Hilbert modular form data - 4.4.2000.1-79.4-a

Formats: - HTML - YAML - JSON - 2024-05-06T05:22:09.619804

• 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': 4, 'dimension': 1, 'disc': 2000, 'field_bad_primes': [2, 5], 'field_label': '4.4.2000.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '4.4.2000.1-79.4-a', 'label_nsuffix': 0, 'label_suffix': 'a', 'level_bad_primes': [79], 'level_ideal': '[79,79,w^3 + 2*w^2 - 2*w - 6]', 'level_label': '79.4', 'level_norm': 79, 'parallel_weight': 2, 'short_label': '79.4-a', 'weight': '[2, 2, 2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[79,79,w^3 + 2*w^2 - 2*w - 6]', 1]], 'hecke_eigenvalues': [0, 0, 4, 0, 8, 8, 8, -12, 0, 0, 4, 0, 8, -12, -12, 0, 8, -8, 16, -12, -4, -1, 14, 10, -14, 2, 10, -10, -10, -16, 8, -12, 16, 16, -20, -4, -16, -2, 14, 6, 6, -16, 0, -4, 16, 16, 8, -16, 0, -4, 4, 0, -8, -20, 4, 28, -12, -32, -36, 8, 0, 16, -16, 32, 28, -30, -30, 18, -14, 24, 0, 0, 12, -28, 20, -32, 0, 24, -16, 0, 20, -38, -14, 34, -30, 0, -24, 8, 32, -8, 12, -8, -16, 38, 6, 6, 6, -14, 2, -22, 10, 32, -24, -20, 16, 16, -44, 20, -44, 16, -16, -8, -8, -12, -4, 8, 8, -40, -40, 24, -36, 36, -12, 40, -44, 0, 16, -4, 0, 20, 0, 48, -36, 16, 40, 16, 40, -22, 42, -22, 42, -4, -36, 48, -16, 0, 44, 36, 48, -6, -38, -4, -48, 0, -8, 8, -16, -40, 20, -16, 32, -48, 24, 6, 14, 6, 30, -18, -50], 'hecke_polynomial': 'x', 'label': '4.4.2000.1-79.4-a'}
• hmf_fields •

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

  
  {'degree': 4, 'discriminant': 2000, 'ideals': ['[1, 1, 1]', '[4, 2, -w^3 - w^2 + 3*w + 4]', '[5, 5, w]', '[16, 2, 2]', '[19, 19, -w^2 + w + 4]', '[19, 19, w^3 - w^2 - 3*w + 1]', '[19, 19, -w^3 - w^2 + 3*w + 1]', '[19, 19, -w^2 - w + 4]', '[20, 10, -w^3 - 2*w^2 + 4*w + 5]', '[25, 5, -2*w^2 + 5]', '[41, 41, w + 3]', '[41, 41, -w^3 + 3*w + 3]', '[41, 41, -w^3 + 3*w - 3]', '[41, 41, w - 3]', '[59, 59, 2*w^2 + w - 7]', '[59, 59, -w^3 - 2*w^2 + 3*w + 3]', '[59, 59, 2*w^3 - w^2 - 7*w + 2]', '[59, 59, w^3 - w^2 - w + 3]', '[61, 61, 3*w^2 - w - 8]', '[61, 61, w^3 + 3*w^2 - 3*w - 7]', '[61, 61, -w^3 + 3*w^2 + 3*w - 7]', '[61, 61, -3*w^2 - w + 8]', '[64, 4, -2*w^3 - 2*w^2 + 6*w + 8]', '[76, 38, -3*w^2 - w + 7]', '[76, 38, -w^3 - 3*w^2 + 3*w + 8]', '[76, 38, -w^3 + 3*w^2 + 3*w - 8]', '[76, 38, -3*w^2 + w + 7]', '[79, 79, -w^3 + 2*w^2 + 2*w - 6]', '[79, 79, w^3 + 2*w^2 - 4*w - 4]', '[79, 79, -w^3 + 2*w^2 + 4*w - 4]', '[79, 79, w^3 + 2*w^2 - 2*w - 6]', '[80, 10, 2*w]', '[81, 3, -3]', '[95, 95, -w^3 + w^2 + 4*w]', '[95, 95, w^3 - w^2 - 2*w + 5]', '[95, 95, w^3 + w^2 - 2*w - 5]', '[95, 95, -w^3 - w^2 + 4*w]', '[100, 10, -w^3 - 3*w^2 + 5*w + 10]', '[101, 101, 2*w^3 + w^2 - 5*w - 2]', '[101, 101, w^3 + w^2 - 5*w - 3]', '[101, 101, -w^3 + w^2 + 5*w - 3]', '[101, 101, -2*w^3 + w^2 + 5*w - 2]', '[121, 11, 3*w^2 - 8]', '[121, 11, -w^2 + 6]', '[125, 5, -2*w^3 + 5*w]', '[139, 139, 2*w^3 - 3*w^2 - 4*w + 7]', '[139, 139, -2*w^3 + 7*w - 4]', '[139, 139, 2*w^3 - 3*w^2 - 8*w + 8]', '[139, 139, -2*w^3 - 3*w^2 + 4*w + 7]', '[164, 82, w^3 + 2*w^2 - 4*w - 3]', '[164, 82, w^3 - 2*w^2 - 2*w + 7]', '[164, 82, w^3 + 2*w^2 - 2*w - 7]', '[164, 82, -w^3 + 2*w^2 + 4*w - 3]', '[179, 179, 3*w^3 + 2*w^2 - 9*w - 3]', '[179, 179, 2*w^2 + 3*w - 7]', '[179, 179, 2*w^2 - 3*w - 7]', '[179, 179, -3*w^3 + 2*w^2 + 9*w - 3]', '[181, 181, 4*w^3 + 2*w^2 - 13*w - 9]', '[181, 181, w^3 + 4*w^2 - 4*w - 12]', '[181, 181, 4*w^3 + 4*w^2 - 14*w - 17]', '[181, 181, -3*w^3 - 3*w^2 + 12*w + 11]', '[199, 199, -3*w^2 + 2*w + 9]', '[199, 199, -2*w^3 + 8*w - 3]', '[199, 199, 2*w^3 - 8*w - 3]', '[199, 199, 2*w^3 + 4*w^2 - 9*w - 14]', '[205, 205, w^2 + 3*w]', '[205, 205, -3*w^3 - w^2 + 9*w + 5]', '[205, 205, 3*w^3 - w^2 - 9*w + 5]', '[205, 205, w^2 - 3*w]', '[236, 118, 2*w^3 + 3*w^2 - 7*w - 13]', '[236, 118, -w^3 - 2*w^2 + 6*w + 7]', '[236, 118, 5*w^3 + 3*w^2 - 17*w - 12]', '[236, 118, -w^3 - 5*w^2 + 5*w + 12]', '[239, 239, -3*w^3 + w^2 + 9*w + 1]', '[239, 239, w^2 - 3*w - 6]', '[239, 239, w^2 + 3*w - 6]', '[239, 239, 3*w^3 + w^2 - 9*w + 1]', '[241, 241, 4*w^2 + w - 11]', '[241, 241, w^3 - w^2 - 4*w + 7]', '[241, 241, -w^3 - w^2 + 4*w + 7]', '[241, 241, 4*w^2 - w - 11]', '[244, 122, 3*w^3 + 7*w^2 - 13*w - 22]', '[244, 122, 3*w^3 + 5*w^2 - 13*w - 18]', '[244, 122, -w^3 + 3*w^2 + w - 8]', '[244, 122, -w^3 - 3*w^2 + 5*w + 12]', '[256, 4, 4]', '[281, 281, 3*w^3 + 2*w^2 - 8*w - 6]', '[281, 281, w^3 + w^2 - 3*w - 7]', '[281, 281, -w^3 + w^2 + 3*w - 7]', '[281, 281, -3*w^3 + 2*w^2 + 8*w - 6]', '[295, 295, 2*w^3 + w^2 - 7*w]', '[295, 295, -2*w^3 - 2*w^2 + 3*w + 5]', '[295, 295, -w^3 + 3*w^2 + 2*w - 10]', '[295, 295, -w^3 + 4*w^2 + 3*w - 5]', '[304, 38, -2*w^2 + 2*w + 8]', '[304, 38, 2*w^3 - 2*w^2 - 6*w + 2]', '[304, 38, -2*w^3 - 2*w^2 + 6*w + 2]', '[304, 38, -2*w^2 - 2*w + 8]', '[305, 305, 3*w^3 + 2*w^2 - 7*w - 5]', '[305, 305, 3*w^3 - w^2 - 8*w]', '[305, 305, -3*w^3 - w^2 + 8*w]', '[305, 305, 3*w^3 - 2*w^2 - 7*w + 5]', '[316, 158, w^3 + 5*w^2 - 5*w - 14]', '[316, 158, 3*w^3 + 5*w^2 - 13*w - 16]', '[316, 158, -3*w^3 - w^2 + 9*w + 4]', '[316, 158, 3*w^3 + 3*w^2 - 11*w - 14]', '[320, 20, -2*w^3 - 4*w^2 + 8*w + 10]', '[324, 6, 3*w^3 + 3*w^2 - 9*w - 12]', '[359, 359, 2*w^3 - 2*w^2 - 5*w + 8]', '[359, 359, -3*w^3 - 2*w^2 + 10*w + 4]', '[359, 359, 3*w^3 - 2*w^2 - 10*w + 4]', '[359, 359, 2*w^3 + 2*w^2 - 5*w - 8]', '[361, 19, -4*w^2 + 11]', '[361, 19, 3*w^3 - 2*w^2 - 8*w + 4]', '[361, 19, -3*w^3 - 2*w^2 + 8*w + 4]', '[361, 19, -w^3 + 2*w^2 + 6*w - 6]', '[361, 19, w^3 + 2*w^2 - 6*w - 6]', '[361, 19, 4*w^2 - 9]', '[361, 361, w^2 - 3*w - 2]', '[361, 361, 3*w^3 - w^2 - 9*w + 3]', '[361, 361, 3*w^3 + w^2 - 9*w - 3]', '[361, 361, -w^2 - 3*w + 2]', '[379, 379, 2*w^3 - 3*w^2 - 8*w + 7]', '[379, 379, -2*w^3 - 3*w^2 + 4*w + 8]', '[379, 379, 2*w^3 - 3*w^2 - 4*w + 8]', '[379, 379, -2*w^3 - 3*w^2 + 8*w + 7]', '[380, 190, -w^3 + 2*w^2 + 6*w - 5]', '[380, 190, 3*w^3 - 2*w^2 - 8*w + 5]', '[380, 190, -3*w^3 - 2*w^2 + 8*w + 5]', '[380, 190, -w^3 - 2*w^2 + 6*w + 5]', '[395, 395, 2*w^3 + w^2 - 4*w - 5]', '[395, 395, 2*w^3 - 3*w^2 - 6*w + 5]', '[395, 395, 2*w^3 + 3*w^2 - 6*w - 5]', '[395, 395, 2*w^3 - w^2 - 4*w + 5]', '[400, 10, -4*w^2 + 10]', '[401, 401, w^3 + w^2 - 6*w - 1]', '[401, 401, 3*w^3 + w^2 - 8*w - 4]', '[401, 401, -3*w^3 + w^2 + 8*w - 4]', '[401, 401, -w^3 + w^2 + 6*w - 1]', '[404, 202, 3*w^3 + w^2 - 11*w - 8]', '[404, 202, 5*w^3 + 7*w^2 - 19*w - 22]', '[404, 202, -3*w^3 - 3*w^2 + 11*w + 8]', '[404, 202, -3*w^3 + w^2 + 9*w + 2]', '[405, 15, -3*w]', '[419, 419, 3*w^3 - 10*w - 4]', '[419, 419, -2*w^3 + 4*w^2 + 5*w - 12]', '[419, 419, 2*w^3 + 4*w^2 - 5*w - 12]', '[419, 419, -3*w^3 + 10*w - 4]', '[421, 421, -w^3 + 6*w + 2]', '[421, 421, 3*w^3 - 8*w - 2]', '[421, 421, -3*w^3 + 8*w - 2]', '[421, 421, w^3 - 6*w + 2]', '[439, 439, w^3 - 3*w^2 - 2*w + 11]', '[439, 439, 2*w^3 + 2*w^2 - 7*w - 3]', '[439, 439, -2*w^3 + 2*w^2 + 7*w - 3]', '[439, 439, -w^3 - 3*w^2 + 2*w + 11]', '[461, 461, 3*w^3 - w^2 - 8*w + 1]', '[461, 461, w^3 + w^2 - 6*w - 4]', '[461, 461, -w^3 + w^2 + 6*w - 4]', '[461, 461, 3*w^3 + w^2 - 8*w - 1]', '[475, 95, -2*w^3 - 3*w^2 + 5*w + 10]', '[475, 95, w^3 + 3*w^2 - 5*w - 5]', '[475, 95, -w^3 + 3*w^2 + 5*w - 5]', '[475, 95, 2*w^3 - 3*w^2 - 5*w + 10]', '[479, 479, -2*w^3 - 5*w^2 + 5*w + 8]', '[479, 479, -4*w^2 + 3*w + 6]', '[479, 479, -4*w^2 - 3*w + 6]', '[479, 479, 2*w^3 - 5*w^2 - 5*w + 8]', '[484, 22, 2*w^3 + 5*w^2 - 9*w - 17]', '[484, 22, -4*w^3 - 5*w^2 + 13*w + 19]', '[499, 499, 2*w^3 + 3*w^2 - 7*w - 6]', '[499, 499, w^3 + 3*w^2 - w - 9]', '[499, 499, -w^3 + 3*w^2 + w - 9]', '[499, 499, -2*w^3 + 3*w^2 + 7*w - 6]', '[500, 10, -3*w^3 + 10*w + 5]', '[505, 505, w^3 + 5*w^2 - 2*w - 10]', '[505, 505, w^3 - 3*w - 5]', '[505, 505, w^3 - 3*w + 5]', '[505, 505, w^3 - 5*w^2 - 2*w + 10]', '[521, 521, -3*w^3 - w^2 + 8*w + 3]', '[521, 521, w^3 + w^2 - 6*w - 2]', '[521, 521, -w^3 + w^2 + 6*w - 2]', '[521, 521, -3*w^3 + w^2 + 8*w - 3]', '[541, 541, 3*w^3 - w^2 - 8*w + 2]', '[541, 541, -w^3 + w^2 + 6*w - 3]', '[541, 541, w^3 + w^2 - 6*w - 3]', '[541, 541, 3*w^3 + w^2 - 8*w - 2]', '[556, 278, w^3 - 6*w^2 + 13]', '[556, 278, -w^3 + 6*w - 1]', '[556, 278, 4*w^3 + w^2 - 13*w - 3]', '[556, 278, -3*w^3 - 2*w^2 + 12*w + 13]', '[599, 599, -2*w^3 + 2*w^2 + 4*w - 7]', '[599, 599, 2*w^3 - 2*w^2 - 8*w + 3]', '[599, 599, -2*w^3 - 2*w^2 + 8*w + 3]', '[599, 599, 2*w^3 + 2*w^2 - 4*w - 7]', '[601, 601, 4*w^3 + 3*w^2 - 12*w - 8]', '[601, 601, -3*w^2 + 4*w + 7]', '[601, 601, -3*w^2 - 4*w + 7]', '[601, 601, -4*w^3 + 3*w^2 + 12*w - 8]', '[605, 55, -w^3 + 6*w]', '[605, 55, 3*w^3 - 8*w]', '[619, 619, -2*w^3 + 3*w^2 + 9*w - 6]', '[619, 619, -w^3 + 3*w^2 + 6*w - 12]', '[619, 619, w^3 + 3*w^2 - 6*w - 12]', '[619, 619, -3*w^3 + 3*w^2 + 8*w - 3]', '[625, 5, 5]', '[641, 641, 4*w^3 - 12*w + 3]', '[641, 641, -w^3 + w^2 + 4*w - 8]', '[641, 641, -w^3 - w^2 + 4*w + 8]', '[641, 641, -4*w^3 + 12*w + 3]', '[656, 82, 2*w + 6]', '[656, 82, -2*w^3 + 6*w + 6]', '[656, 82, -2*w^3 + 6*w - 6]', '[656, 82, 2*w - 6]', '[659, 659, -w^3 + 4*w^2 + 4*w - 6]', '[659, 659, 2*w^3 - 2*w^2 - 3*w + 6]', '[659, 659, -2*w^3 - 2*w^2 + 3*w + 6]', '[659, 659, w^3 + 4*w^2 - 4*w - 6]', '[661, 661, -w^3 + 5*w^2 + 2*w - 11]', '[661, 661, -w^3 + 5*w^2 + 4*w - 14]', '[661, 661, w^3 + 5*w^2 - 4*w - 14]', '[661, 661, w^3 + 5*w^2 - 2*w - 11]', '[695, 695, -3*w^3 + 6*w^2 + 7*w - 10]', '[695, 695, -3*w^2 - 4*w + 10]', '[695, 695, -3*w^3 + 2*w^2 + 8*w - 10]', '[695, 695, -3*w^3 - 6*w^2 + 7*w + 10]', '[701, 701, -2*w^2 + w + 11]', '[701, 701, w^3 - 5*w^2 - 4*w + 13]', '[701, 701, -w^3 - 5*w^2 + 4*w + 13]', '[701, 701, -2*w^2 - w + 11]', '[716, 358, 5*w^3 + 4*w^2 - 20*w - 17]', '[716, 358, -w^2 + w - 3]', '[716, 358, 6*w^3 + 11*w^2 - 23*w - 33]', '[716, 358, -7*w^3 - 2*w^2 + 22*w + 13]', '[719, 719, -2*w^3 + 4*w^2 + 8*w - 9]', '[719, 719, -2*w^3 + 4*w^2 + 4*w - 11]', '[719, 719, 2*w^3 + 4*w^2 - 4*w - 11]', '[719, 719, 2*w^3 + 4*w^2 - 8*w - 9]', '[724, 362, 3*w^3 - 2*w^2 - 10*w + 3]', '[724, 362, -2*w^3 + 3*w^2 + 5*w - 11]', '[724, 362, 2*w^3 + 3*w^2 - 5*w - 11]', '[724, 362, -3*w^3 - 2*w^2 + 10*w + 3]', '[739, 739, 2*w^3 + 3*w^2 - 8*w - 6]', '[739, 739, 3*w^2 - 2*w - 12]', '[739, 739, 3*w^2 + 2*w - 12]', '[739, 739, -2*w^3 + 3*w^2 + 8*w - 6]', '[761, 761, -3*w^3 + 2*w^2 + 10*w - 12]', '[761, 761, -2*w^3 - 6*w^2 + 4*w + 13]', '[761, 761, 2*w^3 - 6*w^2 - 4*w + 13]', '[761, 761, w^3 - w^2 - 7*w - 1]', '[779, 779, 3*w^3 + w^2 - 10*w + 1]', '[779, 779, -w^3 + 4*w^2 + w - 12]', '[779, 779, w^3 - w^2 + 6]', '[779, 779, 4*w^2 - 3*w - 12]', '[779, 779, -2*w^3 - 4*w^2 + 7*w + 8]', '[779, 779, -2*w^3 + w^2 + 4*w - 7]', '[779, 779, 2*w^3 - w^2 - 8*w - 2]', '[779, 779, -3*w^3 + 4*w^2 + 9*w - 8]', '[779, 779, -3*w^3 - 4*w^2 + 9*w + 8]', '[779, 779, 2*w^3 + w^2 - 8*w + 2]', '[779, 779, -2*w^3 - w^2 + 4*w + 7]', '[779, 779, -2*w^3 + 4*w^2 + 7*w - 8]', '[779, 779, -4*w^2 - 3*w + 12]', '[779, 779, -w^3 - w^2 + 6]', '[779, 779, -w^3 - 4*w^2 + w + 12]', '[779, 779, -3*w^3 + w^2 + 10*w + 1]', '[796, 398, -5*w^3 - 10*w^2 + 20*w + 31]', '[796, 398, -3*w^3 - 3*w^2 + 13*w + 8]', '[796, 398, 9*w^3 + 9*w^2 - 31*w - 32]', '[796, 398, w^3 + 5*w^2 - 3*w - 12]', '[820, 410, -w^3 + 3*w^2 + w - 10]', '[820, 410, -2*w^3 + 3*w^2 + 7*w - 5]', '[820, 410, 2*w^3 + 3*w^2 - 7*w - 5]', '[820, 410, -w^3 - 3*w^2 + w + 10]', '[821, 821, -w^3 - 2*w^2 + 3*w + 11]', '[821, 821, -w^3 + 5*w^2 + 3*w - 13]', '[821, 821, w^3 + 5*w^2 - 3*w - 13]', '[821, 821, w^3 - 2*w^2 - 3*w + 11]', '[839, 839, 3*w^3 + 3*w^2 - 11*w - 7]', '[839, 839, 2*w^3 - 3*w^2 - 3*w + 8]', '[839, 839, -2*w^3 - 3*w^2 + 3*w + 8]', '[839, 839, -3*w^3 + 3*w^2 + 11*w - 7]', '[841, 29, 5*w^2 - 14]', '[841, 29, 5*w^2 - 11]', '[859, 859, 2*w^3 + 2*w^2 - 9*w - 2]', '[859, 859, 3*w^3 + 2*w^2 - 7*w - 8]', '[859, 859, -3*w^3 + 2*w^2 + 7*w - 8]', '[859, 859, -2*w^3 + 2*w^2 + 9*w - 2]', '[881, 881, 4*w^3 + 2*w^2 - 12*w - 7]', '[881, 881, 4*w^3 + w^2 - 12*w - 1]', '[881, 881, -4*w^3 + w^2 + 12*w - 1]', '[881, 881, 4*w^3 - 2*w^2 - 12*w + 7]', '[895, 895, 2*w^3 - 3*w^2 - 7*w]', '[895, 895, 2*w^3 + 6*w^2 - 3*w - 15]', '[895, 895, 2*w^3 - 6*w^2 - 3*w + 15]', '[895, 895, 2*w^3 + 3*w^2 - 7*w]', '[905, 905, 2*w^3 + 7*w^2 - 9*w - 20]', '[905, 905, 4*w^3 + 6*w^2 - 17*w - 20]', '[905, 905, 4*w^3 + w^2 - 12*w - 5]', '[905, 905, -3*w^3 - 3*w^2 + 11*w + 15]', '[919, 919, 2*w^3 + 3*w^2 - 5*w - 12]', '[919, 919, 3*w^3 - 3*w^2 - 10*w + 6]', '[919, 919, -3*w^3 - 3*w^2 + 10*w + 6]', '[919, 919, -2*w^3 + 3*w^2 + 5*w - 12]', '[941, 941, w^3 - 2*w - 6]', '[941, 941, w^3 - 4*w - 6]', '[941, 941, -w^3 + 4*w - 6]', '[941, 941, -w^3 + 2*w - 6]', '[944, 118, 4*w^2 + 2*w - 14]', '[944, 118, -2*w^3 - 4*w^2 + 6*w + 6]', '[944, 118, 4*w^3 - 2*w^2 - 14*w + 4]', '[944, 118, 2*w^3 - 2*w^2 - 2*w + 6]', '[956, 478, -9*w^3 - 5*w^2 + 29*w + 24]', '[956, 478, 7*w^3 + 11*w^2 - 25*w - 34]', '[956, 478, w^3 - w^2 - w - 4]', '[956, 478, 3*w^3 + w^2 - 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10*w - 4]', '[1801, 1801, -2*w^3 + w^2 + 10*w - 4]', '[1801, 1801, 4*w^3 + w^2 - 10*w - 1]', '[1805, 95, 2*w^3 - 7*w^2 - 8*w + 20]', '[1805, 95, 2*w^3 + 7*w^2 - 8*w - 20]', '[1805, 95, -4*w^3 + 11*w]', '[1805, 95, w^3 - 7*w]', '[1805, 95, -2*w^3 + 7*w^2 + 4*w - 15]', '[1805, 95, -2*w^3 - 7*w^2 + 4*w + 15]', '[1805, 1805, -w^3 + 6*w^2 + 3*w - 15]', '[1805, 1805, 6*w^2 + w - 15]', '[1805, 1805, 6*w^2 - w - 15]', '[1805, 1805, w^3 + 6*w^2 - 3*w - 15]', '[1844, 922, 6*w^3 + w^2 - 19*w - 11]', '[1844, 922, 7*w^3 + 10*w^2 - 26*w - 31]', '[1844, 922, -3*w^3 - 4*w^2 + 12*w + 9]', '[1844, 922, 4*w^3 + w^2 - 15*w - 9]', '[1861, 1861, -2*w^3 - 7*w^2 + 4*w + 16]', '[1861, 1861, -5*w^3 - 4*w^2 + 13*w + 7]', '[1861, 1861, 5*w^3 - 4*w^2 - 13*w + 7]', '[1861, 1861, 2*w^3 - 7*w^2 - 4*w + 16]', '[1879, 1879, 4*w^2 - 4*w - 13]', '[1879, 1879, -4*w^3 - 4*w^2 + 12*w + 7]', '[1879, 1879, -4*w^3 + 4*w^2 + 12*w - 7]', '[1879, 1879, 4*w^2 + 4*w - 13]', '[1895, 1895, -3*w^3 - 2*w^2 + 7*w + 10]', '[1895, 1895, -3*w^3 - 6*w^2 + 8*w + 10]', '[1895, 1895, -3*w^3 + 6*w^2 + 8*w - 10]', '[1895, 1895, -3*w^3 + 2*w^2 + 7*w - 10]', '[1900, 190, 2*w^3 + w^2 - 5*w + 5]', '[1900, 190, -w^3 - w^2 + 5*w + 10]', '[1900, 190, -w^3 + w^2 + 5*w - 10]', '[1900, 190, -2*w^3 + w^2 + 5*w + 5]', '[1901, 1901, 4*w^3 + w^2 - 10*w - 2]', '[1901, 1901, -2*w^3 + w^2 + 10*w - 3]', '[1901, 1901, 2*w^3 + w^2 - 10*w - 3]', '[1901, 1901, -4*w^3 + w^2 + 10*w - 2]', '[1916, 958, -w^3 - 3*w^2 + 9*w + 12]', '[1916, 958, -w^3 - 8*w^2 + 10*w + 19]', '[1916, 958, 5*w^3 + 4*w^2 - 14*w - 11]', '[1916, 958, 5*w^3 - 3*w^2 - 11*w + 2]', '[1919, 1919, -3*w^3 - 2*w^2 + 4*w - 2]', '[1919, 1919, -4*w^3 + 6*w^2 + 12*w - 13]', '[1919, 1919, -6*w^2 + 4*w + 17]', '[1919, 1919, -2*w^3 - 4*w^2 + 8*w + 7]', '[1919, 1919, -2*w^3 + 4*w^2 + 4*w - 13]', '[1919, 1919, 3*w^3 + 2*w^2 - 12*w - 2]', '[1919, 1919, 3*w^3 - 2*w^2 - 6*w + 8]', '[1919, 1919, 5*w^3 + 2*w^2 - 18*w - 12]', '[1919, 1919, -5*w^3 + 2*w^2 + 18*w - 12]', '[1919, 1919, -3*w^3 - 2*w^2 + 6*w + 8]', '[1919, 1919, -3*w^3 + 2*w^2 + 12*w - 2]', '[1919, 1919, 2*w^3 + 4*w^2 - 4*w - 13]', '[1919, 1919, 2*w^3 - 4*w^2 - 8*w + 7]', '[1919, 1919, -6*w^2 - 4*w + 17]', '[1919, 1919, 4*w^3 + 6*w^2 - 12*w - 13]', '[1919, 1919, 3*w^3 - 2*w^2 - 4*w - 2]', '[1936, 22, 6*w^2 - 16]', '[1936, 22, -2*w^2 + 12]', '[1975, 395, w^3 + 2*w^2 - 10]', '[1975, 395, 3*w^3 - 2*w^2 - 10*w]', '[1975, 395, -3*w^3 - 2*w^2 + 10*w]', '[1975, 395, -w^3 + 2*w^2 - 10]', '[1979, 1979, -3*w^3 + 5*w^2 + 9*w - 9]', '[1979, 1979, 5*w^2 - 3*w - 16]', '[1979, 1979, 5*w^2 + 3*w - 16]', '[1979, 1979, 3*w^3 + 5*w^2 - 9*w - 9]', '[1996, 998, 5*w^3 + 7*w^2 - 21*w - 24]', '[1996, 998, 3*w^3 + 3*w^2 - 11*w - 16]', '[1996, 998, 3*w^3 + 9*w^2 - 13*w - 26]', '[1996, 998, -5*w^3 - w^2 + 15*w + 6]', '[1999, 1999, -2*w^3 + w^2 + 3*w - 8]', '[1999, 1999, -3*w^3 - w^2 + 11*w - 3]', '[1999, 1999, 3*w^3 - w^2 - 11*w - 3]', '[1999, 1999, 2*w^3 + w^2 - 3*w - 8]', '[2000, 10, -4*w^3 + 10*w]', '[2005, 2005, w^3 - 7*w^2 - 4*w + 15]', '[2005, 2005, w^3 - w^2 - w - 5]', '[2005, 2005, w^3 + w^2 - w + 5]', '[2005, 2005, w^3 + 7*w^2 - 4*w - 15]', '[2020, 1010, w^3 + 4*w^2 - 8*w - 15]', '[2020, 1010, 7*w^3 + 6*w^2 - 22*w - 25]', '[2020, 1010, -3*w^3 - 4*w^2 + 8*w + 15]', '[2020, 1010, w^3 - 6*w^2 + 2*w + 15]', '[2025, 15, 6*w^2 - 15]', '[2039, 2039, -4*w^3 + 7*w^2 + 16*w - 19]', '[2039, 2039, 3*w^3 + 5*w^2 - 8*w - 4]', '[2039, 2039, -3*w^3 + 5*w^2 + 8*w - 4]', '[2039, 2039, 4*w^3 + 7*w^2 - 16*w - 19]', '[2081, 2081, -5*w - 3]', '[2081, 2081, 5*w^3 - 15*w - 3]', '[2081, 2081, -5*w^3 + 15*w - 3]', '[2081, 2081, 5*w - 3]', '[2084, 1042, -6*w^3 - 3*w^2 + 21*w + 17]', '[2084, 1042, 5*w^3 + 8*w^2 - 20*w - 23]', '[2084, 1042, -5*w^3 - 6*w^2 + 18*w + 17]', '[2084, 1042, 4*w^3 - w^2 - 13*w - 3]', '[2095, 2095, 5*w^2 - 4*w - 15]', '[2095, 2095, 4*w^3 - 5*w^2 - 12*w + 10]', '[2095, 2095, 4*w^3 + 5*w^2 - 12*w - 10]', '[2095, 2095, -3*w^3 + 4*w^2 + w - 10]', '[2099, 2099, 4*w^3 - 2*w^2 - 15*w + 3]', '[2099, 2099, 3*w^3 - 2*w^2 - 5*w + 7]', '[2099, 2099, -3*w^3 - 2*w^2 + 5*w + 7]', '[2099, 2099, -4*w^3 - 2*w^2 + 15*w + 3]', '[2105, 2105, 7*w^2 - 2*w - 15]', '[2105, 2105, w^2 + 2*w + 5]', '[2105, 2105, -w^2 + 2*w - 5]', '[2105, 2105, -7*w^2 - 2*w + 15]', '[2141, 2141, 5*w^3 + 2*w^2 - 15*w - 4]', '[2141, 2141, 2*w^2 + 5*w - 6]', '[2141, 2141, 2*w^2 - 5*w - 6]', '[2141, 2141, -5*w^3 + 2*w^2 + 15*w - 4]', '[2161, 2161, -w - 7]', '[2161, 2161, w^3 - 3*w - 7]', '[2161, 2161, -w^3 + 3*w - 7]', '[2161, 2161, w - 7]', '[2164, 1082, 5*w^3 - 16*w - 7]', '[2164, 1082, -4*w^3 - 5*w^2 + 15*w + 13]', '[2164, 1082, 6*w^3 + 9*w^2 - 23*w - 27]', '[2164, 1082, 5*w^3 + 2*w^2 - 18*w - 13]', '[2179, 2179, -4*w^3 + 3*w^2 + 14*w - 6]', '[2179, 2179, 2*w^3 + 3*w^2 - 4*w - 12]', '[2179, 2179, -2*w^3 + 3*w^2 + 4*w - 12]', '[2179, 2179, 4*w^3 + 3*w^2 - 14*w - 6]', '[2195, 2195, -3*w^3 + 3*w^2 + 11*w - 5]', '[2195, 2195, 2*w^3 + 3*w^2 - 3*w - 10]', '[2195, 2195, 2*w^3 - 3*w^2 - 3*w + 10]', '[2195, 2195, -3*w^3 - 3*w^2 + 11*w + 5]', '[2221, 2221, -4*w^3 + w^2 + 13*w - 12]', '[2221, 2221, -3*w^3 + 4*w^2 + 14*w - 14]', '[2221, 2221, 8*w^3 + 6*w^2 - 27*w - 22]', '[2221, 2221, 4*w^3 + w^2 - 13*w - 12]', '[2224, 278, 4*w^3 - 6*w^2 - 8*w + 14]', '[2224, 278, -4*w^3 + 14*w - 8]', '[2224, 278, 4*w^3 - 6*w^2 - 16*w + 16]', '[2224, 278, -4*w^3 - 6*w^2 + 8*w + 14]', '[2239, 2239, -4*w^3 - 3*w^2 + 12*w + 3]', '[2239, 2239, 3*w^2 + 4*w - 12]', '[2239, 2239, 3*w^2 - 4*w - 12]', '[2239, 2239, 4*w^3 - 3*w^2 - 12*w + 3]', '[2281, 2281, -6*w^3 - 4*w^2 + 19*w + 14]', '[2281, 2281, -4*w^3 + 2*w^2 + 17*w - 4]', '[2281, 2281, 4*w^3 + 2*w^2 - 17*w - 4]', '[2281, 2281, 6*w^3 - 4*w^2 - 19*w + 14]', '[2299, 209, 3*w^3 + 5*w^2 - 8*w - 17]', '[2299, 209, -w^3 - 5*w^2 + 6*w + 19]', '[2299, 209, -2*w^3 - 4*w^2 + 9*w + 7]', '[2299, 209, 4*w^3 - 2*w^2 - 13*w + 1]', '[2299, 209, 2*w^3 - 4*w^2 - 9*w + 7]', '[2299, 209, -4*w^3 - 2*w^2 + 13*w + 1]', '[2299, 209, -3*w^3 + 5*w^2 + 8*w - 17]', '[2299, 209, w^3 - 5*w^2 - 6*w + 19]', '[2305, 2305, w^3 + w^2 - 4*w + 5]', '[2305, 2305, w^3 + 7*w^2 - w - 15]', '[2305, 2305, -w^3 + 7*w^2 + w - 15]', '[2305, 2305, w^3 - w^2 - 4*w - 5]', '[2339, 2339, 2*w^3 - 7*w^2 - 10*w + 23]', '[2339, 2339, w^3 + 4*w^2 - 8*w - 4]', '[2339, 2339, -w^3 + 4*w^2 + 8*w - 4]', '[2339, 2339, -5*w^3 + 4*w^2 + 14*w - 16]', '[2341, 2341, -5*w^3 + 4*w^2 + 13*w - 8]', '[2341, 2341, -3*w^3 + 8*w^2 + 7*w - 19]', '[2341, 2341, 3*w^3 + 8*w^2 - 7*w - 19]', '[2341, 2341, 5*w^3 + 4*w^2 - 13*w - 8]', '[2375, 95, -3*w^3 - 5*w^2 + 10*w + 10]', '[2375, 95, -w^3 + 5*w^2 - 15]', '[2375, 95, -w^3 - 5*w^2 + 15]', '[2375, 95, -3*w^3 + 5*w^2 + 10*w - 10]', '[2381, 2381, 6*w^3 + 4*w^2 - 19*w - 12]', '[2381, 2381, -4*w^3 + 4*w^2 + 17*w - 12]', '[2381, 2381, 4*w^3 + 4*w^2 - 17*w - 12]', '[2381, 2381, -5*w^3 + 4*w^2 + 11*w - 8]', '[2395, 2395, -5*w^3 - 5*w^2 + 8*w + 10]', '[2395, 2395, -4*w^3 - 3*w^2 + 6*w]', '[2395, 2395, -4*w^3 + 3*w^2 + 6*w]', '[2395, 2395, -5*w^3 + 5*w^2 + 8*w - 10]', '[2396, 1198, w^3 + 7*w^2 - 5*w - 18]', '[2396, 1198, 7*w^3 + 5*w^2 - 23*w - 18]', '[2396, 1198, -5*w^3 - 7*w^2 + 21*w + 22]', '[2396, 1198, 5*w^3 + 3*w^2 - 17*w - 18]', '[2399, 2399, -w^3 + 5*w^2 + w - 17]', '[2399, 2399, 3*w^3 + 2*w^2 - 11*w - 1]', '[2399, 2399, -3*w^3 + 2*w^2 + 11*w - 1]', '[2399, 2399, w^3 + 5*w^2 - w - 17]', '[2401, 7, -7]', '[2404, 1202, 10*w^3 + 9*w^2 - 37*w - 37]', '[2404, 1202, -5*w^3 - 12*w^2 + 22*w + 33]', '[2404, 1202, 3*w^3 + 4*w^2 - 10*w - 7]', '[2404, 1202, -6*w^3 + w^2 + 19*w + 3]', '[2419, 2419, -7*w^3 + 6*w^2 + 23*w - 16]', '[2419, 2419, -6*w^3 + 7*w^2 + 22*w - 21]', '[2419, 2419, -4*w^3 + 7*w^2 + 6*w - 14]', '[2419, 2419, 6*w^3 + w^2 - 20*w - 9]', '[2419, 2419, -4*w^3 + 7*w - 4]', '[2419, 2419, 5*w^3 - 19*w - 4]', '[2419, 2419, 2*w^3 - 6*w^2 + w + 14]', '[2419, 2419, 2*w^3 - 5*w^2 - 10*w + 21]', '[2419, 2419, 2*w^3 + w^2 + 4]', '[2419, 2419, 3*w^3 - 8*w^2 - 14*w + 26]', '[2419, 2419, w^3 + 4*w^2 - 6*w - 4]', '[2419, 2419, 3*w^3 + 4*w^2 - 8*w - 16]', '[2419, 2419, 4*w^3 + 5*w^2 - 10*w - 4]', '[2419, 2419, 2*w^3 + 7*w^2 - 4*w - 21]', '[2419, 2419, -2*w^3 - 7*w^2 + 8*w + 14]', '[2419, 2419, -5*w^3 - 8*w^2 + 12*w + 14]', '[2420, 110, -5*w^3 - 7*w^2 + 19*w + 20]', '[2420, 110, 5*w^3 + w^2 - 17*w - 10]', '[2441, 2441, w^3 + 3*w^2 - 8*w - 9]', '[2441, 2441, 5*w^3 - 3*w^2 - 14*w + 6]', '[2441, 2441, -5*w^3 - 3*w^2 + 14*w + 6]', '[2441, 2441, -w^3 + 3*w^2 + 8*w - 9]', '[2459, 2459, 3*w^3 - 4*w^2 - 11*w + 8]', '[2459, 2459, -w^3 + 4*w^2 + w - 16]', '[2459, 2459, w^3 + 4*w^2 - w - 16]', '[2459, 2459, -3*w^3 - 4*w^2 + 11*w + 8]', '[2476, 1238, -7*w^3 - 5*w^2 + 23*w + 16]', '[2476, 1238, w^3 + 2*w^2 - 2*w - 13]', '[2476, 1238, 11*w^3 + 16*w^2 - 40*w - 53]', '[2476, 1238, 7*w^3 + 11*w^2 - 29*w - 34]', '[2495, 2495, 3*w^3 + 3*w^2 - 6*w - 10]', '[2495, 2495, 3*w^3 - 4*w^2 - 9*w + 5]', '[2495, 2495, 3*w^3 + 4*w^2 - 9*w - 5]', '[2495, 2495, 3*w^3 - 3*w^2 - 6*w + 10]', '[2500, 10, -5*w^3 - 5*w^2 + 15*w + 20]', '[2501, 2501, 3*w^3 + 8*w^2 - 11*w - 24]', '[2501, 2501, 2*w^3 - 7*w^2 - 6*w + 19]', '[2501, 2501, 6*w^3 + 11*w^2 - 16*w - 26]', '[2501, 2501, -2*w^3 - 8*w^2 + 3*w + 16]', '[2501, 2501, 7*w^2 + 2*w - 16]', '[2501, 2501, 4*w^3 - 10*w^2 - 15*w + 26]', '[2501, 2501, -3*w^3 - 10*w^2 + 5*w + 24]', '[2501, 2501, -2*w^3 + 11*w^2 + 12*w - 29]', '[2501, 2501, 2*w^3 + 11*w^2 - 12*w - 29]', '[2501, 2501, 3*w^3 - 10*w^2 - 5*w + 24]', '[2501, 2501, 4*w^3 + 10*w^2 - 15*w - 26]', '[2501, 2501, -7*w^2 + 2*w + 16]', '[2501, 2501, -2*w^3 + 8*w^2 + 3*w - 16]', '[2501, 2501, 6*w^3 - 11*w^2 - 16*w + 26]', '[2501, 2501, -2*w^3 - 7*w^2 + 6*w + 19]', '[2501, 2501, -3*w^3 + 8*w^2 + 11*w - 24]', '[2521, 2521, 3*w^3 - w^2 - 9*w + 11]', '[2521, 2521, -5*w^3 + 2*w^2 + 14*w - 8]', '[2521, 2521, 5*w^3 + 2*w^2 - 14*w - 8]', '[2521, 2521, -3*w^3 - w^2 + 9*w + 11]', '[2525, 505, -w^2 - 5*w]', '[2525, 505, 5*w^3 + w^2 - 15*w - 5]', '[2525, 505, -5*w^3 + w^2 + 15*w - 5]', '[2525, 505, -w^2 + 5*w]', '[2539, 2539, -4*w^3 + 4*w^2 + 14*w - 9]', '[2539, 2539, -2*w^3 - 4*w^2 + 2*w + 11]', '[2539, 2539, 2*w^3 - 4*w^2 - 2*w + 11]', '[2539, 2539, 4*w^3 + 4*w^2 - 14*w - 9]', '[2564, 1282, 5*w^3 + w^2 - 19*w - 8]', '[2564, 1282, 3*w^3 + 4*w^2 - 8*w - 17]', '[2564, 1282, -9*w^3 - 10*w^2 + 30*w + 37]', '[2564, 1282, -11*w^3 - 7*w^2 + 37*w + 32]', '[2579, 2579, -3*w^3 - 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3]', '[9901, 9901, -6*w^3 + w^2 + 15*w - 2]', '[9904, 1238, -4*w^3 + 6*w^2 + 18*w - 12]', '[9904, 1238, -2*w^3 + 6*w^2 + 12*w - 24]', '[9904, 1238, 2*w^3 + 6*w^2 - 12*w - 24]', '[9904, 1238, 4*w^3 + 6*w^2 - 18*w - 12]', '[9941, 9941, -10*w^2 - 2*w + 21]', '[9941, 9941, -2*w^3 - 10*w^2 + 6*w + 29]', '[9941, 9941, 2*w^3 - 10*w^2 - 6*w + 29]', '[9941, 9941, -10*w^2 + 2*w + 21]', '[9980, 4990, 7*w^3 + 4*w^2 - 24*w - 25]', '[9980, 4990, 9*w^3 + 2*w^2 - 26*w - 15]', '[9980, 4990, 3*w^3 + 4*w^2 - 16*w - 15]', '[9980, 4990, -w^3 - 10*w^2 + 6*w + 25]', '[9995, 9995, w^3 - 7*w^2 - 8*w + 10]', '[9995, 9995, w^3 + 4*w^2 + 3*w - 15]', '[9995, 9995, -w^3 + 4*w^2 - 3*w - 15]', '[9995, 9995, w^3 + 7*w^2 - 8*w - 10]', '[10000, 10, 10]'], 'label': '4.4.2000.1', 'narrow_class_no': 2, 'primes': ['[4, 2, -w^3 - w^2 + 3*w + 4]', '[5, 5, w]', '[19, 19, -w^2 + w + 4]', '[19, 19, w^3 - w^2 - 3*w + 1]', '[19, 19, -w^3 - w^2 + 3*w + 1]', '[19, 19, -w^2 - w + 4]', '[41, 41, w + 3]', '[41, 41, -w^3 + 3*w + 3]', '[41, 41, -w^3 + 3*w - 3]', '[41, 41, w - 3]', '[59, 59, 2*w^2 + w - 7]', '[59, 59, -w^3 - 2*w^2 + 3*w + 3]', '[59, 59, 2*w^3 - w^2 - 7*w + 2]', '[59, 59, w^3 - w^2 - w + 3]', '[61, 61, 3*w^2 - w - 8]', '[61, 61, w^3 + 3*w^2 - 3*w - 7]', '[61, 61, -w^3 + 3*w^2 + 3*w - 7]', '[61, 61, -3*w^2 - w + 8]', '[79, 79, -w^3 + 2*w^2 + 2*w - 6]', '[79, 79, w^3 + 2*w^2 - 4*w - 4]', '[79, 79, -w^3 + 2*w^2 + 4*w - 4]', '[79, 79, w^3 + 2*w^2 - 2*w - 6]', '[81, 3, -3]', '[101, 101, 2*w^3 + w^2 - 5*w - 2]', '[101, 101, w^3 + w^2 - 5*w - 3]', '[101, 101, -w^3 + w^2 + 5*w - 3]', '[101, 101, -2*w^3 + w^2 + 5*w - 2]', '[121, 11, 3*w^2 - 8]', '[121, 11, -w^2 + 6]', '[139, 139, 2*w^3 - 3*w^2 - 4*w + 7]', '[139, 139, -2*w^3 + 7*w - 4]', '[139, 139, 2*w^3 - 3*w^2 - 8*w + 8]', '[139, 139, -2*w^3 - 3*w^2 + 4*w + 7]', '[179, 179, 3*w^3 + 2*w^2 - 9*w - 3]', '[179, 179, 2*w^2 + 3*w - 7]', '[179, 179, 2*w^2 - 3*w - 7]', '[179, 179, -3*w^3 + 2*w^2 + 9*w - 3]', '[181, 181, 4*w^3 + 2*w^2 - 13*w - 9]', '[181, 181, w^3 + 4*w^2 - 4*w - 12]', '[181, 181, 4*w^3 + 4*w^2 - 14*w - 17]', '[181, 181, -3*w^3 - 3*w^2 + 12*w + 11]', '[199, 199, -3*w^2 + 2*w + 9]', '[199, 199, -2*w^3 + 8*w - 3]', '[199, 199, 2*w^3 - 8*w - 3]', '[199, 199, 2*w^3 + 4*w^2 - 9*w - 14]', '[239, 239, -3*w^3 + w^2 + 9*w + 1]', '[239, 239, w^2 - 3*w - 6]', '[239, 239, w^2 + 3*w - 6]', '[239, 239, 3*w^3 + w^2 - 9*w + 1]', '[241, 241, 4*w^2 + w - 11]', '[241, 241, w^3 - w^2 - 4*w + 7]', '[241, 241, -w^3 - w^2 + 4*w + 7]', '[241, 241, 4*w^2 - w - 11]', '[281, 281, 3*w^3 + 2*w^2 - 8*w - 6]', '[281, 281, w^3 + w^2 - 3*w - 7]', '[281, 281, -w^3 + w^2 + 3*w - 7]', '[281, 281, -3*w^3 + 2*w^2 + 8*w - 6]', '[359, 359, 2*w^3 - 2*w^2 - 5*w + 8]', '[359, 359, -3*w^3 - 2*w^2 + 10*w + 4]', '[359, 359, 3*w^3 - 2*w^2 - 10*w + 4]', '[359, 359, 2*w^3 + 2*w^2 - 5*w - 8]', '[379, 379, 2*w^3 - 3*w^2 - 8*w + 7]', '[379, 379, -2*w^3 - 3*w^2 + 4*w + 8]', '[379, 379, 2*w^3 - 3*w^2 - 4*w + 8]', '[379, 379, -2*w^3 - 3*w^2 + 8*w + 7]', '[401, 401, w^3 + w^2 - 6*w - 1]', '[401, 401, 3*w^3 + w^2 - 8*w - 4]', '[401, 401, -3*w^3 + w^2 + 8*w - 4]', '[401, 401, -w^3 + w^2 + 6*w - 1]', '[419, 419, 3*w^3 - 10*w - 4]', '[419, 419, -2*w^3 + 4*w^2 + 5*w - 12]', '[419, 419, 2*w^3 + 4*w^2 - 5*w - 12]', '[419, 419, -3*w^3 + 10*w - 4]', '[421, 421, -w^3 + 6*w + 2]', '[421, 421, 3*w^3 - 8*w - 2]', '[421, 421, -3*w^3 + 8*w - 2]', '[421, 421, w^3 - 6*w + 2]', '[439, 439, w^3 - 3*w^2 - 2*w + 11]', '[439, 439, 2*w^3 + 2*w^2 - 7*w - 3]', '[439, 439, -2*w^3 + 2*w^2 + 7*w - 3]', '[439, 439, -w^3 - 3*w^2 + 2*w + 11]', '[461, 461, 3*w^3 - w^2 - 8*w + 1]', '[461, 461, w^3 + w^2 - 6*w - 4]', '[461, 461, -w^3 + w^2 + 6*w - 4]', '[461, 461, 3*w^3 + w^2 - 8*w - 1]', '[479, 479, -2*w^3 - 5*w^2 + 5*w + 8]', '[479, 479, -4*w^2 + 3*w + 6]', '[479, 479, -4*w^2 - 3*w + 6]', '[479, 479, 2*w^3 - 5*w^2 - 5*w + 8]', '[499, 499, 2*w^3 + 3*w^2 - 7*w - 6]', '[499, 499, w^3 + 3*w^2 - w - 9]', '[499, 499, -w^3 + 3*w^2 + w - 9]', '[499, 499, -2*w^3 + 3*w^2 + 7*w - 6]', '[521, 521, -3*w^3 - w^2 + 8*w + 3]', '[521, 521, w^3 + w^2 - 6*w - 2]', '[521, 521, -w^3 + w^2 + 6*w - 2]', '[521, 521, -3*w^3 + w^2 + 8*w - 3]', '[541, 541, 3*w^3 - w^2 - 8*w + 2]', '[541, 541, -w^3 + w^2 + 6*w - 3]', '[541, 541, w^3 + w^2 - 6*w - 3]', '[541, 541, 3*w^3 + w^2 - 8*w - 2]', '[599, 599, -2*w^3 + 2*w^2 + 4*w - 7]', '[599, 599, 2*w^3 - 2*w^2 - 8*w + 3]', '[599, 599, -2*w^3 - 2*w^2 + 8*w + 3]', '[599, 599, 2*w^3 + 2*w^2 - 4*w - 7]', '[601, 601, 4*w^3 + 3*w^2 - 12*w - 8]', '[601, 601, -3*w^2 + 4*w + 7]', '[601, 601, -3*w^2 - 4*w + 7]', '[601, 601, -4*w^3 + 3*w^2 + 12*w - 8]', '[619, 619, -2*w^3 + 3*w^2 + 9*w - 6]', '[619, 619, -w^3 + 3*w^2 + 6*w - 12]', '[619, 619, w^3 + 3*w^2 - 6*w - 12]', '[619, 619, -3*w^3 + 3*w^2 + 8*w - 3]', '[641, 641, 4*w^3 - 12*w + 3]', '[641, 641, -w^3 + w^2 + 4*w - 8]', '[641, 641, -w^3 - w^2 + 4*w + 8]', '[641, 641, -4*w^3 + 12*w + 3]', '[659, 659, -w^3 + 4*w^2 + 4*w - 6]', '[659, 659, 2*w^3 - 2*w^2 - 3*w + 6]', '[659, 659, -2*w^3 - 2*w^2 + 3*w + 6]', '[659, 659, w^3 + 4*w^2 - 4*w - 6]', '[661, 661, -w^3 + 5*w^2 + 2*w - 11]', '[661, 661, -w^3 + 5*w^2 + 4*w - 14]', '[661, 661, w^3 + 5*w^2 - 4*w - 14]', '[661, 661, w^3 + 5*w^2 - 2*w - 11]', '[701, 701, -2*w^2 + w + 11]', '[701, 701, w^3 - 5*w^2 - 4*w + 13]', '[701, 701, -w^3 - 5*w^2 + 4*w + 13]', '[701, 701, -2*w^2 - w + 11]', '[719, 719, -2*w^3 + 4*w^2 + 8*w - 9]', '[719, 719, -2*w^3 + 4*w^2 + 4*w - 11]', '[719, 719, 2*w^3 + 4*w^2 - 4*w - 11]', '[719, 719, 2*w^3 + 4*w^2 - 8*w - 9]', '[739, 739, 2*w^3 + 3*w^2 - 8*w - 6]', '[739, 739, 3*w^2 - 2*w - 12]', '[739, 739, 3*w^2 + 2*w - 12]', '[739, 739, -2*w^3 + 3*w^2 + 8*w - 6]', '[761, 761, -3*w^3 + 2*w^2 + 10*w - 12]', '[761, 761, -2*w^3 - 6*w^2 + 4*w + 13]', '[761, 761, 2*w^3 - 6*w^2 - 4*w + 13]', '[761, 761, w^3 - w^2 - 7*w - 1]', '[821, 821, -w^3 - 2*w^2 + 3*w + 11]', '[821, 821, -w^3 + 5*w^2 + 3*w - 13]', '[821, 821, w^3 + 5*w^2 - 3*w - 13]', '[821, 821, w^3 - 2*w^2 - 3*w + 11]', '[839, 839, 3*w^3 + 3*w^2 - 11*w - 7]', '[839, 839, 2*w^3 - 3*w^2 - 3*w + 8]', '[839, 839, -2*w^3 - 3*w^2 + 3*w + 8]', '[839, 839, -3*w^3 + 3*w^2 + 11*w - 7]', '[841, 29, 5*w^2 - 14]', '[841, 29, 5*w^2 - 11]', '[859, 859, 2*w^3 + 2*w^2 - 9*w - 2]', '[859, 859, 3*w^3 + 2*w^2 - 7*w - 8]', '[859, 859, -3*w^3 + 2*w^2 + 7*w - 8]', '[859, 859, -2*w^3 + 2*w^2 + 9*w - 2]', '[881, 881, 4*w^3 + 2*w^2 - 12*w - 7]', '[881, 881, 4*w^3 + w^2 - 12*w - 1]', '[881, 881, -4*w^3 + w^2 + 12*w - 1]', '[881, 881, 4*w^3 - 2*w^2 - 12*w + 7]', '[919, 919, 2*w^3 + 3*w^2 - 5*w - 12]', '[919, 919, 3*w^3 - 3*w^2 - 10*w + 6]', '[919, 919, -3*w^3 - 3*w^2 + 10*w + 6]', '[919, 919, -2*w^3 + 3*w^2 + 5*w - 12]', '[941, 941, w^3 - 2*w - 6]', '[941, 941, w^3 - 4*w - 6]', '[941, 941, -w^3 + 4*w - 6]', '[941, 941, -w^3 + 2*w - 6]', '[961, 31, -2*w^2 + 11]', '[961, 31, 5*w^2 - 13]']}
• 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, 0, -5, 0, 1], 'conductor': 20, 'degree': 4, 'dirichlet_group': [7, 1, 3, 9], 'disc_abs': 2000, 'disc_rad': 10, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[4, 1]]], [5, [0]], [7, [[4, 1]]], [11, [[2, 2]]], [13, [[4, 1]]], [17, [[4, 1]]], [19, [[1, 4]]], [23, [[4, 1]]], [29, [[2, 2]]], [31, [[2, 2]]], [37, [[4, 1]]], [41, [[1, 4]]], [43, [[4, 1]]], [47, [[4, 1]]], [53, [[4, 1]]], [59, [[1, 4]]]], 'gal_is_abelian': True, 'gal_is_cyclic': True, 'gal_is_solvable': True, 'galois_disc_exponents': [4, 3], 'galois_label': '4T1', 'galt': 1, 'grd': 6.68740304976422, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '4.4.2000.1', 'local_algs': ['2.4.4.2', '5.4.3.2'], 'monogenic': 1, 'num_ram': 2, 'r2': 0, 'ramps': [2, 5], 'rd': 6.68740304976, 'regulator': {'__RealLiteral__': 0, 'data': '1.85281056397', 'prec': 44}, 'res': {}, 'subfield_mults': [1], 'subfields': ['-1.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a^{2} - 3 \\)', '\\( a^{3} + a^{2} - 3 a - 3 \\)', '\\( a^{2} - a - 2 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3']}