Hilbert modular form data - 2.2.13.1-576.2-m

Formats: - HTML - YAML - JSON - 2023-03-22T22:25:43.201332

• 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': 2, 'disc': 13, 'field_bad_primes': [13], 'field_label': '2.2.13.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '2.2.13.1-576.2-m', 'label_nsuffix': 12, 'label_suffix': 'm', 'level_bad_primes': [2, 3], 'level_ideal': '[576, 72, 8*w + 24]', 'level_label': '576.2', 'level_norm': 576, 'parallel_weight': 2, 'short_label': '576.2-m', 'weight': '[2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[3, 3, -w]', -1], ['[4, 2, 2]', -1]], 'hecke_eigenvalues': [0, 'e', 0, '2*e + 2', 'e - 2', '-e + 2', '2*e', '-2*e', 'e - 6', '2*e - 2', '-2*e + 2', '-e + 8', '-e + 8', '-5*e + 6', '-4*e + 6', '4*e - 6', '-2*e - 6', '-2*e - 6', '-2*e + 8', '-2*e + 8', '6*e - 2', '-6*e + 2', '-2*e', '-2*e', -4, 4, 10, -10, '-4*e - 2', '2*e + 8', '2*e + 8', '-3*e - 8', '3*e + 8', '5*e', '5*e', '-4*e + 6', '-4*e + 6', '4*e + 2', '-4*e - 2', '-e + 16', 'e - 16', '4*e - 2', '4*e - 2', '-4*e + 16', '4*e - 16', '-4*e + 8', '-4*e + 8', '-9*e + 8', '-9*e + 8', 'e - 2', '-e + 2', '-8*e + 12', '8*e - 12', '-7*e - 10', '7*e + 10', '-8*e - 8', '8*e + 8', '2*e + 14', '-2*e - 14', '-6*e - 2', '-6*e - 2', -12, -12, '-2*e + 16', '2*e - 16', '-e - 6', '-e - 6', '-3*e - 6', '-3*e - 6', '-e', 'e', 34, '-8*e + 16', '-8*e + 16', '-6*e + 26', '-6*e + 26', '-4*e - 18', '4*e + 18', '-e - 32', 'e + 32', '-3*e - 14', '-3*e - 14', '14*e - 16', '14*e - 16', '11*e + 8', '-11*e - 8', '8*e - 4', '-8*e + 4', '5*e - 24', '-5*e + 24', '-6*e', '6*e', '7*e + 10', '-7*e - 10', '-4*e - 20', '-4*e - 20', '-5*e + 16', '-5*e + 16', '7*e - 16', '-7*e + 16', '-5*e - 10', '5*e + 10', '-9*e', '-9*e', '-6*e + 32', '6*e - 32', '5*e - 14', '5*e - 14', '10*e + 8', '10*e + 8', '4*e + 10', '-4*e - 10', '-2*e', '2*e', '10*e + 2', '-10*e - 2', '-12*e - 12', '12*e + 12', '13*e - 2', '13*e - 2', '-12*e + 10', '12*e - 10', '-20*e + 6', '20*e - 6', -16, 16, '20*e - 8', '20*e - 8', '-8*e - 16', '-8*e - 16', -22, -22, '4*e - 6', '-4*e + 6', '-3*e + 38', '3*e - 38', '22*e - 16', '22*e - 16', '2*e + 10', '2*e + 10', '8*e - 38', '-8*e + 38', '-4*e + 4', '-4*e + 4', '-21*e + 10', '21*e - 10', '-5*e + 24', '-5*e + 24', '-12*e - 24', '12*e + 24', 'e + 24', 'e + 24', '-4*e - 32', '4*e + 32', '-4*e - 8', '-4*e - 8', '-4*e - 26', '-4*e - 26', '-9*e + 6', '9*e - 6', '4*e + 42', '-11*e + 40', '11*e - 40', '10*e + 8', '10*e + 8', '10*e + 14', '10*e + 14', '-6*e - 14', '6*e + 14', '-20*e + 24', '20*e - 24', '8*e + 16', '8*e + 16', '7*e - 14', '-7*e + 14', '-8*e + 8', '-8*e + 8', '-12*e + 42', '-12*e + 42', -20, 20, '10*e - 30', '10*e - 30', '8*e - 14', '-8*e + 14', '-8*e + 22', '-8*e + 22', '-13*e - 10', '-13*e - 10', '-e - 16', '-e - 16', '5*e - 8', '-5*e + 8', '-4*e - 38', '4*e + 38', -22, -22, '2*e', '-2*e', '6*e - 24', '6*e - 24', '-e + 6', '-e + 6', '16*e - 34', '-16*e + 34', -12, 12, '7*e - 16', '7*e - 16', '20*e - 2', '20*e - 2', '-18*e + 14', '18*e - 14', '26*e - 16', '26*e - 16', '-8*e + 16', '-8*e + 16', '-e + 62', 'e - 62', '15*e + 6', '-6*e + 14', '-6*e + 14', '-21*e - 8', '21*e + 8', '-24*e + 22', '-24*e + 22', '-13*e - 30', '13*e + 30', '2*e + 8', '-2*e - 8', '22*e - 16', '22*e - 16', '24*e + 6', '24*e + 6', '-24*e + 4', '-24*e + 4', '-13*e - 34', '13*e + 34', '-e + 8', '-e + 8', '-16*e + 20', '16*e - 20', '12*e - 40', '-12*e + 40', '9*e + 40', '9*e + 40', '12*e - 24', '12*e - 24', '-14*e - 32', '14*e + 32', '6*e + 8', '-6*e - 8', '13*e - 30', '13*e - 30', '24*e - 6', '-24*e + 6', '4*e + 34', '4*e + 34', '8*e - 66', '-8*e + 66', 64, 64, '-e - 40', 'e + 40', -18, '2*e - 26', '2*e - 26', '-13*e + 40', '-13*e + 40', '18*e + 2', '-18*e - 2', '-16*e + 18', '-16*e + 18', '-6*e + 8', '-6*e + 8', '32*e - 10', '32*e - 10', 'e - 8', '-e + 8', '-18*e + 24', '18*e - 24', '-8*e + 56', '8*e - 56', '22*e + 8', '-22*e - 8', '-19*e + 18', '-19*e + 18', '12*e - 14', '-12*e + 14', '-14*e - 10', '14*e + 10', '17*e - 8', '-17*e + 8', '22*e - 2', '22*e - 2', '-26*e + 14', '26*e - 14', '-20*e + 16', '-20*e + 16', '14*e - 26', '-14*e + 26', '-e + 24', 'e - 24', '15*e + 22', '15*e + 22', '4*e', '4*e', '-32*e - 4', '32*e + 4', '3*e - 24', '3*e - 24', '-3*e - 56', '3*e + 56', '10*e - 42', '10*e - 42', '-18*e + 58', '-18*e + 58', '10*e + 56', '-10*e - 56', '-25*e + 18', '25*e - 18', '24*e + 12', '24*e + 12', 'e + 18', 'e + 18', '-8*e + 10', '8*e - 10', '8*e + 36', '8*e + 36', '4*e + 14', '-4*e - 14', '-8*e - 18', '-8*e - 18', '22*e - 8', '-22*e + 8', '-11*e - 54', '-4*e + 46', '4*e - 46', '10*e - 34', '-10*e + 34', '-26*e - 8', '-26*e - 8', '4*e + 64', '4*e + 64', '-5*e + 42', '5*e - 42', '-34*e', '-34*e', '11*e + 16', '-11*e - 16', '12*e - 14', '12*e - 14', '-6*e - 70', '6*e + 70', '-32*e + 16', '-32*e + 16', '-2*e + 34', '-2*e + 34', '-24*e + 14', '24*e - 14', 'e + 2', '-e - 2', '-24*e + 34', '24*e - 34', '4*e - 64', '-4*e + 64', -44, -44, '15*e - 18', '15*e - 18', '-3*e - 42', '-3*e - 42', '5*e + 16', '-5*e - 16', 'e - 48', 'e - 48', '-24*e + 10', '24*e - 10', '36*e - 8', '36*e - 8', '14*e - 10', '14*e - 10', '6*e + 56', '-6*e - 56', '24*e + 18', '-24*e - 18', '12*e + 2', '12*e + 2', '4*e - 6', '4*e - 6', '-22*e - 24', '22*e + 24', '7*e - 56', '7*e - 56', '-15*e + 26', '-15*e + 26', '29*e - 26', '-29*e + 26', '8*e - 60', '8*e - 60', '12*e - 22', '-12*e + 22', '6*e - 16', '6*e - 16', '-11*e + 54', '-11*e + 54', '-16*e - 10', '16*e + 10', '17*e - 24', '-17*e + 24', '7*e', '7*e', '13*e + 14', '13*e + 14', '-4*e - 2', '4*e + 2', '-20*e + 8', '-20*e + 8', '6*e - 16', '-6*e + 16', '-4*e - 14', '4*e + 14', '-29*e - 24', '29*e + 24', '9*e - 16', '-9*e + 16', '12*e + 40', '-12*e - 40', '-33*e + 16', '-33*e + 16', '-8*e + 30', '8*e - 30', '36*e - 36', '36*e - 36', '6*e + 72', '-6*e - 72', '7*e - 74', '7*e - 74', '21*e + 42', '-21*e - 42', '11*e + 8', '11*e + 8', '-13*e + 2', '-13*e + 2', '2*e + 46', '2*e + 46', '-18*e + 38', '18*e - 38', '4*e + 76', '-4*e - 76', '-34*e + 6', '-34*e + 6', '16*e - 20', '16*e - 20', '16*e + 52', '-16*e - 52', '-24*e + 26', '-24*e + 26', '14*e', '14*e', '-48*e + 34', '48*e - 34', '8*e + 44', '8*e + 44', '16*e + 28', '-16*e - 28', '-8*e - 2', '8*e + 2', '-28*e + 64', '28*e - 64', '-e + 86', '-e + 86', '-21*e + 2', '21*e - 2', '23*e - 18', '23*e - 18', '2*e - 22', '-2*e + 22', 'e + 48', '-e - 48', -18, '26*e - 32', '26*e - 32', '38*e - 48', '-38*e + 48', '-6*e - 10', '6*e + 10', '-19*e + 32', '19*e - 32', '-8*e + 40', '-8*e + 40', '-5*e + 88', '-5*e + 88', 86, 86, '5*e + 66', '-5*e - 66', '4*e + 56', '-4*e - 56', '-28*e + 32', '-28*e + 32', '30*e - 18', '30*e - 18', '5*e + 16', '5*e + 16', '35*e - 32', '35*e - 32', '-6*e + 50', '6*e - 50', '-32*e + 10', '-32*e + 10', '12*e - 72', '-12*e + 72', '-12*e + 96', '-12*e + 96', '-9*e - 10', '9*e + 10', '30*e - 48', '-30*e + 48', '-32*e - 26', '-32*e - 26', '-15*e - 24', '15*e + 24', '-20*e - 26', '-20*e - 26', '24*e - 46', '-24*e + 46', '-14*e + 34', '14*e - 34', '2*e - 8', '2*e - 8', '10*e - 16', '10*e - 16', '-5*e + 24', '5*e - 24', '-12*e - 18', '-12*e - 18', '6*e + 74', '-6*e - 74', '-13*e + 96', '13*e - 96', '17*e - 38', '-17*e + 38', '-32*e + 8', '-32*e + 8', '25*e - 38', '-25*e + 38', '-13*e + 72', '-13*e + 72', '-18*e - 48', '18*e + 48', 6, -6, '14*e + 46', '14*e + 46', '-35*e - 16', '-35*e - 16', '11*e + 34', '11*e + 34', '-12*e + 18', '12*e - 18', '-6*e + 88', '6*e - 88', '-5*e + 16', '5*e - 16', '21*e - 48', '21*e - 48', '-18*e + 72', '-18*e + 72', '-26*e + 58', '26*e - 58', '4*e + 70', '-4*e - 70', '-6*e - 88', '-6*e - 88', '-7*e - 58', '-7*e - 58', '-5*e - 8', '5*e + 8', '-2*e - 66', '2*e + 66', '-13*e + 82', '13*e - 82', '-12*e + 22', '-12*e + 22', '28*e - 34', '28*e - 34', '15*e + 10', '-15*e - 10', '17*e + 24', '17*e + 24', '20*e - 40', '-20*e + 40', '-2*e + 10', '2*e - 10', '-8*e - 98', '8*e + 98', '-12*e - 24', '-12*e - 24', '-2*e - 40', '-2*e - 40', '-16*e - 48', '16*e + 48', '-17*e - 26', '17*e + 26', '20*e + 82', '24*e - 44', '24*e - 44', '-16*e - 68', '16*e + 68', '-15*e + 32', '15*e - 32', '16*e + 26', '16*e + 26', 72, 72, '-37*e + 40', '-37*e + 40', '36*e - 26', '-36*e + 26', '-27*e - 56', '-27*e - 56', '16*e - 74', '16*e - 74', '-8*e + 24', '-8*e + 24', '14*e - 16', '-14*e + 16', '16*e - 96', '-16*e + 96', 68, 68, '55*e - 38', '55*e - 38', '28*e - 38', '-28*e + 38', '-12*e + 40', '-12*e + 40', '-4*e + 32', '-4*e + 32', '20*e - 52', '-20*e + 52', '25*e - 90', '-25*e + 90', '7*e - 22', '7*e - 22', '56*e - 14', '56*e - 14', '22*e - 82', '22*e - 82', '-22*e + 16', '22*e - 16', '21*e - 10', '-21*e + 10', '-25*e + 56', '25*e - 56', '15*e + 78', '-15*e - 78', '2*e + 24', '-2*e - 24', '-8*e + 34', '-8*e + 34', '-12*e + 56', '12*e - 56', '40*e - 74', '40*e - 74', '-19*e + 74', '-19*e + 74', '-27*e + 82', '27*e - 82', '4*e + 18', '-4*e - 18', '-3*e - 102', '20*e + 80', '-20*e - 80', '-39*e + 56', '39*e - 56', '-28*e + 66', '-28*e + 66', '-36*e + 16', '-36*e + 16', '11*e - 48', '-11*e + 48', '-36*e + 52', '36*e - 52', '6*e - 34', '6*e - 34', '19*e - 94', '19*e - 94', '-21*e', '-21*e', '56*e - 38', '-56*e + 38', '28*e - 48', '-28*e + 48', '-3*e + 2', '-3*e + 2', '-20*e - 24', '20*e + 24', '-36*e + 2', '-18*e - 26', '18*e + 26', '21*e - 16', '21*e - 16', '40*e - 58', '-40*e + 58', '-22*e', '22*e', '-44*e + 16', '-44*e + 16', '-5*e - 6', '5*e + 6', '-6*e - 16', '-6*e - 16', '16*e - 94', '16*e - 94', '45*e + 16', '45*e + 16', '-14*e - 86', '14*e + 86', '-28*e + 76', '28*e - 76', '4*e - 112', '4*e - 112', '33*e - 66', '33*e - 66', '-36*e + 36', '-36*e + 36', '28*e + 10', '-28*e - 10', '-36*e + 30', '-36*e + 30', '12*e - 40', '-12*e + 40', '-2*e + 112', '2*e - 112', '-17*e + 86', '-17*e + 86', '60*e - 52', '-60*e + 52', '-13*e - 24', '-13*e - 24', '8*e - 130', '-8*e + 130', '36*e + 6', '-36*e - 6', '6*e + 8', '-6*e - 8', '-8*e + 18', '8*e - 18', '51*e - 2', '51*e - 2', '-18*e + 8', '-18*e + 8', '16*e - 50', '16*e - 50', '-41*e - 22', '41*e + 22', '-10*e + 72', '10*e - 72', '-12*e + 58', '-12*e + 58', '24*e - 76', '24*e - 76', '-20*e + 34', '20*e - 34', '-16*e + 20', '-16*e + 20', '-e + 72', 'e - 72', -24, 24, '-52*e + 32', '52*e - 32', '34*e - 64', '-34*e + 64', '-12*e - 54', '-12*e - 54', '-20*e + 110', '20*e - 110', 88, 88, '52*e - 2', '-52*e + 2', '43*e - 72', '43*e - 72', '18*e - 6', '-18*e + 6', '-15*e + 14', '15*e - 14', '28*e + 34', '28*e + 34', '32*e + 68', '32*e + 68', '6*e - 122', '-6*e + 122', '8*e - 52', '8*e - 52', '-23*e - 74', '-23*e - 74', '27*e - 46', '-27*e + 46', '6*e - 48', '-6*e + 48', '10*e + 42', '-10*e - 42', '-20*e - 82', '-20*e - 82', '2*e - 74', '-2*e + 74', '24*e + 24', '24*e + 24', '-53*e + 42', '53*e - 42', '47*e - 46', '47*e - 46', '-2*e - 72', '-2*e - 72', '-24*e - 38', '-24*e - 38', 68, 68, '28*e - 50', '28*e - 50', '-2*e - 94', '-2*e - 94', '-27*e + 22', '27*e - 22', '-41*e - 16', '-41*e - 16', '19*e - 6', '-19*e + 6', '-33*e - 72', '33*e + 72', '-27*e - 22', '-27*e - 22', '-64*e + 40', '64*e - 40', '-24*e - 14', '-24*e - 14', '-28*e + 26', '28*e - 26', '-e + 30', '-e + 30', '-50*e + 2', '50*e - 2', '-4*e - 128', '-4*e - 128', '48*e - 30', '-48*e + 30', '33*e - 56', '-33*e + 56', '11*e + 50', '11*e + 50', '-42*e + 96', '-42*e + 96', '-32*e - 44', '-32*e - 44', '26*e + 94', '26*e + 94', '10*e - 74', '10*e - 74', '12*e - 70', '-12*e + 70', '-25*e + 66', '25*e - 66', '-21*e - 40', '-21*e - 40', '11*e + 64', '-11*e - 64', '-4*e - 54', '-4*e - 54', '-5*e - 82', '-5*e - 82', '6*e + 40', '-6*e - 40', -98, '40*e + 36', '-40*e - 36', '-7*e - 88', '-7*e - 88', '12*e - 106', '-12*e + 106', '-22*e + 88', '22*e - 88', '-14*e - 112', '-14*e - 112', '-47*e - 32', '47*e + 32', '-8*e + 26', '8*e - 26', '4*e + 32', '4*e + 32', '32*e + 50', '32*e + 50', '-39*e + 24', '39*e - 24', '37*e - 8', '-37*e + 8', '24*e + 10', '24*e + 10', '-64*e + 22', '64*e - 22', '26*e', '-26*e', '10*e + 88', '-10*e - 88', '30*e - 96', '30*e - 96', '-4*e - 50', '-4*e - 50', '35*e - 22', '-35*e + 22', '40*e + 28', '-40*e - 28', '8*e - 124', '8*e - 124', '-6*e + 102', '6*e - 102', '-18*e - 78', '-18*e - 78', '-6*e - 110', '6*e + 110', '-17*e + 112', '17*e - 112', '19*e - 2', '19*e - 2', '39*e - 24', '-39*e + 24', '24*e - 78', '24*e - 78', '69*e - 8', '-69*e + 8', '30*e - 10', '30*e - 10', '-24*e - 18', '24*e + 18', '35*e - 6', '35*e - 6', '17*e + 16', '17*e + 16', '67*e - 26', '-67*e + 26', '24*e - 20', '24*e - 20', 64, -64, '-21*e - 70', '-21*e - 70', '10*e + 10', '-10*e - 10', '40*e - 44', '-40*e + 44', '-5*e - 114', '-5*e - 114', '30*e - 18', '-30*e + 18', '-8*e - 22', '-8*e - 22', 96, -96, '48*e - 70', '-48*e + 70', '34*e + 32', '34*e + 32', '-8*e - 122', '-8*e - 122', '36*e - 28', '-36*e + 28', '-24*e + 110', '-24*e + 110', '-8*e + 78', '8*e - 78', '36*e + 56', '36*e + 56', '44*e + 20', '44*e + 20', '-25*e + 48', '-25*e + 48', '-48*e + 38', '48*e - 38', '-35*e + 46', '35*e - 46', '60*e - 32', '-60*e + 32', '26*e + 22', '-26*e - 22', '-6*e + 14', '6*e - 14', '-12*e - 74', '12*e + 74', '-6*e + 128', '-6*e + 128', '26*e - 2', '-26*e + 2', '4*e - 68', '-4*e + 68', '4*e - 162', '12*e - 136', '12*e - 136', '-6*e + 102', '-6*e + 102', '-25*e - 10', '25*e + 10', '9*e - 40', '9*e - 40', '31*e - 66', '31*e - 66', '24*e + 44', '24*e + 44', '24*e - 30', '-24*e + 30', '-40*e - 8', '40*e + 8', '-47*e + 58', '-47*e + 58', '-8*e - 48', '8*e + 48', '-37*e - 32', '37*e + 32', '-40*e + 38', '-40*e + 38', '42*e + 32', '42*e + 32', '-6*e - 56', '-6*e - 56', '-20*e + 4', '20*e - 4', '24*e + 62', '24*e + 62', '16*e - 68', '-16*e + 68', '10*e - 50', '10*e - 50', '29*e - 48', '-29*e + 48', '-6*e - 122', '-6*e - 122', '41*e - 106', '-41*e + 106', '-2*e + 48', '-2*e + 48', '50*e + 10', '50*e + 10', 'e + 10', 'e + 10', '24*e + 28', '-24*e - 28', '-39*e + 6', '39*e - 6', '68*e - 74', '68*e - 74', '-6*e + 96', '6*e - 96', '-12*e - 48', '12*e + 48', '27*e - 40', '27*e - 40', '-14*e + 126', '14*e - 126', '-2*e - 120', '-2*e - 120', '51*e + 46', '-51*e - 46', '-5*e - 32', '-5*e - 32', '34*e + 10', '34*e + 10', '-18*e + 102', '18*e - 102', '-57*e + 38', '57*e - 38', '4*e', '4*e', '-16*e - 50', '-16*e - 50', '9*e - 50', '9*e - 50', 22, -22, '4*e - 26', '-4*e + 26', '45*e - 104', '45*e - 104', '-36*e + 38', '-36*e + 38', '12*e + 128', '12*e + 128', '-7*e - 18', '-7*e - 18', '40*e - 78', '-40*e + 78', '23*e - 110', '23*e - 110', '5*e + 32', '5*e + 32', '-38*e + 8', '38*e - 8', '-52*e - 42', '52*e + 42', '-30*e + 80', '-30*e + 80', '35*e + 82', '-35*e - 82', '-40*e', '-40*e', '-13*e + 8', '13*e - 8', '46*e - 70', '46*e - 70', '38*e + 62', '38*e + 62', '33*e - 78', '-33*e + 78', '-47*e + 112', '-47*e + 112', '48*e + 56', '-48*e - 56', '-54*e - 34', '-54*e - 34', '4*e + 30', '4*e + 30', '31*e', '31*e', '-12*e - 128', '-12*e - 128', '-38*e + 18', '-38*e + 18', '30*e + 16', '30*e + 16', '20*e + 48', '20*e + 48', '76*e - 46', '-76*e + 46', '4*e + 70', '4*e + 70', '47*e + 64', '47*e + 64', '19*e - 64', '-19*e + 64', '2*e - 126', '-2*e + 126', '-7*e - 112', '7*e + 112', '-10*e + 48', '10*e - 48', -118, 118, '-25*e + 6', '25*e - 6', '-23*e - 32', '-23*e - 32', '-14*e + 40', '14*e - 40', '25*e - 50', '25*e - 50', '-60*e + 16', '-60*e + 16', '27*e - 10', '-27*e + 10', '13*e + 120', '13*e + 120', '-16*e + 130', '2*e + 66', '-2*e - 66', '-44*e + 74', '-44*e + 74', '-66*e + 26', '66*e - 26', '-22*e - 24', '-22*e - 24', '18*e - 66', '-18*e + 66', '-34*e', '-34*e', '72*e - 44', '-72*e + 44', '31*e + 38', '-31*e - 38', '31*e + 16', '-31*e - 16', '4*e + 26', '-4*e - 26', '24*e + 84', '-24*e - 84', '42*e - 8', '-42*e + 8', '-61*e + 32', '-61*e + 32', '6*e - 112', '-6*e + 112', '6*e + 54', '-6*e - 54', '32*e - 68', '32*e - 68', '-28*e + 90', '-28*e + 90', '-e + 102', 'e - 102', '55*e + 10', '55*e + 10', '-37*e + 110', '-37*e + 110', '56*e - 30', '56*e - 30', '4*e - 38', '-4*e + 38', '16*e + 120', '-16*e - 120', '-7*e + 48', '7*e - 48', '-21*e + 160', '-21*e + 160', '52*e - 18', '52*e - 18', '59*e - 16', '-59*e + 16', -30, 30, '68*e', '68*e', '77*e - 48', '77*e - 48', '49*e - 48', '49*e - 48', '40*e - 44', '-40*e + 44', '39*e + 74', '-39*e - 74', '13*e + 64', '13*e + 64', '24*e - 82', '-24*e + 82', '-6*e - 54', '-6*e - 54', '40*e - 112', '40*e - 112'], 'hecke_polynomial': 'x^2 - x - 4', 'label': '2.2.13.1-576.2-m'}
• hmf_fields •

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

  
  {'degree': 2, 'discriminant': 13, 'ideals': ['[1, 1, 1]', '[3, 3, -w]', '[3, 3, -w + 1]', '[4, 2, 2]', '[9, 3, 3]', '[9, 9, w + 3]', '[9, 9, -w + 4]', '[12, 6, -2*w]', '[12, 6, -2*w + 2]', '[13, 13, -2*w + 1]', '[16, 4, 4]', '[17, 17, w + 4]', '[17, 17, -w + 5]', '[23, 23, 3*w + 1]', '[23, 23, -3*w + 4]', '[25, 5, 5]', '[27, 9, -3*w]', '[27, 9, -3*w + 3]', '[27, 27, w + 5]', '[27, 27, -w + 6]', '[29, 29, 3*w - 2]', '[29, 29, -3*w + 1]', '[36, 6, 6]', '[36, 18, 2*w + 6]', '[36, 18, -2*w + 8]', '[39, 39, w + 6]', '[39, 39, -w + 7]', '[43, 43, -4*w - 1]', '[43, 43, 4*w - 5]', '[48, 12, -4*w]', '[48, 12, -4*w + 4]', '[49, 7, -7]', '[51, 51, -4*w + 3]', '[51, 51, -2*w + 9]', '[51, 51, 2*w + 7]', '[51, 51, -4*w + 1]', '[52, 26, -4*w + 2]', '[53, 53, -w - 7]', '[53, 53, w - 8]', '[61, 61, -3*w - 8]', '[61, 61, 3*w - 11]', '[64, 8, 8]', '[68, 34, 2*w + 8]', '[68, 34, -2*w + 10]', '[69, 69, -w - 8]', '[69, 69, -5*w - 1]', '[69, 69, 5*w - 6]', '[69, 69, -w + 9]', '[75, 15, -5*w]', '[75, 15, -5*w + 5]', '[79, 79, 5*w - 4]', '[79, 79, 5*w - 1]', '[81, 9, 9]', '[81, 27, 3*w + 9]', '[81, 27, -3*w + 12]', '[81, 81, -5*w + 2]', '[81, 81, -5*w + 3]', '[87, 87, -w - 9]', '[87, 87, 2*w - 11]', '[87, 87, 2*w + 9]', '[87, 87, -w + 10]', '[92, 46, 6*w + 2]', '[92, 46, -6*w + 8]', '[100, 10, 10]', '[101, 101, -6*w - 1]', '[101, 101, 6*w - 7]', '[103, 103, 3*w - 13]', '[103, 103, -3*w - 10]', '[107, 107, -w - 10]', '[107, 107, w - 11]', '[108, 18, -6*w]', '[108, 18, -6*w + 6]', '[108, 54, 2*w + 10]', '[108, 54, -2*w + 12]', '[113, 113, 6*w - 5]', '[113, 113, 6*w - 1]', '[116, 58, 6*w - 4]', '[116, 58, -6*w + 2]', '[117, 39, -6*w + 3]', '[117, 117, -7*w + 10]', '[117, 117, -7*w - 3]', '[121, 11, -11]', '[127, 127, -3*w - 11]', '[127, 127, 3*w - 14]', '[129, 129, w + 11]', '[129, 129, 5*w + 12]', '[129, 129, 5*w - 17]', '[129, 129, w - 12]', '[131, 131, 2*w - 13]', '[131, 131, -2*w - 11]', '[139, 139, -7*w - 1]', '[139, 139, 7*w - 8]', '[144, 12, 12]', '[144, 36, 4*w + 12]', '[144, 36, -4*w + 16]', '[147, 21, 7*w]', '[147, 21, 7*w - 7]', '[153, 51, 3*w + 12]', '[153, 51, -3*w + 15]', '[153, 153, w + 12]', '[153, 153, -7*w + 6]', '[153, 153, -7*w + 1]', '[153, 153, -w + 13]', '[156, 78, 2*w + 12]', '[156, 78, -2*w + 14]', '[157, 157, 7*w - 2]', '[157, 157, 7*w - 5]', '[159, 159, 7*w - 3]', '[159, 159, 8*w + 3]', '[159, 159, 8*w - 11]', '[159, 159, 7*w - 4]', '[169, 13, 13]', '[172, 86, -8*w - 2]', '[172, 86, 8*w - 10]', '[173, 173, 4*w - 17]', '[173, 173, -4*w - 13]', '[179, 179, -w - 13]', '[179, 179, w - 14]', '[181, 181, 3*w - 16]', '[181, 181, -3*w - 13]', '[183, 183, 8*w + 1]', '[183, 183, 11*w + 9]', '[183, 183, 11*w - 20]', '[183, 183, 8*w - 9]', '[191, 191, 9*w - 13]', '[191, 191, -9*w - 4]', '[192, 24, -8*w]', '[192, 24, -8*w + 8]', '[196, 14, -14]', '[199, 199, 8*w - 7]', '[199, 199, 8*w - 1]', '[204, 102, -8*w + 6]', '[204, 102, -4*w + 18]', '[204, 102, 4*w + 14]', '[204, 102, -8*w + 2]', '[207, 69, 9*w + 3]', '[207, 69, -9*w + 12]', '[207, 207, w + 14]', '[207, 207, 8*w - 5]', '[207, 207, -8*w + 3]', '[207, 207, w - 15]', '[208, 52, -8*w + 4]', '[211, 211, -3*w - 14]', '[211, 211, 3*w - 17]', '[212, 106, -2*w - 14]', '[212, 106, 2*w - 16]', '[221, 221, -9*w + 11]', '[221, 221, -9*w - 2]', '[225, 15, 15]', '[225, 45, 5*w + 15]', '[225, 45, -5*w + 20]', '[233, 233, -9*w - 1]', '[233, 233, 9*w - 10]', '[237, 237, -w - 15]', '[237, 237, -4*w - 15]', '[237, 237, 4*w - 19]', '[237, 237, w - 16]', '[243, 27, -9*w]', '[243, 27, -9*w + 9]', '[243, 81, 3*w + 15]', '[243, 81, -3*w + 18]', '[243, 243, -2*w + 17]', '[243, 243, 2*w + 15]', '[244, 122, -6*w - 16]', '[244, 122, 6*w - 22]', '[251, 251, 9*w - 8]', '[251, 251, 9*w - 1]', '[256, 16, 16]', '[257, 257, 9*w - 2]', '[257, 257, 9*w - 7]', '[261, 87, 9*w - 6]', '[261, 87, -9*w + 3]', '[261, 261, -5*w + 21]', '[261, 261, -10*w + 13]', '[261, 261, 10*w + 3]', '[261, 261, -5*w - 16]', '[263, 263, 9*w - 4]', '[263, 263, 9*w - 5]', '[269, 269, -w - 16]', '[269, 269, w - 17]', '[272, 68, 4*w + 16]', '[272, 68, -4*w + 20]', '[276, 138, -2*w - 16]', '[276, 138, -10*w - 2]', '[276, 138, 10*w - 12]', '[276, 138, -2*w + 18]', '[277, 277, 3*w - 19]', '[277, 277, -3*w - 16]', '[283, 283, 11*w - 16]', '[283, 283, -11*w - 5]', '[289, 17, 17]', '[289, 289, -10*w - 1]', '[289, 289, -10*w + 11]', '[299, 299, -5*w - 17]', '[299, 299, -5*w + 22]', '[300, 30, -10*w]', '[300, 30, -10*w + 10]', '[303, 303, w + 17]', '[303, 303, 7*w - 25]', '[303, 303, 7*w + 18]', '[303, 303, w - 18]', '[309, 309, 10*w - 9]', '[309, 309, 13*w + 9]', '[309, 309, 13*w - 22]', '[309, 309, 10*w - 1]', '[311, 311, 2*w - 19]', '[311, 311, -2*w - 17]', '[313, 313, -3*w - 17]', '[313, 313, 3*w - 20]', '[316, 158, 10*w - 8]', '[316, 158, 10*w - 2]', '[321, 321, 10*w - 3]', '[321, 321, 11*w + 3]', '[321, 321, 11*w - 14]', '[321, 321, 10*w - 7]', '[324, 18, 18]', '[324, 54, 6*w + 18]', '[324, 54, -6*w + 24]', '[324, 162, -10*w + 4]', '[324, 162, -10*w + 6]', '[325, 65, -10*w + 5]', '[337, 337, 11*w - 13]', '[337, 337, -11*w - 2]', '[339, 339, -w - 18]', '[339, 339, 5*w - 23]', '[339, 339, -5*w - 18]', '[339, 339, w - 19]', '[347, 347, -12*w - 5]', '[347, 347, 12*w - 17]', '[348, 174, -2*w - 18]', '[348, 174, 4*w - 22]', '[348, 174, 4*w + 18]', '[348, 174, -2*w + 20]', '[351, 117, 3*w + 18]', '[351, 117, -3*w + 21]', '[351, 351, -11*w - 1]', '[351, 351, -11*w + 12]', '[361, 19, -19]', '[363, 33, 11*w]', '[363, 33, 11*w - 11]', '[367, 367, 6*w - 25]', '[367, 367, -6*w - 19]', '[368, 92, 12*w + 4]', '[368, 92, -12*w + 16]', '[373, 373, 11*w - 10]', '[373, 373, 11*w - 1]', '[377, 377, w + 19]', '[377, 377, w - 20]', '[381, 381, 14*w - 23]', '[381, 381, 11*w - 2]', '[381, 381, 11*w - 9]', '[381, 381, 14*w + 9]', '[387, 129, -12*w - 3]', '[387, 129, 12*w - 15]', '[387, 387, -11*w + 8]', '[387, 387, -17*w - 15]', '[387, 387, 17*w - 32]', '[387, 387, 11*w - 3]', '[389, 389, -4*w - 19]', '[389, 389, 4*w - 23]', '[391, 391, -11*w + 7]', '[391, 391, 3*w - 22]', '[391, 391, 3*w + 19]', '[391, 391, 11*w - 4]', '[393, 393, 13*w - 19]', '[393, 393, 11*w - 5]', '[393, 393, 11*w - 6]', '[393, 393, 13*w + 6]', '[400, 20, 20]', '[404, 202, -12*w - 2]', '[404, 202, 12*w - 14]', '[412, 206, 6*w - 26]', '[412, 206, -6*w - 20]', '[417, 417, w + 20]', '[417, 417, 8*w + 21]', '[417, 417, 8*w - 29]', '[417, 417, w - 21]', '[419, 419, -12*w - 1]', '[419, 419, 12*w - 13]', '[425, 85, 5*w + 20]', '[425, 85, -5*w + 25]', '[428, 214, -2*w - 20]', '[428, 214, 2*w - 22]', '[432, 36, -12*w]', '[432, 36, -12*w + 12]', '[432, 108, 4*w + 20]', '[432, 108, -4*w + 24]', '[433, 433, -3*w - 20]', '[433, 433, 3*w - 23]', '[439, 439, 13*w - 17]', '[439, 439, -13*w - 4]', '[441, 21, 21]', '[441, 63, -7*w - 21]', '[441, 63, 7*w - 28]', '[443, 443, 12*w - 11]', '[443, 443, 12*w - 1]', '[452, 226, 12*w - 10]', '[452, 226, 12*w - 2]', '[459, 153, -12*w + 9]', '[459, 153, -6*w + 27]', '[459, 153, 6*w + 21]', '[459, 153, -12*w + 3]', '[459, 459, w + 21]', '[459, 459, -13*w + 16]', '[459, 459, -13*w - 3]', '[459, 459, -w + 22]', '[464, 116, 12*w - 8]', '[464, 116, -12*w + 4]', '[467, 467, 12*w - 7]', '[467, 467, 12*w - 5]', '[468, 78, -12*w + 6]', '[468, 234, -14*w + 20]', '[468, 234, -14*w - 6]', '[471, 471, 5*w - 26]', '[471, 471, 2*w - 23]', '[471, 471, -2*w - 21]', '[471, 471, -5*w - 21]', '[477, 159, -3*w - 21]', '[477, 159, 3*w - 24]', '[477, 477, 4*w - 25]', '[477, 477, -11*w - 24]', '[477, 477, 11*w - 35]', '[477, 477, -4*w - 21]', '[484, 22, -22]', '[491, 491, 7*w - 29]', '[491, 491, -7*w - 22]', '[493, 493, 13*w + 1]', '[493, 493, -14*w - 5]', '[493, 493, 14*w - 19]', '[493, 493, -13*w + 14]', '[503, 503, -w - 22]', '[503, 503, w - 23]', '[507, 39, -13*w]', '[507, 39, -13*w + 13]', '[508, 254, -6*w - 22]', '[508, 254, 6*w - 28]', '[516, 258, 2*w + 22]', '[516, 258, 10*w + 24]', '[516, 258, 10*w - 34]', '[516, 258, 2*w - 24]', '[519, 519, 13*w - 12]', '[519, 519, 17*w - 29]', '[519, 519, 17*w + 12]', '[519, 519, 13*w - 1]', '[521, 521, -15*w + 22]', '[521, 521, 8*w - 31]', '[523, 523, 3*w - 25]', '[523, 523, -3*w - 22]', '[524, 262, 4*w - 26]', '[524, 262, -4*w - 22]', '[529, 23, 23]', '[529, 529, -13*w + 2]', '[529, 529, -13*w + 11]', '[537, 537, 13*w - 3]', '[537, 537, 14*w + 3]', '[537, 537, 14*w - 17]', '[537, 537, 13*w - 10]', '[543, 543, 13*w - 4]', '[543, 543, 16*w - 25]', '[543, 543, 16*w + 9]', '[543, 543, 13*w - 9]', '[547, 547, 13*w - 5]', '[547, 547, 13*w - 8]', '[549, 183, -9*w - 24]', '[549, 183, 9*w - 33]', '[549, 549, -w - 23]', '[549, 549, -20*w - 33]', '[549, 549, 20*w - 53]', '[549, 549, w - 24]', '[556, 278, -14*w - 2]', '[556, 278, 14*w - 16]', '[559, 559, 6*w + 23]', '[559, 559, 6*w - 29]', '[563, 563, 2*w - 25]', '[563, 563, -2*w - 23]', '[569, 569, 5*w - 28]', '[569, 569, -5*w - 23]', '[571, 571, -3*w - 23]', '[571, 571, 3*w - 26]', '[573, 573, 13*w - 40]', '[573, 573, 4*w + 23]', '[573, 573, 4*w - 27]', '[573, 573, 13*w + 27]', '[575, 115, 15*w + 5]', '[575, 115, -15*w + 20]', '[576, 24, 24]', '[576, 72, 8*w + 24]', '[576, 72, -8*w + 32]', '[588, 42, 14*w]', '[588, 42, 14*w - 14]', '[597, 597, -w - 24]', '[597, 597, -7*w - 24]', '[597, 597, 7*w - 31]', '[597, 597, w - 25]', '[599, 599, -15*w - 4]', '[599, 599, 15*w - 19]', '[601, 601, 14*w - 13]', '[601, 601, 14*w - 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86]', '[9931, 9931, 61*w - 77]', '[9931, 9931, -61*w - 16]', '[9941, 9941, -7*w - 97]', '[9941, 9941, 7*w - 104]', '[9949, 9949, 36*w - 137]', '[9949, 9949, -36*w - 101]', '[9967, 9967, 56*w - 43]', '[9967, 9967, 56*w - 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
  gal_is_abelian	boolean
  gal_is_cyclic	boolean
  gal_is_solvable	boolean
  galois_label	text
  galt	integer
  index	integer
  inessentialp	integer[]
  is_galois	boolean
  iso_number	smallint
  label	text
  local_algs	text[]
  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
  torsion_gen	text
  units	jsonb
  unitsGmodule	jsonb
  unitsType	text
  zk	jsonb

  
  {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-3, -1, 1], 'conductor': 13, 'degree': 2, 'dirichlet_group': [1, 12], 'disc_abs': 13, 'disc_rad': 13, 'disc_sign': 1, 'frobs': [[2, [[2, 1]]], [3, [[1, 2]]], [5, [[2, 1]]], [7, [[2, 1]]], [11, [[2, 1]]], [13, [0]], [17, [[1, 2]]], [19, [[2, 1]]], [23, [[1, 2]]], [29, [[1, 2]]], [31, [[2, 1]]], [37, [[2, 1]]], [41, [[2, 1]]], [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_label': '2T1', 'galt': 1, 'index': 1, 'inessentialp': [], 'is_galois': True, 'iso_number': 1, 'label': '2.2.13.1', 'local_algs': ['13.2.1.1'], 'monogenic': 1, 'num_ram': 1, 'r2': 0, 'ramps': [13], 'rd': 3.60555127546, 'regulator': {'__RealLiteral__': 0, 'data': '1.19476321729', 'prec': 44}, 'res': {}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a + 1 \\)'], 'used_grh': False, 'zk': ['1', 'a']}