Hilbert modular form data - 3.3.697.1-17.1-f

Formats: - HTML - YAML - JSON - 2024-05-19T22:04:12.072151

• hmf_forms •

  Column	Type
  deg	smallint
  dimension	integer
  disc	bigint
  field_bad_primes	integer[]
  field_label	text
  is_CM	text
  is_base_change	text
  label	text
  label_nsuffix	smallint
  label_suffix	text
  level_bad_primes	integer[]
  level_ideal	text
  level_label	text
  level_norm	integer
  parallel_weight	smallint
  short_label	text
  weight	text

  
  {'deg': 3, 'dimension': 1, 'disc': 697, 'field_bad_primes': [17, 41], 'field_label': '3.3.697.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '3.3.697.1-17.1-f', 'label_nsuffix': 5, 'label_suffix': 'f', 'level_bad_primes': [17], 'level_ideal': '[17, 17, -w^2 + w + 8]', 'level_label': '17.1', 'level_norm': 17, 'parallel_weight': 2, 'short_label': '17.1-f', 'weight': '[2, 2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[17, 17, -w^2 + w + 8]', -1]], 'hecke_eigenvalues': [4, 1, 2, -4, -2, -2, 1, 2, -4, -6, 2, 8, 6, -6, 4, -2, 8, 6, 10, 12, -4, 6, 0, 12, -10, 10, 0, -12, -8, 20, 4, 2, -6, 22, -22, -16, -14, -6, -6, 2, -12, -24, -10, -10, -10, -8, 24, 12, -8, 22, -4, -4, 28, -10, 16, -6, -4, -22, 20, 30, 0, 18, 18, -6, -34, -20, -14, -8, 6, -32, -10, -16, 26, -4, 4, 4, -14, 6, 2, 2, -10, 16, -4, -26, -16, 30, 42, -12, 6, 2, 10, 2, -46, -20, -10, 10, -36, 40, -12, 12, 26, -12, 14, 20, 36, 24, -4, 42, 40, -14, 30, -36, -34, 20, -24, -20, -30, -34, -30, -8, 46, -32, 38, 24, -36, -24, -24, -4, 6, -54, -26, -42, 18, -16, 6, -2, -22, -24, 6, -22, 26, 10, 36, 42, 44, -26, 12, -12, 0, -16, 42, -38, -18, -26, 32, 48, 18, -52, -24, -26, -10, -8, -40, 58], 'hecke_polynomial': 'x', 'label': '3.3.697.1-17.1-f'}
• hmf_fields •

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

  
  {'degree': 3, 'discriminant': 697, 'ideals': ['[1, 1, 1]', '[5, 5, w]', '[8, 2, 2]', '[11, 11, -w^2 + 2*w + 4]', '[11, 11, -w + 2]', '[11, 11, w - 1]', '[13, 13, -w^2 + w + 4]', '[17, 17, -w^2 + w + 8]', '[17, 17, -w^2 + w + 3]', '[19, 19, -w^2 + 6]', '[23, 23, -w^2 + 3]', '[25, 5, w^2 - 7]', '[25, 25, w^2 - 2*w - 5]', '[27, 3, -3]', '[31, 31, w^2 - 2*w - 8]', '[37, 37, w^2 - 2*w - 6]', '[40, 10, 2*w]', '[41, 41, -w - 4]', '[41, 41, w^2 - 2*w - 7]', '[47, 47, 2*w^2 - 3*w - 7]', '[53, 53, -w^2 + w + 9]', '[55, 55, 2*w^2 - 3*w - 10]', '[55, 55, -w^2 + 2*w]', '[55, 55, 2*w^2 - w - 10]', '[61, 61, 3*w^2 - 2*w - 17]', '[64, 4, 4]', '[65, 65, w^2 - 3*w - 5]', '[67, 67, 2*w - 1]', '[73, 73, 2*w^2 - 2*w - 9]', '[85, 85, w^2 + w - 5]', '[85, 85, -w + 5]', '[88, 22, -2*w^2 + 4*w + 8]', '[88, 22, -2*w + 4]', '[88, 22, 2*w - 2]', '[89, 89, 2*w^2 - 3*w - 11]', '[95, 95, -w - 5]', '[97, 97, 2*w^2 - w - 9]', '[97, 97, w^2 - 3*w - 6]', '[97, 97, 2*w - 3]', '[101, 101, 3*w^2 - 4*w - 13]', '[104, 26, -2*w^2 + 2*w + 8]', '[107, 107, 2*w^2 - 3*w - 14]', '[113, 113, 2*w^2 - 3*w - 12]', '[115, 115, -w^2 + w + 10]', '[121, 11, -w^2 + 3*w + 9]', '[121, 11, w^2 + w - 6]', '[121, 11, -w^2 - 2*w + 3]', '[121, 121, 2*w^2 - 3*w - 13]', '[121, 121, w^2 - 2*w + 1]', '[121, 121, w^2 - 3*w - 7]', '[125, 5, 5]', '[125, 125, -2*w^2 + 2*w + 5]', '[127, 127, -w^2 + w - 1]', '[127, 127, 2*w^2 - 2*w - 7]', '[127, 127, w^2 + 3*w - 1]', '[131, 131, w^2 - 3*w - 8]', '[135, 15, -3*w]', '[136, 34, -2*w^2 + 2*w + 16]', '[136, 34, -2*w^2 + 2*w + 6]', '[137, 137, 2*w^2 - w - 8]', '[139, 139, 4*w^2 - 5*w - 19]', '[143, 143, w^2 - 2*w - 11]', '[143, 143, 2*w^2 - 4*w - 9]', '[143, 143, 2*w^2 - 7]', '[149, 149, w^2 + w - 7]', '[151, 151, w^2 - 4*w - 6]', '[152, 38, -2*w^2 + 12]', '[155, 155, -2*w^2 - w + 5]', '[157, 157, w^2 + w - 9]', '[163, 163, w^2 + w - 8]', '[169, 13, 2*w^2 - w - 7]', '[169, 169, -w + 6]', '[173, 173, w^2 - 5*w - 3]', '[179, 179, -w - 6]', '[184, 46, -2*w^2 + 6]', '[185, 185, -2*w^2 + w + 5]', '[187, 187, 2*w^2 - 13]', '[187, 187, 2*w^2 + w - 4]', '[187, 187, -2*w - 7]', '[187, 187, 2*w^2 - 5*w - 8]', '[187, 187, -w^2 - 2]', '[187, 187, 2*w^2 - w - 6]', '[191, 191, w^2 + 2*w - 4]', '[197, 197, 3*w - 1]', '[200, 10, 2*w^2 - 14]', '[200, 50, 2*w^2 - 4*w - 10]', '[205, 205, -w^2 - 4*w]', '[205, 205, -2*w^2 + 5]', '[209, 209, w^2 - w - 11]', '[209, 209, w^2 - 4*w - 7]', '[209, 209, -3*w^2 + 3*w + 14]', '[216, 6, -6]', '[221, 221, w^2 - 2*w + 2]', '[221, 221, w^2 + 3*w - 2]', '[229, 229, 3*w^2 - 4*w - 18]', '[233, 233, -w^2 + w - 2]', '[233, 233, -3*w^2 + 4*w + 11]', '[233, 233, 3*w^2 - w - 14]', '[235, 235, -3*w^2 + 7*w + 10]', '[239, 239, 3*w^2 - 5*w - 14]', '[241, 241, w^2 - 4*w - 11]', '[247, 247, -3*w^2 + 4*w + 19]', '[248, 62, 2*w^2 - 4*w - 16]', '[253, 253, -2*w^2 + 4*w + 11]', '[253, 253, w^2 - 4*w - 8]', '[253, 253, -3*w + 2]', '[257, 257, -2*w^2 + 2*w + 17]', '[263, 263, 3*w^2 - 3*w - 23]', '[265, 265, w^2 + 2*w - 5]', '[269, 269, w^2 - 2*w - 12]', '[275, 55, w^2 - 5*w - 2]', '[275, 55, -2*w^2 + 5*w + 9]', '[275, 55, -w^2 + 12]', '[275, 275, -3*w^2 + 4*w + 10]', '[275, 275, -w^2 + 4*w + 10]', '[275, 275, -2*w^2 - w + 10]', '[277, 277, w^2 - 4*w - 9]', '[281, 281, 4*w^2 - 2*w - 21]', '[283, 283, 3*w^2 - 3*w - 13]', '[289, 17, -3*w^2 + 2*w + 14]', '[289, 17, 2*w^2 - 3*w - 1]', '[289, 289, -w + 7]', '[293, 293, 3*w^2 - 4*w - 9]', '[296, 74, 2*w^2 - 4*w - 12]', '[297, 33, 3*w^2 - 6*w - 12]', '[297, 33, 3*w - 6]', '[297, 33, -3*w + 3]', '[299, 299, w + 7]', '[305, 305, -2*w^2 + 4*w + 15]', '[320, 20, 4*w]', '[323, 323, -3*w + 4]', '[323, 323, -2*w^2 + 4*w + 13]', '[325, 65, w^2 + 3]', '[325, 325, 3*w - 5]', '[328, 82, -2*w - 8]', '[328, 82, 2*w^2 - 4*w - 14]', '[331, 331, w^2 + 3*w - 3]', '[335, 335, 2*w^2 - w]', '[337, 337, w^2 + 2*w - 6]', '[341, 341, w^2 - w - 12]', '[341, 341, -3*w^2 + w + 13]', '[341, 341, 4*w^2 - 3*w - 21]', '[343, 7, -7]', '[351, 39, 3*w^2 - 3*w - 12]', '[361, 19, w^2 - 5*w - 1]', '[361, 361, w^2 - 2*w + 3]', '[365, 365, -2*w^2 + 5*w + 10]', '[367, 367, w^2 - 5*w - 8]', '[373, 373, w^2 + 2*w - 16]', '[373, 373, 2*w^2 + w - 11]', '[373, 373, 3*w^2 - 2*w - 13]', '[376, 94, 4*w^2 - 6*w - 14]', '[379, 379, -w^2 + w - 3]', '[383, 383, 2*w^2 - 6*w - 9]', '[391, 391, -3*w^2 + 3*w + 7]', '[391, 391, w^2 + w + 4]', '[401, 401, w^2 + 2*w - 7]', '[403, 403, 3*w^2 - 17]', '[407, 407, 4*w^2 - 5*w - 17]', '[407, 407, -3*w^2 + 3*w + 11]', '[407, 407, -w^2 + 3*w - 4]', '[419, 419, 3*w^2 - 6*w - 13]', '[421, 421, 4*w^2 - 5*w - 26]', '[424, 106, -2*w^2 + 2*w + 18]', '[425, 85, -3*w^2 + 11]', '[425, 85, 3*w^2 - 5*w - 16]', '[425, 425, -w^2 + 5*w]', '[425, 425, 4*w^2 - 5*w - 25]', '[431, 431, 4*w - 1]', '[437, 437, 2*w - 9]', '[439, 439, w^2 - 5*w - 9]', '[439, 439, w^2 - 2*w - 13]', '[439, 439, 4*w^2 - 7*w - 17]', '[440, 110, 4*w^2 - 6*w - 20]', '[440, 110, -2*w^2 + 4*w]', '[440, 110, 4*w^2 - 2*w - 20]', '[443, 443, 3*w^2 - 3*w - 8]', '[443, 443, w^2 - 13]', '[443, 443, 3*w^2 - w - 12]', '[445, 445, -3*w^2 + 3*w + 10]', '[449, 449, 4*w^2 - 6*w - 13]', '[451, 451, w^2 + 2*w - 8]', '[451, 451, 2*w^2 - 5*w - 11]', '[451, 451, -3*w^2 + 2*w + 12]', '[451, 451, 4*w^2 - 4*w - 19]', '[451, 451, -w^2 - 3*w + 4]', '[451, 451, w - 8]', '[457, 457, w^2 + 2*w - 11]', '[459, 51, 3*w^2 - 3*w - 24]', '[459, 51, 3*w^2 - 3*w - 9]', '[461, 461, -w - 8]', '[461, 461, -w^2 + 5*w - 1]', '[461, 461, 2*w^2 + w - 12]', '[463, 463, 3*w^2 + w - 9]', '[475, 95, -w^2 + 5*w + 12]', '[475, 475, 4*w^2 - 3*w - 20]', '[481, 481, w^2 + 2*w - 9]', '[485, 485, -3*w^2 + w + 5]', '[485, 485, -w^2 + 5*w + 10]', '[485, 485, 2*w^2 - 3*w]', '[487, 487, 5*w^2 - 3*w - 27]', '[488, 122, 6*w^2 - 4*w - 34]', '[499, 499, 4*w^2 - w - 24]', '[499, 499, w^2 - 5*w - 11]', '[499, 499, 5*w^2 - 4*w - 27]', '[503, 503, 3*w^2 - 5*w - 22]', '[503, 503, 3*w^2 - 5*w - 17]', '[503, 503, 5*w^2 - 8*w - 22]', '[505, 505, -4*w^2 + 8*w + 15]', '[509, 509, -w^2 - 4]', '[512, 8, 8]', '[513, 57, 3*w^2 - 18]', '[517, 517, 7*w^2 - 13*w - 24]', '[517, 517, -5*w^2 + 10*w + 17]', '[517, 517, -5*w^2 + 13*w + 7]', '[520, 130, 2*w^2 - 6*w - 10]', '[527, 527, 7*w^2 - 8*w - 49]', '[527, 527, 2*w^2 + 2*w - 9]', '[529, 23, 4*w^2 - 5*w - 16]', '[529, 529, 3*w^2 - 7*w - 12]', '[533, 533, 2*w^2 + w - 13]', '[533, 533, 3*w^2 - w - 11]', '[535, 535, -3*w^2 + 10]', '[536, 134, 4*w - 2]', '[541, 541, 2*w^2 + w - 17]', '[547, 547, -w^2 + 2*w - 4]', '[547, 547, 3*w^2 - 6*w - 14]', '[547, 547, 2*w^2 - 5*w - 17]', '[557, 557, 5*w^2 - 2*w - 31]', '[563, 563, 3*w^2 - 5*w - 18]', '[565, 565, -3*w^2 + 2*w + 10]', '[571, 571, -w^2 + w - 4]', '[571, 571, w^2 - 6*w - 2]', '[571, 571, 3*w^2 + w - 8]', '[575, 115, 3*w^2 - 5*w - 21]', '[575, 575, w^2 + 3*w - 5]', '[577, 577, 2*w^2 - w - 19]', '[583, 583, -3*w^2 + 23]', '[583, 583, -4*w^2 + 6*w + 21]', '[583, 583, 2*w^2 + w - 14]', '[584, 146, 4*w^2 - 4*w - 18]', '[587, 587, 2*w^2 - 5*w - 13]', '[589, 589, 7*w^2 - 3*w - 38]', '[593, 593, 2*w^2 + w - 16]', '[599, 599, 3*w^2 - 19]', '[599, 599, 3*w^2 - 5*w - 19]', '[599, 599, 4*w^2 - w - 18]', '[605, 55, w^2 + w + 5]', '[605, 55, -3*w^2 + 5*w + 20]', '[605, 55, -4*w^2 + w + 25]', '[605, 605, -3*w^2 + w + 10]', '[605, 605, 2*w^2 + w - 15]', '[605, 605, 3*w^2 + w - 15]', '[607, 607, 4*w^2 - 2*w - 19]', '[611, 611, -2*w^2 + 6*w - 3]', '[617, 617, 4*w^2 - 3*w - 19]', '[619, 619, 4*w^2 - 7*w - 18]', '[621, 69, 3*w^2 - 9]', '[625, 25, 5*w]', '[625, 25, 2*w^2 - 5*w - 14]', '[625, 625, w^2 - 3*w + 5]', '[629, 629, 5*w^2 - 6*w - 33]', '[629, 629, 4*w - 3]', '[635, 635, -2*w^2 + 7*w + 10]', '[635, 635, w^2 - 8*w - 5]', '[635, 635, 3*w^2 + 6*w + 5]', '[643, 643, 3*w^2 + w - 7]', '[643, 643, 2*w^2 - 2*w - 19]', '[643, 643, 5*w^2 - 8*w - 16]', '[653, 653, 3*w^2 - w - 9]', '[653, 653, 2*w^2 - 6*w - 11]', '[653, 653, 3*w^2 - w - 7]', '[655, 655, -3*w^2 - w + 5]', '[659, 659, w^2 - 2*w - 14]', '[661, 661, 5*w^2 - 6*w - 31]', '[661, 661, w^2 - 14]', '[661, 661, w - 9]', '[671, 671, 8*w^2 - 8*w - 49]', '[671, 671, -5*w^2 + 6*w + 32]', '[671, 671, 4*w^2 - w - 28]', '[673, 673, -2*w^2 + 4*w - 1]', '[673, 673, 4*w^2 - w - 26]', '[673, 673, 6*w^2 - 5*w - 33]', '[675, 15, -3*w^2 + 21]', '[675, 75, -3*w^2 + 6*w + 15]', '[677, 677, 3*w^2 - 8]', '[680, 170, 2*w^2 + 2*w - 10]', '[680, 170, -2*w + 10]', '[685, 685, -w^2 + 6*w + 10]', '[689, 689, -5*w^2 + 4*w + 26]', '[695, 695, -5*w^2 + 9*w + 20]', '[697, 697, 6*w^2 - 7*w - 41]', '[697, 697, 3*w^2 - 7]', '[697, 697, 3*w^2 - 5*w - 27]', '[697, 697, w^2 + 3*w - 6]', '[703, 703, 5*w^2 - 3*w - 26]', '[704, 44, -4*w^2 + 8*w + 16]', '[704, 44, -4*w + 8]', '[704, 44, 4*w - 4]', '[712, 178, 4*w^2 - 6*w - 22]', '[713, 713, 4*w^2 + 3*w - 14]', '[715, 715, -2*w^2 - 4*w + 5]', '[715, 715, 3*w^2 - 3*w - 25]', '[715, 715, -4*w^2 + 5*w + 10]', '[719, 719, 6*w^2 - 7*w - 29]', '[719, 719, 4*w^2 - 6*w - 29]', '[719, 719, 4*w^2 - 5*w - 14]', '[727, 727, 4*w^2 - 4*w - 31]', '[729, 9, -9]', '[737, 737, 5*w^2 - 8*w - 14]', '[737, 737, -2*w^2 + 5*w - 2]', '[737, 737, 2*w^2 - 3*w + 1]', '[743, 743, w^2 - w - 14]', '[745, 745, w^2 + 5]', '[755, 755, -4*w^2 + w + 5]', '[757, 757, 5*w^2 - 8*w - 23]', '[760, 190, -2*w - 10]', '[761, 761, w^2 - 6*w - 11]', '[761, 761, 4*w - 7]', '[761, 761, 4*w^2 - 3*w - 18]', '[773, 773, -5*w^2 + 10*w + 18]', '[775, 155, -8*w^2 + 5*w + 46]', '[775, 775, -2*w^2 + 3*w + 20]', '[776, 194, 4*w^2 - 2*w - 18]', '[776, 194, 2*w^2 - 6*w - 12]', '[776, 194, 4*w - 6]', '[779, 779, 4*w^2 + w - 19]', '[779, 779, 6*w^2 - 3*w - 32]', '[785, 785, w^2 - 2*w + 5]', '[787, 787, 5*w^2 - 7*w - 19]', '[793, 793, 6*w^2 - 5*w - 43]', '[797, 797, 4*w^2 - 5*w - 12]', '[797, 797, 3*w^2 + w - 16]', '[797, 797, 3*w^2 - 6*w - 16]', '[799, 799, -4*w^2 + 9*w + 4]', '[799, 799, 6*w^2 - 6*w - 31]', '[803, 803, -w^2 + 6*w - 6]', '[803, 803, -4*w^2 + 7*w + 19]', '[803, 803, 6*w^2 - 9*w - 28]', '[808, 202, 6*w^2 - 8*w - 26]', '[811, 811, w^2 + 3*w - 7]', '[815, 815, w^2 - w + 5]', '[821, 821, 4*w^2 - 6*w - 23]', '[829, 829, 2*w^2 + 2*w - 11]', '[829, 829, 2*w^2 - 7*w - 11]', '[829, 829, 5*w^2 - 5*w - 24]', '[832, 52, -4*w^2 + 4*w + 16]', '[837, 93, 3*w^2 - 6*w - 24]', '[845, 65, -w^2 + 7*w + 10]', '[845, 845, -w^2 + 6*w]', '[851, 851, 2*w^2 + 3*w - 8]', '[853, 853, 2*w^2 - 6*w - 19]', '[856, 214, 4*w^2 - 6*w - 28]', '[857, 857, w^2 + 4*w - 4]', '[865, 865, -5*w^2 + 4*w + 5]', '[871, 871, 3*w^2 - 7*w - 14]', '[877, 877, -w^2 - w - 6]', '[881, 881, -4*w^2 + 4*w + 9]', '[883, 883, 2*w^2 - 6*w - 13]', '[893, 893, 5*w^2 - 7*w - 27]', '[895, 895, -w^2 - 6*w]', '[901, 901, -9*w^2 + 8*w + 62]', '[901, 901, -4*w^2 + 3*w + 17]', '[904, 226, 4*w^2 - 6*w - 24]', '[907, 907, 3*w^2 - 6*w - 17]', '[911, 911, w^2 + 3*w - 8]', '[919, 919, 4*w^2 - 8*w - 17]', '[920, 230, -2*w^2 + 2*w + 20]', '[925, 185, -6*w^2 + 5*w + 32]', '[925, 925, -w + 10]', '[935, 935, w + 10]', '[935, 935, w^2 - 2*w - 15]', '[935, 935, w^2 - 15]', '[935, 935, -4*w^2 + 15]', '[935, 935, 4*w^2 - 4*w - 15]', '[935, 935, 5*w^2 - 3*w - 25]', '[937, 937, 4*w^2 - 6*w - 27]', '[941, 941, 4*w^2 - 2*w - 17]', '[943, 943, 4*w^2 + 4*w - 7]', '[943, 943, 3*w^2 + 3*w - 11]', '[947, 947, 3*w^2 - 8*w - 13]', '[949, 949, w^2 + w - 16]', '[955, 955, 2*w^2 + 3*w + 5]', '[961, 31, 6*w^2 - 7*w - 39]', '[961, 961, 6*w^2 - 7*w - 37]', '[967, 967, 5*w - 2]', '[968, 22, -2*w^2 + 6*w + 18]', '[968, 22, 2*w^2 + 2*w - 12]', '[968, 22, -2*w^2 - 4*w + 6]', '[968, 242, 4*w^2 - 6*w - 26]', '[968, 242, 2*w^2 - 4*w + 2]', '[968, 242, 2*w^2 - 6*w - 14]', '[971, 971, 5*w^2 - 9*w - 21]', '[977, 977, 3*w^2 + w - 17]', '[979, 979, -w^2 + 5*w - 9]', '[979, 979, 7*w^2 - 9*w - 32]', '[979, 979, -5*w^2 + 6*w + 21]', '[983, 983, 2*w - 11]', '[985, 985, 3*w^2 - w]', '[991, 991, 6*w^2 - 7*w - 38]', '[991, 991, w^2 + 3*w - 9]', '[991, 991, w^2 + 3*w - 13]', '[997, 997, 4*w^2 - w - 16]', '[997, 997, 5*w - 12]', '[997, 997, 3*w^2 - 2*w - 26]', '[999, 111, 3*w^2 - 6*w - 18]', '[1000, 10, 10]', '[1000, 250, -4*w^2 + 4*w + 10]', '[1007, 1007, -8*w^2 + 4*w + 49]', '[1009, 1009, -w^2 + 6*w - 4]', '[1013, 1013, 5*w^2 - 8*w - 24]', '[1013, 1013, 2*w^2 - 7*w - 12]', '[1013, 1013, w^2 - 3*w - 16]', '[1016, 254, -2*w^2 + 2*w - 2]', '[1016, 254, 4*w^2 - 4*w - 14]', '[1016, 254, 2*w^2 + 6*w - 2]', '[1019, 1019, w^2 - 7*w - 2]', '[1025, 205, -4*w^2 + 23]', '[1025, 205, -7*w^2 + 5*w + 39]', '[1025, 1025, -w^2 + w + 15]', '[1025, 1025, -2*w^2 + 6*w + 15]', '[1031, 1031, 4*w^2 - 3*w - 16]', '[1031, 1031, -w^2 + 6*w - 3]', '[1031, 1031, 2*w^2 - 6*w - 17]', '[1037, 1037, 3*w^2 - 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14*w - 43]', '[9931, 9931, 5*w^2 - 16*w - 26]', '[9935, 9935, 6*w^2 - 22*w - 15]', '[9941, 9941, -11*w^2 + 23*w + 39]', '[9943, 9943, 11*w^2 - 21*w - 43]', '[9944, 2486, 6*w - 26]', '[9944, 2486, 14*w^2 - 16*w - 68]', '[9944, 2486, -10*w^2 + 10*w + 44]', '[9949, 9949, 5*w^2 - 14*w - 29]', '[9953, 9953, 7*w^2 - 13*w - 52]', '[9967, 9967, 6*w^2 - 13*w - 36]', '[9973, 9973, w^2 - 5*w - 28]', '[9977, 9977, 12*w^2 - 16*w - 49]', '[9977, 9977, -4*w^2 + 11*w - 8]', '[9977, 9977, -9*w^2 + 10*w + 32]', '[9979, 9979, 11*w - 4]', '[9979, 9979, 10*w^2 - 14*w - 69]', '[9983, 9983, -w^2 + w - 17]', '[9985, 9985, -3*w^2 - 14*w]', '[9992, 2498, 2*w - 22]', '[9995, 9995, -3*w^2 - 9*w + 10]'], 'label': '3.3.697.1', 'narrow_class_no': 2, 'primes': ['[5, 5, w]', '[8, 2, 2]', '[11, 11, -w^2 + 2*w + 4]', '[11, 11, -w + 2]', '[11, 11, w - 1]', '[13, 13, -w^2 + w + 4]', '[17, 17, -w^2 + w + 8]', '[17, 17, -w^2 + w + 3]', '[19, 19, -w^2 + 6]', '[23, 23, -w^2 + 3]', '[25, 5, w^2 - 7]', '[27, 3, -3]', '[31, 31, w^2 - 2*w - 8]', '[37, 37, w^2 - 2*w - 6]', '[41, 41, -w - 4]', '[41, 41, w^2 - 2*w - 7]', '[47, 47, 2*w^2 - 3*w - 7]', '[53, 53, -w^2 + w + 9]', '[61, 61, 3*w^2 - 2*w - 17]', '[67, 67, 2*w - 1]', '[73, 73, 2*w^2 - 2*w - 9]', '[89, 89, 2*w^2 - 3*w - 11]', '[97, 97, 2*w^2 - w - 9]', '[97, 97, w^2 - 3*w - 6]', '[97, 97, 2*w - 3]', '[101, 101, 3*w^2 - 4*w - 13]', '[107, 107, 2*w^2 - 3*w - 14]', '[113, 113, 2*w^2 - 3*w - 12]', '[127, 127, -w^2 + w - 1]', '[127, 127, 2*w^2 - 2*w - 7]', '[127, 127, w^2 + 3*w - 1]', '[131, 131, w^2 - 3*w - 8]', '[137, 137, 2*w^2 - w - 8]', '[139, 139, 4*w^2 - 5*w - 19]', '[149, 149, w^2 + w - 7]', '[151, 151, w^2 - 4*w - 6]', '[157, 157, w^2 + w - 9]', '[163, 163, w^2 + w - 8]', '[169, 13, 2*w^2 - w - 7]', '[173, 173, w^2 - 5*w - 3]', '[179, 179, -w - 6]', '[191, 191, w^2 + 2*w - 4]', '[197, 197, 3*w - 1]', '[229, 229, 3*w^2 - 4*w - 18]', '[233, 233, -w^2 + w - 2]', '[233, 233, -3*w^2 + 4*w + 11]', '[233, 233, 3*w^2 - w - 14]', '[239, 239, 3*w^2 - 5*w - 14]', '[241, 241, w^2 - 4*w - 11]', '[257, 257, -2*w^2 + 2*w + 17]', '[263, 263, 3*w^2 - 3*w - 23]', '[269, 269, w^2 - 2*w - 12]', '[277, 277, w^2 - 4*w - 9]', '[281, 281, 4*w^2 - 2*w - 21]', '[283, 283, 3*w^2 - 3*w - 13]', '[293, 293, 3*w^2 - 4*w - 9]', '[331, 331, w^2 + 3*w - 3]', '[337, 337, w^2 + 2*w - 6]', '[343, 7, -7]', '[361, 19, w^2 - 5*w - 1]', '[367, 367, w^2 - 5*w - 8]', '[373, 373, w^2 + 2*w - 16]', '[373, 373, 2*w^2 + w - 11]', '[373, 373, 3*w^2 - 2*w - 13]', '[379, 379, -w^2 + w - 3]', '[383, 383, 2*w^2 - 6*w - 9]', '[401, 401, w^2 + 2*w - 7]', '[419, 419, 3*w^2 - 6*w - 13]', '[421, 421, 4*w^2 - 5*w - 26]', '[431, 431, 4*w - 1]', '[439, 439, w^2 - 5*w - 9]', '[439, 439, w^2 - 2*w - 13]', '[439, 439, 4*w^2 - 7*w - 17]', '[443, 443, 3*w^2 - 3*w - 8]', '[443, 443, w^2 - 13]', '[443, 443, 3*w^2 - w - 12]', '[449, 449, 4*w^2 - 6*w - 13]', '[457, 457, w^2 + 2*w - 11]', '[461, 461, -w - 8]', '[461, 461, -w^2 + 5*w - 1]', '[461, 461, 2*w^2 + w - 12]', '[463, 463, 3*w^2 + w - 9]', '[487, 487, 5*w^2 - 3*w - 27]', '[499, 499, 4*w^2 - w - 24]', '[499, 499, w^2 - 5*w - 11]', '[499, 499, 5*w^2 - 4*w - 27]', '[503, 503, 3*w^2 - 5*w - 22]', '[503, 503, 3*w^2 - 5*w - 17]', '[503, 503, 5*w^2 - 8*w - 22]', '[509, 509, -w^2 - 4]', '[529, 23, 4*w^2 - 5*w - 16]', '[541, 541, 2*w^2 + w - 17]', '[547, 547, -w^2 + 2*w - 4]', '[547, 547, 3*w^2 - 6*w - 14]', '[547, 547, 2*w^2 - 5*w - 17]', '[557, 557, 5*w^2 - 2*w - 31]', '[563, 563, 3*w^2 - 5*w - 18]', '[571, 571, -w^2 + w - 4]', '[571, 571, w^2 - 6*w - 2]', '[571, 571, 3*w^2 + w - 8]', '[577, 577, 2*w^2 - w - 19]', '[587, 587, 2*w^2 - 5*w - 13]', '[593, 593, 2*w^2 + w - 16]', '[599, 599, 3*w^2 - 19]', '[599, 599, 3*w^2 - 5*w - 19]', '[599, 599, 4*w^2 - w - 18]', '[607, 607, 4*w^2 - 2*w - 19]', '[617, 617, 4*w^2 - 3*w - 19]', '[619, 619, 4*w^2 - 7*w - 18]', '[643, 643, 3*w^2 + w - 7]', '[643, 643, 2*w^2 - 2*w - 19]', '[643, 643, 5*w^2 - 8*w - 16]', '[653, 653, 3*w^2 - w - 9]', '[653, 653, 2*w^2 - 6*w - 11]', '[653, 653, 3*w^2 - w - 7]', '[659, 659, w^2 - 2*w - 14]', '[661, 661, 5*w^2 - 6*w - 31]', '[661, 661, w^2 - 14]', '[661, 661, w - 9]', '[673, 673, -2*w^2 + 4*w - 1]', '[673, 673, 4*w^2 - w - 26]', '[673, 673, 6*w^2 - 5*w - 33]', '[677, 677, 3*w^2 - 8]', '[719, 719, 6*w^2 - 7*w - 29]', '[719, 719, 4*w^2 - 6*w - 29]', '[719, 719, 4*w^2 - 5*w - 14]', '[727, 727, 4*w^2 - 4*w - 31]', '[743, 743, w^2 - w - 14]', '[757, 757, 5*w^2 - 8*w - 23]', '[761, 761, w^2 - 6*w - 11]', '[761, 761, 4*w - 7]', '[761, 761, 4*w^2 - 3*w - 18]', '[773, 773, -5*w^2 + 10*w + 18]', '[787, 787, 5*w^2 - 7*w - 19]', '[797, 797, 4*w^2 - 5*w - 12]', '[797, 797, 3*w^2 + w - 16]', '[797, 797, 3*w^2 - 6*w - 16]', '[811, 811, w^2 + 3*w - 7]', '[821, 821, 4*w^2 - 6*w - 23]', '[829, 829, 2*w^2 + 2*w - 11]', '[829, 829, 2*w^2 - 7*w - 11]', '[829, 829, 5*w^2 - 5*w - 24]', '[853, 853, 2*w^2 - 6*w - 19]', '[857, 857, w^2 + 4*w - 4]', '[877, 877, -w^2 - w - 6]', '[881, 881, -4*w^2 + 4*w + 9]', '[883, 883, 2*w^2 - 6*w - 13]', '[907, 907, 3*w^2 - 6*w - 17]', '[911, 911, w^2 + 3*w - 8]', '[919, 919, 4*w^2 - 8*w - 17]', '[937, 937, 4*w^2 - 6*w - 27]', '[941, 941, 4*w^2 - 2*w - 17]', '[947, 947, 3*w^2 - 8*w - 13]', '[961, 31, 6*w^2 - 7*w - 39]', '[967, 967, 5*w - 2]', '[971, 971, 5*w^2 - 9*w - 21]', '[977, 977, 3*w^2 + w - 17]', '[983, 983, 2*w - 11]', '[991, 991, 6*w^2 - 7*w - 38]', '[991, 991, w^2 + 3*w - 9]', '[991, 991, w^2 + 3*w - 13]', '[997, 997, 4*w^2 - w - 16]', '[997, 997, 5*w - 12]', '[997, 997, 3*w^2 - 2*w - 26]']}
• 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, -7, 0, 1], 'conductor': 0, 'degree': 3, 'dirichlet_group': [], 'disc_abs': 697, 'disc_rad': 697, 'disc_sign': 1, 'frobs': [[2, [[3, 1]]], [3, [[3, 1]]], [5, [[2, 1], [1, 1]]], [7, [[3, 1]]], [11, [[1, 3]]], [13, [[2, 1], [1, 1]]], [17, [0]], [19, [[2, 1], [1, 1]]], [23, [[2, 1], [1, 1]]], [29, [[3, 1]]], [31, [[2, 1], [1, 1]]], [37, [[2, 1], [1, 1]]], [41, [0]], [43, [[3, 1]]], [47, [[2, 1], [1, 1]]], [53, [[2, 1], [1, 1]]], [59, [[3, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [3, 3], 'galois_label': '3T2', 'galt': 2, 'grd': 26.40075756488817, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '3.3.697.1', 'local_algs': ['17.1.0.1', '17.2.1.2', '41.1.0.1', '41.2.1.2'], 'monogenic': 1, 'num_ram': 2, 'r2': 0, 'ramps': [17, 41], 'rd': 8.86633751079, 'regulator': {'__RealLiteral__': 0, 'data': '2.71184965988', 'prec': 44}, 'res': {'gal': ['1,-29,34,31,-28,-2,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a^{2} - a - 6 \\)', '\\( a + 2 \\)'], 'unitsGmodule': [[3, 1], [5, 1]], 'used_grh': False, 'zk': ['1', 'a', 'a^2']}