2 + w - 8]', '[414, 138, 5*w^2 - 7*w - 38]', '[414, 414, -3*w^2 + 8*w + 14]', '[416, 52, -2*w^2 + 6*w + 10]', '[416, 52, -6*w^2 + 10*w + 50]', '[416, 52, -2*w^2 + 6*w + 22]', '[416, 104, 2*w^2 - 2*w]', '[416, 104, -2*w^2 - 6*w]', '[416, 104, 2*w^2 - 6*w]', '[416, 416, -4*w^2 + 13*w + 4]', '[416, 416, 5*w^2 - 6*w - 40]', '[416, 416, 3*w - 4]', '[417, 417, w^2 + 2*w - 5]', '[419, 419, 3*w^2 - 6*w - 25]', '[419, 419, 4*w^2 - 7*w - 27]', '[419, 419, 4*w^2 - 6*w - 29]', '[422, 422, 2*w^2 - 5*w - 18]', '[426, 426, -7*w^2 + 11*w + 54]', '[428, 214, 3*w^2 - 5*w - 19]', '[428, 428, -w^2 - 5*w - 8]', '[432, 12, 6*w + 12]', '[432, 12, -3*w^2 + 3*w + 27]', '[432, 48, 3*w^2 - 6*w - 24]', '[432, 108, 2*w^2 - 2*w - 4]', '[432, 108, -3*w^2 + 11*w - 1]', '[432, 432, -4*w^2 + 11*w + 12]', '[433, 433, 8*w^2 - 13*w - 61]', '[433, 433, -6*w^2 + 23*w - 3]', '[433, 433, -w^2 - 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22*w - 71]', '[1899, 1899, -11*w^2 + 18*w + 89]', '[1901, 1901, 3*w^2 - 2*w - 9]', '[1901, 1901, 3*w^2 - 2*w - 37]', '[1902, 1902, -5*w^2 + w + 66]', '[1902, 1902, -5*w^2 + 10*w + 42]', '[1902, 1902, 4*w^2 - 17*w + 6]', '[1906, 1906, 6*w^2 - 7*w - 42]', '[1907, 1907, 6*w^2 - 8*w - 57]', '[1907, 1907, -3*w^2 - 2*w - 3]', '[1907, 1907, w - 13]', '[1912, 478, -8*w - 10]', '[1912, 1912, -4*w^2 + 11*w + 20]', '[1913, 1913, 6*w^2 - 12*w - 35]', '[1916, 958, 13*w^2 - 39*w - 33]', '[1916, 1916, -3*w^2 + 7*w]', '[1917, 213, 3*w^2 - 6*w - 33]', '[1917, 1917, -3*w^2 + 14*w + 47]', '[1921, 1921, 2*w^2 - 8*w + 7]', '[1922, 62, -9*w^2 - w + 42]', '[1922, 62, 2*w^2 - 5*w - 26]', '[1922, 62, 5*w^2 + 14*w + 2]', '[1922, 1922, -3*w^2 - 12*w - 14]', '[1922, 1922, 7*w^2 - 9*w - 66]', '[1922, 1922, 5*w^2 - 5*w - 42]', '[1924, 962, 13*w^2 - 23*w - 95]', '[1924, 962, w^2 + 3*w + 9]', '[1924, 962, -w^2 + w + 19]', '[1924, 1924, 2*w^2 + 3*w - 40]', '[1924, 1924, 3*w - 16]', '[1924, 1924, 4*w^2 - 3*w - 32]', '[1926, 642, w^2 + w - 22]', '[1926, 1926, -3*w^2 + 7*w + 34]', '[1929, 1929, -7*w^2 + 16*w + 35]', '[1933, 1933, 3*w^2 - 43]', '[1941, 1941, -5*w^2 + 2*w + 1]', '[1941, 1941, -2*w^2 - 9*w - 13]', '[1941, 1941, -2*w^2 + 8*w + 13]', '[1942, 1942, -w^2 - 4*w - 10]', '[1942, 1942, -3*w^2 + 8*w + 22]', '[1942, 1942, -2*w^2 - 7*w + 2]', '[1944, 18, -6*w^2 + 12*w + 42]', '[1944, 54, 6*w^2 - 12*w - 54]', '[1944, 72, -3*w^2 - 3*w + 12]', '[1944, 216, -3*w^2 + 6*w]', '[1944, 486, -4*w^2 + 8*w + 18]', '[1944, 1944, 3*w^2 + 8*w + 8]', '[1948, 974, 9*w^2 - 11*w - 81]', '[1948, 974, 3*w^2 - 9*w - 17]', '[1948, 974, -3*w^2 + 9*w - 1]', '[1948, 1948, -9*w^2 + 23*w + 40]', '[1948, 1948, 3*w^2 - 9*w - 32]', '[1948, 1948, -9*w^2 + 11*w + 72]', '[1949, 1949, 4*w^2 - 6*w - 23]', '[1951, 1951, 4*w^2 - 12*w - 17]', '[1952, 244, 6*w^2 - 6*w - 58]', '[1952, 488, 2*w^2 - 8*w - 24]', '[1952, 1952, -7*w^2 + 13*w + 52]', '[1954, 1954, -2*w^2 - 7*w - 10]', '[1956, 978, 5*w^2 - 3*w - 29]', '[1956, 1956, -9*w^2 + 14*w + 68]', '[1962, 654, -w^2 + 8*w + 10]', '[1962, 654, 4*w^2 - 11*w - 46]', '[1962, 654, w^2 + 7*w + 14]', '[1962, 1962, -4*w^2 + w + 50]', '[1962, 1962, -13*w^2 + 20*w + 102]', '[1962, 1962, -w^2 - 3*w + 10]', '[1963, 1963, -9*w - 17]', '[1963, 1963, 4*w^2 - 9*w - 35]', '[1963, 1963, 3*w^2 - 12*w - 11]', '[1966, 1966, 6*w^2 - 21*w - 2]', '[1968, 492, -2*w^2 - 4]', '[1968, 492, 7*w^2 - 19*w - 23]', '[1968, 1968, 3*w^2 - 11*w + 4]', '[1973, 1973, 2*w^2 - 12*w - 9]', '[1977, 1977, 5*w - 7]', '[1979, 1979, 4*w^2 - 7*w - 21]', '[1979, 1979, -9*w^2 + 32*w + 7]', '[1979, 1979, 8*w^2 - 9*w - 75]', '[1982, 1982, -3*w^2 - 2]', '[1983, 1983, 2*w^2 - 9*w - 11]', '[1984, 124, 8*w + 12]', '[1984, 124, -8*w^2 + 12*w + 60]', '[1984, 124, 12*w + 28]', '[1984, 248, -w^2 - 3*w + 21]', '[1984, 248, 5*w^2 - w - 25]', '[1984, 248, -9*w^2 + 13*w + 69]', '[1984, 496, 10*w + 24]', '[1984, 496, 6*w^2 - 10*w - 56]', '[1984, 496, 4*w^2 - 10*w - 24]', '[1984, 1984, 5*w^2 - 8*w - 48]', '[1984, 1984, 4*w^2 - 15*w - 12]', '[1984, 1984, 3*w^2 + 7*w - 4]', '[1986, 1986, 4*w^2 - 3*w - 22]', '[1987, 1987, 3*w^2 - 8*w - 27]', '[1989, 663, -w^2 + 8*w + 19]', '[1989, 663, -4*w^2 + 14*w + 13]', '[1989, 663, -5*w^2 + 10*w + 41]', '[1989, 1989, -8*w - 11]', '[1989, 1989, 6*w^2 - 16*w - 19]', '[1989, 1989, 4*w^2 - 8*w - 9]', '[1993, 1993, 8*w^2 - 16*w - 49]', '[1998, 222, 15*w^2 - 24*w - 126]', '[1998, 1998, -6*w^2 + 11*w + 38]', '[1999, 1999, 12*w^2 - 21*w - 89]', '[2000, 20, -10*w - 20]', '[2000, 20, 5*w^2 - 5*w - 45]', '[2000, 80, -5*w^2 + 10*w + 40]', '[2003, 2003, 6*w + 17]', '[2006, 2006, -7*w^2 + 8*w + 50]', '[2007, 669, -4*w^2 - 4*w + 7]', '[2007, 2007, -8*w^2 + 11*w + 73]', '[2011, 2011, 5*w^2 - 2*w - 27]', '[2018, 2018, 5*w^2 + 4*w - 14]', '[2019, 2019, -8*w^2 + 17*w + 49]', '[2022, 2022, -11*w - 26]', '[2022, 2022, 3*w^2 - 13*w + 2]', '[2022, 2022, -3*w^2 + w + 34]', '[2026, 2026, 5*w^2 - 9*w - 30]', '[2027, 2027, 10*w^2 - 30*w - 23]', '[2028, 78, w^2 - 11*w - 3]', '[2028, 78, -3*w^2 - w + 17]', '[2028, 78, 3*w^2 - 13*w - 1]', '[2028, 156, 8*w^2 - 13*w - 72]', '[2028, 156, 4*w^2 - 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2*w - 5]', '[31, 31, 2*w + 3]', '[31, 31, -2*w^2 + 3*w + 15]', '[31, 31, 3*w + 7]', '[37, 37, 3*w^2 - 4*w - 27]', '[41, 41, -2*w^2 + 7*w + 1]', '[59, 59, w^2 - 3]', '[61, 61, 4*w^2 - 12*w - 11]', '[71, 71, w^2 - 2*w - 11]', '[97, 97, 3*w + 5]', '[101, 101, 2*w^2 - 6*w - 7]', '[103, 103, 2*w^2 - 3*w - 19]', '[107, 107, -3*w^2 + 10*w + 3]', '[109, 109, -w - 5]', '[109, 109, 5*w^2 - 8*w - 41]', '[109, 109, 2*w^2 - 2*w - 21]', '[113, 113, -4*w - 3]', '[125, 5, -5]', '[127, 127, 2*w^2 - 2*w - 17]', '[131, 131, 2*w - 3]', '[137, 137, 2*w^2 - 5*w - 5]', '[137, 137, w^2 - 4*w - 13]', '[137, 137, 2*w - 5]', '[139, 139, 2*w^2 - 3*w - 13]', '[151, 151, 2*w^2 - 9]', '[163, 163, 2*w^2 - 5*w - 11]', '[173, 173, -2*w^2 + 8*w - 1]', '[179, 179, w^2 - 15]', '[181, 181, -w^2 + 11]', '[191, 191, 3*w - 1]', '[193, 193, -6*w^2 + 16*w + 23]', '[197, 197, 2*w^2 - 8*w + 3]', '[199, 199, 4*w^2 - 5*w - 35]', '[211, 211, 2*w - 9]', '[223, 223, 3*w^2 - 8*w - 13]', '[227, 227, 3*w^2 + 2*w - 11]', '[227, 227, w^2 - 4*w - 15]', '[227, 227, w - 7]', '[229, 229, -4*w^2 + 15*w - 1]', '[239, 239, -4*w - 5]', '[257, 257, 2*w^2 + w - 9]', '[263, 263, -w^2 - 6*w - 7]', '[269, 269, w^2 - 4*w - 7]', '[277, 277, 4*w^2 - 7*w - 33]', '[281, 281, 6*w^2 - 17*w - 19]', '[281, 281, 3*w^2 - 8*w - 9]', '[281, 281, -5*w - 1]', '[289, 17, -2*w^2 + 9*w - 5]', '[293, 293, -3*w^2 + 8*w + 7]', '[293, 293, 2*w^2 + 5*w - 1]', '[293, 293, 6*w^2 - 10*w - 47]', '[307, 307, 2*w^2 - 2*w - 3]', '[313, 313, 2*w^2 - 4*w - 7]', '[317, 317, 3*w^2 - 6*w - 17]', '[317, 317, 2*w^2 - 7*w - 7]', '[317, 317, 2*w^2 + 2*w - 7]', '[331, 331, 2*w^2 + 7*w + 7]', '[337, 337, w^2 - 4*w - 9]', '[337, 337, 3*w^2 - 4*w - 29]', '[337, 337, w^2 - 6*w - 5]', '[343, 7, -7]', '[347, 347, 2*w^2 + 4*w - 3]', '[349, 349, 2*w^2 - w - 25]', '[359, 359, -2*w^2 - w + 5]', '[379, 379, 4*w^2 - 9*w - 23]', '[379, 379, -5*w^2 + 18*w + 3]', '[379, 379, 2*w^2 - 3*w - 21]', '[383, 383, -w^2 + 6*w - 7]', '[397, 397, 2*w^2 - 7]', '[401, 401, 9*w^2 - 28*w - 21]', '[419, 419, 3*w^2 - 6*w - 25]', '[419, 419, 4*w^2 - 7*w - 27]', '[419, 419, 4*w^2 - 6*w - 29]', '[433, 433, 8*w^2 - 13*w - 61]', '[433, 433, -6*w^2 + 23*w - 3]', '[433, 433, -w^2 - 3]', '[443, 443, -2*w^2 + 5*w + 15]', '[449, 449, -7*w^2 + 12*w + 51]', '[457, 457, 2*w^2 - 2*w - 9]', '[457, 457, -w^2 - 6*w - 1]', '[457, 457, 6*w^2 - 11*w - 43]', '[461, 461, -5*w^2 + 6*w + 45]', '[463, 463, 2*w^2 - 5*w - 17]', '[463, 463, 3*w - 5]', '[463, 463, 2*w^2 - 3*w - 7]', '[467, 467, -3*w^2 + 10*w + 9]', '[479, 479, 3*w - 7]', '[487, 487, 7*w^2 - 20*w - 23]', '[487, 487, -4*w - 11]', '[487, 487, 5*w + 7]', '[509, 509, 2*w^2 - 2*w - 5]', '[523, 523, -8*w^2 + 28*w + 7]', '[529, 23, 2*w^2 - w - 7]', '[541, 541, 3*w^2 + 2*w - 9]', '[547, 547, -6*w - 1]', '[557, 557, 2*w^2 - 13]', '[563, 563, w - 9]', '[569, 569, -8*w^2 + 27*w + 9]', '[571, 571, 5*w^2 - 14*w - 15]', '[577, 577, w^2 + 4*w + 7]', '[587, 587, 4*w^2 - 4*w - 27]', '[593, 593, 2*w^2 + 5*w + 5]', '[599, 599, -2*w - 9]', '[599, 599, -w^2 + 6*w - 1]', '[599, 599, 2*w^2 - w - 19]', '[607, 607, 4*w - 13]', '[617, 617, -5*w - 13]', '[617, 617, -w^2 - 2*w - 5]', '[617, 617, 4*w^2 - 16*w + 5]', '[619, 619, 3*w^2 - 8*w - 15]', '[643, 643, -6*w - 11]', '[647, 647, -w^2 + 17]', '[647, 647, 2*w^2 - 9*w - 7]', '[647, 647, 2*w^2 - 6*w - 21]', '[659, 659, 4*w^2 - 8*w - 23]', '[661, 661, 2*w - 11]', '[673, 673, 3*w^2 - 13]', '[677, 677, 5*w^2 - 16*w - 13]', '[677, 677, -3*w^2 - 4*w + 3]', '[677, 677, 5*w^2 - 6*w - 43]', '[691, 691, 6*w^2 - 12*w - 37]', '[701, 701, -3*w^2 + 12*w - 1]', '[709, 709, -6*w^2 + 21*w + 7]', '[719, 719, -w^2 + 6*w - 3]', '[733, 733, -w - 9]', '[733, 733, 2*w^2 + w - 11]', '[733, 733, -2*w^2 + 9*w - 3]', '[739, 739, 6*w^2 - 17*w - 21]', '[743, 743, -2*w^2 - 6*w + 1]', '[751, 751, 4*w^2 - 8*w - 29]', '[751, 751, -w^2 - 8*w - 11]', '[751, 751, 4*w^2 - 21]', '[757, 757, 2*w^2 - 9*w - 1]', '[761, 761, -4*w^2 + 10*w + 15]', '[809, 809, w^2 + 2*w - 19]', '[811, 811, -7*w - 17]', '[823, 823, 3*w^2 - 17]', '[827, 827, -9*w - 19]', '[857, 857, 4*w^2 + 14*w + 9]', '[857, 857, 4*w^2 - 16*w + 3]', '[857, 857, 4*w^2 - 6*w - 27]', '[859, 859, -2*w^2 + 5*w - 1]', '[863, 863, 12*w^2 - 37*w - 29]', '[877, 877, 3*w^2 - 6*w - 7]', '[877, 877, 3*w^2 - 6*w - 31]', '[877, 877, 3*w^2 - 6*w - 13]', '[907, 907, 8*w^2 - 14*w - 57]', '[907, 907, 4*w^2 - 7*w - 25]', '[907, 907, 8*w^2 - 24*w - 19]', '[911, 911, -3*w - 11]', '[919, 919, -16*w^2 + 53*w + 23]', '[929, 929, 2*w^2 - 6*w - 19]', '[937, 937, w^2 - 6*w - 15]', '[937, 937, 3*w^2 - 4*w - 17]', '[937, 937, -3*w^2 + 12*w + 1]', '[941, 941, -2*w^2 + 6*w + 15]', '[947, 947, -2*w^2 - 3*w + 7]', '[953, 953, 2*w^2 - 25]', '[971, 971, 3*w^2 - 10*w - 11]', '[971, 971, 3*w^2 - 12*w + 5]', '[971, 971, -4*w^2 + 10*w + 9]', '[977, 977, 2*w^2 - 8*w - 9]', '[983, 983, -5*w^2 + 8*w + 35]', '[991, 991, 4*w^2 + 5*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[]
  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
  torsion_gen_coeffs	numeric[]
  units	jsonb
  unitsGmodule	jsonb
  unitsType	text
  units_coeffs	numeric[]
  zk	jsonb

  
  {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-4, -9, -1, 1], 'conductor': 0, 'degree': 3, 'dirichlet_group': [], 'disc_abs': 1901, 'disc_rad': 1901, 'disc_sign': 1, 'frobs': [[2, [[2, 1], [1, 1]]], [3, [[2, 1], [1, 1]]], [5, [[3, 1]]], [7, [[3, 1]]], [11, [[3, 1]]], [13, [[1, 3]]], [17, [[2, 1], [1, 1]]], [19, [[3, 1]]], [23, [[2, 1], [1, 1]]], [29, [[3, 1]]], [31, [[1, 3]]], [37, [[2, 1], [1, 1]]], [41, [[2, 1], [1, 1]]], [43, [[3, 1]]], [47, [[3, 1]]], [53, [[3, 1]]], [59, [[2, 1], [1, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [3], 'galois_label': '3T2', 'galt': 2, 'grd': 43.60045871318328, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '3.3.1901.1', 'local_algs': ['m1901.1.1.0', 'm1901.2.1.1'], 'monogenic': 1, 'narrow_class_group': [], 'narrow_class_number': 1, 'num_ram': 1, 'r2': 0, 'ramps': [1901], 'rd': 12.3877958316, 'regulator': {'__RealLiteral__': 0, 'data': '10.6608693118', 'prec': 44}, 'res': {'gal': ['279,-456,-10,184,-48,-2,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( 2 a + 1 \\)', '\\( a^{2} - 5 \\)'], 'unitsGmodule': [[3, 1], [5, 1]], 'used_grh': False, 'zk': ['1', 'a', 'a^2']}