Hilbert modular form data - 2.2.136.1-18.1-a

Formats: - HTML - YAML - JSON - 2024-04-16T06:56:56.550995

• 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': 136, 'field_bad_primes': [2, 17], 'field_label': '2.2.136.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '2.2.136.1-18.1-a', 'label_nsuffix': 0, 'label_suffix': 'a', 'level_bad_primes': [2, 3], 'level_ideal': '[18, 6, 3*w - 18]', 'level_label': '18.1', 'level_norm': 18, 'parallel_weight': 2, 'short_label': '18.1-a', 'weight': '[2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[2, 2, w - 6]', -1], ['[3, 3, w + 1]', 1], ['[3, 3, w + 2]', -1]], 'hecke_eigenvalues': [1, -1, 1, -2, 2, 0, 0, 2, -6, 6, 2, -2, 8, 8, 10, 10, -10, 10, 10, 16, 16, 8, -8, -14, 14, -8, -8, 0, 0, 2, 2, -16, 16, 8, 8, 4, -4, 10, -14, 14, -10, 10, -8, -8, -18, 18, 0, 0, -16, -16, 12, -12, 0, 0, 2, 2, 16, 16, -6, 6, 32, 32, 22, -22, -22, -22, 16, -16, 18, -18, 12, -12, -14, -14, 0, 0, -38, 4, -4, -24, -24, -22, 22, 10, 10, -4, 4, 34, 34, -22, -22, -24, -24, -24, 24, 10, -10, 10, -8, 8, -30, -30, -20, 20, 2, 2, -46, -46, 40, 40, -4, 4, -8, -8, 36, -36, -32, -32, -34, 34, 42, -42, -44, 44, -40, 40, -6, 6, 48, 48, 18, 18, -30, -30, 32, -32, 20, -20, 10, -10, -32, 32, -14, 14, 16, 16, 38, -38, 8, -8, 0, 0, 2, 2, 30, -30, -8, 8, -6, -6, -38, 8, 8, -22, -22, -18, 18], 'hecke_polynomial': 'x', 'label': '2.2.136.1-18.1-a'}
• hmf_fields •

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

  
  {'degree': 2, 'discriminant': 136, 'ideals': ['[1, 1, 1]', '[2, 2, w - 6]', '[3, 3, w + 1]', '[3, 3, w + 2]', '[4, 2, 2]', '[5, 5, w + 2]', '[5, 5, w + 3]', '[6, 6, w + 2]', '[6, 6, w + 4]', '[8, 4, 2*w - 12]', '[9, 3, 3]', '[9, 9, -w + 5]', '[9, 9, -w - 5]', '[10, 10, w + 2]', '[10, 10, w + 8]', '[11, 11, w + 1]', '[11, 11, w + 10]', '[12, 6, 2*w + 2]', '[12, 6, 2*w + 4]', '[15, 15, 2*w - 11]', '[15, 15, -w - 7]', '[15, 15, -w + 7]', '[15, 15, -2*w - 11]', '[16, 4, 4]', '[17, 17, -3*w + 17]', '[18, 6, 3*w - 18]', '[18, 18, w + 4]', '[18, 18, w - 4]', '[20, 10, 2*w + 4]', '[20, 10, 2*w + 6]', '[22, 22, w + 10]', '[22, 22, w + 12]', '[24, 12, 2*w + 4]', '[24, 12, 2*w + 8]', '[25, 5, 5]', '[25, 25, -w - 3]', '[25, 25, -w + 3]', '[27, 9, 3*w + 3]', '[27, 9, 3*w + 6]', '[27, 27, w + 13]', '[27, 27, w + 14]', '[29, 29, w + 11]', '[29, 29, w + 18]', '[30, 30, -w - 2]', '[30, 30, -w - 8]', '[30, 30, -w + 8]', '[30, 30, w - 2]', '[32, 8, 4*w - 24]', '[33, 33, -w - 1]', '[33, 33, 2*w - 13]', '[33, 33, 2*w + 13]', '[33, 33, w - 1]', '[34, 34, w]', '[36, 6, 6]', '[36, 18, -2*w + 10]', '[36, 18, -2*w - 10]', '[37, 37, w + 16]', '[37, 37, w + 21]', '[40, 20, 2*w + 4]', '[40, 20, 2*w + 16]', '[44, 22, 2*w + 2]', '[44, 22, 2*w + 20]', '[45, 15, 3*w + 6]', '[45, 15, 3*w + 9]', '[45, 45, w + 13]', '[45, 45, w + 22]', '[45, 45, w + 23]', '[45, 45, w + 32]', '[47, 47, -w - 9]', '[47, 47, w - 9]', '[48, 12, 4*w + 4]', '[48, 12, 4*w + 8]', '[49, 7, -7]', '[50, 10, -5*w + 30]', '[50, 50, 3*w + 16]', '[50, 50, 3*w - 16]', '[51, 51, w + 17]', '[51, 51, w + 34]', '[54, 18, 3*w + 6]', '[54, 18, 3*w + 12]', '[54, 54, w + 14]', '[54, 54, w + 40]', '[55, 55, 3*w - 19]', '[55, 55, -2*w + 9]', '[55, 55, -2*w - 9]', '[55, 55, -3*w - 19]', '[58, 58, w + 18]', '[58, 58, w + 40]', '[60, 30, 4*w - 22]', '[60, 30, -2*w - 14]', '[60, 30, -2*w + 14]', '[60, 30, -4*w - 22]', '[61, 61, w + 20]', '[61, 61, w + 41]', '[64, 8, 8]', '[66, 66, w + 10]', '[66, 66, -5*w - 28]', '[66, 66, 5*w - 28]', '[66, 66, w - 10]', '[68, 34, -6*w + 34]', '[72, 12, 6*w - 36]', '[72, 36, 2*w + 8]', '[72, 36, 2*w - 8]', '[74, 74, w + 16]', '[74, 74, w + 58]', '[75, 15, 5*w + 5]', '[75, 15, 5*w + 10]', '[75, 75, w + 22]', '[75, 75, w + 28]', '[75, 75, w + 47]', '[75, 75, w + 53]', '[80, 20, 4*w + 8]', '[80, 20, 4*w + 12]', '[81, 9, 9]', '[81, 27, -3*w + 15]', '[81, 27, -3*w - 15]', '[81, 81, -4*w + 25]', '[81, 81, 4*w + 25]', '[85, 85, w + 17]', '[85, 85, w + 68]', '[87, 87, w + 11]', '[87, 87, -2*w + 7]', '[87, 87, 2*w + 7]', '[87, 87, w - 11]', '[88, 44, 2*w + 20]', '[88, 44, 2*w + 24]', '[89, 89, 2*w - 15]', '[89, 89, -2*w - 15]', '[90, 30, 3*w + 6]', '[90, 30, 3*w + 24]', '[90, 90, w + 22]', '[90, 90, w + 32]', '[90, 90, w + 58]', '[90, 90, w + 68]', '[94, 94, -15*w + 88]', '[94, 94, -3*w + 20]', '[96, 24, 4*w + 8]', '[96, 24, 4*w + 16]', '[98, 14, -7*w + 42]', '[99, 33, 3*w + 3]', '[99, 33, 3*w + 30]', '[99, 99, w + 23]', '[99, 99, w + 32]', '[99, 99, w + 67]', '[99, 99, w + 76]', '[100, 10, 10]', '[100, 50, -2*w - 6]', '[100, 50, -2*w + 6]', '[102, 102, w + 34]', '[102, 102, w + 68]', '[103, 103, -14*w + 81]', '[103, 103, 4*w - 21]', '[107, 107, w + 26]', '[107, 107, w + 81]', '[108, 18, 6*w + 6]', '[108, 18, 6*w + 12]', '[108, 54, 2*w + 26]', '[108, 54, 2*w + 28]', '[109, 109, w + 19]', '[109, 109, w + 90]', '[110, 110, w + 12]', '[110, 110, 3*w - 14]', '[110, 110, 3*w + 14]', '[110, 110, -w + 12]', '[111, 111, 5*w - 31]', '[111, 111, 2*w - 5]', '[111, 111, -2*w - 5]', '[111, 111, 5*w + 31]', '[116, 58, 2*w + 22]', '[116, 58, 2*w + 36]', '[120, 60, -2*w - 4]', '[120, 60, -2*w - 16]', '[120, 60, -2*w + 16]', '[120, 60, 2*w - 4]', '[121, 11, 11]', '[121, 121, -5*w + 27]', '[121, 121, -5*w - 27]', '[122, 122, w + 20]', '[122, 122, w + 102]', '[125, 25, 5*w + 10]', '[125, 25, 5*w + 15]', '[125, 125, w + 28]', '[125, 125, w + 97]', '[127, 127, 2*w - 3]', '[127, 127, -2*w - 3]', '[128, 16, 8*w - 48]', '[131, 131, w + 54]', '[131, 131, w + 77]', '[132, 66, -2*w - 2]', '[132, 66, 4*w - 26]', '[132, 66, 4*w + 26]', '[132, 66, 2*w - 2]', '[135, 45, 6*w - 33]', '[135, 45, -3*w - 21]', '[135, 45, -3*w + 21]', '[135, 45, -6*w - 33]', '[135, 135, w + 13]', '[135, 135, 2*w - 1]', '[135, 135, -2*w - 1]', '[135, 135, w - 13]', '[136, 68, 2*w]', '[137, 137, -3*w - 13]', '[137, 137, 3*w - 13]', '[139, 139, w + 27]', '[139, 139, w + 112]', '[141, 141, w + 38]', '[141, 141, w + 56]', '[141, 141, w + 85]', '[141, 141, w + 103]', '[144, 12, 12]', '[144, 36, -4*w + 20]', '[144, 36, -4*w - 20]', '[145, 145, -12*w - 71]', '[145, 145, -7*w - 39]', '[145, 145, -7*w + 39]', '[145, 145, 12*w - 71]', '[147, 21, 7*w + 7]', '[147, 21, 7*w + 14]', '[148, 74, 2*w + 32]', '[148, 74, 2*w + 42]', '[150, 30, 5*w + 10]', '[150, 30, 5*w + 20]', '[150, 150, w + 22]', '[150, 150, w + 28]', '[150, 150, w + 122]', '[150, 150, w + 128]', '[151, 151, 8*w - 45]', '[151, 151, -10*w + 57]', '[153, 51, -9*w + 51]', '[153, 153, -2*w + 17]', '[153, 153, 2*w + 17]', '[160, 40, 4*w + 8]', '[160, 40, 4*w + 32]', '[162, 18, 9*w - 54]', '[162, 54, 3*w + 12]', '[162, 54, 3*w - 12]', '[162, 162, -w - 14]', '[162, 162, w - 14]', '[163, 163, w + 69]', '[163, 163, w + 94]', '[165, 165, w + 23]', '[165, 165, w + 32]', '[165, 165, w + 43]', '[165, 165, w + 67]', '[165, 165, w + 98]', '[165, 165, w + 122]', '[165, 165, w + 133]', '[165, 165, w + 142]', '[169, 13, -13]', '[170, 170, w + 68]', '[170, 170, w + 102]', '[173, 173, w + 42]', '[173, 173, w + 131]', '[174, 174, 19*w - 110]', '[174, 174, 5*w + 32]', '[174, 174, 5*w - 32]', '[174, 174, -5*w + 26]', '[176, 44, 4*w + 4]', '[176, 44, 4*w + 40]', '[178, 178, -3*w + 22]', '[178, 178, -27*w + 158]', '[180, 30, 6*w + 12]', '[180, 30, 6*w + 18]', '[180, 90, 2*w + 26]', '[180, 90, 2*w + 44]', '[180, 90, 2*w + 46]', '[180, 90, 2*w + 64]', '[181, 181, w + 45]', '[181, 181, w + 136]', '[183, 183, 7*w - 43]', '[183, 183, 4*w - 19]', '[183, 183, 4*w + 19]', '[183, 183, -7*w - 43]', '[185, 185, -4*w - 27]', '[185, 185, -3*w + 11]', '[185, 185, -3*w - 11]', '[185, 185, 4*w - 27]', '[187, 187, w + 34]', '[187, 187, w + 153]', '[188, 94, -2*w - 18]', '[188, 94, 2*w - 18]', '[191, 191, -w - 15]', '[191, 191, w - 15]', '[192, 24, 8*w + 8]', '[192, 24, 8*w + 16]', '[196, 14, -14]', '[197, 197, w + 25]', '[197, 197, w + 172]', '[198, 66, 3*w + 30]', '[198, 66, 3*w + 36]', '[198, 198, w + 32]', '[198, 198, w + 76]', '[198, 198, w + 122]', '[198, 198, w + 166]', '[200, 20, -10*w + 60]', '[200, 100, 6*w + 32]', '[200, 100, 6*w - 32]', '[204, 102, 2*w + 34]', '[204, 102, 2*w + 68]', '[206, 206, -3*w - 10]', '[206, 206, 3*w - 10]', '[211, 211, w + 33]', '[211, 211, w + 178]', '[214, 214, w + 26]', '[214, 214, w + 188]', '[216, 36, 6*w + 12]', '[216, 36, 6*w + 24]', '[216, 108, 2*w + 28]', '[216, 108, 2*w + 80]', '[218, 218, w + 90]', '[218, 218, w + 128]', '[220, 110, 6*w - 38]', '[220, 110, -4*w + 18]', '[220, 110, -4*w - 18]', '[220, 110, -6*w - 38]', '[222, 222, w + 16]', '[222, 222, 7*w - 38]', '[222, 222, -17*w + 98]', '[222, 222, w - 16]', '[223, 223, -3*w - 23]', '[223, 223, 3*w - 23]', '[225, 15, 15]', '[225, 45, 5*w - 25]', '[225, 45, 5*w + 25]', '[225, 75, -3*w - 9]', '[225, 75, -3*w + 9]', '[225, 225, -8*w + 49]', '[225, 225, -2*w + 19]', '[225, 225, 2*w + 19]', '[225, 225, 8*w + 49]', '[227, 227, w + 48]', '[227, 227, w + 179]', '[232, 116, 2*w + 36]', '[232, 116, 2*w + 80]', '[235, 235, w + 38]', '[235, 235, w + 103]', '[235, 235, w + 132]', '[235, 235, w + 197]', '[239, 239, -5*w + 33]', '[239, 239, -23*w + 135]', '[240, 60, 8*w - 44]', '[240, 60, -4*w - 28]', '[240, 60, -4*w + 28]', '[240, 60, -8*w - 44]', '[242, 22, -11*w + 66]', '[242, 242, 3*w - 8]', '[242, 242, 3*w + 8]', '[243, 27, 9*w + 9]', '[243, 27, 9*w + 18]', '[243, 81, 3*w + 39]', '[243, 81, 3*w + 42]', '[243, 243, w + 95]', '[243, 243, w + 148]', '[244, 122, 2*w + 40]', '[244, 122, 2*w + 82]', '[245, 35, 7*w + 14]', '[245, 35, 7*w + 21]', '[250, 50, 5*w + 10]', '[250, 50, 5*w + 40]', '[250, 250, w + 28]', '[250, 250, w + 222]', '[254, 254, -15*w + 86]', '[254, 254, 9*w - 50]', '[255, 255, -w - 17]', '[255, 255, -4*w - 17]', '[255, 255, 4*w - 17]', '[255, 255, -w + 17]', '[256, 16, 16]', '[257, 257, -3*w - 7]', '[257, 257, 3*w - 7]', '[261, 87, 3*w + 33]', '[261, 87, 3*w + 54]', '[261, 261, w + 40]', '[261, 261, w + 76]', '[261, 261, w + 185]', '[261, 261, w + 221]', '[262, 262, w + 54]', '[262, 262, w + 208]', '[263, 263, -24*w + 139]', '[263, 263, 6*w - 31]', '[264, 132, 2*w + 20]', '[264, 132, -10*w - 56]', '[264, 132, 10*w - 56]', '[264, 132, 2*w - 20]', '[267, 267, w + 37]', '[267, 267, w + 52]', '[267, 267, w + 215]', '[267, 267, w + 230]', '[269, 269, w + 29]', '[269, 269, w + 240]', '[270, 90, -3*w - 6]', '[270, 90, -3*w - 24]', '[270, 90, -3*w + 24]', '[270, 90, 3*w - 6]', '[270, 270, 11*w - 62]', '[270, 270, 7*w + 44]', '[270, 270, 7*w - 44]', '[270, 270, -11*w - 62]', '[271, 271, -9*w + 55]', '[271, 271, -15*w + 89]', '[272, 68, -12*w + 68]', '[274, 274, 5*w - 24]', '[274, 274, -31*w + 180]', '[275, 55, 5*w + 5]', '[275, 55, 5*w + 50]', '[275, 275, w + 78]', '[275, 275, w + 122]', '[275, 275, w + 153]', '[275, 275, w + 197]', '[277, 277, w + 119]', '[277, 277, w + 158]', '[278, 278, w + 112]', '[278, 278, w + 166]', '[281, 281, 3*w - 5]', '[281, 281, -3*w - 5]', '[282, 282, w + 38]', '[282, 282, w + 56]', '[282, 282, w + 226]', '[282, 282, w + 244]', '[283, 283, w + 113]', '[283, 283, w + 170]', '[288, 24, 12*w - 72]', '[288, 72, 4*w + 16]', '[288, 72, 4*w - 16]', '[289, 17, 17]', '[290, 290, w + 18]', '[290, 290, 3*w + 4]', '[290, 290, 3*w - 4]', '[290, 290, -w + 18]', '[294, 42, 7*w + 14]', '[294, 42, 7*w + 28]', '[296, 148, 2*w + 32]', '[296, 148, 2*w + 116]', '[297, 99, -3*w - 3]', '[297, 99, 6*w - 39]', '[297, 99, 6*w + 39]', '[297, 99, 3*w - 3]', '[297, 297, -4*w + 29]', '[297, 297, -7*w + 37]', '[297, 297, 7*w + 37]', '[297, 297, -4*w - 29]', '[300, 30, 10*w + 10]', '[300, 30, 10*w + 20]', '[300, 150, 2*w + 44]', '[300, 150, 2*w + 56]', '[300, 150, 2*w + 94]', '[300, 150, 2*w + 106]', '[302, 302, 3*w - 2]', '[302, 302, -3*w - 2]', '[305, 305, -3*w - 1]', '[305, 305, -2*w + 21]', '[305, 305, -2*w - 21]', '[305, 305, 3*w - 1]', '[306, 102, 3*w]', '[306, 306, -5*w - 34]', '[306, 306, 5*w - 34]', '[309, 309, w + 31]', '[309, 309, w + 134]', '[309, 309, w + 175]', '[309, 309, w + 278]', '[317, 317, w + 44]', '[317, 317, w + 273]', '[319, 319, -4*w + 15]', '[319, 319, 3*w - 25]', '[319, 319, -3*w - 25]', '[319, 319, -4*w - 15]', '[320, 40, 8*w + 16]', '[320, 40, 8*w + 24]', '[321, 321, -10*w + 61]', '[321, 321, -5*w - 23]', '[321, 321, -5*w + 23]', '[321, 321, -16*w + 95]', '[324, 18, 18]', '[324, 54, -6*w + 30]', '[324, 54, -6*w - 30]', '[324, 162, -8*w + 50]', '[324, 162, 8*w + 50]', '[326, 326, w + 94]', '[326, 326, w + 232]', '[327, 327, -w - 19]', '[327, 327, 8*w + 43]', '[327, 327, 8*w - 43]', '[327, 327, w - 19]', '[330, 330, w + 32]', '[330, 330, w + 98]', '[330, 330, w + 122]', '[330, 330, w + 142]', '[330, 330, w + 188]', '[330, 330, w + 208]', '[330, 330, w + 232]', '[330, 330, w + 298]', '[333, 111, 3*w + 48]', '[333, 111, 3*w + 63]', '[333, 333, w + 58]', '[333, 333, w + 95]', '[333, 333, w + 238]', '[333, 333, w + 275]', '[338, 26, -13*w + 78]', '[340, 170, 2*w + 34]', '[340, 170, 2*w + 136]', '[346, 346, w + 42]', '[346, 346, w + 304]', '[347, 347, w + 46]', '[347, 347, w + 301]', '[348, 174, 2*w + 22]', '[348, 174, -4*w + 14]', '[348, 174, 4*w + 14]', '[348, 174, 2*w - 22]', '[352, 88, 4*w + 40]', '[352, 88, 4*w + 48]', '[353, 353, 9*w - 49]', '[353, 353, -21*w + 121]', '[356, 178, 4*w - 30]', '[356, 178, -4*w - 30]', '[359, 359, -25*w + 147]', '[359, 359, -7*w + 45]', '[360, 60, 6*w + 12]', '[360, 60, 6*w + 48]', '[360, 180, 2*w + 44]', '[360, 180, 2*w + 64]', '[360, 180, 2*w + 116]', '[360, 180, 2*w + 136]', '[361, 19, -19]', '[362, 362, w + 136]', '[362, 362, w + 226]', '[363, 33, 11*w + 11]', '[363, 33, 11*w + 22]', '[363, 363, w + 43]', '[363, 363, w + 164]', '[363, 363, w + 199]', '[363, 363, w + 320]', '[366, 366, w + 20]', '[366, 366, -5*w + 22]', '[366, 366, -5*w - 22]', '[366, 366, -w + 20]', '[370, 370, 7*w + 36]', '[370, 370, 3*w + 26]', '[370, 370, -3*w + 26]', '[370, 370, 7*w - 36]', '[374, 374, w + 34]', '[374, 374, w + 340]', '[375, 75, -10*w + 55]', '[375, 75, 5*w + 35]', '[375, 75, 5*w - 35]', '[375, 75, 10*w + 55]', '[375, 375, -11*w + 67]', '[375, 375, 4*w + 13]', '[375, 375, -4*w + 13]', '[375, 375, -11*w - 67]', '[376, 188, -30*w + 176]', '[376, 188, -6*w + 40]', '[379, 379, w + 105]', '[379, 379, w + 274]', '[381, 381, w + 62]', '[381, 381, w + 65]', '[381, 381, w + 316]', '[381, 381, w + 319]', '[382, 382, -21*w + 124]', '[382, 382, -9*w + 56]', '[383, 383, 6*w - 29]', '[383, 383, -36*w + 209]', '[384, 48, 8*w + 16]', '[384, 48, 8*w + 32]', '[392, 28, -14*w + 84]', '[393, 393, -19*w + 109]', '[393, 393, 2*w - 23]', '[393, 393, 2*w + 23]', '[393, 393, 11*w - 61]', '[394, 394, w + 172]', '[394, 394, w + 222]', '[396, 66, 6*w + 6]', '[396, 66, 6*w + 60]', '[396, 198, 2*w + 46]', '[396, 198, 2*w + 64]', '[396, 198, 2*w + 134]', '[396, 198, 2*w + 152]', '[397, 397, w + 35]', '[397, 397, w + 362]', '[400, 20, 20]', '[400, 100, -4*w - 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153]', '[9809, 9809, -20*w + 153]', '[9810, 3270, 27*w + 186]', '[9810, 3270, -21*w + 72]', '[9810, 3270, 21*w + 72]', '[9810, 3270, 27*w - 186]', '[9810, 9810, -17*w + 4]', '[9810, 9810, -59*w + 358]', '[9810, 9810, -49*w + 268]', '[9810, 9810, 11*w + 118]', '[9810, 9810, 11*w - 118]', '[9810, 9810, 49*w + 268]', '[9810, 9810, -59*w - 358]', '[9810, 9810, 17*w + 4]', '[9812, 4906, 2*w + 728]', '[9812, 4906, 2*w + 2066]', '[9812, 4906, 2*w + 2840]', '[9812, 4906, 2*w + 4178]', '[9816, 4908, 2*w + 172]', '[9816, 4908, 2*w + 1808]', '[9816, 4908, 2*w + 3100]', '[9816, 4908, 2*w + 4736]', '[9817, 9817, -17*w - 3]', '[9817, 9817, 17*w - 3]', '[9819, 3273, 3*w + 603]', '[9819, 3273, 3*w + 2670]', '[9819, 9819, w + 1292]', '[9819, 9819, w + 4163]', '[9819, 9819, w + 5656]', '[9819, 9819, w + 8527]', '[9822, 9822, -29*w + 196]', '[9822, 9822, -17*w + 2]', '[9822, 9822, 17*w + 2]', '[9822, 9822, -29*w - 196]', '[9825, 1965, 95*w - 545]', '[9825, 1965, -10*w + 115]', '[9825, 1965, -10*w - 115]', '[9825, 1965, -55*w + 305]', '[9825, 9825, 17*w + 1]', '[9825, 9825, -52*w + 319]', '[9825, 9825, 29*w - 137]', '[9825, 9825, 28*w - 191]', '[9825, 9825, 28*w + 191]', '[9825, 9825, -29*w - 137]', '[9825, 9825, -52*w - 319]', '[9825, 9825, -17*w + 1]', '[9826, 578, 17*w]', '[9829, 9829, w + 3381]', '[9829, 9829, w + 6448]', '[9832, 4916, 2*w + 2336]', '[9832, 4916, 2*w + 2580]', '[9836, 4918, 2*w + 1274]', '[9836, 4918, 2*w + 3644]', '[9837, 3279, 3*w + 987]', '[9837, 3279, 3*w + 2292]', '[9837, 9837, w + 329]', '[9837, 9837, w + 2515]', '[9837, 9837, w + 7322]', '[9837, 9837, w + 9508]', '[9839, 9839, 36*w - 185]', '[9839, 9839, -36*w - 185]', '[9846, 3282, 3*w + 1170]', '[9846, 3282, 3*w + 2112]', '[9846, 9846, w + 2578]', '[9846, 9846, w + 4766]', '[9846, 9846, w + 5080]', '[9846, 9846, w + 7268]', '[9850, 1970, 5*w + 860]', '[9850, 1970, 5*w + 1110]', '[9850, 9850, w + 172]', '[9850, 9850, w + 222]', '[9850, 9850, w + 9628]', '[9850, 9850, w + 9678]', '[9852, 4926, -32*w + 158]', '[9852, 4926, 46*w + 286]', '[9852, 4926, -46*w + 286]', '[9852, 4926, -32*w - 158]', '[9860, 4930, 18*w - 34]', '[9860, 4930, -4*w + 102]', '[9860, 4930, 4*w + 102]', '[9860, 4930, 18*w + 34]', '[9864, 1644, 30*w - 144]', '[9864, 1644, -186*w + 1080]', '[9864, 4932, -2*w - 100]', '[9864, 4932, -50*w - 308]', '[9864, 4932, -50*w + 308]', '[9864, 4932, -2*w + 100]', '[9866, 9866, w + 4568]', '[9866, 9866, w + 5298]', '[9873, 3291, -102*w + 603]', '[9873, 3291, -48*w + 297]', '[9873, 9873, -31*w + 151]', '[9873, 9873, -19*w - 49]', '[9873, 9873, -19*w + 49]', '[9873, 9873, -31*w - 151]', '[9879, 9879, 20*w + 61]', '[9879, 9879, -35*w - 227]', '[9879, 9879, -40*w - 211]', '[9879, 9879, 13*w - 125]', '[9879, 9879, -13*w - 125]', '[9879, 9879, 40*w - 211]', '[9879, 9879, -35*w + 227]', '[9879, 9879, 20*w - 61]', '[9882, 1098, 9*w + 180]', '[9882, 1098, 9*w + 918]', '[9882, 3294, 3*w + 1038]', '[9882, 3294, 3*w + 1524]', '[9882, 3294, 3*w + 1770]', '[9882, 3294, 3*w + 2256]', '[9882, 9882, w + 1444]', '[9882, 9882, w + 1606]', '[9882, 9882, w + 8276]', '[9882, 9882, w + 8438]', '[9883, 9883, w + 1277]', '[9883, 9883, w + 8606]', '[9886, 9886, -265*w + 1542]', '[9886, 9886, 23*w - 90]', '[9888, 2472, 4*w + 536]', '[9888, 2472, 4*w + 1112]', '[9888, 2472, 4*w + 1360]', '[9888, 2472, 4*w + 1936]', '[9892, 4946, -142*w + 822]', '[9892, 4946, 38*w - 198]', '[9895, 9895, -22*w - 81]', '[9895, 9895, -3*w - 101]', '[9895, 9895, 3*w - 101]', '[9895, 9895, -22*w + 81]', '[9900, 330, 30*w + 30]', '[9900, 330, 30*w + 300]', '[9900, 990, 10*w + 230]', '[9900, 990, 10*w + 320]', '[9900, 990, 10*w + 670]', '[9900, 990, 10*w + 760]', '[9900, 1650, 6*w + 468]', '[9900, 1650, 6*w + 732]', '[9900, 1650, 6*w + 918]', '[9900, 1650, 6*w + 1182]', '[9900, 4950, 2*w + 244]', '[9900, 4950, 2*w + 856]', '[9900, 4950, 2*w + 944]', '[9900, 4950, 2*w + 2044]', '[9900, 4950, 2*w + 2906]', '[9900, 4950, 2*w + 4006]', '[9900, 4950, 2*w + 4094]', '[9900, 4950, 2*w + 4706]', '[9901, 9901, w + 3553]', '[9901, 9901, w + 6348]', '[9902, 9902, -213*w + 1238]', '[9902, 9902, 27*w - 122]', '[9903, 9903, 56*w - 311]', '[9903, 9903, -23*w + 167]', '[9903, 9903, -23*w - 167]', '[9903, 9903, -94*w + 539]', '[9904, 2476, 4*w + 668]', '[9904, 2476, 4*w + 1808]', '[9908, 4954, 2*w + 2018]', '[9908, 4954, 2*w + 2936]', '[9914, 9914, w + 918]', '[9914, 9914, w + 8996]', '[9917, 9917, w + 244]', '[9917, 9917, w + 2077]', '[9917, 9917, w + 7840]', '[9917, 9917, w + 9673]', '[9923, 9923, w + 2265]', '[9923, 9923, w + 7658]', '[9924, 4962, -50*w + 274]', '[9924, 4962, 8*w + 110]', '[9924, 4962, -8*w + 110]', '[9924, 4962, -50*w - 274]', '[9925, 1985, 5*w + 175]', '[9925, 1985, 5*w + 1810]', '[9925, 9925, w + 1553]', '[9925, 9925, w + 2347]', '[9925, 9925, w + 7578]', '[9925, 9925, w + 8372]', '[9927, 3309, 18*w - 33]', '[9927, 3309, -18*w - 33]', '[9927, 9927, -19*w + 149]', '[9927, 9927, 41*w - 259]', '[9927, 9927, 41*w + 259]', '[9927, 9927, -19*w - 149]', '[9929, 9929, -62*w + 375]', '[9929, 9929, -80*w + 477]', '[9931, 9931, w + 4879]', '[9931, 9931, w + 5052]', '[9939, 9939, w + 223]', '[9939, 9939, w + 3536]', '[9939, 9939, w + 6403]', '[9939, 9939, w + 9716]', '[9942, 9942, w + 1184]', '[9942, 9942, w + 4498]', '[9942, 9942, w + 5444]', '[9942, 9942, w + 8758]', '[9943, 9943, -116*w + 669]', '[9943, 9943, -57*w + 347]', '[9943, 9943, -87*w + 517]', '[9943, 9943, 46*w - 249]', '[9953, 9953, -128*w + 753]', '[9953, 9953, -21*w - 71]', '[9953, 9953, 21*w - 71]', '[9953, 9953, -38*w + 243]', '[9955, 9955, w + 1222]', '[9955, 9955, w + 3213]', '[9955, 9955, w + 3937]', '[9955, 9955, w + 4027]', '[9955, 9955, w + 5928]', '[9955, 9955, w + 6018]', '[9955, 9955, w + 6742]', '[9955, 9955, w + 8733]', '[9957, 9957, w + 331]', '[9957, 9957, w + 3650]', '[9957, 9957, w + 6307]', '[9957, 9957, w + 9626]', '[9965, 9965, w + 173]', '[9965, 9965, w + 3813]', '[9965, 9965, w + 6152]', '[9965, 9965, w + 9792]', '[9966, 9966, -w - 100]', '[9966, 9966, 5*w + 104]', '[9966, 9966, 35*w + 178]', '[9966, 9966, -43*w + 230]', '[9966, 9966, -43*w - 230]', '[9966, 9966, 35*w - 178]', '[9966, 9966, -5*w + 104]', '[9966, 9966, w - 100]', '[9970, 9970, 21*w - 158]', '[9970, 9970, 19*w + 48]', '[9970, 9970, -19*w + 48]', '[9970, 9970, 21*w + 158]', '[9972, 1662, 6*w + 714]', '[9972, 1662, 6*w + 948]', '[9972, 4986, 2*w + 316]', '[9972, 4986, 2*w + 1900]', '[9972, 4986, 2*w + 3086]', '[9972, 4986, 2*w + 4670]', '[9973, 9973, w + 2814]', '[9973, 9973, w + 7159]', '[9974, 9974, w + 3250]', '[9974, 9974, w + 6724]', '[9977, 9977, -57*w + 317]', '[9977, 9977, -14*w + 129]', '[9977, 9977, -14*w - 129]', '[9977, 9977, 57*w + 317]', '[9980, 4990, -24*w - 98]', '[9980, 4990, 34*w - 222]', '[9980, 4990, -34*w - 222]', '[9980, 4990, -24*w + 98]', '[9988, 4994, -12*w + 122]', '[9988, 4994, -26*w + 114]', '[9988, 4994, 26*w + 114]', '[9988, 4994, -12*w - 122]', '[9990, 3330, 3*w + 174]', '[9990, 3330, 3*w + 714]', '[9990, 3330, 3*w + 1284]', '[9990, 3330, 3*w + 1506]', '[9990, 3330, 3*w + 1824]', '[9990, 3330, 3*w + 2046]', '[9990, 3330, 3*w + 2616]', '[9990, 3330, 3*w + 3156]', '[9990, 9990, w + 608]', '[9990, 9990, w + 2902]', '[9990, 9990, w + 3092]', '[9990, 9990, w + 3388]', '[9990, 9990, w + 6602]', '[9990, 9990, w + 6898]', '[9990, 9990, w + 7088]', '[9990, 9990, w + 9382]', '[9992, 4996, -18*w - 32]', '[9992, 4996, 18*w - 32]', '[9996, 714, 14*w + 238]', '[9996, 714, 14*w + 476]', '[9998, 9998, -7*w - 108]', '[9998, 9998, 7*w - 108]', '[10000, 100, 100]', '[10000, 500, 20*w + 60]', '[10000, 500, 20*w - 60]', '[10000, 2500, -24*w + 172]', '[10000, 2500, 24*w + 172]'], 'label': '2.2.136.1', 'narrow_class_no': 4, 'primes': ['[2, 2, w - 6]', '[3, 3, w + 1]', '[3, 3, w + 2]', '[5, 5, w + 2]', '[5, 5, w + 3]', '[11, 11, w + 1]', '[11, 11, w + 10]', '[17, 17, -3*w + 17]', '[29, 29, w + 11]', '[29, 29, w + 18]', '[37, 37, w + 16]', '[37, 37, w + 21]', '[47, 47, -w - 9]', '[47, 47, w - 9]', '[49, 7, -7]', '[61, 61, w + 20]', '[61, 61, w + 41]', '[89, 89, 2*w - 15]', '[89, 89, -2*w - 15]', '[103, 103, -14*w + 81]', '[103, 103, 4*w - 21]', '[107, 107, w + 26]', '[107, 107, w + 81]', '[109, 109, w + 19]', '[109, 109, w + 90]', '[127, 127, 2*w - 3]', '[127, 127, -2*w - 3]', '[131, 131, w + 54]', '[131, 131, w + 77]', '[137, 137, -3*w - 13]', '[137, 137, 3*w - 13]', '[139, 139, w + 27]', '[139, 139, w + 112]', '[151, 151, 8*w - 45]', '[151, 151, -10*w + 57]', '[163, 163, w + 69]', '[163, 163, w + 94]', '[169, 13, -13]', '[173, 173, w + 42]', '[173, 173, w + 131]', '[181, 181, w + 45]', '[181, 181, w + 136]', '[191, 191, -w - 15]', '[191, 191, w - 15]', '[197, 197, w + 25]', '[197, 197, w + 172]', '[211, 211, w + 33]', '[211, 211, w + 178]', '[223, 223, -3*w - 23]', '[223, 223, 3*w - 23]', '[227, 227, w + 48]', '[227, 227, w + 179]', '[239, 239, -5*w + 33]', '[239, 239, -23*w + 135]', '[257, 257, -3*w - 7]', '[257, 257, 3*w - 7]', '[263, 263, -24*w + 139]', '[263, 263, 6*w - 31]', '[269, 269, w + 29]', '[269, 269, w + 240]', '[271, 271, -9*w + 55]', '[271, 271, -15*w + 89]', '[277, 277, w + 119]', '[277, 277, w + 158]', '[281, 281, 3*w - 5]', '[281, 281, -3*w - 5]', '[283, 283, w + 113]', '[283, 283, w + 170]', '[317, 317, w + 44]', '[317, 317, w + 273]', '[347, 347, w + 46]', '[347, 347, w + 301]', '[353, 353, 9*w - 49]', '[353, 353, -21*w + 121]', '[359, 359, -25*w + 147]', '[359, 359, -7*w + 45]', '[361, 19, -19]', '[379, 379, w + 105]', '[379, 379, w + 274]', '[383, 383, 6*w - 29]', '[383, 383, -36*w + 209]', '[397, 397, w + 35]', '[397, 397, w + 362]', '[409, 409, -5*w - 21]', '[409, 409, 5*w - 21]', '[419, 419, w + 156]', '[419, 419, w + 263]', '[433, 433, -12*w + 73]', '[433, 433, -18*w + 107]', '[457, 457, 6*w + 41]', '[457, 457, -6*w + 41]', '[463, 463, -4*w - 9]', '[463, 463, 4*w - 9]', '[499, 499, w + 212]', '[499, 499, w + 287]', '[529, 23, -23]', '[541, 541, w + 121]', '[541, 541, w + 420]', '[547, 547, w + 157]', '[547, 547, w + 390]', '[569, 569, -28*w + 165]', '[569, 569, -10*w + 63]', '[571, 571, w + 264]', '[571, 571, w + 307]', '[577, 577, -47*w + 273]', '[577, 577, 7*w - 33]', '[593, 593, 2*w - 27]', '[593, 593, -2*w - 27]', '[599, 599, -6*w - 25]', '[599, 599, 6*w - 25]', '[619, 619, w + 167]', '[619, 619, w + 452]', '[631, 631, -15*w + 91]', '[631, 631, -21*w + 125]', '[643, 643, w + 57]', '[643, 643, w + 586]', '[647, 647, -11*w + 69]', '[647, 647, -29*w + 171]', '[653, 653, w + 120]', '[653, 653, w + 533]', '[677, 677, w + 64]', '[677, 677, w + 613]', '[683, 683, w + 248]', '[683, 683, w + 435]', '[691, 691, w + 322]', '[691, 691, w + 369]', '[709, 709, w + 265]', '[709, 709, w + 444]', '[727, 727, -9*w + 59]', '[727, 727, -39*w + 229]', '[761, 761, -27*w + 155]', '[761, 761, 15*w - 83]', '[769, 769, 5*w - 9]', '[769, 769, -5*w - 9]', '[787, 787, w + 63]', '[787, 787, w + 724]', '[811, 811, w + 70]', '[811, 811, w + 741]', '[821, 821, w + 149]', '[821, 821, w + 672]', '[827, 827, w + 193]', '[827, 827, w + 634]', '[853, 853, w + 253]', '[853, 853, w + 600]', '[863, 863, -6*w - 19]', '[863, 863, 6*w - 19]', '[877, 877, w + 339]', '[877, 877, w + 538]', '[907, 907, w + 74]', '[907, 907, w + 833]', '[919, 919, -3*w - 35]', '[919, 919, 3*w - 35]', '[937, 937, 7*w - 27]', '[937, 937, -7*w - 27]', '[941, 941, w + 144]', '[941, 941, w + 797]', '[947, 947, w + 292]', '[947, 947, w + 655]', '[953, 953, 2*w - 33]', '[953, 953, -2*w - 33]', '[961, 31, -31]', '[967, 967, 9*w - 61]', '[967, 967, -9*w - 61]', '[977, 977, -4*w - 39]', '[977, 977, 4*w - 39]', '[997, 997, w + 55]', '[997, 997, w + 942]']}
• 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': [2], 'class_number': 2, 'cm': False, 'coeffs': [-34, 0, 1], 'conductor': 136, 'degree': 2, 'dirichlet_group': [1, 101], 'disc_abs': 136, 'disc_rad': 34, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[1, 2]]], [5, [[1, 2]]], [7, [[2, 1]]], [11, [[1, 2]]], [13, [[2, 1]]], [17, [0]], [19, [[2, 1]]], [23, [[2, 1]]], [29, [[1, 2]]], [31, [[2, 1]]], [37, [[1, 2]]], [41, [[2, 1]]], [43, [[2, 1]]], [47, [[1, 2]]], [53, [[2, 1]]], [59, [[2, 1]]]], 'gal_is_abelian': True, 'gal_is_cyclic': True, 'gal_is_solvable': True, 'galois_disc_exponents': [3, 1], 'galois_label': '2T1', 'galt': 1, 'grd': 11.661903789690601, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '2.2.136.1', 'local_algs': ['2.2.3.1', '17.2.1.1'], 'monogenic': 1, 'num_ram': 2, 'r2': 0, 'ramps': [2, 17], 'rd': 11.6619037897, 'regulator': {'__RealLiteral__': 0, 'data': '4.24829109791', 'prec': 44}, 'res': {}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( 6 a - 35 \\)'], 'used_grh': False, 'zk': ['1', 'a']}