Hilbert modular form data - 2.2.221.1-9.1-d

Formats: - HTML - YAML - JSON - 2024-05-22T20:19:14.221528

• 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': 221, 'field_bad_primes': [13, 17], 'field_label': '2.2.221.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '2.2.221.1-9.1-d', 'label_nsuffix': 3, 'label_suffix': 'd', 'level_bad_primes': [3], 'level_ideal': '[9, 3, 3]', 'level_label': '9.1', 'level_norm': 9, 'parallel_weight': 2, 'short_label': '9.1-d', 'weight': '[2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[9, 3, 3]', 1]], 'hecke_eigenvalues': [-3, 0, 0, 4, -4, -1, -4, 4, -2, 2, 4, -4, 8, -8, 8, -8, 4, 4, -6, -6, 12, -12, 0, 0, 16, -16, -6, -6, 0, 0, -8, 8, 8, 8, 2, 2, -20, 20, -12, 12, 4, 4, 8, 8, 0, 0, -16, 16, 12, -12, -16, 16, 12, 12, 2, 2, 24, 24, -32, 32, -22, 26, 26, -20, 20, 6, 6, -8, 8, 24, -24, 20, -20, -2, -2, 20, 20, 8, -8, -4, -4, -12, 12, -4, 4, 20, 20, 36, -36, 12, 12, 30, 40, -40, 44, 44, -26, -26, -8, -8, -24, 24, -36, 36, -4, 4, 32, 32, 4, 4, -12, 12, -20, 20, 34, 34, -40, 40, -8, -8, -36, 36, -38, -38, 12, -12, -18, -18, 4, -4, -32, 32, 12, -12, 2, 2, -44, 44, 58, -24, 24, 4, 4, 40, -40, 20, 20, -24, -24, -24, 24, 26, 26, 48, -48, 12, -12, -42, -42, 36, 36, -20, 20], 'hecke_polynomial': 'x', 'label': '2.2.221.1-9.1-d'}
• hmf_fields •

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

  
  {'degree': 2, 'discriminant': 221, 'ideals': ['[1, 1, 1]', '[4, 2, 2]', '[5, 5, w]', '[5, 5, w + 4]', '[7, 7, w + 2]', '[7, 7, w + 4]', '[9, 3, 3]', '[11, 11, w]', '[11, 11, w + 10]', '[13, 13, w + 6]', '[16, 4, 4]', '[17, 17, -w - 8]', '[20, 10, 2*w]', '[20, 10, 2*w + 8]', '[25, 5, 5]', '[25, 25, -w - 5]', '[25, 25, -w + 6]', '[28, 14, 2*w + 4]', '[28, 14, 2*w + 8]', '[31, 31, w + 14]', '[31, 31, w + 16]', '[35, 35, -w - 4]', '[35, 35, w + 9]', '[35, 35, -w + 10]', '[35, 35, -w + 5]', '[36, 6, 6]', '[37, 37, w + 15]', '[37, 37, w + 21]', '[41, 41, w + 18]', '[41, 41, w + 22]', '[43, 43, -w - 3]', '[43, 43, w - 4]', '[44, 22, 2*w]', '[44, 22, 2*w + 20]', '[45, 15, 3*w]', '[45, 15, 3*w + 12]', '[49, 7, 7]', '[49, 49, -w - 2]', '[49, 49, -w + 3]', '[52, 26, 2*w + 12]', '[53, 53, -w - 1]', '[53, 53, w - 2]', '[55, 55, w]', '[55, 55, -w - 10]', '[55, 55, w - 11]', '[55, 55, w - 1]', '[63, 21, 3*w + 6]', '[63, 21, 3*w + 12]', '[64, 8, 8]', '[65, 65, w + 19]', '[65, 65, w + 45]', '[68, 34, -2*w - 16]', '[71, 71, w + 23]', '[71, 71, w + 47]', '[73, 73, w + 20]', '[73, 73, w + 52]', '[77, 77, -w - 11]', '[77, 77, 2*w - 13]', '[77, 77, 2*w + 11]', '[77, 77, w - 12]', '[80, 20, 4*w]', '[80, 20, 4*w + 16]', '[81, 9, 9]', '[85, 85, w + 25]', '[85, 85, w + 59]', '[91, 91, w + 32]', '[91, 91, w + 58]', '[97, 97, w + 33]', '[97, 97, w + 63]', '[99, 33, 3*w]', '[99, 33, 3*w + 30]', '[100, 10, 10]', '[100, 50, -2*w - 10]', '[100, 50, -2*w + 12]', '[101, 101, -w - 12]', '[101, 101, w - 13]', '[103, 103, 2*w - 19]', '[103, 103, -2*w - 17]', '[109, 109, w + 24]', '[109, 109, w + 84]', '[112, 28, 4*w + 8]', '[112, 28, 4*w + 16]', '[117, 39, 3*w + 18]', '[119, 119, w + 25]', '[119, 119, w + 93]', '[121, 11, 11]', '[121, 121, -2*w + 11]', '[121, 121, -2*w - 9]', '[124, 62, 2*w + 28]', '[124, 62, 2*w + 32]', '[125, 25, 5*w]', '[125, 25, 5*w + 20]', '[125, 125, w + 30]', '[125, 125, w + 94]', '[127, 127, -w - 13]', '[127, 127, w - 14]', '[140, 70, -2*w - 8]', '[140, 70, 2*w + 18]', '[140, 70, -2*w + 20]', '[140, 70, -2*w + 10]', '[143, 143, w + 32]', '[143, 143, w + 110]', '[144, 12, 12]', '[148, 74, 2*w + 30]', '[148, 74, 2*w + 42]', '[153, 51, -3*w - 24]', '[155, 155, -w - 14]', '[155, 155, 3*w - 20]', '[155, 155, 3*w + 17]', '[155, 155, w - 15]', '[157, 157, 2*w - 9]', '[157, 157, -2*w - 7]', '[163, 163, w + 29]', '[163, 163, w + 133]', '[164, 82, 2*w + 36]', '[164, 82, 2*w + 44]', '[167, 167, w + 43]', '[167, 167, w + 123]', '[169, 13, 13]', '[172, 86, -2*w - 6]', '[172, 86, 2*w - 8]', '[175, 35, 5*w + 10]', '[175, 35, 5*w + 20]', '[175, 175, w + 30]', '[175, 175, w + 44]', '[175, 175, w + 130]', '[175, 175, w + 144]', '[176, 44, 4*w]', '[176, 44, 4*w + 40]', '[179, 179, 2*w - 21]', '[179, 179, -2*w - 19]', '[180, 30, 6*w]', '[180, 30, 6*w + 24]', '[185, 185, -w - 15]', '[185, 185, 2*w - 7]', '[185, 185, -2*w - 5]', '[185, 185, -w + 16]', '[187, 187, w + 76]', '[187, 187, w + 110]', '[191, 191, -3*w - 16]', '[191, 191, 3*w - 19]', '[193, 193, w + 37]', '[193, 193, w + 155]', '[196, 14, 14]', '[196, 98, -2*w - 4]', '[196, 98, -2*w + 6]', '[197, 197, w + 78]', '[197, 197, w + 118]', '[205, 205, 3*w - 28]', '[205, 205, 2*w - 5]', '[205, 205, -2*w - 3]', '[205, 205, 3*w + 25]', '[208, 52, 4*w + 24]', '[212, 106, -2*w - 2]', '[212, 106, 2*w - 4]', '[215, 215, w + 39]', '[215, 215, w + 89]', '[215, 215, w + 125]', '[215, 215, w + 175]', '[217, 217, -w - 16]', '[217, 217, 2*w - 3]', '[217, 217, 2*w + 1]', '[217, 217, w - 17]', '[220, 110, 2*w]', '[220, 110, -2*w - 20]', '[220, 110, 2*w - 22]', '[220, 110, 2*w - 2]', '[221, 221, -2*w + 1]', '[225, 15, 15]', '[225, 75, -3*w - 15]', '[225, 75, -3*w + 18]', '[227, 227, w + 34]', '[227, 227, w + 192]', '[241, 241, w + 35]', '[241, 241, w + 205]', '[245, 35, 7*w]', '[245, 35, 7*w + 28]', '[245, 245, w + 95]', '[245, 245, w + 100]', '[245, 245, w + 144]', '[245, 245, w + 149]', '[251, 251, -w - 17]', '[251, 251, w - 18]', '[252, 42, 6*w + 12]', '[252, 42, 6*w + 24]', '[256, 16, 16]', '[257, 257, 3*w - 17]', '[257, 257, -3*w - 14]', '[259, 259, -5*w - 31]', '[259, 259, 3*w + 26]', '[259, 259, 3*w - 29]', '[259, 259, 5*w - 36]', '[260, 130, 2*w + 38]', '[260, 130, 2*w + 90]', '[263, 263, 2*w - 23]', '[263, 263, -2*w - 21]', '[265, 265, w + 54]', '[265, 265, w + 104]', '[265, 265, w + 160]', '[265, 265, w + 210]', '[272, 68, -4*w - 32]', '[275, 55, 5*w]', '[275, 55, 5*w + 50]', '[275, 275, w + 44]', '[275, 275, w + 55]', '[275, 275, w + 219]', '[275, 275, w + 230]', '[279, 93, 3*w + 42]', '[279, 93, 3*w + 48]', '[284, 142, 2*w + 46]', '[284, 142, 2*w + 94]', '[287, 287, -w - 18]', '[287, 287, 3*w + 13]', '[287, 287, -3*w + 16]', '[287, 287, -w + 19]', '[289, 17, 17]', '[292, 146, 2*w + 40]', '[292, 146, 2*w + 104]', '[301, 301, w + 39]', '[301, 301, w + 46]', '[301, 301, w + 254]', '[301, 301, w + 261]', '[308, 154, -2*w - 22]', '[308, 154, 4*w - 26]', '[308, 154, 4*w + 22]', '[308, 154, 2*w - 24]', '[315, 105, -3*w - 12]', '[315, 105, 3*w + 27]', '[315, 105, -3*w + 30]', '[315, 105, -3*w + 15]', '[317, 317, w + 40]', '[317, 317, w + 276]', '[320, 40, 8*w]', '[320, 40, 8*w + 32]', '[324, 18, 18]', '[325, 65, 5*w + 30]', '[325, 325, -w - 19]', '[325, 325, w - 20]', '[333, 111, 3*w + 45]', '[333, 111, 3*w + 63]', '[340, 170, 2*w + 50]', '[340, 170, 2*w + 118]', '[341, 341, -4*w + 37]', '[341, 341, -3*w + 14]', '[341, 341, -3*w - 11]', '[341, 341, 4*w + 33]', '[343, 49, 7*w + 14]', '[343, 49, 7*w + 28]', '[343, 343, w + 149]', '[343, 343, w + 193]', '[355, 355, 4*w + 21]', '[355, 355, 2*w - 25]', '[355, 355, -2*w - 23]', '[355, 355, 4*w - 25]', '[361, 19, -19]', '[364, 182, 2*w + 64]', '[364, 182, 2*w + 116]', '[365, 365, -w - 20]', '[365, 365, 3*w + 10]', '[365, 365, 3*w - 13]', '[365, 365, w - 21]', '[369, 123, 3*w + 54]', '[369, 123, 3*w + 66]', '[371, 371, w + 51]', '[371, 371, w + 107]', '[371, 371, w + 263]', '[371, 371, w + 319]', '[373, 373, 3*w - 31]', '[373, 373, -3*w - 28]', '[379, 379, w + 166]', '[379, 379, w + 212]', '[385, 385, w + 44]', '[385, 385, w + 65]', '[385, 385, w + 109]', '[385, 385, w + 165]', '[385, 385, w + 219]', '[385, 385, w + 275]', '[385, 385, w + 319]', '[385, 385, w + 340]', '[387, 129, -3*w - 9]', '[387, 129, 3*w - 12]', '[388, 194, 2*w + 66]', '[388, 194, 2*w + 126]', '[389, 389, 5*w - 34]', '[389, 389, -5*w - 29]', '[396, 66, 6*w]', '[396, 66, 6*w + 60]', '[397, 397, w + 66]', '[397, 397, w + 330]', '[400, 20, 20]', '[400, 100, -4*w - 20]', '[400, 100, -4*w + 24]', '[401, 401, w + 53]', '[401, 401, w + 347]', '[403, 403, w + 45]', '[403, 403, w + 357]', '[404, 202, -2*w - 24]', '[404, 202, 2*w - 26]', '[405, 45, 9*w]', '[405, 45, 9*w + 36]', '[407, 407, -w - 21]', '[407, 407, 3*w - 11]', '[407, 407, -3*w - 8]', '[407, 407, -w + 22]', '[412, 206, 4*w - 38]', '[412, 206, -4*w - 34]', '[425, 85, -5*w - 40]', '[425, 425, 3*w + 7]', '[425, 425, 3*w - 10]', '[431, 431, w + 126]', '[431, 431, w + 304]', '[433, 433, -3*w - 29]', '[433, 433, 3*w - 32]', '[436, 218, 2*w + 48]', '[436, 218, 2*w + 168]', '[441, 21, 21]', '[441, 147, -3*w - 6]', '[441, 147, -3*w + 9]', '[443, 443, 4*w - 23]', '[443, 443, -4*w - 19]', '[448, 56, 8*w + 16]', '[448, 56, 8*w + 32]', '[449, 449, w + 195]', '[449, 449, w + 253]', '[451, 451, -w - 22]', '[451, 451, 5*w + 28]', '[451, 451, -5*w + 33]', '[451, 451, -w + 23]', '[455, 455, 3*w - 8]', '[455, 455, 2*w - 27]', '[455, 455, -2*w - 25]', '[455, 455, 3*w + 5]', '[467, 467, -3*w - 4]', '[467, 467, 3*w - 7]', '[468, 78, 6*w + 36]', '[473, 473, w + 132]', '[473, 473, w + 175]', '[473, 473, w + 297]', '[473, 473, w + 340]', '[476, 238, 2*w + 50]', '[476, 238, 2*w + 186]', '[477, 159, -3*w - 3]', '[477, 159, 3*w - 6]', '[479, 479, w + 49]', '[479, 479, w + 429]', '[481, 481, w + 58]', '[481, 481, w + 422]', '[484, 22, 22]', '[484, 242, -4*w + 22]', '[484, 242, -4*w - 18]', '[485, 485, 4*w + 35]', '[485, 485, 3*w - 5]', '[485, 485, -3*w - 2]', '[485, 485, 4*w - 39]', '[487, 487, w + 141]', '[487, 487, w + 345]', '[491, 491, -3*w - 1]', '[491, 491, 3*w - 4]', '[495, 165, 3*w]', '[495, 165, -3*w - 30]', '[495, 165, 3*w - 33]', '[495, 165, 3*w - 3]', '[496, 124, 4*w + 56]', '[496, 124, 4*w + 64]', '[497, 497, -w - 23]', '[497, 497, 3*w - 2]', '[497, 497, 3*w - 1]', '[497, 497, w - 24]', '[499, 499, w + 50]', '[499, 499, w + 448]', '[500, 50, 10*w]', '[500, 50, 10*w + 40]', '[500, 250, 2*w + 60]', '[500, 250, 2*w + 188]', '[505, 505, w + 189]', '[505, 505, w + 214]', '[505, 505, w + 290]', '[505, 505, w + 315]', '[508, 254, -2*w - 26]', '[508, 254, 2*w - 28]', '[511, 511, -6*w - 47]', '[511, 511, 5*w - 32]', '[511, 511, 5*w + 27]', '[511, 511, 6*w - 53]', '[515, 515, w + 60]', '[515, 515, w + 145]', '[515, 515, w + 369]', '[515, 515, w + 454]', '[523, 523, -4*w - 17]', '[523, 523, 4*w - 21]', '[527, 527, w + 76]', '[527, 527, w + 450]', '[529, 23, -23]', '[533, 533, w + 227]', '[533, 533, w + 305]', '[539, 77, 7*w]', '[539, 77, 7*w + 70]', '[539, 539, w + 198]', '[539, 539, w + 242]', '[539, 539, w + 296]', '[539, 539, w + 340]', '[541, 541, w + 77]', '[541, 541, w + 463]', '[545, 545, w + 24]', '[545, 545, 6*w - 41]', '[545, 545, -6*w - 35]', '[545, 545, w - 25]', '[559, 559, -10*w - 73]', '[559, 559, 3*w + 31]', '[560, 140, -4*w - 16]', '[560, 140, 4*w + 36]', '[560, 140, -4*w + 40]', '[560, 140, -4*w + 20]', '[563, 563, 2*w - 29]', '[563, 563, -2*w - 27]', '[567, 63, 9*w + 18]', '[567, 63, 9*w + 36]', '[569, 569, -5*w - 26]', '[569, 569, 5*w - 31]', '[572, 286, 2*w + 64]', '[572, 286, 2*w + 220]', '[576, 24, 24]', '[583, 583, w + 54]', '[583, 583, w + 263]', '[583, 583, w + 319]', '[583, 583, w + 528]', '[585, 195, 3*w + 57]', '[585, 195, 3*w + 135]', '[592, 148, 4*w + 60]', '[592, 148, 4*w + 84]', '[595, 595, -w - 25]', '[595, 595, 4*w - 19]', '[595, 595, 4*w + 15]', '[595, 595, w - 26]', '[599, 599, -5*w - 42]', '[599, 599, 5*w - 47]', '[605, 55, 11*w]', '[605, 55, 11*w + 44]', '[605, 605, w + 55]', '[605, 605, w + 65]', '[605, 605, w + 539]', '[605, 605, w + 549]', '[612, 102, -6*w - 48]', '[617, 617, w + 138]', '[617, 617, w + 478]', '[619, 619, w + 229]', '[619, 619, w + 389]', '[620, 310, -2*w - 28]', '[620, 310, 6*w - 40]', '[620, 310, 6*w + 34]', '[620, 310, 2*w - 30]', '[625, 25, 25]', '[625, 125, -5*w - 25]', '[625, 125, -5*w + 30]', '[625, 625, 3*w + 32]', '[625, 625, -3*w + 35]', '[628, 314, 4*w - 18]', '[628, 314, -4*w - 14]', '[629, 629, w + 280]', '[629, 629, w + 348]', '[635, 635, w + 140]', '[635, 635, w + 240]', '[635, 635, w + 394]', '[635, 635, w + 494]', '[637, 91, 7*w + 42]', '[637, 637, 4*w - 41]', '[637, 637, -4*w - 37]', '[639, 213, 3*w + 69]', '[639, 213, 3*w + 141]', '[643, 643, w + 67]', '[643, 643, w + 575]', '[647, 647, -w - 26]', '[647, 647, w - 27]', '[652, 326, 2*w + 58]', '[652, 326, 2*w + 266]', '[656, 164, 4*w + 72]', '[656, 164, 4*w + 88]', '[657, 219, 3*w + 60]', '[657, 219, 3*w + 156]', '[659, 659, -4*w - 13]', '[659, 659, 4*w - 17]', '[668, 334, 2*w + 86]', '[668, 334, 2*w + 246]', '[676, 26, 26]', '[679, 679, -5*w + 29]', '[679, 679, -2*w + 31]', '[679, 679, -2*w - 29]', '[679, 679, 5*w + 24]', '[683, 683, w + 257]', '[683, 683, w + 425]', '[688, 172, -4*w - 12]', '[688, 172, 4*w - 16]', '[689, 689, -8*w - 61]', '[689, 689, 5*w + 43]', '[691, 691, w + 87]', '[691, 691, w + 603]', '[693, 231, -3*w - 33]', '[693, 231, 6*w - 39]', '[693, 231, 6*w + 33]', '[693, 231, 3*w - 36]', '[697, 697, w + 59]', '[697, 697, w + 637]', '[700, 70, 10*w + 20]', '[700, 70, 10*w + 40]', '[700, 350, 2*w + 60]', '[700, 350, 2*w + 88]', '[700, 350, 2*w + 260]', '[700, 350, 2*w + 288]', '[701, 701, -w - 27]', '[701, 701, w - 28]', '[704, 88, 8*w]', '[704, 88, 8*w + 80]', '[707, 707, w + 88]', '[707, 707, w + 214]', '[707, 707, w + 492]', '[707, 707, w + 618]', '[709, 709, w + 318]', '[709, 709, w + 390]', '[715, 715, -6*w + 55]', '[715, 715, -4*w + 15]', '[715, 715, -4*w - 11]', '[715, 715, 6*w + 49]', '[716, 358, 4*w - 42]', '[716, 358, -4*w - 38]', '[720, 60, 12*w]', '[720, 60, 12*w + 48]', '[721, 721, w + 60]', '[721, 721, w + 163]', '[721, 721, w + 557]', '[721, 721, w + 660]', '[727, 727, 7*w - 48]', '[727, 727, -7*w - 41]', '[729, 27, 27]', '[731, 731, -5*w - 23]', '[731, 731, 12*w + 79]', '[740, 370, -2*w - 30]', '[740, 370, 4*w - 14]', '[740, 370, -4*w - 10]', '[740, 370, -2*w + 32]', '[743, 743, w + 72]', '[743, 743, w + 670]', '[748, 374, 2*w + 152]', '[748, 374, 2*w + 220]', '[757, 757, -w - 28]', '[757, 757, w - 29]', '[763, 763, 4*w + 9]', '[763, 763, -3*w + 37]', '[763, 763, -3*w - 34]', '[763, 763, -4*w + 13]', '[764, 382, -6*w - 32]', '[764, 382, 6*w - 38]', '[765, 255, 3*w + 75]', '[765, 255, 3*w + 177]', '[772, 386, 2*w + 74]', '[772, 386, 2*w + 310]', '[775, 155, 5*w + 70]', '[775, 155, 5*w + 80]', '[775, 775, w + 169]', '[775, 775, w + 355]', '[775, 775, w + 419]', '[775, 775, w + 605]', '[781, 781, 5*w + 44]', '[781, 781, -5*w + 27]', '[781, 781, -5*w - 22]', '[781, 781, -5*w + 49]', '[784, 28, 28]', '[784, 196, -4*w - 8]', '[784, 196, -4*w + 12]', '[785, 785, w + 74]', '[785, 785, w + 239]', '[785, 785, w + 545]', '[785, 785, w + 710]', '[787, 787, w + 236]', '[787, 787, w + 550]', '[788, 394, 2*w + 156]', '[788, 394, 2*w + 236]', '[797, 797, -4*w - 39]', '[797, 797, 4*w - 43]', '[803, 803, -4*w + 11]', '[803, 803, -2*w + 33]', '[803, 803, 2*w + 31]', '[803, 803, -4*w - 7]', '[811, 811, w + 182]', '[811, 811, w + 628]', '[815, 815, -w - 29]', '[815, 815, 7*w + 40]', '[815, 815, 7*w - 47]', '[815, 815, w - 30]', '[819, 273, 3*w + 96]', '[819, 273, 3*w + 174]', '[820, 410, 6*w - 56]', '[820, 410, 4*w - 10]', '[820, 410, -4*w - 6]', '[820, 410, 6*w + 50]', '[821, 821, w + 64]', '[821, 821, w + 756]', '[827, 827, w + 380]', '[827, 827, w + 446]', '[829, 829, -5*w - 21]', '[829, 829, 5*w - 26]', '[832, 104, 8*w + 48]', '[833, 119, -7*w - 56]', '[833, 833, 6*w + 31]', '[833, 833, 6*w - 37]', '[835, 835, -4*w - 5]', '[835, 835, -3*w - 35]', '[835, 835, -3*w + 38]', '[835, 835, 4*w - 9]', '[839, 839, w + 302]', '[839, 839, w + 536]', '[841, 29, -29]', '[845, 65, 13*w]', '[845, 65, 13*w + 52]', '[847, 77, 11*w + 22]', '[847, 77, 11*w + 44]', '[847, 847, w + 65]', '[847, 847, w + 186]', '[847, 847, w + 660]', '[847, 847, w + 781]', '[848, 212, -4*w - 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102]', '[9556, 4778, 20*w - 122]', '[9567, 3189, -9*w - 114]', '[9567, 3189, 9*w - 123]', '[9569, 9569, -15*w - 46]', '[9569, 9569, 13*w - 144]', '[9569, 9569, 13*w + 131]', '[9569, 9569, 15*w - 61]', '[9571, 9571, 45*w + 326]', '[9571, 9571, 11*w + 122]', '[9572, 4786, 16*w - 162]', '[9572, 4786, -16*w - 146]', '[9580, 4790, -2*w - 98]', '[9580, 4790, -22*w + 142]', '[9580, 4790, 22*w + 120]', '[9580, 4790, -2*w + 100]', '[9583, 259, 37*w + 74]', '[9583, 259, 37*w + 148]', '[9583, 9583, w + 1094]', '[9583, 9583, w + 3012]', '[9583, 9583, w + 6570]', '[9583, 9583, w + 8488]', '[9584, 2396, -20*w - 168]', '[9584, 2396, 20*w - 188]', '[9603, 3201, -3*w - 99]', '[9603, 3201, -21*w + 132]', '[9603, 3201, 21*w + 111]', '[9603, 3201, -3*w + 102]', '[9604, 98, 98]', '[9604, 686, -14*w - 28]', '[9604, 686, -14*w + 42]', '[9604, 4802, 10*w + 118]', '[9604, 4802, -10*w + 128]', '[9620, 4810, 18*w + 82]', '[9620, 4810, -38*w - 280]', '[9620, 4810, 14*w + 136]', '[9620, 4810, -18*w + 100]', '[9621, 3207, -15*w - 141]', '[9621, 3207, 15*w - 156]', '[9623, 9623, 24*w - 161]', '[9623, 9623, -24*w - 137]', '[9625, 1925, 5*w + 220]', '[9625, 1925, 5*w + 325]', '[9625, 1925, 5*w + 545]', '[9625, 1925, 5*w + 825]', '[9625, 1925, 5*w + 1095]', '[9625, 1925, 5*w + 1375]', '[9625, 1925, 5*w + 1595]', '[9625, 1925, 5*w + 1700]', '[9625, 9625, w + 219]', '[9625, 9625, w + 1969]', '[9625, 9625, w + 3530]', '[9625, 9625, w + 4344]', '[9625, 9625, w + 5280]', '[9625, 9625, w + 6094]', '[9625, 9625, w + 7655]', '[9625, 9625, w + 9405]', '[9639, 1071, 9*w + 225]', '[9639, 1071, 9*w + 837]', '[9643, 9643, -19*w - 92]', '[9643, 9643, 19*w - 111]', '[9644, 4822, 2*w + 1342]', '[9644, 4822, 2*w + 3478]', '[9647, 9647, -w - 98]', '[9647, 9647, -17*w - 71]', '[9647, 9647, 17*w - 88]', '[9647, 9647, -w + 99]', '[9653, 1379, 7*w + 546]', '[9653, 1379, 7*w + 826]', '[9653, 9653, w + 3427]', '[9653, 9653, w + 4412]', '[9653, 9653, w + 5240]', '[9653, 9653, w + 6225]', '[9655, 9655, 16*w + 59]', '[9655, 9655, 18*w - 175]', '[9655, 9655, -18*w - 157]', '[9655, 9655, 16*w - 75]', '[9659, 9659, w + 4530]', '[9659, 9659, w + 5128]', '[9661, 9661, w + 2613]', '[9661, 9661, w + 7047]', '[9667, 9667, w + 828]', '[9667, 9667, w + 2209]', '[9667, 9667, w + 7457]', '[9667, 9667, w + 8838]', '[9673, 9673, 71*w + 483]', '[9673, 9673, -14*w - 27]', '[9675, 645, -15*w - 45]', '[9675, 645, 15*w - 60]', '[9675, 3225, 27*w - 237]', '[9675, 3225, -6*w + 111]', '[9675, 3225, -6*w - 105]', '[9675, 3225, 27*w + 210]', '[9679, 9679, w + 1176]', '[9679, 9679, w + 8502]', '[9680, 220, 44*w]', '[9680, 220, 44*w + 176]', '[9680, 2420, 4*w + 220]', '[9680, 2420, 4*w + 260]', '[9680, 2420, 4*w + 2156]', '[9680, 2420, 4*w + 2196]', '[9689, 9689, -8*w - 111]', '[9689, 9689, 8*w - 119]', '[9700, 970, 10*w + 330]', '[9700, 970, 10*w + 630]', '[9700, 4850, 2*w + 260]', '[9700, 4850, 2*w + 2260]', '[9700, 4850, 2*w + 2588]', '[9700, 4850, 2*w + 4588]', '[9713, 9713, w + 220]', '[9713, 9713, w + 3311]', '[9713, 9713, w + 6401]', '[9713, 9713, w + 9492]', '[9719, 9719, w + 2744]', '[9719, 9719, w + 6974]', '[9724, 4862, 2*w + 220]', '[9724, 4862, 2*w + 4640]', '[9725, 1945, 25*w - 170]', '[9725, 1945, -25*w - 145]', '[9725, 9725, 4*w - 105]', '[9725, 9725, 59*w - 479]', '[9725, 9725, 59*w + 420]', '[9725, 9725, 4*w + 101]', '[9731, 9731, w + 909]', '[9731, 9731, w + 4350]', '[9731, 9731, w + 5380]', '[9731, 9731, w + 8821]', '[9733, 9733, -12*w - 127]', '[9733, 9733, 12*w - 139]', '[9740, 4870, 14*w - 40]', '[9740, 4870, 22*w + 180]', '[9740, 4870, 22*w - 202]', '[9740, 4870, -14*w - 26]', '[9748, 4874, 2*w + 1712]', '[9748, 4874, 2*w + 3160]', '[9749, 9749, 5*w - 108]', '[9749, 9749, -5*w - 103]', '[9755, 9755, w + 2504]', '[9755, 9755, w + 4455]', '[9755, 9755, w + 5299]', '[9755, 9755, w + 7250]', '[9761, 9761, w + 261]', '[9761, 9761, w + 942]', '[9761, 9761, w + 8818]', '[9761, 9761, w + 9499]', '[9765, 3255, 3*w + 327]', '[9765, 3255, 3*w + 600]', '[9765, 3255, 3*w + 972]', '[9765, 3255, 3*w + 1350]', '[9765, 3255, 3*w + 1902]', '[9765, 3255, 3*w + 2280]', '[9765, 3255, 3*w + 2652]', '[9765, 3255, 3*w + 2925]', '[9767, 9767, 23*w - 151]', '[9767, 9767, -23*w - 128]', '[9769, 9769, w + 2386]', '[9769, 9769, w + 7382]', '[9779, 9779, -39*w + 292]', '[9779, 9779, -15*w + 59]', '[9779, 9779, -25*w + 223]', '[9779, 9779, -2*w + 101]', '[9779, 9779, 2*w + 99]', '[9779, 9779, 25*w + 198]', '[9779, 9779, -15*w - 44]', '[9779, 9779, -39*w - 253]', '[9781, 9781, w + 3696]', '[9781, 9781, w + 6084]', '[9787, 9787, w + 633]', '[9787, 9787, w + 9153]', '[9788, 4894, 16*w - 74]', '[9788, 4894, -16*w - 58]', '[9792, 408, -24*w - 192]', '[9793, 9793, 17*w + 152]', '[9793, 9793, -29*w - 177]', '[9793, 9793, 29*w - 206]', '[9793, 9793, 17*w - 169]', '[9797, 9797, w + 1906]', '[9797, 9797, w + 3749]', '[9797, 9797, w + 6047]', '[9797, 9797, w + 7890]', '[9801, 99, 99]', '[9801, 1089, -18*w + 99]', '[9801, 1089, -18*w - 81]', '[9805, 9805, 3*w - 103]', '[9805, 9805, 14*w - 39]', '[9805, 9805, -9*w + 124]', '[9805, 9805, 17*w - 87]', '[9805, 9805, 17*w + 70]', '[9805, 9805, -9*w - 115]', '[9805, 9805, -14*w - 25]', '[9805, 9805, -3*w - 100]', '[9811, 9811, 19*w - 182]', '[9811, 9811, -19*w - 163]', '[9820, 4910, 2*w + 328]', '[9820, 4910, 2*w + 1310]', '[9820, 4910, 2*w + 3598]', '[9820, 4910, 2*w + 4580]', '[9827, 9827, 28*w + 169]', '[9827, 9827, -11*w - 123]', '[9827, 9827, 11*w - 134]', '[9827, 9827, 28*w - 197]', '[9833, 9833, w + 799]', '[9833, 9833, w + 9033]', '[9836, 4918, 2*w + 2156]', '[9836, 4918, 2*w + 2760]', '[9841, 9841, -22*w - 119]', '[9841, 9841, -35*w - 223]', '[9845, 9845, w + 99]', '[9845, 9845, -21*w + 131]', '[9845, 9845, -19*w + 110]', '[9845, 9845, -41*w + 341]', '[9845, 9845, 41*w + 300]', '[9845, 9845, -19*w - 91]', '[9845, 9845, -21*w - 110]', '[9845, 9845, -w + 100]', '[9851, 9851, -10*w - 119]', '[9851, 9851, 10*w - 129]', '[9865, 9865, w + 329]', '[9865, 9865, w + 4275]', '[9865, 9865, w + 5589]', '[9865, 9865, w + 9535]', '[9868, 4934, -14*w - 24]', '[9868, 4934, 14*w - 38]', '[9872, 2468, 4*w + 552]', '[9872, 2468, 4*w + 1912]', '[9881, 9881, -16*w - 147]', '[9881, 9881, -15*w - 43]', '[9881, 9881, 15*w - 58]', '[9881, 9881, 16*w - 163]', '[9887, 9887, w + 2234]', '[9887, 9887, w + 7652]', '[9891, 3297, 3*w + 222]', '[9891, 3297, 3*w + 1188]', '[9891, 3297, 3*w + 2106]', '[9891, 3297, 3*w + 3072]', '[9892, 4946, -6*w - 106]', '[9892, 4946, 6*w - 112]', '[9900, 330, 30*w]', '[9900, 330, 30*w + 300]', '[9900, 1650, 6*w + 264]', '[9900, 1650, 6*w + 330]', '[9900, 1650, 6*w + 1314]', '[9900, 1650, 6*w + 1380]', '[9901, 9901, w + 2861]', '[9901, 9901, w + 7039]', '[9904, 2476, 4*w + 916]', '[9904, 2476, 4*w + 1556]', '[9907, 9907, -14*w - 137]', '[9907, 9907, 14*w - 151]', '[9908, 4954, 2*w + 1726]', '[9908, 4954, 2*w + 3226]', '[9911, 9911, w + 263]', '[9911, 9911, w + 637]', '[9911, 9911, w + 9273]', '[9911, 9911, w + 9647]', '[9919, 9919, -15*w - 142]', '[9919, 9919, -16*w + 73]', '[9919, 9919, 16*w + 57]', '[9919, 9919, -15*w + 157]', '[9920, 1240, -8*w - 112]', '[9920, 1240, 24*w - 160]', '[9920, 1240, 24*w + 136]', '[9920, 1240, 8*w - 120]', '[9925, 1985, 5*w + 330]', '[9925, 1985, 5*w + 1650]', '[9925, 9925, w + 330]', '[9925, 9925, w + 4830]', '[9925, 9925, w + 5094]', '[9925, 9925, w + 9594]', '[9929, 9929, 14*w - 37]', '[9929, 9929, -14*w - 23]', '[9932, 4966, -74*w - 522]', '[9932, 4966, 4*w + 102]', '[9940, 4970, 2*w + 330]', '[9940, 4970, 2*w + 1040]', '[9940, 4970, 2*w + 1940]', '[9940, 4970, 2*w + 2318]', '[9940, 4970, 2*w + 2650]', '[9940, 4970, 2*w + 3028]', '[9940, 4970, 2*w + 3928]', '[9940, 4970, 2*w + 4638]', '[9941, 9941, 20*w - 189]', '[9941, 9941, -20*w - 169]', '[9945, 3315, 3*w + 330]', '[9945, 3315, 3*w + 2982]', '[9949, 9949, 7*w - 116]', '[9949, 9949, -7*w - 109]', '[9961, 9961, 17*w + 69]', '[9961, 9961, -5*w - 104]', '[9961, 9961, -5*w + 109]', '[9961, 9961, -17*w + 86]', '[9965, 9965, w + 1274]', '[9965, 9965, w + 4704]', '[9965, 9965, w + 5260]', '[9965, 9965, w + 8690]', '[9973, 9973, w + 607]', '[9973, 9973, w + 9365]', '[9980, 4990, -2*w - 100]', '[9980, 4990, 18*w - 98]', '[9980, 4990, 18*w + 80]', '[9980, 4990, 2*w - 102]', '[9981, 3327, 15*w - 57]', '[9981, 3327, -15*w - 42]', '[9988, 4994, -14*w - 22]', '[9988, 4994, -18*w + 176]', '[9988, 4994, 18*w + 158]', '[9988, 4994, -14*w + 36]', '[9989, 9989, w + 1388]', '[9989, 9989, w + 1465]', '[9989, 9989, w + 8523]', '[9989, 9989, w + 8600]', '[9991, 9991, w + 4592]', '[9991, 9991, w + 4883]', '[9991, 9991, w + 5107]', '[9991, 9991, w + 5398]', '[9999, 3333, 3*w + 264]', '[9999, 3333, 3*w + 1551]', '[9999, 3333, 3*w + 1779]', '[9999, 3333, 3*w + 3066]', '[10000, 100, 100]', '[10000, 500, -20*w - 100]', '[10000, 500, -20*w + 120]', '[10000, 2500, 12*w + 128]', '[10000, 2500, -12*w + 140]'], 'label': '2.2.221.1', 'narrow_class_no': 4, 'primes': ['[4, 2, 2]', '[5, 5, w]', '[5, 5, w + 4]', '[7, 7, w + 2]', '[7, 7, w + 4]', '[9, 3, 3]', '[11, 11, w]', '[11, 11, w + 10]', '[13, 13, w + 6]', '[17, 17, -w - 8]', '[31, 31, w + 14]', '[31, 31, w + 16]', '[37, 37, w + 15]', '[37, 37, w + 21]', '[41, 41, w + 18]', '[41, 41, w + 22]', '[43, 43, -w - 3]', '[43, 43, w - 4]', '[53, 53, -w - 1]', '[53, 53, w - 2]', '[71, 71, w + 23]', '[71, 71, w + 47]', '[73, 73, w + 20]', '[73, 73, w + 52]', '[97, 97, w + 33]', '[97, 97, w + 63]', '[101, 101, -w - 12]', '[101, 101, w - 13]', '[103, 103, 2*w - 19]', '[103, 103, -2*w - 17]', '[109, 109, w + 24]', '[109, 109, w + 84]', '[127, 127, -w - 13]', '[127, 127, w - 14]', '[157, 157, 2*w - 9]', '[157, 157, -2*w - 7]', '[163, 163, w + 29]', '[163, 163, w + 133]', '[167, 167, w + 43]', '[167, 167, w + 123]', '[179, 179, 2*w - 21]', '[179, 179, -2*w - 19]', '[191, 191, -3*w - 16]', '[191, 191, 3*w - 19]', '[193, 193, w + 37]', '[193, 193, w + 155]', '[197, 197, w + 78]', '[197, 197, w + 118]', '[227, 227, w + 34]', '[227, 227, w + 192]', '[241, 241, w + 35]', '[241, 241, w + 205]', '[251, 251, -w - 17]', '[251, 251, w - 18]', '[257, 257, 3*w - 17]', '[257, 257, -3*w - 14]', '[263, 263, 2*w - 23]', '[263, 263, -2*w - 21]', '[317, 317, w + 40]', '[317, 317, w + 276]', '[361, 19, -19]', '[373, 373, 3*w - 31]', '[373, 373, -3*w - 28]', '[379, 379, w + 166]', '[379, 379, w + 212]', '[389, 389, 5*w - 34]', '[389, 389, -5*w - 29]', '[397, 397, w + 66]', '[397, 397, w + 330]', '[401, 401, w + 53]', '[401, 401, w + 347]', '[431, 431, w + 126]', '[431, 431, w + 304]', '[433, 433, -3*w - 29]', '[433, 433, 3*w - 32]', '[443, 443, 4*w - 23]', '[443, 443, -4*w - 19]', '[449, 449, w + 195]', '[449, 449, w + 253]', '[467, 467, -3*w - 4]', '[467, 467, 3*w - 7]', '[479, 479, w + 49]', '[479, 479, w + 429]', '[487, 487, w + 141]', '[487, 487, w + 345]', '[491, 491, -3*w - 1]', '[491, 491, 3*w - 4]', '[499, 499, w + 50]', '[499, 499, w + 448]', '[523, 523, -4*w - 17]', '[523, 523, 4*w - 21]', '[529, 23, -23]', '[541, 541, w + 77]', '[541, 541, w + 463]', '[563, 563, 2*w - 29]', '[563, 563, -2*w - 27]', '[569, 569, -5*w - 26]', '[569, 569, 5*w - 31]', '[599, 599, -5*w - 42]', '[599, 599, 5*w - 47]', '[617, 617, w + 138]', '[617, 617, w + 478]', '[619, 619, w + 229]', '[619, 619, w + 389]', '[643, 643, w + 67]', '[643, 643, w + 575]', '[647, 647, -w - 26]', '[647, 647, w - 27]', '[659, 659, -4*w - 13]', '[659, 659, 4*w - 17]', '[683, 683, w + 257]', '[683, 683, w + 425]', '[691, 691, w + 87]', '[691, 691, w + 603]', '[701, 701, -w - 27]', '[701, 701, w - 28]', '[709, 709, w + 318]', '[709, 709, w + 390]', '[727, 727, 7*w - 48]', '[727, 727, -7*w - 41]', '[743, 743, w + 72]', '[743, 743, w + 670]', '[757, 757, -w - 28]', '[757, 757, w - 29]', '[787, 787, w + 236]', '[787, 787, w + 550]', '[797, 797, -4*w - 39]', '[797, 797, 4*w - 43]', '[811, 811, w + 182]', '[811, 811, w + 628]', '[821, 821, w + 64]', '[821, 821, w + 756]', '[827, 827, w + 380]', '[827, 827, w + 446]', '[829, 829, -5*w - 21]', '[829, 829, 5*w - 26]', '[839, 839, w + 302]', '[839, 839, w + 536]', '[841, 29, -29]', '[853, 853, w + 377]', '[853, 853, w + 475]', '[859, 859, 4*w - 7]', '[859, 859, -4*w - 3]', '[877, 877, w + 98]', '[877, 877, w + 778]', '[883, 883, 4*w - 3]', '[883, 883, 4*w - 1]', '[919, 919, 5*w - 24]', '[919, 919, -5*w - 19]', '[929, 929, w + 423]', '[929, 929, w + 505]', '[937, 937, -w - 31]', '[937, 937, w - 32]', '[941, 941, w + 81]', '[941, 941, w + 859]', '[947, 947, w + 171]', '[947, 947, w + 775]', '[953, 953, 7*w - 64]', '[953, 953, -7*w - 57]', '[971, 971, 5*w - 51]', '[971, 971, -5*w - 46]', '[983, 983, w + 70]', '[983, 983, w + 912]']}
• 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': [-55, -1, 1], 'conductor': 221, 'degree': 2, 'dirichlet_group': [1, 220], 'disc_abs': 221, 'disc_rad': 221, 'disc_sign': 1, 'frobs': [[2, [[2, 1]]], [3, [[2, 1]]], [5, [[1, 2]]], [7, [[1, 2]]], [11, [[1, 2]]], [13, [0]], [17, [0]], [19, [[2, 1]]], [23, [[2, 1]]], [29, [[2, 1]]], [31, [[1, 2]]], [37, [[1, 2]]], [41, [[1, 2]]], [43, [[1, 2]]], [47, [[2, 1]]], [53, [[1, 2]]], [59, [[2, 1]]]], 'gal_is_abelian': True, 'gal_is_cyclic': True, 'gal_is_solvable': True, 'galois_disc_exponents': [1, 1], 'galois_label': '2T1', 'galt': 1, 'grd': 14.866068747318506, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '2.2.221.1', 'local_algs': ['13.2.1.1', '17.2.1.1'], 'monogenic': 1, 'num_ram': 2, 'r2': 0, 'ramps': [13, 17], 'rd': 14.8660687473, 'regulator': {'__RealLiteral__': 0, 'data': '2.70357583093', 'prec': 44}, 'res': {}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a + 7 \\)'], 'used_grh': False, 'zk': ['1', 'a']}