Hilbert modular form data - 3.3.404.1-9.2-b

Formats: - HTML - YAML - JSON - 2024-05-26T23:01:28.436490

• 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': 404, 'field_bad_primes': [2, 101], 'field_label': '3.3.404.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '3.3.404.1-9.2-b', 'label_nsuffix': 1, 'label_suffix': 'b', 'level_bad_primes': [3], 'level_ideal': '[9, 9, w^2 - w - 3]', 'level_label': '9.2', 'level_norm': 9, 'parallel_weight': 2, 'short_label': '9.2-b', 'weight': '[2, 2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [], 'hecke_eigenvalues': [0, 0, 2, 4, 6, -6, -10, -4, 2, -6, -4, -10, -4, 2, -6, 0, 8, 8, 2, 0, 6, -10, 8, 14, 0, -6, 8, 14, -18, 2, -18, -16, -4, 12, -10, -4, -12, -6, -12, -6, 0, 18, 20, 8, -16, 20, 8, 12, -24, 18, -10, 0, -24, 6, 8, 26, 14, 14, -28, 30, 12, 14, 32, 20, -12, 26, -18, -4, 20, -28, -18, -24, -24, 6, 2, 24, 2, -22, 14, -18, -30, -16, 20, 24, 26, 12, 8, 12, 12, -4, -6, 6, 18, 18, -4, -28, -18, 6, -24, -4, -10, 18, -42, 6, 24, 38, -6, -30, -6, 24, -6, 6, 12, 38, -10, -12, 18, 36, -40, 8, 20, -46, 6, 14, 26, 32, -10, 6, -6, -48, -34, -6, 0, 42, 6, -6, 38, -18, -36, -54, -4, 36, 48, -24, 0, 54, 24, -16, -10, -40, -10, 44, 36, -10, -30, 20, 0, 0, 42, -22, 24, -28, 2, -18, 0, -24, -12, 18, -10, -52, 2], 'hecke_polynomial': 'x', 'label': '3.3.404.1-9.2-b'}
• hmf_fields •

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

  
  {'degree': 3, 'discriminant': 404, 'ideals': ['[1, 1, 1]', '[2, 2, -w - 1]', '[3, 3, w^2 - 2*w - 2]', '[4, 2, w^2 - 2*w - 3]', '[6, 6, -w + 1]', '[7, 7, -w + 2]', '[8, 2, 2]', '[9, 3, w^2 - 2]', '[9, 9, w^2 - w - 3]', '[11, 11, -w^2 + 2*w + 4]', '[12, 6, w^2 - 2*w - 5]', '[14, 14, w^2 - w - 2]', '[16, 4, -2*w - 2]', '[18, 6, w^2 - 3*w - 2]', '[18, 18, -w^2 - w + 2]', '[21, 21, -w^2 + 4]', '[22, 22, -w - 3]', '[24, 6, 2*w^2 - 4*w - 4]', '[27, 3, 3]', '[27, 27, -w + 4]', '[28, 14, -w^2 + 2*w + 7]', '[29, 29, -2*w + 1]', '[32, 4, 2*w^2 - 4*w - 6]', '[33, 33, 2*w - 5]', '[36, 6, -w^2 + 5]', '[36, 18, w^2 - 2*w + 1]', '[37, 37, 2*w^2 - 4*w - 3]', '[37, 37, -w^2 + 3*w + 3]', '[37, 37, 2*w^2 - w - 8]', '[41, 41, w^2 - 4*w + 2]', '[42, 42, w^2 - 3*w + 2]', '[43, 43, -2*w^2 + 2*w + 7]', '[43, 43, -2*w^2 + 3*w + 6]', '[43, 43, -w^2 + 6]', '[44, 22, -w^2 + 4*w - 1]', '[48, 12, -2*w + 2]', '[49, 7, w^2 + w - 3]', '[49, 49, 2*w^2 - w - 6]', '[53, 53, 2*w^2 - 5*w - 4]', '[54, 6, -3*w - 3]', '[54, 54, w^2 - 3*w - 4]', '[56, 14, -2*w + 4]', '[58, 58, w^2 - 3*w - 6]', '[59, 59, 2*w - 3]', '[61, 61, -w - 4]', '[63, 21, w^2 - 3*w - 5]', '[63, 63, 2*w^2 - 4*w - 7]', '[64, 4, 4]', '[66, 66, -2*w^2 + 3*w + 5]', '[67, 67, -2*w^2 - w + 2]', '[72, 6, 2*w^2 - 4]', '[72, 18, 2*w^2 - 2*w - 6]', '[73, 73, 2*w^2 - 3*w - 12]', '[74, 74, 2*w^2 - w - 9]', '[74, 74, -w^2 + w + 8]', '[74, 74, w - 5]', '[77, 77, -2*w^2 + 6*w + 3]', '[81, 9, 2*w^2 - 3*w - 4]', '[81, 9, 3*w^2 - 6*w - 6]', '[81, 81, -w^2 + 2*w + 8]', '[82, 82, 2*w^2 - 3*w - 3]', '[83, 83, -2*w - 5]', '[84, 42, w^2 - 4*w - 3]', '[86, 86, -3*w^2 + 7*w + 6]', '[86, 86, w^2 + w - 4]', '[86, 86, 2*w^2 - w - 5]', '[87, 87, 3*w^2 - 8*w - 4]', '[88, 22, -2*w^2 + 4*w + 8]', '[89, 89, -w^2 + 2*w - 2]', '[96, 12, 2*w^2 - 4*w - 10]', '[97, 97, -2*w + 7]', '[97, 97, -2*w^2 + 3]', '[97, 97, 2*w^2 - 2*w - 5]', '[98, 14, -2*w^2 + 5*w - 1]', '[98, 98, 2*w^2 - 5*w - 5]', '[99, 33, 2*w^2 - 7]', '[99, 99, 2*w^2 - w - 10]', '[101, 101, w^2 - 3*w - 9]', '[101, 101, 2*w^2 - 4*w - 9]', '[103, 103, w^2 - 3*w + 3]', '[106, 106, w^2 - w + 2]', '[108, 6, 3*w^2 - 6*w - 9]', '[108, 54, -3*w^2 + 2*w + 13]', '[109, 109, -w^2 + 4*w + 8]', '[111, 111, 4*w + 5]', '[111, 111, -2*w^2 + 2*w + 3]', '[111, 111, 2*w^2 - w - 4]', '[112, 28, 2*w^2 - 2*w - 4]', '[113, 113, 3*w^2 - 3*w - 11]', '[116, 58, 3*w^2 - 6*w - 5]', '[118, 118, -2*w^2 + w + 3]', '[121, 11, w^2 - 4*w - 4]', '[121, 121, -3*w + 2]', '[122, 122, w^2 + 5*w + 4]', '[123, 123, -w^2 - w + 5]', '[125, 5, -5]', '[126, 42, 4*w^2 - 9*w - 5]', '[126, 126, w + 5]', '[127, 127, 4*w^2 - 7*w - 14]', '[128, 8, -4*w - 4]', '[129, 129, -3*w^2 + 2*w + 10]', '[129, 129, -w^2 + 5*w - 1]', '[129, 129, 4*w^2 - 9*w - 4]', '[132, 66, w^2 + 2*w - 3]', '[134, 134, -3*w^2 + 5*w + 8]', '[139, 139, 3*w^2 - 4*w - 10]', '[144, 12, 2*w^2 - 6*w - 4]', '[144, 36, -2*w^2 - 2*w + 4]', '[146, 146, -w^2 + 5*w + 10]', '[147, 21, -2*w^2 + 5*w + 6]', '[147, 147, -w^2 + w + 9]', '[148, 74, w^2 - 4*w - 7]', '[148, 74, -w^2 + 4*w - 5]', '[148, 74, -w^2 + 4*w + 5]', '[149, 149, w - 6]', '[151, 151, -w^2 - w + 9]', '[154, 154, w^2 + w - 6]', '[159, 159, 5*w^2 - 15*w + 1]', '[162, 18, -2*w^2 + 3*w + 13]', '[162, 18, -3*w + 3]', '[162, 162, w^2 - 5*w + 4]', '[163, 163, -w^2 - w - 3]', '[164, 82, -w^2 + 2*w + 9]', '[166, 166, -w^2 + 5*w - 2]', '[167, 167, -3*w^2 - 2*w + 6]', '[168, 42, -2*w^2 + 8]', '[172, 86, -w^2 + 2*w - 3]', '[172, 86, -3*w^2 + 8*w - 1]', '[172, 86, 3*w^2 - 8*w - 5]', '[173, 173, w^2 + w - 7]', '[174, 174, -w^2 - w + 8]', '[176, 44, -2*w - 6]', '[177, 177, -5*w^2 + 12*w + 8]', '[178, 178, 5*w + 3]', '[179, 179, -3*w^2 + 6*w + 10]', '[179, 179, -2*w^2 + 6*w - 3]', '[179, 179, -3*w^2 + 2*w + 20]', '[183, 183, -3*w^2 + 5*w + 7]', '[189, 21, -3*w + 6]', '[189, 189, 2*w^2 - 5*w - 12]', '[191, 191, 3*w - 4]', '[192, 12, 4*w^2 - 8*w - 8]', '[194, 194, 2*w^2 - 5*w - 7]', '[194, 194, -4*w^2 + 7*w + 11]', '[194, 194, -2*w^2 - 3*w + 3]', '[196, 14, -3*w^2 + 4*w + 9]', '[196, 98, w^2 + 3]', '[198, 66, -w^2 + 3*w - 4]', '[198, 198, -3*w^2 + w + 8]', '[199, 199, w^2 + 2*w - 4]', '[201, 201, -w^2 + w - 3]', '[202, 202, w^2 + 7*w + 8]', '[202, 202, 3*w + 7]', '[203, 203, 2*w^2 - 5*w + 2]', '[206, 206, w^2 - 5*w - 4]', '[212, 106, 3*w^2 - 10*w + 5]', '[216, 6, 6]', '[216, 54, -2*w + 8]', '[218, 218, -3*w^2 + 5*w + 6]', '[219, 219, -5*w^2 + 7*w + 19]', '[222, 222, -3*w^2 + 5*w + 4]', '[222, 222, w^2 - 3*w - 10]', '[222, 222, 4*w^2 - 11*w - 5]', '[223, 223, -w - 6]', '[223, 223, 3*w - 10]', '[223, 223, -7*w^2 + 14*w + 18]', '[224, 28, -2*w^2 + 4*w + 14]', '[226, 226, -3*w^2 - w + 8]', '[229, 229, -3*w^2 + 10*w - 2]', '[231, 231, -4*w^2 + 4*w + 15]', '[232, 58, -4*w + 2]', '[233, 233, 2*w^2 - 9]', '[233, 233, 2*w^2 - 5*w - 8]', '[233, 233, 3*w^2 - 5*w - 5]', '[236, 118, -5*w^2 + 10*w + 11]', '[241, 241, -w^2 + 5*w + 9]', '[242, 22, 2*w^2 + 3*w + 3]', '[242, 242, 2*w^2 - 5*w - 11]', '[243, 9, 3*w^2 - 6]', '[243, 27, 3*w^2 - 3*w - 9]', '[243, 243, 4*w^2 - 6*w - 13]', '[244, 122, -3*w^2 + 6*w + 11]', '[246, 246, 3*w^2 + w - 4]', '[249, 249, -3*w^2 + 4*w + 8]', '[250, 10, 5*w + 5]', '[252, 42, -w^2 + 11]', '[252, 126, 3*w^2 - 10*w + 1]', '[254, 254, -w^2 + w + 10]', '[256, 8, 4*w^2 - 8*w - 12]', '[257, 257, -3*w^2 + 10]', '[258, 258, -3*w^2 + 7*w + 8]', '[258, 258, -2*w^2 + 5*w + 9]', '[258, 258, -w + 7]', '[259, 259, -2*w^2 - 2*w + 5]', '[259, 259, -4*w^2 + 8*w + 7]', '[259, 259, w^2 + 3*w - 3]', '[261, 87, 4*w^2 - 3*w - 14]', '[261, 261, w^2 - 5*w - 5]', '[263, 263, 2*w^2 - 5*w - 10]', '[264, 66, 4*w - 10]', '[267, 267, -6*w^2 + 14*w + 7]', '[268, 134, w^2 + 2*w - 5]', '[269, 269, w^2 - 7*w + 11]', '[271, 271, -7*w^2 + 11*w + 25]', '[277, 277, -6*w^2 + 9*w + 22]', '[278, 278, -2*w^2 - w + 7]', '[283, 283, -5*w^2 + 11*w + 7]', '[283, 283, w^2 - 2*w - 10]', '[283, 283, -3*w^2 + w + 7]', '[287, 287, 3*w^2 - 2*w - 8]', '[288, 12, -2*w^2 + 10]', '[288, 36, 2*w^2 - 4*w + 2]', '[291, 291, -w^2 + 2*w - 4]', '[291, 291, 9*w^2 - 20*w - 16]', '[291, 291, w^2 - 4*w + 6]', '[292, 146, -7*w^2 + 10*w + 31]', '[293, 293, 6*w + 11]', '[294, 42, -w^2 - w - 4]', '[294, 294, w^2 - 5*w - 8]', '[296, 74, 4*w^2 - 8*w - 6]', '[296, 74, -2*w^2 + 6*w + 6]', '[296, 74, 4*w^2 - 2*w - 16]', '[297, 33, -3*w^2 + 6*w + 12]', '[297, 297, -4*w^2 + 8*w + 5]', '[298, 298, -w^2 + 5*w + 6]', '[301, 301, -3*w^2 + 4*w + 4]', '[301, 301, 2*w^2 - 8*w + 1]', '[301, 301, -5*w^2 + 11*w + 5]', '[302, 302, 3*w^2 - 3*w - 8]', '[303, 303, -4*w^2 + 5*w + 14]', '[303, 303, -w^2 - 2*w + 12]', '[308, 154, -3*w^2 + 5]', '[309, 309, 2*w + 7]', '[311, 311, -w^2 + 5*w + 7]', '[313, 313, 4*w - 3]', '[318, 318, 5*w^2 - 11*w - 6]', '[319, 319, -3*w^2 + 4*w + 6]', '[324, 18, w^2 - 6*w + 7]', '[324, 18, 3*w^2 - 6*w - 15]', '[324, 162, 3*w^2 - 4*w - 5]', '[326, 326, -w^2 + 5*w - 8]', '[327, 327, 2*w^2 - 11]', '[328, 82, 2*w^2 - 8*w + 4]', '[331, 331, -3*w^2 + 9*w + 5]', '[332, 166, -3*w^2 + 6*w + 13]', '[333, 111, w^2 + 4]', '[333, 111, 2*w^2 + 3*w - 4]', '[333, 111, 2*w^2 - 13]', '[333, 333, -3*w^2 + 8*w - 2]', '[333, 333, w^2 - 3*w + 5]', '[333, 333, w^2 + 2*w - 6]', '[334, 334, w^2 - w + 4]', '[336, 84, 2*w^2 - 6*w + 4]', '[337, 337, 4*w^2 - 7*w - 20]', '[339, 339, -2*w^2 + w + 16]', '[343, 7, 7]', '[343, 343, 3*w^2 - 6*w - 14]', '[344, 86, -4*w^2 + 4*w + 14]', '[344, 86, -4*w^2 + 6*w + 12]', '[344, 86, -2*w^2 + 12]', '[346, 346, -3*w^2 + w + 6]', '[347, 347, 3*w^2 - w - 13]', '[348, 174, 3*w^2 - 2*w - 7]', '[349, 349, 3*w^2 - 3*w - 7]', '[352, 44, -2*w^2 + 8*w - 2]', '[353, 353, -3*w^2 + 7*w + 9]', '[354, 354, -2*w^2 + 5*w - 3]', '[356, 178, -5*w^2 + 12*w + 9]', '[358, 358, -w - 7]', '[358, 358, 4*w^2 - 7*w - 17]', '[358, 358, -2*w^2 + 7*w + 5]', '[363, 33, 2*w^2 - 8*w + 3]', '[363, 363, 5*w^2 - 13*w - 7]', '[366, 366, w^2 + 3*w - 4]', '[369, 123, 2*w^2 - 6*w - 7]', '[369, 369, 4*w^2 - 9*w - 10]', '[371, 371, 7*w^2 - 16*w - 10]', '[375, 15, -5*w^2 + 10*w + 10]', '[378, 42, 3*w^2 - 3*w - 6]', '[378, 378, 4*w^2 - 7*w - 9]', '[379, 379, 2*w - 9]', '[379, 379, -4*w + 9]', '[379, 379, -4*w^2 + 11*w + 6]', '[381, 381, 5*w^2 - 8*w - 24]', '[382, 382, -3*w^2 + w + 4]', '[383, 383, 4*w^2 - 8*w - 13]', '[383, 383, 2*w^2 + w - 8]', '[383, 383, 3*w^2 - 3*w - 5]', '[384, 24, -4*w + 4]', '[387, 129, -5*w^2 + 9*w + 13]', '[387, 129, w^2 - 3*w - 11]', '[387, 129, 2*w^2 - 6*w - 13]', '[387, 387, 2*w^2 - 2*w - 15]', '[387, 387, 4*w^2 - 7*w - 18]', '[387, 387, 3*w^2 - 5*w - 19]', '[388, 194, 9*w^2 - 18*w - 23]', '[388, 194, w^2 + 2*w - 7]', '[388, 194, -w^2 - 2*w + 11]', '[389, 389, 3*w^2 - 2*w - 6]', '[392, 14, 2*w^2 + 2*w - 6]', '[392, 98, 4*w^2 - 2*w - 12]', '[396, 66, -w^2 + 6*w + 5]', '[396, 198, -3*w^2 + 8*w + 7]', '[397, 397, -6*w^2 + 13*w + 10]', '[398, 398, -4*w^2 - 3*w + 3]', '[401, 401, w^2 - w - 11]', '[402, 402, -4*w^2 + 3*w + 13]', '[404, 202, -5*w^2 + 8*w + 23]', '[404, 202, -3*w^2 + 2*w + 21]', '[406, 406, 4*w^2 - 5*w - 13]', '[407, 407, -6*w - 7]', '[407, 407, -w^2 + 6*w - 6]', '[407, 407, -w + 8]', '[409, 409, -5*w^2 + 5*w + 19]', '[409, 409, -2*w^2 - 5*w + 2]', '[409, 409, -3*w^2 - w + 9]', '[412, 206, 3*w^2 + 4*w + 3]', '[413, 413, -2*w^2 + 7*w - 6]', '[417, 417, -4*w + 13]', '[419, 419, w^2 - 12]', '[424, 106, 4*w^2 - 10*w - 8]', '[427, 427, w^2 + 2*w - 8]', '[431, 431, 3*w^2 + 5*w - 3]', '[432, 12, -6*w - 6]', '[432, 108, 2*w^2 - 6*w - 8]', '[433, 433, w^2 + 2*w - 10]', '[436, 218, 3*w^2 - 4*w - 19]', '[438, 438, 3*w^2 - w - 14]', '[439, 439, 4*w - 5]', '[441, 21, -w^2 + 6*w - 4]', '[441, 63, -3*w^2 + 11*w - 5]', '[441, 147, 4*w^2 - 6*w - 11]', '[441, 441, 5*w^2 - 14*w - 6]', '[443, 443, 4*w^2 - 7*w - 8]', '[444, 222, w^2 - 2*w - 11]', '[444, 222, -w^2 + 6*w - 5]', '[444, 222, -w^2 - 2*w + 9]', '[446, 446, -3*w^2 + 7*w + 10]', '[446, 446, 3*w - 11]', '[446, 446, w^2 + 7*w + 6]', '[447, 447, -7*w^2 + 15*w + 13]', '[448, 28, -4*w + 8]', '[451, 451, w^2 - 5*w - 13]', '[452, 226, -5*w^2 + 4*w + 27]', '[453, 453, -4*w^2 + 2*w + 17]', '[457, 457, w^2 + 7*w + 5]', '[458, 458, -4*w^2 + 7*w + 5]', '[461, 461, 4*w^2 - 4*w - 13]', '[462, 462, -5*w^2 + 11*w + 12]', '[463, 463, 2*w^2 - 5*w - 16]', '[464, 116, 2*w^2 - 6*w - 12]', '[466, 466, -4*w^2 - w + 7]', '[466, 466, w^2 + 3*w + 6]', '[466, 466, -w^2 - 5*w + 2]', '[467, 467, 2*w^2 + 2*w - 21]', '[469, 469, -w^2 + 6*w + 6]', '[472, 118, 4*w - 6]', '[473, 473, -2*w^2 + 7*w + 6]', '[473, 473, w^2 + w + 5]', '[473, 473, 2*w^2 - 4*w + 3]', '[477, 159, -w^2 - 3*w + 5]', '[477, 477, -4*w + 7]', '[479, 479, 2*w^2 - 6*w - 9]', '[482, 482, -4*w^2 + 7*w + 7]', '[484, 22, w^2 - 4*w + 7]', '[484, 242, 5*w^2 - 10*w - 9]', '[486, 18, 3*w^2 - 9*w - 6]', '[486, 54, -3*w^2 - 3*w + 6]', '[486, 486, -2*w^2 - w + 9]', '[487, 487, w^2 + 3*w - 15]', '[488, 122, -2*w - 8]', '[489, 489, -4*w^2 + 7*w + 6]', '[492, 246, 5*w^2 - 8*w - 15]', '[498, 498, 2*w^2 + 3*w - 5]', '[500, 10, -5*w^2 + 10*w + 15]', '[501, 501, 2*w^2 - 6*w - 11]', '[503, 503, -3*w^2 + 10*w - 6]', '[504, 42, 2*w^2 - 6*w - 10]', '[504, 126, 4*w^2 - 8*w - 14]', '[508, 254, w^2 - 6*w - 9]', '[509, 509, 4*w^2 - 5*w - 12]', '[509, 509, 5*w^2 - 7*w - 17]', '[509, 509, 3*w^2 - w - 15]', '[511, 511, 5*w^2 - 4*w - 26]', '[512, 8, 8]', '[514, 514, w^2 - 3*w + 6]', '[516, 258, -w^2 - 5]', '[516, 258, -w^2 - 4*w - 7]', '[516, 258, w^2 - 6*w - 7]', '[518, 518, 5*w - 3]', '[518, 518, 3*w^2 - 7*w + 2]', '[518, 518, -2*w^2 + 7*w + 15]', '[519, 519, -6*w^2 + 13*w + 14]', '[522, 174, 4*w^2 - 9*w - 11]', '[522, 522, -4*w^2 + w + 15]', '[523, 523, 3*w^2 - 8*w - 8]', '[526, 526, w^2 + 5*w + 8]', '[528, 132, -4*w^2 + 6*w + 10]', '[531, 177, -w^2 + 6*w + 8]', '[531, 531, -3*w^2 + 7*w + 11]', '[534, 534, -2*w^2 + 9*w - 1]', '[536, 134, -4*w^2 - 2*w + 4]', '[537, 537, -w - 8]', '[537, 537, -2*w^2 + 10*w - 11]', '[537, 537, -7*w^2 + 9*w + 37]', '[538, 538, 5*w^2 - 9*w - 12]', '[539, 77, 4*w^2 - 3*w - 12]', '[539, 539, 5*w^2 - 3*w - 21]', '[542, 542, 3*w^2 - w - 18]', '[547, 547, 5*w^2 - 6*w - 18]', '[549, 183, -5*w^2 - 3*w + 7]', '[549, 549, -4*w^2 + 2*w + 11]', '[554, 554, 3*w^2 - w - 16]', '[556, 278, -3*w^2 + 23]', '[557, 557, -w^2 - 2*w + 16]', '[557, 557, -2*w^2 + 5*w - 4]', '[557, 557, 8*w^2 - 13*w - 30]', '[566, 566, -w^2 + 7*w - 2]', '[566, 566, 7*w + 9]', '[566, 566, -7*w^2 + 11*w + 24]', '[567, 63, -3*w^2 + 12]', '[567, 63, 5*w^2 - 12*w - 10]', '[567, 567, -3*w^2 + w + 17]', '[571, 571, -6*w^2 + 11*w + 20]', '[573, 573, -7*w^2 + 17*w + 11]', '[574, 574, 5*w^2 - 13*w - 8]', '[576, 12, 4*w^2 - 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16]', '[9871, 9871, 5*w^2 + 22*w + 14]', '[9872, 2468, 10*w^2 - 14*w - 24]', '[9874, 9874, 7*w^2 + 13*w + 12]', '[9876, 4938, -13*w^2 + 10*w + 63]', '[9879, 9879, 11*w^2 - 16*w - 10]', '[9879, 9879, -9*w^2 + 7*w + 11]', '[9879, 9879, -w^2 - 18*w - 14]', '[9881, 9881, -10*w^2 + 13*w + 26]', '[9882, 1098, 3*w^2 + 9*w - 12]', '[9882, 1098, 7*w^2 - 15*w - 50]', '[9882, 9882, 11*w - 17]', '[9883, 9883, -3*w^2 + 17*w + 29]', '[9884, 4942, -11*w^2 + 20*w + 53]', '[9886, 9886, 2*w^2 + 19*w + 13]', '[9886, 9886, 11*w^2 - 17*w - 28]', '[9886, 9886, 7*w^2 - w - 46]', '[9887, 9887, w^2 + 5*w - 31]', '[9888, 1236, 10*w^2 - 12*w - 10]', '[9897, 9897, -23*w^2 + 53*w + 33]', '[9898, 1414, w^2 + w + 18]', '[9898, 1414, -10*w^2 + 25*w + 23]', '[9898, 9898, -2*w^2 - w + 31]', '[9898, 9898, -7*w^2 + 17*w + 36]', '[9901, 9901, 9*w^2 - 4*w - 18]', '[9902, 9902, -5*w^2 - 9*w + 12]', '[9903, 9903, 7*w^2 - 20*w - 20]', '[9907, 9907, 12*w^2 - 23*w - 42]', '[9907, 9907, 3*w^2 - 18*w - 14]', '[9907, 9907, 2*w^2 - 5*w - 28]', '[9908, 4954, -15*w^2 + 30*w + 43]', '[9912, 2478, 2*w^2 - 4*w - 28]', '[9914, 9914, -11*w^2 + 19*w + 14]', '[9916, 4958, -5*w^2 + 16*w + 45]', '[9916, 4958, 9*w^2 - 10*w - 15]', '[9916, 4958, -9*w^2 + 26*w + 17]', '[9921, 9921, 13*w^2 - 40*w + 12]', '[9922, 902, 2*w^2 - 19*w + 3]', '[9922, 9922, 12*w^2 - 19*w - 33]', '[9923, 9923, 3*w^2 - 16*w - 24]', '[9923, 9923, 10*w^2 - 6*w - 27]', '[9923, 9923, -9*w^2 + 32*w - 12]', '[9924, 4962, -7*w^2 + 16*w + 51]', '[9924, 4962, -9*w^2 + 10*w + 17]', '[9924, 4962, -w^2 + 6*w + 25]', '[9926, 9926, -12*w^2 + 31*w + 21]', '[9927, 3309, -7*w^2 + 24*w + 56]', '[9927, 9927, -15*w^2 + 25*w + 77]', '[9931, 9931, 2*w^2 - 8*w - 29]', '[9931, 9931, -13*w^2 + 25*w + 43]', '[9931, 9931, 14*w^2 - 18*w - 51]', '[9933, 9933, -9*w^2 + 5*w + 19]', '[9933, 9933, -3*w^2 - 8*w + 14]', '[9933, 9933, -8*w^2 - 7*w + 18]', '[9934, 9934, 4*w^2 + 5*w - 41]', '[9938, 9938, -11*w + 19]', '[9938, 9938, -13*w^2 + 3*w + 36]', '[9938, 9938, -12*w^2 - 15*w + 13]', '[9942, 9942, -3*w^2 - 5*w + 44]', '[9943, 9943, 6*w^2 + 12*w + 13]', '[9944, 2486, 16*w^2 - 14*w - 76]', '[9947, 203, 14*w - 7]', '[9947, 9947, 9*w^2 - 8*w - 20]', '[9949, 9949, -4*w^2 - 2*w - 11]', '[9952, 1244, 2*w^2 - 30]', '[9953, 9953, -25*w^2 + 56*w + 42]', '[9953, 9953, -5*w^2 - 2*w + 30]', '[9953, 9953, 11*w - 18]', '[9961, 9961, 16*w^2 - 25*w - 70]', '[9961, 9961, 17*w^2 - 28*w - 54]', '[9961, 9961, -5*w^2 + 23*w - 19]', '[9963, 369, 6*w^2 - 18*w - 21]', '[9963, 1107, 12*w^2 - 27*w - 30]', '[9963, 9963, -10*w^2 + 3*w + 40]', '[9966, 9966, -15*w^2 + 29*w + 46]', '[9967, 9967, -21*w^2 + 31*w + 79]', '[9968, 2492, -10*w^2 + 14*w + 12]', '[9969, 9969, 6*w^2 - 7*w - 44]', '[9972, 1662, -11*w^2 + 18*w + 25]', '[9972, 4986, 3*w^2 - 14*w - 37]', '[9973, 9973, -16*w^2 + 33*w + 42]', '[9974, 9974, -8*w^2 - w + 29]', '[9976, 2494, -4*w^2 + 16*w + 22]', '[9976, 2494, -8*w^2 + 22*w + 20]', '[9976, 2494, 2*w^2 - 4*w + 16]', '[9977, 9977, -25*w^2 + 61*w + 23]', '[9978, 9978, 9*w^2 - 7*w - 20]', '[9978, 9978, -10*w^2 - w + 17]', '[9978, 9978, -15*w^2 + 17*w + 58]', '[9981, 3327, 4*w^2 - 21*w + 4]', '[9981, 9981, -2*w^2 - 19*w - 18]', '[9983, 9983, 14*w^2 - 23*w - 68]', '[9986, 9986, -12*w^2 - 11*w + 19]', '[9989, 9989, -6*w^2 + 19*w - 14]', '[9989, 9989, -13*w^2 + 13*w + 47]', '[9989, 9989, -22*w^2 + 29*w + 114]', '[9991, 9991, 11*w^2 - 19*w - 21]', '[9991, 9991, 9*w^2 - 9*w - 13]', '[9991, 9991, 11*w^2 - 8*w - 34]', '[9993, 9993, -18*w^2 + 41*w + 22]', '[9998, 9998, w^2 + 7*w + 20]', '[9999, 3333, -16*w^2 + 12*w + 59]', '[9999, 3333, -19*w^2 + 3*w + 59]', '[9999, 9999, -20*w^2 + 23*w + 84]', '[9999, 9999, -20*w^2 + 16*w + 85]'], 'label': '3.3.404.1', 'narrow_class_no': 1, 'primes': ['[2, 2, -w - 1]', '[3, 3, w^2 - 2*w - 2]', '[7, 7, -w + 2]', '[9, 3, w^2 - 2]', '[11, 11, -w^2 + 2*w + 4]', '[29, 29, -2*w + 1]', '[37, 37, 2*w^2 - 4*w - 3]', '[37, 37, -w^2 + 3*w + 3]', '[37, 37, 2*w^2 - w - 8]', '[41, 41, w^2 - 4*w + 2]', '[43, 43, -2*w^2 + 2*w + 7]', '[43, 43, -2*w^2 + 3*w + 6]', '[43, 43, -w^2 + 6]', '[49, 7, w^2 + w - 3]', '[53, 53, 2*w^2 - 5*w - 4]', '[59, 59, 2*w - 3]', '[61, 61, -w - 4]', '[67, 67, -2*w^2 - w + 2]', '[73, 73, 2*w^2 - 3*w - 12]', '[83, 83, -2*w - 5]', '[89, 89, -w^2 + 2*w - 2]', '[97, 97, -2*w + 7]', '[97, 97, -2*w^2 + 3]', '[97, 97, 2*w^2 - 2*w - 5]', '[101, 101, w^2 - 3*w - 9]', '[101, 101, 2*w^2 - 4*w - 9]', '[103, 103, w^2 - 3*w + 3]', '[109, 109, -w^2 + 4*w + 8]', '[113, 113, 3*w^2 - 3*w - 11]', '[121, 11, w^2 - 4*w - 4]', '[125, 5, -5]', '[127, 127, 4*w^2 - 7*w - 14]', '[139, 139, 3*w^2 - 4*w - 10]', '[149, 149, w - 6]', '[151, 151, -w^2 - w + 9]', '[163, 163, -w^2 - w - 3]', '[167, 167, -3*w^2 - 2*w + 6]', '[173, 173, w^2 + w - 7]', '[179, 179, -3*w^2 + 6*w + 10]', '[179, 179, -2*w^2 + 6*w - 3]', '[179, 179, -3*w^2 + 2*w + 20]', '[191, 191, 3*w - 4]', '[199, 199, w^2 + 2*w - 4]', '[223, 223, -w - 6]', '[223, 223, 3*w - 10]', '[223, 223, -7*w^2 + 14*w + 18]', '[229, 229, -3*w^2 + 10*w - 2]', '[233, 233, 2*w^2 - 9]', '[233, 233, 2*w^2 - 5*w - 8]', '[233, 233, 3*w^2 - 5*w - 5]', '[241, 241, -w^2 + 5*w + 9]', '[257, 257, -3*w^2 + 10]', '[263, 263, 2*w^2 - 5*w - 10]', '[269, 269, w^2 - 7*w + 11]', '[271, 271, -7*w^2 + 11*w + 25]', '[277, 277, -6*w^2 + 9*w + 22]', '[283, 283, -5*w^2 + 11*w + 7]', '[283, 283, w^2 - 2*w - 10]', '[283, 283, -3*w^2 + w + 7]', '[293, 293, 6*w + 11]', '[311, 311, -w^2 + 5*w + 7]', '[313, 313, 4*w - 3]', '[331, 331, -3*w^2 + 9*w + 5]', '[337, 337, 4*w^2 - 7*w - 20]', '[347, 347, 3*w^2 - w - 13]', '[349, 349, 3*w^2 - 3*w - 7]', '[353, 353, -3*w^2 + 7*w + 9]', '[379, 379, 2*w - 9]', '[379, 379, -4*w + 9]', '[379, 379, -4*w^2 + 11*w + 6]', '[383, 383, 4*w^2 - 8*w - 13]', '[383, 383, 2*w^2 + w - 8]', '[383, 383, 3*w^2 - 3*w - 5]', '[389, 389, 3*w^2 - 2*w - 6]', '[397, 397, -6*w^2 + 13*w + 10]', '[401, 401, w^2 - w - 11]', '[409, 409, -5*w^2 + 5*w + 19]', '[409, 409, -2*w^2 - 5*w + 2]', '[409, 409, -3*w^2 - w + 9]', '[419, 419, w^2 - 12]', '[431, 431, 3*w^2 + 5*w - 3]', '[433, 433, w^2 + 2*w - 10]', '[439, 439, 4*w - 5]', '[443, 443, 4*w^2 - 7*w - 8]', '[457, 457, w^2 + 7*w + 5]', '[461, 461, 4*w^2 - 4*w - 13]', '[463, 463, 2*w^2 - 5*w - 16]', '[467, 467, 2*w^2 + 2*w - 21]', '[479, 479, 2*w^2 - 6*w - 9]', '[487, 487, w^2 + 3*w - 15]', '[503, 503, -3*w^2 + 10*w - 6]', '[509, 509, 4*w^2 - 5*w - 12]', '[509, 509, 5*w^2 - 7*w - 17]', '[509, 509, 3*w^2 - w - 15]', '[523, 523, 3*w^2 - 8*w - 8]', '[547, 547, 5*w^2 - 6*w - 18]', '[557, 557, -w^2 - 2*w + 16]', '[557, 557, -2*w^2 + 5*w - 4]', '[557, 557, 8*w^2 - 13*w - 30]', '[571, 571, -6*w^2 + 11*w + 20]', '[577, 577, -6*w^2 + 12*w + 17]', '[593, 593, w^2 + 4*w - 4]', '[593, 593, 6*w^2 - 4*w - 25]', '[593, 593, -2*w^2 - 3*w + 24]', '[599, 599, 4*w^2 - 6*w - 9]', '[613, 613, 4*w^2 - 8*w - 15]', '[617, 617, -5*w + 12]', '[641, 641, 5*w - 4]', '[647, 647, 2*w^2 + w - 16]', '[653, 653, 3*w^2 - 7*w - 13]', '[653, 653, 3*w^2 - 9*w - 7]', '[653, 653, w^2 - 2*w - 12]', '[659, 659, -6*w^2 + 6*w + 23]', '[661, 661, -w^2 + 2*w - 6]', '[673, 673, -2*w^2 + 7*w + 14]', '[683, 683, 4*w^2 - 4*w - 11]', '[683, 683, -2*w^2 - 3*w + 6]', '[683, 683, -5*w^2 - 2*w + 12]', '[691, 691, -5*w^2 - 4*w + 4]', '[691, 691, 6*w^2 - 4*w - 21]', '[691, 691, 4*w^2 - 5*w - 10]', '[709, 709, 8*w + 11]', '[719, 719, -2*w - 9]', '[733, 733, -w^2 + 4*w - 8]', '[739, 739, 4*w^2 - w - 16]', '[751, 751, -w^2 - 6]', '[757, 757, w^2 - 7*w - 7]', '[761, 761, 2*w^2 + w - 14]', '[761, 761, -10*w^2 + 16*w + 35]', '[761, 761, 5*w^2 - 2*w - 34]', '[769, 769, -4*w^2 - w + 12]', '[773, 773, 4*w^2 - w - 8]', '[797, 797, -3*w^2 + 22]', '[809, 809, w^2 + 7*w + 11]', '[809, 809, 4*w^2 - 8*w - 19]', '[809, 809, 5*w^2 - 7*w - 29]', '[811, 811, 3*w^2 + w - 11]', '[821, 821, 5*w^2 - 9*w - 21]', '[821, 821, -9*w^2 + 14*w + 32]', '[821, 821, -11*w^2 + 20*w + 34]', '[823, 823, 5*w^2 - 7*w - 15]', '[827, 827, w^2 + w - 15]', '[827, 827, 2*w^2 - 8*w - 7]', '[827, 827, 2*w^2 - 7*w - 12]', '[839, 839, 2*w^2 + 2*w - 9]', '[839, 839, 5*w - 6]', '[839, 839, w^2 - w - 13]', '[841, 29, -2*w^2 + w - 4]', '[853, 853, 3*w^2 - 14]', '[853, 853, 2*w^2 - w - 18]', '[853, 853, 2*w^2 - 2*w - 17]', '[859, 859, -3*w^2 + 11*w - 9]', '[863, 863, -w^2 + 7*w - 5]', '[877, 877, -3*w - 10]', '[881, 881, w^2 + 10*w + 12]', '[883, 883, 6*w^2 - 7*w - 22]', '[887, 887, 6*w^2 - 8*w - 21]', '[887, 887, -9*w^2 + 19*w + 21]', '[887, 887, -6*w^2 + 11*w + 14]', '[907, 907, 4*w^2 - 14*w + 9]', '[911, 911, 4*w^2 - 4*w - 7]', '[919, 919, w^2 + 4*w - 6]', '[937, 937, -4*w^2 + 2*w + 7]', '[941, 941, 4*w^2 - 3*w - 6]', '[947, 947, 2*w^2 - 4*w - 17]', '[953, 953, 2*w^2 + 6*w - 3]', '[971, 971, -3*w^2 - w + 29]', '[983, 983, -5*w^2 + 14*w + 8]', '[991, 991, 2*w^2 + 4*w - 29]', '[991, 991, -6*w^2 + w + 16]', '[991, 991, 3*w^2 - 8*w - 12]']}
• 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, -5, -1, 1], 'conductor': 0, 'degree': 3, 'dirichlet_group': [], 'disc_abs': 404, 'disc_rad': 202, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[2, 1], [1, 1]]], [5, [[3, 1]]], [7, [[2, 1], [1, 1]]], [11, [[2, 1], [1, 1]]], [13, [[3, 1]]], [17, [[3, 1]]], [19, [[3, 1]]], [23, [[3, 1]]], [29, [[2, 1], [1, 1]]], [31, [[3, 1]]], [37, [[1, 3]]], [41, [[2, 1], [1, 1]]], [43, [[1, 3]]], [47, [[3, 1]]], [53, [[2, 1], [1, 1]]], [59, [[2, 1], [1, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [4, 3], 'galois_label': '3T2', 'galt': 2, 'grd': 15.953183133116863, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '3.3.404.1', 'local_algs': ['2.3.2.1', '101.1.0.1', '101.2.1.1'], 'monogenic': 1, 'num_ram': 2, 'r2': 0, 'ramps': [2, 101], 'rd': 7.39254179171, 'regulator': {'__RealLiteral__': 0, 'data': '3.75987912189', 'prec': 44}, 'res': {'gal': ['9,-39,26,25,-10,-3,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a \\)', '\\( a^{2} + a - 1 \\)'], 'unitsGmodule': [[4, 1], [5, 1]], 'used_grh': False, 'zk': ['1', 'a', 'a^2']}