Hilbert modular form data - 2.2.57.1-192.1-d

Formats: - HTML - YAML - JSON - 2025-09-12T17:52:53.938430

• 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': 2, 'dimension': 1, 'disc': 57, 'field_bad_primes': [3, 19], 'field_label': '2.2.57.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '2.2.57.1-192.1-d', 'label_nsuffix': 3, 'label_suffix': 'd', 'level_bad_primes': [2, 3], 'level_ideal': '[192, 24, -32*w - 104]', 'level_label': '192.1', 'level_norm': 192, 'parallel_weight': 2, 'short_label': '192.1-d', 'weight': '[2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[2, 2, -w + 4]', 1], ['[2, 2, -w - 3]', -1], ['[3, 3, -4*w - 13]', -1]], 'hecke_eigenvalues': [0, 0, 1, -2, 0, 2, 4, 8, 2, 2, -6, -8, 8, 6, -2, 0, -6, 6, 0, 0, -6, 2, 6, 0, 18, -8, 6, 6, -2, -6, 12, 4, -14, -4, -8, 24, 6, 0, -2, 18, 18, 0, -4, 8, -8, 12, 4, 10, -4, -8, -26, 26, 10, -20, -32, -6, 28, 18, 6, 20, -4, -2, 34, -6, 4, 8, -22, 6, -22, 2, 8, -8, -24, 14, -14, 18, 18, -6, 28, 8, 16, -10, -26, 6, -4, 0, 30, 18, 0, 18, -12, -18, 8, -30, -2, 16, 30, 40, 6, -20, -12, 22, -10, 0, 14, 36, 6, -10, 34, -16, 26, -18, 0, -36, 12, 28, -12, 10, 22, -12, -48, -20, 48, 2, 42, 16, -32, -26, -30, -20, -40, -36, 12, -50, 32, 24, -4, 20, -18, 12, -18, -36, 10, 28, -32, -12, 0, 38, -26, 20, -18, -50, 10, 40, -16, 2, -6, 24, 22, 0, 2, 34, -32, -30, -38, 48, -42, 54, 58, -38, 16, 26, 20, 4, -42, 38, 4, -8, 10, 20, -28, 36, -4, 40, -48, -4, 6, 50, -32, -8, 14, 56, -2, 34, 28, 30, -14, -18, 54, 14, 34, -54, -6, 54, 56, -32, -56, -28, 62, -38, 24, 0, -62, -4, 32, -60, -8, -12, -10, 54, 48, -20, -70, -54, -12, -32, -26, -24, 70, -16, 42, -8, 18, 8, 20, -26, 28, 6, 24, -12, 40, 2, -50, 48, -2, 36, 62, 12, 0, -32, -24, -30, 36, -54, -16, -24, -34, 8, 34, -58, 38, 58, -72, -52, -56, -8, -18, -22, 14, -6, 78, 68, -56, 28, -10, -74, 4, 0, -54, -72, 10, 20, 44, -34, -6, -68, 54, -14, 52, 6, -38, 42, 42, -52, -12, -60, 50, -64, -52, 6, -22, -44, -50, -16, 72, -6, -20, 30, -70, -44, -12, 58, -6, -16, -62, -32, -28, -26, -46, -46, -6, -2, -20, 18, 16, 44, 14, 68, -54, -14, 44, 18, 20, 44, -54, -14, 12, -80, -32, 20, 18, 30, 60, 90, -60, -44, 20, -10, -62, -48, 28, -58, 0, 74, -66, 34, -68, 60, -68, -60, -2, 26, 10, -42, 20, -80, 2, 46, 16, -60, -14, -30, -18, -78, -68, 96, -56, 64, -64, 16, -18, -92, -94, 66, -86, -88, -24, 38, -84, 28, 72, -6, -54, -18, -14, -28, -34, -18, 24, 20, -70, -94, -96, -6, 50, -24, 36, -60, -90, 62, 64, 46, -100, 44, -58, 30, 24, -36, 34, -98, -12, -58, -28, -20, 8, -20, -76, -20, 62, 42, 66, -90, -88, 54, 4, -44, -32, 68, -6, -42, -46, -26, 0, 42, -18, 8, -30, 6, -90, 30, -48, 82, 82, 16, 0, -18, 44, -12, 40, -52, 20, 56, -10, -74, -34, -88, -110, -16, 34, 78, -40, -78, -56, 2, -38, -20, 90, -18, 2, -84, -4, 0, 78, 2, -48, -20, -42, 72, 46, 70, -28, 30, 60, 70, 8, -76, -108, -90, 2, -8, 20, 72, 118, 66, -46, 6, 116, -36, -82, 54, -60, 14, 2, 2, -38, 88, -94, 40, -66, 60, 10, 58, 32, 4, 52, 18, 82, -60, 46, 6, -90, -60, 0, 10, 82, -120, 46, 4, 20, 58, -102, -12, 20, -12, 92, 72, 66, -14, -84, 60, -42, -46, 8, 24, -46, 8, -100, -74, 34, 94, -66, 34, 6, -74, 82, -28, 120, 26, 62, 22, -96, 46, 58, 90, 44, 76, -52, -32, 0, -108, -98, -62, 24, -28, 94, 94, 20, 12, -106, 48, 116, 100, -14, 20, -22, 76, 40, 92, 16, -78, 72, 102, -72, -32, 90, -52, 56, -68, 86, -88, 60, 24, -76, -10, 40, 92, 36, -46, 120, -110, -96, -114, -130, -6, 24, -76, -60, 34, 94, -66, 56, -16, 96, 52, -42, -86, -24, 120, 50, 18, 60, 82, -44, 92, 50, 14, 54, -116, -88, 62, 54, 60, 30, 24, -72, 40, -28, 10, 98, 38, -48, -46, 4, -98, -54, -30, -4, 136, -72, -4, 92, -86, 10, 30, 38, -24, -72, 46, -98, -28, -20, -40, -44, -70, 60, 128, 102, -26, -74, 98, 56, -48, -124, -18, -102, -12, 10, -52, 88, 128, -12, 18, -128, 116, -86, 118, 90, -18, 100, 118, -6, 112, -12, 84, 68, -12, 20, 104, 40, 38, -110, -68, -48, -44, 130, 42, 132, -122, -32, -28, 84, -18, 10, -40, 8, -76, -24, 106, 32, -100, 24, 24, 126, 84, -38, 114, -50, -4, 24, -20, 94, -120, 62, 34, -10, 38, -100, 16, 50, -88, -46, 40, -72, 6, -88, -52, -10, 0, 18, -114, 16, 78, -72, -50, 66, 18, 68, 16, -76, 132, 36, -116, 92, 110, 86, -96, 98, 10, -46, -8, 102, -40, -80, 54, -116, -106, -120, -92, 20, -98, 114, 110, 20, 94, -138, -2, 96, 148, 110, -30, -56, -118, -106, 142, -10, -112, 32, -36, -40, -36, -28, 78, 116, -2, -134, -48, -24, -68, -122, 126, 10, 152, 126, -34, 140, 66, 44, -4, -128, 78, 92, 76, -116, 70, -78, -6, -132, 76, 88, 56, -72, -42, -84, 110, -6, -52, -16, -136, 82, -70, -32, -74, -70, -34, 52, 12, 142, -94, -26, 96, -14, -148, -64, -108, -26, -50, -38, -58, -50, 64, -118, 122, 144, -96, 34, 54, -62, -68, -76, -118, -26, -4, 102, -52, 6, -152, -52, 32, 2, -54, -20, 16, 154, -58, 96, 102, -66, -58, 48, -122, 142, 20, 0, -120, -78, -26, -142, 56, 12, -4, 108, 162, 6, 30, 86, 98, -98, 14, -18, -136, -32, -134, 26, 12, -124, -126, 38, -60, 132, 58, 90, -54, 54, -24, -134, -18, -40, -52, 48, -46, -46, 14, 154, -22, 42, 136, 146, -102, 6, 80, 104, -90, 50, -112, 104, -84, -140, -12, 128, 40, -22, 56, -164, 12, 28, -14, -118, -122, 60, -104, -62, -56, -94, 116, 36, 10, 2, -12, -52, 132, -76, 12, 128, 16, 136, 48, 112, 162, -18, 12, -102, 126, -26, -60, -28, 66, -118, 170, -114, -52, 48, 48, 34, -10, 70, 168, -76, 62, 68, 120, 142, 0, 40, -82, 54, -102, 66, 34, 86, 4, 152, 130, -24, 54, -18, -74, -6, -74, -118, 74, 70, -84, -12, 34, -50, -126, 172, 34, -146, 16, 56, 12, -66, -86, -126, -18, 154, 34, -152, -112, 36, 138, 110, -60, 110, 60, 60, -20, 4, -54, -26, -16, 124, -70, -22, 64, 4, 30, -78, 78, -42, 140, 4, 46, -122, 32, 162, -126, -108, 100, -74, 108, -16, -58, -118, -156, 70, 120, -86, 116, -24, -52, -30, 4, -22, 54, 138, 102, 2, 84, -92, 114, 4, -24, 6, 16, 120, 2, -30, 22, 26, -156, -116, -12, 172, -20, -156, -56, 124, -118, 62, 72, 6, 114, 18, -90, -140, -68, 180, -144, 88, -10, 24, -76, 140, 18, 44, -10, -160, 48, -20, 54, -90, 40, -54, -94, 78, 148, -106, 88, -158, -60, 116, -2, -56, -38, 12, -110, -110, -160, 150, -94, -126, -74, -8, -162, 92, 40, 78, 132, 82, 20, 58, 92, -138, 94, 34, -106, -12, -88, -100, 164, 20, 80, 66, -92, -64, -24, 46, -150, 166, -18, 42, 82, -182, 30, 168, 170, 16, -18, 36, -20, 32, 66, -8, -14, -168, 156, -124, 20, 150, -118, 24, 90, 72, -182, 100, -44, -154, -92, 168, 102], 'hecke_polynomial': 'x', 'label': '2.2.57.1-192.1-d'}
• hmf_fields •

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

  
  {'degree': 2, 'discriminant': 57, 'ideals': ['[1, 1, 1]', '[2, 2, -w + 4]', '[2, 2, -w - 3]', '[3, 3, -4*w - 13]', '[4, 2, 2]', '[4, 4, -3*w + 13]', '[4, 4, 3*w + 10]', '[6, 6, -w + 5]', '[6, 6, w + 4]', '[7, 7, -2*w - 7]', '[7, 7, -2*w + 9]', '[8, 4, -2*w + 8]', '[8, 4, -2*w - 6]', '[8, 8, -w - 2]', '[8, 8, -w + 3]', '[9, 3, 3]', '[12, 6, -8*w - 26]', '[12, 12, -w - 1]', '[12, 12, -w + 2]', '[14, 14, w]', '[14, 14, -5*w - 16]', '[14, 14, 5*w - 21]', '[14, 14, -w + 1]', '[16, 4, 4]', '[16, 8, -6*w + 26]', '[16, 8, 6*w + 20]', '[16, 16, w + 5]', '[16, 16, -w + 6]', '[18, 6, -3*w + 12]', '[18, 6, -3*w - 9]', '[19, 19, 10*w + 33]', '[21, 21, 2*w - 7]', '[21, 21, -2*w - 5]', '[24, 12, -2*w + 10]', '[24, 12, 2*w + 8]', '[24, 24, -5*w + 22]', '[24, 24, 5*w + 17]', '[25, 5, 5]', '[27, 9, -12*w - 39]', '[28, 14, -4*w - 14]', '[28, 14, -4*w + 18]', '[28, 28, w + 6]', '[28, 28, 3*w + 11]', '[28, 28, 3*w - 14]', '[28, 28, w - 7]', '[29, 29, -6*w - 19]', '[29, 29, -6*w + 25]', '[32, 8, -4*w + 16]', '[32, 8, -4*w - 12]', '[32, 16, -2*w - 4]', '[32, 16, -2*w + 6]', '[32, 32, -9*w + 38]', '[32, 32, -9*w - 29]', '[36, 6, 6]', '[36, 12, -9*w + 39]', '[36, 12, 9*w + 30]', '[38, 38, -3*w + 11]', '[38, 38, -3*w - 8]', '[41, 41, 2*w - 5]', '[41, 41, -2*w - 3]', '[42, 42, -w - 7]', '[42, 42, 13*w + 43]', '[42, 42, 13*w - 56]', '[42, 42, -w + 8]', '[43, 43, 2*w - 11]', '[43, 43, 2*w + 9]', '[48, 12, -16*w - 52]', '[48, 24, -2*w - 2]', '[48, 24, -2*w + 4]', '[48, 48, -7*w - 22]', '[48, 48, -7*w + 29]', '[49, 7, 7]', '[49, 49, -8*w + 35]', '[49, 49, 8*w + 27]', '[50, 10, -5*w + 20]', '[50, 10, -5*w - 15]', '[53, 53, 2*w - 3]', '[53, 53, -2*w - 1]', '[54, 18, -3*w + 15]', '[54, 18, 3*w + 12]', '[56, 28, 2*w]', '[56, 28, -10*w - 32]', '[56, 28, 10*w - 42]', '[56, 28, -2*w + 2]', '[56, 56, -13*w + 55]', '[56, 56, 3*w + 7]', '[56, 56, -3*w + 10]', '[56, 56, 13*w + 42]', '[57, 57, -2*w + 1]', '[58, 58, w + 8]', '[58, 58, 7*w + 24]', '[58, 58, -7*w + 31]', '[58, 58, -w + 9]', '[59, 59, 4*w - 15]', '[59, 59, 4*w + 11]', '[61, 61, -4*w - 15]', '[61, 61, -4*w + 19]', '[63, 21, -6*w - 21]', '[63, 21, -6*w + 27]', '[64, 8, 8]', '[64, 16, -12*w + 52]', '[64, 16, 12*w + 40]', '[64, 32, 2*w + 10]', '[64, 32, -2*w + 12]', '[64, 64, -5*w + 23]', '[64, 64, 5*w + 18]', '[71, 71, 8*w + 25]', '[71, 71, 8*w - 33]', '[72, 12, -6*w + 24]', '[72, 12, -6*w - 18]', '[72, 24, -3*w - 6]', '[72, 24, -3*w + 9]', '[73, 73, -16*w - 53]', '[73, 73, 24*w + 79]', '[75, 15, -20*w - 65]', '[76, 38, 20*w + 66]', '[76, 76, w + 9]', '[76, 76, -w + 10]', '[81, 9, 9]', '[82, 82, 11*w - 48]', '[82, 82, -3*w + 16]', '[82, 82, -3*w - 13]', '[82, 82, 11*w + 37]', '[84, 42, 4*w - 14]', '[84, 42, -4*w - 10]', '[84, 84, -5*w + 19]', '[84, 84, -11*w + 46]', '[84, 84, 11*w + 35]', '[84, 84, 5*w + 14]', '[86, 86, 27*w + 88]', '[86, 86, -3*w + 8]', '[86, 86, 3*w + 5]', '[86, 86, -27*w + 115]', '[87, 87, -2*w + 13]', '[87, 87, 2*w + 11]', '[89, 89, 14*w + 45]', '[89, 89, 14*w - 59]', '[96, 24, -4*w + 20]', '[96, 24, 4*w + 16]', '[96, 48, -10*w + 44]', '[96, 48, 10*w + 34]', '[96, 96, w + 10]', '[96, 96, -w + 11]', '[98, 14, 7*w - 28]', '[98, 14, 7*w + 21]', '[98, 98, -9*w - 28]', '[98, 98, -3*w - 4]', '[98, 98, -3*w + 7]', '[98, 98, -9*w + 37]', '[100, 10, 10]', '[100, 20, -15*w + 65]', '[100, 20, 15*w + 50]', '[106, 106, -5*w - 19]', '[106, 106, 9*w + 31]', '[106, 106, 9*w - 40]', '[106, 106, -5*w + 24]', '[107, 107, -4*w - 9]', '[107, 107, 4*w - 13]', '[108, 18, -24*w - 78]', '[108, 36, -3*w - 3]', '[108, 36, -3*w + 6]', '[112, 28, -8*w - 28]', '[112, 28, -8*w + 36]', '[112, 56, 2*w + 12]', '[112, 56, 6*w + 22]', '[112, 56, 6*w - 28]', '[112, 56, 2*w - 14]', '[112, 112, -19*w - 63]', '[112, 112, -3*w - 14]', '[112, 112, -3*w + 17]', '[112, 112, -19*w + 82]', '[113, 113, 6*w - 23]', '[113, 113, 6*w + 17]', '[114, 114, -7*w + 32]', '[114, 114, 7*w + 25]', '[116, 58, -12*w - 38]', '[116, 58, -12*w + 50]', '[116, 116, -3*w + 5]', '[116, 116, -5*w - 13]', '[116, 116, -5*w + 18]', '[116, 116, -3*w - 2]', '[118, 118, -w - 11]', '[118, 118, 23*w - 99]', '[118, 118, -23*w - 76]', '[118, 118, w - 12]', '[121, 11, -11]', '[122, 122, 21*w - 89]', '[122, 122, -3*w - 1]', '[122, 122, 3*w - 4]', '[122, 122, -21*w - 68]', '[123, 123, 46*w + 151]', '[123, 123, -14*w - 47]', '[126, 42, 3*w]', '[126, 42, -15*w - 48]', '[126, 42, 15*w - 63]', '[126, 42, -3*w + 3]', '[128, 16, -8*w + 32]', '[128, 16, -8*w - 24]', '[128, 32, -4*w - 8]', '[128, 32, -4*w + 12]', '[128, 64, -18*w + 76]', '[128, 64, -18*w - 58]', '[128, 128, -3*w + 2]', '[128, 128, -3*w + 1]', '[129, 129, 10*w + 31]', '[129, 129, -10*w + 41]', '[133, 133, 4*w - 21]', '[133, 133, 4*w + 17]', '[139, 139, 2*w - 15]', '[139, 139, -2*w - 13]', '[142, 142, -w - 12]', '[142, 142, -13*w - 44]', '[142, 142, 13*w - 57]', '[142, 142, w - 13]', '[144, 12, 12]', '[144, 24, -18*w + 78]', '[144, 24, 18*w + 60]', '[144, 48, 3*w + 15]', '[144, 48, -3*w + 18]', '[146, 146, 7*w - 27]', '[146, 146, -5*w + 17]', '[146, 146, 5*w + 12]', '[146, 146, -7*w - 20]', '[147, 21, 28*w + 91]', '[147, 147, -4*w + 11]', '[147, 147, -4*w - 7]', '[150, 30, -5*w + 25]', '[150, 30, 5*w + 20]', '[152, 76, -6*w + 22]', '[152, 76, -6*w - 16]', '[152, 152, -13*w + 54]', '[152, 152, -13*w - 41]', '[157, 157, 12*w - 53]', '[157, 157, 12*w + 41]', '[159, 159, -22*w - 73]', '[159, 159, 38*w + 125]', '[162, 18, -9*w + 36]', '[162, 18, -9*w - 27]', '[163, 163, -6*w - 23]', '[163, 163, -6*w + 29]', '[164, 82, 4*w - 10]', '[164, 82, -4*w - 6]', '[164, 164, 11*w + 34]', '[164, 164, -35*w - 114]', '[164, 164, 35*w - 149]', '[164, 164, -11*w + 45]', '[167, 167, 56*w + 183]', '[167, 167, 16*w + 51]', '[168, 84, -2*w - 14]', '[168, 84, 26*w + 86]', '[168, 84, 26*w - 112]', '[168, 84, -2*w + 16]', '[168, 168, w + 13]', '[168, 168, 11*w + 38]', '[168, 168, 11*w - 49]', '[168, 168, w - 14]', '[169, 13, -13]', '[171, 57, 30*w + 99]', '[172, 86, 4*w - 22]', '[172, 86, 4*w + 18]', '[172, 172, -17*w + 74]', '[172, 172, -7*w + 33]', '[172, 172, -7*w - 26]', '[172, 172, -17*w - 57]', '[173, 173, 22*w + 71]', '[173, 173, 42*w + 137]', '[174, 174, -5*w - 11]', '[174, 174, -19*w - 61]', '[174, 174, -19*w + 80]', '[174, 174, -5*w + 16]', '[175, 35, -10*w - 35]', '[175, 35, -10*w + 45]', '[177, 177, -8*w - 29]', '[177, 177, 8*w - 37]', '[178, 178, 9*w - 41]', '[178, 178, 3*w - 19]', '[178, 178, -3*w - 16]', '[178, 178, -9*w - 32]', '[179, 179, -4*w - 5]', '[179, 179, 4*w - 9]', '[183, 183, 8*w - 31]', '[183, 183, -8*w - 23]', '[189, 63, 6*w - 21]', '[189, 63, -6*w - 15]', '[192, 24, -32*w - 104]', '[192, 48, -4*w - 4]', '[192, 48, -4*w + 8]', '[192, 96, -14*w - 44]', '[192, 96, -14*w + 58]', '[192, 192, -7*w - 19]', '[192, 192, -7*w + 26]', '[196, 14, 14]', '[196, 28, 21*w - 91]', '[196, 28, -21*w - 70]', '[196, 98, -16*w + 70]', '[196, 98, 16*w + 54]', '[196, 196, w + 14]', '[196, 196, -5*w + 26]', '[196, 196, 5*w + 21]', '[196, 196, -w + 15]', '[199, 199, 2*w - 17]', '[199, 199, -2*w - 15]', '[200, 20, -10*w + 40]', '[200, 20, -10*w - 30]', '[200, 40, -5*w - 10]', '[200, 40, -5*w + 15]', '[203, 203, -12*w - 37]', '[203, 203, 4*w - 7]', '[203, 203, -4*w - 3]', '[203, 203, 12*w - 49]', '[212, 106, 4*w - 6]', '[212, 106, -4*w - 2]', '[212, 212, 29*w - 123]', '[212, 212, 17*w + 54]', '[212, 212, -17*w + 71]', '[212, 212, -29*w - 94]', '[213, 213, -4*w - 19]', '[213, 213, 4*w - 23]', '[214, 214, 25*w + 83]', '[214, 214, -3*w - 17]', '[214, 214, -3*w + 20]', '[214, 214, 25*w - 108]', '[216, 36, -6*w + 30]', '[216, 36, 6*w + 24]', '[216, 72, -15*w + 66]', '[216, 72, 15*w + 51]', '[219, 219, -4*w - 1]', '[219, 219, 4*w - 5]', '[224, 56, 4*w]', '[224, 56, -20*w - 64]', '[224, 56, 20*w - 84]', '[224, 56, -4*w + 4]', '[224, 112, -26*w + 110]', '[224, 112, 6*w + 14]', '[224, 112, -6*w + 20]', '[224, 112, 26*w + 84]', '[224, 224, 9*w - 35]', '[224, 224, 5*w - 14]', '[224, 224, -5*w - 9]', '[224, 224, -9*w - 26]', '[225, 15, 15]', '[226, 226, -w - 15]', '[226, 226, 29*w - 125]', '[226, 226, -29*w - 96]', '[226, 226, w - 16]', '[227, 227, 4*w - 3]', '[227, 227, 4*w - 1]', '[228, 114, -4*w + 2]', '[228, 228, -23*w + 97]', '[228, 228, -23*w - 74]', '[229, 229, 20*w - 87]', '[229, 229, -20*w - 67]', '[232, 116, 2*w + 16]', '[232, 116, 14*w + 48]', '[232, 116, -14*w + 62]', '[232, 116, -2*w + 18]', '[232, 232, 7*w + 27]', '[232, 232, -33*w + 142]', '[232, 232, 33*w + 109]', '[232, 232, -7*w + 34]', '[236, 118, 8*w - 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489]', '[5987, 5987, 116*w + 373]', '[6043, 6043, 14*w - 101]', '[6043, 6043, -14*w - 87]', '[6067, 6067, 74*w + 253]', '[6067, 6067, 74*w - 327]', '[6091, 6091, -126*w - 419]', '[6091, 6091, 254*w + 835]', '[6101, 6101, -30*w - 67]', '[6101, 6101, 30*w - 97]', '[6113, 6113, 22*w - 39]', '[6113, 6113, -22*w - 17]', '[6131, 6131, -28*w - 57]', '[6131, 6131, 28*w - 85]', '[6163, 6163, 86*w + 291]', '[6163, 6163, 86*w - 377]', '[6197, 6197, 94*w - 393]', '[6197, 6197, 94*w + 299]', '[6199, 6199, -18*w - 95]', '[6199, 6199, 18*w - 113]', '[6211, 6211, 6*w - 85]', '[6211, 6211, -6*w - 79]', '[6217, 6217, 72*w - 319]', '[6217, 6217, 72*w + 247]', '[6221, 6221, -22*w - 15]', '[6221, 6221, 22*w - 37]', '[6229, 6229, 12*w - 97]', '[6229, 6229, -12*w - 85]', '[6241, 79, -79]', '[6263, 6263, 48*w + 139]', '[6263, 6263, 48*w - 187]', '[6269, 6269, -26*w - 45]', '[6269, 6269, 26*w - 71]', '[6271, 6271, 246*w + 809]', '[6271, 6271, -134*w - 445]', '[6277, 6277, 116*w - 503]', '[6277, 6277, -116*w - 387]', '[6299, 6299, 84*w + 265]', '[6299, 6299, 84*w - 349]', '[6311, 6311, -32*w - 75]', '[6311, 6311, 32*w - 107]', '[6323, 6323, 148*w + 479]', '[6323, 6323, 228*w + 743]', '[6329, 6329, 174*w + 565]', '[6329, 6329, 194*w + 631]', '[6343, 6343, 2*w - 81]', '[6343, 6343, -2*w - 79]', '[6359, 6359, -24*w - 31]', '[6359, 6359, 24*w - 55]', '[6427, 6427, -142*w - 471]', '[6427, 6427, 238*w + 783]', '[6449, 6449, 106*w - 445]', '[6449, 6449, 106*w + 339]', '[6469, 6469, 68*w - 303]', '[6469, 6469, 68*w + 235]', '[6473, 6473, 34*w - 117]', '[6473, 6473, 34*w + 83]', '[6491, 6491, 52*w + 153]', '[6491, 6491, 52*w - 205]', '[6547, 6547, -42*w + 199]', '[6547, 6547, -42*w - 157]', '[6551, 6551, 168*w + 545]', '[6551, 6551, 208*w + 677]', '[6553, 6553, 16*w - 109]', '[6553, 6553, -16*w - 93]', '[6563, 6563, 44*w - 167]', '[6563, 6563, 44*w + 123]', '[6569, 6569, 130*w + 419]', '[6569, 6569, 270*w + 881]', '[6571, 6571, 66*w + 229]', '[6571, 6571, 66*w - 295]', '[6619, 6619, -18*w - 97]', '[6619, 6619, 18*w - 115]', '[6637, 6637, -44*w - 163]', '[6637, 6637, -44*w + 207]', '[6653, 6653, 38*w + 99]', '[6653, 6653, 38*w - 137]', '[6661, 6661, 4*w - 85]', '[6661, 6661, -4*w - 81]', '[6673, 6673, 104*w - 453]', '[6673, 6673, 104*w + 349]', '[6701, 6701, 22*w - 25]', '[6701, 6701, -22*w - 3]', '[6719, 6719, 96*w + 305]', '[6719, 6719, 96*w - 401]', '[6733, 6733, 268*w + 881]', '[6733, 6733, -132*w - 439]', '[6779, 6779, 60*w + 181]', '[6779, 6779, 60*w - 241]', '[6781, 6781, -60*w - 211]', '[6781, 6781, 60*w - 271]', '[6791, 6791, 72*w + 223]', '[6791, 6791, 72*w - 295]', '[6833, 6833, 22*w - 3]', '[6833, 6833, 22*w - 19]', '[6841, 6841, -56*w - 199]', '[6841, 6841, 56*w - 255]', '[6869, 6869, 34*w - 115]', '[6869, 6869, -34*w - 81]', '[6883, 6883, -6*w - 83]', '[6883, 6883, 6*w - 89]', '[6889, 83, -83]', '[6899, 6899, 236*w + 769]', '[6899, 6899, 156*w + 505]', '[6911, 6911, 48*w - 185]', '[6911, 6911, 48*w + 137]', '[6947, 6947, -28*w - 51]', '[6947, 6947, 28*w - 79]', '[6961, 6961, -16*w - 95]', '[6961, 6961, 16*w - 111]', '[6983, 6983, 24*w - 47]', '[6983, 6983, -24*w - 23]', '[6997, 6997, -4*w - 83]', '[6997, 6997, 4*w - 87]', '[7013, 7013, 82*w + 257]', '[7013, 7013, 82*w - 339]', '[7019, 7019, 36*w + 89]', '[7019, 7019, 36*w - 125]', '[7027, 7027, 22*w - 129]', '[7027, 7027, -22*w - 107]', '[7039, 7039, 10*w - 97]', '[7039, 7039, -10*w - 87]', '[7043, 7043, 92*w + 291]', '[7043, 7043, 92*w - 383]', '[7069, 7069, 20*w - 123]', '[7069, 7069, -20*w - 103]', '[7109, 7109, 114*w + 365]', '[7109, 7109, 114*w - 479]', '[7121, 7121, 38*w - 135]', '[7121, 7121, 38*w + 97]', '[7127, 7127, 216*w + 703]', '[7127, 7127, 176*w + 571]', '[7129, 7129, -40*w + 193]', '[7129, 7129, -40*w - 153]', '[7207, 7207, -14*w - 93]', '[7207, 7207, 14*w - 107]', '[7211, 7211, 132*w + 425]', '[7211, 7211, 132*w - 557]', '[7237, 7237, -156*w - 517]', '[7237, 7237, 244*w + 803]', '[7243, 7243, -34*w + 171]', '[7243, 7243, -34*w - 137]', '[7247, 7247, 24*w - 43]', '[7247, 7247, -24*w - 19]', '[7253, 7253, 62*w + 187]', '[7253, 7253, 62*w - 249]', '[7297, 7297, 88*w + 299]', '[7297, 7297, 88*w - 387]', '[7321, 7321, 120*w - 521]', '[7321, 7321, -120*w - 401]', '[7349, 7349, 30*w - 89]', '[7349, 7349, -30*w - 59]', '[7351, 7351, 110*w + 369]', '[7351, 7351, 110*w - 479]', '[7369, 7369, -8*w - 87]', '[7369, 7369, 8*w - 95]', '[7411, 7411, -10*w - 89]', '[7411, 7411, 10*w - 99]', '[7417, 7417, -24*w - 113]', '[7417, 7417, 24*w - 137]', '[7451, 7451, -28*w - 47]', '[7451, 7451, 28*w - 75]', '[7459, 7459, 70*w - 313]', '[7459, 7459, 70*w + 243]', '[7481, 7481, 190*w + 617]', '[7481, 7481, 210*w + 683]', '[7499, 7499, 244*w + 795]', '[7499, 7499, 164*w + 531]', '[7517, 7517, 26*w - 59]', '[7517, 7517, -26*w - 33]', '[7523, 7523, 84*w + 263]', '[7523, 7523, 84*w - 347]', '[7549, 7549, 68*w - 305]', '[7549, 7549, 68*w + 237]', '[7573, 7573, -212*w - 699]', '[7573, 7573, -188*w - 621]', '[7577, 7577, 94*w - 391]', '[7577, 7577, 94*w + 297]', '[7583, 7583, 24*w - 37]', '[7583, 7583, -24*w - 13]', '[7589, 7589, 110*w + 351]', '[7589, 7589, 110*w - 461]', '[7639, 7639, -50*w - 183]', '[7639, 7639, 50*w - 233]', '[7681, 7681, -64*w - 225]', '[7681, 7681, 64*w - 289]', '[7687, 7687, 2*w - 89]', '[7687, 7687, -2*w - 87]', '[7691, 7691, -28*w - 45]', '[7691, 7691, 28*w - 73]', '[7699, 7699, -118*w - 395]', '[7699, 7699, 118*w - 513]', '[7703, 7703, -32*w - 67]', '[7703, 7703, 32*w - 99]', '[7723, 7723, -62*w - 219]', '[7723, 7723, 62*w - 281]', '[7727, 7727, 184*w + 597]', '[7727, 7727, 224*w + 729]', '[7753, 7753, 56*w - 257]', '[7753, 7753, -56*w - 201]', '[7759, 7759, -58*w - 207]', '[7759, 7759, 58*w - 265]', '[7793, 7793, 122*w - 513]', '[7793, 7793, 122*w + 391]', '[7817, 7817, 146*w + 471]', '[7817, 7817, 286*w + 933]', '[7823, 7823, 72*w + 221]', '[7823, 7823, 72*w - 293]', '[7841, 7841, 90*w + 283]', '[7841, 7841, 90*w - 373]', '[7867, 7867, 82*w + 281]', '[7867, 7867, 82*w - 363]', '[7873, 7873, -136*w - 453]', '[7873, 7873, 136*w - 589]', '[7907, 7907, 52*w - 201]', '[7907, 7907, 52*w + 149]', '[7919, 7919, -24*w - 5]', '[7919, 7919, 24*w - 29]', '[7927, 7927, 18*w - 121]', '[7927, 7927, -18*w - 103]', '[7937, 7937, 58*w + 171]', '[7937, 7937, 58*w - 229]', '[7951, 7951, -6*w - 89]', '[7951, 7951, 6*w - 95]', '[8009, 8009, -34*w - 75]', '[8009, 8009, 34*w - 109]', '[8039, 8039, -24*w - 1]', '[8039, 8039, 24*w - 25]', '[8053, 8053, 4*w - 93]', '[8053, 8053, -4*w - 89]', '[8069, 8069, 50*w + 141]', '[8069, 8069, 50*w - 191]', '[8087, 8087, 24*w - 23]', '[8087, 8087, 24*w - 1]', '[8093, 8093, 198*w + 643]', '[8093, 8093, 218*w + 709]', '[8101, 8101, -36*w + 181]', '[8101, 8101, -36*w - 145]', '[8123, 8123, 172*w + 557]', '[8123, 8123, 252*w + 821]', '[8147, 8147, -28*w - 41]', '[8147, 8147, 28*w - 69]', '[8167, 8167, 78*w - 347]', '[8167, 8167, 78*w + 269]', '[8179, 8179, -10*w - 93]', '[8179, 8179, 10*w - 103]', '[8209, 8209, -32*w - 135]', '[8209, 8209, -32*w + 167]', '[8233, 8233, -16*w - 101]', '[8233, 8233, 16*w - 117]', '[8237, 8237, 42*w - 151]', '[8237, 8237, 42*w + 109]', '[8263, 8263, -46*w - 173]', '[8263, 8263, -46*w + 219]', '[8269, 8269, 92*w - 405]', '[8269, 8269, 92*w + 313]', '[8273, 8273, 266*w + 867]', '[8273, 8273, 166*w + 537]', '[8293, 8293, 76*w + 263]', '[8293, 8293, 76*w - 339]', '[8297, 8297, 78*w - 319]', '[8297, 8297, 78*w + 241]', '[8329, 8329, -152*w - 505]', '[8329, 8329, 288*w + 947]', '[8363, 8363, 28*w - 67]', '[8363, 8363, -28*w - 39]', '[8377, 8377, -48*w + 227]', '[8377, 8377, -48*w - 179]', '[8387, 8387, 92*w - 381]', '[8387, 8387, 92*w + 289]', '[8429, 8429, 54*w + 155]', '[8429, 8429, 54*w - 209]', '[8443, 8443, 14*w - 113]', '[8443, 8443, -14*w - 99]', '[8461, 8461, 20*w - 129]', '[8461, 8461, -20*w - 109]', '[8501, 8501, 130*w + 417]', '[8501, 8501, 130*w - 547]', '[8521, 8521, -160*w - 531]', '[8521, 8521, 280*w + 921]', '[8543, 8543, 136*w + 437]', '[8543, 8543, 136*w - 573]', '[8599, 8599, -142*w - 473]', '[8599, 8599, 142*w - 615]', '[8609, 8609, -26*w - 19]', '[8609, 8609, 26*w - 45]', '[8623, 8623, 54*w - 251]', '[8623, 8623, -54*w - 197]', '[8663, 8663, 32*w - 93]', '[8663, 8663, -32*w - 61]', '[8689, 8689, -168*w - 557]', '[8689, 8689, 272*w + 895]', '[8693, 8693, 98*w - 407]', '[8693, 8693, 98*w + 309]', '[8707, 8707, 58*w - 267]', '[8707, 8707, -58*w - 209]', '[8713, 8713, 64*w - 291]', '[8713, 8713, -64*w - 227]', '[8719, 8719, -42*w - 163]', '[8719, 8719, -42*w + 205]', '[8737, 8737, 112*w - 489]', '[8737, 8737, 112*w + 377]', '[8753, 8753, 42*w + 107]', '[8753, 8753, 42*w - 149]', '[8779, 8779, 2*w - 95]', '[8779, 8779, -2*w - 93]', '[8803, 8803, -122*w - 409]', '[8803, 8803, 122*w - 531]', '[8807, 8807, 48*w + 131]', '[8807, 8807, 48*w - 179]', '[8819, 8819, 44*w - 159]', '[8819, 8819, 44*w + 115]', '[8821, 8821, 100*w + 339]', '[8821, 8821, 100*w - 439]', '[8831, 8831, 80*w + 247]', '[8831, 8831, 80*w - 327]', '[8837, 8837, 46*w + 123]', '[8837, 8837, 46*w - 169]', '[8839, 8839, -18*w - 107]', '[8839, 8839, 18*w - 125]', '[8849, 8849, -26*w - 15]', '[8849, 8849, 26*w - 41]', '[8863, 8863, 26*w - 149]', '[8863, 8863, -26*w - 123]', '[8867, 8867, 76*w - 309]', '[8867, 8867, 76*w + 233]', '[8893, 8893, -44*w - 169]', '[8893, 8893, -44*w + 213]', '[8933, 8933, 174*w + 563]', '[8933, 8933, 274*w + 893]', '[8941, 8941, -20*w - 111]', '[8941, 8941, 20*w - 131]', '[8951, 8951, 120*w + 383]', '[8951, 8951, 120*w - 503]', '[8963, 8963, 28*w - 61]', '[8963, 8963, -28*w - 33]', '[8999, 8999, 200*w + 649]', '[8999, 8999, 240*w + 781]', '[9007, 9007, -38*w + 191]', '[9007, 9007, -38*w - 153]', '[9013, 9013, 84*w - 373]', '[9013, 9013, 84*w + 289]', '[9049, 9049, -192*w - 635]', '[9049, 9049, -248*w - 817]', '[9059, 9059, 36*w - 115]', '[9059, 9059, -36*w - 79]', '[9067, 9067, 98*w + 333]', '[9067, 9067, 98*w - 431]', '[9091, 9091, -6*w - 95]', '[9091, 9091, 6*w - 101]', '[9127, 9127, -34*w + 177]', '[9127, 9127, -34*w - 143]', '[9161, 9161, 302*w + 985]', '[9161, 9161, 162*w + 523]', '[9173, 9173, 66*w - 263]', '[9173, 9173, 66*w + 197]', '[9181, 9181, -4*w - 95]', '[9181, 9181, 4*w - 99]', '[9209, 9209, 110*w + 349]', '[9209, 9209, 110*w - 459]', '[9227, 9227, 316*w + 1031]', '[9227, 9227, 156*w + 503]', '[9241, 9241, -40*w - 159]', '[9241, 9241, -40*w + 199]', '[9277, 9277, 28*w - 157]', '[9277, 9277, -28*w - 129]', '[9283, 9283, 294*w + 967]', '[9283, 9283, -166*w - 551]', '[9293, 9293, 86*w - 353]', '[9293, 9293, 86*w + 267]', '[9319, 9319, -50*w + 237]', '[9319, 9319, -50*w - 187]', '[9323, 9323, -28*w - 29]', '[9323, 9323, 28*w - 57]', '[9341, 9341, -38*w - 87]', '[9341, 9341, 38*w - 125]', '[9349, 9349, 108*w - 473]', '[9349, 9349, 108*w + 365]', '[9377, 9377, -26*w - 3]', '[9377, 9377, 26*w - 29]', '[9391, 9391, -10*w - 99]', '[9391, 9391, 10*w - 109]', '[9397, 9397, 12*w - 113]', '[9397, 9397, -12*w - 101]', '[9403, 9403, 78*w - 349]', '[9403, 9403, 78*w + 271]', '[9409, 97, -97]', '[9413, 9413, 78*w - 317]', '[9413, 9413, 78*w + 239]', '[9419, 9419, 116*w - 485]', '[9419, 9419, 116*w + 369]', '[9421, 9421, -36*w - 149]', '[9421, 9421, -36*w + 185]', '[9433, 9433, -32*w + 171]', '[9433, 9433, -32*w - 139]', '[9437, 9437, -26*w - 1]', '[9437, 9437, 26*w - 27]', '[9461, 9461, -30*w - 43]', '[9461, 9461, 30*w - 73]', '[9463, 9463, 286*w + 941]', '[9463, 9463, -174*w - 577]', '[9491, 9491, 28*w - 55]', '[9491, 9491, -28*w - 27]', '[9511, 9511, 94*w - 415]', '[9511, 9511, 94*w + 321]', '[9521, 9521, 58*w - 225]', '[9521, 9521, 58*w + 167]', '[9533, 9533, 26*w - 23]', '[9533, 9533, 26*w - 3]', '[9547, 9547, 2*w - 99]', '[9547, 9547, -2*w - 97]', '[9551, 9551, -32*w - 55]', '[9551, 9551, 32*w - 87]', '[9601, 9601, -56*w - 205]', '[9601, 9601, 56*w - 261]', '[9619, 9619, -182*w - 603]', '[9619, 9619, 278*w + 915]', '[9629, 9629, 26*w - 11]', '[9629, 9629, 26*w - 15]', '[9631, 9631, 106*w + 359]', '[9631, 9631, 106*w - 465]', '[9649, 9649, -72*w - 253]', '[9649, 9649, 72*w - 325]', '[9661, 9661, -44*w - 171]', '[9661, 9661, -44*w + 215]', '[9689, 9689, -30*w - 41]', '[9689, 9689, 30*w - 71]', '[9697, 9697, 8*w - 107]', '[9697, 9697, -8*w - 99]', '[9719, 9719, 56*w - 215]', '[9719, 9719, 56*w + 159]', '[9733, 9733, -68*w - 241]', '[9733, 9733, 68*w - 309]', '[9739, 9739, -62*w - 223]', '[9739, 9739, 62*w - 285]', '[9743, 9743, 128*w + 409]', '[9743, 9743, 128*w - 537]', '[9749, 9749, -34*w - 65]', '[9749, 9749, 34*w - 99]', '[9803, 9803, -28*w - 23]', '[9803, 9803, 28*w - 51]', '[9811, 9811, 10*w - 111]', '[9811, 9811, -10*w - 101]', '[9829, 9829, -12*w - 103]', '[9829, 9829, 12*w - 115]', '[9833, 9833, 62*w - 243]', '[9833, 9833, 62*w + 181]', '[9857, 9857, 134*w + 429]', '[9857, 9857, 134*w - 563]', '[9859, 9859, 262*w + 863]', '[9859, 9859, -198*w - 655]', '[9967, 9967, -26*w - 127]', '[9967, 9967, 26*w - 153]', '[9973, 9973, -4*w - 99]', '[9973, 9973, 4*w - 103]']}
• 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': [-14, -1, 1], 'conductor': 57, 'degree': 2, 'dirichlet_group': [1, 56], 'disc_abs': 57, 'disc_rad': 57, 'disc_sign': 1, 'frobs': [[2, [[1, 2]]], [3, [0]], [5, [[2, 1]]], [7, [[1, 2]]], [11, [[2, 1]]], [13, [[2, 1]]], [17, [[2, 1]]], [19, [0]], [23, [[2, 1]]], [29, [[1, 2]]], [31, [[2, 1]]], [37, [[2, 1]]], [41, [[1, 2]]], [43, [[1, 2]]], [47, [[2, 1]]], [53, [[1, 2]]], [59, [[1, 2]]]], 'gal_is_abelian': True, 'gal_is_cyclic': True, 'gal_is_solvable': True, 'galois_disc_exponents': [1, 1], 'galois_label': '2T1', 'galt': 1, 'grd': 7.54983443527075, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '2.2.57.1', 'local_algs': ['3.1.2.1a1.2', '19.1.2.1a1.1'], 'monogenic': 1, 'narrow_class_group': [2], 'narrow_class_number': 2, 'num_ram': 2, 'r2': 0, 'ramps': [3, 19], 'rd': 7.54983443527, 'regulator': {'__RealLiteral__': 0, 'data': '5.71041605276', 'prec': 44}, 'res': {}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( 40 a + 131 \\)'], 'used_grh': False, 'zk': ['1', 'a']}