Hilbert modular form data - 2.2.213.1-3.1-b

Formats: - HTML - YAML - JSON - 2024-05-21T05:49:27.114616

• 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': 6, 'disc': 213, 'field_bad_primes': [3, 71], 'field_label': '2.2.213.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '2.2.213.1-3.1-b', 'label_nsuffix': 1, 'label_suffix': 'b', 'level_bad_primes': [3], 'level_ideal': '[3, 3, w - 8]', 'level_label': '3.1', 'level_norm': 3, 'parallel_weight': 2, 'short_label': '3.1-b', 'weight': '[2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[3, 3, w - 8]', 1]], 'hecke_eigenvalues': [-1, '-7/482*e^4 + 255/482*e^2 - 219/241', '-e', 'e', '-1/482*e^5 + 1/241*e^3 + 1349/482*e', '1/482*e^5 - 1/241*e^3 - 1349/482*e', '11/241*e^4 - 504/241*e^2 + 3236/241', '11/241*e^4 - 504/241*e^2 + 3236/241', '5/482*e^5 - 251/482*e^3 + 1086/241*e', '-5/482*e^5 + 251/482*e^3 - 1086/241*e', '19/482*e^4 - 761/482*e^2 - 886/241', '-19/482*e^4 + 761/482*e^2 - 78/241', '-19/482*e^4 + 761/482*e^2 - 78/241', '-2/241*e^5 + 249/482*e^3 - 3521/482*e', '2/241*e^5 - 249/482*e^3 + 3521/482*e', '-43/482*e^4 + 1773/482*e^2 - 1724/241', '-43/482*e^4 + 1773/482*e^2 - 1724/241', '-5/482*e^5 + 251/482*e^3 - 845/241*e', '5/482*e^5 - 251/482*e^3 + 845/241*e', '-16/241*e^4 + 755/241*e^2 - 3962/241', '2/241*e^5 - 249/482*e^3 + 3521/482*e', '-2/241*e^5 + 249/482*e^3 - 3521/482*e', '1/241*e^5 - 2/241*e^3 - 1590/241*e', '-1/241*e^5 + 2/241*e^3 + 1590/241*e', 0, '-5/241*e^4 + 251/241*e^2 + 238/241', '-5/241*e^4 + 251/241*e^2 + 238/241', '-7/482*e^4 + 255/482*e^2 + 504/241', '-7/482*e^4 + 255/482*e^2 + 504/241', '20/241*e^4 - 763/241*e^2 + 976/241', '20/241*e^4 - 763/241*e^2 + 976/241', '-10/241*e^4 + 261/241*e^2 + 3850/241', '-10/241*e^4 + 261/241*e^2 + 3850/241', '-11/482*e^5 + 252/241*e^3 - 2513/482*e', '11/482*e^5 - 252/241*e^3 + 2513/482*e', '3/482*e^5 - 3/241*e^3 - 3565/482*e', '-3/482*e^5 + 3/241*e^3 + 3565/482*e', '3/241*e^5 - 253/482*e^3 + 1305/482*e', '-3/241*e^5 + 253/482*e^3 - 1305/482*e', '-31/482*e^4 + 1267/482*e^2 - 1624/241', '-31/482*e^4 + 1267/482*e^2 - 1624/241', '22/241*e^4 - 1008/241*e^2 + 6954/241', '22/241*e^4 - 1008/241*e^2 + 6954/241', '7/482*e^4 - 255/482*e^2 - 22/241', '-7/482*e^5 + 248/241*e^3 - 7427/482*e', '7/482*e^5 - 248/241*e^3 + 7427/482*e', '-3/241*e^5 + 253/482*e^3 - 1305/482*e', '3/241*e^5 - 253/482*e^3 + 1305/482*e', '9/241*e^4 - 259/241*e^2 - 1296/241', '9/241*e^4 - 259/241*e^2 - 1296/241', '18/241*e^4 - 759/241*e^2 + 5120/241', '18/241*e^4 - 759/241*e^2 + 5120/241', '1/241*e^5 - 2/241*e^3 - 1590/241*e', '-1/241*e^5 + 2/241*e^3 + 1590/241*e', '35/241*e^4 - 1516/241*e^2 + 7974/241', '35/241*e^4 - 1516/241*e^2 + 7974/241', '-5/241*e^5 + 251/241*e^3 - 2413/241*e', '5/241*e^5 - 251/241*e^3 + 2413/241*e', '-7/482*e^5 + 248/241*e^3 - 7909/482*e', '7/482*e^5 - 248/241*e^3 + 7909/482*e', '7/482*e^5 - 248/241*e^3 + 9837/482*e', '-7/482*e^5 + 248/241*e^3 - 9837/482*e', '-58/241*e^4 + 2526/241*e^2 - 9000/241', '-58/241*e^4 + 2526/241*e^2 - 9000/241', '105/482*e^4 - 4789/482*e^2 + 11238/241', '105/482*e^4 - 4789/482*e^2 + 11238/241', '-3/241*e^5 + 253/482*e^3 + 623/482*e', '3/241*e^5 - 253/482*e^3 - 623/482*e', '-13/241*e^4 + 749/241*e^2 - 7286/241', '-13/241*e^4 + 749/241*e^2 - 7286/241', '-6/241*e^5 + 265/482*e^3 + 8235/482*e', '6/241*e^5 - 265/482*e^3 - 8235/482*e', '-8/241*e^5 + 257/241*e^3 + 1875/241*e', '8/241*e^5 - 257/241*e^3 - 1875/241*e', '5/241*e^5 - 261/482*e^3 - 5055/482*e', '-5/241*e^5 + 261/482*e^3 + 5055/482*e', '63/482*e^4 - 3259/482*e^2 + 12816/241', '63/482*e^4 - 3259/482*e^2 + 12816/241', '-75/482*e^4 + 3283/482*e^2 - 7614/241', '-75/482*e^4 + 3283/482*e^2 - 7614/241', '-40/241*e^4 + 1767/241*e^2 - 4844/241', '-40/241*e^4 + 1767/241*e^2 - 4844/241', '-3/241*e^5 + 247/241*e^3 - 4147/241*e', '3/241*e^5 - 247/241*e^3 + 4147/241*e', '-23/482*e^5 + 505/241*e^3 - 5123/482*e', '23/482*e^5 - 505/241*e^3 + 5123/482*e', '-1/241*e^5 + 245/482*e^3 - 5737/482*e', '1/241*e^5 - 245/482*e^3 + 5737/482*e', '33/482*e^4 - 1271/482*e^2 - 1894/241', '33/482*e^4 - 1271/482*e^2 - 1894/241', '3/482*e^5 - 247/482*e^3 + 1712/241*e', '-3/482*e^5 + 247/482*e^3 - 1712/241*e', '13/482*e^5 - 254/241*e^3 + 779/482*e', '-13/482*e^5 + 254/241*e^3 - 779/482*e', '-1/482*e^5 + 1/241*e^3 + 2313/482*e', '1/482*e^5 - 1/241*e^3 - 2313/482*e', '93/482*e^4 - 3319/482*e^2 - 2840/241', '93/482*e^4 - 3319/482*e^2 - 2840/241', '1/241*e^5 - 2/241*e^3 - 2072/241*e', '-1/241*e^5 + 2/241*e^3 + 2072/241*e', '-11/482*e^5 + 745/482*e^3 - 6920/241*e', '11/482*e^5 - 745/482*e^3 + 6920/241*e', '-8/241*e^5 + 257/241*e^3 + 1875/241*e', '8/241*e^5 - 257/241*e^3 - 1875/241*e', '-33/241*e^4 + 1753/241*e^2 - 11636/241', '-33/241*e^4 + 1753/241*e^2 - 11636/241', '-17/482*e^4 + 1721/482*e^2 - 11308/241', '-17/482*e^4 + 1721/482*e^2 - 11308/241', '25/482*e^5 - 1255/482*e^3 + 5189/241*e', '-25/482*e^5 + 1255/482*e^3 - 5189/241*e', '75/482*e^4 - 3283/482*e^2 + 5204/241', '75/482*e^4 - 3283/482*e^2 + 5204/241', '-11/482*e^4 + 263/482*e^2 + 4166/241', '-11/482*e^4 + 263/482*e^2 + 4166/241', '-11/482*e^5 + 263/482*e^3 + 2479/241*e', '11/482*e^5 - 263/482*e^3 - 2479/241*e', '27/241*e^4 - 1259/241*e^2 + 9126/241', '27/241*e^4 - 1259/241*e^2 + 9126/241', '-149/482*e^4 + 6323/482*e^2 - 11444/241', '-149/482*e^4 + 6323/482*e^2 - 11444/241', '7/241*e^5 - 751/482*e^3 + 7383/482*e', '-7/241*e^5 + 751/482*e^3 - 7383/482*e', '7/241*e^5 - 496/241*e^3 + 7668/241*e', '-7/241*e^5 + 496/241*e^3 - 7668/241*e', '17/482*e^5 - 499/241*e^3 + 14181/482*e', '-17/482*e^5 + 499/241*e^3 - 14181/482*e', '85/482*e^4 - 3303/482*e^2 + 628/241', '85/482*e^4 - 3303/482*e^2 + 628/241', '4/241*e^5 - 249/241*e^3 + 3039/241*e', '-4/241*e^5 + 249/241*e^3 - 3039/241*e', '-2/241*e^5 + 249/482*e^3 - 5449/482*e', '2/241*e^5 - 249/482*e^3 + 5449/482*e', '-15/482*e^5 + 497/241*e^3 - 13505/482*e', '15/482*e^5 - 497/241*e^3 + 13505/482*e', '69/482*e^4 - 2307/482*e^2 - 5932/241', '69/482*e^4 - 2307/482*e^2 - 5932/241', '3/482*e^5 - 3/241*e^3 - 2119/482*e', '-3/482*e^5 + 3/241*e^3 + 2119/482*e', '5/482*e^4 + 231/482*e^2 - 1324/241', '5/482*e^4 + 231/482*e^2 - 1324/241', '9/482*e^5 - 741/482*e^3 + 6823/241*e', '-9/482*e^5 + 741/482*e^3 - 6823/241*e', '-34/241*e^4 + 1755/241*e^2 - 11974/241', '-34/241*e^4 + 1755/241*e^2 - 11974/241', '87/482*e^4 - 3307/482*e^2 - 9638/241', '75/482*e^4 - 2801/482*e^2 + 1830/241', '75/482*e^4 - 2801/482*e^2 + 1830/241', '15/482*e^5 - 753/482*e^3 + 2535/241*e', '-15/482*e^5 + 753/482*e^3 - 2535/241*e', '71/241*e^4 - 3275/241*e^2 + 12430/241', '71/241*e^4 - 3275/241*e^2 + 12430/241', '-7/241*e^5 + 255/241*e^3 + 1008/241*e', '7/241*e^5 - 255/241*e^3 - 1008/241*e', '-23/482*e^5 + 769/482*e^3 + 2379/241*e', '23/482*e^5 - 769/482*e^3 - 2379/241*e', '62/241*e^4 - 2534/241*e^2 + 11798/241', '-5/482*e^4 + 1215/482*e^2 - 11690/241', '-5/482*e^4 + 1215/482*e^2 - 11690/241'], 'hecke_polynomial': 'x^6 - 80*x^4 + 1699*x^2 - 4192', 'label': '2.2.213.1-3.1-b'}
• hmf_fields •

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

  
  {'degree': 2, 'discriminant': 213, 'ideals': ['[1, 1, 1]', '[3, 3, w - 8]', '[4, 2, 2]', '[9, 3, 3]', '[11, 11, -w + 7]', '[11, 11, -w - 6]', '[12, 6, 2*w - 16]', '[16, 4, 4]', '[17, 17, -2*w + 15]', '[17, 17, -2*w - 13]', '[19, 19, -w - 8]', '[19, 19, -w + 9]', '[23, 23, -w - 5]', '[23, 23, -w + 6]', '[25, 5, 5]', '[27, 9, 3*w - 24]', '[33, 33, w + 4]', '[33, 33, w - 5]', '[36, 6, 6]', '[37, 37, -w - 9]', '[37, 37, w - 10]', '[41, 41, -w - 3]', '[41, 41, w - 4]', '[43, 43, -2*w + 17]', '[43, 43, -7*w + 55]', '[44, 22, -2*w + 14]', '[44, 22, -2*w - 12]', '[47, 47, -w - 2]', '[47, 47, w - 3]', '[48, 12, 4*w - 32]', '[49, 7, -7]', '[51, 51, w + 1]', '[51, 51, w - 2]', '[53, 53, -w]', '[53, 53, w - 1]', '[57, 57, -w - 10]', '[57, 57, -w + 11]', '[59, 59, -7*w + 54]', '[59, 59, 3*w - 22]', '[64, 8, 8]', '[68, 34, -4*w + 30]', '[68, 34, -4*w - 26]', '[69, 69, 2*w - 13]', '[69, 69, 2*w + 11]', '[71, 71, -5*w + 38]', '[73, 73, -3*w + 25]', '[73, 73, -8*w + 63]', '[75, 15, 5*w - 40]', '[76, 38, -2*w - 16]', '[76, 38, -2*w + 18]', '[79, 79, -w - 11]', '[79, 79, w - 12]', '[81, 9, 9]', '[92, 46, -2*w - 10]', '[92, 46, -2*w + 12]', '[99, 33, -3*w + 21]', '[99, 33, -3*w - 18]', '[100, 10, 10]', '[103, 103, -w - 12]', '[103, 103, w - 13]', '[108, 18, 6*w - 48]', '[109, 109, -4*w + 33]', '[109, 109, -9*w + 71]', '[111, 111, -2*w + 19]', '[111, 111, -17*w + 133]', '[113, 113, 2*w - 11]', '[113, 113, -2*w - 9]', '[121, 11, 11]', '[121, 121, 3*w + 23]', '[121, 121, -3*w + 26]', '[123, 123, -11*w + 85]', '[123, 123, 4*w - 29]', '[129, 129, -w - 13]', '[129, 129, w - 14]', '[132, 66, 2*w + 8]', '[132, 66, 2*w - 10]', '[137, 137, 3*w - 20]', '[137, 137, -3*w - 17]', '[141, 141, 5*w - 37]', '[141, 141, -10*w + 77]', '[144, 12, 12]', '[147, 21, -7*w + 56]', '[148, 74, -2*w - 18]', '[148, 74, 2*w - 20]', '[149, 149, 2*w - 9]', '[149, 149, -2*w - 7]', '[151, 151, -5*w + 41]', '[151, 151, -10*w + 79]', '[153, 51, -6*w + 45]', '[153, 51, -6*w - 39]', '[157, 157, -w - 14]', '[157, 157, w - 15]', '[159, 159, -8*w + 61]', '[159, 159, 7*w - 53]', '[164, 82, -2*w - 6]', '[164, 82, 2*w - 8]', '[169, 13, -13]', '[171, 57, -3*w - 24]', '[171, 57, -3*w + 27]', '[172, 86, -4*w + 34]', '[172, 86, -14*w + 110]', '[173, 173, -3*w - 16]', '[173, 173, 3*w - 19]', '[176, 44, -4*w + 28]', '[176, 44, -4*w - 24]', '[177, 177, 2*w - 7]', '[177, 177, -2*w - 5]', '[187, 187, w + 15]', '[187, 187, -2*w + 21]', '[187, 187, 2*w + 19]', '[187, 187, -w + 16]', '[188, 94, -2*w - 4]', '[188, 94, 2*w - 6]', '[192, 24, 8*w - 64]', '[196, 14, -14]', '[197, 197, 2*w - 5]', '[197, 197, -2*w - 3]', '[199, 199, -6*w + 49]', '[199, 199, -11*w + 87]', '[204, 102, 2*w + 2]', '[204, 102, 2*w - 4]', '[207, 69, -3*w - 15]', '[207, 69, -3*w + 18]', '[209, 209, -5*w - 31]', '[209, 209, 2*w - 3]', '[209, 209, -2*w - 1]', '[209, 209, 5*w - 36]', '[212, 106, -2*w]', '[212, 106, 2*w - 2]', '[213, 213, 2*w - 1]', '[219, 219, -w - 16]', '[219, 219, w - 17]', '[223, 223, 3*w - 28]', '[223, 223, -3*w - 25]', '[225, 15, 15]', '[227, 227, 4*w - 27]', '[227, 227, -4*w - 23]', '[228, 114, -2*w - 20]', '[228, 114, -2*w + 22]', '[229, 229, -15*w + 118]', '[229, 229, -5*w + 42]', '[236, 118, -14*w + 108]', '[236, 118, 6*w - 44]', '[237, 237, -19*w + 149]', '[237, 237, -4*w + 35]', '[239, 239, 3*w - 17]', '[239, 239, -3*w - 14]', '[243, 27, 9*w - 72]', '[253, 253, w + 17]', '[253, 253, -7*w + 57]', '[253, 253, 7*w + 50]', '[253, 253, -w + 18]', '[256, 16, 16]', '[257, 257, 7*w - 52]', '[257, 257, -13*w + 100]', '[269, 269, -3*w - 13]', '[269, 269, 3*w - 16]', '[271, 271, 2*w - 23]', '[271, 271, -2*w - 21]', '[272, 68, -8*w + 60]', '[272, 68, -8*w - 52]', '[275, 55, -5*w + 35]', '[275, 55, -5*w - 30]', '[276, 138, 4*w - 26]', '[276, 138, 4*w + 22]', '[277, 277, -3*w - 26]', '[277, 277, 3*w - 29]', '[281, 281, -11*w + 84]', '[281, 281, 9*w - 68]', '[284, 142, -10*w + 76]', '[289, 17, 17]', '[289, 289, w + 18]', '[289, 289, -w + 19]', '[292, 146, -6*w + 50]', '[292, 146, -16*w + 126]', '[297, 99, 3*w + 12]', '[297, 99, 3*w - 15]', '[300, 30, 10*w - 80]', '[304, 76, -4*w - 32]', '[304, 76, -4*w + 36]', '[309, 309, -5*w + 43]', '[309, 309, -20*w + 157]', '[313, 313, -8*w + 65]', '[313, 313, -13*w + 103]', '[316, 158, -2*w - 22]', '[316, 158, 2*w - 24]', '[317, 317, -19*w + 147]', '[317, 317, 6*w - 43]', '[323, 323, -4*w - 21]', '[323, 323, 3*w - 14]', '[323, 323, -3*w - 11]', '[323, 323, 4*w - 25]', '[324, 18, 18]', '[327, 327, -w - 19]', '[327, 327, w - 20]', '[333, 111, -3*w - 27]', '[333, 111, 3*w - 30]', '[339, 339, 5*w - 34]', '[339, 339, -25*w + 194]', '[347, 347, -3*w - 10]', '[347, 347, 3*w - 13]', '[353, 353, 7*w - 51]', '[353, 353, -18*w + 139]', '[361, 19, 19]', '[361, 361, 7*w + 51]', '[361, 361, -7*w + 58]', '[363, 33, 11*w - 88]', '[363, 363, 2*w - 25]', '[363, 363, -2*w - 23]', '[367, 367, -w - 20]', '[367, 367, w - 21]', '[368, 92, -4*w - 20]', '[368, 92, -4*w + 24]', '[369, 123, -3*w - 9]', '[369, 123, 3*w - 12]', '[373, 373, 4*w - 37]', '[373, 373, -4*w - 33]', '[379, 379, -9*w + 73]', '[379, 379, -14*w + 111]', '[383, 383, -17*w + 131]', '[383, 383, 8*w - 59]', '[387, 129, -6*w + 51]', '[387, 129, -21*w + 165]', '[389, 389, 3*w - 11]', '[389, 389, -3*w - 8]', '[391, 391, 5*w + 39]', '[391, 391, -3*w + 31]', '[391, 391, 3*w + 28]', '[391, 391, -5*w + 44]', '[396, 66, -6*w + 42]', '[396, 66, -6*w - 36]', '[400, 20, 20]', '[401, 401, -5*w - 28]', '[401, 401, 5*w - 33]', '[407, 407, 16*w + 107]', '[407, 407, 3*w + 7]', '[407, 407, 3*w - 10]', '[407, 407, 16*w - 123]', '[409, 409, -w - 21]', '[409, 409, w - 22]', '[411, 411, 4*w - 23]', '[411, 411, -41*w + 319]', '[412, 206, -2*w - 24]', '[412, 206, 2*w - 26]', '[423, 141, -3*w - 6]', '[423, 141, 3*w - 9]', '[425, 85, -10*w + 75]', '[425, 85, -10*w - 65]', '[432, 36, 12*w - 96]', '[436, 218, -8*w + 66]', '[436, 218, -18*w + 142]', '[437, 437, -11*w - 72]', '[437, 437, -3*w + 8]', '[437, 437, 3*w + 5]', '[437, 437, 11*w - 83]', '[441, 21, -21]', '[443, 443, -12*w + 91]', '[443, 443, -13*w + 99]', '[444, 222, -4*w + 38]', '[444, 222, -34*w + 266]', '[447, 447, -23*w + 178]', '[447, 447, 7*w - 50]', '[449, 449, -3*w - 4]', '[449, 449, 3*w - 7]', '[451, 451, 10*w - 81]', '[451, 451, -3*w - 29]', '[451, 451, -3*w + 32]', '[451, 451, 10*w + 71]', '[452, 226, 4*w - 22]', '[452, 226, -4*w - 18]', '[453, 453, -w - 22]', '[453, 453, w - 23]', '[459, 153, 3*w + 3]', '[459, 153, 3*w - 6]', '[461, 461, 5*w - 32]', '[461, 461, -5*w - 27]', '[463, 463, 2*w - 27]', '[463, 463, -2*w - 25]', '[467, 467, 3*w - 5]', '[467, 467, -3*w - 2]', '[471, 471, -22*w + 173]', '[471, 471, -7*w + 59]', '[473, 473, -6*w + 41]', '[473, 473, -3*w - 1]', '[473, 473, -3*w + 4]', '[473, 473, -6*w - 35]', '[475, 95, -5*w - 40]', '[475, 95, -5*w + 45]', '[477, 159, -3*w]', '[477, 159, 3*w - 3]', '[479, 479, 3*w - 2]', '[479, 479, 3*w - 1]', '[484, 22, 22]', '[484, 242, 6*w + 46]', '[484, 242, -6*w + 52]', '[491, 491, -4*w - 17]', '[491, 491, 4*w - 21]', '[492, 246, -22*w + 170]', '[492, 246, 8*w - 58]', '[499, 499, -w - 23]', '[499, 499, w - 24]', '[507, 39, -13*w + 104]', '[513, 171, -3*w - 30]', '[513, 171, -3*w + 33]', '[516, 258, -2*w - 26]', '[516, 258, 2*w - 28]', '[517, 517, -4*w - 35]', '[517, 517, 9*w + 65]', '[517, 517, 9*w - 74]', '[517, 517, -4*w + 39]', '[519, 519, -40*w + 311]', '[519, 519, 5*w - 31]', '[528, 132, 4*w + 16]', '[528, 132, 4*w - 20]', '[529, 23, 23]', '[529, 529, -11*w + 89]', '[529, 529, 11*w + 78]', '[531, 177, -21*w + 162]', '[531, 177, 9*w - 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143]', '[9636, 4818, 46*w - 344]', '[9636, 4818, 20*w - 118]', '[9636, 4818, 20*w + 98]', '[9636, 4818, 46*w + 298]', '[9643, 9643, 18*w - 173]', '[9643, 9643, -18*w - 155]', '[9644, 4822, -22*w - 116]', '[9644, 4822, 22*w - 138]', '[9647, 9647, 37*w - 270]', '[9647, 9647, 24*w - 157]', '[9647, 9647, 24*w + 133]', '[9647, 9647, 37*w + 233]', '[9649, 9649, -w - 98]', '[9649, 9649, w - 99]', '[9653, 1379, 14*w - 35]', '[9653, 1379, -14*w - 21]', '[9661, 9661, -23*w - 183]', '[9661, 9661, 23*w - 206]', '[9663, 9663, -16*w - 55]', '[9663, 9663, 16*w - 71]', '[9664, 1208, -40*w + 328]', '[9664, 1208, -80*w + 632]', '[9675, 645, -30*w + 255]', '[9675, 645, -105*w + 825]', '[9676, 4838, -52*w + 418]', '[9676, 4838, -20*w - 166]', '[9676, 4838, 20*w - 186]', '[9676, 4838, -62*w + 494]', '[9677, 9677, 21*w - 128]', '[9677, 9677, -21*w - 107]', '[9684, 1614, -18*w - 78]', '[9684, 1614, 18*w - 96]', '[9689, 9689, 17*w - 84]', '[9689, 9689, -17*w - 67]', '[9707, 9707, 28*w + 165]', '[9707, 9707, 84*w - 647]', '[9707, 9707, 84*w + 563]', '[9707, 9707, 28*w - 193]', '[9708, 4854, 14*w - 34]', '[9708, 4854, -14*w - 20]', '[9717, 9717, 47*w - 352]', '[9717, 9717, -206*w + 1603]', '[9717, 9717, 19*w - 107]', '[9717, 9717, -73*w + 560]', '[9719, 9719, -25*w - 141]', '[9719, 9719, 25*w - 166]', '[9725, 1945, 15*w - 55]', '[9725, 1945, -15*w - 40]', '[9727, 9727, -14*w - 135]', '[9727, 9727, 14*w - 149]', '[9729, 3243, 24*w + 189]', '[9729, 3243, -9*w - 114]', '[9729, 3243, -9*w + 123]', '[9729, 3243, 24*w - 213]', '[9732, 4866, -34*w + 284]', '[9732, 4866, -94*w + 740]', '[9733, 9733, -17*w - 150]', '[9733, 9733, 17*w - 167]', '[9739, 9739, -109*w + 856]', '[9739, 9739, -29*w + 248]', '[9747, 171, -57*w + 456]', '[9747, 3249, 6*w - 111]', '[9747, 3249, -6*w - 105]', '[9749, 9749, 27*w - 184]', '[9749, 9749, -27*w - 157]', '[9751, 1393, -42*w + 343]', '[9751, 1393, -77*w + 609]', '[9753, 9753, -139*w + 1079]', '[9753, 9753, 26*w - 175]', '[9756, 1626, 12*w - 138]', '[9756, 1626, -12*w - 126]', '[9757, 9757, -4*w + 105]', '[9757, 9757, 87*w - 686]', '[9757, 9757, 87*w + 599]', '[9757, 9757, -4*w - 101]', '[9759, 9759, -50*w + 403]', '[9759, 9759, -65*w + 517]', '[9761, 9761, -14*w - 19]', '[9761, 9761, 31*w - 219]', '[9761, 9761, -114*w + 883]', '[9761, 9761, 14*w - 33]', '[9771, 9771, 35*w - 253]', '[9771, 9771, -100*w + 773]', '[9775, 1955, 25*w + 195]', '[9775, 1955, -15*w + 155]', '[9775, 1955, 15*w + 140]', '[9775, 1955, -25*w + 220]', '[9777, 9777, -16*w + 161]', '[9777, 9777, -181*w + 1415]', '[9781, 9781, -28*w + 241]', '[9781, 9781, -113*w + 887]', '[9787, 9787, 2*w - 101]', '[9787, 9787, -2*w - 99]', '[9788, 4894, -16*w - 54]', '[9788, 4894, 16*w - 70]', '[9792, 408, -48*w + 360]', '[9792, 408, -48*w - 312]', '[9799, 9799, 5*w - 108]', '[9799, 9799, -26*w + 227]', '[9799, 9799, -121*w + 949]', '[9799, 9799, -5*w - 103]', '[9801, 99, 99]', '[9801, 1089, 27*w + 207]', '[9801, 1089, -27*w + 234]', '[9804, 4902, 10*w + 118]', '[9804, 4902, 44*w + 314]', '[9804, 4902, 44*w - 358]', '[9804, 4902, 10*w - 128]', '[9808, 2452, -48*w + 388]', '[9808, 2452, -68*w + 540]', '[9809, 9809, 23*w - 147]', '[9809, 9809, 107*w + 721]', '[9809, 9809, 107*w - 828]', '[9809, 9809, 23*w + 124]', '[9812, 4906, 92*w + 618]', '[9812, 4906, 14*w - 32]', '[9812, 4906, 14*w + 18]', '[9812, 4906, 92*w - 710]', '[9813, 9813, 11*w - 133]', '[9813, 9813, -11*w - 122]', '[9817, 9817, -8*w - 111]', '[9817, 9817, 8*w - 119]', '[9819, 3273, -15*w - 39]', '[9819, 3273, 15*w - 54]', '[9823, 9823, 46*w + 327]', '[9823, 9823, -21*w - 172]', '[9823, 9823, 7*w + 108]', '[9823, 9823, 3*w - 103]', '[9823, 9823, -3*w - 100]', '[9823, 9823, -7*w + 115]', '[9823, 9823, 21*w - 193]', '[9823, 9823, -46*w + 373]', '[9833, 9833, -83*w + 639]', '[9833, 9833, 42*w - 311]', '[9839, 9839, -17*w - 66]', '[9839, 9839, 17*w - 83]', '[9847, 9847, -w - 99]', '[9847, 9847, -19*w - 161]', '[9847, 9847, 19*w - 180]', '[9847, 9847, w - 100]', '[9851, 9851, 20*w - 117]', '[9851, 9851, -20*w - 97]', '[9857, 9857, 18*w - 95]', '[9857, 9857, -18*w - 77]', '[9861, 9861, 49*w + 319]', '[9861, 9861, -14*w - 17]', '[9861, 9861, -14*w + 31]', '[9861, 9861, 49*w - 368]', '[9871, 9871, -98*w + 771]', '[9871, 9871, -33*w + 277]', '[9897, 9897, -173*w + 1345]', '[9897, 9897, 22*w - 137]', '[9900, 330, -30*w + 210]', '[9900, 330, -30*w - 180]', '[9901, 9901, -55*w + 441]', '[9901, 9901, -60*w + 479]', '[9907, 9907, 13*w - 144]', '[9907, 9907, -13*w - 131]', '[9908, 4954, -14*w - 16]', '[9908, 4954, 14*w - 30]', '[9909, 3303, -84*w + 663]', '[9909, 3303, -39*w + 321]', '[9911, 9911, -21*w - 106]', '[9911, 9911, 15*w + 38]', '[9911, 9911, 16*w - 69]', '[9911, 9911, 19*w + 87]', '[9911, 9911, -19*w + 106]', '[9911, 9911, -16*w - 53]', '[9911, 9911, -15*w + 53]', '[9911, 9911, 21*w - 127]', '[9924, 4962, -70*w + 536]', '[9924, 4962, 50*w - 376]', '[9936, 828, 24*w - 156]', '[9936, 828, 24*w + 132]', '[9948, 4974, -22*w + 200]', '[9948, 4974, -142*w + 1112]', '[9949, 9949, -91*w + 717]', '[9949, 9949, -36*w + 299]', '[9953, 9953, -14*w - 15]', '[9953, 9953, -82*w + 631]', '[9953, 9953, 43*w - 319]', '[9953, 9953, 14*w - 29]', '[9963, 1107, -99*w + 765]', '[9963, 1107, 36*w - 261]', '[9964, 4982, -6*w - 106]', '[9964, 4982, 4*w - 106]', '[9964, 4982, -4*w - 102]', '[9964, 4982, 6*w - 112]', '[9967, 9967, 9*w - 124]', '[9967, 9967, -9*w - 115]', '[9971, 767, -91*w + 702]', '[9971, 767, 39*w - 286]', '[9972, 1662, -18*w - 156]', '[9972, 1662, 18*w - 174]', '[9981, 3327, -69*w + 528]', '[9981, 3327, 51*w - 384]', '[9987, 9987, 17*w - 82]', '[9987, 9987, -17*w - 65]', '[9988, 4994, -2*w - 100]', '[9988, 4994, 102*w + 700]', '[9988, 4994, 102*w - 802]', '[9988, 4994, -2*w + 102]', '[9996, 714, -14*w - 14]', '[9996, 714, -14*w + 28]', '[10000, 100, 100]'], 'label': '2.2.213.1', 'narrow_class_no': 2, 'primes': ['[3, 3, w - 8]', '[4, 2, 2]', '[11, 11, -w + 7]', '[11, 11, -w - 6]', '[17, 17, -2*w + 15]', '[17, 17, -2*w - 13]', '[19, 19, -w - 8]', '[19, 19, -w + 9]', '[23, 23, -w - 5]', '[23, 23, -w + 6]', '[25, 5, 5]', '[37, 37, -w - 9]', '[37, 37, w - 10]', '[41, 41, -w - 3]', '[41, 41, w - 4]', '[43, 43, -2*w + 17]', '[43, 43, -7*w + 55]', '[47, 47, -w - 2]', '[47, 47, w - 3]', '[49, 7, -7]', '[53, 53, -w]', '[53, 53, w - 1]', '[59, 59, -7*w + 54]', '[59, 59, 3*w - 22]', '[71, 71, -5*w + 38]', '[73, 73, -3*w + 25]', '[73, 73, -8*w + 63]', '[79, 79, -w - 11]', '[79, 79, w - 12]', '[103, 103, -w - 12]', '[103, 103, w - 13]', '[109, 109, -4*w + 33]', '[109, 109, -9*w + 71]', '[113, 113, 2*w - 11]', '[113, 113, -2*w - 9]', '[137, 137, 3*w - 20]', '[137, 137, -3*w - 17]', '[149, 149, 2*w - 9]', '[149, 149, -2*w - 7]', '[151, 151, -5*w + 41]', '[151, 151, -10*w + 79]', '[157, 157, -w - 14]', '[157, 157, w - 15]', '[169, 13, -13]', '[173, 173, -3*w - 16]', '[173, 173, 3*w - 19]', '[197, 197, 2*w - 5]', '[197, 197, -2*w - 3]', '[199, 199, -6*w + 49]', '[199, 199, -11*w + 87]', '[223, 223, 3*w - 28]', '[223, 223, -3*w - 25]', '[227, 227, 4*w - 27]', '[227, 227, -4*w - 23]', '[229, 229, -15*w + 118]', '[229, 229, -5*w + 42]', '[239, 239, 3*w - 17]', '[239, 239, -3*w - 14]', '[257, 257, 7*w - 52]', '[257, 257, -13*w + 100]', '[269, 269, -3*w - 13]', '[269, 269, 3*w - 16]', '[271, 271, 2*w - 23]', '[271, 271, -2*w - 21]', '[277, 277, -3*w - 26]', '[277, 277, 3*w - 29]', '[281, 281, -11*w + 84]', '[281, 281, 9*w - 68]', '[313, 313, -8*w + 65]', '[313, 313, -13*w + 103]', '[317, 317, -19*w + 147]', '[317, 317, 6*w - 43]', '[347, 347, -3*w - 10]', '[347, 347, 3*w - 13]', '[353, 353, 7*w - 51]', '[353, 353, -18*w + 139]', '[367, 367, -w - 20]', '[367, 367, w - 21]', '[373, 373, 4*w - 37]', '[373, 373, -4*w - 33]', '[379, 379, -9*w + 73]', '[379, 379, -14*w + 111]', '[383, 383, -17*w + 131]', '[383, 383, 8*w - 59]', '[389, 389, 3*w - 11]', '[389, 389, -3*w - 8]', '[401, 401, -5*w - 28]', '[401, 401, 5*w - 33]', '[409, 409, -w - 21]', '[409, 409, w - 22]', '[443, 443, -12*w + 91]', '[443, 443, -13*w + 99]', '[449, 449, -3*w - 4]', '[449, 449, 3*w - 7]', '[461, 461, 5*w - 32]', '[461, 461, -5*w - 27]', '[463, 463, 2*w - 27]', '[463, 463, -2*w - 25]', '[467, 467, 3*w - 5]', '[467, 467, -3*w - 2]', '[479, 479, 3*w - 2]', '[479, 479, 3*w - 1]', '[491, 491, -4*w - 17]', '[491, 491, 4*w - 21]', '[499, 499, -w - 23]', '[499, 499, w - 24]', '[547, 547, -w - 24]', '[547, 547, w - 25]', '[563, 563, 4*w - 19]', '[563, 563, -4*w - 15]', '[571, 571, 2*w - 29]', '[571, 571, -2*w - 27]', '[577, 577, 3*w - 34]', '[577, 577, -3*w - 31]', '[599, 599, -27*w + 209]', '[599, 599, 8*w - 57]', '[613, 613, -12*w + 97]', '[613, 613, -17*w + 135]', '[643, 643, -3*w - 32]', '[643, 643, 3*w - 35]', '[653, 653, 9*w - 65]', '[653, 653, -26*w + 201]', '[683, 683, 4*w - 15]', '[683, 683, -4*w - 11]', '[701, 701, 10*w - 73]', '[701, 701, -25*w + 193]', '[739, 739, 5*w - 48]', '[739, 739, -5*w - 43]', '[743, 743, -24*w + 185]', '[743, 743, 11*w - 81]', '[761, 761, -6*w - 31]', '[761, 761, 6*w - 37]', '[773, 773, -31*w + 240]', '[773, 773, 9*w - 64]', '[787, 787, 6*w - 55]', '[787, 787, -6*w - 49]', '[809, 809, 13*w - 97]', '[809, 809, -22*w + 169]', '[811, 811, 2*w - 33]', '[811, 811, -2*w - 31]', '[827, 827, 4*w - 7]', '[827, 827, -4*w - 3]', '[829, 829, -4*w - 39]', '[829, 829, 4*w - 43]', '[841, 29, -29]', '[853, 853, -3*w - 35]', '[853, 853, 3*w - 38]', '[863, 863, 16*w - 121]', '[863, 863, -19*w + 145]', '[877, 877, -w - 30]', '[877, 877, w - 31]', '[887, 887, 7*w - 45]', '[887, 887, -7*w - 38]', '[911, 911, -5*w - 18]', '[911, 911, 5*w - 23]', '[961, 31, -31]', '[997, 997, 4*w - 45]', '[997, 997, -4*w - 41]']}
• 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': [-53, -1, 1], 'conductor': 213, 'degree': 2, 'dirichlet_group': [1, 212], 'disc_abs': 213, 'disc_rad': 213, 'disc_sign': 1, 'frobs': [[2, [[2, 1]]], [3, [0]], [5, [[2, 1]]], [7, [[2, 1]]], [11, [[1, 2]]], [13, [[2, 1]]], [17, [[1, 2]]], [19, [[1, 2]]], [23, [[1, 2]]], [29, [[2, 1]]], [31, [[2, 1]]], [37, [[1, 2]]], [41, [[1, 2]]], [43, [[1, 2]]], [47, [[1, 2]]], [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': 14.594519519326424, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '2.2.213.1', 'local_algs': ['3.2.1.2', '71.2.1.1'], 'monogenic': 1, 'num_ram': 2, 'r2': 0, 'ramps': [3, 71], 'rd': 14.5945195193, 'regulator': {'__RealLiteral__': 0, 'data': '4.29027173584', 'prec': 44}, 'res': {}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( 5 a + 34 \\)'], 'used_grh': False, 'zk': ['1', 'a']}