Hilbert modular form data - 3.3.785.1-23.3-b

Formats: - HTML - YAML - JSON - 2024-05-05T21:10:29.856987

• 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': 3, 'disc': 785, 'field_bad_primes': [5, 157], 'field_label': '3.3.785.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '3.3.785.1-23.3-b', 'label_nsuffix': 1, 'label_suffix': 'b', 'level_bad_primes': [23], 'level_ideal': '[23, 23, -w^2 + 8]', 'level_label': '23.3', 'level_norm': 23, 'parallel_weight': 2, 'short_label': '23.3-b', 'weight': '[2, 2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[23, 23, -w^2 + 8]', 1]], 'hecke_eigenvalues': ['e', -3, 'e^2 - e - 4', '-e - 1', '-2*e^2 + 3*e + 3', '2*e^2 - 5*e - 2', '-e + 2', 'e^2 - 6', 'e^2 - e - 3', -1, '-3*e^2 + 7*e + 7', '-3*e + 5', 0, '-3*e^2 + 2*e + 11', '-3*e^2 + 12', '-6*e^2 + 12*e + 12', '3*e^2 - 6*e - 8', 'e^2 - 3', '8*e^2 - 14*e - 14', '2*e^2 - 7*e - 7', '-4*e^2 + 4*e + 5', '-e^2 - 5*e + 12', '-5*e^2 + 5*e + 19', '2*e^2 - 4*e - 10', '5*e^2 - 14*e - 13', '-4*e^2 + 6*e + 12', '2*e^2 - 8*e - 3', 'e - 11', '-3*e^2 + 6*e + 11', '4*e + 1', '7*e^2 - 16*e - 19', '3*e^2 - 12*e + 4', '-7*e^2 + 19*e + 13', '2*e^2 + e - 23', '3*e - 6', '5*e^2 - 14*e - 10', '-3*e^2 + 15*e', '-4*e^2 + 10*e + 11', '-e^2 + 7*e - 16', '4*e^2 - 4*e - 10', '5*e^2 - 9*e + 3', '-6*e^2 + 9*e + 15', '5*e^2 - 14*e - 21', '-2*e^2 - e - 4', '-e^2 + 3*e - 9', '-7*e^2 + 13*e - 2', '4*e^2 - 7*e - 2', '6*e^2 - 13*e - 22', '9*e^2 - 10*e - 25', '2*e^2 - 8*e - 12', '-8*e^2 + 17*e + 24', '5*e^2 - 5*e - 11', '-3*e^2 + 3*e - 4', '5*e^2 - 11*e - 8', '-9*e^2 + 21*e + 15', '-6*e^2 + 16*e + 13', '-e^2 - 2*e + 13', '6*e^2 - 17*e - 23', '-3*e^2 + 2*e - 1', '-3*e^2 + 3*e + 9', '-2*e^2 + 14*e + 6', '-e^2 + 10*e - 8', '4*e^2 - 2*e + 4', '-5*e^2 + 5*e - 3', '7*e^2 - 18*e', -3, '-6*e^2 + 12*e + 5', '-e^2 - 5*e + 25', '-3*e^2 + 6*e - 3', '-3*e^2 + 6*e + 23', '-e + 17', '13*e^2 - 25*e - 16', '3*e^2 - 3*e - 3', '-7*e - 1', '-6*e^2 + 24*e + 12', '8*e^2 - 20*e - 26', '-6*e^2 + 13*e - 11', '-3*e^2 + 9*e + 20', 'e^2 + 11*e - 22', '15*e^2 - 24*e - 27', 'e^2 + 14*e - 13', '8*e^2 - 5*e - 21', '-7*e^2 + 22*e + 23', '11*e^2 - 8*e - 36', '-10*e^2 + 31*e + 23', '-2*e^2 + 2*e - 11', '-7*e^2 + 19*e + 1', '-14*e^2 + 31*e + 16', '6*e^2 - 15*e + 12', '-5*e^2 + 9*e + 15', '17*e^2 - 31*e - 34', '-2*e^2 - 6*e + 30', '-5*e^2 + 5*e - 3', '-e^2 - 2*e + 2', '2*e^2 - e - 37', '-2*e^2 + 17*e - 7', '4*e^2 - 10*e - 15', 'e^2 + 6*e - 30', 'e^2 + 5*e + 9', '-5*e^2 + 14*e + 8', '-10*e^2 + 19*e + 40', '6*e^2 + 3*e - 45', 'e^2 - 13*e + 2', '-14*e^2 + 35*e + 34', '7*e^2 - 4*e - 6', '11*e^2 - 22*e - 4', '-3*e^2 + 8*e - 10', '5*e^2 - e - 31', '2*e^2 + e + 7', '-6*e^2 + 5*e - 7', '4*e^2 - 5*e + 19', '4*e^2 - 15*e - 21', '-5*e^2 - e + 37', '-4*e^2 - 2*e + 7', '-e^2 + 7*e + 17', '3*e^2 - 16*e - 16', '-e^2 + 16*e - 1', '2*e^2 + 9*e - 3', '2*e^2 - 4*e - 10', '4*e + 1', '-15*e - 3', '6*e^2 - 15*e + 1', 'e^2 - 4*e - 31', '-2*e^2 - 4*e + 17', '-5*e^2 + 13*e + 34', '8*e^2 - 26*e - 23', '13*e^2 - 16*e - 31', '15*e - 15', '2*e^2 + 7*e + 10', '-11*e^2 + 26*e + 41', '-10*e^2 + 29*e + 17', '3*e^2 - 18*e', '6*e^2 + 5*e - 49', '-8*e^2 + 17*e - 12', '-4*e^2 - 2*e + 48', '-6*e^2 + 3', '10*e^2 - 20*e - 44', '-7*e^2 + 22*e + 26', '-2*e^2 + 2*e - 1', '6*e^2 - 27', '-9*e^2 + 21*e + 18', '-5*e^2 + 20*e - 22', '11*e^2 - 11*e - 30', '-14*e^2 + 26*e + 32', '-4*e^2 - 2*e - 9', '-11*e^2 + 20*e + 35', '-6*e^2 + 15*e + 28', '-6*e^2 - 9*e + 28', '-14*e^2 + 38*e + 29', '9*e^2 - 10*e - 16', '-2*e^2 - 10*e + 25', '11*e^2 - 35*e - 24', '4*e^2 - 22*e - 14', '15*e^2 - 15*e - 42', '-3*e^2 + 5*e - 28', '-9*e^2 + 15*e + 21', 'e^2 - 4*e - 7', '5*e^2 + e - 13', '11*e^2 - 4*e - 25', -39, '-3*e^2 + 5*e - 10', 'e^2 - 7*e + 8', '-15*e^2 + 37*e + 34', '8*e^2 - 5*e - 13', '-15*e^2 + 12*e + 45'], 'hecke_polynomial': 'x^3 - 2*x^2 - 3*x + 1', 'label': '3.3.785.1-23.3-b'}
• hmf_fields •

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

  
  {'degree': 3, 'discriminant': 785, 'ideals': ['[1, 1, 1]', '[3, 3, w - 2]', '[5, 5, w]', '[5, 5, -w + 3]', '[8, 2, 2]', '[9, 3, w^2 + w - 4]', '[9, 9, w + 1]', '[13, 13, w + 3]', '[15, 15, w^2 - 4]', '[15, 15, w^2 - w - 5]', '[17, 17, -w^2 + w + 3]', '[23, 23, w^2 - 2]', '[23, 23, w^2 - 3]', '[23, 23, -w^2 + 8]', '[24, 6, 2*w - 4]', '[25, 5, w^2 + 2*w]', '[25, 5, -w^2 + w + 6]', '[25, 25, -w^2 - w + 5]', '[27, 3, 3]', '[27, 27, w^2 - w - 2]', '[29, 29, w - 4]', '[37, 37, w^2 + w - 8]', '[39, 39, w^2 + w - 6]', '[40, 10, 2*w]', '[40, 10, -2*w + 6]', '[41, 41, w^2 + 2*w - 4]', '[45, 15, 2*w^2 + 2*w - 5]', '[45, 15, w^2 + w - 7]', '[45, 45, w^2 + w]', '[45, 45, -w^2 + 2*w + 3]', '[47, 47, 2*w^2 + w - 8]', '[51, 51, -w - 4]', '[59, 59, -2*w^2 - 3*w + 6]', '[61, 61, -2*w - 1]', '[64, 4, 4]', '[65, 65, -w^2 + 9]', '[65, 65, w^2 + 3*w]', '[67, 67, -2*w - 3]', '[69, 69, -w^2 + 3*w + 1]', '[69, 69, -w^2 - 3*w + 1]', '[69, 69, -2*w^2 + w + 9]', '[72, 6, 2*w^2 + 2*w - 8]', '[72, 18, 2*w + 2]', '[75, 15, 2*w^2 - 2*w - 7]', '[75, 15, w^2 + 2*w - 5]', '[75, 75, w - 5]', '[79, 79, 2*w^2 - 9]', '[81, 9, -w^2 + 2*w + 4]', '[81, 9, 3*w - 6]', '[81, 81, w^2 + 2*w + 1]', '[85, 85, -3*w + 5]', '[85, 85, -2*w^2 - w + 11]', '[87, 87, w^2 - 6*w + 8]', '[104, 26, 2*w + 6]', '[109, 109, w^2 + 2*w - 6]', '[109, 109, 2*w^2 + w - 14]', '[109, 109, -w^2 - w - 1]', '[111, 111, -4*w + 11]', '[113, 113, 2*w^2 + w - 12]', '[115, 115, -w - 5]', '[115, 115, 2*w^2 - 3*w - 4]', '[115, 115, -w^2 + 2*w + 5]', '[115, 115, w^2 + 3*w - 5]', '[115, 115, 2*w^2 - 4*w - 1]', '[115, 115, -2*w^2 - w + 6]', '[117, 39, 2*w^2 - w - 8]', '[117, 117, -2*w + 7]', '[120, 30, 2*w^2 - 8]', '[120, 30, 2*w^2 - 2*w - 10]', '[123, 123, w^2 - 2*w + 3]', '[125, 5, 5]', '[125, 25, -w^2 - 2*w + 10]', '[125, 25, -2*w^2 - 3*w + 7]', '[125, 125, -2*w^2 - w + 5]', '[127, 127, w^2 - 3*w - 2]', '[131, 131, -4*w^2 - 5*w + 9]', '[135, 15, 3*w]', '[135, 15, -3*w + 9]', '[135, 135, w^2 - 10]', '[135, 135, 2*w^2 + 2*w - 9]', '[136, 34, -2*w^2 + 2*w + 6]', '[137, 137, w^2 + 2*w - 7]', '[137, 137, 3*w + 8]', '[137, 137, 2*w^2 + w - 17]', '[139, 139, 3*w^2 + 2*w - 11]', '[141, 141, -w^2 + 2*w + 6]', '[145, 145, w^2 - 4*w]', '[145, 145, -w^2 + 7*w - 12]', '[149, 149, w - 6]', '[151, 151, w^2 + 2*w - 9]', '[153, 51, w^2 - 2*w - 7]', '[153, 153, -w^2 - 2*w + 8]', '[157, 157, -w^2 - 2*w + 13]', '[157, 157, 2*w^2 - 7]', '[163, 163, w^2 + 3*w + 3]', '[163, 163, 2*w^2 - 3*w - 3]', '[163, 163, 2*w^2 - w - 7]', '[167, 167, 3*w^2 + w - 13]', '[169, 13, 2*w^2 + 5*w - 1]', '[169, 169, -2*w^2 + 2*w + 11]', '[173, 173, w^2 + 2*w + 2]', '[177, 177, -w^2 - 2]', '[179, 179, 4*w^2 + 2*w - 19]', '[181, 181, w^2 + 3*w - 6]', '[183, 183, -2*w^2 + 3*w + 2]', '[184, 46, 2*w^2 - 4]', '[184, 46, 2*w^2 - 6]', '[184, 46, -2*w^2 + 16]', '[185, 185, 2*w^2 - 2*w - 5]', '[185, 185, w^2 + 5*w - 19]', '[191, 191, 3*w^2 + 2*w - 14]', '[192, 12, 4*w - 8]', '[193, 193, w^2 - 3*w - 3]', '[195, 195, 2*w^2 - 5]', '[195, 195, -2*w^2 - 5*w + 3]', '[197, 197, 3*w^2 - 2*w - 13]', '[200, 10, 2*w^2 + 4*w]', '[200, 10, -2*w^2 + 2*w + 12]', '[200, 50, -2*w^2 - 2*w + 10]', '[201, 201, -2*w^2 + w + 6]', '[205, 205, 3*w^2 + 2*w - 5]', '[205, 205, 4*w - 7]', '[207, 69, 2*w^2 + 5*w - 2]', '[207, 69, w^2 + 4*w + 2]', '[207, 69, -w^2 - w - 2]', '[207, 207, -2*w^2 + 2*w + 13]', '[207, 207, 2*w^2 + 4*w - 7]', '[207, 207, 2*w^2 + 3*w - 8]', '[211, 211, -w - 6]', '[216, 6, 6]', '[216, 54, 2*w^2 - 2*w - 4]', '[221, 221, -3*w^2 + 14]', '[223, 223, -w^2 + w - 3]', '[223, 223, -3*w - 2]', '[223, 223, 2*w^2 - 2*w - 3]', '[225, 15, 2*w^2 - w - 5]', '[225, 15, -w^2 - 4*w + 1]', '[225, 45, w^2 - 3*w + 5]', '[225, 45, -w^2 + w + 11]', '[225, 75, 2*w^2 - 4*w - 5]', '[225, 225, -3*w^2 - 2*w + 10]', '[229, 229, 2*w^2 - w - 4]', '[232, 58, 2*w - 8]', '[233, 233, 2*w + 7]', '[235, 235, 3*w^2 + 4*w - 10]', '[235, 235, 3*w^2 - w - 14]', '[237, 237, -2*w^2 + 3*w + 8]', '[239, 239, -3*w - 4]', '[239, 239, w^2 - 11]', '[239, 239, 4*w^2 - w - 21]', '[241, 241, 3*w^2 + w - 19]', '[243, 9, 3*w^2 + 3*w - 12]', '[243, 27, 3*w + 3]', '[243, 243, w^2 + 3*w - 7]', '[251, 251, -w^2 - 4*w - 1]', '[255, 255, -w^2 - 4*w]', '[255, 255, w^2 + w - 12]', '[257, 257, w - 7]', '[261, 87, -2*w^2 - 2*w + 11]', '[261, 261, w^2 - 3*w - 4]', '[263, 263, 3*w^2 + w - 12]', '[269, 269, 3*w^2 - 4*w - 11]', '[271, 271, 4*w^2 + 6*w - 11]', '[277, 277, -4*w^2 - 3*w + 17]', '[283, 283, 5*w^2 + 4*w - 18]', '[289, 17, 3*w^2 + 2*w - 9]', '[289, 289, -3*w^2 - 2*w + 6]', '[295, 295, -3*w + 10]', '[295, 295, -w^2 - 3*w + 8]', '[296, 74, 2*w^2 + 2*w - 16]', '[299, 299, 4*w^2 + 4*w - 11]', '[299, 299, 5*w - 11]', '[299, 299, -2*w^2 - 3*w + 9]', '[305, 305, 2*w^2 - 5*w - 3]', '[305, 305, -2*w^2 - w]', '[307, 307, -2*w^2 - w + 18]', '[307, 307, w^2 + 2*w + 3]', '[307, 307, -w^2 - 3]', '[312, 78, 2*w^2 + 2*w - 12]', '[313, 313, 3*w^2 - 13]', '[317, 317, 3*w^2 - 2*w - 12]', '[320, 20, 4*w]', '[320, 20, -4*w + 12]', '[325, 65, -w^2 + 3*w + 5]', '[325, 65, -3*w^2 - 2*w + 8]', '[325, 325, -3*w^2 + 3*w + 10]', '[327, 327, w^2 - 4*w + 7]', '[327, 327, w^2 + 4*w - 18]', '[327, 327, -5*w + 7]', '[328, 82, 2*w^2 + 4*w - 8]', '[331, 331, w^2 + 3*w - 9]', '[331, 331, w^2 + 3*w - 11]', '[331, 331, w^2 + 3*w + 4]', '[333, 111, -2*w^2 + w + 17]', '[333, 333, 3*w^2 - w - 13]', '[335, 335, -2*w^2 - 3*w]', '[335, 335, 2*w^2 - 3*w - 9]', '[339, 339, -w^2 - 2*w + 14]', '[343, 7, -7]', '[345, 345, w + 7]', '[345, 345, 3*w^2 - 5*w - 5]', '[345, 345, w^2 + w + 3]', '[345, 345, -2*w^2 - 2*w + 15]', '[345, 345, w^2 - 4*w - 2]', '[345, 345, -w^2 - 3*w + 10]', '[347, 347, 2*w^2 + 2*w - 13]', '[351, 39, 3*w + 9]', '[351, 351, 3*w^2 + w - 11]', '[353, 353, 4*w^2 + 5*w - 13]', '[359, 359, 3*w^2 + 6*w - 1]', '[360, 30, 4*w^2 + 4*w - 10]', '[360, 30, 2*w^2 + 2*w - 14]', '[360, 90, 2*w^2 + 2*w]', '[360, 90, -2*w^2 + 4*w + 6]', '[369, 123, 4*w^2 + 7*w - 4]', '[369, 369, 4*w^2 + 4*w - 9]', '[375, 15, 5*w - 10]', '[375, 75, -w^2 + w - 4]', '[375, 75, w^2 - 3*w - 10]', '[375, 375, 4*w^2 - w - 20]', '[376, 94, 4*w^2 + 2*w - 16]', '[377, 377, w^2 - w - 12]', '[379, 379, w^2 - 3*w - 6]', '[381, 381, -4*w^2 + 10*w - 1]', '[383, 383, 3*w^2 - 23]', '[383, 383, w^2 - 12]', '[383, 383, 3*w^2 + 3*w - 13]', '[391, 391, 2*w - 9]', '[391, 391, -w^2 + 3*w - 6]', '[391, 391, 2*w^2 + 4*w + 1]', '[393, 393, -w^2 - 5*w + 2]', '[395, 395, 2*w^2 + 3*w - 10]', '[395, 395, 4*w^2 - 3*w - 17]', '[401, 401, -6*w^2 - 7*w + 16]', '[405, 45, w^2 - 2*w + 5]', '[405, 45, -w^2 + 2*w + 13]', '[405, 45, 3*w^2 - 12]', '[405, 45, 3*w^2 - 3*w - 15]', '[405, 405, -w^2 - 4*w + 15]', '[405, 405, -w + 8]', '[408, 102, -2*w - 8]', '[409, 409, -4*w^2 + 3*w + 21]', '[411, 411, w^2 - 5*w + 9]', '[411, 411, 3*w^2 + 2*w - 16]', '[411, 411, -w^2 - 7*w + 24]', '[417, 417, -w^2 + 3*w + 7]', '[421, 421, w^2 - 3*w - 9]', '[423, 141, 2*w^2 + 8*w + 7]', '[423, 423, 5*w^2 + 5*w - 18]', '[425, 85, -3*w^2 - 2*w + 23]', '[425, 85, -3*w^2 - w + 10]', '[425, 425, -2*w^2 + 3*w + 10]', '[433, 433, w^2 - 3*w - 8]', '[433, 433, w^2 + 4*w - 8]', '[433, 433, 3*w^2 - w - 12]', '[435, 435, -4*w^2 + 5*w + 15]', '[435, 435, -3*w^2 + 2*w + 11]', '[439, 439, -4*w - 11]', '[447, 447, w^2 - 8*w + 12]', '[449, 449, 2*w^2 + 3*w - 19]', '[453, 453, w^2 - 7*w + 13]', '[457, 457, w^2 - 4*w - 3]', '[459, 51, -3*w^2 + 3*w + 9]', '[459, 459, -w^2 - 5*w - 4]', '[461, 461, 5*w^2 + 6*w - 16]', '[461, 461, -2*w^2 + 3*w + 16]', '[461, 461, 2*w^2 + 4*w - 9]', '[467, 467, 3*w^2 - 4*w - 12]', '[471, 471, -w^2 + 11*w - 21]', '[471, 471, -2*w^2 + 5*w + 4]', '[472, 118, -4*w^2 - 6*w + 12]', '[479, 479, 3*w^2 + w - 9]', '[481, 481, 5*w^2 + w - 29]', '[487, 487, 5*w^2 + 2*w - 22]', '[488, 122, -4*w - 2]', '[489, 489, -5*w^2 + 15*w - 4]', '[489, 489, 2*w^2 + 3*w - 11]', '[489, 489, -3*w^2 + 7*w + 4]', '[491, 491, 3*w^2 - 11]', '[493, 493, 4*w^2 - 7*w - 7]', '[499, 499, 5*w^2 + w - 24]', '[501, 501, -2*w^2 + 3*w + 11]', '[503, 503, 3*w^2 + 2*w - 17]', '[503, 503, 3*w^2 + w - 7]', '[503, 503, 2*w^2 - 4*w - 7]', '[507, 39, 3*w^2 + w - 8]', '[507, 507, -3*w^2 - 4*w + 2]', '[509, 509, 3*w - 11]', '[512, 8, 8]', '[519, 519, w^2 + 4*w - 9]', '[520, 130, -2*w^2 + 18]', '[520, 130, 2*w^2 + 6*w]', '[521, 521, 3*w^2 - 3*w - 16]', '[523, 523, -w - 8]', '[529, 23, 4*w^2 - w - 19]', '[529, 23, 3*w^2 - w - 11]', '[529, 23, 2*w^2 + w + 1]', '[529, 529, -3*w^2 - 3*w + 14]', '[529, 529, w^2 + w + 4]', '[529, 529, -w^2 - 4*w + 14]', '[531, 177, w^2 - 5*w - 1]', '[531, 531, w^2 - 8*w + 9]', '[533, 533, 6*w^2 + 8*w - 17]', '[536, 134, -4*w - 6]', '[537, 537, -2*w^2 + w + 18]', '[541, 541, 6*w^2 + 7*w - 19]', '[543, 543, 2*w^2 - 6*w + 7]', '[545, 545, 3*w^2 - 5]', '[545, 545, -3*w^2 - 5*w + 32]', '[545, 545, -w^2 + 4*w - 8]', '[545, 545, -3*w^2 + 2*w + 10]', '[545, 545, 6*w - 13]', '[545, 545, -2*w^2 - 7*w + 5]', '[547, 547, 3*w^2 + 4*w - 12]', '[549, 183, -5*w^2 - 5*w + 14]', '[549, 549, -2*w^2 - 3*w - 1]', '[552, 138, -2*w^2 + 6*w + 2]', '[552, 138, -2*w^2 - 6*w + 2]', '[552, 138, -4*w^2 + 2*w + 18]', '[555, 555, -7*w^2 + 4*w + 35]', '[555, 555, -4*w^2 + 3*w + 22]', '[557, 557, 2*w^2 - 3*w - 12]', '[563, 563, 4*w^2 + 3*w - 12]', '[563, 563, 4*w^2 + w - 17]', '[563, 563, -w^2 - 5*w - 3]', '[565, 565, 3*w^2 - 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7*w - 64]', '[9665, 9665, -7*w^2 - 17*w - 5]', '[9673, 9673, w^2 + 13*w - 32]', '[9677, 9677, 6*w^2 + 6*w - 43]', '[9679, 9679, 6*w^2 + 6*w - 41]', '[9683, 9683, -8*w^2 - 8*w + 37]', '[9683, 9683, -7*w^2 - 11*w + 28]', '[9683, 9683, 13*w^2 - 7*w - 82]', '[9685, 9685, -2*w^2 - 12*w - 5]', '[9685, 9685, 5*w^2 + 3*w - 49]', '[9689, 9689, 12*w^2 + 14*w - 41]', '[9693, 1077, 9*w^2 + 18*w - 3]', '[9693, 9693, 11*w^2 + 10*w - 28]', '[9697, 9697, -9*w^2 + 8*w + 48]', '[9704, 2426, 2*w^2 - 12*w - 36]', '[9704, 2426, 2*w^2 - 12*w - 4]', '[9704, 2426, 2*w^2 - 12*w + 26]', '[9705, 9705, -11*w^2 + 6*w + 50]', '[9705, 9705, -4*w^2 + 8*w + 27]', '[9715, 9715, -3*w^2 - 10]', '[9715, 9715, 9*w^2 - 15*w - 26]', '[9717, 9717, 7*w^2 - 4*w - 17]', '[9719, 9719, 10*w^2 + w - 44]', '[9720, 90, 12*w^2 + 12*w - 30]', '[9720, 90, 6*w^2 + 6*w - 42]', '[9720, 270, 6*w^2 + 6*w]', '[9720, 270, -6*w^2 + 12*w + 18]', '[9720, 2430, 12*w^2 + 10*w - 38]', '[9720, 2430, 4*w^2 - 8*w - 30]', '[9721, 9721, -9*w + 31]', '[9721, 9721, 10*w^2 + 5*w - 54]', '[9721, 9721, -5*w^2 + 6*w + 49]', '[9729, 3243, 23*w^2 + 26*w - 71]', '[9729, 3243, -14*w^2 - 14*w + 41]', '[9729, 3243, 25*w^2 + 34*w - 64]', '[9729, 9729, 18*w^2 + 5*w - 94]', '[9729, 9729, 12*w^2 + 25*w - 14]', '[9729, 9729, 7*w^2 + 20*w + 4]', '[9731, 9731, 7*w^2 - 6*w - 11]', '[9733, 9733, 8*w^2 + w - 27]', '[9736, 2434, 16*w^2 + 22*w - 44]', '[9739, 9739, -4*w^2 - 5*w - 6]', '[9741, 9741, -10*w^2 + 8*w + 39]', '[9743, 9743, 2*w^2 - 9*w - 22]', '[9745, 9745, -9*w^2 + w + 68]', '[9745, 9745, 3*w^2 + 14*w + 10]', '[9749, 9749, 7*w^2 - 6*w - 14]', '[9755, 9755, -4*w^2 + 13*w + 7]', '[9755, 9755, 7*w^2 - 3*w - 15]', '[9755, 9755, 2*w^2 + 15*w - 48]', '[9755, 9755, 2*w^2 + 11*w - 25]', '[9755, 9755, 10*w^2 + 11*w - 10]', '[9755, 9755, 13*w^2 - 20*w - 32]', '[9759, 9759, 7*w^2 - 3*w - 16]', '[9763, 9763, -w^2 - 12*w - 27]', '[9767, 9767, 3*w^2 + 3*w - 38]', '[9771, 9771, -3*w^2 + 13*w + 4]', '[9775, 1955, -3*w^2 - 6*w - 10]', '[9775, 1955, 9*w^2 - 9*w - 44]', '[9775, 1955, -6*w^2 - 7*w]', '[9775, 1955, 6*w^2 - 11*w - 21]', '[9775, 1955, -w^2 + 11*w + 26]', '[9775, 1955, -w^2 + 13*w]', '[9775, 9775, -8*w^2 + 13*w + 10]', '[9775, 9775, 5*w^2 + 7*w - 35]', '[9775, 9775, 3*w^2 + 10*w - 25]', '[9777, 9777, -w^2 - 7*w + 33]', '[9783, 3261, -17*w^2 - 17*w + 53]', '[9783, 9783, -5*w^2 - 12*w - 7]', '[9784, 2446, -2*w^2 + 8*w + 36]', '[9787, 9787, 3*w^2 - 9*w - 17]', '[9787, 9787, -15*w^2 - 13*w + 58]', '[9787, 9787, 10*w^2 + 14*w - 33]', '[9789, 9789, 3*w^2 - 23*w + 34]', '[9792, 204, 4*w^2 - 8*w - 28]', '[9792, 612, -4*w^2 - 8*w + 32]', '[9795, 9795, -5*w^2 - 7*w + 40]', '[9795, 9795, w^2 + 3*w + 17]', '[9799, 9799, 6*w^2 + 9*w - 29]', '[9799, 9799, 13*w^2 + 14*w - 31]', '[9799, 9799, 4*w^2 - 8*w - 29]', '[9803, 9803, w^2 + 2*w - 27]', '[9803, 9803, 3*w^2 + 11*w - 23]', '[9803, 9803, 8*w^2 + 6*w - 43]', '[9809, 9809, 10*w^2 - 5*w - 44]', '[9811, 9811, w^2 - 10*w - 21]', '[9813, 9813, -12*w^2 + 11*w + 47]', '[9815, 9815, 9*w^2 + 5*w - 66]', '[9815, 9815, 9*w^2 + 4*w - 30]', '[9816, 2454, 14*w^2 - 18*w - 44]', '[9817, 9817, -3*w^2 + 9*w + 43]', '[9817, 9817, 15*w^2 + 18*w - 47]', '[9817, 9817, 7*w^2 - 4*w - 13]', '[9819, 3273, 2*w^2 - 7*w + 19]', '[9819, 9819, 9*w^2 - 19*w - 1]', '[9825, 1965, -2*w^2 - 3*w - 13]', '[9825, 1965, 4*w^2 + 8*w - 35]', '[9825, 9825, 11*w^2 + 10*w - 25]', '[9829, 9829, -w^2 + 3*w - 19]', '[9831, 9831, -w^2 - 16*w + 51]', '[9833, 9833, 7*w^2 - 6*w - 12]', '[9837, 3279, -11*w^2 + w + 53]', '[9837, 3279, 2*w^2 + 2*w + 13]', '[9837, 3279, -w^2 - w - 17]', '[9837, 9837, 3*w^2 + 2*w - 37]', '[9837, 9837, -7*w^2 + 6*w + 13]', '[9837, 9837, 7*w^2 - 5*w - 12]', '[9839, 9839, 8*w^2 + 11*w - 31]', '[9839, 9839, 9*w^2 + 8*w - 41]', '[9839, 9839, -w^2 - 12*w - 16]', '[9843, 9843, -2*w^2 + 9*w + 17]', '[9853, 9853, -w^2 + 6*w - 22]', '[9859, 9859, 5*w^2 - 8*w - 29]', '[9864, 822, 2*w^2 + 8*w + 16]', '[9864, 822, 10*w^2 - 2*w - 46]', '[9864, 822, -14*w^2 - 2*w + 86]', '[9864, 2466, 8*w^2 + 2*w - 24]', '[9864, 2466, -2*w^2 - 4*w + 34]', '[9864, 2466, 10*w^2 - 8*w - 54]', '[9865, 9865, -2*w^2 - 27*w + 84]', '[9865, 9865, -7*w^2 + 15*w + 15]', '[9871, 9871, 11*w^2 + w - 51]', '[9875, 395, 10*w^2 - 45]', '[9875, 1975, 11*w^2 - 8*w - 60]', '[9875, 1975, -2*w^2 - 13*w - 13]', '[9875, 9875, -2*w^2 - 7*w - 15]', '[9881, 9881, w^2 - 3*w - 26]', '[9883, 9883, 5*w^2 + 8*w - 58]', '[9883, 9883, 4*w^2 + 8*w - 33]', '[9883, 9883, 7*w^2 - 9*w - 33]', '[9885, 9885, 7*w^2 - 5*w - 15]', '[9885, 9885, -3*w^2 - 14*w + 4]', '[9885, 9885, -16*w^2 + 85]', '[9885, 9885, -17*w^2 + 5*w + 115]', '[9885, 9885, -2*w^2 + 13*w + 39]', '[9885, 9885, -17*w^2 - 6*w + 86]', '[9887, 9887, 6*w^2 - 9*w - 28]', '[9893, 9893, 9*w^2 - 3*w - 38]', '[9895, 9895, 9*w^2 - w - 38]', '[9895, 9895, 10*w^2 - 9*w - 50]', '[9896, 2474, 4*w^2 + 8*w - 34]', '[9897, 9897, -2*w^2 + 11*w + 7]', '[9907, 9907, 2*w^2 + 14*w + 17]', '[9917, 9917, 15*w^2 + 10*w - 58]', '[9921, 9921, 7*w^2 - 4*w - 14]', '[9923, 9923, 14*w^2 + 5*w - 73]', '[9923, 9923, 9*w^2 + 22*w - 3]', '[9923, 9923, 3*w^2 + 12*w - 22]', '[9927, 3309, -7*w^2 + 8*w + 52]', '[9927, 9927, 8*w^2 + 5*w - 48]', '[9929, 9929, 4*w^2 + 9*w - 54]', '[9935, 9935, 7*w^2 - 4*w - 15]', '[9935, 9935, 4*w^2 - 19*w + 5]', '[9935, 9935, 2*w^2 + 16*w - 51]', '[9935, 9935, -13*w^2 - 14*w + 30]', '[9935, 9935, -7*w^2 + 34*w - 44]', '[9935, 9935, -5*w^2 - 7*w + 36]', '[9939, 9939, -6*w^2 + 19*w + 1]', '[9941, 9941, w^2 + 4*w - 29]', '[9943, 9943, 4*w^2 + 9*w - 27]', '[9943, 9943, 11*w^2 + 4*w - 77]', '[9943, 9943, 8*w^2 - 63]', '[9945, 3315, 7*w^2 - 17*w - 10]', '[9945, 3315, 7*w^2 - 5*w - 13]', '[9945, 9945, -10*w^2 - 7*w + 30]', '[9945, 9945, -8*w^2 - 5*w + 57]', '[9947, 203, 7*w - 28]', '[9953, 9953, -w^2 - 2*w - 17]', '[9957, 9957, 5*w^2 + 5*w + 3]', '[9959, 9959, 13*w - 1]', '[9959, 9959, 16*w^2 - 5*w - 86]', '[9959, 9959, -7*w^2 - 8*w + 34]', '[9959, 9959, 5*w^2 + 7*w - 39]', '[9959, 9959, 12*w^2 - 7*w - 74]', '[9959, 9959, 2*w^2 - w + 14]', '[9959, 9959, w^2 + 17*w - 9]', '[9959, 9959, -6*w^2 - 11*w + 26]', '[9959, 9959, -w^2 + 26]', '[9963, 369, 12*w^2 + 21*w - 12]', '[9963, 1107, 12*w^2 + 12*w - 27]', '[9963, 9963, 7*w^2 + 5*w - 2]', '[9965, 9965, 5*w^2 + 7*w - 56]', '[9965, 9965, w^2 - 10*w - 10]', '[9967, 9967, 9*w^2 - 7*w - 33]', '[9971, 767, -4*w^2 + 3*w + 41]', '[9971, 9971, -10*w^2 - 5*w + 36]', '[9973, 9973, 6*w^2 - 8*w - 33]', '[9979, 9979, 4*w^2 - 3*w + 9]', '[9979, 9979, 12*w^2 - 17*w - 39]', '[9979, 9979, 7*w^2 + 6*w - 54]', '[9983, 9983, 2*w^2 - 9*w - 18]', '[9985, 9985, -9*w^2 + 13*w]', '[9985, 9985, 9*w^2 - 40*w + 39]', '[9987, 9987, 11*w^2 - 3*w - 53]', '[9992, 2498, -2*w^2 + 6*w - 18]', '[9993, 9993, -11*w^2 + 10*w + 42]', '[9997, 9997, -12*w - 23]', '[9997, 9997, 8*w^2 - 7*w - 67]', '[9997, 9997, -5*w^2 - 16*w - 3]'], 'label': '3.3.785.1', 'narrow_class_no': 1, 'primes': ['[3, 3, w - 2]', '[5, 5, w]', '[5, 5, -w + 3]', '[8, 2, 2]', '[9, 3, w^2 + w - 4]', '[13, 13, w + 3]', '[17, 17, -w^2 + w + 3]', '[23, 23, w^2 - 2]', '[23, 23, w^2 - 3]', '[23, 23, -w^2 + 8]', '[29, 29, w - 4]', '[37, 37, w^2 + w - 8]', '[41, 41, w^2 + 2*w - 4]', '[47, 47, 2*w^2 + w - 8]', '[59, 59, -2*w^2 - 3*w + 6]', '[61, 61, -2*w - 1]', '[67, 67, -2*w - 3]', '[79, 79, 2*w^2 - 9]', '[109, 109, w^2 + 2*w - 6]', '[109, 109, 2*w^2 + w - 14]', '[109, 109, -w^2 - w - 1]', '[113, 113, 2*w^2 + w - 12]', '[127, 127, w^2 - 3*w - 2]', '[131, 131, -4*w^2 - 5*w + 9]', '[137, 137, w^2 + 2*w - 7]', '[137, 137, 3*w + 8]', '[137, 137, 2*w^2 + w - 17]', '[139, 139, 3*w^2 + 2*w - 11]', '[149, 149, w - 6]', '[151, 151, w^2 + 2*w - 9]', '[157, 157, -w^2 - 2*w + 13]', '[157, 157, 2*w^2 - 7]', '[163, 163, w^2 + 3*w + 3]', '[163, 163, 2*w^2 - 3*w - 3]', '[163, 163, 2*w^2 - w - 7]', '[167, 167, 3*w^2 + w - 13]', '[169, 13, 2*w^2 + 5*w - 1]', '[173, 173, w^2 + 2*w + 2]', '[179, 179, 4*w^2 + 2*w - 19]', '[181, 181, w^2 + 3*w - 6]', '[191, 191, 3*w^2 + 2*w - 14]', '[193, 193, w^2 - 3*w - 3]', '[197, 197, 3*w^2 - 2*w - 13]', '[211, 211, -w - 6]', '[223, 223, -w^2 + w - 3]', '[223, 223, -3*w - 2]', '[223, 223, 2*w^2 - 2*w - 3]', '[229, 229, 2*w^2 - w - 4]', '[233, 233, 2*w + 7]', '[239, 239, -3*w - 4]', '[239, 239, w^2 - 11]', '[239, 239, 4*w^2 - w - 21]', '[241, 241, 3*w^2 + w - 19]', '[251, 251, -w^2 - 4*w - 1]', '[257, 257, w - 7]', '[263, 263, 3*w^2 + w - 12]', '[269, 269, 3*w^2 - 4*w - 11]', '[271, 271, 4*w^2 + 6*w - 11]', '[277, 277, -4*w^2 - 3*w + 17]', '[283, 283, 5*w^2 + 4*w - 18]', '[289, 17, 3*w^2 + 2*w - 9]', '[307, 307, -2*w^2 - w + 18]', '[307, 307, w^2 + 2*w + 3]', '[307, 307, -w^2 - 3]', '[313, 313, 3*w^2 - 13]', '[317, 317, 3*w^2 - 2*w - 12]', '[331, 331, w^2 + 3*w - 9]', '[331, 331, w^2 + 3*w - 11]', '[331, 331, w^2 + 3*w + 4]', '[343, 7, -7]', '[347, 347, 2*w^2 + 2*w - 13]', '[353, 353, 4*w^2 + 5*w - 13]', '[359, 359, 3*w^2 + 6*w - 1]', '[379, 379, w^2 - 3*w - 6]', '[383, 383, 3*w^2 - 23]', '[383, 383, w^2 - 12]', '[383, 383, 3*w^2 + 3*w - 13]', '[401, 401, -6*w^2 - 7*w + 16]', '[409, 409, -4*w^2 + 3*w + 21]', '[421, 421, w^2 - 3*w - 9]', '[433, 433, w^2 - 3*w - 8]', '[433, 433, w^2 + 4*w - 8]', '[433, 433, 3*w^2 - w - 12]', '[439, 439, -4*w - 11]', '[449, 449, 2*w^2 + 3*w - 19]', '[457, 457, w^2 - 4*w - 3]', '[461, 461, 5*w^2 + 6*w - 16]', '[461, 461, -2*w^2 + 3*w + 16]', '[461, 461, 2*w^2 + 4*w - 9]', '[467, 467, 3*w^2 - 4*w - 12]', '[479, 479, 3*w^2 + w - 9]', '[487, 487, 5*w^2 + 2*w - 22]', '[491, 491, 3*w^2 - 11]', '[499, 499, 5*w^2 + w - 24]', '[503, 503, 3*w^2 + 2*w - 17]', '[503, 503, 3*w^2 + w - 7]', '[503, 503, 2*w^2 - 4*w - 7]', '[509, 509, 3*w - 11]', '[521, 521, 3*w^2 - 3*w - 16]', '[523, 523, -w - 8]', '[541, 541, 6*w^2 + 7*w - 19]', '[547, 547, 3*w^2 + 4*w - 12]', '[557, 557, 2*w^2 - 3*w - 12]', '[563, 563, 4*w^2 + 3*w - 12]', '[563, 563, 4*w^2 + w - 17]', '[563, 563, -w^2 - 5*w - 3]', '[569, 569, w^2 - 4*w - 4]', '[577, 577, w^2 - w - 13]', '[587, 587, 4*w^2 + 3*w - 8]', '[587, 587, 2*w^2 - 3*w - 13]', '[587, 587, 2*w^2 + 3*w - 18]', '[593, 593, 4*w - 13]', '[599, 599, w - 9]', '[613, 613, -w^2 + 3*w - 7]', '[613, 613, w^2 + 5*w + 2]', '[613, 613, 3*w^2 - 3*w - 17]', '[617, 617, w^2 + 5*w + 8]', '[641, 641, 4*w^2 + 3*w - 11]', '[641, 641, w^2 + w - 14]', '[641, 641, 3*w^2 - 2*w - 9]', '[647, 647, 2*w^2 + 3*w - 13]', '[653, 653, 3*w^2 - 8]', '[659, 659, 5*w^2 + 4*w - 21]', '[659, 659, 2*w^2 - 4*w - 19]', '[659, 659, -2*w^2 - 6*w + 9]', '[677, 677, -6*w - 13]', '[691, 691, 6*w - 11]', '[701, 701, 3*w^2 - 3*w - 19]', '[719, 719, 2*w^2 + 3*w - 16]', '[727, 727, 3*w^2 + 4*w - 13]', '[733, 733, 3*w^2 - w - 8]', '[739, 739, 2*w^2 + 4*w - 11]', '[739, 739, 4*w^2 - 3*w - 24]', '[739, 739, 3*w^2 - w - 6]', '[743, 743, 4*w^2 - 2*w - 17]', '[751, 751, -w - 9]', '[761, 761, 5*w^2 + 5*w - 19]', '[769, 769, w^2 - 4*w - 6]', '[769, 769, -5*w - 1]', '[769, 769, 2*w^2 - 19]', '[773, 773, 2*w^2 - 6*w - 3]', '[797, 797, 4*w^2 - 17]', '[809, 809, -7*w^2 - 4*w + 29]', '[811, 811, 6*w^2 + 3*w - 29]', '[823, 823, 4*w^2 + 2*w - 13]', '[823, 823, -w^2 - 4*w - 7]', '[823, 823, 4*w^2 + 4*w - 17]', '[827, 827, -2*w^2 - 3*w - 2]', '[829, 829, -w^2 + w - 6]', '[829, 829, -w^2 + 4*w - 9]', '[829, 829, -2*w^2 + 3*w + 21]', '[839, 839, 6*w^2 - 2*w - 31]', '[841, 29, w^2 + 3*w + 6]', '[853, 853, -7*w^2 - 6*w + 27]', '[859, 859, 6*w - 1]', '[881, 881, w^2 + 5*w - 16]', '[907, 907, 2*w^2 + 7*w + 7]', '[919, 919, w^2 - 4*w - 9]', '[953, 953, -4*w^2 - w + 32]', '[967, 967, 5*w^2 - 5*w - 18]', '[971, 971, 3*w^2 - 4*w - 24]', '[977, 977, 2*w^2 + 4*w + 3]', '[997, 997, w^2 + 5*w - 12]', '[997, 997, 5*w^2 - 3*w - 22]', '[997, 997, 3*w^2 + 8*w - 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': [5, -6, -1, 1], 'conductor': 0, 'degree': 3, 'dirichlet_group': [], 'disc_abs': 785, 'disc_rad': 785, 'disc_sign': 1, 'frobs': [[2, [[3, 1]]], [3, [[2, 1], [1, 1]]], [5, [0]], [7, [[3, 1]]], [11, [[3, 1]]], [13, [[2, 1], [1, 1]]], [17, [[2, 1], [1, 1]]], [19, [[3, 1]]], [23, [[1, 3]]], [29, [[2, 1], [1, 1]]], [31, [[3, 1]]], [37, [[2, 1], [1, 1]]], [41, [[2, 1], [1, 1]]], [43, [[3, 1]]], [47, [[2, 1], [1, 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, 3], 'galois_label': '3T2', 'galt': 2, 'grd': 28.0178514522438, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '3.3.785.1', 'local_algs': ['5.1.0.1', '5.2.1.2', '157.1.0.1', '157.2.1.2'], 'monogenic': 1, 'num_ram': 2, 'r2': 0, 'ramps': [5, 157], 'rd': 9.22479135747, 'regulator': {'__RealLiteral__': 0, 'data': '4.09826602583', 'prec': 44}, 'res': {'gal': ['-40,20,76,-25,-33,0,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a - 1 \\)', '\\( a^{2} - a - 4 \\)'], 'unitsGmodule': [[3, 1], [5, 1]], 'used_grh': False, 'zk': ['1', 'a', 'a^2']}